diff --git a/Makefile b/Makefile
index 2ffe9a6..08b42e1 100644
--- a/Makefile
+++ b/Makefile
@@ -1,4 +1,4 @@
-all: clangnosan clangsan gccnosan gccsan
+all: clangnosan clangsan gccnosan gccsan gccavx2 clangavx512
 #TODO: re-enable GCC once multidimensional indexing in `requires` is fixed:
 # https://gcc.gnu.org/bugzilla/show_bug.cgi?id=111493
 
@@ -13,6 +13,13 @@ buildclang/nosan/:
 
 buildclang/test/:
 	CXXFLAGS="" CXX=clang++ cmake -S test -B buildclang/test/ -DCMAKE_BUILD_TYPE=Debug -DUSE_SANITIZER='Address;Undefined'
+	
+buildgcc/avx2/:
+	CXXFLAGS="-march=haswell" CXX=g++ cmake -S test -B buildgcc/avx2/ -DCMAKE_BUILD_TYPE=Debug
+
+buildclang/avx512/:
+	CXXFLAGS="-march=skylake-avx512 -mprefer-vector-width=512" CXX=clang++ cmake -S test -B buildclang/avx512/ -DCMAKE_BUILD_TYPE=Debug
+
 
 gccnosan: buildgcc/nosan/
 	cmake --build buildgcc/nosan/
@@ -30,5 +37,13 @@ clangsan: buildclang/test/
 	cmake --build buildclang/test/ 
 	cmake --build buildclang/test/ --target test
 
+gccavx2: buildgcc/avx2/
+	cmake --build buildgcc/avx2/
+	cmake --build buildgcc/avx2/ --target test
+
+clangavx512: buildclang/avx512/
+	cmake --build buildclang/avx512/
+	cmake --build buildclang/avx512/ --target test
+
 clean:
 	rm -r buildclang #buildgcc
diff --git a/README.md b/README.md
index e264b85..a464bd9 100644
--- a/README.md
+++ b/README.md
@@ -12,4 +12,7 @@ Copying, e.g. from an expression template to an array, is done via `destination
 `operator=` is reserved for copying the actual objects, rather than referenced memory, as this seems to be the behavior C++ views.
 Thus if `A` and `B` are views, `A = B` will make `A` the same view as `B`, while `A << B` will copy memory from `B` to `A`.
 
+Vectors are interpreted as row vectors by default. `v.t()` or `transpose(v)` may be used to transpose.
+`A[_,i]` is a column-vector, `A[i,_]` a row-vector.
+
 This repository was created using the [ModernCppStarter](https://github.com/TheLartians/ModernCppStarter).
diff --git a/benchmark/CMakeLists.txt b/benchmark/CMakeLists.txt
new file mode 100644
index 0000000..667902e
--- /dev/null
+++ b/benchmark/CMakeLists.txt
@@ -0,0 +1,118 @@
+cmake_minimum_required(VERSION 3.23)
+
+project(MathBenchmarks LANGUAGES C CXX)
+
+option(ENABLE_NATIVE_COMPILATION "Compile with -march=native" ON)
+option(ENABLE_WIDE_VECTORS "Compile with 512bit vectors if available" ON)
+option(ENABLE_OPENMP "Use OpenMP for a multithreading benchmark" OFF)
+
+# --- Import tools ----
+
+include(../cmake/tools.cmake)
+
+# ---- Dependencies ----
+
+include(../cmake/CPM.cmake)
+
+# ---- compile_commands.json ----
+set(CMAKE_EXPORT_COMPILE_COMMANDS ON)
+
+CPMAddPackage(
+  NAME benchmark
+  GITHUB_REPOSITORY google/benchmark
+  VERSION 1.8.3
+  OPTIONS "BENCHMARK_ENABLE_TESTING Off" "BENCHMARK_ENABLE_LIBPFM On" "BENCHMARK_ENABLE_WERROR Off"
+          "BENCHMARK_ENABLE_EXCEPTIONS Off" SYSTEM TRUE
+)
+if(benchmark_ADDED)
+  # enable c++11 to avoid compilation errors
+  set_target_properties(benchmark PROPERTIES CXX_STANDARD 11)
+endif()
+
+# FetchContent_Declare( Math GIT_REPOSITORY git@github.com:LoopModels/Math.git GIT_TAG origin/main )
+# FetchContent_MakeAvailable(Math)
+
+# file(GLOB_RECURSE headers CONFIGURE_DEPENDS ${CMAKE_CURRENT_SOURCE_DIR}/include/*.hpp)
+file(GLOB benchmarks CONFIGURE_DEPENDS ${CMAKE_CURRENT_SOURCE_DIR}/*.cpp)
+
+add_executable(${PROJECT_NAME} ${benchmarks})
+
+message(STATUS "PROJECT_BINARY_DIR: ${PROJECT_BINARY_DIR}")
+message(STATUS "PROJECT_SOURCE_DIR: ${PROJECT_SOURCE_DIR}")
+message(STATUS "LLVM_INCLUDE_DIRS: ${LLVM_INCLUDE_DIRS}")
+
+target_include_directories(
+  ${PROJECT_NAME} PRIVATE ${PROJECT_SOURCE_DIR}/../include # ${PROJECT_SOURCE_DIR}/include
+)
+if(ENABLE_OPENMP)
+  find_package(OpenMP)
+  target_link_libraries(${PROJECT_NAME} OpenMP::OpenMP_CXX)
+endif()
+target_link_libraries(${PROJECT_NAME} PRIVATE benchmark::benchmark_main)
+
+if((CMAKE_CXX_COMPILER_ID MATCHES "Clang") OR (CMAKE_CXX_COMPILER_ID MATCHES "IntelLLVM"))
+  target_compile_options(${PROJECT_NAME} PRIVATE -ferror-limit=2 -fcolor-diagnostics)
+elseif(CMAKE_CXX_COMPILER_ID MATCHES "GNU")
+  target_compile_options(
+    ${PROJECT_NAME} PRIVATE -fmax-errors=2 -fconcepts-diagnostics-depth=4
+                            -fno-semantic-interposition -fdiagnostics-color=always -fverbose-asm
+  )
+endif()
+
+if(ENABLE_NATIVE_COMPILATION)
+  if(CMAKE_CXX_COMPILER_ID MATCHES "IntelLLVM")
+    target_compile_options(${PROJECT_NAME} PRIVATE -xhost)
+    if(ENABLE_WIDE_VECTORS)
+      target_compile_options(${PROJECT_NAME} PRIVATE -qopt-zmm-usage=high)
+    endif()
+  else()
+    target_compile_options(${PROJECT_NAME} PRIVATE -march=native) # -fno-unroll-loops)
+    if(ENABLE_WIDE_VECTORS)
+      check_cxx_compiler_flag("-mprefer-vector-width=512" VEC512)
+      if(VEC512)
+        target_compile_options(${PROJECT_NAME} PRIVATE -mprefer-vector-width=512)
+      endif()
+    endif()
+  endif()
+endif()
+set_target_properties(
+  ${PROJECT_NAME}
+  PROPERTIES CXX_STANDARD 23
+             CXX_VISIBILITY_PRESET hidden
+             VISIBILITY_INLINES_HIDDEN ON
+)
+set_target_properties(
+  ${PROJECT_NAME} PROPERTIES ENVIRONMENT WORKING_DIRECTORY=${PROJECT_BINARY_DIR}
+)
+
+target_compile_options(
+  ${PROJECT_NAME}
+  PRIVATE -fno-exceptions
+          -fno-rtti
+          -fstrict-aliasing
+          -fno-plt
+          -fstrict-overflow
+          -fomit-frame-pointer
+          -fno-signed-zeros
+          -fassociative-math
+          -ffinite-math-only
+          -funsafe-math-optimizations
+          -fno-trapping-math
+          -Wall
+          -Wshadow
+          -Wextra
+          -save-temps
+          -Werror
+)
+if(ENABLE_OPENMP)
+  if(CMAKE_CXX_COMPILER_ID MATCHES "IntelLLVM")
+    target_compile_options(${PROJECT_NAME} PRIVATE -fiopenmp)
+  else()
+    target_compile_options(${PROJECT_NAME} PRIVATE -fopenmp)
+  endif()
+else()
+  target_compile_options(${PROJECT_NAME} PRIVATE -fopenmp-simd)
+endif()
+if(CMAKE_SYSTEM_PROCESSOR MATCHES "(x86)|(X86)|(amd64)|(AMD64)")
+  target_compile_options(${PROJECT_NAME} PRIVATE -masm=intel)
+endif()
diff --git a/benchmark/dual_benchmark.cpp b/benchmark/dual_benchmark.cpp
new file mode 100644
index 0000000..cb09df8
--- /dev/null
+++ b/benchmark/dual_benchmark.cpp
@@ -0,0 +1,195 @@
+
+#include "include/randdual.hpp"
+#include <Math/Array.hpp>
+#include <Math/Dual.hpp>
+#include <Math/LinearAlgebra.hpp>
+#include <Math/Matrix.hpp>
+#include <Math/StaticArrays.hpp>
+#include <Utilities/Invariant.hpp>
+#include <algorithm>
+#include <array>
+#include <benchmark/benchmark.h>
+#include <concepts>
+#include <cstdint>
+#include <random>
+#include <ranges>
+
+using poly::math::Dual, poly::math::SquareMatrix, poly::math::SquareDims,
+  poly::math::I, poly::math::URand;
+
+[[gnu::noinline]] void prod(auto &c, const auto &a, const auto &b) {
+  c = a * b;
+}
+
+static void BM_dual8x2prod(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 8>, 2>;
+  D a = URand<D>{}(rng0), b = URand<D>{}(rng0), c;
+  for (auto _ : state) {
+    prod(c, a, b);
+    benchmark::DoNotOptimize(c);
+  }
+}
+BENCHMARK(BM_dual8x2prod);
+
+template <typename T, ptrdiff_t N, bool SIMDArry = false> struct ManualDual {
+  T value;
+  poly::math::SVector<T, N> partials;
+};
+
+template <std::floating_point T, ptrdiff_t N> struct ManualDual<T, N, false> {
+  T value;
+  poly::simd::Vec<N, T> partials;
+};
+template <std::floating_point T, ptrdiff_t N> struct ManualDual<T, N, true> {
+  T value;
+  poly::math::StaticArray<T, 1, N, false> partials;
+};
+template <typename T, ptrdiff_t N, bool B>
+[[gnu::always_inline]] constexpr auto operator*(const ManualDual<T, N, B> &a,
+                                                const ManualDual<T, N, B> &b)
+  -> ManualDual<T, N, B> {
+  return {a.value * b.value, a.value * b.partials + b.value * a.partials};
+}
+template <typename T, ptrdiff_t N, bool B>
+[[gnu::always_inline]] constexpr auto operator*(const ManualDual<T, N, B> &a,
+                                                const T &b)
+  -> ManualDual<T, N, B> {
+  return {a.value * b, b * a.partials};
+}
+template <typename T, ptrdiff_t N, bool B>
+[[gnu::always_inline]] constexpr auto operator*(const T &a,
+                                                const ManualDual<T, N, B> &b)
+  -> ManualDual<T, N, B> {
+  return {b.value * a, a * b.partials};
+}
+template <typename T, ptrdiff_t N, bool B>
+[[gnu::always_inline]] constexpr auto operator+(const ManualDual<T, N, B> &a,
+                                                const ManualDual<T, N, B> &b)
+  -> ManualDual<T, N, B> {
+  return {a.value + b.value, a.partials + b.partials};
+}
+template <typename T, ptrdiff_t N, bool B>
+[[gnu::always_inline]] constexpr auto operator+(const ManualDual<T, N, B> &a,
+                                                const T &b)
+  -> ManualDual<T, N, B> {
+  return {a.value + b, a.partials};
+}
+template <typename T, ptrdiff_t N, bool B>
+[[gnu::always_inline]] constexpr auto operator+(const T &a,
+                                                const ManualDual<T, N, B> &b)
+  -> ManualDual<T, N, B> {
+  return {b.value + a, b.partials};
+}
+// template <typename T, ptrdiff_t M, ptrdiff_t N>
+// [[gnu::noinline]] void prod_manual(ManualDual<ManualDual<T, M>, N> &c,
+//                                    const ManualDual<ManualDual<T, M>, N> &a,
+//                                    const ManualDual<ManualDual<T, M>, N> &b)
+//                                    {
+//   // return {val * other.val, val * other.partials + other.val * partials};
+//   c.value= a.value* b.value;
+//   c.partials = a.value* b.partials+ b.value* a.partials;
+// }
+
+template <ptrdiff_t M, ptrdiff_t N, bool SIMDArray> auto setup_manual() {
+  using D = ManualDual<ManualDual<double, M, SIMDArray>, N>;
+  std::mt19937_64 rng0;
+  D a{}, b{}, c{};
+  a.value.value = URand<double>{}(rng0);
+  b.value.value = URand<double>{}(rng0);
+  for (ptrdiff_t j = 0; j < M; ++j) {
+    a.value.partials[j] = URand<double>{}(rng0);
+    b.value.partials[j] = URand<double>{}(rng0);
+  }
+  for (ptrdiff_t i = 0; i < N; ++i) {
+    a.partials[i].value = URand<double>{}(rng0);
+    b.partials[i].value = URand<double>{}(rng0);
+    for (ptrdiff_t j = 0; j < M; ++j) {
+      a.partials[i].partials[j] = URand<double>{}(rng0);
+      b.partials[i].partials[j] = URand<double>{}(rng0);
+    }
+  }
+  return std::array<D, 3>{a, b, c};
+}
+
+static void BM_dual8x2prod_manual(benchmark::State &state) {
+  auto [a, b, c] = setup_manual<8, 2, false>();
+  for (auto _ : state) {
+    prod(c, a, b);
+    benchmark::DoNotOptimize(c);
+  }
+}
+BENCHMARK(BM_dual8x2prod_manual);
+
+static void BM_dual8x2prod_simdarray(benchmark::State &state) {
+  auto [a, b, c] = setup_manual<8, 2, true>();
+  for (auto _ : state) {
+    prod(c, a, b);
+    benchmark::DoNotOptimize(c);
+  }
+}
+BENCHMARK(BM_dual8x2prod_simdarray);
+
+static void BM_dual7x2prod(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 7>, 2>;
+  static_assert(std::same_as<double, poly::math::scalarize_elt_cast_t<
+                                       Dual<Dual<double, 7, true>, 2, true>>>);
+  // static_assert(sizeof(D) == sizeof(Dual<Dual<double, 8>, 2>));
+  static_assert(poly::utils::Compressible<D>);
+  D a = URand<D>{}(rng0), b = URand<D>{}(rng0), c;
+  for (auto _ : state) {
+    prod(c, a, b);
+    benchmark::DoNotOptimize(c);
+  }
+}
+BENCHMARK(BM_dual7x2prod);
+
+static void BM_dual7x2prod_manual(benchmark::State &state) {
+  auto [a, b, c] = setup_manual<7, 2, false>();
+  for (auto _ : state) {
+    prod(c, a, b);
+    benchmark::DoNotOptimize(c);
+  }
+}
+BENCHMARK(BM_dual7x2prod_manual);
+
+static void BM_dual7x2prod_simdarray(benchmark::State &state) {
+  auto [a, b, c] = setup_manual<7, 2, true>();
+  for (auto _ : state) {
+    prod(c, a, b);
+    benchmark::DoNotOptimize(c);
+  }
+}
+BENCHMARK(BM_dual7x2prod_simdarray);
+
+static void BM_dual6x2prod(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 6>, 2>;
+  // static_assert(sizeof(D) == sizeof(Dual<Dual<double, 8>, 2>));
+  static_assert(poly::utils::Compressible<D>);
+  D a = URand<D>{}(rng0), b = URand<D>{}(rng0), c;
+  for (auto _ : state) {
+    prod(c, a, b);
+    benchmark::DoNotOptimize(c);
+  }
+}
+BENCHMARK(BM_dual6x2prod);
+
+static void BM_dual6x2prod_manual(benchmark::State &state) {
+  auto [a, b, c] = setup_manual<6, 2, false>();
+  for (auto _ : state) {
+    prod(c, a, b);
+    benchmark::DoNotOptimize(c);
+  }
+}
+BENCHMARK(BM_dual6x2prod_manual);
+
+static void BM_dual6x2prod_simdarray(benchmark::State &state) {
+  auto [a, b, c] = setup_manual<6, 2, true>();
+  for (auto _ : state) {
+    prod(c, a, b);
+    benchmark::DoNotOptimize(c);
+  }
+}
+BENCHMARK(BM_dual6x2prod_simdarray);
diff --git a/benchmark/dual_elt_benchmarks.cpp b/benchmark/dual_elt_benchmarks.cpp
new file mode 100644
index 0000000..bbb1227
--- /dev/null
+++ b/benchmark/dual_elt_benchmarks.cpp
@@ -0,0 +1,149 @@
+
+#include "include/randdual.hpp"
+#include <benchmark/benchmark.h>
+
+using poly::math::Dual, poly::math::SquareDims, poly::math::SquareMatrix,
+  poly::math::MutArray, poly::math::Array, poly::math::URand,
+  poly::containers::tie, poly::containers::Tuple;
+
+template <typename A, typename... As, typename B, typename... Bs>
+constexpr void tuplecheck(Tuple<A, As...> &, const Tuple<B, Bs...> &) {
+  using C = poly::math::scalarize_via_cast_t<
+    std::remove_cvref_t<decltype(std::declval<A>().view())>>;
+  static_assert(
+    !std::same_as<C, void> &&
+    poly::math::ScalarizeViaCastTo<C, As..., decltype(std::declval<B>().view()),
+                                   Bs...>());
+}
+
+template <typename T, typename S>
+[[gnu::noinline]] void eltmul(MutArray<T, S> A, double t) {
+  A *= t;
+}
+
+template <typename T, typename S>
+[[gnu::noinline]] void eltadd(MutArray<T, S> C, Array<T, S> A, Array<T, S> B) {
+  static_assert(
+    std::same_as<double, poly::math::scalarize_via_cast_t<MutArray<T, S>>>);
+  static_assert(
+    std::same_as<double, poly::math::scalarize_via_cast_t<decltype(A + B)>>);
+  C << A + B;
+}
+template <typename T, typename S>
+[[gnu::noinline]] void eltaddsub(MutArray<T, S> C, MutArray<T, S> D,
+                                 Array<T, S> A, Array<T, S> B) {
+  {
+    auto lval{tie(C, D)};
+    tuplecheck(lval, Tuple(A + B, A - B));
+  }
+  tie(C, D) << Tuple(A + B, A - B);
+}
+
+template <ptrdiff_t N> static void BM_dualNdoublemul(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<double, N>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  double t = 1.00000000001;
+  for (auto b : state) eltmul(A, t);
+}
+
+template <ptrdiff_t M, ptrdiff_t N>
+static void BM_dualMxNdoublemul(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, M>, N>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  double t = 1.00000000001;
+  for (auto b : state) eltmul(A, t);
+}
+
+template <ptrdiff_t N> static void BM_dualNadd(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using T = Dual<double, N>;
+  SquareDims<> dim{state.range(0)};
+  SquareMatrix<T> A{dim}, B{dim}, C{dim};
+  for (auto &&a : A) a = URand<T>{}(rng0);
+  for (auto &&b : B) b = URand<T>{}(rng0);
+  for (auto b : state) eltadd(C, A, B);
+}
+template <ptrdiff_t M, ptrdiff_t N>
+static void BM_dualMxNadd(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using T = Dual<Dual<double, M>, N>;
+  SquareDims<> dim{state.range(0)};
+  SquareMatrix<T> A{dim}, B{dim}, C{dim};
+  for (auto &&a : A) a = URand<T>{}(rng0);
+  for (auto &&b : B) b = URand<T>{}(rng0);
+  for (auto b : state) eltadd(C, A, B);
+}
+template <ptrdiff_t N> static void BM_dualNaddsub(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using T = Dual<double, N>;
+  SquareDims<> dim{state.range(0)};
+  SquareMatrix<T> A{dim}, B{dim}, C{dim}, D{dim};
+  for (auto &&a : A) a = URand<T>{}(rng0);
+  for (auto &&b : B) b = URand<T>{}(rng0);
+  for (auto b : state) eltaddsub(C, D, A, B);
+}
+template <ptrdiff_t M, ptrdiff_t N>
+static void BM_dualMxNaddsub(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using T = Dual<Dual<double, M>, N>;
+  SquareDims<> dim{state.range(0)};
+  SquareMatrix<T> A{dim}, B{dim}, C{dim}, D{dim};
+  for (auto &&a : A) a = URand<T>{}(rng0);
+  for (auto &&b : B) b = URand<T>{}(rng0);
+  for (auto b : state) eltaddsub(C, D, A, B);
+}
+
+BENCHMARK(BM_dualNadd<1>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNadd<2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNadd<3>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNadd<4>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNadd<5>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNadd<6>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNadd<7>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNadd<8>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNadd<1, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNadd<2, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNadd<3, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNadd<4, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNadd<5, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNadd<6, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNadd<7, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNadd<8, 2>)->DenseRange(2, 10, 1);
+
+BENCHMARK(BM_dualNaddsub<1>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNaddsub<2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNaddsub<3>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNaddsub<4>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNaddsub<5>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNaddsub<6>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNaddsub<7>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNaddsub<8>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNaddsub<1, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNaddsub<2, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNaddsub<3, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNaddsub<4, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNaddsub<5, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNaddsub<6, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNaddsub<7, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNaddsub<8, 2>)->DenseRange(2, 10, 1);
+
+BENCHMARK(BM_dualNdoublemul<1>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNdoublemul<2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNdoublemul<3>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNdoublemul<4>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNdoublemul<5>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNdoublemul<6>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNdoublemul<7>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualNdoublemul<8>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNdoublemul<1, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNdoublemul<2, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNdoublemul<3, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNdoublemul<4, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNdoublemul<5, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNdoublemul<6, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNdoublemul<7, 2>)->DenseRange(2, 10, 1);
+BENCHMARK(BM_dualMxNdoublemul<8, 2>)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark.cpp b/benchmark/expm_benchmark.cpp
new file mode 100644
index 0000000..a771b1b
--- /dev/null
+++ b/benchmark/expm_benchmark.cpp
@@ -0,0 +1,9 @@
+#include "include/expm.hpp"
+
+static void BM_expm(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  SquareMatrix<double> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<double>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+BENCHMARK(BM_expm)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark1.cpp b/benchmark/expm_benchmark1.cpp
new file mode 100644
index 0000000..e431e85
--- /dev/null
+++ b/benchmark/expm_benchmark1.cpp
@@ -0,0 +1,11 @@
+#include "include/expm.hpp"
+
+static void BM_expm_dual1(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<double, 1>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+
+BENCHMARK(BM_expm_dual1)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark1x2.cpp b/benchmark/expm_benchmark1x2.cpp
new file mode 100644
index 0000000..e070605
--- /dev/null
+++ b/benchmark/expm_benchmark1x2.cpp
@@ -0,0 +1,10 @@
+#include "include/expm.hpp"
+
+static void BM_expm_dual1x2(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 1>, 2>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+BENCHMARK(BM_expm_dual1x2)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark2.cpp b/benchmark/expm_benchmark2.cpp
new file mode 100644
index 0000000..7206515
--- /dev/null
+++ b/benchmark/expm_benchmark2.cpp
@@ -0,0 +1,10 @@
+#include "include/expm.hpp"
+
+static void BM_expm_dual2(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<double, 2>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+BENCHMARK(BM_expm_dual2)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark2x2.cpp b/benchmark/expm_benchmark2x2.cpp
new file mode 100644
index 0000000..ff74b54
--- /dev/null
+++ b/benchmark/expm_benchmark2x2.cpp
@@ -0,0 +1,11 @@
+#include "include/expm.hpp"
+
+static void BM_expm_dual2x2(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 2>, 2>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+
+BENCHMARK(BM_expm_dual2x2)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark3.cpp b/benchmark/expm_benchmark3.cpp
new file mode 100644
index 0000000..e88d0b8
--- /dev/null
+++ b/benchmark/expm_benchmark3.cpp
@@ -0,0 +1,10 @@
+#include "include/expm.hpp"
+
+static void BM_expm_dual3(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<double, 3>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+BENCHMARK(BM_expm_dual3)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark3x2.cpp b/benchmark/expm_benchmark3x2.cpp
new file mode 100644
index 0000000..65e96f9
--- /dev/null
+++ b/benchmark/expm_benchmark3x2.cpp
@@ -0,0 +1,10 @@
+#include "include/expm.hpp"
+
+static void BM_expm_dual3x2(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 3>, 2>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+BENCHMARK(BM_expm_dual3x2)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark4.cpp b/benchmark/expm_benchmark4.cpp
new file mode 100644
index 0000000..ac799b6
--- /dev/null
+++ b/benchmark/expm_benchmark4.cpp
@@ -0,0 +1,10 @@
+#include "include/expm.hpp"
+
+static void BM_expm_dual4(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<double, 4>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+BENCHMARK(BM_expm_dual4)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark4x2.cpp b/benchmark/expm_benchmark4x2.cpp
new file mode 100644
index 0000000..dca8287
--- /dev/null
+++ b/benchmark/expm_benchmark4x2.cpp
@@ -0,0 +1,10 @@
+#include "include/expm.hpp"
+
+static void BM_expm_dual4x2(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 4>, 2>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+BENCHMARK(BM_expm_dual4x2)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark5.cpp b/benchmark/expm_benchmark5.cpp
new file mode 100644
index 0000000..431e496
--- /dev/null
+++ b/benchmark/expm_benchmark5.cpp
@@ -0,0 +1,10 @@
+#include "include/expm.hpp"
+
+static void BM_expm_dual5(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<double, 5>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+BENCHMARK(BM_expm_dual5)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark5x2.cpp b/benchmark/expm_benchmark5x2.cpp
new file mode 100644
index 0000000..25ed2e1
--- /dev/null
+++ b/benchmark/expm_benchmark5x2.cpp
@@ -0,0 +1,10 @@
+#include "include/expm.hpp"
+
+static void BM_expm_dual5x2(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 5>, 2>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+BENCHMARK(BM_expm_dual5x2)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark6.cpp b/benchmark/expm_benchmark6.cpp
new file mode 100644
index 0000000..2ac8a16
--- /dev/null
+++ b/benchmark/expm_benchmark6.cpp
@@ -0,0 +1,10 @@
+#include "include/expm.hpp"
+
+static void BM_expm_dual6(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<double, 6>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+BENCHMARK(BM_expm_dual6)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark6x2.cpp b/benchmark/expm_benchmark6x2.cpp
new file mode 100644
index 0000000..5702dfd
--- /dev/null
+++ b/benchmark/expm_benchmark6x2.cpp
@@ -0,0 +1,10 @@
+#include "include/expm.hpp"
+
+static void BM_expm_dual6x2(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 6>, 2>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+BENCHMARK(BM_expm_dual6x2)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark7.cpp b/benchmark/expm_benchmark7.cpp
new file mode 100644
index 0000000..6a0ad4f
--- /dev/null
+++ b/benchmark/expm_benchmark7.cpp
@@ -0,0 +1,10 @@
+#include "include/expm.hpp"
+
+static void BM_expm_dual7(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<double, 7>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+BENCHMARK(BM_expm_dual7)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark7x2.cpp b/benchmark/expm_benchmark7x2.cpp
new file mode 100644
index 0000000..dcf0671
--- /dev/null
+++ b/benchmark/expm_benchmark7x2.cpp
@@ -0,0 +1,32 @@
+#include "include/expm.hpp"
+
+static void BM_expm_dual7x2(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 7>, 2>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  static_assert(
+    std::same_as<poly::math::ElementwiseBinaryOp<
+                   poly::math::Array<D, SquareDims<>, true>,
+                   poly::math::Array<D, SquareDims<>, true>, std::plus<>>,
+                 decltype(A + A)>);
+  static_assert(
+    std::same_as<double, poly::math::scalarize_via_cast_t<
+                           poly::math::Array<D, SquareDims<>, true>>>);
+  static_assert(
+    std::same_as<double, poly::math::scalarize_via_cast_t<decltype(A + A)>>);
+  static_assert(
+    std::same_as<
+      poly::math::ElementwiseBinaryOp<poly::math::Array<D, SquareDims<>, true>,
+                                      double, std::multiplies<>>,
+      decltype(A * 2.3)>);
+  static_assert(
+    std::same_as<double, poly::math::scalarize_via_cast_t<decltype(A * 2.3)>>);
+  static_assert(
+    std::same_as<double, poly::math::scalarize_via_cast_t<decltype(2.3 * A)>>);
+  static_assert(poly::math::ScalarizeViaCastTo<
+                poly::math::scalarize_via_cast_t<decltype(view(A))>,
+                decltype(2.3 * A)>());
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+BENCHMARK(BM_expm_dual7x2)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark8.cpp b/benchmark/expm_benchmark8.cpp
new file mode 100644
index 0000000..6da850d
--- /dev/null
+++ b/benchmark/expm_benchmark8.cpp
@@ -0,0 +1,10 @@
+#include "include/expm.hpp"
+
+static void BM_expm_dual8(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<double, 8>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+BENCHMARK(BM_expm_dual8)->DenseRange(2, 10, 1);
diff --git a/benchmark/expm_benchmark8x2.cpp b/benchmark/expm_benchmark8x2.cpp
new file mode 100644
index 0000000..d82b4c7
--- /dev/null
+++ b/benchmark/expm_benchmark8x2.cpp
@@ -0,0 +1,10 @@
+#include "include/expm.hpp"
+
+static void BM_expm_dual8x2(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 8>, 2>;
+  SquareMatrix<D> A{SquareDims{{state.range(0)}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) expbench(A);
+}
+BENCHMARK(BM_expm_dual8x2)->DenseRange(2, 10, 1);
diff --git a/benchmark/include/expm.hpp b/benchmark/include/expm.hpp
new file mode 100644
index 0000000..4dcb818
--- /dev/null
+++ b/benchmark/include/expm.hpp
@@ -0,0 +1,136 @@
+#pragma once
+#ifndef expm_hpp_INCLUDED
+#define expm_hpp_INCLUDED
+
+#include "randdual.hpp"
+#include <Containers/TinyVector.hpp>
+#include <Math/Array.hpp>
+#include <Math/Dual.hpp>
+#include <Math/LinearAlgebra.hpp>
+#include <Math/Matrix.hpp>
+#include <Math/StaticArrays.hpp>
+#include <Utilities/Invariant.hpp>
+#include <algorithm>
+#include <benchmark/benchmark.h>
+#include <cstdint>
+#include <random>
+#include <ranges>
+// auto x = Dual<Dual<double, 4>, 2>{1.0};
+// auto y = x * 3.4;
+namespace poly::math {
+static_assert(std::convertible_to<int, Dual<double, 4>>);
+static_assert(std::convertible_to<int, Dual<Dual<double, 4>, 2>>);
+
+template <typename T>
+constexpr void evalpoly(MutSquarePtrMatrix<T> B, MutSquarePtrMatrix<T> A,
+                        SquarePtrMatrix<T> C, const auto &p) {
+  ptrdiff_t N = p.size();
+  invariant(N > 0);
+  invariant(ptrdiff_t(B.numRow()), ptrdiff_t(C.numRow()));
+  if (N & 1) std::swap(A, B);
+  B << p[0] * C + p[1] * I;
+  for (ptrdiff_t i = 2; i < N; ++i) {
+    std::swap(A, B);
+    B << A * C + p[i] * I;
+  }
+}
+
+template <AbstractMatrix T> constexpr auto opnorm1(const T &A) {
+  using S = decltype(value(std::declval<utils::eltype_t<T>>()));
+  auto [M, N] = shape(A);
+  invariant(M > 0);
+  invariant(N > 0);
+  S a{};
+  for (ptrdiff_t n = 0; n < N; ++n) {
+    S s{};
+    for (ptrdiff_t m = 0; m < M; ++m) s += std::abs(value(A[m, n]));
+    a = std::max(a, s);
+  }
+  return a;
+  // Vector<S> v{N};
+  // for (ptrdiff_t n = 0; n < N; ++n)
+  //   v[n] = std::abs(value(A[0, n]));
+  // for (ptrdiff_t m = 1; m < M; ++m)
+  //   for (ptrdiff_t n = 0; n < N; ++n)
+  //     v[n] += std::abs(value(A[m, n]));
+  // return *std::max_element(v.begin(), v.end());
+}
+
+/// computes ceil(log2(x)) for x >= 1
+constexpr auto log2ceil(double x) -> ptrdiff_t {
+  invariant(x >= 1);
+  uint64_t u = std::bit_cast<uint64_t>(x) - 1;
+  auto y = ptrdiff_t((u >> 52) - 1022);
+  invariant(y >= 0);
+  return y;
+}
+
+template <typename T> constexpr void expm(MutSquarePtrMatrix<T> A) {
+  ptrdiff_t n = ptrdiff_t(A.numRow()), s = 0;
+  SquareMatrix<T> A2{SquareDims<>{{n}}}, U_{SquareDims<>{{n}}};
+  MutSquarePtrMatrix<T> U{U_};
+  if (double nA = opnorm1(A); nA <= 0.015) {
+    A2 << A * A;
+    U << A * (A2 + 60.0 * I);
+    A << 12.0 * A2 + 120.0 * I;
+  } else {
+    SquareMatrix<T> B{SquareDims<>{{n}}};
+    if (nA <= 2.1) {
+      A2 << A * A;
+      containers::TinyVector<double, 5> p0, p1;
+      if (nA > 0.95) {
+        p0 = {1.0, 3960.0, 2162160.0, 302702400.0, 8821612800.0};
+        p1 = {90.0, 110880.0, 3.027024e7, 2.0756736e9, 1.76432256e10};
+      } else if (nA > 0.25) {
+        p0 = {1.0, 1512.0, 277200.0, 8.64864e6};
+        p1 = {56.0, 25200.0, 1.99584e6, 1.729728e7};
+      } else {
+        p0 = {1.0, 420.0, 15120.0};
+        p1 = {30.0, 3360.0, 30240.0};
+      }
+      evalpoly(B, U, A2, p0);
+      U << A * B;
+      evalpoly(A, B, A2, p1);
+    } else {
+      // s = std::max(unsigned(std::ceil(std::log2(nA / 5.4))), 0);
+      s = nA > 5.4 ? log2ceil(nA / 5.4) : 0;
+      if (s & 1) {       // we'll swap `U` and `A` an odd number of times
+        std::swap(A, U); // so let them switch places
+        A << U * exp2(-s);
+      } else if (s > 0) A *= exp2(-s);
+      A2 << A * A;
+      // here we take an estrin (instead of horner) approach to cut down flops
+      SquareMatrix<T> A4{A2 * A2}, A6{A2 * A4};
+      B << A6 * (A6 + 16380 * A4 + 40840800 * A2) +
+             (33522128640 * A6 + 10559470521600 * A4 + 1187353796428800 * A2) +
+             32382376266240000 * I;
+      U << A * B;
+      A << A6 * (182 * A6 + 960960 * A4 + 1323241920 * A2) +
+             (670442572800 * A6 + 129060195264000 * A4 +
+              7771770303897600 * A2) +
+             64764752532480000 * I;
+    }
+  }
+  containers::tie(A, U) << containers::Tuple(A + U, A - U);
+  LU::ldiv(U, MutPtrMatrix<T>(A));
+  for (; s--; std::swap(A, U)) U << A * A;
+}
+
+} // namespace poly::math
+
+using poly::math::Dual, poly::math::SquareDims, poly::math::SquareMatrix,
+  poly::math::URand;
+
+auto expwork(const auto &A) {
+  SquareMatrix<poly::math::eltype_t<decltype(A)>> C{SquareDims{A.numRow()}},
+    B{A};
+  expm(B);
+  for (size_t i = 0; i < 8; ++i) {
+    expm(C << A * exp2(-double(i)));
+    B += C;
+  }
+  return B;
+}
+void expbench(const auto &A) { benchmark::DoNotOptimize(expwork(A)); }
+
+#endif // expm_hpp_INCLUDED
diff --git a/benchmark/include/randdual.hpp b/benchmark/include/randdual.hpp
new file mode 100644
index 0000000..2ab16dd
--- /dev/null
+++ b/benchmark/include/randdual.hpp
@@ -0,0 +1,26 @@
+#pragma once
+#ifndef randdual_hpp_INCLUDED
+#define randdual_hpp_INCLUDED
+
+#include <Math/Dual.hpp>
+#include <cstddef>
+#include <random>
+
+namespace poly::math {
+template <class T> struct URand {};
+
+template <class T, ptrdiff_t N> struct URand<Dual<T, N>> {
+  auto operator()(std::mt19937_64 &rng) -> Dual<T, N> {
+    Dual<T, N> x{URand<T>{}(rng)};
+    for (size_t i = 0; i < N; ++i) x.gradient()[i] = URand<T>{}(rng);
+    return x;
+  }
+};
+template <> struct URand<double> {
+  auto operator()(std::mt19937_64 &rng) -> double {
+    return std::uniform_real_distribution<double>(-2, 2)(rng);
+  }
+};
+} // namespace poly::math
+
+#endif // randdual_hpp_INCLUDED
diff --git a/benchmark/integer_matrix_benchmarks.cpp b/benchmark/integer_matrix_benchmarks.cpp
new file mode 100644
index 0000000..6a8e3b3
--- /dev/null
+++ b/benchmark/integer_matrix_benchmarks.cpp
@@ -0,0 +1,26 @@
+#include "Math/LinearAlgebra.hpp"
+#include "Math/NormalForm.hpp"
+#include <Utilities/MatrixStringParse.hpp>
+#include <benchmark/benchmark.h>
+#include <random>
+
+using namespace poly;
+
+static void BM_normal_form(benchmark::State &state) {
+  using math::_;
+  std::mt19937_64 rng0;
+  std::uniform_int_distribution<> distrib(-10, 10);
+  ptrdiff_t d = state.range(0), numIter = 100;
+  math::DenseDims dim{math::DenseDims<>{{numIter * d}, {d}}};
+  math::DenseMatrix<int64_t> A{dim}, B{dim}, C{dim}, D{dim};
+  for (auto &&x : C) x = distrib(rng0);
+  for (auto &&x : D) x = distrib(rng0);
+  for (auto b : state) {
+    A << C;
+    B << D;
+    for (ptrdiff_t n = 0; n < numIter; ++n)
+      math::NormalForm::solveSystem(A[_(n * d, (n + 1) * d), _],
+                                    B[_(n * d, (n + 1) * d), _]);
+  }
+}
+BENCHMARK(BM_normal_form)->DenseRange(2, 10, 1);
diff --git a/benchmark/simplex_benchmark.cpp b/benchmark/simplex_benchmark.cpp
new file mode 100644
index 0000000..c09a502
--- /dev/null
+++ b/benchmark/simplex_benchmark.cpp
@@ -0,0 +1,1131 @@
+#include <Math/Simplex.hpp>
+#include <Utilities/MatrixStringParse.hpp>
+#include <benchmark/benchmark.h>
+
+using poly::utils::operator""_mat, poly::math::_;
+
+static void BM_Simplex0(benchmark::State &state) {
+  poly::math::DenseMatrix<int64_t> tableau{
+    "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 1 0 1 -1 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
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+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
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+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
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+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;"
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+    "0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 "
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+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
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+    "0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 -1 0 -1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
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+    "0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
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+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
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+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
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+    "-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 1 0 -1 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
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+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 1 0 -1 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;"
+    "1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;"
+    "1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ;"
+    "1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 "
+    "1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]"_mat};
+
+  tableau[0, _] << -5859553999884210514;
+  poly::alloc::OwningArena<> alloc;
+  ptrdiff_t numCon = ptrdiff_t(tableau.numRow()) - 1;
+  ptrdiff_t numVar = ptrdiff_t(tableau.numCol()) - 1;
+  poly::utils::Valid<poly::math::Simplex> simpBackup{
+    poly::math::Simplex::create(&alloc, numCon, numVar)};
+  simpBackup->getTableau() << tableau;
+  // Simplex simpBackup{tableau};
+  poly::utils::Valid<poly::math::Simplex> simp{poly::math::Simplex::create(
+    &alloc, simpBackup->getNumCons(), simpBackup->getNumVars())};
+  // Vector<Rational> sol(37);
+  for (auto b : state) {
+    *simp << *simpBackup;
+    bool fail = simp->initiateFeasible();
+    assert(!fail);
+    if (!fail) simp->rLexMinLast(37);
+  }
+  alloc.reset();
+}
+BENCHMARK(BM_Simplex0);
+
+static void BM_Simplex1(benchmark::State &state) {
+  poly::math::IntMatrix<> tableau{
+    "[0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 -1 0 0 725849473193 "
+    "94205055327856 11 11 11 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 -1 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 "
+    "0 0 -1 0 725849473193 94205055277312 6 6 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 "
+    "0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 1 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 -2 0 -1 0 2 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 -1 0 0 0 "
+    "0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 -2 0 -1 0 2 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 -1 0 0 "
+    "0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 1 -1 0 0 1 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 1 -1 0 0 0 0 0 0 1 -1 0 0 0 0 0 1 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 2 0 1 0 -2 0 -1 0 0 1 -1 0 0 0 0 0 0 0 -2 0 0 -1 -1 0 0 0 0 1 0 0 "
+    "0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 2 0 1 0 -2 0 -1 0 1 -1 0 0 0 0 0 0 0 -2 0 0 -1 -1 0 0 0 0 0 0 0 1 0 "
+    "0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 -1 0 -1 0 -1 0 "
+    "-1 0 -1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 -1 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 -1 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 "
+    "0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 -1 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 -1 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 -1 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 -1 0 2 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 "
+    "0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 "
+    "0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 -1 0 2 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 "
+    "1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 "
+    "0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 1 -1 0 0 0 0 0 "
+    "0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 1 -1 0 0 0 0 0 0 1 "
+    "-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 -2 0 -1 0 0 1 -1 0 0 0 0 0 0 0 -2 "
+    "0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 "
+    "0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 -2 0 -1 0 1 -1 0 0 0 0 0 0 0 -2 0 0 "
+    "-1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 "
+    "0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -2 0 0 -2 2 0 0 "
+    "-1 0 -1 0 -1 0 -1 0 -1 -2 -1 2 -3 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 "
+    "0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 -1 0 2 0 1 0 "
+    "0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 "
+    "0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 -1 0 2 0 1 0 0 "
+    "0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 "
+    "0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 0 "
+    "0 0 0 0 0 1 -1 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 "
+    "0 0 0 1 -1 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 -2 0 -1 0 "
+    "0 1 -1 0 0 0 0 0 0 0 -2 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 "
+    "0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 -2 0 -1 0 1 "
+    "-1 0 0 0 0 0 0 0 -2 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 "
+    "0 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 2 -2 0 0 -2 2 0 0 -1 0 -1 0 -1 0 -1 0 -1 -2 -1 2 -3 0 1 1 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 -1 0 0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 -1 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "-1 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "-1 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 "
+    "0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 ;"
+    "0 0 0 -2 0 -1 0 2 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 "
+    "0 0 0 0 0 0 0 0 ;"
+    "0 0 -2 0 -1 0 2 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 "
+    "0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 ;"
+    "0 0 0 0 1 0 0 0 -1 0 0 0 0 0 1 -1 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 ;"
+    "0 0 0 2 0 1 0 -2 0 -1 0 0 1 -1 0 0 0 0 0 0 0 -2 0 0 -1 -1 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 "
+    "0 0 0 0 0 0 0 0 0 ;"
+    "0 0 2 0 1 0 -2 0 -1 0 1 -1 0 0 0 0 0 0 0 -2 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 "
+    "0 0 0 0 0 0 0 0 0 ;"
+    "1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "
+    "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 "
+    "0 0 0 0 0 0 0 0 0 ]"_mat};
+
+  poly::alloc::OwningArena<> alloc;
+  ptrdiff_t numCon = ptrdiff_t(tableau.numRow()) - 1;
+  ptrdiff_t numVar = ptrdiff_t(tableau.numCol()) - 1;
+  poly::utils::Valid<poly::math::Simplex> simpBackup{
+    poly::math::Simplex::create(&alloc, numCon, numVar, 0)};
+  simpBackup->getTableau() << tableau;
+  poly::utils::Valid<poly::math::Simplex> simp{poly::math::Simplex::create(
+    &alloc, simpBackup->getNumCons(), simpBackup->getNumVars(), 0)};
+  for (auto b : state) {
+    *simp << *simpBackup;
+    bool fail = simp->initiateFeasible();
+    assert(!fail);
+    if (!fail) simp->rLexMinLast(15);
+  }
+}
+BENCHMARK(BM_Simplex1);
diff --git a/benchmark/tensor_benchmark.cpp b/benchmark/tensor_benchmark.cpp
new file mode 100644
index 0000000..df06604
--- /dev/null
+++ b/benchmark/tensor_benchmark.cpp
@@ -0,0 +1,202 @@
+
+#include "include/randdual.hpp"
+#include <Math/Array.hpp>
+#include <Math/Dual.hpp>
+#include <Math/LinearAlgebra.hpp>
+#include <Math/Matrix.hpp>
+#include <Math/StaticArrays.hpp>
+#include <Utilities/Invariant.hpp>
+#include <algorithm>
+#include <array>
+#include <benchmark/benchmark.h>
+#include <concepts>
+#include <cstdint>
+#include <random>
+#include <ranges>
+
+using poly::math::Dual, poly::math::SquareMatrix, poly::math::SquareDims,
+  poly::math::I, poly::math::URand;
+
+static void BM_dual8x2dApI(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 8>, 2>;
+  ptrdiff_t dim = state.range(0);
+  SquareMatrix<D> A{SquareDims{{dim}}};
+  SquareMatrix<D> B{SquareDims{{dim}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) benchmark::DoNotOptimize(B << 12.0 * A + 120.0 * I);
+}
+BENCHMARK(BM_dual8x2dApI)->DenseRange(2, 10, 1);
+
+static void BM_dual8x2BmApI(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 8>, 2>;
+  ptrdiff_t dim = state.range(0);
+  SquareMatrix<D> A{SquareDims{{dim}}};
+  SquareMatrix<D> B{SquareDims{{dim}}};
+  SquareMatrix<D> C{SquareDims{{dim}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto &&b : B) b = URand<D>{}(rng0);
+  for (auto b : state) benchmark::DoNotOptimize(C << B * (A + 60.0 * I));
+}
+BENCHMARK(BM_dual8x2BmApI)->DenseRange(2, 10, 1);
+
+template <size_t M, size_t N>
+void BtimesAplusdI(
+  poly::math::MutSquarePtrMatrix<std::array<std::array<double, M>, N>> C,
+  poly::math::MutSquarePtrMatrix<std::array<std::array<double, M>, N>> A,
+  poly::math::MutSquarePtrMatrix<std::array<std::array<double, M>, N>> B,
+  double doffset) {
+  using T = std::array<std::array<double, M>, N>;
+  poly::utils::invariant(C.numRow() == A.numRow());
+  poly::utils::invariant(C.numRow() == B.numRow());
+  ptrdiff_t D = ptrdiff_t(C.numRow());
+  POLYMATHNOVECTORIZE
+  for (ptrdiff_t r = 0; r < D; ++r) {
+    POLYMATHNOVECTORIZE
+    for (ptrdiff_t c = 0; c < D; ++c) {
+      T x{};
+      POLYMATHNOVECTORIZE
+      for (ptrdiff_t k = 0; k < D; ++k) {
+        // x += B[r, k] * A[k, c];
+        T &Brk = B[r, k];
+        T &Akc = A[k, c];
+        // x[0] += Brk[0] * Akc[0];
+        x[0][0] += Brk[0][0] * (Akc[0][0] + doffset * (r == c));
+        POLYMATHVECTORIZE
+        for (size_t i = 1; i < M; ++i)
+          x[0][i] += Brk[0][0] * Akc[0][i] + Brk[0][i] * Akc[0][0];
+        POLYMATHNOVECTORIZE
+        for (size_t o = 1; o < N; ++o) {
+          // x[o] += Brk[0]*Akc[o];
+          x[o][0] += Brk[0][0] * Akc[o][0];
+          POLYMATHVECTORIZE
+          for (size_t i = 1; i < M; ++i)
+            x[o][i] += Brk[0][0] * Akc[o][i] + Brk[0][i] * Akc[o][0];
+          // x[o] += Brk[o]*Akc[0];
+          x[o][0] += Brk[o][0] * Akc[0][0];
+          POLYMATHVECTORIZE
+          for (size_t i = 1; i < M; ++i)
+            x[o][i] += Brk[o][0] * Akc[0][i] + Brk[o][i] * Akc[0][0];
+        }
+      }
+      C[r, c] = x;
+    }
+  }
+}
+
+static void BM_dual8x2BmApI_manual(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = std::array<std::array<double, 9>, 3>;
+  ptrdiff_t dim = state.range(0);
+  SquareMatrix<D> A{SquareDims{{dim}}};
+  SquareMatrix<D> B{SquareDims{{dim}}};
+  SquareMatrix<D> C{SquareDims{{dim}}};
+  for (ptrdiff_t i = 0, L = dim * dim; i < L; ++i) {
+    for (ptrdiff_t j = 0; j < 3; ++j) {
+      for (ptrdiff_t k = 0; k < 9; ++k) {
+        A[i][j][k] = URand<double>{}(rng0);
+        B[i][j][k] = URand<double>{}(rng0);
+      }
+    }
+  }
+  for (auto b : state) BtimesAplusdI(C, A, B, 60.0);
+}
+BENCHMARK(BM_dual8x2BmApI_manual)->DenseRange(2, 10, 1);
+
+static void BM_dual7x2dApI(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 7>, 2>;
+  static_assert(poly::utils::Compressible<Dual<double, 7>>);
+  static_assert(poly::utils::Compressible<D>);
+  static_assert(sizeof(poly::utils::compressed_t<D>) == (24 * sizeof(double)));
+  static_assert(sizeof(D) == (24 * sizeof(double)));
+  ptrdiff_t dim = state.range(0);
+  SquareMatrix<D> A{SquareDims{{dim}}};
+  SquareMatrix<D> B{SquareDims{{dim}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) benchmark::DoNotOptimize(B << 12.0 * A + 120.0 * I);
+}
+BENCHMARK(BM_dual7x2dApI)->DenseRange(2, 10, 1);
+
+static void BM_dual7x2BmApI(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 7>, 2>;
+  ptrdiff_t dim = state.range(0);
+  SquareMatrix<D> A{SquareDims{{dim}}};
+  SquareMatrix<D> B{SquareDims{{dim}}};
+  SquareMatrix<D> C{SquareDims{{dim}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto &&b : B) b = URand<D>{}(rng0);
+  for (auto b : state) benchmark::DoNotOptimize(C << B * (A + 60.0 * I));
+}
+BENCHMARK(BM_dual7x2BmApI)->DenseRange(2, 10, 1);
+
+static void BM_dual7x2BmApI_manual(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = std::array<std::array<double, 8>, 3>;
+  ptrdiff_t dim = state.range(0);
+  SquareMatrix<D> A{SquareDims{{dim}}};
+  SquareMatrix<D> B{SquareDims{{dim}}};
+  SquareMatrix<D> C{SquareDims{{dim}}};
+  for (ptrdiff_t i = 0, L = dim * dim; i < L; ++i) {
+    for (ptrdiff_t j = 0; j < 3; ++j) {
+      for (ptrdiff_t k = 0; k < 8; ++k) {
+        A[i][j][k] = URand<double>{}(rng0);
+        B[i][j][k] = URand<double>{}(rng0);
+      }
+    }
+  }
+  for (auto b : state) BtimesAplusdI(C, A, B, 60.0);
+}
+BENCHMARK(BM_dual7x2BmApI_manual)->DenseRange(2, 10, 1);
+
+static void BM_dual6x2dApI(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 6>, 2>;
+  static_assert(poly::utils::Compressible<Dual<double, 6>>);
+  static_assert(poly::utils::Compressible<D>);
+  static_assert(sizeof(poly::utils::compressed_t<D>) == (21 * sizeof(double)));
+  static_assert(sizeof(D) == (24 * sizeof(double)));
+  // static_assert(sizeof(D) == sizeof(Dual<Dual<double, 8>, 2>));
+  ptrdiff_t dim = state.range(0);
+  SquareMatrix<D> A{SquareDims{{dim}}};
+  SquareMatrix<D> B{SquareDims{{dim}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto b : state) benchmark::DoNotOptimize(B << 12.0 * A + 120.0 * I);
+}
+BENCHMARK(BM_dual6x2dApI)->DenseRange(2, 10, 1);
+
+static void BM_dual6x2BmApI(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  using D = Dual<Dual<double, 6>, 2>;
+  ptrdiff_t dim = state.range(0);
+  SquareMatrix<D> A{SquareDims{{dim}}};
+  SquareMatrix<D> B{SquareDims{{dim}}};
+  SquareMatrix<D> C{SquareDims{{dim}}};
+  for (auto &&a : A) a = URand<D>{}(rng0);
+  for (auto &&b : B) b = URand<D>{}(rng0);
+  for (auto b : state) benchmark::DoNotOptimize(C << B * (A + 60.0 * I));
+}
+BENCHMARK(BM_dual6x2BmApI)->DenseRange(2, 10, 1);
+
+static void BM_dual6x2BmApI_manual(benchmark::State &state) {
+  std::mt19937_64 rng0;
+  constexpr size_t Dcount = 6;
+  constexpr size_t N = Dcount + 1;
+  using D = std::array<std::array<double, N>, 3>;
+  ptrdiff_t dim = state.range(0);
+  SquareMatrix<D> A{SquareDims{{dim}}};
+  SquareMatrix<D> B{SquareDims{{dim}}};
+  SquareMatrix<D> C{SquareDims{{dim}}};
+  for (ptrdiff_t i = 0, L = dim * dim; i < L; ++i) {
+    for (ptrdiff_t j = 0; j < 3; ++j) {
+      for (size_t k = 0; k < N; ++k) {
+        A[i][j][k] = URand<double>{}(rng0);
+        B[i][j][k] = URand<double>{}(rng0);
+      }
+    }
+  }
+  for (auto b : state) BtimesAplusdI(C, A, B, 60.0);
+}
+BENCHMARK(BM_dual6x2BmApI_manual)->DenseRange(2, 10, 1);
diff --git a/compile_commands.json b/compile_commands.json
index 0397689..7657903 100644
--- a/compile_commands.json
+++ b/compile_commands.json
@@ -1,538 +1,917 @@
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+{
+  "directory": "/home/chriselrod/Documents/progwork/cxx/Math/buildclang/bench/_deps/benchmark-build/src",
+  "command": "/bin/clang++ -DBENCHMARK_HAS_PTHREAD_AFFINITY -DBENCHMARK_STATIC_DEFINE -DHAVE_POSIX_REGEX -DHAVE_PTHREAD_AFFINITY -DHAVE_STD_REGEX -DHAVE_STEADY_CLOCK -DHAVE_THREAD_SAFETY_ATTRIBUTES -I/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/include -I/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src -Wall -Wextra -Wshadow -Wfloat-equal -Wold-style-cast -Wsuggest-override -pedantic -pedantic-errors -Wshorten-64-to-32 -fstrict-aliasing -Wno-deprecated-declarations -fno-exceptions -Wstrict-aliasing -Wthread-safety -O3 -DNDEBUG -std=c++11 -fvisibility=hidden -fvisibility-inlines-hidden -c /home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src/string_util.h",
+  "file": "/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src/string_util.h"
+},
+
+{
+  "directory": "/home/chriselrod/Documents/progwork/cxx/Math/buildclang/bench/_deps/benchmark-build/src",
+  "command": "/bin/clang++ -DBENCHMARK_HAS_PTHREAD_AFFINITY -DBENCHMARK_STATIC_DEFINE -DHAVE_POSIX_REGEX -DHAVE_PTHREAD_AFFINITY -DHAVE_STD_REGEX -DHAVE_STEADY_CLOCK -DHAVE_THREAD_SAFETY_ATTRIBUTES -I/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/include -I/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src -Wall -Wextra -Wshadow -Wfloat-equal -Wold-style-cast -Wsuggest-override -pedantic -pedantic-errors -Wshorten-64-to-32 -fstrict-aliasing -Wno-deprecated-declarations -fno-exceptions -Wstrict-aliasing -Wthread-safety -O3 -DNDEBUG -std=c++11 -fvisibility=hidden -fvisibility-inlines-hidden -c /home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src/thread_timer.h",
+  "file": "/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src/thread_timer.h"
+},
+
+{
+  "directory": "/home/chriselrod/Documents/progwork/cxx/Math/buildclang/bench/_deps/benchmark-build/src",
+  "command": "/bin/clang++ -DBENCHMARK_HAS_PTHREAD_AFFINITY -DBENCHMARK_STATIC_DEFINE -DHAVE_POSIX_REGEX -DHAVE_PTHREAD_AFFINITY -DHAVE_STD_REGEX -DHAVE_STEADY_CLOCK -DHAVE_THREAD_SAFETY_ATTRIBUTES -I/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/include -I/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src -Wall -Wextra -Wshadow -Wfloat-equal -Wold-style-cast -Wsuggest-override -pedantic -pedantic-errors -Wshorten-64-to-32 -fstrict-aliasing -Wno-deprecated-declarations -fno-exceptions -Wstrict-aliasing -Wthread-safety -O3 -DNDEBUG -std=c++11 -fvisibility=hidden -fvisibility-inlines-hidden -c /home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src/timers.h",
+  "file": "/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src/timers.h"
+},
+
+{
+  "directory": "/home/chriselrod/Documents/progwork/cxx/Math/buildclang/bench/_deps/benchmark-build/src",
+  "command": "/bin/clang++ -DBENCHMARK_HAS_PTHREAD_AFFINITY -DBENCHMARK_STATIC_DEFINE -DHAVE_POSIX_REGEX -DHAVE_PTHREAD_AFFINITY -DHAVE_STD_REGEX -DHAVE_STEADY_CLOCK -DHAVE_THREAD_SAFETY_ATTRIBUTES -I/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/include -I/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src -Wall -Wextra -Wshadow -Wfloat-equal -Wold-style-cast -Wsuggest-override -pedantic -pedantic-errors -Wshorten-64-to-32 -fstrict-aliasing -Wno-deprecated-declarations -fno-exceptions -Wstrict-aliasing -Wthread-safety -O3 -DNDEBUG -std=c++11 -fvisibility=hidden -fvisibility-inlines-hidden -c /home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src/benchmark_register.h",
+  "file": "/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src/benchmark_register.h"
+},
+
+{
+  "directory": "/home/chriselrod/Documents/progwork/cxx/Math/buildclang/bench/_deps/benchmark-build/src",
+  "command": "/bin/clang++ -DBENCHMARK_HAS_PTHREAD_AFFINITY -DBENCHMARK_STATIC_DEFINE -DHAVE_POSIX_REGEX -DHAVE_PTHREAD_AFFINITY -DHAVE_STD_REGEX -DHAVE_STEADY_CLOCK -DHAVE_THREAD_SAFETY_ATTRIBUTES -I/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/include -I/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src -Wall -Wextra -Wshadow -Wfloat-equal -Wold-style-cast -Wsuggest-override -pedantic -pedantic-errors -Wshorten-64-to-32 -fstrict-aliasing -Wno-deprecated-declarations -fno-exceptions -Wstrict-aliasing -Wthread-safety -O3 -DNDEBUG -std=c++11 -fvisibility=hidden -fvisibility-inlines-hidden -c /home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src/arraysize.h",
+  "file": "/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src/arraysize.h"
+},
+
+{
+  "directory": "/home/chriselrod/Documents/progwork/cxx/Math/buildclang/bench/_deps/benchmark-build/src",
+  "command": "/bin/clang++ -DBENCHMARK_HAS_PTHREAD_AFFINITY -DBENCHMARK_STATIC_DEFINE -DHAVE_POSIX_REGEX -DHAVE_PTHREAD_AFFINITY -DHAVE_STD_REGEX -DHAVE_STEADY_CLOCK -DHAVE_THREAD_SAFETY_ATTRIBUTES -I/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/include -I/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src -Wall -Wextra -Wshadow -Wfloat-equal -Wold-style-cast -Wsuggest-override -pedantic -pedantic-errors -Wshorten-64-to-32 -fstrict-aliasing -Wno-deprecated-declarations -fno-exceptions -Wstrict-aliasing -Wthread-safety -O3 -DNDEBUG -std=c++11 -fvisibility=hidden -fvisibility-inlines-hidden -c /home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src/cycleclock.h",
+  "file": "/home/chriselrod/.cache/CPM/benchmark/6ab6f9ea5fa3003095935f1af4b6b363c23ce9d7/src/cycleclock.h"
 }
 ]
diff --git a/include/Alloc/Mallocator.hpp b/include/Alloc/Mallocator.hpp
index b4c1279..bccac0e 100644
--- a/include/Alloc/Mallocator.hpp
+++ b/include/Alloc/Mallocator.hpp
@@ -1,6 +1,8 @@
 #pragma once
 
+#include <concepts>
 #include <cstddef>
+#include <new>
 #ifdef USING_MIMALLOC
 // #include <mimalloc-new-delete.h>
 #include <mimalloc.h>
@@ -10,6 +12,9 @@
 #else
 #include <cstdlib>
 #endif
+#ifdef __cpp_lib_allocate_at_least
+#include <memory>
+#endif
 namespace poly::alloc {
 
 #ifdef __cpp_lib_allocate_at_least
diff --git a/include/Containers/Storage.hpp b/include/Containers/Storage.hpp
index 1eb51f8..242f984 100644
--- a/include/Containers/Storage.hpp
+++ b/include/Containers/Storage.hpp
@@ -1,5 +1,9 @@
 #pragma once
+#include <algorithm>
+#include <bit>
 #include <cstddef>
+#include <cstdint>
+#include <type_traits>
 
 namespace poly::containers {
 template <typename T, ptrdiff_t N> struct Storage {
@@ -14,4 +18,62 @@ template <typename T, ptrdiff_t N> struct Storage {
 template <typename T> struct alignas(T) Storage<T, 0> {
   static constexpr auto data() -> T * { return nullptr; }
 };
+
+template <class T>
+concept SizeMultiple8 = (sizeof(T) % 8) == 0;
+
+template <class S> struct DefaultCapacityType {
+  using type = int;
+};
+template <SizeMultiple8 S> struct DefaultCapacityType<S> {
+  using type = std::ptrdiff_t;
+};
+template <class S>
+using default_capacity_type_t = typename DefaultCapacityType<S>::type;
+
+static_assert(!SizeMultiple8<uint32_t>);
+static_assert(SizeMultiple8<uint64_t>);
+static_assert(std::is_same_v<default_capacity_type_t<uint32_t>, int32_t>);
+static_assert(std::is_same_v<default_capacity_type_t<uint64_t>, int64_t>);
+
+template <class T, class S> consteval auto PreAllocStorage() -> ptrdiff_t {
+  constexpr ptrdiff_t totalBytes = 128;
+  constexpr ptrdiff_t remainingBytes =
+    totalBytes - sizeof(T *) - sizeof(S) - sizeof(default_capacity_type_t<S>);
+  constexpr ptrdiff_t N = remainingBytes / sizeof(T);
+  return std::max<ptrdiff_t>(0, N);
+}
+consteval auto log2Floor(uint64_t x) -> uint64_t {
+  return 63 - std::countl_zero(x);
+}
+consteval auto log2Ceil(uint64_t x) -> uint64_t {
+  return 64 - std::countl_zero(x - 1);
+}
+// NOLINTNEXTLINE(misc-no-recursion)
+consteval auto bisectFindSquare(uint64_t l, uint64_t h, uint64_t N)
+  -> uint64_t {
+  if (l == h) return l;
+  uint64_t m = (l + h) / 2;
+  if (m * m >= N) return bisectFindSquare(l, m, N);
+  return bisectFindSquare(m + 1, h, N);
+}
+template <class T, class S>
+consteval auto PreAllocSquareStorage() -> ptrdiff_t {
+  // 2* because we want to allow more space for matrices
+  // also removes need for other checks; log2Floor(2)==1
+  constexpr ptrdiff_t SN = 2 * PreAllocStorage<T, S>();
+  if constexpr (SN <= 0) return 0;
+  else {
+    constexpr uint64_t N = uint64_t(SN);
+    static_assert(N < 128);
+    // a fairly naive algorirthm for computing the next square `N`
+    // sqrt(x) = x^(1/2) = exp2(log2(x)/2)
+    constexpr uint64_t R = log2Floor(N) / 2;
+    static_assert(R < 63);
+    constexpr uint64_t L = uint64_t(1) << R;
+    constexpr uint64_t H = uint64_t(1) << ((log2Ceil(N) + 1) / 2);
+    return ptrdiff_t(bisectFindSquare(L, H, N));
+  }
+}
+
 } // namespace poly::containers
diff --git a/include/Containers/Tuple.hpp b/include/Containers/Tuple.hpp
new file mode 100644
index 0000000..44b24af
--- /dev/null
+++ b/include/Containers/Tuple.hpp
@@ -0,0 +1,134 @@
+#pragma once
+#ifndef POLY_CONTAIERS_Tuple_hpp_INCLUDED
+#define POLY_CONTAIERS_Tuple_hpp_INCLUDED
+
+namespace poly::containers {
+template <typename T, typename... Ts> struct Tuple;
+template <typename T, typename... Ts>
+[[gnu::always_inline]] constexpr auto cattuple(T, Tuple<Ts...>)
+  -> Tuple<T, Ts...>;
+
+template <typename T, typename... Ts> struct Tuple {
+  [[no_unique_address]] T head;
+  [[no_unique_address]] Tuple<Ts...> tail;
+  constexpr Tuple(T head_, Ts... tail_) : head(head_), tail(tail_...){};
+  constexpr Tuple(T head_, Tuple<Ts...> tail_) : head(head_), tail(tail_){};
+
+  constexpr Tuple(const Tuple &) = default;
+  template <size_t I> auto get() -> auto & {
+    if constexpr (I == 0) return head;
+    else return tail.template get<I - 1>();
+  }
+  template <size_t I> [[nodiscard]] auto get() const -> const auto & {
+    if constexpr (I == 0) return head;
+    else return tail.template get<I - 1>();
+  }
+  constexpr void apply(const auto &f) {
+    f(head);
+    tail.apply(f);
+  }
+  template <typename U, typename... Us>
+  constexpr void apply(const Tuple<U, Us...> &x, const auto &f)
+  requires(sizeof...(Ts) == sizeof...(Us))
+  {
+    f(head, x.head);
+    tail.apply(x.tail, f);
+  }
+  constexpr auto map(const auto &f) const {
+    return cattuple(f(head), tail.map(f));
+  }
+  template <typename U, typename... Us>
+  constexpr auto map(const Tuple<U, Us...> &x, const auto &f) const
+  requires(sizeof...(Ts) == sizeof...(Us))
+  {
+    return cattuple(f(head, x.head), tail.map(x.tail, f));
+  }
+  template <typename U, typename... Us>
+  inline constexpr void operator<<(const Tuple<U, Us...> &)
+  requires(sizeof...(Ts) == sizeof...(Us));
+  template <typename U, typename... Us>
+  inline constexpr void operator+=(const Tuple<U, Us...> &)
+  requires(sizeof...(Ts) == sizeof...(Us));
+  template <typename U, typename... Us>
+  inline constexpr void operator-=(const Tuple<U, Us...> &)
+  requires(sizeof...(Ts) == sizeof...(Us));
+  template <typename U, typename... Us>
+  inline constexpr void operator*=(const Tuple<U, Us...> &)
+  requires(sizeof...(Ts) == sizeof...(Us));
+  template <typename U, typename... Us>
+  inline constexpr void operator/=(const Tuple<U, Us...> &)
+  requires(sizeof...(Ts) == sizeof...(Us));
+  template <typename U, typename... Us>
+  constexpr auto operator=(Tuple<U, Us...> x) -> Tuple &requires(
+    std::assignable_from<T, U> &&... &&std::assignable_from<Ts, Us>) {
+    head = x.head;
+    tail = x.tail;
+    return *this;
+  }
+};
+template <typename T, typename... Ts>
+[[gnu::always_inline]] constexpr auto cattuple(T x, Tuple<Ts...> y)
+  -> Tuple<T, Ts...> {
+  return {x, y};
+}
+template <typename T> struct Tuple<T> {
+  [[no_unique_address]] T head;
+  constexpr Tuple(T head_) : head(head_){};
+  constexpr Tuple(const Tuple &) = default;
+  template <size_t I> auto get() -> T & {
+    static_assert(I == 0);
+    return head;
+  }
+  template <size_t I> [[nodiscard]] auto get() const -> const T & {
+    static_assert(I == 0);
+    return head;
+  }
+  constexpr auto operator=(const Tuple &) -> Tuple & = default;
+  constexpr void apply(const auto &f) { f(head); }
+  template <typename U> constexpr void apply(const Tuple<U> &x, const auto &f) {
+    f(head, x.head);
+  }
+  constexpr auto map(const auto &f) const -> Tuple<decltype(f(head))> {
+    return {f(head)};
+  }
+  template <typename U>
+  constexpr auto map(const Tuple<U> &x, const auto &f) const
+    -> Tuple<decltype(f(head, x.head))> {
+    return {f(head, x.head)};
+  }
+  template <typename U> inline constexpr void operator<<(const Tuple<U> &);
+  template <typename U> inline constexpr void operator+=(const Tuple<U> &);
+  template <typename U> inline constexpr void operator-=(const Tuple<U> &);
+  template <typename U> inline constexpr void operator*=(const Tuple<U> &);
+  template <typename U> inline constexpr void operator/=(const Tuple<U> &);
+
+  template <typename U>
+  constexpr auto operator=(Tuple<U> x)
+    -> Tuple &requires(std::assignable_from<T, U>) {
+      head = x.head;
+      return *this;
+    }
+};
+
+template <typename... Ts> Tuple(Ts...) -> Tuple<Ts...>;
+
+template <typename... Ts> constexpr auto tie(Ts &...x) -> Tuple<Ts &...> {
+  return {x...};
+}
+} // namespace poly::containers
+
+template <typename T, typename... Ts>
+struct std::tuple_size<poly::containers::Tuple<T, Ts...>>
+  : public std::integral_constant<size_t, 1 + sizeof...(Ts)> {};
+
+template <typename T, typename... Ts>
+struct std::tuple_element<0, poly::containers::Tuple<T, Ts...>> {
+  using type = T;
+};
+template <size_t I, typename T, typename... Ts>
+struct std::tuple_element<I, poly::containers::Tuple<T, Ts...>> {
+  using type =
+    typename std::tuple_element<I - 1, poly::containers::Tuple<Ts...>>::type;
+};
+
+#endif // Tuple_hpp_INCLUDED
diff --git a/include/Math/Array.hpp b/include/Math/Array.hpp
index d82596c..c84dc9d 100644
--- a/include/Math/Array.hpp
+++ b/include/Math/Array.hpp
@@ -9,9 +9,10 @@
 #include "Math/Matrix.hpp"
 #include "Math/MatrixDimensions.hpp"
 #include "Math/Rational.hpp"
-#include "Math/Vector.hpp"
 #include "Utilities/Invariant.hpp"
 #include "Utilities/Optional.hpp"
+#include "Utilities/Reference.hpp"
+#include "Utilities/TypeCompression.hpp"
 #include "Utilities/TypePromotion.hpp"
 #include "Utilities/Valid.hpp"
 #include <algorithm>
@@ -47,8 +48,12 @@
 #endif
 
 namespace poly::math {
-template <class T, class S, ptrdiff_t N = PreAllocStorage<T, S>(),
-          class A = alloc::Mallocator<T>>
+template <typename S>
+concept Dimension = VectorDimension<S> != MatrixDimension<S>;
+template <class T, Dimension S,
+          ptrdiff_t N =
+            containers::PreAllocStorage<utils::compressed_t<T>, S>(),
+          class A = alloc::Mallocator<utils::compressed_t<T>>>
 struct ManagedArray;
 
 template <typename T>
@@ -63,8 +68,67 @@ void print_obj(std::ostream &os, const std::pair<F, S> &x) {
 };
 using utils::Valid, utils::Optional;
 
-template <class T, class S> struct Array;
-template <class T, class S> struct MutArray;
+template <class T, Dimension S, bool Compress = utils::Compressible<T>>
+struct Array;
+template <class T, Dimension S, bool Compress = utils::Compressible<T>>
+struct MutArray;
+
+// Cases we need to consider:
+// 1. Slice-indexing
+// 2.a. `ptrdiff_t` indexing, not compressed
+// 2.b. `ptrdiff_t` indexing, compressed
+// 3.a.i. Vector indexing, contig, no mask
+// 3.a.ii. Vector indexing, contig, mask
+// 3.b.i. Vector indexing, discontig, no mask
+// 3.b.ii. Vector indexing, discontig, mask
+// all of the above for `T*` and `const T*`
+template <typename T, typename P, typename S, typename I>
+[[gnu::flatten, gnu::always_inline]] constexpr auto index(P *ptr, S shape,
+                                                          I i) noexcept
+  -> decltype(auto) {
+  auto offset = calcOffset(shape, i);
+  auto newDim = calcNewDim(shape, i);
+  invariant(ptr != nullptr);
+  using D = decltype(newDim);
+  if constexpr (simd::index::issimd<D>) return simd::ref(ptr + offset, newDim);
+  else {
+    constexpr bool Compress = !std::same_as<T, std::remove_const_t<P>>;
+    if constexpr (!std::same_as<D, Empty>)
+      if constexpr (std::is_const_v<P>)
+        return Array<T, D, Compress>{ptr + offset, newDim};
+      else return MutArray<T, D, Compress>{ptr + offset, newDim};
+    else if constexpr (!Compress) return ptr[offset];
+    else if constexpr (std::is_const_v<P>) return T::decompress(ptr + offset);
+    else return utils::Reference<T>{ptr + offset};
+  }
+}
+// for (row/col)vectors, we drop the row/col, essentially broadcasting
+template <typename T, typename P, typename S, typename R, typename C>
+[[gnu::flatten, gnu::always_inline]] constexpr auto index(P *ptr, S shape, R wr,
+                                                          C wc) noexcept
+  -> decltype(auto) {
+  if constexpr (MatrixDimension<S>) {
+    auto r = unwrapRow(wr);
+    auto c = unwrapCol(wc);
+    auto offset = calcOffset(shape, r, c);
+    auto newDim = calcNewDim(shape, r, c);
+    using D = decltype(newDim);
+    if constexpr (simd::index::issimd<D>)
+      return simd::ref(ptr + offset, newDim);
+    else {
+      constexpr bool Compress = !std::same_as<T, std::remove_const_t<P>>;
+      if constexpr (!std::same_as<D, Empty>)
+        if constexpr (std::is_const_v<P>)
+          return Array<T, D, Compress>{ptr + offset, newDim};
+        else return MutArray<T, D, Compress>{ptr + offset, newDim};
+      else if constexpr (!Compress) return ptr[offset];
+      else if constexpr (std::is_const_v<P>) return T::decompress(ptr + offset);
+      else return utils::Reference<T>{ptr + offset};
+    }
+  } else if constexpr (std::same_as<S, StridedRange>)
+    return index<T>(ptr, shape, unwrapRow(wr));
+  else return index<T>(ptr, shape, unwrapCol(wc));
+}
 
 template <typename T, bool Column = false> struct SliceIterator {
   using stride_type = std::conditional_t<Column, StridedRange, ptrdiff_t>;
@@ -72,7 +136,8 @@ template <typename T, bool Column = false> struct SliceIterator {
     std::conditional_t<std::is_const_v<T>,
                        Array<std::remove_cvref_t<T>, stride_type>,
                        MutArray<std::remove_reference_t<T>, stride_type>>;
-  T *data;
+  using storage_type = utils::compressed_t<T>;
+  storage_type *data;
   ptrdiff_t len;
   ptrdiff_t rowStride;
   ptrdiff_t idx;
@@ -148,39 +213,48 @@ template <typename T, bool Column = false> struct SliceRange {
   }
 };
 /// Constant Array
-template <class T, class S> struct POLY_MATH_GSL_POINTER Array {
+template <class T, Dimension S, bool Compress>
+struct POLY_MATH_GSL_POINTER Array {
   static_assert(!std::is_const_v<T>, "T shouldn't be const");
   static_assert(std::is_trivially_destructible_v<T>,
                 "maybe should add support for destroying");
+
+  using storage_type = std::conditional_t<Compress, utils::compressed_t<T>, T>;
   using value_type = T;
   using reference = T &;
   using const_reference = const T &;
   using size_type = ptrdiff_t;
   using difference_type = int;
-  using iterator = T *;
-  using const_iterator = const T *;
-  using pointer = T *;
-  using const_pointer = const T *;
+  using iterator = storage_type *;
+  using const_iterator = const storage_type *;
+  using pointer = storage_type *;
+  using const_pointer = const storage_type *;
   using concrete = std::true_type;
 
+  static constexpr bool isdense =
+    std::convertible_to<S, ptrdiff_t> || std::convertible_to<S, DenseDims<>>;
+  static constexpr bool flatstride = isdense || std::same_as<S, StridedRange>;
+  static_assert(flatstride != std::same_as<S, StridedDims<>>);
+
   constexpr Array() = default;
   constexpr Array(const Array &) = default;
   constexpr Array(Array &&) noexcept = default;
   constexpr auto operator=(const Array &) -> Array & = default;
   constexpr auto operator=(Array &&) noexcept -> Array & = default;
-  constexpr Array(const T *p, S s) : ptr(p), sz(s) {}
-  constexpr Array(Valid<const T> p, S s) : ptr(p), sz(s) {}
+  constexpr Array(const storage_type *p, S s) : ptr(p), sz(s) {}
+  constexpr Array(Valid<const storage_type> p, S s) : ptr(p), sz(s) {}
   template <ptrdiff_t R, ptrdiff_t C>
-  constexpr Array(const T *p, Row<R> r, Col<C> c) : ptr(p), sz(S{r, c}) {}
+  constexpr Array(const storage_type *p, Row<R> r, Col<C> c)
+    : ptr(p), sz(S{r, c}) {}
   template <ptrdiff_t R, ptrdiff_t C>
-  constexpr Array(Valid<const T> p, Row<R> r, Col<C> c)
+  constexpr Array(Valid<const storage_type> p, Row<R> r, Col<C> c)
     : ptr(p), sz(dimension<S>(r, c)) {}
   template <std::convertible_to<S> V>
   constexpr Array(Array<T, V> a) : ptr(a.data()), sz(a.dim()) {}
   template <size_t N>
   constexpr Array(const std::array<T, N> &a) : ptr(a.data()), sz(N) {}
   [[nodiscard, gnu::returns_nonnull]] constexpr auto data() const noexcept
-    -> const T * {
+    -> const storage_type * {
     invariant(ptr != nullptr);
     return ptr;
   }
@@ -190,26 +264,33 @@ template <class T, class S> struct POLY_MATH_GSL_POINTER Array {
     -> StridedIterator<const T>
   requires(std::is_same_v<S, StridedRange>)
   {
-    const T *p = ptr;
+    const storage_type *p = ptr;
     return StridedIterator{p, sz.stride};
   }
   [[nodiscard]] constexpr auto begin() const noexcept
-    -> const T *requires(!std::is_same_v<S, StridedRange>) { return ptr; }
+    -> const storage_type *requires(isdense) { return ptr; }
 
-  [[nodiscard]] constexpr auto end() const noexcept {
+  [[nodiscard]] constexpr auto end() const noexcept
+  requires(flatstride)
+  {
     return begin() + ptrdiff_t(sz);
   }
-  [[nodiscard]] constexpr auto rbegin() const noexcept {
+  [[nodiscard]] constexpr auto rbegin() const noexcept
+  requires(flatstride)
+  {
     return std::reverse_iterator(end());
   }
-  [[nodiscard]] constexpr auto rend() const noexcept {
+  [[nodiscard]] constexpr auto rend() const noexcept
+  requires(flatstride)
+  {
     return std::reverse_iterator(begin());
   }
   [[nodiscard]] constexpr auto front() const noexcept -> const T & {
-    return *begin();
+    return *ptr;
   }
   [[nodiscard]] constexpr auto back() const noexcept -> const T & {
-    return *(end() - 1);
+    if constexpr (flatstride) return *(end() - 1);
+    else return ptr[sride(sz) * ptrdiff_t(row(sz)) - 1];
   }
   // indexing has two components:
   // 1. offsetting the pointer
@@ -217,22 +298,15 @@ template <class T, class S> struct POLY_MATH_GSL_POINTER Array {
   // static constexpr auto slice(Valid<T>, Index<S> auto i){
   //   auto
   // }
-  [[gnu::flatten]] constexpr auto operator[](Index<S> auto i) const noexcept
-    -> decltype(auto) {
-    auto offset = calcOffset(sz, i);
-    auto newDim = calcNewDim(sz, i);
-    invariant(ptr != nullptr);
-    if constexpr (std::is_same_v<decltype(newDim), Empty>)
-      return static_cast<const T *>(ptr)[offset];
-    else return Array<T, decltype(newDim)>{ptr + offset, newDim};
+  [[gnu::flatten, gnu::always_inline]] constexpr auto
+  operator[](Index<S> auto i) const noexcept -> decltype(auto) {
+    return index<T>(ptr, sz, i);
   }
-  // for vectors, we just drop the column, essentially broadcasting
+  // for (row/col)vectors, we drop the row/col, essentially broadcasting
   template <class R, class C>
-  [[gnu::flatten]] constexpr auto operator[](R r, C c) const noexcept
-    -> decltype(auto) {
-    if constexpr (MatrixDimension<S>)
-      return (*this)[CartesianIndex(unwrapRow(r), unwrapCol(c))];
-    else return (*this)[ptrdiff_t(r)];
+  [[gnu::flatten, gnu::always_inline]] constexpr auto
+  operator[](R r, C c) const noexcept -> decltype(auto) {
+    return index<T>(ptr, sz, r, c);
   }
   [[nodiscard]] constexpr auto minRowCol() const -> ptrdiff_t {
     return std::min(ptrdiff_t(numRow()), ptrdiff_t(numCol()));
@@ -257,31 +331,23 @@ template <class T, class S> struct POLY_MATH_GSL_POINTER Array {
     return N;
   }
 
-  [[nodiscard]] constexpr auto numRow() const noexcept
-  requires(MatrixDimension<S>)
-  {
-    return Row(sz);
+  [[nodiscard]] constexpr auto numRow() const noexcept {
+    if constexpr (std::convertible_to<S, ptrdiff_t>) return Row<1>{};
+    else return row(sz);
   }
-  [[nodiscard]] constexpr auto numCol() const noexcept
-  requires(MatrixDimension<S>)
-  {
-    return Col(sz);
-  }
-  [[nodiscard]] constexpr auto rowStride() const noexcept
-  requires(MatrixDimension<S>)
-  {
-    return RowStride(sz);
+  [[nodiscard]] constexpr auto numCol() const noexcept { return col(sz); }
+  [[nodiscard]] constexpr auto rowStride() const noexcept {
+    if constexpr (std::integral<S>) return RowStride<1>{};
+    else return stride(sz);
   }
   [[nodiscard]] constexpr auto empty() const -> bool { return sz == S{}; }
   [[nodiscard]] constexpr auto size() const noexcept {
     if constexpr (StaticInt<S>) return S{};
-    else if constexpr (std::integral<S>) return sz;
-    else if constexpr (std::is_same_v<S, StridedRange>) return ptrdiff_t(sz);
-    else return CartesianIndex{ptrdiff_t(Row(sz)), ptrdiff_t(Col(sz))};
+    else return ptrdiff_t(sz);
   }
   [[nodiscard]] constexpr auto dim() const noexcept -> S { return sz; }
   constexpr void clear() { sz = S{}; }
-  [[nodiscard]] constexpr auto transpose() const { return Transpose{*this}; }
+  [[nodiscard]] constexpr auto t() const { return Transpose{*this}; }
   [[nodiscard]] constexpr auto isExchangeMatrix() const -> bool
   requires(MatrixDimension<S>)
   {
@@ -342,6 +408,39 @@ template <class T, class S> struct POLY_MATH_GSL_POINTER Array {
     return ret;
     // return std::reduce(begin(), end());
   }
+  // interpret a bigger object as smaller
+  template <typename U> [[nodiscard]] auto reinterpret() const {
+    static_assert(sizeof(storage_type) % sizeof(U) == 0);
+    static_assert(std::same_as<U, double>);
+    if constexpr (std::same_as<U, T>) return *this;
+    else {
+      auto r = unwrapRow(numRow());
+      auto c = unwrapCol(numCol());
+      constexpr auto ratio = sizeof(storage_type) / sizeof(U);
+#ifdef __cpp_lib_start_lifetime_as
+      U *p = std::start_lifetime_as_array(reinterpret_cast<const U *>(data()),
+                                          ratio * ptrdiff_t(rowStride()) * r);
+#else
+      const U *p = std::launder(reinterpret_cast<const U *>(data()));
+#endif
+      if constexpr (IsOne<decltype(r)>) {
+        if constexpr (StaticInt<decltype(c)>)
+          return Array<U, std::integral_constant<ptrdiff_t, c * ratio>>{p, {}};
+        else return Array<U, ptrdiff_t>{p, c * ratio};
+      } else if constexpr (DenseLayout<S>) {
+        return Array<U, DenseDims<>>(p, DenseDims(row(r), col(c * ratio)));
+      } else {
+        ptrdiff_t stride = ptrdiff_t(rowStride()) * ratio;
+        if constexpr (IsOne<decltype(c)>) {
+          constexpr auto sr = std::integral_constant<ptrdiff_t, ratio>{};
+          return Array<U, StridedDims<-1, ratio, -1>>(
+            p, StridedDims(row(r), col(sr), rowStride(stride)));
+        } else
+          return Array<U, StridedDims<>>(
+            p, StridedDims(row(r), col(c * ratio), rowStride(stride)));
+      }
+    }
+  }
   friend inline void PrintTo(const Array &x, ::std::ostream *os) { *os << x; }
 #ifndef NDEBUG
   [[gnu::used]] void dump() const {
@@ -371,7 +470,7 @@ template <class T, class S> struct POLY_MATH_GSL_POINTER Array {
 #endif
 protected:
   // NOLINTNEXTLINE(misc-non-private-member-variables-in-classes)
-  const T *ptr;
+  const storage_type *ptr;
   // NOLINTNEXTLINE(misc-non-private-member-variables-in-classes)
   [[no_unique_address]] S sz{};
 };
@@ -385,20 +484,22 @@ template <class T, DenseLayout S>
   return M <=> N;
 };
 
-template <class T, class S>
-struct POLY_MATH_GSL_POINTER MutArray : Array<T, S>,
-                                        ArrayOps<T, S, MutArray<T, S>> {
+template <class T, Dimension S, bool Compress>
+struct POLY_MATH_GSL_POINTER MutArray
+  : Array<T, S, Compress>,
+    ArrayOps<T, S, MutArray<T, S, Compress>> {
   using BaseT = Array<T, S>;
   // using BaseT::BaseT;
   using BaseT::operator[], BaseT::data, BaseT::begin, BaseT::end, BaseT::rbegin,
     BaseT::rend, BaseT::front, BaseT::back;
+  using storage_type = typename BaseT::storage_type;
 
   constexpr MutArray(const MutArray &) = default;
   constexpr MutArray(MutArray &&) noexcept = default;
   constexpr auto operator=(const MutArray &) -> MutArray & = delete;
   // constexpr auto operator=(const MutArray &) -> MutArray & = default;
   constexpr auto operator=(MutArray &&) noexcept -> MutArray & = default;
-  constexpr MutArray(T *p, S s) : BaseT(p, s) {}
+  constexpr MutArray(storage_type *p, S s) : BaseT(p, s) {}
 
   constexpr void truncate(S nz) {
     S oz = this->sz;
@@ -419,7 +520,7 @@ struct POLY_MATH_GSL_POINTER MutArray : Array<T, S>,
       ptrdiff_t rowsToCopy = newM;
       if (rowsToCopy && (--rowsToCopy) && (copyCols)) {
         // truncation, we need to copy rows to increase stride
-        T *src = data(), *dst = src;
+        storage_type *src = data(), *dst = src;
         do {
           src += oldX;
           dst += newX;
@@ -466,15 +567,16 @@ struct POLY_MATH_GSL_POINTER MutArray : Array<T, S>,
 
   template <class... Args>
   constexpr MutArray(Args &&...args)
-    : Array<T, S>(std::forward<Args>(args)...) {}
+    : Array<T, S, Compress>(std::forward<Args>(args)...) {}
 
   template <std::convertible_to<T> U, std::convertible_to<S> V>
   constexpr MutArray(Array<U, V> a) : Array<T, S>(a) {}
   template <size_t N>
   constexpr MutArray(std::array<T, N> &a) : Array<T, S>(a.data(), N) {}
-  [[nodiscard, gnu::returns_nonnull]] constexpr auto data() noexcept -> T * {
+  [[nodiscard, gnu::returns_nonnull]] constexpr auto data() noexcept
+    -> storage_type * {
     invariant(this->ptr != nullptr);
-    return const_cast<T *>(this->ptr);
+    return const_cast<storage_type *>(this->ptr);
   }
   [[nodiscard]] constexpr auto wrappedPtr() noexcept -> Valid<T> {
     return data();
@@ -483,11 +585,12 @@ struct POLY_MATH_GSL_POINTER MutArray : Array<T, S>,
   [[nodiscard]] constexpr auto begin() noexcept -> StridedIterator<T>
   requires(std::is_same_v<S, StridedRange>)
   {
-    return StridedIterator{const_cast<T *>(this->ptr), this->sz.stride};
+    return StridedIterator{const_cast<storage_type *>(this->ptr),
+                           this->sz.stride};
   }
   [[nodiscard]] constexpr auto begin() noexcept
-    -> T *requires(!std::is_same_v<S, StridedRange>) {
-      return const_cast<T *>(this->ptr);
+    -> storage_type *requires(!std::is_same_v<S, StridedRange>) {
+      return const_cast<storage_type *>(this->ptr);
     }
 
   [[nodiscard]] constexpr auto end() noexcept {
@@ -498,7 +601,8 @@ struct POLY_MATH_GSL_POINTER MutArray : Array<T, S>,
   // {
   //   return this->ptr;
   // }
-  // [[nodiscard, gnu::returns_nonnull]] constexpr auto end() noexcept -> T *
+  // [[nodiscard, gnu::returns_nonnull]] constexpr auto end() noexcept ->
+  // storage_type *
   // {
   //   return this->ptr + ptrdiff_t(this->sz);
   // }
@@ -510,21 +614,16 @@ struct POLY_MATH_GSL_POINTER MutArray : Array<T, S>,
   }
   constexpr auto front() noexcept -> T & { return *begin(); }
   constexpr auto back() noexcept -> T & { return *(end() - 1); }
-  [[gnu::flatten]] constexpr auto operator[](Index<S> auto i) noexcept
-    -> decltype(auto) {
-    auto offset = calcOffset(this->sz, i);
-    auto newDim = calcNewDim(this->sz, i);
-    if constexpr (std::is_same_v<decltype(newDim), Empty>)
-      return data()[offset];
-    else return MutArray<T, decltype(newDim)>{data() + offset, newDim};
+  [[gnu::flatten, gnu::always_inline]] constexpr auto
+  operator[](Index<S> auto i) noexcept -> decltype(auto) {
+    return index<T>(data(), this->sz, i);
   }
   // TODO: switch to operator[] when we enable c++23
   template <class R, class C>
-  [[gnu::flatten]] constexpr auto operator[](R r, C c) noexcept
+  [[gnu::flatten, gnu::always_inline]] constexpr auto operator[](R r,
+                                                                 C c) noexcept
     -> decltype(auto) {
-    if constexpr (MatrixDimension<S>)
-      return (*this)[CartesianIndex(unwrapRow(r), unwrapCol(c))];
-    else return (*this)[ptrdiff_t(r)];
+    return index<T>(data(), this->sz, r, c);
   }
   constexpr void fill(T value) {
     std::fill_n(this->data(), ptrdiff_t(this->dim()), value);
@@ -556,7 +655,7 @@ struct POLY_MATH_GSL_POINTER MutArray : Array<T, S>,
            newRow = ptrdiff_t{Row(this->sz)} - 1;
       this->sz.set(Row<>{newRow});
       if ((col == 0) || (r == newRow)) return;
-      T *dst = data() + ptrdiff_t(r) * col;
+      storage_type *dst = data() + ptrdiff_t(r) * col;
       std::copy_n(dst + col, (newRow - ptrdiff_t(r)) * col, dst);
     } else {
       static_assert(std::convertible_to<S, StridedDims<>>);
@@ -567,14 +666,14 @@ struct POLY_MATH_GSL_POINTER MutArray : Array<T, S>,
       if ((col == 0) || (r == newRow)) return;
       invariant(col <= stride);
       if ((col + (512 / (sizeof(T)))) <= stride) {
-        T *dst = data() + ptrdiff_t(r) * stride;
+        storage_type *dst = data() + ptrdiff_t(r) * stride;
         for (ptrdiff_t m = ptrdiff_t(r); m < newRow; ++m) {
-          T *src = dst + stride;
+          storage_type *src = dst + stride;
           std::copy_n(src, col, dst);
           dst = src;
         }
       } else {
-        T *dst = data() + ptrdiff_t(r) * stride;
+        storage_type *dst = data() + ptrdiff_t(r) * stride;
         std::copy_n(dst + stride, (newRow - ptrdiff_t(r)) * stride, dst);
       }
     }
@@ -592,8 +691,8 @@ struct POLY_MATH_GSL_POINTER MutArray : Array<T, S>,
       if ((colsToCopy == 0) || (row == 0)) return;
       // we only need to copy if memory shifts position
       for (ptrdiff_t m = 0; m < row; ++m) {
-        T *dst = data() + m * newCol + ptrdiff_t(c);
-        T *src = data() + m * oldCol + ptrdiff_t(c) + 1;
+        storage_type *dst = data() + m * newCol + ptrdiff_t(c);
+        storage_type *src = data() + m * oldCol + ptrdiff_t(c) + 1;
         std::copy_n(src, colsToCopy, dst);
       }
     } else {
@@ -606,7 +705,7 @@ struct POLY_MATH_GSL_POINTER MutArray : Array<T, S>,
       if ((colsToCopy == 0) || (row == 0)) return;
       // we only need to copy if memory shifts position
       for (ptrdiff_t m = 0; m < row; ++m) {
-        T *dst = data() + m * stride + ptrdiff_t(c);
+        storage_type *dst = data() + m * stride + ptrdiff_t(c);
         std::copy_n(dst + 1, colsToCopy, dst);
       }
     }
@@ -636,9 +735,45 @@ struct POLY_MATH_GSL_POINTER MutArray : Array<T, S>,
     return {data(), ptrdiff_t(Row(this->sz)), ptrdiff_t(RowStride(this->sz)),
             ptrdiff_t(Col(this->sz))};
   }
+  template <typename U> [[nodiscard]] auto reinterpret() {
+    static_assert(sizeof(storage_type) % sizeof(U) == 0);
+    static_assert(std::same_as<U, double>);
+    if constexpr (std::same_as<U, T>) return *this;
+    else {
+      auto r = unwrapRow(this->numRow());
+      auto c = unwrapCol(this->numCol());
+      constexpr size_t ratio = sizeof(storage_type) / sizeof(U);
+#ifdef __cpp_lib_start_lifetime_as
+      U *p = std::start_lifetime_as_array(reinterpret_cast<const U *>(data()),
+                                          ratio * ptrdiff_t(rowStride()) * r);
+#else
+      U *p = std::launder(reinterpret_cast<U *>(data()));
+#endif
+      if constexpr (IsOne<decltype(r)>) {
+        if constexpr (StaticInt<decltype(c)>)
+          return MutArray<U, std::integral_constant<ptrdiff_t, c * ratio>>(
+            p, std::integral_constant<ptrdiff_t, c * ratio>{});
+        else return MutArray<U, ptrdiff_t>{p, c * ratio};
+      } else if constexpr (DenseLayout<S>) {
+        return MutArray<U, DenseDims<>>(p, DenseDims(row(r), col(c * ratio)));
+      } else {
+        ptrdiff_t stride = ptrdiff_t(this->rowStride()) * ratio;
+        if constexpr (IsOne<decltype(c)>) {
+          constexpr auto sr = std::integral_constant<ptrdiff_t, ratio>{};
+          return MutArray<U, StridedDims<-1, ratio, -1>>(
+            p, StridedDims(row(r), col(sr), rowStride(stride)));
+        } else
+          return MutArray<U, StridedDims<>>(
+            p, StridedDims(row(r), col(c * ratio), rowStride(stride)));
+      }
+    }
+  }
 };
 
-template <typename T, typename S> MutArray(T *, S) -> MutArray<T, S>;
+template <typename T, typename S>
+Array(T *, S) -> Array<utils::decompressed_t<T>, S>;
+template <typename T, typename S>
+MutArray(T *, S) -> MutArray<utils::decompressed_t<T>, S>;
 
 template <typename T, typename S> MutArray(MutArray<T, S>) -> MutArray<T, S>;
 
@@ -662,6 +797,13 @@ static_assert(std::convertible_to<MutArray<int64_t, SquareDims<>>,
                                   MutArray<int64_t, StridedDims<>>>);
 static_assert(std::convertible_to<MutArray<int64_t, DenseDims<>>,
                                   MutArray<int64_t, StridedDims<>>>);
+static_assert(AbstractVector<Array<int64_t, ptrdiff_t>>);
+static_assert(!AbstractVector<Array<int64_t, StridedDims<>>>);
+static_assert(AbstractMatrix<Array<int64_t, StridedDims<>>>);
+static_assert(RowVector<Array<int64_t, ptrdiff_t>>);
+static_assert(ColVector<Transpose<Array<int64_t, ptrdiff_t>>>);
+static_assert(ColVector<Array<int64_t, StridedRange>>);
+static_assert(RowVector<Transpose<Array<int64_t, StridedRange>>>);
 
 template <typename T>
 auto operator*(SliceIterator<T, false> it)
@@ -681,15 +823,16 @@ static_assert(std::ranges::range<SliceRange<int64_t, false>>);
 
 /// Non-owning view of a managed array, capable of resizing,
 /// but not of re-allocating in case the capacity is exceeded.
-template <class T, class S>
+template <class T, Dimension S>
 struct POLY_MATH_GSL_POINTER ResizeableView : MutArray<T, S> {
   using BaseT = MutArray<T, S>;
-  using U = default_capacity_type_t<S>;
+  using U = containers::default_capacity_type_t<S>;
+  using storage_type = typename BaseT::storage_type;
   constexpr ResizeableView() noexcept : BaseT(nullptr, 0), capacity(0) {}
-  constexpr ResizeableView(T *p, S s, U c) noexcept
+  constexpr ResizeableView(storage_type *p, S s, U c) noexcept
     : BaseT(p, s), capacity(c) {}
   constexpr ResizeableView(alloc::Arena<> *a, S s, U c) noexcept
-    : ResizeableView{a->template allocate<T>(c), s, c} {}
+    : ResizeableView{a->template allocate<storage_type>(c), s, c} {}
 
   [[nodiscard]] constexpr auto isFull() const -> bool {
     return U(this->sz) == capacity;
@@ -906,12 +1049,14 @@ static_assert(std::is_trivially_move_assignable_v<MutArray<void *, ptrdiff_t>>);
 /// Non-owning view of a managed array, capable of reallocating, etc.
 /// It does not own memory. Mostly, it serves to drop the inlined
 /// stack capacity of the `ManagedArray` from the type.
-template <class T, class S, class A = alloc::Mallocator<T>>
+template <class T, Dimension S,
+          class A = alloc::Mallocator<utils::compressed_t<T>>>
 struct POLY_MATH_GSL_POINTER ReallocView : ResizeableView<T, S> {
   using BaseT = ResizeableView<T, S>;
-  using U = default_capacity_type_t<S>;
-  constexpr ReallocView(T *p, S s, U c) noexcept : BaseT(p, s, c) {}
-  constexpr ReallocView(T *p, S s, U c, A alloc) noexcept
+  using U = containers::default_capacity_type_t<S>;
+  using storage_type = typename BaseT::storage_type;
+  constexpr ReallocView(storage_type *p, S s, U c) noexcept : BaseT(p, s, c) {}
+  constexpr ReallocView(storage_type *p, S s, U c, A alloc) noexcept
     : BaseT(p, s, c), allocator(alloc) {}
 
   [[nodiscard]] constexpr auto newCapacity() const -> U {
@@ -1110,12 +1255,13 @@ struct POLY_MATH_GSL_POINTER ReallocView : ResizeableView<T, S> {
   [[no_unique_address]] A allocator{};
 
   constexpr void allocateAtLeast(U len) {
-    alloc::AllocResult<T> res = alloc::alloc_at_least(allocator, len);
+    alloc::AllocResult<storage_type> res =
+      alloc::alloc_at_least(allocator, len);
     this->ptr = res.ptr;
     this->capacity = res.count;
   }
   [[nodiscard]] auto firstElt() const -> const void * {
-    using AS = ArrayAlignmentAndSize<T, S, A>;
+    using AS = ArrayAlignmentAndSize<storage_type, S, A>;
 // AS is not a standard layout type, as more than one layer of the hierarchy
 // contain non-static data members. Using `offsetof` is conditionally supported
 // by some compilers as of c++17 (it was UB prior). Both Clang and GCC support
@@ -1145,7 +1291,7 @@ struct POLY_MATH_GSL_POINTER ReallocView : ResizeableView<T, S> {
     if (wasAllocated()) allocator.deallocate(this->data(), this->capacity);
   }
   // this method should be called whenever the buffer lives
-  void maybeDeallocate(T *newPtr, U newCapacity) noexcept {
+  void maybeDeallocate(storage_type *newPtr, U newCapacity) noexcept {
     maybeDeallocate();
     this->ptr = newPtr;
     this->capacity = newCapacity;
@@ -1181,11 +1327,12 @@ concept AbstractSimilar =
 /// or at least build ManagedArrays bypassing the constructors listed here.
 /// This caused invalid frees, as the pointer still pointed to the old
 /// stack memory.
-template <class T, class S, ptrdiff_t N, class A>
+template <class T, Dimension S, ptrdiff_t N, class A>
 struct POLY_MATH_GSL_OWNER ManagedArray : ReallocView<T, S, A> {
   static_assert(std::is_trivially_destructible_v<T>);
   using BaseT = ReallocView<T, S, A>;
-  using U = default_capacity_type_t<S>;
+  using U = containers::default_capacity_type_t<S>;
+  using storage_type = typename BaseT::storage_type;
   // We're deliberately not initializing storage.
 #if !defined(__clang__) && defined(__GNUC__)
 #pragma GCC diagnostic push
@@ -1249,32 +1396,7 @@ struct POLY_MATH_GSL_OWNER ManagedArray : ReallocView<T, S, A> {
     : BaseT{memory.data(), S(b.dim()), U(N), b.get_allocator()} {
     U len = U(this->sz);
     this->growUndef(len);
-    if constexpr (DenseLayout<D> && DenseLayout<S>) {
-      std::copy_n(b.data(), len, this->data());
-    } else if constexpr (MatrixDimension<D> && MatrixDimension<S>) {
-      invariant(b.numRow() == this->numRow());
-      invariant(b.numCol() == this->numCol());
-      for (ptrdiff_t m = 0; m < this->numRow(); ++m) {
-        POLYMATHVECTORIZE
-        for (ptrdiff_t n = 0; n < this->numCol(); ++n) (*this)(m, n) = b(m, n);
-      }
-    } else if constexpr (MatrixDimension<D>) {
-      ptrdiff_t j = 0;
-      for (ptrdiff_t m = 0; m < b.numRow(); ++m) {
-        POLYMATHVECTORIZE
-        for (ptrdiff_t n = 0; n < b.numCol(); ++n) (*this)(j++) = b(m, n);
-      }
-    } else if constexpr (MatrixDimension<S>) {
-      ptrdiff_t j = 0;
-      for (ptrdiff_t m = 0; m < this->numRow(); ++m) {
-        POLYMATHVECTORIZE
-        for (ptrdiff_t n = 0; n < this->numCol(); ++n) (*this)(m, n) = b(j++);
-      }
-    } else {
-      T *p = this->data();
-      POLYMATHVECTORIZE
-      for (ptrdiff_t i = 0; i < len; ++i) p[i] = b[i];
-    }
+    (*this) << b;
   }
   template <std::convertible_to<T> Y, size_t M>
   constexpr ManagedArray(std::array<Y, M> il) noexcept
@@ -1306,7 +1428,7 @@ struct POLY_MATH_GSL_OWNER ManagedArray : ReallocView<T, S, A> {
   }
   template <AbstractSimilar<S> V>
   constexpr ManagedArray(const V &b) noexcept
-    : BaseT{memory.data(), S(b.size()), U(N)} {
+    : BaseT{memory.data(), S(shape(b)), U(N)} {
     U len = U(this->sz);
     this->growUndef(len);
     (*this) << b;
@@ -1450,7 +1572,7 @@ struct POLY_MATH_GSL_OWNER ManagedArray : ReallocView<T, S, A> {
   }
 
 private:
-  [[no_unique_address]] containers::Storage<T, N> memory;
+  [[no_unique_address]] containers::Storage<storage_type, N> memory;
 };
 
 static_assert(std::move_constructible<ManagedArray<intptr_t, ptrdiff_t>>);
@@ -1474,7 +1596,7 @@ static_assert(
   sizeof(ManagedArray<int64_t, SquareDims<>, 64, alloc::Mallocator<int64_t>>) ==
   536);
 
-template <class T, ptrdiff_t N = PreAllocStorage<T, ptrdiff_t>()>
+template <class T, ptrdiff_t N = containers::PreAllocStorage<T, ptrdiff_t>()>
 using Vector = ManagedArray<T, ptrdiff_t, N>;
 template <class T> using PtrVector = Array<T, ptrdiff_t>;
 template <class T> using MutPtrVector = MutArray<T, ptrdiff_t>;
@@ -1506,7 +1628,8 @@ template <class T, ptrdiff_t L = 64>
 using DenseMatrix = ManagedArray<T, DenseDims<>, L>;
 template <class T> using SquarePtrMatrix = Array<T, SquareDims<>>;
 template <class T> using MutSquarePtrMatrix = MutArray<T, SquareDims<>>;
-template <class T, ptrdiff_t L = PreAllocSquareStorage<T, SquareDims<>>()>
+template <class T, ptrdiff_t L = containers::PreAllocSquareStorage<
+                     utils::compressed_t<T>, SquareDims<>>()>
 using SquareMatrix = ManagedArray<T, SquareDims<>, L>;
 
 static_assert(sizeof(PtrMatrix<int64_t>) ==
@@ -1720,7 +1843,7 @@ constexpr auto getMaxDigits(PtrMatrix<T> A) -> Vector<T> {
 template <typename T>
 inline auto printMatrix(std::ostream &os, PtrMatrix<T> A) -> std::ostream & {
   // std::ostream &printMatrix(std::ostream &os, T const &A) {
-  auto [M, N] = A.size();
+  auto [M, N] = shape(A);
   if ((!M) || (!N)) return os << "[ ]";
   // first, we determine the number of digits needed per column
   auto maxDigits{getMaxDigits(A)};
@@ -1749,7 +1872,7 @@ inline auto printMatrix(std::ostream &os, PtrMatrix<T> A) -> std::ostream & {
 inline auto printMatrix(std::ostream &os, PtrMatrix<double> A)
   -> std::ostream & {
   // std::ostream &printMatrix(std::ostream &os, T const &A) {
-  auto [M, N] = A.size();
+  auto [M, N] = shape(A);
   if ((!M) || (!N)) return os << "[ ]";
   // first, we determine the number of digits needed per column
   Vector<char, 512> digits;
@@ -1823,5 +1946,6 @@ inline auto operator<<(std::ostream &os, Array<T, DenseDims<R, C>> A)
 
 static_assert(std::same_as<const int64_t &,
                            decltype(std::declval<PtrMatrix<int64_t>>()[0, 0])>);
+static_assert(std::is_trivially_copyable_v<MutArray<int64_t, ptrdiff_t>>);
 
 } // namespace poly::math
diff --git a/include/Math/ArrayOps.hpp b/include/Math/ArrayOps.hpp
index f347650..1cbb1cc 100644
--- a/include/Math/ArrayOps.hpp
+++ b/include/Math/ArrayOps.hpp
@@ -1,26 +1,125 @@
 #pragma once
 
+#include "Containers/Tuple.hpp"
 #include "Math/Indexing.hpp"
 #include "Math/Matrix.hpp"
 #include "Math/UniformScaling.hpp"
-#include "Math/Vector.hpp"
+#include "SIMD/Unroll.hpp"
+#include "Utilities/Assign.hpp"
+#include "Utilities/LoopMacros.hpp"
 #include <algorithm>
 #include <cstring>
 #include <type_traits>
 
-#if defined __GNUC__ && __GNUC__ >= 8
-#define POLYMATHVECTORIZE _Pragma("GCC ivdep")
-// #define POLYMATHVECTORIZE _Pragma("GCC unroll 2") _Pragma("GCC ivdep")
-// #elif defined __clang__
-// #define POLYMATHVECTORIZE _Pragma("clang loop vectorize(enable)")
-// _Pragma("clang loop vectorize(enable) interleave_count(2)")
-#else
-#define POLYMATHVECTORIZE
-#endif
+#define CASTTOSCALARIZE
 
 namespace poly::math {
+// scalars broadcast
+template <typename S>
+[[gnu::always_inline]] constexpr auto get(const auto &s, auto) {
+  return s;
+}
+template <typename S>
+[[gnu::always_inline]] constexpr auto get(const auto &s, auto, auto) {
+  return s;
+}
+template <typename S, LinearlyIndexable<S> V>
+[[gnu::always_inline]] constexpr auto get(const V &v, auto i) {
+  return v[i];
+}
+template <typename S, CartesianIndexable<S> V>
+[[gnu::always_inline]] constexpr auto get(const V &v, auto i, auto j) {
+  return v[i, j];
+}
+template <typename T, typename S>
+concept OnlyLinearlyIndexable = LinearlyIndexable<S> && !CartesianIndexable<S>;
+template <typename S, OnlyLinearlyIndexable<S> V>
+[[gnu::always_inline]] constexpr auto get(const V &v, auto i, auto j) {
+  static_assert(AbstractVector<V>);
+  if constexpr (RowVector<V>) return v[j];
+  else return v[i];
+}
+
+template <typename T> struct ScalarizeViaCast {
+  using type = void;
+};
+template <typename T>
+using scalarize_via_cast_t = typename ScalarizeViaCast<T>::type;
+template <typename To, typename From>
+constexpr bool ScalarizeViaCastToImpl =
+  std::same_as<To, scalarize_via_cast_t<std::remove_cvref_t<From>>>;
+template <typename To, typename... U>
+consteval auto ScalarizeViaCastTo() -> bool {
+  return (... && ScalarizeViaCastToImpl<To, U>);
+}
+
+template <typename T, typename U> constexpr auto reinterpret(U x) {
+  if constexpr (std::same_as<T, U>) return x;
+  else return x.template reinterpret<T>();
+}
+
+// returns Unroll, Iters, Remainder
+template <ptrdiff_t R> consteval auto unrollf() -> std::array<ptrdiff_t, 2> {
+  if (R <= 5) return {0, R};
+  if (R == 7) return {0, 7};
+  if ((R % 4) == 0) return {4, 0};
+  if ((R % 3) == 0) return {3, 0};
+  if ((R % 5) == 0) return {5, 0};
+  if ((R % 7) == 0) return {7, 0};
+  return {4, R % 4};
+}
+
+template <typename D, typename S>
+constexpr void fastCopy(D *d, const S *s, size_t N) {
+  if (!N) return;
+  // if constexpr (std::same_as<D, S> && std::is_trivially_copyable_v<D>)
+  //   std::memcpy(d, s, N * sizeof(D));
+  // else
+  std::copy_n(s, N, d);
+}
+
+template <typename T>
+concept IsOne =
+  std::same_as<std::remove_cvref_t<T>, std::integral_constant<ptrdiff_t, 1>>;
+// inputs must be `ptrdiff_t` or `std::integral_constant<ptrdiff_t,value>`
+template <typename X, typename Y>
+[[gnu::always_inline]] constexpr auto check_sizes(X x, Y y) {
+  if constexpr (std::same_as<ptrdiff_t, X>) {
+    if constexpr (std::same_as<ptrdiff_t, Y>) {
+      invariant(x, y);
+      return x;
+    } else {
+      constexpr ptrdiff_t L = y;
+      invariant(x, L);
+      return std::integral_constant<ptrdiff_t, L>{};
+    }
+  } else if constexpr (std::same_as<ptrdiff_t, Y>) {
+    constexpr ptrdiff_t L = x;
+    invariant(L, y);
+    return std::integral_constant<ptrdiff_t, L>{};
+  } else {
+    static_assert(x == y);
+    return std::integral_constant<ptrdiff_t, ptrdiff_t(x)>{};
+  }
+}
+template <typename A, typename B>
+[[gnu::always_inline]] constexpr auto promote_shape(const A &a, const B &b) {
+  auto sa = shape(a);
+  if constexpr (!std::convertible_to<B, utils::eltype_t<A>>) {
+    auto M = unwrapRow(numRows(b));
+    auto N = unwrapCol(numCols(b));
+    if constexpr (IsOne<decltype(M)>)
+      if constexpr (IsOne<decltype(N)>) return sa;
+      else return CartesianIndex(sa.row, check_sizes(sa.col, N));
+    else if constexpr (IsOne<decltype(N)>)
+      return CartesianIndex(check_sizes(sa.row, M), sa.col);
+    else return CartesianIndex(check_sizes(sa.row, M), check_sizes(sa.col, N));
+  } else return sa;
+}
+
 template <typename T> class SmallSparseMatrix;
 template <class T, class S, class P> class ArrayOps {
+
   static_assert(std::is_copy_assignable_v<T> ||
                 (std::is_trivially_copyable_v<T> &&
                  std::is_trivially_move_assignable_v<T>));
@@ -31,208 +130,376 @@ template <class T, class S, class P> class ArrayOps {
     return static_cast<const P *>(this)->data();
   }
   constexpr auto size_() const { return static_cast<const P *>(this)->size(); }
-  constexpr auto dim_() const -> S {
-    return static_cast<const P *>(this)->dim();
-  }
   constexpr auto Self() -> P & { return *static_cast<P *>(this); }
   [[nodiscard]] constexpr auto nr() const -> ptrdiff_t {
     return ptrdiff_t(static_cast<const P *>(this)->numRow());
   }
-  [[nodiscard]] constexpr auto nc() const -> ptrdiff_t {
-    return ptrdiff_t(static_cast<const P *>(this)->numCol());
-  }
-  [[nodiscard]] constexpr auto rs() const -> ptrdiff_t {
-    return ptrdiff_t(static_cast<const P *>(this)->rowStride());
+  [[nodiscard]] constexpr auto nc() const {
+    return unwrapCol(static_cast<const P *>(this)->numCol());
   }
-
-public:
-  template <std::convertible_to<T> Y>
-  [[gnu::flatten]] constexpr auto operator<<(const UniformScaling<Y> &B)
-    -> P & {
-    static_assert(MatrixDimension<S>);
-    std::fill_n(data_(), ptrdiff_t(this->dim()), T{});
-    this->diag() << B.value;
-    return *static_cast<P *>(this);
+  [[nodiscard]] constexpr auto rs() const {
+    return unwrapRow(static_cast<const P *>(this)->rowStride());
   }
-  [[gnu::flatten]] constexpr auto operator<<(const SmallSparseMatrix<T> &B)
-    -> P &;
-  [[gnu::flatten]] constexpr auto operator<<(const AbstractVector auto &B)
-    -> P & {
-    P &self{Self()};
-    if constexpr (MatrixDimension<S>) {
-      ptrdiff_t M = nr(), N = nc();
-      invariant(M, B.size());
-      for (ptrdiff_t i = 0; i < M; ++i) {
-        T Bi = B[i];
-        POLYMATHVECTORIZE
-        for (ptrdiff_t j = 0; j < N; ++j) self[i, j] = Bi;
+  template <typename I, typename R, typename Op>
+  [[gnu::always_inline]] static void vcopyToSIMD(P &self, const auto &B, I L,
+                                                 R row, Op op) {
+    // TODO: if `R` is a row index, maybe don't fully unroll static `L`
+    // We're going for very short SIMD vectors to focus on small sizes
+    if constexpr (StaticInt<I>) {
+      constexpr ptrdiff_t SL = ptrdiff_t(L);
+      constexpr std::array<ptrdiff_t, 3> vdr = simd::VectorDivRem<SL, T>();
+      constexpr ptrdiff_t W = vdr[0];
+      constexpr ptrdiff_t fulliter = vdr[1];
+      constexpr ptrdiff_t remainder = vdr[2];
+      if constexpr (remainder > 0) {
+        auto u{simd::index::unrollmask<fulliter + 1, W>(L, 0)};
+        utils::assign(self, B, row, u, op);
+      } else {
+        simd::index::Unroll<fulliter, W> u{0};
+        utils::assign(self, B, row, u, op);
       }
     } else {
-      ptrdiff_t L = size_();
-      invariant(L, ptrdiff_t(B.size()));
-      if constexpr (std::is_copy_assignable_v<T>) {
-        POLYMATHVECTORIZE
-        for (ptrdiff_t i = 0; i < L; ++i) self[i] = B[i];
-      } else {
-        // MutArray is trivially copyable and move-assignable
-        // we require triviality to avoid silently being slow.
-        // we should fix it if hitting another case.
-        POLYMATHVECTORIZE
-        for (ptrdiff_t i = 0; i < L; ++i) self[i] = auto{B[i]};
+      constexpr ptrdiff_t W = simd::Width<T>;
+      for (ptrdiff_t i = 0;; i += W) {
+        auto u{simd::index::unrollmask<1, W>(L, i)};
+        if (!u) break;
+        utils::assign(self, B, row, u, op);
       }
     }
-    return self;
   }
 
-  [[gnu::flatten]] constexpr auto operator<<(const AbstractMatrix auto &B)
-    -> P & {
-    static_assert(MatrixDimension<S>);
-    ptrdiff_t M = nr(), N = nc();
-    invariant(M, ptrdiff_t(B.numRow()));
-    invariant(N, ptrdiff_t(B.numCol()));
+  template <typename Op> void vcopyTo(const auto &B, Op op) {
+    // static_assert(sizeof(utils::eltype_t<decltype(B)>) <= 8);
     P &self{Self()};
-    if constexpr (DenseLayout<S> &&
-                  DataMatrix<std::remove_cvref_t<decltype(B)>> &&
-                  DenseLayout<std::remove_cvref_t<decltype(B.dim())>>) {
-      if constexpr (std::is_copy_assignable_v<T>)
-        std::copy_n(B.data(), M * N, data_());
-      else std::memcpy(data_(), M * N * sizeof(T), B.data());
+    auto [M, N] = promote_shape(self, B);
+    // if constexpr (std::same_as<Op, utils::CopyAssign> && DenseLayout<S> &&
+    //               DenseTensor<std::remove_cvref_t<decltype(B)>>) {
+    //   if constexpr (std::is_trivially_copyable_v<T>)
+    //     std::memcpy(data_(), B.begin(), M * N * sizeof(T));
+    //   else std::copy_n(B.begin(), M * N, data_());
+    // } else
+#ifdef CASTTOSCALARIZE
+    using E = math::scalarize_via_cast_t<
+      std::remove_cvref_t<decltype(std::declval<P>().view())>>;
+    if constexpr (!std::same_as<E, void> &&
+                  ((math::ScalarizeViaCastTo<E, decltype(B)>()) ||
+                   (std::same_as<std::remove_cvref_t<decltype(B)>, double> &&
+                    std::same_as<Op, std::multiplies<>>))) {
+      auto d{reinterpret<E>(Self())};
+      if constexpr (std::same_as<Op, utils::CopyAssign>) d << reinterpret<E>(B);
+      else d << op(d, reinterpret<E>(B));
+    } else if constexpr (simd::SIMDSupported<T>) {
+#else
+    if constexpr (simd::SIMDSupported<T>) {
+#endif
+      if constexpr (IsOne<decltype(M)>)
+        vcopyToSIMD(self, B, N, utils::NoRowIndex{}, op);
+      else if constexpr (IsOne<decltype(N)>)
+        vcopyToSIMD(self, B, M, utils::NoRowIndex{}, op);
+      else if constexpr (StaticInt<decltype(M)>) {
+        constexpr std::array<ptrdiff_t, 2> UIR = unrollf<ptrdiff_t(M)>();
+        constexpr ptrdiff_t U = UIR[0];
+        if constexpr (U != 0)
+          for (ptrdiff_t r = 0; r < (M - U + 1); r += U)
+            vcopyToSIMD(self, B, N, simd::index::Unroll<U>{r}, op);
+        constexpr ptrdiff_t R = UIR[1];
+        if constexpr (R != 0)
+          vcopyToSIMD(self, B, N, simd::index::Unroll<R>{M - R}, op);
+      } else {
+        ptrdiff_t r = 0;
+        for (; r < (M - 3); r += 4)
+          vcopyToSIMD(self, B, N, simd::index::Unroll<4>{r}, op);
+        switch (M & 3) {
+        case 0: return;
+        case 1: return vcopyToSIMD(self, B, N, simd::index::Unroll<1>{r}, op);
+        case 2: return vcopyToSIMD(self, B, N, simd::index::Unroll<2>{r}, op);
+        default: return vcopyToSIMD(self, B, N, simd::index::Unroll<3>{r}, op);
+        }
+      }
+    } else if constexpr (AbstractVector<P>) {
+      ptrdiff_t L = IsOne<decltype(N)> ? M : N;
+      if constexpr (!std::is_copy_assignable_v<T> &&
+                    std::same_as<Op, utils::CopyAssign>) {
+        POLYMATHIVDEP
+        for (ptrdiff_t j = 0; j < L; ++j)
+          if constexpr (std::convertible_to<decltype(B), T>) self[j] = auto{B};
+          else self[j] = auto{B[j]};
+      } else {
+        POLYMATHIVDEP
+        for (ptrdiff_t j = 0; j < L; ++j)
+          utils::assign(self, B, utils::NoRowIndex{}, j, op);
+      }
     } else {
-      for (ptrdiff_t i = 0; i < M; ++i) {
-        if constexpr (std::is_copy_assignable_v<T>) {
-          POLYMATHVECTORIZE
-          for (ptrdiff_t j = 0; j < N; ++j) self[i, j] = B[i, j];
+      ptrdiff_t R = ptrdiff_t(M), C = ptrdiff_t(N);
+      POLYMATHNOVECTORIZE
+      for (ptrdiff_t i = 0; i < R; ++i) {
+        if constexpr (!std::is_copy_assignable_v<T> &&
+                      std::same_as<Op, utils::CopyAssign>) {
+          POLYMATHIVDEP
+          for (ptrdiff_t j = 0; j < C; ++j)
+            if constexpr (std::convertible_to<decltype(B), T>)
+              self[i, j] = auto{B};
+            else if constexpr (RowVector<decltype(B)>) self[i, j] = auto{B[j]};
+            else if constexpr (ColVector<decltype(B)>) self[i, j] = auto{B[i]};
+            else self[i, j] = auto{B[i, j]};
         } else {
-          POLYMATHVECTORIZE
-          for (ptrdiff_t j = 0; j < N; ++j) self[i, j] = auto{B[i, j]};
+          POLYMATHIVDEP
+          for (ptrdiff_t j = 0; j < C; ++j) utils::assign(self, B, i, j, op);
         }
       }
     }
-    return self;
   }
+  // template <typename Op> constexpr void copyTo(const auto &B, Op op) {
+  //   using C = math::scalarize_via_cast_t<
+  //     std::remove_cvref_t<decltype(std::declval<P>().view())>>;
+  //   if constexpr (!std::same_as<C, void> &&
+  //                 ((math::ScalarizeViaCastTo<C, decltype(B)>()) ||
+  //                  (std::same_as<std::remove_cvref_t<decltype(B)>, double> &&
+  //                   std::same_as<Op, std::multiplies<>>))) {
+  //     auto d{reinterpret<C>(Self())};
+  //     if constexpr (std::same_as<Op, utils::CopyAssign>) d <<
+  //     reinterpret<C>(B); else d << op(d, reinterpret<C>(B));
+  //   } else vcopyTo(B, op);
+  // }
+
+public:
   template <std::convertible_to<T> Y>
-  [[gnu::flatten]] constexpr auto operator<<(const Y &b) -> P & {
-    P &self{Self()};
-    if constexpr (DenseLayout<S>) {
-      std::fill_n(data_(), ptrdiff_t(dim_()), T(b));
-    } else if constexpr (std::is_same_v<S, StridedRange>) {
-      POLYMATHVECTORIZE
-      for (ptrdiff_t c = 0, L = size_(); c < L; ++c) self[c] = b;
-    } else {
-      ptrdiff_t M = nr(), N = nc(), X = rs();
-      T *p = data_();
-      for (ptrdiff_t r = 0; r < M; ++r, p += X) std::fill_n(p, N, T(b));
-    }
-    return self;
-  }
-  [[gnu::flatten]] constexpr auto operator+=(const AbstractMatrix auto &B)
+  [[gnu::flatten]] constexpr auto operator<<(const UniformScaling<Y> &B)
     -> P & {
     static_assert(MatrixDimension<S>);
-    ptrdiff_t M = nr(), N = nc();
-    invariant(M, ptrdiff_t(B.numRow()));
-    invariant(N, ptrdiff_t(B.numCol()));
-    P &self{Self()};
-    for (ptrdiff_t r = 0; r < M; ++r) {
-      POLYMATHVECTORIZE
-      for (ptrdiff_t c = 0; c < N; ++c) self[r, c] += B[r, c];
-    }
-    return self;
+    std::fill_n(data_(), ptrdiff_t(this->dim()), T{});
+    this->diag() << B.value;
+    return *static_cast<P *>(this);
   }
-  [[gnu::flatten]] constexpr auto operator-=(const AbstractMatrix auto &B)
-    -> P & {
-    static_assert(MatrixDimension<S>);
-    ptrdiff_t M = nr(), N = nc();
-    invariant(M, ptrdiff_t(B.numRow()));
-    invariant(N, ptrdiff_t(B.numCol()));
-    P &self{Self()};
-    for (ptrdiff_t r = 0; r < M; ++r) {
-      POLYMATHVECTORIZE
-      for (ptrdiff_t c = 0; c < N; ++c) self[r, c] -= B[r, c];
-    }
-    return self;
+  [[gnu::flatten]] constexpr auto operator<<(const SmallSparseMatrix<T> &B)
+    -> P &;
+
+  [[gnu::flatten]] constexpr auto operator<<(const auto &B) -> P & {
+    vcopyTo(B, utils::CopyAssign{});
+    return Self();
   }
-  [[gnu::flatten]] constexpr auto operator+=(const AbstractVector auto &B)
-    -> P & {
-    P &self{Self()};
-    if constexpr (MatrixDimension<S>) {
-      ptrdiff_t M = nr(), N = nc();
-      invariant(M, B.size());
-      for (ptrdiff_t r = 0; r < M; ++r) {
-        auto Br = B[r];
-        POLYMATHVECTORIZE
-        for (ptrdiff_t c = 0; c < N; ++c) self[r, c] += Br;
-      }
-    } else {
-      ptrdiff_t L = size_();
-      invariant(L, ptrdiff_t(B.size()));
-      POLYMATHVECTORIZE
-      for (ptrdiff_t i = 0; i < L; ++i) self[i] += B[i];
-    }
-    return self;
+  [[gnu::flatten]] constexpr auto operator+=(const auto &B) -> P & {
+    vcopyTo(B, std::plus<>{});
+    return Self();
   }
-  template <std::convertible_to<T> Y>
-  [[gnu::flatten]] constexpr auto operator+=(Y b) -> P & {
-    P &self{Self()};
-    if constexpr (MatrixDimension<S> && !DenseLayout<S>) {
-      ptrdiff_t M = nr(), N = nc();
-      for (ptrdiff_t r = 0; r < M; ++r) {
-        POLYMATHVECTORIZE
-        for (ptrdiff_t c = 0; c < N; ++c) self[r, c] += b;
-      }
-    } else {
-      POLYMATHVECTORIZE
-      for (ptrdiff_t i = 0, L = size_(); i < L; ++i) self[i] += b;
-    }
-    return self;
+  [[gnu::flatten]] constexpr auto operator-=(const auto &B) -> P & {
+    vcopyTo(B, std::minus<>{});
+    return Self();
   }
-  [[gnu::flatten]] constexpr auto operator-=(const AbstractVector auto &B)
-    -> P & {
-    P &self{Self()};
-    if constexpr (MatrixDimension<S>) {
-      ptrdiff_t M = nr(), N = nc();
-      invariant(M == B.size());
-      for (ptrdiff_t r = 0; r < M; ++r) {
-        auto Br = B[r];
-        POLYMATHVECTORIZE
-        for (ptrdiff_t c = 0; c < N; ++c) self[r, c] -= Br;
-      }
+  [[gnu::flatten]] constexpr auto operator*=(const auto &B) -> P & {
+    vcopyTo(B, std::multiplies<>{});
+    return Self();
+  }
+  [[gnu::flatten]] constexpr auto operator/=(const auto &B) -> P & {
+    vcopyTo(B, std::divides<>{});
+    return Self();
+  }
+};
+
+} // namespace poly::math
+
+namespace poly::containers {
+
+namespace tupletensorops {
+// FIXME:
+// Need to do all loads before all stores!!!
+// This is because we want to support fusing loops where we may be overwriting
+// inputs, e.g. `tie(x,y) << Tuple(x - y, x + y);`
+template <typename A, typename... As, typename B, typename... Bs, typename I,
+          typename R>
+[[gnu::always_inline]] inline void
+vcopyToSIMD(Tuple<A, As...> &dst, const Tuple<B, Bs...> &src, I L, R row) {
+  // TODO: if `R` is a row index, maybe don't fully unroll static `L`
+  // We're going for very short SIMD vectors to focus on small sizes
+  using T = std::common_type_t<utils::eltype_t<A>, utils::eltype_t<As>...,
+                               utils::eltype_t<B>, utils::eltype_t<Bs>...>;
+  if constexpr (math::StaticInt<I>) {
+    constexpr ptrdiff_t SL = ptrdiff_t(L);
+    constexpr std::array<ptrdiff_t, 3> vdr = simd::VectorDivRem<SL, T>();
+    constexpr ptrdiff_t W = vdr[0];
+    constexpr ptrdiff_t fulliter = vdr[1];
+    constexpr ptrdiff_t remainder = vdr[2];
+    if constexpr (remainder > 0) {
+      auto u{simd::index::unrollmask<fulliter + 1, W>(L, 0)};
+      if constexpr (std::same_as<R, utils::NoRowIndex>)
+        dst.apply(src.map([=](const auto &s) { return get<T>(s, u); }),
+                  [=](auto &d, const auto &s) { d[u] = s; });
+      else
+        dst.apply(src.map([=](const auto &s) { return get<T>(s, row, u); }),
+                  [=](auto &d, const auto &s) { d[row, u] = s; });
+    } else if constexpr (std::same_as<R, utils::NoRowIndex>) {
+      simd::index::Unroll<fulliter, W> u{0};
+      dst.apply(src.map([=](const auto &s) { return get<T>(s, u); }),
+                [=](auto &d, const auto &s) { d[u] = s; });
     } else {
-      ptrdiff_t L = size_();
-      invariant(L == B.size());
-      POLYMATHVECTORIZE
-      for (ptrdiff_t i = 0; i < L; ++i) self[i] -= B[i];
+      simd::index::Unroll<fulliter, W> u{0};
+      dst.apply(src.map([=](const auto &s) { return get<T>(s, row, u); }),
+                [=](auto &d, const auto &s) { d[row, u] = s; });
+    }
+  } else {
+    constexpr ptrdiff_t W = simd::Width<T>;
+    for (ptrdiff_t i = 0;; i += W) {
+      auto u{simd::index::unrollmask<1, W>(L, i)};
+      if (!u) break;
+      if constexpr (std::same_as<R, utils::NoRowIndex>)
+        dst.apply(src.map([=](const auto &s) { return get<T>(s, u); }),
+                  [=](auto &d, const auto &s) { d[u] = s; });
+      else
+        dst.apply(src.map([=](const auto &s) { return get<T>(s, row, u); }),
+                  [=](auto &d, const auto &s) { d[row, u] = s; });
     }
-    return self;
   }
-  template <std::convertible_to<T> Y>
-  [[gnu::flatten]] constexpr auto operator*=(Y b) -> P & {
-    P &self{Self()};
-    if constexpr (MatrixDimension<S> && !DenseLayout<S>) {
-      ptrdiff_t M = nr(), N = nc();
-      for (ptrdiff_t r = 0; r < M; ++r) {
-        POLYMATHVECTORIZE
-        for (ptrdiff_t c = 0; c < N; ++c) self[r, c] *= b;
+}
+
+// template <typename A, typename B>
+// [[gnu::always_inline]] constexpr auto promote_shape(const Tuple<A> &a,
+//                                                     const Tuple<B> &b) {
+//   return math::promote_shape(a.head, b.head);
+// }
+template <typename A, typename... As, typename B, typename... Bs>
+[[gnu::always_inline]] inline constexpr auto
+promote_shape(const Tuple<A, As...> &a, const Tuple<B, Bs...> &b)
+requires(sizeof...(As) == sizeof...(Bs))
+{
+  auto h = math::promote_shape(a.head, b.head);
+  if constexpr (sizeof...(As) == 0) return h;
+  else {
+    auto [Mh, Nh] = h;
+    auto [Mt, Nt] = promote_shape(a.tail, b.tail);
+    return math::CartesianIndex(math::check_sizes(Mh, Mt),
+                                math::check_sizes(Nh, Nt));
+  }
+}
+template <typename A, typename... As, typename B, typename... Bs>
+[[gnu::always_inline]] inline constexpr void
+vcopyTo(Tuple<A, As...> &dst, const Tuple<B, Bs...> &src) {
+  using T = std::common_type_t<utils::eltype_t<A>, utils::eltype_t<As>...,
+                               utils::eltype_t<B>, utils::eltype_t<Bs>...>;
+  // static_assert(sizeof(T) <= 8);
+  auto [M, N] = promote_shape(dst, src);
+  if constexpr (simd::SIMDSupported<std::remove_cvref_t<T>>) {
+    if constexpr (math::IsOne<decltype(M)>)
+      vcopyToSIMD(dst, src, N, utils::NoRowIndex{});
+    else if constexpr (math::IsOne<decltype(N)>)
+      vcopyToSIMD(dst, src, M, utils::NoRowIndex{});
+    else if constexpr (math::StaticInt<decltype(M)>) {
+      constexpr std::array<ptrdiff_t, 2> UIR = math::unrollf<ptrdiff_t(M)>();
+      constexpr ptrdiff_t U = UIR[0];
+      if constexpr (U != 0)
+        for (ptrdiff_t r = 0; r < (M - U + 1); r += U)
+          vcopyToSIMD(dst, src, N, simd::index::Unroll<U>{r});
+      constexpr ptrdiff_t R = UIR[1];
+      if constexpr (R != 0)
+        vcopyToSIMD(dst, src, N, simd::index::Unroll<R>{M - R});
+    } else {
+      ptrdiff_t r = 0;
+      for (; r < (M - 3); r += 4)
+        vcopyToSIMD(dst, src, N, simd::index::Unroll<4>{r});
+      switch (M & 3) {
+      case 0: return;
+      case 1: return vcopyToSIMD(dst, src, N, simd::index::Unroll<1>{r});
+      case 2: return vcopyToSIMD(dst, src, N, simd::index::Unroll<2>{r});
+      default: return vcopyToSIMD(dst, src, N, simd::index::Unroll<3>{r});
       }
+    }
+  } else if constexpr (math::AbstractVector<A>) {
+    ptrdiff_t L = math::IsOne<decltype(N)> ? M : N;
+    if constexpr (!std::is_copy_assignable_v<T>) {
+      POLYMATHIVDEP
+      for (ptrdiff_t j = 0; j < L; ++j)
+        dst.apply(src.map([=](const auto &s) {
+          if constexpr (std::convertible_to<decltype(s), T>) return s;
+          else return s[j];
+        }),
+                  [=](auto &d, auto s) { d[j] = s; });
     } else {
-      POLYMATHVECTORIZE
-      for (ptrdiff_t c = 0, L = ptrdiff_t(dim_()); c < L; ++c) self[c] *= b;
+      POLYMATHIVDEP
+      for (ptrdiff_t j = 0; j < L; ++j)
+        dst.apply(src.map([=](const auto &s) { return s[j]; }),
+                  [=](auto &d, const auto &s) { d[j] = s; });
     }
-    return self;
-  }
-  template <std::convertible_to<T> Y>
-  [[gnu::flatten]] constexpr auto operator/=(Y b) -> P & {
-    P &self{Self()};
-    if constexpr (MatrixDimension<S> && !DenseLayout<S>) {
-      ptrdiff_t M = nr(), N = nc();
-      for (ptrdiff_t r = 0; r < M; ++r) {
-        POLYMATHVECTORIZE
-        for (ptrdiff_t c = 0; c < N; ++c) self[r, c] /= b;
+  } else {
+    ptrdiff_t R = ptrdiff_t(M), C = ptrdiff_t(N);
+    POLYMATHNOVECTORIZE
+    for (ptrdiff_t i = 0; i < R; ++i) {
+      if constexpr (!std::is_copy_assignable_v<T>) {
+        POLYMATHIVDEP
+        for (ptrdiff_t j = 0; j < C; ++j)
+          dst.apply(src.map([=](const auto &s) {
+            if constexpr (std::convertible_to<decltype(s), T>) return auto{s};
+            else if constexpr (math::RowVector<decltype(s)>) return auto{s[j]};
+            else if constexpr (math::ColVector<decltype(s)>) return auto{s[i]};
+            else return auto{s[i, j]};
+          }),
+                    [=](auto &d, const auto &s) { d[i, j] = s; });
+      } else {
+        POLYMATHIVDEP
+        for (ptrdiff_t j = 0; j < C; ++j)
+          dst.apply(src.map([=](const auto &s) { return s[i, j]; }),
+                    [=](auto &d, const auto &s) { d[i, j] = s; });
       }
-    } else {
-      POLYMATHVECTORIZE
-      for (ptrdiff_t c = 0, L = ptrdiff_t(dim_()); c < L; ++c) self[c] /= b;
     }
-    return self;
   }
-};
-} // namespace poly::math
+}
+}; // namespace tupletensorops
+// Note: these are inlined, because we want
+// the compiler to be exposed to which arrays
+// are identical, in case of re-use, so that
+// they can share pointers.
+template <typename A, typename... As>
+template <typename B, typename... Bs>
+[[gnu::flatten, gnu::always_inline]] inline constexpr void
+Tuple<A, As...>::operator<<(const Tuple<B, Bs...> &src)
+requires(sizeof...(As) == sizeof...(Bs))
+{
+#ifndef CASTTOSCALARIZE
+  tupletensorops::vcopyTo(*this, src);
+#else
+  using C = math::scalarize_via_cast_t<
+    std::remove_cvref_t<decltype(std::declval<A>().view())>>;
+  if constexpr ((!std::same_as<C, void>)&&math::ScalarizeViaCastTo<
+                  C, As..., decltype(std::declval<B>().view()), Bs...>()) {
+    using T = std::common_type_t<utils::eltype_t<A>, utils::eltype_t<As>...,
+                                 utils::eltype_t<B>, utils::eltype_t<Bs>...>;
+    if constexpr ((sizeof(T) % (sizeof(C) * simd::Width<C>)) != 0) {
+      auto dst{map([](auto &d) { return math::reinterpret<C>(d); })};
+      tupletensorops::vcopyTo(
+        dst, src.map([](const auto &s) { return math::reinterpret<C>(s); }));
+    } else tupletensorops::vcopyTo(*this, src);
+  } else tupletensorops::vcopyTo(*this, src);
+#endif
+}
+template <typename A, typename... As>
+template <typename B, typename... Bs>
+[[gnu::always_inline]] inline constexpr void
+Tuple<A, As...>::operator+=(const Tuple<B, Bs...> &src)
+requires(sizeof...(As) == sizeof...(Bs))
+{
+  (*this) << map(src, [](const auto &d, const auto &s) { return d + s; });
+}
+template <typename A, typename... As>
+template <typename B, typename... Bs>
+[[gnu::always_inline]] inline constexpr void
+Tuple<A, As...>::operator-=(const Tuple<B, Bs...> &src)
+requires(sizeof...(As) == sizeof...(Bs))
+{
+  (*this) << map(src, [](const auto &d, const auto &s) { return d - s; });
+}
+template <typename A, typename... As>
+template <typename B, typename... Bs>
+[[gnu::always_inline]] inline constexpr void
+Tuple<A, As...>::operator*=(const Tuple<B, Bs...> &src)
+requires(sizeof...(As) == sizeof...(Bs))
+{
+  (*this) << map(src, [](const auto &d, const auto &s) { return d * s; });
+}
+template <typename A, typename... As>
+template <typename B, typename... Bs>
+[[gnu::always_inline]] inline constexpr void
+Tuple<A, As...>::operator/=(const Tuple<B, Bs...> &src)
+requires(sizeof...(As) == sizeof...(Bs))
+{
+  (*this) << map(src, [](const auto &d, const auto &s) { return d / s; });
+}
+
+} // namespace poly::containers
diff --git a/include/Math/AxisTypes.hpp b/include/Math/AxisTypes.hpp
index 45ef37e..a41510c 100644
--- a/include/Math/AxisTypes.hpp
+++ b/include/Math/AxisTypes.hpp
@@ -172,12 +172,10 @@ constexpr auto operator==(RowStride<> y, ptrdiff_t x) -> bool {
 constexpr auto operator==(RowStride<> x, RowStride<> y) -> bool {
   return ptrdiff_t(x) == ptrdiff_t(y);
 }
-constexpr auto operator<=>(ptrdiff_t x, RowStride<> y)
-  -> std::strong_ordering {
+constexpr auto operator<=>(ptrdiff_t x, RowStride<> y) -> std::strong_ordering {
   return x <=> ptrdiff_t(y);
 }
-constexpr auto operator<=>(RowStride<> x, ptrdiff_t y)
-  -> std::strong_ordering {
+constexpr auto operator<=>(RowStride<> x, ptrdiff_t y) -> std::strong_ordering {
   return ptrdiff_t(x) <=> y;
 }
 constexpr auto operator<=>(RowStride<> x, RowStride<> y)
@@ -210,11 +208,13 @@ template <ptrdiff_t M> constexpr auto standardizeRangeBound(Col<M> x) {
   else return std::integral_constant<ptrdiff_t, M>{};
 }
 
-template <ptrdiff_t M> constexpr auto unwrapRow(Row<M> x) -> ptrdiff_t {
-  return ptrdiff_t(x);
+template <ptrdiff_t M> constexpr auto unwrapRow(Row<M> x) {
+  if constexpr (M == -1) return ptrdiff_t(x);
+  else return std::integral_constant<ptrdiff_t, M>{};
 }
-template <ptrdiff_t M> constexpr auto unwrapCol(Col<M> x) -> ptrdiff_t {
-  return ptrdiff_t(x);
+template <ptrdiff_t M> constexpr auto unwrapCol(Col<M> x) {
+  if constexpr (M == -1) return ptrdiff_t(x);
+  else return std::integral_constant<ptrdiff_t, M>{};
 }
 constexpr auto unwrapRow(auto x) { return x; }
 constexpr auto unwrapCol(auto x) { return x; }
diff --git a/include/Math/Constraints.hpp b/include/Math/Constraints.hpp
index 6157031..12ecda0 100644
--- a/include/Math/Constraints.hpp
+++ b/include/Math/Constraints.hpp
@@ -69,7 +69,7 @@ constexpr void eraseConstraintImpl(MutDensePtrMatrix<int64_t> A, ptrdiff_t _i,
                                    ptrdiff_t _j) {
   invariant(_i != _j);
   ptrdiff_t i = std::min(_i, _j), j = std::max(_i, _j);
-  const auto [M, N] = A.size();
+  const auto [M, N] = shape(A);
   ptrdiff_t lastRow = M - 1;
   ptrdiff_t penuRow = lastRow - 1;
   if (j == penuRow) {
@@ -92,7 +92,7 @@ constexpr void eraseConstraint(MutDensePtrMatrix<int64_t> &A, ptrdiff_t i,
 
 constexpr auto substituteEqualityImpl(MutDensePtrMatrix<int64_t> E,
                                       const ptrdiff_t i) -> Row<> {
-  const auto [numConstraints, numVar] = E.size();
+  const auto [numConstraints, numVar] = shape(E);
   ptrdiff_t minNonZero = numVar + 1;
   ptrdiff_t rowMinNonZero = numConstraints;
   for (ptrdiff_t j = 0; j < numConstraints; ++j)
@@ -137,7 +137,7 @@ constexpr auto
 substituteEqualityPairImpl(std::array<MutDensePtrMatrix<int64_t>, 2> AE,
                            ptrdiff_t i) -> Row<> {
   auto [A, E] = AE;
-  const auto [numConstraints, numVar] = E.size();
+  const auto [numConstraints, numVar] = shape(E);
   ptrdiff_t minNonZero = numVar + 1;
   ptrdiff_t rowMinNonZero = numConstraints;
   for (ptrdiff_t j = 0; j < numConstraints; ++j) {
@@ -403,7 +403,7 @@ constexpr auto uniqueConstraint(DensePtrMatrix<int64_t> A, Row<> r) -> bool {
 [[nodiscard]] constexpr auto removeRedundantRows(MutDensePtrMatrix<int64_t> A,
                                                  MutDensePtrMatrix<int64_t> B)
   -> std::array<Row<>, 2> {
-  auto [M, N] = B.size();
+  auto [M, N] = shape(B);
   for (ptrdiff_t r = 0, c = 0; c++ < N && r < M;)
     if (!NormalForm::pivotRows(B, Col<>{c == N ? 0 : c}, Row<>{M}, Row<>{r}))
       NormalForm::reduceColumnStack(A, B, c == N ? 0 : c, r++);
diff --git a/include/Math/Constructors.hpp b/include/Math/Constructors.hpp
index 683c6af..a95c507 100644
--- a/include/Math/Constructors.hpp
+++ b/include/Math/Constructors.hpp
@@ -9,7 +9,7 @@ using alloc::Arena, alloc::WArena, alloc::OwningArena, utils::eltype_t;
 template <alloc::FreeAllocator A>
 constexpr auto vector(A a, ptrdiff_t M)
   -> ManagedArray<eltype_t<A>, ptrdiff_t,
-                  PreAllocStorage<eltype_t<A>, ptrdiff_t>(), A> {
+                  containers::PreAllocStorage<eltype_t<A>, ptrdiff_t>(), A> {
   return {M, a};
 }
 
@@ -36,7 +36,7 @@ constexpr auto vector(Arena<SlabSize, BumpUp> *alloc, ptrdiff_t M)
 template <alloc::FreeAllocator A>
 constexpr auto vector(A a, ptrdiff_t M, eltype_t<A> x)
   -> ManagedArray<eltype_t<A>, ptrdiff_t,
-                  PreAllocStorage<eltype_t<A>, ptrdiff_t>(), A> {
+                  containers::PreAllocStorage<eltype_t<A>, ptrdiff_t>(), A> {
   return {M, x, a};
 }
 
@@ -62,9 +62,9 @@ constexpr auto vector(Arena<SlabSize, BumpUp> *alloc, ptrdiff_t M, T x)
 }
 
 template <alloc::FreeAllocator A>
-constexpr auto matrix(A a, ptrdiff_t M)
-  -> ManagedArray<eltype_t<A>, SquareDims<>,
-                  PreAllocSquareStorage<eltype_t<A>, SquareDims<>>(), A> {
+constexpr auto matrix(A a, ptrdiff_t M) -> ManagedArray<
+  eltype_t<A>, SquareDims<>,
+  containers::PreAllocSquareStorage<eltype_t<A>, SquareDims<>>(), A> {
   return {SquareDims<>{{M}}, a};
 }
 
@@ -84,9 +84,9 @@ constexpr auto matrix(Arena<SlabSize, BumpUp> *alloc, ptrdiff_t M)
   return {alloc->template allocate<T>(M * M), SquareDims<>{{M}}};
 }
 template <alloc::FreeAllocator A>
-constexpr auto matrix(A a, ptrdiff_t M, eltype_t<A> x)
-  -> ManagedArray<eltype_t<A>, SquareDims<>,
-                  PreAllocSquareStorage<eltype_t<A>, SquareDims<>>(), A> {
+constexpr auto matrix(A a, ptrdiff_t M, eltype_t<A> x) -> ManagedArray<
+  eltype_t<A>, SquareDims<>,
+  containers::PreAllocSquareStorage<eltype_t<A>, SquareDims<>>(), A> {
   return {SquareDims<>{{M}}, x, a};
 }
 template <class T, alloc::FreeAllocator A>
@@ -113,7 +113,8 @@ constexpr auto matrix(Arena<SlabSize, BumpUp> *alloc, ptrdiff_t M, T x)
 template <alloc::FreeAllocator A, ptrdiff_t R, ptrdiff_t C>
 constexpr auto matrix(A a, Row<R> M, Col<C> N)
   -> ManagedArray<eltype_t<A>, DenseDims<R, C>,
-                  PreAllocStorage<eltype_t<A>, DenseDims<R, C>>(), A> {
+                  containers::PreAllocStorage<eltype_t<A>, DenseDims<R, C>>(),
+                  A> {
   return {DenseDims{M, N}, a};
 }
 template <class T, alloc::FreeAllocator A, ptrdiff_t R, ptrdiff_t C>
@@ -136,7 +137,8 @@ constexpr auto matrix(Arena<SlabSize, BumpUp> *alloc, Row<R> M, Col<C> N)
 template <alloc::FreeAllocator A, ptrdiff_t R, ptrdiff_t C>
 constexpr auto matrix(A a, Row<R> M, Col<C> N, eltype_t<A> x)
   -> ManagedArray<eltype_t<A>, DenseDims<R, C>,
-                  PreAllocStorage<eltype_t<A>, DenseDims<R, C>>(), A> {
+                  containers::PreAllocStorage<eltype_t<A>, DenseDims<R, C>>(),
+                  A> {
   return {DenseDims{M, N}, x, a};
 }
 template <class T, alloc::FreeAllocator A, ptrdiff_t R, ptrdiff_t C>
@@ -162,11 +164,12 @@ constexpr auto matrix(Arena<SlabSize, BumpUp> *alloc, Row<R> M, Col<C> N, T x)
 }
 
 template <alloc::FreeAllocator A>
-constexpr auto identity(A a, ptrdiff_t M)
-  -> ManagedArray<eltype_t<A>, SquareDims<>,
-                  PreAllocSquareStorage<eltype_t<A>, SquareDims<>>(), A> {
+constexpr auto identity(A a, ptrdiff_t M) -> ManagedArray<
+  eltype_t<A>, SquareDims<>,
+  containers::PreAllocSquareStorage<eltype_t<A>, SquareDims<>>(), A> {
   ManagedArray<eltype_t<A>, SquareDims<>,
-               PreAllocSquareStorage<eltype_t<A>, SquareDims<>>(), A>
+               containers::PreAllocSquareStorage<eltype_t<A>, SquareDims<>>(),
+               A>
     B{SquareDims<>{Row<>{M}}, eltype_t<A>{}, a};
   B.diag() << eltype_t<A>{1};
   return B;
diff --git a/include/Math/Dual.hpp b/include/Math/Dual.hpp
index 92db0c4..ca094c1 100644
--- a/include/Math/Dual.hpp
+++ b/include/Math/Dual.hpp
@@ -12,11 +12,101 @@
 
 namespace poly::math {
 
-template <class T, ptrdiff_t N> class Dual {
+template <class T, ptrdiff_t N, bool Compress = false> struct Dual {
+  static_assert(Compress);
+  utils::compressed_t<T> val{};
+  SVector<T, N, true> partials{T{}};
+
+  using decompressed_type = Dual<utils::decompressed_t<T>, N, false>;
+  constexpr operator decompressed_type() const {
+    return decompressed_type::decompress(this);
+  }
+  [[nodiscard]] constexpr auto value() -> T { return val; }
+  [[nodiscard]] constexpr auto value() const -> const T & { return val; }
+  [[nodiscard]] constexpr auto gradient() -> SVector<T, N, true> & {
+    return partials;
+  }
+  [[nodiscard]] constexpr auto gradient() const -> const SVector<T, N, true> & {
+    return partials;
+  }
+
+  [[gnu::always_inline]] constexpr auto operator-() const & -> Dual {
+    return {-val, -partials};
+  }
+  [[gnu::always_inline]] constexpr auto
+  operator+(const Dual &other) const & -> Dual {
+    return {val + other.val, partials + other.partials};
+  }
+  [[gnu::always_inline]] constexpr auto operator-(const Dual &other) const
+    -> Dual {
+    return {val - other.val, partials - other.partials};
+  }
+  [[gnu::always_inline]] constexpr auto operator+=(const Dual &other)
+    -> Dual & {
+    val += other.val;
+    partials += other.partials;
+    return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator-=(const Dual &other)
+    -> Dual & {
+    val -= other.val;
+    partials -= other.partials;
+    return *this;
+  }
+};
+
+template <simd::SIMDSupported T, ptrdiff_t N>
+requires(std::popcount(size_t(N)) > 1)
+struct Dual<T, N, true> {
+  SVector<T, N + 1, true> data{T{}};
+
+  using decompressed_type = Dual<utils::decompressed_t<T>, N, false>;
+  constexpr operator decompressed_type() const {
+    return decompressed_type::decompress(this);
+  }
+  [[nodiscard]] constexpr auto value() -> T { return data[0]; }
+  [[nodiscard]] constexpr auto value() const -> const T & { return data[0]; }
+  [[nodiscard]] constexpr auto gradient()
+    -> MutArray<T, std::integral_constant<ptrdiff_t, N>> {
+    return {data.data() + 1, {}};
+  }
+  [[nodiscard]] constexpr auto gradient() const
+    -> Array<T, std::integral_constant<ptrdiff_t, N>> {
+    return {data.data() + 1, {}};
+  }
+
+  [[gnu::always_inline]] constexpr auto operator-() const & -> Dual {
+    return {-data};
+  }
+  [[gnu::always_inline]] constexpr auto
+  operator+(const Dual &other) const & -> Dual {
+    return {data + other.data};
+  }
+  [[gnu::always_inline]] constexpr auto operator-(const Dual &other) const
+    -> Dual {
+    return {data - other.data};
+  }
+  [[gnu::always_inline]] constexpr auto operator+=(const Dual &other)
+    -> Dual & {
+    data += other.data;
+    return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator-=(const Dual &other)
+    -> Dual & {
+    data -= other.data;
+    return *this;
+  }
+};
+
+template <class T, ptrdiff_t N> struct Dual<T, N, false> {
+  // default decompressed separates the value and partials
   T val{};
-  SVector<T, N> partials{T{}};
+  SVector<T, N, false> partials{T{}};
+
+  using compressed_type = Dual<utils::compressed_t<T>, N, true>;
+  using decompressed_type = Dual<utils::decompressed_t<T>, N, false>;
+  static_assert(std::same_as<Dual, decompressed_type>);
 
-public:
   constexpr Dual() = default;
   constexpr Dual(T v) : val(v) {}
   constexpr Dual(T v, ptrdiff_t n) : val(v) { partials[n] = T{1}; }
@@ -33,132 +123,589 @@ template <class T, ptrdiff_t N> class Dual {
   [[nodiscard]] constexpr auto gradient(ptrdiff_t i) const -> const T & {
     return partials[i];
   }
-  constexpr auto operator-() const & -> Dual { return {-val, -partials}; }
-  constexpr auto operator+(const Dual &other) const & -> Dual {
+  [[gnu::always_inline]] constexpr auto operator-() const & -> Dual {
+    return {-val, -partials};
+  }
+  [[gnu::always_inline]] constexpr auto
+  operator+(const Dual &other) const & -> Dual {
     return {val + other.val, partials + other.partials};
   }
-  constexpr auto operator-(const Dual &other) const -> Dual {
+  [[gnu::always_inline]] constexpr auto operator-(const Dual &other) const
+    -> Dual {
     return {val - other.val, partials - other.partials};
   }
-  constexpr auto operator*(const Dual &other) const -> Dual {
+  [[gnu::always_inline]] constexpr auto operator*(const Dual &other) const
+    -> Dual {
     return {val * other.val, val * other.partials + other.val * partials};
   }
-  constexpr auto operator/(const Dual &other) const -> Dual {
+  [[gnu::always_inline]] constexpr auto operator/(const Dual &other) const
+    -> Dual {
     return {val / other.val, (other.val * partials - val * other.partials) /
                                (other.val * other.val)};
   }
-  constexpr auto operator+=(const Dual &other) -> Dual & {
+  [[gnu::always_inline]] constexpr auto
+  operator+(const T &other) const & -> Dual
+  requires(!std::same_as<T, double>)
+  {
+    return {val + other, partials};
+  }
+  [[gnu::always_inline]] constexpr auto operator-(const T &other) const -> Dual
+  requires(!std::same_as<T, double>)
+  {
+    return {val - other, partials};
+  }
+  [[gnu::always_inline]] constexpr auto operator*(const T &other) const -> Dual
+  requires(!std::same_as<T, double>)
+  {
+    return {val * other, partials * other};
+  }
+  [[gnu::always_inline]] constexpr auto operator/(const T &other) const -> Dual
+  requires(!std::same_as<T, double>)
+  {
+    return {val / other, partials / other};
+  }
+  [[gnu::always_inline]] constexpr auto operator+=(const Dual &other)
+    -> Dual & {
     val += other.val;
     partials += other.partials;
     return *this;
   }
-  constexpr auto operator-=(const Dual &other) -> Dual & {
+  [[gnu::always_inline]] constexpr auto operator-=(const Dual &other)
+    -> Dual & {
     val -= other.val;
     partials -= other.partials;
     return *this;
   }
-  constexpr auto operator*=(const Dual &other) -> Dual & {
-    val *= other.val;
+  [[gnu::always_inline]] constexpr auto operator*=(const Dual &other)
+    -> Dual & {
     partials << val * other.partials + other.val * partials;
+    val *= other.val;
     return *this;
   }
-  constexpr auto operator/=(const Dual &other) -> Dual & {
-    val /= other.val;
+  [[gnu::always_inline]] constexpr auto operator/=(const Dual &other)
+    -> Dual & {
     partials << (other.val * partials - val * other.partials) /
                   (other.val * other.val);
+    val /= other.val;
     return *this;
   }
-  constexpr auto operator+(double other) const & -> Dual {
+  [[gnu::always_inline]] constexpr auto
+  operator+(double other) const & -> Dual {
     return {val + other, partials};
   }
-  constexpr auto operator-(double other) const -> Dual {
+  [[gnu::always_inline]] constexpr auto operator-(double other) const -> Dual {
     return {val - other, partials};
   }
-  constexpr auto operator*(double other) const -> Dual {
-    return {val * other, other * partials};
+  [[gnu::always_inline]] constexpr auto operator*(double other) const -> Dual {
+    return {val * other, partials * other};
   }
-  constexpr auto operator/(double other) const -> Dual {
+  [[gnu::always_inline]] constexpr auto operator/(double other) const -> Dual {
     return {val / other, partials / other};
   }
-  constexpr auto operator+=(double other) -> Dual & {
+  [[gnu::always_inline]] constexpr auto operator+=(double other) -> Dual & {
     val += other;
     return *this;
   }
-  constexpr auto operator-=(double other) -> Dual & {
+  [[gnu::always_inline]] constexpr auto operator-=(double other) -> Dual & {
     val -= other;
     return *this;
   }
-  constexpr auto operator*=(double other) -> Dual & {
+  [[gnu::always_inline]] constexpr auto operator*=(double other) -> Dual & {
     val *= other;
     partials *= other;
     return *this;
   }
-  constexpr auto operator/=(double other) -> Dual & {
+  [[gnu::always_inline]] constexpr auto operator/=(double other) -> Dual & {
     val /= other;
     partials /= other;
     return *this;
   }
-  constexpr auto operator==(const Dual &other) const -> bool {
+  [[gnu::always_inline]] constexpr auto operator==(const Dual &other) const
+    -> bool {
     return val == other.val; // && grad == other.grad;
   }
-  constexpr auto operator!=(const Dual &other) const -> bool {
+  [[gnu::always_inline]] constexpr auto operator!=(const Dual &other) const
+    -> bool {
     return val != other.val; // || grad != other.grad;
   }
+  constexpr auto operator<(const Dual &other) const -> bool {
+    return val < other.val;
+  }
+  constexpr auto operator>(const Dual &other) const -> bool {
+    return val > other.val;
+  }
+  constexpr auto operator<=(const Dual &other) const -> bool {
+    return val <= other.val;
+  }
+  constexpr auto operator>=(const Dual &other) const -> bool {
+    return val >= other.val;
+  }
   constexpr auto operator==(double other) const -> bool { return val == other; }
   constexpr auto operator!=(double other) const -> bool { return val != other; }
   constexpr auto operator<(double other) const -> bool { return val < other; }
   constexpr auto operator>(double other) const -> bool { return val > other; }
   constexpr auto operator<=(double other) const -> bool { return val <= other; }
   constexpr auto operator>=(double other) const -> bool { return val >= other; }
+  constexpr auto operator==(T other) const -> bool
+  requires(!std::same_as<T, double>)
+  {
+    return val == other;
+  }
+  constexpr auto operator!=(T other) const -> bool
+  requires(!std::same_as<T, double>)
+  {
+    return val != other;
+  }
+  constexpr auto operator<(T other) const -> bool
+  requires(!std::same_as<T, double>)
+  {
+    return val < other;
+  }
+  constexpr auto operator>(T other) const -> bool
+  requires(!std::same_as<T, double>)
+  {
+    return val > other;
+  }
+  constexpr auto operator<=(T other) const -> bool
+  requires(!std::same_as<T, double>)
+  {
+    return val <= other;
+  }
+  constexpr auto operator>=(T other) const -> bool
+  requires(!std::same_as<T, double>)
+  {
+    return val >= other;
+  }
+  constexpr void compress(compressed_type *p) const {
+    utils::compress(val, &(p->val));
+    partials.compress(&(p->partials));
+  }
+  static constexpr auto decompress(const compressed_type *p) -> Dual {
+    return {utils::decompress<T>(&(p->val)),
+            SVector<T, N>::decompress(&(p->partials))};
+  }
+  // constexpr void compress(compressed_type *p) const {
+  //   utils::compress(val, &(p->data[0]));
+  //   p->gradient() << partials;
+  // }
+  // static constexpr auto decompress(const compressed_type *p) -> Dual {
+  //   return {utils::decompress<T>(&(p->data[0])), SVector<T,
+  //   N>(p->gradient())};
+  // }
+  constexpr operator compressed_type() const {
+    compressed_type ret;
+    compress(&ret);
+    return ret;
+  }
+};
+
+template <simd::SIMDSupported T, ptrdiff_t N>
+requires(std::popcount(size_t(N)) > 1)
+struct Dual<T, N, false> {
+  static constexpr ptrdiff_t value_idx = 0; // N;
+  static constexpr ptrdiff_t partial_offset = value_idx != N;
+  using data_type = SVector<T, N + 1, false>;
+  data_type data{T{}};
+  using compressed_type = Dual<T, N, true>;
+  using decompressed_type = Dual<T, N, false>;
+
+  using V = typename data_type::V;
+  static constexpr ptrdiff_t W = data_type::W;
+  // constexpr Dual() = default;
+  constexpr Dual() = default;
+  constexpr Dual(T v) { data[value_idx] = v; }
+  constexpr Dual(T v, ptrdiff_t n) {
+    data[value_idx] = v;
+    data[partial_offset + n] = T{1};
+  }
+  // constexpr Dual(T v, ptrdiff_t n, T p) {
+  //   data[value_idx] = v;
+  //   data[partial_offset + n] = p;
+  // }
+  constexpr Dual(T v, AbstractVector auto g) {
+    value() = v;
+    gradient() << g;
+  }
+  constexpr Dual(SVector<T, N + 1> d) : data{d} {}
+  constexpr Dual(const AbstractVector auto &d)
+  requires(std::convertible_to<utils::eltype_t<decltype(d)>, T>)
+    : data{d} {}
+  constexpr Dual(std::integral auto v) { value() = v; }
+  constexpr Dual(std::floating_point auto v) { value() = v; }
+  constexpr auto value() -> T & { return data[value_idx]; }
+  constexpr auto gradient()
+    -> MutArray<T, std::integral_constant<ptrdiff_t, N>> {
+    return {data.data() + partial_offset, {}};
+  }
+  [[nodiscard]] constexpr auto value() const -> T { return data[value_idx]; }
+  // zeros out partial part of the vector
+  [[nodiscard]] constexpr auto vvalue() const -> V {
+    // return data[value_idx];
+    return (simd::range<W, int64_t>() == simd::Vec<W, int64_t>{})
+             ? data.memory_[0]
+             : V{};
+  }
+  // broadcasts value across register
+  [[nodiscard]] constexpr auto vbvalue() const -> V {
+    return simd::vbroadcast<W, T>(data.memory_[0]);
+  }
+  [[nodiscard]] constexpr auto gradient() const
+    -> Array<T, std::integral_constant<ptrdiff_t, N>> {
+    return {data.data() + partial_offset, {}};
+  }
+
+  constexpr auto operator-() const & -> Dual { return {-data}; }
+  constexpr auto operator+(const Dual &other) const & -> Dual {
+    return {data + other.data};
+  }
+  constexpr auto operator-(const Dual &other) const -> Dual {
+    return {data - other.data};
+  }
+  constexpr auto operator*(const Dual &other) const -> Dual {
+    // TODO: either update remaining methods to match this style,
+    // or figure out how to get `conditional`'s codegen quality to match
+    Dual ret;
+    V vt = vbvalue(), vo = other.vbvalue(), x = vt * other.data.memory_[0];
+    x = simd::firstoff<W, int64_t>() ? x + vo * data.memory_[0] : x;
+    ret.data.memory_[0] = x;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t i = 1; i < data_type::L; ++i)
+      ret.data.memory_[i] = vt * other.data.memory_[i] + vo * data.memory_[i];
+    return ret;
+    // return {conditional(std::plus<>{},
+    //                     elementwise_not_equal(_(0, N + 1), value_idx),
+    //                     value() * other.data, data * other.value())};
+  }
+  constexpr auto operator/(const Dual &other) const -> Dual {
+    Dual ret;
+    V vt = vbvalue(), vo = other.vbvalue(), vo2 = vo * vo,
+      x = vo * data.memory_[0];
+    ret.data.memory_[0] =
+      (simd::firstoff<W, int64_t>() ? x - vt * other.data.memory_[0] : x) / vo2;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t i = 1; i < data_type::L; ++i)
+      ret.data.memory_[i] =
+        (vo * data.memory_[i] - vt * other.data.memory_[i]) / vo2;
+    return ret;
+    // val = value() / other.value()
+    // partials = (other.value() * gradient() - value() * other.gradient()) /
+    // (other.value() * other.value())
+    // partials = (gradient()) / (other.value())
+    //  - (value() * other.gradient()) / (other.value() * other.value())
+    // T v{other.value()};
+    // return {conditional(std::minus<>{},
+    //                     elementwise_not_equal(_(0, N + 1), value_idx), data /
+    //                     v, value() * other.data / (v * v))};
+  }
+  constexpr auto operator+=(const Dual &other) -> Dual & {
+    data += other.data;
+    return *this;
+  }
+  constexpr auto operator-=(const Dual &other) -> Dual & {
+    data -= other.data;
+    return *this;
+  }
+  constexpr auto operator*=(const Dual &other) -> Dual & {
+    V vt = vbvalue(), vo = other.vbvalue(), x = vt * other.data.memory_[0];
+    data.memory_[0] =
+      simd::firstoff<W, int64_t>() ? x + vo * data.memory_[0] : x;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t i = 1; i < data_type::L; ++i)
+      data.memory_[i] = vt * other.data.memory_[i] + vo * data.memory_[i];
+    // data << conditional(std::plus<>{},
+    //                     elementwise_not_equal(_(0, N + 1), value_idx),
+    //                     value() * other.data, data * other.value());
+    return *this;
+  }
+  constexpr auto operator/=(const Dual &other) -> Dual & {
+    V vt = vbvalue(), vo = other.vbvalue(), vo2 = vo * vo,
+      x = vo * data.memory_[0];
+    data.memory_[0] =
+      (simd::firstoff<W, int64_t>() ? x - vt * other.data.memory_[0] : x) / vo2;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t i = 1; i < data_type::L; ++i)
+      data.memory_[i] =
+        (vo * data.memory_[i] - vt * other.data.memory_[i]) / vo2;
+    // T v{other.value()};
+    // data << conditional(std::minus<>{},
+    //                     elementwise_not_equal(_(0, N + 1), value_idx), data /
+    //                     v, value() * other.data / (v * v));
+    return *this;
+  }
+  constexpr auto operator+(double other) const & -> Dual {
+    Dual ret = *this;
+    ret.data.memory_[0] += simd::Vec<SVector<T, N + 1>::W, T>{other};
+    return ret;
+  }
+  constexpr auto operator-(double other) const -> Dual {
+    Dual ret = *this;
+    ret.data.memory_[0] -= simd::Vec<SVector<T, N + 1>::W, T>{other};
+    return ret;
+  }
+  constexpr auto operator*(double other) const -> Dual {
+    return {data * other};
+  }
+  constexpr auto operator/(double other) const -> Dual {
+    return {data / other};
+  }
+  constexpr auto operator+=(double other) -> Dual & {
+    data.memory_[0] += simd::Vec<SVector<T, N + 1>::W, T>{other};
+    return *this;
+  }
+  constexpr auto operator-=(double other) -> Dual & {
+    data.memory_[0] -= simd::Vec<SVector<T, N + 1>::W, T>{other};
+    return *this;
+  }
+  constexpr auto operator*=(double other) -> Dual & {
+    data *= other;
+    return *this;
+  }
+  constexpr auto operator/=(double other) -> Dual & {
+    data /= other;
+    return *this;
+  }
+  constexpr auto operator==(const Dual &other) const -> bool {
+    return value() == other.value(); // && grad == other.grad;
+  }
+  constexpr auto operator!=(const Dual &other) const -> bool {
+    return value() != other.value(); // || grad != other.grad;
+  }
+  constexpr auto operator==(double other) const -> bool {
+    return value() == other;
+  }
+  constexpr auto operator!=(double other) const -> bool {
+    return value() != other;
+  }
+  constexpr auto operator<(double other) const -> bool {
+    return value() < other;
+  }
+  constexpr auto operator>(double other) const -> bool {
+    return value() > other;
+  }
+  constexpr auto operator<=(double other) const -> bool {
+    return value() <= other;
+  }
+  constexpr auto operator>=(double other) const -> bool {
+    return value() >= other;
+  }
   constexpr auto operator<(const Dual &other) const -> bool {
-    return val < other.val;
+    return value() < other.value();
   }
   constexpr auto operator>(const Dual &other) const -> bool {
-    return val > other.val;
+    return value() > other.value();
   }
   constexpr auto operator<=(const Dual &other) const -> bool {
-    return val <= other.val;
+    return value() <= other.value();
   }
   constexpr auto operator>=(const Dual &other) const -> bool {
-    return val >= other.val;
+    return value() >= other.value();
+  }
+
+  friend constexpr auto exp(Dual x) -> Dual {
+    return {conditional(std::multiplies<>{},
+                        elementwise_not_equal(_(0, N + 1), value_idx),
+                        exp(x.value()), x.data)};
+  }
+
+  friend constexpr auto operator+(double other, Dual x) -> Dual {
+    return {other + x.data};
+  }
+  friend constexpr auto operator-(double other, Dual x) -> Dual {
+    return {other - x.data};
+  }
+  friend constexpr auto operator*(double other, Dual x) -> Dual {
+    return {other * x.data};
+  }
+  friend constexpr auto operator/(double a, Dual b) -> Dual {
+    Dual ret;
+    V vt = simd::vbroadcast<W, double>(a), vo = b.vbvalue(), vo2 = vo * vo,
+      x = vo * simd::Vec<W, double>{a};
+    ret.data.memory_[0] =
+      (simd::firstoff<W, int64_t>() ? x - vt * b.data.memory_[0] : x) / vo2;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t i = 1; i < data_type::L; ++i)
+      ret.data.memory_[i] = (-vt * b.data.memory_[i]) / vo2;
+    return ret;
+    // T v = other / x.value();
+    // return {conditional(std::multiplies<>{},
+    //                     elementwise_not_equal(_(0, N + 1), value_idx), v,
+    //                     -x.data / x.value())};
+    // return {v, -v * x.gradient() / (x.value())};
   }
+  constexpr void compress(compressed_type *p) const { p->data << data; }
+  static constexpr auto decompress(const compressed_type *p) -> Dual {
+    return {SVector<T, N + 1, false>{p->data}};
+  }
+  constexpr operator compressed_type() const {
+    compressed_type ret;
+    compress(&ret);
+    return ret;
+  }
+};
+static_assert(!std::convertible_to<Array<Dual<double, 7, true>,
+                                         std::integral_constant<ptrdiff_t, 2>>,
+                                   Dual<double, 7, false>>);
+static_assert(utils::Compressible<Dual<double, 7>>);
+static_assert(utils::Compressible<Dual<double, 8>>);
+static_assert(
+  AbstractVector<
+    Conditional<poly::math::ElementwiseBinaryOp<poly::math::Range<long, long>,
+                                                long, std::not_equal_to<void>>,
+                poly::math::ElementwiseBinaryOp<
+                  double, poly::math::StaticArray<double, 1, 8, false>,
+                  std::multiplies<void>>,
+                poly::math::ElementwiseBinaryOp<
+                  poly::math::StaticArray<double, 1, 8, false>, double,
+                  std::multiplies<void>>,
+                std::plus<void>>>);
+
+template <typename T> struct IsDualImpl : std::false_type {};
+template <typename T, ptrdiff_t N, bool Compress>
+struct IsDualImpl<Dual<T, N, Compress>> : std::true_type {};
+template <typename T>
+concept IsDual = IsDualImpl<T>::value;
+
+// We want to support casting compressed `Dual` arrays to `double`
+// when possible as a performance optimization.
+// This is possible with
+// 1. Dual<T,N> (+/-) Dual<T,N>
+// 2. Dual<T,N> * double or double * Dual<T,N>
+// 3. Dual<T,N> / double
+// 4. Simple copies
+template <typename T> struct ScalarizeEltViaCast {
+  using type = void;
+};
+template <typename T>
+using scalarize_elt_cast_t = typename ScalarizeEltViaCast<T>::type;
+template <typename T, ptrdiff_t N>
+struct ScalarizeEltViaCast<Dual<T, N, true>> {
+  using type = std::conditional_t<std::same_as<T, double>, double,
+                                  scalarize_elt_cast_t<T>>;
+};
+
+template <typename T> struct ScalarizeViaCast<Elementwise<std::negate<>, T>> {
+  using type = scalarize_via_cast_t<T>;
+};
+template <typename T>
+concept AdditiveOp =
+  std::same_as<T, std::plus<>> || std::same_as<T, std::minus<>>;
+template <typename T>
+concept MultiplicativeOp =
+  std::same_as<T, std::multiplies<>> || std::same_as<T, std::divides<>>;
+template <typename T>
+concept EltIsDual = IsDual<utils::eltype_t<T>>;
+
+template <typename T, typename S> struct ScalarizeViaCast<Array<T, S, true>> {
+  using type = scalarize_elt_cast_t<utils::compressed_t<T>>;
+};
+template <typename T, typename S>
+struct ScalarizeViaCast<MutArray<T, S, true>> {
+  using type = scalarize_elt_cast_t<utils::compressed_t<T>>;
+};
+
+template <typename T>
+concept EltCastableDual =
+  EltIsDual<T> && std::same_as<scalarize_via_cast_t<T>, double>;
+template <AdditiveOp Op, EltCastableDual A, EltCastableDual B>
+struct ScalarizeViaCast<ElementwiseBinaryOp<A, B, Op>> {
+  // when we cast, we expand into rows, thus col vectors don't work
+  // as they'd have to become matrices, and then number of rows
+  // won't match up, unless both inputs were a ColVector
+  // It is unclear if the case where both inputs are ColVectors is worth
+  // the complexity, as the benefit from this optimization is being
+  // able to handle things contiguously, which we in that case.
+  using type = std::conditional_t<
+    (ColVector<A> || ColVector<B>) ||
+      (!std::same_as<utils::eltype_t<A>, utils::eltype_t<B>>),
+    void, double>;
+};
+template <MultiplicativeOp Op, EltCastableDual A, std::convertible_to<double> T>
+struct ScalarizeViaCast<ElementwiseBinaryOp<A, T, Op>> {
+  using type = double;
+};
+template <EltCastableDual B, std::convertible_to<double> T>
+struct ScalarizeViaCast<ElementwiseBinaryOp<T, B, std::multiplies<>>> {
+  using type = double;
 };
+
 template <class T, ptrdiff_t N> Dual(T, SVector<T, N>) -> Dual<T, N>;
 
 template <class T, ptrdiff_t N>
-constexpr auto operator+(double other, Dual<T, N> x) -> Dual<T, N> {
+[[gnu::always_inline]] constexpr auto operator+(const T &a, const Dual<T, N> &b)
+  -> Dual<T, N>
+requires(!std::same_as<T, double>)
+{
+  return {a + b.val, b.partials};
+}
+template <class T, ptrdiff_t N>
+[[gnu::always_inline]] constexpr auto operator-(const T &a, const Dual<T, N> &b)
+  -> Dual<T, N>
+requires(!std::same_as<T, double>)
+{
+  return {a - b.val, -b.partials};
+}
+template <class T, ptrdiff_t N>
+[[gnu::always_inline]] constexpr auto operator*(const T &a, const Dual<T, N> &b)
+  -> Dual<T, N>
+requires(!std::same_as<T, double>)
+{
+  // Dual res;
+  // res.val = val * other.val;
+  // res.partials << val * other.partials + other.val * partials;
+  // return res;
+  return {a * b.val, a * b.partials};
+}
+template <class T, ptrdiff_t N>
+[[gnu::always_inline]] constexpr auto operator/(const T &a, const Dual<T, N> &b)
+  -> Dual<T, N>
+requires(!std::same_as<T, double>)
+{
+  return {a / b.val, (-a * b.partials) / (b.val * b.val)};
+}
+template <class T, ptrdiff_t N>
+[[gnu::always_inline]] constexpr auto operator+(double other,
+                                                const Dual<T, N> &x)
+  -> Dual<T, N> {
   return {x.value() + other, x.gradient()};
 }
 template <class T, ptrdiff_t N>
-constexpr auto operator-(double other, Dual<T, N> x) -> Dual<T, N> {
+[[gnu::always_inline]] constexpr auto operator-(double other,
+                                                const Dual<T, N> &x)
+  -> Dual<T, N> {
   return {x.value() - other, -x.gradient()};
 }
 template <class T, ptrdiff_t N>
-constexpr auto operator*(double other, Dual<T, N> x) -> Dual<T, N> {
+[[gnu::always_inline]] constexpr auto operator*(double other,
+                                                const Dual<T, N> &x)
+  -> Dual<T, N> {
   return {x.value() * other, other * x.gradient()};
 }
 template <class T, ptrdiff_t N>
-constexpr auto operator/(double other, Dual<T, N> x) -> Dual<T, N> {
+[[gnu::always_inline]] constexpr auto operator/(double other,
+                                                const Dual<T, N> &x)
+  -> Dual<T, N> {
   return {other / x.value(), -other * x.gradient() / (x.value() * x.value())};
 }
-template <class T, ptrdiff_t N> constexpr auto exp(Dual<T, N> x) -> Dual<T, N> {
+template <class T, ptrdiff_t N>
+constexpr auto exp(const Dual<T, N> &x) -> Dual<T, N> {
   T expx = exp(x.value());
   return {expx, expx * x.gradient()};
 }
 template <class T, ptrdiff_t N>
-constexpr auto sigmoid(Dual<T, N> x) -> Dual<T, N> {
+constexpr auto sigmoid(const Dual<T, N> &x) -> Dual<T, N> {
   T s = sigmoid(x.value());
   return {s, (s - s * s) * x.gradient()};
 }
 template <class T, ptrdiff_t N>
-constexpr auto softplus(Dual<T, N> x) -> Dual<T, N> {
+constexpr auto softplus(const Dual<T, N> &x) -> Dual<T, N> {
   return {softplus(x.value()), sigmoid(x.value()) * x.gradient()};
 }
-template <class T, ptrdiff_t N> constexpr auto log(Dual<T, N> x) -> Dual<T, N> {
+template <class T, ptrdiff_t N>
+constexpr auto log(const Dual<T, N> &x) -> Dual<T, N> {
   return {log2(x.value()), x.gradient() / x.value()};
 }
 template <class T, ptrdiff_t N>
-constexpr auto log2(Dual<T, N> x) -> Dual<T, N> {
+constexpr auto log2(const Dual<T, N> &x) -> Dual<T, N> {
   constexpr double log2 = 0.6931471805599453; // log(2);
   return {log2(x.value()), x.gradient() / (log2 * x.value())};
 }
@@ -221,6 +768,8 @@ template <ptrdiff_t N, AbstractVector T> struct DualVector {
     return v;
   }
   [[nodiscard]] constexpr auto size() const -> ptrdiff_t { return x.size(); }
+  [[nodiscard]] constexpr auto numRow() const -> Row<1> { return {}; }
+  [[nodiscard]] constexpr auto numCol() const -> Col<> { return {x.size()}; }
   [[nodiscard]] constexpr auto view() const -> DualVector { return *this; }
 };
 static_assert(AbstractVector<DualVector<8, PtrVector<double>>>);
@@ -257,10 +806,15 @@ constexpr auto gradient(alloc::Arena<> *arena, PtrVector<double> x,
   }
 }
 // only computes the upper triangle blocks
-constexpr auto extractDualValRecurse(std::floating_point auto x) { return x; }
+template <class T, ptrdiff_t N, bool Compress>
+constexpr auto value(const Dual<T, N, Compress> &x) {
+  return value(x.value());
+}
+// this can call `value` on a compressed `Dual`, whichh is why we need `value`
+// to be defined on it.`
 template <class T, ptrdiff_t N>
-constexpr auto extractDualValRecurse(const Dual<T, N> &x) {
-  return extractDualValRecurse(x.value());
+constexpr auto value(utils::Reference<Dual<T, N>> x) {
+  return value(x.c->value());
 }
 
 /// fills the lower triangle of the hessian
diff --git a/include/Math/EmptyArrays.hpp b/include/Math/EmptyArrays.hpp
index 848fdfc..3ac3dcf 100644
--- a/include/Math/EmptyArrays.hpp
+++ b/include/Math/EmptyArrays.hpp
@@ -17,7 +17,7 @@ template <typename T> struct EmptyMatrix {
 
   static constexpr auto data() -> T * { return nullptr; }
   static constexpr auto operator[](ptrdiff_t, ptrdiff_t) -> T { return 0; }
-  static constexpr auto size() -> CartesianIndex<ptrdiff_t, ptrdiff_t> {
+  static constexpr auto shape() -> CartesianIndex<ptrdiff_t, ptrdiff_t> {
     return {0, 0};
   }
   static constexpr auto view() -> EmptyMatrix<T> { return EmptyMatrix<T>{}; }
diff --git a/include/Math/Indexing.hpp b/include/Math/Indexing.hpp
index 277a29a..f665517 100644
--- a/include/Math/Indexing.hpp
+++ b/include/Math/Indexing.hpp
@@ -2,6 +2,7 @@
 #include "Math/AxisTypes.hpp"
 #include "Math/Iterators.hpp"
 #include "Math/MatrixDimensions.hpp"
+#include "SIMD/Indexing.hpp"
 #include <cstddef>
 
 namespace poly::math {
@@ -16,6 +17,8 @@ namespace poly::math {
     return os << "end";
   }
 } end;
+/// TODO: remove `OffsetBegin`
+/// We probably won't support non-zero-based indexing
 struct OffsetBegin {
   [[no_unique_address]] ptrdiff_t offset;
   friend inline auto operator<<(std::ostream &os, OffsetBegin r)
@@ -65,7 +68,8 @@ concept ScalarIndex =
   [[nodiscard]] inline constexpr auto operator()(auto B, auto E) const {
     return Range{standardizeRangeBound(B), standardizeRangeBound(E)};
   }
-} _; // NOLINT(bugprone-reserved-identifier)
+} _;
+
 constexpr auto canonicalize(ptrdiff_t e, ptrdiff_t) -> ptrdiff_t { return e; }
 constexpr auto canonicalize(Begin, ptrdiff_t) -> ptrdiff_t { return 0; }
 constexpr auto canonicalize(OffsetBegin b, ptrdiff_t) -> ptrdiff_t {
@@ -142,16 +146,6 @@ constexpr auto calcOffset(ptrdiff_t, Colon) -> ptrdiff_t { return 0; }
 constexpr auto calcOffset(SquareDims<>, ptrdiff_t i) -> ptrdiff_t { return i; }
 constexpr auto calcOffset(DenseDims<>, ptrdiff_t i) -> ptrdiff_t { return i; }
 
-template <class R, class C>
-[[nodiscard]] inline constexpr auto calcOffset(StridedDims<> d,
-                                               CartesianIndex<R, C> i)
-  -> ptrdiff_t {
-  ptrdiff_t r =
-    ptrdiff_t(RowStride<>(d)) * calcOffset(ptrdiff_t(Row<>(d)), i.row);
-  ptrdiff_t c = calcOffset(ptrdiff_t(Col<>(d)), i.col);
-  return r + c;
-}
-
 struct StridedRange {
   [[no_unique_address]] ptrdiff_t len;
   [[no_unique_address]] ptrdiff_t stride;
@@ -161,35 +155,57 @@ struct StridedRange {
     return os << "Length: " << x.len << " (stride: " << x.stride << ")";
   }
 };
+
+template <ptrdiff_t U, ptrdiff_t W, typename M>
+constexpr auto calcOffset(ptrdiff_t len, simd::index::Unroll<U, W, M> i) {
+  if constexpr (std::same_as<M, simd::mask::None<W>>)
+    invariant((i.index + U * W - 1) < len);
+  else invariant(i.index + (U - 1) * W + i.mask.lastUnmasked() - 1 < len);
+  return i.index;
+}
+
 template <class I> constexpr auto calcOffset(StridedRange d, I i) -> ptrdiff_t {
   return d.stride * calcOffset(d.len, i);
 }
-constexpr auto is_integral_const(auto) -> bool { return false; }
-template <typename T, T V>
-constexpr auto is_integral_const(std::integral_constant<T, V>) -> bool {
-  return true;
+
+template <class R, class C>
+[[nodiscard]] inline constexpr auto calcOffset(StridedDims<> d, R r, C c)
+  -> ptrdiff_t {
+  return ptrdiff_t(stride(d)) * calcOffset(ptrdiff_t(Row<>(d)), r) +
+         calcOffset(ptrdiff_t(Col<>(d)), c);
 }
 
+// constexpr auto is_integral_const(auto) -> bool { return false; }
+// template <typename T, T V>
+// constexpr auto is_integral_const(std::integral_constant<T, V>) -> bool {
+//   return true;
+// }
+constexpr auto row(StridedRange r) -> Row<> { return {r.len}; }
+constexpr auto col(StridedRange) -> Col<1> { return {}; }
+constexpr auto stride(StridedRange r) -> RowStride<> { return {r.stride}; }
+
 template <typename T>
 concept StaticInt =
   std::is_same_v<T, std::integral_constant<typename T::value_type, T::value>>;
 
-template <class T>
+template <typename T>
 concept DenseLayout =
   std::integral<T> || std::is_convertible_v<T, DenseDims<>> || StaticInt<T>;
 
 static_assert(StaticInt<std::integral_constant<ptrdiff_t, 3>>);
 static_assert(!StaticInt<int64_t>);
 
-template <class D>
+template <typename D>
 concept VectorDimension =
   std::integral<D> || std::same_as<D, StridedRange> || StaticInt<D>;
 
 // Concept for aligning array dimensions with indices.
 template <class I, class D>
 concept Index =
-  (VectorDimension<D> && (ScalarIndex<I> || AbstractSlice<I>)) ||
-  (DenseLayout<D> && ScalarIndex<I>) || (MatrixDimension<D> && requires(I i) {
+  (VectorDimension<D> &&
+   (ScalarIndex<I> || AbstractSlice<I> || simd::index::issimd<I>)) ||
+  (DenseLayout<D> && (ScalarIndex<I> || simd::index::issimd<I>)) ||
+  (MatrixDimension<D> && requires(I i) {
     { i.row };
     { i.col };
   });
@@ -221,7 +237,7 @@ constexpr auto calcNewDim(StridedRange len, Range<B, E> r) -> StridedRange {
   return StridedRange{ptrdiff_t(calcNewDim(len.len, r)), len.stride};
 }
 template <ScalarIndex R, ScalarIndex C>
-constexpr auto calcNewDim(StridedDims<>, CartesianIndex<R, C>) -> Empty {
+constexpr auto calcNewDim(StridedDims<>, R, C) -> Empty {
   return {};
 }
 constexpr auto calcNewDim(std::integral auto len, Colon) -> ptrdiff_t {
@@ -231,31 +247,66 @@ constexpr auto calcNewDim(StaticInt auto len, Colon) { return len; };
 constexpr auto calcNewDim(StridedRange len, Colon) { return len; };
 
 template <AbstractSlice B, ScalarIndex C>
-constexpr auto calcNewDim(StridedDims<> d, CartesianIndex<B, C> i) {
-  ptrdiff_t rowDims = ptrdiff_t(calcNewDim(ptrdiff_t(Row(d)), i.row));
+constexpr auto calcNewDim(StridedDims<> d, B b, C) {
+  ptrdiff_t rowDims = ptrdiff_t(calcNewDim(ptrdiff_t(Row(d)), b));
   return StridedRange{rowDims, ptrdiff_t(RowStride(d))};
 }
 
 template <ScalarIndex R, AbstractSlice C>
-constexpr auto calcNewDim(StridedDims<> d, CartesianIndex<R, C> i) {
-  return calcNewDim(ptrdiff_t(Col(d)), i.col);
+constexpr auto calcNewDim(StridedDims<> d, R, C c) {
+  return calcNewDim(ptrdiff_t(Col(d)), c);
 }
 
 template <AbstractSlice B, AbstractSlice C>
-constexpr auto calcNewDim(StridedDims<> d, CartesianIndex<B, C> i) {
-  auto rowDims = calcNewDim(ptrdiff_t(Row(d)), i.row);
-  auto colDims = calcNewDim(ptrdiff_t(Col(d)), i.col);
+constexpr auto calcNewDim(StridedDims<> d, B r, C c) {
+  auto rowDims = calcNewDim(ptrdiff_t(Row(d)), r);
+  auto colDims = calcNewDim(ptrdiff_t(Col(d)), c);
   return StridedDims(row(rowDims), col(colDims), RowStride(d));
 }
 template <AbstractSlice B>
-constexpr auto calcNewDim(DenseDims<> d, CartesianIndex<B, Colon> i) {
-  auto rowDims = calcNewDim(ptrdiff_t(Row(d)), i.row);
+constexpr auto calcNewDim(DenseDims<> d, B r, Colon) {
+  auto rowDims = calcNewDim(ptrdiff_t(Row(d)), r);
   return DenseDims(row(rowDims), Col(d));
 }
 template <AbstractSlice B>
-constexpr auto calcNewDim(SquareDims<> d, CartesianIndex<B, Colon> i) {
-  auto rowDims = calcNewDim(ptrdiff_t(Row(d)), i.row);
+constexpr auto calcNewDim(SquareDims<> d, B r, Colon) {
+  auto rowDims = calcNewDim(ptrdiff_t(Row(d)), r);
   return DenseDims(row(rowDims), Col(d));
 }
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename M>
+constexpr auto calcNewDim(StridedDims<> d, simd::index::Unroll<R>,
+                          simd::index::Unroll<C, W, M> c) {
+  return simd::index::UnrollDims<R, C, W, M>{c.mask, RowStride(d)};
+}
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename M>
+constexpr auto calcNewDim(StridedDims<> d, simd::index::Unroll<C, W, M> r,
+                          simd::index::Unroll<R>) {
+  return simd::index::UnrollDims<R, C, W, M, true>{r.mask, RowStride(d)};
+}
+
+template <ptrdiff_t C, ptrdiff_t W, typename M>
+constexpr auto calcNewDim(StridedDims<> d, ptrdiff_t,
+                          simd::index::Unroll<C, W, M> c) {
+  return simd::index::UnrollDims<1, C, W, M>{c.mask, RowStride(d)};
+}
+template <ptrdiff_t R, ptrdiff_t W, typename M>
+constexpr auto calcNewDim(StridedDims<> d, simd::index::Unroll<R, W, M> r,
+                          ptrdiff_t) {
+  if constexpr (W == 1)
+    return simd::index::UnrollDims<R, 1, 1, M>{r.mask, RowStride(d)};
+  else return simd::index::UnrollDims<1, R, W, M, true>{r.mask, RowStride(d)};
+}
+
+template <ptrdiff_t U, ptrdiff_t W, typename M>
+constexpr auto calcNewDim(ptrdiff_t, simd::index::Unroll<U, W, M> i) {
+  return simd::index::UnrollDims<1, U, W, M, false, 1>{i.mask, RowStride<1>{}};
+}
+
+template <ptrdiff_t U, ptrdiff_t W, typename M>
+constexpr auto calcNewDim(StridedRange x, simd::index::Unroll<U, W, M> i) {
+  if constexpr (W == 1)
+    return simd::index::UnrollDims<U, 1, 1, M, false, -1>{i.mask, stride(x)};
+  else return simd::index::UnrollDims<1, U, W, M, true, -1>{i.mask, stride(x)};
+}
 
 } // namespace poly::math
diff --git a/include/Math/Iterators.hpp b/include/Math/Iterators.hpp
index c0ce5ac..606bbba 100644
--- a/include/Math/Iterators.hpp
+++ b/include/Math/Iterators.hpp
@@ -49,6 +49,7 @@ template <std::integral B, std::integral E> struct Range<B, E> {
   [[nodiscard]] constexpr auto operator[](value_type i) const -> value_type {
     return b + i;
   }
+  [[nodiscard]] constexpr auto operator[](auto i) const { return i + b; }
 };
 constexpr auto standardizeRangeBound(auto x) { return x; }
 constexpr auto standardizeRangeBound(std::unsigned_integral auto x) {
diff --git a/include/Math/LinearAlgebra.hpp b/include/Math/LinearAlgebra.hpp
index dfa42d9..06ae35a 100644
--- a/include/Math/LinearAlgebra.hpp
+++ b/include/Math/LinearAlgebra.hpp
@@ -1,4 +1,5 @@
 #pragma once
+#include "Containers/Pair.hpp"
 #include "Math/Array.hpp"
 #include "Math/Constructors.hpp"
 #include "Math/Math.hpp"
@@ -9,18 +10,17 @@ namespace LU {
 [[nodiscard]] constexpr auto ldivrat(SquarePtrMatrix<Rational> F,
                                      PtrVector<unsigned> ipiv,
                                      MutPtrMatrix<Rational> rhs) -> bool {
-  auto [M, N] = rhs.size();
+  auto [M, N] = shape(rhs);
   invariant(ptrdiff_t(F.numRow()), ptrdiff_t(M));
   // permute rhs
-  for (ptrdiff_t i = 0; i < M; ++i) {
-    unsigned ip = ipiv[i];
-    if (i != ip)
+  for (ptrdiff_t i = 0; i < M; ++i)
+    if (unsigned ip = ipiv[i]; i != ip)
       for (ptrdiff_t j = 0; j < M; ++j) std::swap(rhs[ip, j], rhs[i, j]);
-  }
+
   // LU x = rhs
   // L y = rhs // L is UnitLowerTriangular
-  for (ptrdiff_t n = 0; n < N; ++n) {
-    for (ptrdiff_t m = 0; m < M; ++m) {
+  for (ptrdiff_t m = 0; m < M; ++m) {
+    for (ptrdiff_t n = 0; n < N; ++n) {
       Rational Ymn = rhs[m, n];
       for (ptrdiff_t k = 0; k < m; ++k)
         if (Ymn.fnmadd(F[m, k], rhs[k, n])) return true;
@@ -28,8 +28,8 @@ namespace LU {
     }
   }
   // U x = y
-  for (ptrdiff_t n = 0; n < N; ++n) {
-    for (auto m = ptrdiff_t(M); m--;) {
+  for (ptrdiff_t m = M; m--;) {
+    for (ptrdiff_t n = 0; n < N; ++n) {
       Rational Ymn = rhs[m, n];
       for (ptrdiff_t k = m + 1; k < M; ++k)
         if (Ymn.fnmadd(F[m, k], rhs[k, n])) return true;
@@ -41,44 +41,34 @@ namespace LU {
 }
 template <class S>
 constexpr void ldiv(SquarePtrMatrix<S> F, PtrVector<unsigned> ipiv,
-                    MutPtrMatrix<S> rhs) {
-  auto [M, N] = rhs.size();
-  invariant(ptrdiff_t(F.numRow()), ptrdiff_t(M));
+                    MutPtrMatrix<S> R) {
+  auto [M, N] = shape(R);
+  invariant(ptrdiff_t(F.numRow()), M);
+  invariant(M > 0);
   // permute rhs
-  for (ptrdiff_t i = 0; i < M; ++i) {
-    unsigned ip = ipiv[i];
-    if (i != ip)
-      for (ptrdiff_t j = 0; j < M; ++j) std::swap(rhs[ip, j], rhs[i, j]);
-  }
+  for (ptrdiff_t i = 0; i < M; ++i)
+    if (unsigned ip = ipiv[i]; i != ip)
+      for (ptrdiff_t j = 0; j < M; ++j) std::swap(R[ip, j], R[i, j]);
+
   // LU x = rhs
   // L y = rhs // L is UnitLowerTriangular
-  for (ptrdiff_t n = 0; n < N; ++n) {
-    for (ptrdiff_t m = 0; m < M; ++m) {
-      S Ymn = rhs[m, n];
-      for (ptrdiff_t k = 0; k < m; ++k) Ymn -= F[m, k] * rhs[k, n];
-      rhs[m, n] = Ymn;
-    }
-  }
+  for (ptrdiff_t m = 1; m < M; ++m) R[m, _] -= F[m, _(0, m)] * R[_(0, m), _];
   // U x = y
-  for (ptrdiff_t n = 0; n < N; ++n) {
-    for (auto m = ptrdiff_t(M); m--;) {
-      S Ymn = rhs[m, n];
-      for (ptrdiff_t k = m + 1; k < M; ++k) Ymn -= F[m, k] * rhs[k, n];
-      rhs[m, n] = Ymn / F[m, m];
-    }
-  }
+  R[last, _] /= F[last, last];
+  for (ptrdiff_t m = M - 1; m--;)
+    R[m, _] << (R[m, _] - F[m, _(m + 1, end)] * R[_(m + 1, end), _]) / F[m, m];
 }
 
 [[nodiscard]] constexpr auto rdivrat(SquarePtrMatrix<Rational> F,
                                      PtrVector<unsigned> ipiv,
                                      MutPtrMatrix<Rational> rhs) -> bool {
-  auto [M, N] = rhs.size();
+  auto [M, N] = shape(rhs);
   invariant(ptrdiff_t(F.numCol()), ptrdiff_t(N));
   // PA = LU
   // x LU = rhs
   // y U = rhs
-  for (ptrdiff_t n = 0; n < N; ++n) {
-    for (ptrdiff_t m = 0; m < M; ++m) {
+  for (ptrdiff_t m = 0; m < M; ++m) {
+    for (ptrdiff_t n = 0; n < N; ++n) {
       Rational Ymn = rhs[m, n];
       for (ptrdiff_t k = 0; k < n; ++k)
         if (Ymn.fnmadd(rhs[m, k], F[k, n])) return true;
@@ -87,9 +77,8 @@ constexpr void ldiv(SquarePtrMatrix<S> F, PtrVector<unsigned> ipiv,
     }
   }
   // x L = y
-  for (auto n = ptrdiff_t(N); n--;) {
-    // for (ptrdiff_t n = 0; n < N; ++n) {
-    for (ptrdiff_t m = 0; m < M; ++m) {
+  for (ptrdiff_t m = 0; m < M; ++m) {
+    for (ptrdiff_t n = N; n--;) {
       Rational Xmn = rhs[m, n];
       for (ptrdiff_t k = n + 1; k < N; ++k)
         if (Xmn.fnmadd(rhs[m, k], F[k, n])) return true;
@@ -97,38 +86,27 @@ constexpr void ldiv(SquarePtrMatrix<S> F, PtrVector<unsigned> ipiv,
     }
   }
   // permute rhs
-  for (auto j = ptrdiff_t(N); j--;) {
-    unsigned jp = ipiv[j];
-    if (j != jp)
+  for (auto j = ptrdiff_t(N); j--;)
+    if (unsigned jp = ipiv[j]; j != jp)
       for (ptrdiff_t i = 0; i < M; ++i) std::swap(rhs[i, jp], rhs[i, j]);
-  }
 
   return false;
 }
 template <class S>
 constexpr void rdiv(SquarePtrMatrix<S> F, PtrVector<unsigned> ipiv,
                     MutPtrMatrix<S> rhs) {
-  auto [M, N] = rhs.size();
-  invariant(ptrdiff_t(F.numCol()), ptrdiff_t(N));
+  auto [M, N] = shape(rhs);
+  invariant(ptrdiff_t(F.numCol()), N);
+  invariant(N > 0);
   // PA = LU
   // x LU = rhs
   // y U = rhs
-  for (ptrdiff_t n = 0; n < N; ++n) {
-    for (ptrdiff_t m = 0; m < M; ++m) {
-      S Ymn = rhs[m, n];
-      for (ptrdiff_t k = 0; k < n; ++k) Ymn -= rhs[m, k] * F[k, n];
-      rhs[m, n] = Ymn / F[n, n];
-    }
-  }
+  rhs[_, 0] /= F[0, 0];
+  for (ptrdiff_t n = 1; n < N; ++n)
+    rhs[_, n] << (rhs[_, n] - rhs[_, _(0, n)] * F[_(0, n), n]) / F[n, n];
   // x L = y
-  for (auto n = ptrdiff_t(N); n--;) {
-    // for (ptrdiff_t n = 0; n < N; ++n) {
-    for (ptrdiff_t m = 0; m < M; ++m) {
-      S Xmn = rhs[m, n];
-      for (ptrdiff_t k = n + 1; k < N; ++k) Xmn -= rhs[m, k] * F[k, n];
-      rhs[m, n] = Xmn;
-    }
-  }
+  for (ptrdiff_t n = N - 1; n--;)
+    rhs[_, n] -= rhs[_, _(n + 1, end)] * F[_(n + 1, end), n];
   // permute rhs
   for (auto j = ptrdiff_t(N); j--;)
     if (unsigned jp = ipiv[j]; j != jp)
@@ -169,8 +147,8 @@ template <class T, ptrdiff_t L> class Fact {
   }
   [[nodiscard]] constexpr auto perm() const -> Vector<unsigned> {
     Col M = F.numCol();
-    Vector<unsigned> perm;
-    for (ptrdiff_t m = 0; m < M; ++m) perm.push_back(m);
+    Vector<unsigned> perm{M};
+    for (ptrdiff_t m = 0; m < M; ++m) perm[m] = m;
     for (ptrdiff_t m = 0; m < M; ++m) std::swap(perm[m], perm[ipiv[m]]);
     return perm;
   }
@@ -187,16 +165,17 @@ template <ptrdiff_t L>
   auto ipiv{vector(alloc::Mallocator<unsigned>{}, ptrdiff_t(M))};
   // Vector<unsigned> ipiv{.s = unsigned(M)};
   invariant(ptrdiff_t(ipiv.size()), ptrdiff_t(M));
-  for (ptrdiff_t i = 0; i < M; ++i) ipiv[i] = i;
-  for (ptrdiff_t k = 0; k < M; ++k) {
+  for (ptrdiff_t k = 0;; ++k) {
     ptrdiff_t kp = k;
-    for (; kp < M; ++kp) {
+    for (;; ++kp) {
+      if (kp == M) return {};
       if (A[kp, k] == 0) continue;
       ipiv[k] = kp;
       break;
     }
     if (kp != k)
       for (ptrdiff_t j = 0; j < M; ++j) std::swap(A[kp, j], A[k, j]);
+    if (k + 1 == M) break;
     Rational invAkk = A[k, k].inv();
     for (ptrdiff_t i = k + 1; i < M; ++i)
       if (std::optional<Rational> Aik = A[i, k].safeMul(invAkk)) A[i, k] = *Aik;
@@ -216,23 +195,22 @@ template <ptrdiff_t L>
   return Fact<Rational, L>{std::move(A), std::move(ipiv)};
 }
 template <typename S> constexpr auto factImpl(MutSquarePtrMatrix<S> A) {
+  using V = decltype(value(S{}));
   Row M = A.numRow();
   auto ipiv{vector(alloc::Mallocator<unsigned>{}, ptrdiff_t(M))};
   invariant(ptrdiff_t(ipiv.size()), ptrdiff_t(M));
-  for (ptrdiff_t i = 0; i < M; ++i) ipiv[i] = i;
-  for (ptrdiff_t k = 0; k < M; ++k) {
-    ptrdiff_t kp = k;
-    for (; kp < M; ++kp) {
-      if (A[kp, k] == 0) continue;
-      ipiv[k] = kp;
-      break;
-    }
-    if (kp != k)
-      for (ptrdiff_t j = 0; j < M; ++j) std::swap(A[kp, j], A[k, j]);
+  for (ptrdiff_t k = 0;; ++k) {
+    containers::Pair<ptrdiff_t, V> mi{-1, {}};
+    for (ptrdiff_t i = k; i < M; ++i)
+      if (V v = std::abs(value(A[i, k])); v > mi.second) mi = {i, v};
+    invariant(mi.first >= 0); // TODO: return info?
+    ipiv[k] = mi.first;
+    if (mi.first != k)
+      for (ptrdiff_t j = 0; j < M; ++j) std::swap(A[mi.first, j], A[k, j]);
+    if (k + 1 == M) break;
     S invAkk = 1.0 / A[k, k];
-    for (ptrdiff_t i = k + 1; i < M; ++i) A[i, k] = A[i, k] * invAkk;
     for (ptrdiff_t i = k + 1; i < M; ++i)
-      for (ptrdiff_t j = k + 1; j < M; ++j) A[i, j] -= A[i, k] * A[k, j];
+      A[i, _(k + 1, end)] -= (A[i, k] *= invAkk) * A[k, _(k + 1, end)];
   }
   return ipiv;
 }
@@ -278,55 +256,49 @@ namespace LDL {
 /// NOT OWNING
 /// TODO: make the API consistent between LU and LDL
 template <typename T> class Fact {
-  MutSquarePtrMatrix<T> fact;
+  MutSquarePtrMatrix<T> F;
 
 public:
-  constexpr Fact(MutSquarePtrMatrix<T> A) : fact{A} {};
+  constexpr Fact(MutSquarePtrMatrix<T> A) : F{A} {};
 
-  constexpr void ldiv(MutPtrMatrix<T> rhs) {
-    ptrdiff_t M = ptrdiff_t(rhs.numRow());
-    invariant(ptrdiff_t(fact.numRow()), M);
+  constexpr void ldiv(MutPtrMatrix<T> R) {
+    ptrdiff_t M = ptrdiff_t(R.numRow());
+    invariant(ptrdiff_t(F.numRow()), M);
     // LD^-1L' x = rhs
     // L y = rhs // L is UnitLowerTriangular
-    for (ptrdiff_t m = 0; m < M; ++m)
-      rhs[m, _] -= rhs[_(0, m), _].transpose() * fact[m, _(0, m)];
-
+    for (ptrdiff_t m = 1; m < M; ++m) R[m, _] -= F[m, _(0, m)] * R[_(0, m), _];
     // D^-1 L' x = y
     // L' x = D y
-    for (ptrdiff_t m = M; m--;) {
-      rhs[m, _] *= fact[m, m];
-      rhs[m, _] -= rhs[_(m + 1, M), _].transpose() * fact[_(m + 1, M), m];
-    }
+    R[last, _] *= F[last, last];
+    for (ptrdiff_t m = M - 1; m--;)
+      R[m, _] << R[m, _] * F[m, m] - F[_(m + 1, M), m].t() * R[_(m + 1, M), _];
   }
-  constexpr void ldiv(MutPtrVector<T> rhs) {
-    ptrdiff_t M = rhs.size();
-    invariant(ptrdiff_t(fact.numRow()), M);
+  constexpr void ldiv(MutPtrVector<T> R) {
+    ptrdiff_t M = R.size();
+    invariant(ptrdiff_t(F.numRow()), M);
     // LD^-1L' x = rhs
     // L y = rhs // L is UnitLowerTriangular
-    for (ptrdiff_t m = 0; m < M; ++m)
-      rhs[m] -= fact[m, _(0, m)].transpose() * rhs[_(0, m)];
+    for (ptrdiff_t m = 1; m < M; ++m) R[m] -= R[_(0, m)] * F[m, _(0, m)].t();
     // D^-1 L' x = y
     // L' x = D y
-    for (ptrdiff_t m = M; m--;) {
-      rhs[m] *= fact[m, m];
-      rhs[m] -= fact[_(m + 1, M), m].transpose() * rhs[_(m + 1, M)];
-    }
+    R[last] *= F[last, last];
+    for (ptrdiff_t m = M - 1; m--;)
+      R[m] = R[m] * F[m, m] - R[_(m + 1, M)] * F[_(m + 1, M), m];
   }
   constexpr void ldiv(MutPtrVector<T> dst, TrivialVec auto src) {
     ptrdiff_t M = dst.size();
-    invariant(M == src.size());
-    invariant(ptrdiff_t(fact.numRow()), M);
+    invariant(M, ptrdiff_t(src.size()));
+    invariant(ptrdiff_t(F.numRow()), M);
     // LD^-1L' x = rhs
     // L y = rhs // L is UnitLowerTriangular
-    for (ptrdiff_t m = 0; m < M; ++m)
-      dst[m] = src[m] - fact[m, _(0, m)].transpose() * dst[_(0, m)];
-
+    dst[0] = src[0];
+    for (ptrdiff_t m = 1; m < M; ++m)
+      dst[m] = src[m] - dst[_(0, m)] * F[m, _(0, m)].t();
     // D^-1 L' x = y
     // L' x = D y
-    for (ptrdiff_t m = M; m--;) {
-      dst[m] *= fact[m, m];
-      dst[m] -= fact[_(m + 1, M), m].transpose() * dst[_(m + 1, M)];
-    }
+    dst[last] *= F[last, last];
+    for (ptrdiff_t m = M - 1; m--;)
+      dst[m] = dst[m] * F[m, m] - dst[_(m + 1, M)] * F[_(m + 1, M), m];
   }
 };
 
@@ -334,15 +306,14 @@ template <bool ForcePD = false, typename T>
 constexpr auto factorize(MutSquarePtrMatrix<T> A) -> Fact<T> {
   Row M = A.numRow();
   invariant(ptrdiff_t(M), ptrdiff_t(A.numCol()));
-  for (ptrdiff_t k = 0; k < M; ++k) {
+  for (ptrdiff_t k = 0;; ++k) {
     T Akk = A[k, k];
     if constexpr (ForcePD) Akk = std::max(Akk, T(0.001));
     T invAkk = A[k, k] = 1.0 / Akk;
+    if (k + 1 == M) break;
     A[_(k + 1, M), k] *= invAkk;
-    for (ptrdiff_t i = k + 1; i < M; ++i) {
-      T Aik = A[i, k] * Akk;
-      for (ptrdiff_t j = k + 1; j <= i; ++j) A[i, j] -= Aik * A[j, k];
-    }
+    for (ptrdiff_t i = k + 1; i < M; ++i)
+      A[i, _(k + 1, i + 1)] -= (A[i, k] * Akk) * A[_(k + 1, i + 1), k];
   }
   return Fact{A};
 }
diff --git a/include/Math/Math.hpp b/include/Math/Math.hpp
index 1a66e22..55a0425 100644
--- a/include/Math/Math.hpp
+++ b/include/Math/Math.hpp
@@ -7,6 +7,7 @@
 #include "Math/Indexing.hpp"
 #include "Math/Matrix.hpp"
 #include "Math/MatrixDimensions.hpp"
+#include "Utilities/LoopMacros.hpp"
 #include "Utilities/Parameters.hpp"
 #include "Utilities/TypePromotion.hpp"
 #include <algorithm>
@@ -18,11 +19,10 @@
 #include <utility>
 
 namespace poly::math {
+/// Extract the value of a `Dual` number
+constexpr auto value(std::floating_point auto x) { return x; }
 struct Rational;
 
-template <class A>
-concept VecOrMat = AbstractVector<A> || AbstractMatrix<A>;
-
 template <class T, class C>
 concept RangeOffsetPair =
   (std::convertible_to<T, Range<ptrdiff_t, ptrdiff_t>> &&
@@ -32,14 +32,15 @@ concept RangeOffsetPair =
 
 template <class T, class C>
 concept Compatible =
-  (VecOrMat<C> && std::convertible_to<T, utils::eltype_t<C>>) ||
-  (VecOrMat<T> && std::convertible_to<C, utils::eltype_t<T>>) ||
+  (AbstractTensor<C> && std::convertible_to<T, utils::eltype_t<C>>) ||
+  (AbstractTensor<T> && std::convertible_to<C, utils::eltype_t<T>>) ||
   (AbstractVector<C> && AbstractVector<T>) ||
   (AbstractMatrix<C> && AbstractMatrix<T>);
 
 template <class A, class B> struct ElTypes {
   using eltype =
-    std::conditional_t<VecOrMat<B> & std::convertible_to<A, utils::eltype_t<B>>,
+    std::conditional_t<AbstractTensor<B> &
+                         std::convertible_to<A, utils::eltype_t<B>>,
                        A, utils::eltype_t<A>>;
 };
 // returns the element type of `A` when used in a binary op with `B`
@@ -51,14 +52,11 @@ concept Trivial =
 template <typename T, typename C>
 concept TrivialCompatible = Trivial<T> && Compatible<T, C>;
 template <typename T>
-concept TrivialVecOrMat = Trivial<T> && VecOrMat<T>;
+concept TrivialTensor = Trivial<T> && AbstractTensor<T>;
 template <typename T>
 concept TrivialVec = Trivial<T> && AbstractVector<T>;
 template <typename T>
 concept TrivialMat = Trivial<T> && AbstractMatrix<T>;
-template <typename T>
-concept TrivialDataMatrix = Trivial<T> && DataMatrix<T>;
-
 //   // TODO: binary func invocable trait?
 // template <typename Op, typename T, typename S>
 // concept BinaryFunction = std::is_invocable_v<Op, T, S>;
@@ -67,6 +65,7 @@ template <typename Op, typename A, typename B>
 concept BinaryFuncOfElts =
   std::is_invocable_v<Op, indextype_t<A, B>, indextype_t<B, A>>;
 
+// TODO: make this part of ArrayOps!!!
 [[gnu::flatten]] constexpr auto operator==(const AbstractMatrix auto &A,
                                            const AbstractMatrix auto &B)
   -> bool {
@@ -82,48 +81,43 @@ concept BinaryFuncOfElts =
 template <typename Op, typename A> struct Elementwise {
   using value_type =
     decltype(std::declval<Op>()(std::declval<utils::eltype_t<A>>()));
+  static constexpr bool has_reduction_loop = HasInnerReduction<A>;
   [[no_unique_address]] Op op;
   [[no_unique_address]] A a;
-  constexpr auto operator[](ptrdiff_t i) const { return op(a[i]); }
-  constexpr auto operator[](ptrdiff_t i, ptrdiff_t j) const
-  requires(AbstractMatrix<A>)
+  constexpr auto operator[](auto i) const
+  requires(LinearlyIndexableOrConvertible<A, value_type>)
+  {
+    return op(a[i]);
+  }
+  constexpr auto operator[](auto i, auto j) const
+  requires(CartesianIndexableOrConvertible<A, value_type>)
   {
     return op(a[i, j]);
   }
 
-  [[nodiscard]] constexpr auto size() const { return a.size(); }
-  [[nodiscard]] constexpr auto dim() const { return a.dim(); }
-  [[nodiscard]] constexpr auto numRow() const -> Row<>
-  requires(AbstractMatrix<A>)
+  [[nodiscard]] constexpr auto size() const
+  requires(DefinesSize<A>)
+  {
+    return a.size();
+  }
+  [[nodiscard]] constexpr auto numRow() const
+  requires(DefinesShape<A>)
   {
     return a.numRow();
   }
-  [[nodiscard]] constexpr auto numCol() const -> Col<>
-  requires(AbstractMatrix<A>)
+  [[nodiscard]] constexpr auto numCol() const
+  requires(DefinesShape<A>)
   {
     return a.numCol();
   }
   [[nodiscard]] constexpr auto view() const { return *this; };
+  template <typename T> constexpr auto reinterpret() {
+    auto ra = math::reinterpret<T>(a);
+    return Elementwise<Op, decltype(ra)>(op, ra);
+  }
 };
 template <typename Op, typename A> Elementwise(Op, A) -> Elementwise<Op, A>;
 
-// scalars broadcast
-template <typename S> constexpr auto get(const S &s, ptrdiff_t) -> S {
-  return s;
-}
-template <typename S>
-constexpr auto get(const S &s, ptrdiff_t, ptrdiff_t) -> S {
-  return s;
-}
-template <typename S, LinearlyIndexable<S> V>
-constexpr auto get(const V &v, ptrdiff_t i) -> S {
-  return v[i];
-}
-template <typename S, CartesianIndexable<S> V>
-constexpr auto get(const V &v, ptrdiff_t i, ptrdiff_t j) -> S {
-  return v[i, j];
-}
-
 constexpr auto size(const std::integral auto) -> ptrdiff_t { return 1; }
 constexpr auto size(const std::floating_point auto) -> ptrdiff_t { return 1; }
 constexpr auto size(const AbstractVector auto &x) -> ptrdiff_t {
@@ -156,118 +150,141 @@ struct ElementwiseBinaryOp {
   using elta = indextype_t<A, B>;
   using eltb = indextype_t<B, A>;
 
-  using value_type =
-    decltype(std::declval<Op>()(std::declval<elta>(), std::declval<eltb>()));
-  // using value_type = utils::promote_eltype_t<A, B>;
+  static constexpr bool has_reduction_loop =
+    HasInnerReduction<A> || HasInnerReduction<B>;
+  using common = std::common_type_t<elta, eltb>;
+  using value_type = decltype(std::declval<Op>()(std::declval<common>(),
+                                                 std::declval<common>()));
   using concrete = is_concrete_t<A, B>;
   static constexpr bool isvector = AbstractVector<A> || AbstractVector<B>;
   static constexpr bool ismatrix = AbstractMatrix<A> || AbstractMatrix<B>;
+  static_assert(isvector != ismatrix);
 
   [[no_unique_address]] Op op;
   [[no_unique_address]] A a;
   [[no_unique_address]] B b;
-  constexpr auto operator[](ptrdiff_t i) const -> value_type
-  requires LinearlyIndexableOrConvertible<A, elta> &&
-           LinearlyIndexableOrConvertible<B, eltb>
+  constexpr auto operator[](auto i) const
+  requires LinearlyIndexableOrConvertible<A, common> &&
+           LinearlyIndexableOrConvertible<B, common>
   {
-    return op(get<elta>(a, i), get<eltb>(b, i));
+    if constexpr (LinearlyIndexable<A, common>)
+      if constexpr (LinearlyIndexable<B, common>) return op(a[i], b[i]);
+      else return op(a[i], b);
+    else if constexpr (LinearlyIndexable<B, common>) return op(a, b[i]);
+    else return op(a, b);
   }
-  constexpr auto operator[](ptrdiff_t i, ptrdiff_t j) const -> value_type
-  requires CartesianIndexableOrConvertible<A, elta> &&
-           CartesianIndexableOrConvertible<B, eltb>
-  {
-    return op(get<elta>(a, i, j), get<eltb>(b, i, j));
+  constexpr auto operator[](auto i, auto j) const {
+    if constexpr (CartesianIndexable<A, common>)
+      if constexpr (CartesianIndexable<B, common>) return op(a[i, j], b[i, j]);
+      else if constexpr (std::convertible_to<B, common>) return op(a[i, j], b);
+      else if constexpr (RowVector<B>) return op(a[i, j], b[j]);
+      else return op(a[i, j], b[i]);
+    else if constexpr (std::convertible_to<A, common>)
+      if constexpr (CartesianIndexable<B, common>) return op(a, b[i, j]);
+      else if constexpr (std::convertible_to<B, common>) return op(a, b);
+      else if constexpr (RowVector<B>) return op(a, b[j]);
+      else return op(a, b[i]);
+    else if constexpr (RowVector<A>)
+      if constexpr (CartesianIndexable<B, common>) return op(a[j], b[i, j]);
+      else if constexpr (std::convertible_to<B, common>) return op(a[j], b);
+      else if constexpr (RowVector<B>) return op(a[j], b[j]);
+      else return op(a[j], b[i]);
+    else if constexpr (CartesianIndexable<B, common>) return op(a[i], b[i, j]);
+    else if constexpr (std::convertible_to<B, common>) return op(a[i], b);
+    else if constexpr (RowVector<B>) return op(a[i], b[j]);
+    else return op(a[i], b[i]);
   }
 
-  [[nodiscard]] constexpr auto numRow() const -> Row<>
+  [[nodiscard]] constexpr auto numRow() const
   requires(ismatrix)
   {
     if constexpr (AbstractMatrix<A> && AbstractMatrix<B>) {
       if constexpr (HasConcreteSize<A>)
-        if constexpr (HasConcreteSize<B>) {
-          const Row N = a.numRow();
-          invariant(N, b.numRow());
-          return N;
-        } else return a.numRow();
+        if constexpr (HasConcreteSize<B>)
+          return row(check_sizes(unwrapRow(a.numRow()), unwrapRow(b.numRow())));
+        else return a.numRow();
       else if constexpr (HasConcreteSize<B>) return b.numRow();
       else return Row<>{0};
     } else if constexpr (AbstractMatrix<A>) return a.numRow();
-    else if constexpr (AbstractMatrix<B>) return b.numRow();
+    else return b.numRow();
   }
-  [[nodiscard]] constexpr auto numCol() const -> Col<>
+  [[nodiscard]] constexpr auto numCol() const
   requires(ismatrix)
   {
     if constexpr (AbstractMatrix<A> && AbstractMatrix<B>) {
       if constexpr (HasConcreteSize<A>)
-        if constexpr (HasConcreteSize<B>) {
-          const Col N = a.numCol();
-          invariant(N, b.numCol());
-          return N;
-        } else return a.numCol();
+        if constexpr (HasConcreteSize<B>)
+          return col(check_sizes(unwrapCol(a.numCol()), unwrapCol(b.numCol())));
+        else return a.numCol();
       else if constexpr (HasConcreteSize<B>) return b.numCol();
       else return Col<>{0};
     } else if constexpr (AbstractMatrix<A>) return a.numCol();
-    else if constexpr (AbstractMatrix<B>) return b.numCol();
-  }
-  [[nodiscard]] constexpr auto dim() const {
-    if constexpr (isvector) return size();
-    else return DenseDims{numRow(), numCol()};
+    else return b.numCol();
   }
-
   [[nodiscard]] constexpr auto size() const {
-    if constexpr (AbstractVector<A> && AbstractVector<B>) {
-      const ptrdiff_t N = a.size();
-      invariant(N == b.size());
-      return N;
-    } else if constexpr (AbstractVector<A>) return ptrdiff_t(a.size());
-    else if constexpr (AbstractVector<B>) return ptrdiff_t(b.size());
-    else
-      return CartesianIndex<ptrdiff_t, ptrdiff_t>{ptrdiff_t(numRow()),
-                                                  ptrdiff_t(numCol())};
+    if constexpr (ismatrix) return unwrapRow(numRow()) * unwrapCol(numCol());
+    else if constexpr (AbstractVector<A> && AbstractVector<B>)
+      return check_sizes(a.size(), b.size());
+    else if constexpr (AbstractVector<A>) return a.size();
+    else return b.size();
   }
   [[nodiscard]] constexpr auto view() const -> auto & { return *this; };
+  template <typename T> constexpr auto reinterpret() {
+    auto ra = math::reinterpret<T>(a);
+    auto rb = math::reinterpret<T>(b);
+    return ElementwiseBinaryOp<decltype(ra), decltype(rb), Op>(op, ra, rb);
+  }
 };
 
-template <TrivialVecOrMat C, Trivial A, Trivial B> struct AbstractSelect {
+template <TrivialTensor C, Trivial A, Trivial B> struct AbstractSelect {
   using value_type = std::common_type_t<utils::eltype_t<A>, utils::eltype_t<B>>;
   static constexpr bool isvector = AbstractVector<C>;
-  static constexpr bool ismatrix = AbstractMatrix<C>;
   [[no_unique_address]] C c;
   [[no_unique_address]] A a;
   [[no_unique_address]] B b;
 
-  [[nodiscard]] constexpr auto numRow() const -> Row<>
-  requires(ismatrix)
-  {
-    Row m = c.numRow();
-    if constexpr (AbstractMatrix<A>) invariant(m, a.numRow());
-    if constexpr (AbstractMatrix<B>) invariant(m, b.numRow());
-    return m;
-  }
-  [[nodiscard]] constexpr auto numCol() const -> Col<>
-  requires(ismatrix)
+  [[nodiscard]] constexpr auto numRow() const
+  requires(!isvector)
   {
-    Col n = c.numCol();
-    if constexpr (AbstractMatrix<A>) invariant(n, a.numCol());
-    if constexpr (AbstractMatrix<B>) invariant(n, b.numCol());
-    return n;
+    auto n = unwrapRow(c.numRow());
+    if constexpr (AbstractMatrix<A>) {
+      auto nn = check_sizes(n, unwrapRow(a.numRow()));
+      if constexpr (AbstractMatrix<B>)
+        return row(check_sizes(nn, unwrapRow(b.numRow())));
+      else return row(nn);
+    } else if (AbstractMatrix<B>)
+      return row(check_sizes(n, unwrapRow(b.numRow())));
+    else return row(n);
   }
-  [[nodiscard]] constexpr auto dim() const -> DenseDims<>
-  requires(ismatrix)
+  [[nodiscard]] constexpr auto numCol() const
+  requires(!isvector)
   {
-    return {numRow(), numCol()};
+    auto n = unwrapCol(c.numCol());
+    if constexpr (AbstractMatrix<A>) {
+      auto nn = check_sizes(n, unwrapCol(a.numCol()));
+      if constexpr (AbstractMatrix<B>)
+        return col(check_sizes(nn, unwrapCol(b.numCol())));
+      else return col(nn);
+    } else if (AbstractMatrix<B>)
+      return col(check_sizes(n, unwrapCol(b.numCol())));
+    else return col(n);
   }
   [[nodiscard]] constexpr auto size() const {
-    if constexpr (ismatrix)
-      return CartesianIndex<Row<>, Col<>>{numRow(), numCol()};
-    else {
-      ptrdiff_t N = c.size();
-      if constexpr (AbstractVector<A>) invariant(ptrdiff_t(a.size()), N);
-      if constexpr (AbstractVector<B>) invariant(ptrdiff_t(b.size()), N);
-      return N;
+    if constexpr (!isvector) {
+      return unwrapRow(numRow()) * unwrapCol(numCol());
+    } else {
+      auto N = c.size();
+      if constexpr (AbstractVector<A>) {
+        auto M = check_sizes(N, a.size());
+        if constexpr (AbstractVector<B>) return check_sizes(M, b.size());
+        else return M;
+      } else if constexpr (AbstractVector<B>) {
+        return check_sizes(N, b.size());
+      } else {
+        return N;
+      }
     }
   }
-  [[nodiscard]] constexpr auto view() const -> auto & { return *this; };
 };
 
 inline constexpr auto view(const Trivial auto &x) { return x; }
@@ -275,40 +292,52 @@ inline constexpr auto view(const auto &x) { return x.view(); }
 template <class T, class S> constexpr auto view(const Array<T, S> &x) {
   return x;
 }
-constexpr auto transpose(const auto &a) { return Transpose{view(a)}; }
-template <typename T> constexpr auto transpose(const Transpose<T> &a) -> T {
-  return a.transpose();
-}
 
-template <TrivialVecOrMat C, Trivial A, Trivial B>
+template <TrivialTensor C, Trivial A, Trivial B>
 struct Select : public AbstractSelect<C, A, B> {
   using value_type = AbstractSelect<C, A, B>::value_type;
-  constexpr auto operator[](ptrdiff_t i) const -> value_type
-  requires LinearlyIndexableOrConvertible<C, bool> &&
+  static constexpr bool has_reduction_loop =
+    HasInnerReduction<A> || HasInnerReduction<B>;
+  constexpr auto operator[](auto i) const
+  requires LinearlyIndexable<C, bool> &&
            LinearlyIndexableOrConvertible<A, value_type> &&
            LinearlyIndexableOrConvertible<B, value_type>
   {
-    return get<bool>(this->c, i) ? get<value_type>(this->a, i)
-                                 : get<value_type>(this->b, i);
+    if constexpr (LinearlyIndexable<A, value_type>)
+      if constexpr (LinearlyIndexable<B, value_type>)
+        return this->c[i] ? this->a[i] : this->b[i];
+      else return this->c[i] ? this->a[i] : this->b;
+    else if constexpr (LinearlyIndexable<B, value_type>)
+      return this->c[i] ? this->a : this->b[i];
+    else return this->c[i] ? this->a : this->b;
   }
-  constexpr auto operator[](ptrdiff_t i, ptrdiff_t j) const -> value_type
+  constexpr auto operator[](auto i, auto j) const
   requires CartesianIndexableOrConvertible<C, bool> &&
            CartesianIndexableOrConvertible<A, value_type> &&
            CartesianIndexableOrConvertible<B, value_type>
   {
-    return get<bool>(this->c, i, j) ? get<value_type>(this->a, i, j)
-                                    : get<value_type>(this->b, i, j);
+    if constexpr (CartesianIndexable<A, value_type>)
+      if constexpr (CartesianIndexable<B, value_type>)
+        return this->c[i, j] ? this->a[i, j] : this->b[i, j];
+      else return this->c[i, j] ? this->a[i, j] : this->b;
+    else if constexpr (CartesianIndexable<B, value_type>)
+      return this->c[i, j] ? this->a : this->b[i, j];
+    else return this->c[i, j] ? this->a : this->b;
   }
+  [[nodiscard]] constexpr auto view() const -> Select { return *this; };
 };
-template <TrivialVecOrMat C, Trivial A, Trivial B>
+template <TrivialTensor C, Trivial A, Trivial B>
 Select(C c, A a, B b) -> Select<C, A, B>;
-constexpr auto select(const VecOrMat auto &c, const auto &a, const auto &b) {
+constexpr auto select(const AbstractTensor auto &c, const auto &a,
+                      const auto &b) {
   return Select(view(c), view(a), view(b));
 }
 
-template <TrivialVecOrMat C, Trivial A, Trivial B, BinaryFuncOfElts<A, B> Op>
+template <TrivialTensor C, Trivial A, Trivial B, BinaryFuncOfElts<A, B> Op>
 struct Conditional : public AbstractSelect<C, A, B> {
   using value_type = AbstractSelect<C, A, B>::value_type;
+  static constexpr bool has_reduction_loop =
+    HasInnerReduction<A> || HasInnerReduction<B>;
   [[no_unique_address]] Op op;
 
   constexpr auto operator[](ptrdiff_t i) const -> value_type
@@ -316,19 +345,89 @@ struct Conditional : public AbstractSelect<C, A, B> {
            LinearlyIndexableOrConvertible<A, value_type> &&
            LinearlyIndexableOrConvertible<B, value_type>
   {
-    auto x = get<value_type>(this->a, i);
-    return get<bool>(this->c, i) ? op(x, get<value_type>(this->b, i)) : x;
+    if constexpr (LinearlyIndexable<A, value_type>)
+      if constexpr (LinearlyIndexable<B, value_type>)
+        return this->c[i] ? op(this->a[i], this->b[i]) : this->a[i];
+      else return this->c[i] ? op(this->a[i], this->b) : this->a[i];
+    else if constexpr (LinearlyIndexable<B, value_type>)
+      return this->c[i] ? op(this->a, this->b[i]) : this->a;
+    else return this->c[i] ? op(this->a, this->b) : this->a;
+  }
+  template <ptrdiff_t U, ptrdiff_t W, typename M>
+  constexpr auto operator[](simd::index::Unroll<U, W, M> i) const
+  requires LinearlyIndexableOrConvertible<C, bool> &&
+           LinearlyIndexableOrConvertible<A, value_type> &&
+           LinearlyIndexableOrConvertible<B, value_type>
+  {
+    if constexpr (W == 1) {
+      auto c = this->c[i];
+      simd::Unroll<U, 1, 1, value_type> x = get<value_type>(this->a, i),
+                                        y = op(x, get<value_type>(this->b, i));
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t u = 0; u < U; ++u)
+        x.data[u] = c.data[u] ? y.data[u] : x.data[u];
+      return x;
+    } else if constexpr (LinearlyIndexable<A, value_type>) {
+      auto c = get<bool>(this->c, i);
+      simd::Unroll<1, U, W, value_type> x = get<value_type>(this->a, i),
+                                        y = op(x, get<value_type>(this->b, i));
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t u = 0; u < U; ++u)
+        x.data[u] = c.data[u] ? y.data[u] : x.data[u];
+      return x;
+    } else if constexpr (LinearlyIndexable<B, value_type>) {
+      auto c = this->c[i];
+      using V = simd::Vec<W, value_type>;
+      value_type x_ = get<value_type>(this->a, i);
+      V x = simd::vbroadcast<W, value_type>(x_);
+      simd::Unroll<1, U, W, value_type> y = op(x, get<value_type>(this->b, i));
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t u = 0; u < U; ++u)
+        if constexpr (LinearlyIndexable<B, value_type>)
+          y.data[u] = c.data[u] ? y.data[u] : x;
+      return y;
+    } else {
+      auto c = this->c[i];
+      using V = simd::Vec<W, value_type>;
+      value_type x_ = get<value_type>(this->a, i);
+      value_type y_ = op(x_, get<value_type>(this->b, i));
+      V x = simd::vbroadcast<W, value_type>(x_),
+        y = simd::vbroadcast<W, value_type>(y_);
+      simd::Unroll<1, U, W, value_type> z;
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t u = 0; u < U; ++u) z.data[u] = c.data[u] ? y : x;
+      return z;
+    }
+    //   auto c = get<bool>(this->c, i);
+    //   auto x = get<value_type>(this->a, i);
+    //   auto y = op(x, get<value_type>(this->b, i));
+    //   simd::Unroll<1, U, W, value_type> z;
+    //   POLYMATHFULLUNROLL
+    //   for (ptrdiff_t u = 0; u < U; ++u)
+    //     if constexpr (LinearlyIndexable<A, value_type>)
+    //       z.data[u] = !c.data[u] ? x.data[u] : y.data[u];
+    //     else if constexpr (LinearlyIndexable<B, value_type>)
+    //       z.data[u] = !c.data[u] ? x : y.data[u];
+    //     else z.data[u] = c.data[u] ? y : x;
+    //   return z;
+    // }
   }
-  constexpr auto operator[](ptrdiff_t i, ptrdiff_t j) const -> value_type
+  constexpr auto operator[](auto i, auto j) const
   requires CartesianIndexableOrConvertible<C, bool> &&
            CartesianIndexableOrConvertible<A, value_type> &&
            CartesianIndexableOrConvertible<B, value_type>
   {
-    auto x = get<value_type>(this->a, i, j);
-    return get<bool>(this->c, i, j) ? op(x, get<value_type>(this->b, i, j)) : x;
+    if constexpr (LinearlyIndexable<A, value_type>)
+      if constexpr (LinearlyIndexable<B, value_type>)
+        return this->c[i, j] ? op(this->a[i, j], this->b[i, j]) : this->a[i, j];
+      else return this->c[i, j] ? op(this->a[i, j], this->b) : this->a[i, j];
+    else if constexpr (LinearlyIndexable<B, value_type>)
+      return this->c[i, j] ? op(this->a, this->b[i, j]) : this->a;
+    else return this->c[i, j] ? op(this->a, this->b) : this->a;
   }
+  [[nodiscard]] constexpr auto view() const -> Conditional { return *this; };
 };
-constexpr auto conditional(auto op, const VecOrMat auto &c, const auto &a,
+constexpr auto conditional(auto op, const AbstractTensor auto &c, const auto &a,
                            const auto &b) {
   auto vc = view(c);
   auto va = view(a);
@@ -337,47 +436,94 @@ constexpr auto conditional(auto op, const VecOrMat auto &c, const auto &a,
     {vc, va, vb}, op};
 }
 
-template <AbstractMatrix A, AbstractMatrix B> struct MatMatMul {
+template <AbstractTensor A, AbstractTensor B> struct MatMatMul {
   using value_type = utils::promote_eltype_t<A, B>;
   using concrete = is_concrete_t<A, B>;
+  static constexpr bool has_reduction_loop = true;
+  static constexpr bool ismata = AbstractMatrix<A>;
+  static constexpr bool ismatb = AbstractMatrix<B>;
+  static_assert((ismata && (ismatb || ColVector<B>)) ||
+                (RowVector<A> && ismatb) || (ColVector<A> && RowVector<B>));
+  static constexpr bool ismatrix = ismata && ismatb;
+  // we could have
+  // ColVector * RowVector
+  // RowVector * Matrix
+  // Matrix * ColVector
+  // Matrix * Matrix
   [[no_unique_address]] A a;
   [[no_unique_address]] B b;
-  constexpr auto operator[](ptrdiff_t i, ptrdiff_t j) const -> value_type {
+  [[gnu::always_inline]] constexpr auto operator[](auto i, auto j) const
+  requires(ismatrix)
+  {
     static_assert(AbstractMatrix<B>, "B should be an AbstractMatrix");
-    value_type s{};
+    invariant(ptrdiff_t(a.numCol()) > 0);
+    decltype(a[i, 0] * b[0, j] + a[i, 1] * b[1, j]) s{};
+    POLYMATHNOVECTORIZE
     for (ptrdiff_t k = 0; k < ptrdiff_t(a.numCol()); ++k)
       s += a[i, k] * b[k, j];
     return s;
   }
-  [[nodiscard]] constexpr auto numRow() const -> Row<> { return a.numRow(); }
-  [[nodiscard]] constexpr auto numCol() const -> Col<> { return b.numCol(); }
-  [[nodiscard]] constexpr auto size() const
-    -> CartesianIndex<ptrdiff_t, ptrdiff_t> {
-    invariant(ptrdiff_t(a.numCol()) == ptrdiff_t(b.numRow()));
-    return {ptrdiff_t(numRow()), ptrdiff_t(numCol())};
+  // If `T isa Dual<Dual<double,7>,2>`, we would not want to construct
+  // intermediates that require masked loads/stores, as compilers have
+  // trouble optimizing these away.
+  // We can imagine two strategies for avoiding this:
+  // 1. Do not write/construct any intermediates, but write into the result
+  // directly.
+  // 2. Decompress/compress on load/store, so temporaries do not need masks.
+  // `1.` seems ideal, but harder to implement.
+  // For example, here, `s` would have to alias the result. Then we also have
+  // `s +=`, which would have to invoke somehow call
+  // `Dual<Dual<double,7>,2>::operator+=` without storing.
+  // Or, we'd need a method that can see through it, so we operate on the
+  // teminal values, but still in one go to only have one instance of the
+  // reduction loop. Thus, `1.` seems conceptually simple but without a clear
+  // implementation strategy.
+  //
+  //
+  [[gnu::always_inline]] constexpr auto operator[](auto i) const
+  requires(!ismatrix)
+  {
+    if constexpr (RowVector<A>) {
+      invariant(a.size() == b.numRow());
+      invariant(a.size() > 0);
+      decltype(a[0] * b[0, i] + a[1] * b[1, i]) s{};
+      POLYMATHNOVECTORIZE
+      for (ptrdiff_t k = 0; k < a.numCol(); ++k) {
+        POLYMATHFAST
+        s += a[k] * b[k, i];
+      }
+      return s;
+    } else { // ColVector<B>
+      invariant(a.numCol() == b.size());
+      invariant(b.size() > 0);
+      decltype(a[i, 0] * b[0] + a[i, 1] * b[1]) s{};
+      for (ptrdiff_t k = 0; k < a.numCol(); ++k) {
+        POLYMATHFAST
+        s += a[i, k] * b[k];
+      }
+      return s;
+    }
   }
-  [[nodiscard]] constexpr auto dim() const -> DenseDims<> {
-    invariant(ptrdiff_t(a.numCol()) == ptrdiff_t(b.numRow()));
-    return {numRow(), numCol()};
+  [[nodiscard]] constexpr auto numRow() const
+  requires(ismatrix)
+  {
+    return a.numRow();
   }
-  [[nodiscard]] constexpr auto view() const { return *this; };
-  [[nodiscard]] constexpr auto transpose() const { return Transpose{*this}; };
-};
-template <AbstractMatrix A, AbstractVector B> struct MatVecMul {
-  using value_type = utils::promote_eltype_t<A, B>;
-  using concrete = is_concrete_t<A, B>;
-  [[no_unique_address]] A a;
-  [[no_unique_address]] B b;
-  constexpr auto operator[](ptrdiff_t i) const -> value_type {
-    invariant(a.numCol() == b.size());
-    value_type s = 0;
-    for (ptrdiff_t k = 0; k < a.numCol(); ++k) s += a[i, k] * b[k];
-    return s;
+  [[nodiscard]] constexpr auto numCol() const
+  requires(ismatrix)
+  {
+    return b.numCol();
   }
-  [[nodiscard]] constexpr auto size() const -> ptrdiff_t {
-    return ptrdiff_t(a.numRow());
+  [[nodiscard]] constexpr auto size() const {
+    if constexpr (ismata)
+      if constexpr (ismatb)
+        return unwrapRow(a.numRow()) * unwrapCol(b.numCol());
+      else return unwrapRow(a.numRow());
+    else if constexpr (RowVector<A>) return unwrapCol(b.numCol());
+    else a.size() * b.size();
   }
-  constexpr auto view() const { return *this; };
+  [[nodiscard]] constexpr auto view() const { return *this; };
+  [[nodiscard]] constexpr auto t() const { return Transpose{*this}; };
 };
 
 //
@@ -552,36 +698,92 @@ static_assert(AbstractMatrix<Elementwise<std::negate<>, PtrMatrix<int64_t>>>);
 static_assert(AbstractMatrix<Array<int64_t, SquareDims<>>>);
 static_assert(AbstractMatrix<ManagedArray<int64_t, SquareDims<>>>);
 
-constexpr auto operator*(const VecOrMat auto &a, const VecOrMat auto &b) {
-  auto AA{a.view()};
-  auto BB{b.view()};
-  if constexpr (AbstractVector<decltype(BB)>) {
-    if constexpr (AbstractVector<decltype(AA)>) {
-      ElementwiseBinaryOp(std::multiplies<>{}, AA, BB);
-    } else {
-      invariant(ptrdiff_t(AA.numCol()) == BB.size());
-      return MatVecMul<decltype(AA), decltype(BB)>{.a = AA, .b = BB};
+constexpr auto abs2(auto x) { return x * x; }
+template <AbstractTensor B> constexpr auto norm2(const B &A) {
+  utils::eltype_t<B> s = 0;
+  if constexpr (!LinearlyIndexable<B, utils::eltype_t<B>>) {
+    for (ptrdiff_t i = 0; i < A.numRow(); ++i) {
+      for (ptrdiff_t j = 0; j < A.numCol(); ++j) {
+        POLYMATHFAST
+        s += abs2(A[i, j]);
+      }
+    }
+  } else
+    for (ptrdiff_t j = 0, L = ptrdiff_t(A.size()); j < L; ++j) {
+      POLYMATHFAST
+      s += abs2(A[j]);
     }
-  } else {
-    invariant(ptrdiff_t(AA.numCol()) == ptrdiff_t(BB.numRow()));
-    return MatMatMul<decltype(AA), decltype(BB)>{.a = AA, .b = BB};
+  return s;
+}
+
+constexpr auto norm2(const auto &a) {
+  decltype(a[0] * a[0] + a[1] * a[1]) s{};
+  for (auto x : a) {
+    POLYMATHFAST
+    s += abs2(x, x);
+  }
+  return s;
+}
+constexpr auto dot(const auto &a, const auto &b) {
+  ptrdiff_t L = a.size();
+  invariant(L, b.size());
+  decltype(a[0] * b[0] + a[1] * b[1]) s{};
+  for (ptrdiff_t i = 0; i < L; ++i) {
+    POLYMATHFAST
+    s += a[i] * b[i];
   }
+  return s;
+}
+
+// we can have RowVector*RowVector or ColVector*ColVector(elementwise)
+// RowVector*ColVector (dot product)
+// Matrix*ColVector
+// RowVector*Matrix
+// Matrix*Matrix
+// We can't have vector*matrix
+constexpr auto operator*(const AbstractTensor auto &a,
+                         const AbstractTensor auto &b) {
+  auto AA{a.view()};
+  auto BB{b.view()};
+  invariant(ptrdiff_t(numCols(AA)), ptrdiff_t(numRows(BB)));
+  if constexpr (RowVector<decltype(AA)> && ColVector<decltype(BB)>)
+    return dot(AA, BB.t());
+  else if constexpr (AbstractVector<decltype(AA)> &&
+                     AbstractVector<decltype(BB)>)
+    return ElementwiseBinaryOp(std::multiplies<>{}, AA, BB);
+  else return MatMatMul<decltype(AA), decltype(BB)>{.a = AA, .b = BB};
 }
 template <AbstractVector M, utils::ElementOf<M> S>
 constexpr auto operator*(const M &b, S a) {
-  return ElementwiseBinaryOp(std::multiplies<>{}, view(b), view(a));
+  using T = utils::eltype_t<M>;
+  if constexpr (sizeof(T) <= 8)
+    return ElementwiseBinaryOp(std::multiplies<>{}, view(b),
+                               utils::eltype_t<M>(a));
+  else return ElementwiseBinaryOp(std::multiplies<>{}, view(b), a);
 }
 template <AbstractVector M, utils::ElementOf<M> S>
 constexpr auto operator*(S a, const M &b) {
-  return ElementwiseBinaryOp(std::multiplies<>{}, view(a), view(b));
+  using T = utils::eltype_t<M>;
+  if constexpr (sizeof(T) <= 8)
+    return ElementwiseBinaryOp(std::multiplies<>{}, utils::eltype_t<M>(a),
+                               view(b));
+  else return ElementwiseBinaryOp(std::multiplies<>{}, a, view(b));
 }
 template <AbstractMatrix M, utils::ElementOf<M> S>
 constexpr auto operator*(S a, const M &b) {
-  return ElementwiseBinaryOp(std::multiplies<>{}, view(a), view(b));
+  using T = utils::eltype_t<M>;
+  if constexpr (sizeof(T) <= 8)
+    return ElementwiseBinaryOp(std::multiplies<>{}, utils::eltype_t<M>(a),
+                               view(b));
+  else return ElementwiseBinaryOp(std::multiplies<>{}, a, view(b));
 }
 template <AbstractMatrix M, utils::ElementOf<M> S>
 constexpr auto operator*(const M &b, S a) {
-  return ElementwiseBinaryOp(std::multiplies<>{}, view(b), view(a));
+  using T = utils::eltype_t<M>;
+  if constexpr (sizeof(T) <= 8)
+    return ElementwiseBinaryOp(std::multiplies<>{}, view(b),
+                               utils::eltype_t<M>(a));
+  else return ElementwiseBinaryOp(std::multiplies<>{}, view(b), a);
 }
 
 template <class A, Compatible<A> B>
@@ -653,16 +855,6 @@ static_assert(AbstractMatrix<MatMatMul<PtrMatrix<int64_t>, PtrMatrix<int64_t>>>,
               "MatMul is not an AbstractMatrix!");
 static_assert(AbstractMatrix<Transpose<PtrMatrix<int64_t>>>);
 
-template <AbstractVector V>
-constexpr auto operator*(const Transpose<V> &at, const AbstractVector auto &b) {
-  utils::promote_eltype_t<V, decltype(b)> s{};
-  auto a = at.transpose();
-  ptrdiff_t l = a.size();
-  invariant(l == b.size());
-  for (ptrdiff_t i = 0; i < l; ++i) s += a[i] * b[i];
-  return s;
-}
-
 static_assert(
   AbstractVector<decltype(-std::declval<StridedVector<int64_t>>())>);
 static_assert(
@@ -706,20 +898,11 @@ template <typename T, typename I> struct SliceView {
   auto operator[](ptrdiff_t j) const -> const T & { return a[i[j]]; }
   [[nodiscard]] constexpr auto size() const -> ptrdiff_t { return i.size(); }
   constexpr auto view() -> SliceView<T, I> { return *this; }
+  [[nodiscard]] constexpr auto numRow() const -> Row<1> { return {}; }
+  [[nodiscard]] constexpr auto numCol() const { return col(size()); }
 };
 
 static_assert(AbstractVector<SliceView<int64_t, unsigned>>);
-constexpr auto abs2(auto x) { return x * x; }
-
-template <VecOrMat B> constexpr auto norm2(const B &A) {
-  utils::eltype_t<B> s = 0;
-  if constexpr (!LinearlyIndexable<B, utils::eltype_t<B>>) {
-    for (ptrdiff_t i = 0; i < A.numRow(); ++i)
-      for (ptrdiff_t j = 0; j < A.numCol(); ++j) s += abs2(A[i, j]);
-  } else
-    for (ptrdiff_t j = 0, L = ptrdiff_t(A.dim()); j < L; ++j) s += abs2(A[j]);
-  return s;
-}
 
 // template <class T, size_t N> struct Zip {
 //   std::array<T, N> a;
diff --git a/include/Math/Matrix.hpp b/include/Math/Matrix.hpp
index 8ba87c2..1ddd5dd 100644
--- a/include/Math/Matrix.hpp
+++ b/include/Math/Matrix.hpp
@@ -1,49 +1,96 @@
 #pragma once
 #include "Math/AxisTypes.hpp"
 #include "Math/MatrixDimensions.hpp"
-#include "Math/Vector.hpp"
 #include "Utilities/TypePromotion.hpp"
 #include <cstddef>
 #include <type_traits>
 
 namespace poly::math {
 
+template <typename T, typename S = utils::eltype_t<T>>
+concept LinearlyIndexable = requires(T t, ptrdiff_t i) {
+  { t[i] } -> std::convertible_to<S>;
+};
 template <typename T, typename S = utils::eltype_t<T>>
 concept CartesianIndexable = requires(T t, ptrdiff_t i) {
   { t[i, i] } -> std::convertible_to<S>;
 };
+// The `OrConvertible` concepts are for expression templates
+template <typename T, typename S>
+concept LinearlyIndexableOrConvertible =
+  LinearlyIndexable<T, S> || std::convertible_to<T, S>;
 template <typename T, typename S>
 concept CartesianIndexableOrConvertible =
   CartesianIndexable<T, S> || std::convertible_to<T, S>;
 
 template <typename T>
-concept AbstractMatrixCore =
-  utils::HasEltype<T> && CartesianIndexable<T> && requires(T t) {
-    { t.numRow() } -> std::convertible_to<Row<>>;
-    { t.numCol() } -> std::convertible_to<Col<>>;
-    { t.size() } -> std::same_as<CartesianIndex<ptrdiff_t, ptrdiff_t>>;
-    { t.dim() } -> std::convertible_to<StridedDims<>>;
-    // {
-    //     std::remove_reference_t<T>::canResize
-    //     } -> std::same_as<const bool &>;
-    // {t.extendOrAssertSize(i, i)};
-  };
+concept DefinesSize = requires(T t) {
+  { t.size() } -> std::convertible_to<ptrdiff_t>;
+};
+
 template <typename T>
-concept AbstractMatrix = AbstractMatrixCore<T> && requires(T t, ptrdiff_t i) {
-  { t.view() } -> AbstractMatrixCore;
+concept DefinesShape = requires(T t) {
+  { t.numRow() } -> std::convertible_to<Row<>>;
+  { t.numCol() } -> std::convertible_to<Col<>>;
 };
+
 template <typename T>
-concept HasDataPtr = requires(T t) {
-  { t.data() } -> std::same_as<utils::eltype_t<T> *>;
+concept ShapelessSize = DefinesSize<T> && (!DefinesShape<T>);
+template <typename T>
+concept PrimitiveScalar = std::integral<T> || std::floating_point<T>;
+
+constexpr auto numRows(const DefinesShape auto &A) { return A.numRow(); }
+constexpr auto numCols(const DefinesShape auto &A) { return A.numCol(); }
+
+constexpr auto numRows(const ShapelessSize auto &) -> Row<1> { return {}; }
+constexpr auto numCols(const ShapelessSize auto &A) { return col(A.size()); }
+
+constexpr auto shape(const auto &x) {
+  return CartesianIndex(unwrapRow(numRows(x)), unwrapCol(numCols(x)));
+}
+
+template <typename T>
+concept LinearlyIndexableTensor =
+  DefinesSize<T> && utils::HasEltype<T> && LinearlyIndexable<T>;
+
+template <typename T>
+concept RowVectorCore = LinearlyIndexableTensor<T> && requires(T t) {
+  { numRows(t) } -> std::same_as<Row<1>>;
+};
+template <typename T>
+concept ColVectorCore = LinearlyIndexableTensor<T> && requires(T t) {
+  { numCols(t) } -> std::same_as<Col<1>>;
+};
+template <typename T>
+concept RowVector = RowVectorCore<T> && requires(T t) {
+  { t.view() } -> RowVectorCore;
 };
 template <typename T>
-concept DataMatrix = AbstractMatrix<T> && HasDataPtr<T>;
+concept ColVector = ColVectorCore<T> && requires(T t) {
+  { t.view() } -> ColVectorCore;
+};
 template <typename T>
-concept TemplateMatrix = AbstractMatrix<T> && (!HasDataPtr<T>);
+concept AbstractVector = RowVector<T> || ColVector<T>;
 
 template <typename T>
-concept AbstractRowMajorMatrix = AbstractMatrix<T> && requires(T t) {
-  { t.rowStride() } -> std::convertible_to<RowStride<>>;
+concept AbstractMatrixCore =
+  DefinesShape<T> && utils::HasEltype<T> && CartesianIndexable<T>;
+template <typename T>
+concept AbstractMatrix =
+  AbstractMatrixCore<T> && !AbstractVector<T> && requires(T t) {
+    { t.view() } -> AbstractMatrixCore;
+  };
+
+template <typename T>
+concept AbstractTensor = AbstractVector<T> || AbstractMatrix<T>;
+
+template <typename T>
+concept HasDataPtr = requires(T t) {
+  { t.data() } -> std::same_as<utils::eltype_t<T> *>;
+};
+template <typename T>
+concept DenseTensor = AbstractTensor<T> && requires(T t) {
+  { t.begin() } -> std::convertible_to<const utils::eltype_t<T> *>;
 };
 
 template <ptrdiff_t M> constexpr auto transpose_dim(Col<M> c) {
@@ -56,39 +103,66 @@ template <ptrdiff_t M> constexpr auto transpose_dim(Row<M> r) {
 }
 
 template <typename A> struct Transpose {
-  static_assert(AbstractMatrix<A> || AbstractVector<A>,
+  static_assert(AbstractTensor<A>,
                 "Argument to transpose is not a matrix or vector.");
   static_assert(std::is_trivially_copyable_v<A>,
                 "Argument to transpose is not trivially copyable.");
 
   using value_type = utils::eltype_t<A>;
+  static constexpr bool has_reduction_loop = HasInnerReduction<A>;
   [[no_unique_address]] A a;
-  constexpr auto operator[](ptrdiff_t i, ptrdiff_t j) const -> value_type {
-    if constexpr (AbstractMatrix<A>) return a[j, i];
-    else {
-      invariant(i == 0);
-      return a[j];
-    }
+  constexpr auto operator[](auto i) const
+  requires(AbstractVector<A>)
+  {
+    return a[i];
+  }
+  constexpr auto operator[](auto i, auto j) const
+  requires(AbstractMatrix<A>)
+  {
+    return a[j, i];
   }
   [[nodiscard]] constexpr auto numRow() const {
-    if constexpr (AbstractMatrix<A>) return transpose_dim(a.numCol());
-    else return Row<1>{};
+    return transpose_dim(a.numCol());
   }
   [[nodiscard]] constexpr auto numCol() const {
-    if constexpr (AbstractMatrix<A>) return transpose_dim(a.numRow());
-    else return col(a.size());
+    return transpose_dim(a.numRow());
   }
   [[nodiscard]] constexpr auto view() const -> auto & { return *this; };
-  [[nodiscard]] constexpr auto size() const
-    -> CartesianIndex<ptrdiff_t, ptrdiff_t> {
-    return {ptrdiff_t(numRow()), ptrdiff_t(numCol())};
-  }
+  [[nodiscard]] constexpr auto size() const { return a.size(); }
   [[nodiscard]] constexpr auto dim() const {
     return DenseDims(numRow(), numCol());
   }
   constexpr Transpose(A b) : a(b) {}
-  constexpr auto transpose() const -> A { return a; }
+  constexpr auto t() const -> A { return a; }
+  constexpr auto operator<<(const auto &b) -> Transpose<A> & {
+    a << transpose(b);
+    return *this;
+  }
+  constexpr auto operator+=(const auto &b) -> Transpose<A> & {
+    a += transpose(b);
+    return *this;
+  }
+  constexpr auto operator-=(const auto &b) -> Transpose<A> & {
+    a -= transpose(b);
+    return *this;
+  }
+  constexpr auto operator*=(const auto &b) -> Transpose<A> & {
+    a *= transpose(b);
+    return *this;
+  }
+  constexpr auto operator/=(const auto &b) -> Transpose<A> & {
+    a /= transpose(b);
+    return *this;
+  }
 };
 template <typename A> Transpose(A) -> Transpose<A>;
 
+template <typename T> constexpr auto transpose(const T &a) {
+  if constexpr (requires(T t) {
+                  { t.t() } -> AbstractTensor;
+                })
+    return a.t();
+  else return Transpose{view(a)};
+}
+
 } // namespace poly::math
diff --git a/include/Math/MatrixDimensions.hpp b/include/Math/MatrixDimensions.hpp
index 7dc6319..20d916d 100644
--- a/include/Math/MatrixDimensions.hpp
+++ b/include/Math/MatrixDimensions.hpp
@@ -10,18 +10,39 @@ template <ptrdiff_t R = -1, ptrdiff_t C = -1> struct DenseDims;
 template <ptrdiff_t R = -1, ptrdiff_t C = -1, ptrdiff_t X = -1>
 struct StridedDims;
 
+// template <class From, class To>
+// concept ConvertibleToButNot =
+//   std::convertible_to<From, To> && (!std::same_as<From, To>);
+
 template <class R, class C> struct CartesianIndex {
   [[no_unique_address]] R row;
   [[no_unique_address]] C col;
   explicit constexpr operator Row<>() const { return {row}; }
   explicit constexpr operator Col<>() const { return {col}; }
   constexpr auto operator==(const CartesianIndex &) const -> bool = default;
-  constexpr operator SquareDims<>()
-  requires(std::same_as<R, ptrdiff_t> && std::same_as<C, ptrdiff_t>);
-  constexpr operator DenseDims<>()
-  requires(std::same_as<R, ptrdiff_t> && std::same_as<C, ptrdiff_t>);
-  constexpr operator StridedDims<>()
-  requires(std::same_as<R, ptrdiff_t> && std::same_as<C, ptrdiff_t>);
+  constexpr operator CartesianIndex<ptrdiff_t, ptrdiff_t>() const
+  requires(std::convertible_to<R, ptrdiff_t> &&
+           std::convertible_to<C, ptrdiff_t> &&
+           (!(std::same_as<R, ptrdiff_t> && std::same_as<C, ptrdiff_t>)))
+  {
+    return {ptrdiff_t(row), ptrdiff_t(col)};
+  }
+  // FIXME: Do we need this??
+  // Either document why, or delete this method.
+  constexpr operator ptrdiff_t() const
+  requires(std::same_as<R, std::integral_constant<ptrdiff_t, 1>>)
+  {
+    return col;
+  }
+  constexpr operator SquareDims<>() const
+  requires(std::convertible_to<R, ptrdiff_t> &&
+           std::convertible_to<C, ptrdiff_t>);
+  constexpr operator DenseDims<>() const
+  requires(std::convertible_to<R, ptrdiff_t> &&
+           std::convertible_to<C, ptrdiff_t>);
+  constexpr operator StridedDims<>() const
+  requires(std::convertible_to<R, ptrdiff_t> &&
+           std::convertible_to<C, ptrdiff_t>);
 };
 template <class R, class C> CartesianIndex(R, C) -> CartesianIndex<R, C>;
 
@@ -179,6 +200,16 @@ template <ptrdiff_t R, ptrdiff_t C> struct DenseDims {
   {
     return {M, N};
   }
+  constexpr operator ptrdiff_t() const
+  requires(R == 1)
+  {
+    return ptrdiff_t(N);
+  }
+  constexpr operator std::integral_constant<ptrdiff_t, C>() const
+  requires((R == 1) && (C != -1))
+  {
+    return {};
+  }
   friend inline auto operator<<(std::ostream &os, DenseDims x)
     -> std::ostream & {
     return os << x.M << " x " << x.N;
@@ -300,31 +331,38 @@ constexpr inline auto DenseDims<R, C>::operator=(SquareDims<R> D)
   };
 
 template <class R, class C>
-constexpr inline CartesianIndex<R, C>::operator SquareDims<>()
-requires(std::same_as<R, ptrdiff_t> && std::same_as<C, ptrdiff_t>)
+constexpr inline CartesianIndex<R, C>::operator SquareDims<>() const
+requires(std::convertible_to<R, ptrdiff_t> && std::convertible_to<C, ptrdiff_t>)
 {
   invariant(row, col);
   return SquareDims{Row<>{row}};
 }
 template <class R, class C>
-constexpr inline CartesianIndex<R, C>::operator DenseDims<>()
-requires(std::same_as<R, ptrdiff_t> && std::same_as<C, ptrdiff_t>)
+constexpr inline CartesianIndex<R, C>::operator DenseDims<>() const
+requires(std::convertible_to<R, ptrdiff_t> && std::convertible_to<C, ptrdiff_t>)
 {
   return DenseDims{Row<>{row}, Col<>{col}};
 }
 template <class R, class C>
-constexpr inline CartesianIndex<R, C>::operator StridedDims<>()
-requires(std::same_as<R, ptrdiff_t> && std::same_as<C, ptrdiff_t>)
+constexpr inline CartesianIndex<R, C>::operator StridedDims<>() const
+requires(std::convertible_to<R, ptrdiff_t> && std::convertible_to<C, ptrdiff_t>)
 {
   return StridedDims{Row<>{row}, Col<>{col}, RowStride<>{col}};
 }
 
+template <typename T, typename S>
+concept different = !std::same_as<T, S>;
+
 template <typename D>
 concept MatrixDimension = requires(D d) {
   { d } -> std::convertible_to<StridedDims<-1, -1, -1>>;
+  { Row(d) } -> different<Row<1>>;
+  { Col(d) } -> different<Col<1>>;
 };
 static_assert(MatrixDimension<SquareDims<>>);
 static_assert(MatrixDimension<DenseDims<>>);
+static_assert(!MatrixDimension<DenseDims<1>>);
+static_assert(!MatrixDimension<DenseDims<-1, 1>>);
 static_assert(MatrixDimension<StridedDims<>>);
 static_assert(MatrixDimension<SquareDims<8>>);
 static_assert(MatrixDimension<DenseDims<8, 8>>);
@@ -340,6 +378,9 @@ concept PromoteDimFrom = (!std::same_as<T, S>)&&std::convertible_to<S, T>;
 
 constexpr auto row(MatrixDimension auto s) { return Row(s); }
 constexpr auto col(MatrixDimension auto s) { return Col(s); }
-constexpr auto rowStride(MatrixDimension auto s) { return RowStride(s); }
+constexpr auto stride(MatrixDimension auto s) { return RowStride(s); }
+
+template <typename T>
+concept HasInnerReduction = bool(T::has_reduction_loop);
 
 } // namespace poly::math
diff --git a/include/Math/NormalForm.hpp b/include/Math/NormalForm.hpp
index 20928c3..834b683 100644
--- a/include/Math/NormalForm.hpp
+++ b/include/Math/NormalForm.hpp
@@ -1,5 +1,6 @@
 #pragma once
 
+#include "Containers/Tuple.hpp"
 #include "Math/Array.hpp"
 #include "Math/Comparisons.hpp"
 #include "Math/Constructors.hpp"
@@ -14,6 +15,7 @@
 #include <cstdint>
 
 namespace poly::math::NormalForm {
+using containers::Tuple, containers::tie;
 
 constexpr auto gcdxScale(int64_t a, int64_t b) -> std::array<int64_t, 4> {
   if (constexpr_abs(a) == 1) return {a, 0, a, b};
@@ -29,32 +31,46 @@ constexpr void zeroSupDiagonal(MutPtrMatrix<int64_t> A,
     int64_t Aii = A[i, i];
     if (int64_t Aji = A[j, i]) {
       const auto [p, q, Aiir, Aijr] = gcdxScale(Aii, Aji);
-      for (ptrdiff_t k = 0; k < minMN; ++k) {
-        int64_t Aki = A[i, k];
-        int64_t Akj = A[j, k];
-        int64_t Kki = K[i, k];
-        int64_t Kkj = K[j, k];
-        // when k == i, then
-        // p * Aii + q * Akj == r, so we set A(i,i) = r
-        A[i, k] = p * Aki + q * Akj;
-        // Aii/r * Akj - Aij/r * Aki = 0
-        A[j, k] = Aiir * Akj - Aijr * Aki;
-        // Mirror for K
-        K[i, k] = p * Kki + q * Kkj;
-        K[j, k] = Aiir * Kkj - Aijr * Kki;
-      }
-      for (auto k = ptrdiff_t(N); k < M; ++k) {
-        int64_t Kki = K[i, k];
-        int64_t Kkj = K[j, k];
-        K[i, k] = p * Kki + q * Kkj;
-        K[j, k] = Aiir * Kkj - Aijr * Kki;
+
+      {
+        MutPtrVector<int64_t> Ai{A[i, _(0, minMN)]}, Aj{A[j, _(0, minMN)]},
+          Ki{K[i, _(0, minMN)]}, Kj{K[j, _(0, minMN)]};
+        tie(Ai, Aj, Ki, Kj) << Tuple(p * Ai + q * Aj, Aiir * Aj - Aijr * Ai,
+                                     p * Ki + q * Kj, Aiir * Kj - Aijr * Ki);
       }
-      for (auto k = ptrdiff_t(M); k < N; ++k) {
-        int64_t Aki = A[i, k];
-        int64_t Akj = A[j, k];
-        A[i, k] = p * Aki + q * Akj;
-        A[j, k] = Aiir * Akj - Aijr * Aki;
+      if (ptrdiff_t(M) > ptrdiff_t(N)) {
+        MutPtrVector<int64_t> Ki{K[i, _(N, M)]}, Kj{K[j, _(N, M)]};
+        tie(Ki, Kj) << Tuple(p * Ki + q * Kj, Aiir * Kj - Aijr * Ki);
+      } else if (ptrdiff_t(N) > ptrdiff_t(M)) {
+        MutPtrVector<int64_t> Ai{A[i, _(M, N)]}, Aj{A[j, _(M, N)]};
+        tie(Ai, Aj) << Tuple(p * Ai + q * Aj, Aiir * Aj - Aijr * Ai);
       }
+      // for (ptrdiff_t k = 0; k < minMN; ++k) {
+      //   int64_t Aki = A[i, k];
+      //   int64_t Akj = A[j, k];
+      //   int64_t Kki = K[i, k];
+      //   int64_t Kkj = K[j, k];
+      //   // when k == i, then
+      //   // p * Aii + q * Akj == r, so we set A(i,i) = r
+      //   A[i, k] = p * Aki + q * Akj;
+      //   // Aii/r * Akj - Aij/r * Aki = 0
+      //   A[j, k] = Aiir * Akj - Aijr * Aki;
+      //   // Mirror for K
+      //   K[i, k] = p * Kki + q * Kkj;
+      //   K[j, k] = Aiir * Kkj - Aijr * Kki;
+      // }
+      // for (auto k = ptrdiff_t(N); k < M; ++k) {
+      //   int64_t Kki = K[i, k];
+      //   int64_t Kkj = K[j, k];
+      //   K[i, k] = p * Kki + q * Kkj;
+      //   K[j, k] = Aiir * Kkj - Aijr * Kki;
+      // }
+      // for (auto k = ptrdiff_t(M); k < N; ++k) {
+      //   int64_t Aki = A[i, k];
+      //   int64_t Akj = A[j, k];
+      //   A[i, k] = p * Aki + q * Akj;
+      //   A[j, k] = Aiir * Akj - Aijr * Aki;
+      // }
     }
   }
 }
@@ -70,20 +86,24 @@ constexpr void zeroSubDiagonal(MutPtrMatrix<int64_t> A,
   } else {
     invariant(Akk == 1);
   }
-  ptrdiff_t minMN = std::min(ptrdiff_t(M), ptrdiff_t(N));
+  ptrdiff_t Mi = ptrdiff_t(M), Ni = ptrdiff_t(N), minMN = std::min(Mi, Ni);
   for (ptrdiff_t z = 0; z < k; ++z) {
     // eliminate `A(k,z)`
-    if (int64_t Akz = A[z, k]) {
-      // A(k, k) == 1, so A(k,z) -= Akz * 1;
-      // A(z,_) -= Akz * A(k,_);
-      // K(z,_) -= Akz * K(k,_);
-      for (ptrdiff_t i = 0; i < minMN; ++i) {
-        A[z, i] -= Akz * A[k, i];
-        K[z, i] -= Akz * K[k, i];
-      }
-      for (auto i = ptrdiff_t(N); i < M; ++i) K[z, i] -= Akz * K[k, i];
-      for (auto i = ptrdiff_t(M); i < N; ++i) A[z, i] -= Akz * A[k, i];
-    }
+    int64_t Akz = A[z, k];
+    if (!Akz) continue;
+    // A(k, k) == 1, so A(k,z) -= Akz * 1;
+    // A(z,_) -= Akz * A(k,_);
+    // K(z,_) -= Akz * K(k,_);
+    Tuple(A[z, _(0, minMN)], K[z, _(0, minMN)]) -=
+      Tuple(Akz * A[k, _(0, minMN)], Akz * K[k, _(0, minMN)]);
+    if (Mi > Ni) K[z, _(Ni, Mi)] -= Akz * K[k, _(Ni, Mi)];
+    else if (Ni > Mi) A[z, _(Mi, Ni)] -= Akz * A[k, _(Mi, Ni)];
+    // for (ptrdiff_t i = 0; i < minMN; ++i) {
+    //   A[z, i] -= Akz * A[k, i];
+    //   K[z, i] -= Akz * K[k, i];
+    // }
+    // for (auto i = ptrdiff_t(N); i < M; ++i) K[z, i] -= Akz * K[k, i];
+    // for (auto i = ptrdiff_t(M); i < N; ++i) A[z, i] -= Akz * A[k, i];
   }
 }
 
@@ -119,15 +139,15 @@ constexpr auto pivotRows(MutPtrMatrix<int64_t> A, ptrdiff_t i, Row<> N)
 constexpr void dropCol(MutPtrMatrix<int64_t> A, ptrdiff_t i, Row<> M, Col<> N) {
   // if any rows are left, we shift them up to replace it
   if (N <= i) return;
-  for (ptrdiff_t m = 0; m < M; ++m)
-    for (ptrdiff_t n = i; n < N; ++n) A[m, n] = A[m, n + 1];
+  for (ptrdiff_t m = 0; m < M; ++m) A[m, _(i, N)] << A[m, _(i, N) + 1];
+  // for (ptrdiff_t n = i; n < N; ++n) A[m, n] = A[m, n + 1];
 }
 
 constexpr auto orthogonalizeBang(MutDensePtrMatrix<int64_t> &A)
   -> std::pair<SquareMatrix<int64_t>, Vector<unsigned>> {
   // we try to orthogonalize with respect to as many rows of `A` as we can
   // prioritizing earlier rows.
-  auto [M, N] = A.size();
+  auto [M, N] = shape(A);
   SquareMatrix<int64_t> K{identity(alloc::Mallocator<int64_t>{}, unsigned(M))};
   Vector<unsigned> included;
   included.reserve(std::min(ptrdiff_t(M), ptrdiff_t(N)));
@@ -160,7 +180,7 @@ constexpr auto orthogonalize(IntMatrix<> A)
 }
 
 constexpr void zeroSupDiagonal(MutPtrMatrix<int64_t> A, Col<> c, Row<> r) {
-  auto [M, N] = A.size();
+  auto [M, N] = shape(A);
   for (ptrdiff_t j = ptrdiff_t(r) + 1; j < M; ++j) {
     int64_t Aii = A[r, c];
     if (int64_t Aij = A[j, c]) {
@@ -176,7 +196,7 @@ constexpr void zeroSupDiagonal(MutPtrMatrix<int64_t> A, Col<> c, Row<> r) {
 constexpr void zeroSupDiagonal(std::array<MutPtrMatrix<int64_t>, 2> AB, Col<> c,
                                Row<> r) {
   auto [A, B] = AB;
-  auto [M, N] = A.size();
+  auto [M, N] = shape(A);
   const Col K = B.numCol();
   invariant(M, ptrdiff_t(B.numRow()));
   for (ptrdiff_t j = ptrdiff_t(r) + 1; j < M; ++j) {
@@ -317,7 +337,7 @@ constexpr void removeZeroRows(MutDensePtrMatrix<int64_t> &A) {
 // pass by value, returns number of rows to truncate
 constexpr auto simplifySystemImpl(MutPtrMatrix<int64_t> A,
                                   ptrdiff_t colInit = 0) -> Row<> {
-  auto [M, N] = A.size();
+  auto [M, N] = shape(A);
   for (ptrdiff_t r = 0, c = colInit; c < N && r < M; ++c)
     if (!pivotRows(A, Col<>{c}, Row<>{M}, Row<>{r}))
       reduceColumn(A, Col<>{c}, Row<>{r++});
@@ -342,7 +362,7 @@ constexpr void reduceColumn(std::array<MutPtrMatrix<int64_t>, 2> AB, Col<> c,
   reduceSubDiagonal(AB, c, r);
 }
 constexpr void simplifySystemsImpl(std::array<MutPtrMatrix<int64_t>, 2> AB) {
-  auto [M, N] = AB[0].size();
+  auto [M, N] = shape(AB[0]);
   for (ptrdiff_t r = 0, c = 0; c < N && r < M; ++c)
     if (!pivotRowsPair(AB, Col<>{c}, Row<>{M}, Row<>{r}))
       reduceColumn(AB, Col<>{c}, Row<>{r++});
@@ -460,7 +480,9 @@ constexpr void zeroColumn(MutPtrMatrix<int64_t> A, Col<> c, Row<> r) {
   const Row M = A.numRow();
   for (ptrdiff_t j = 0; j < r; ++j) {
     int64_t Arc = A[r, c];
+    invariant(Arc != std::numeric_limits<int64_t>::min());
     if (int64_t Ajc = A[j, c]) {
+      invariant(Ajc != std::numeric_limits<int64_t>::min());
       int64_t g = gcd(Arc, Ajc);
       A[j, _] << (Arc / g) * A[j, _] - (Ajc / g) * A[r, _];
     }
@@ -490,18 +512,19 @@ constexpr auto pivotRowsBareiss(MutPtrMatrix<int64_t> A, ptrdiff_t i, Row<> M,
 }
 constexpr void bareiss(MutPtrMatrix<int64_t> A,
                        MutPtrVector<ptrdiff_t> pivots) {
-  const auto [M, N] = A.size();
+  const auto [M, N] = shape(A);
   invariant(ptrdiff_t(pivots.size()), std::min(M, N));
   int64_t prev = 1, pivInd = 0;
   for (ptrdiff_t r = 0, c = 0; c < N && r < M; ++c) {
     if (auto piv = pivotRowsBareiss(A, c, Row<>{M}, Row<>{r})) {
       pivots[pivInd++] = *piv;
+      auto j{_(c + 1, N)};
       for (ptrdiff_t k = r + 1; k < M; ++k) {
-        for (ptrdiff_t j = c + 1; j < N; ++j) {
-          auto uAkj = A[r, c] * A[k, j] - A[k, c] * A[r, j], Akj = uAkj / prev;
-          invariant(uAkj, Akj * prev);
-          A[k, j] = Akj;
-        }
+        A[k, j] << (A[r, c] * A[k, j] - A[k, c] * A[r, j]) / prev;
+        // for (ptrdiff_t j = c + 1; j < N; ++j) {
+        //   auto uAkj = A[r, c] * A[k, j] - A[k, c] * A[r, j], Akj = uAkj /
+        //   prev; invariant(uAkj, Akj * prev); A[k, j] = Akj;
+        // }
         A[k, r] = 0;
       }
       prev = A[r++, c];
@@ -570,7 +593,7 @@ constexpr auto updateForNewRow(MutPtrMatrix<int64_t> A) -> ptrdiff_t {
 /// Once \f$\textbf{A}\f$ has been diagonalized, the solution is trivial.
 /// Both inputs are overwritten with the product of the left multiplications.
 constexpr void solveSystem(MutPtrMatrix<int64_t> A, MutPtrMatrix<int64_t> B) {
-  const auto [M, N] = A.size();
+  const auto [M, N] = shape(A);
   for (ptrdiff_t r = 0, c = 0; c < N && r < M; ++c)
     if (!pivotRowsPair({A, B}, Col<>{c}, Row<>{M}, Row<>{r}))
       zeroColumnPair({A, B}, Col<>{c}, Row<>{r++});
@@ -584,7 +607,7 @@ constexpr void solveSystem(MutPtrMatrix<int64_t> A, ptrdiff_t K) {
 }
 // diagonalizes A(0:K,1:K+1)
 constexpr void solveSystemSkip(MutPtrMatrix<int64_t> A) {
-  const auto [M, N] = A.size();
+  const auto [M, N] = shape(A);
   for (ptrdiff_t r = 0, c = 1; c < N && r < M; ++c)
     if (!pivotRows(A, Col<>{c}, Row<>{M}, Row<>{r}))
       zeroColumn(A, Col<>{c}, Row<>{r++});
diff --git a/include/Math/Simplex.hpp b/include/Math/Simplex.hpp
index 0543678..b213971 100644
--- a/include/Math/Simplex.hpp
+++ b/include/Math/Simplex.hpp
@@ -185,6 +185,11 @@ class Simplex {
     inCanonicalForm = false;
 #endif
     auto C{getConstraints()};
+#ifndef NDEBUG
+    for (ptrdiff_t r = 0, R = ptrdiff_t(numRows(C)); r < R; ++r)
+      for (ptrdiff_t c = 0, N = ptrdiff_t(numCols(C)); c < N; ++c)
+        invariant(C[r, c] != std::numeric_limits<int64_t>::min());
+#endif
     NormalForm::solveSystemSkip(C);
     truncateConstraints(ptrdiff_t(NormalForm::numNonZeroRows(C)));
   }
@@ -683,7 +688,7 @@ class Simplex {
                              A[_, _(1, end)], B[_, _(1, end)]);
     auto consts{simplex->getConstants()};
     consts[_(0, numSlack)] << A[_, 0];
-    consts[_(numSlack, numSlack + numStrict)] << B[_, 0];
+    if (numStrict) consts[_(numSlack, numSlack + numStrict)] << B[_, 0];
     // for (ptrdiff_t i = 0; i < numSlack; ++i) consts[i] = A(i, 0);
     // for (ptrdiff_t i = 0; i < numStrict; ++i) consts[i + numSlack] = B(i, 0);
     if (!simplex->initiateFeasible()) return simplex;
@@ -782,7 +787,7 @@ class Simplex {
     // subSimp.tableau(0, 1) = 0;
     auto fC{getTableau()};
     auto sC{subSimp->getTableau()};
-    sC[_, 0] << fC[_, 0] - fC[_, _(1 + off, 1 + off + numFix)] * x;
+    sC[_, 0] << fC[_, 0] - fC[_, _(1 + off, 1 + off + numFix)] * x.t();
     // sC(_, 0) = fC(_, 0);
     // for (ptrdiff_t i = 0; i < numFix; ++i)
     //     sC(_, 0) -= x(i) * fC(_, i + 1 + off);
@@ -812,7 +817,7 @@ class Simplex {
     auto fC{getConstraints()};
     auto sC{subSimp->getConstraints()};
     sC[_, 0] << fC[_(begin, numRow), 0] -
-                  fC[_(begin, numRow), _(off, off + numFix)] * x;
+                  fC[_(begin, numRow), _(off, off + numFix)] * x.t();
     sC[_, _(1, off)] << fC[_(begin, numRow), _(1, off)];
     return subSimp->initiateFeasible();
   }
diff --git a/include/Math/SmallSparseMatrix.hpp b/include/Math/SmallSparseMatrix.hpp
index 82d3cde..00b17c0 100644
--- a/include/Math/SmallSparseMatrix.hpp
+++ b/include/Math/SmallSparseMatrix.hpp
@@ -90,7 +90,7 @@ template <class T, class S, class P>
 [[gnu::flatten]] constexpr auto
 ArrayOps<T, S, P>::operator<<(const SmallSparseMatrix<T> &B) -> P & {
   static_assert(MatrixDimension<S>);
-  ptrdiff_t M = nr(), N = nc(), k = 0;
+  ptrdiff_t M = ptrdiff_t(nr()), N = ptrdiff_t(nc()), k = 0;
   invariant(M, ptrdiff_t(B.numRow()));
   invariant(N, ptrdiff_t(B.numCol()));
   T *mem = data_();
@@ -98,7 +98,7 @@ ArrayOps<T, S, P>::operator<<(const SmallSparseMatrix<T> &B) -> P & {
   PtrVector<uint32_t> rws = B.getRows();
   for (ptrdiff_t i = 0; i < M; ++i) {
     uint32_t m = rws[i] & 0x00ffffff;
-    ptrdiff_t j = 0, l = rs() * i;
+    ptrdiff_t j = 0, l = ptrdiff_t(rs()) * i;
     while (m) {
       uint32_t tz = std::countr_zero(m);
       m >>= tz + 1;
diff --git a/include/Math/StaticArrays.hpp b/include/Math/StaticArrays.hpp
index 44f7754..299acbf 100644
--- a/include/Math/StaticArrays.hpp
+++ b/include/Math/StaticArrays.hpp
@@ -1,36 +1,77 @@
 #pragma once
 #include "Math/Array.hpp"
+#include "Math/Indexing.hpp"
+#include "Utilities/Reference.hpp"
 #include <type_traits>
 #include <utility>
+
 namespace poly::math {
 
 static_assert(
   AbstractSimilar<PtrVector<int64_t>, std::integral_constant<unsigned int, 4>>);
 
-// TODO: add MatrixDimension support
-template <typename T>
-concept StaticSize = StaticInt<T>;
+template <ptrdiff_t N, typename T>
+constexpr ptrdiff_t VecLen =
+  (N < poly::simd::Width<T>) ? ptrdiff_t(std::bit_ceil(uint64_t(N)))
+                             : poly::simd::Width<T>;
 
-template <class T, StaticSize S>
-struct StaticArray : public ArrayOps<T, S, StaticArray<T, S>> {
-  static constexpr ptrdiff_t capacity = ptrdiff_t{S{}};
-  T memory_[capacity]; // NOLINT(modernize-avoid-c-arrays)
+template <typename T, ptrdiff_t L>
+consteval auto paddedSize() -> std::array<ptrdiff_t, 2> {
+  constexpr ptrdiff_t WF = poly::simd::Width<T>;
+  constexpr ptrdiff_t W = L < WF ? ptrdiff_t(std::bit_ceil(uint64_t(L))) : WF;
+  constexpr ptrdiff_t N = ((L + W - 1) / W);
+  return {N, W};
+}
+template <typename T, ptrdiff_t L, ptrdiff_t Align>
+consteval auto calcPaddedCols() -> ptrdiff_t {
+  constexpr ptrdiff_t a = Align / sizeof(T);
+  if constexpr (a <= 1) return L;
+  else return ((L + a - 1) / a) * a;
+}
+template <typename T, ptrdiff_t L> consteval auto alignSIMD() -> size_t {
+  if constexpr (!simd::SIMDSupported<T>) return alignof(T);
+  else return alignof(simd::Vec<VecLen<L, T>, T>);
+}
 
-  using value_type = T;
-  using reference = T &;
-  using const_reference = const T &;
-  using size_type = unsigned;
-  using difference_type = int;
-  using iterator = T *;
-  using const_iterator = const T *;
-  using pointer = T *;
-  using const_pointer = const T *;
+template <class T, ptrdiff_t M, ptrdiff_t N, bool Compress>
+using StaticDims = std::conditional_t<
+  M == 1, std::integral_constant<ptrdiff_t, N>,
+  std::conditional_t<
+    Compress || (((N * sizeof(T)) % VecLen<N, T>) == 0), DenseDims<M, N>,
+    StridedDims<M, N, calcPaddedCols<T, N, alignSIMD<T, N>()>()>>>;
+
+template <class T, ptrdiff_t M, ptrdiff_t N, bool Compress = false>
+struct StaticArray : public ArrayOps<T, StaticDims<T, M, N, Compress>,
+                                     StaticArray<T, M, N, Compress>> {
+  using storage_type = std::conditional_t<Compress, utils::compressed_t<T>, T>;
+  static constexpr ptrdiff_t Align =
+    Compress ? alignof(storage_type) : alignSIMD<T, N>();
+  static constexpr ptrdiff_t PaddedCols = calcPaddedCols<T, N, Align>();
+  static constexpr ptrdiff_t capacity = M * PaddedCols;
+
+  static_assert(alignof(storage_type) <= Align);
+
+  alignas(Align) storage_type memory_[capacity];
+
+  using value_type = utils::decompressed_t<T>;
+  using reference = decltype(utils::ref((storage_type *)nullptr, 0));
+  using const_reference =
+    decltype(utils::ref((const storage_type *)nullptr, 0));
+  using size_type = ptrdiff_t;
+  using difference_type = ptrdiff_t;
+  using iterator = storage_type *;
+  using const_iterator = const storage_type *;
+  using pointer = storage_type *;
+  using const_pointer = const storage_type *;
   using concrete = std::true_type;
-  constexpr explicit StaticArray(){}; // NOLINT(modernize-use-equals-default)
-  constexpr explicit StaticArray(const T &x) noexcept {
-    (*this) << x;
-    // std::fill_n(data(), capacity, x);
-  }
+
+  // if Compress=false, we have a compressed_t
+  // if Compress=true, we should already be compressed
+  using compressed_type = StaticArray<utils::compressed_t<T>, M, N, true>;
+  using decompressed_type = StaticArray<value_type, M, N, false>;
+  using S = StaticDims<T, M, N, Compress>;
+  constexpr StaticArray(){}; // NOLINT(modernize-use-equals-default)
+  constexpr explicit StaticArray(const T &x) noexcept { (*this) << x; }
   constexpr explicit StaticArray(
     const std::convertible_to<T> auto &x) noexcept {
     (*this) << x;
@@ -42,12 +83,23 @@ struct StaticArray : public ArrayOps<T, S, StaticArray<T, S>> {
       (*this) << *list.begin();
       return;
     }
-    invariant(list.size(), size_t(capacity));
-    std::copy(list.begin(), list.end(), data());
+    invariant(list.size() <= size_t(capacity));
+    std::copy_n(list.begin(), list.size(), data());
   }
   template <AbstractSimilar<S> V> constexpr StaticArray(const V &b) noexcept {
     (*this) << b;
   }
+
+  constexpr void compress(compressed_type *p) const
+  requires(std::same_as<StaticArray, decompressed_type>)
+  {
+    *p << *this;
+  }
+  static constexpr auto decompress(const compressed_type *p) -> StaticArray
+  requires(std::same_as<StaticArray, decompressed_type>)
+  {
+    return StaticArray{*p};
+  }
   [[nodiscard]] constexpr auto data() const noexcept -> const T * {
     return memory_;
   }
@@ -79,22 +131,15 @@ struct StaticArray : public ArrayOps<T, S, StaticArray<T, S>> {
   //   auto
   // }
   constexpr auto operator[](Index<S> auto i) const noexcept -> decltype(auto) {
-    auto offset = calcOffset(S{}, i);
-    auto newDim = calcNewDim(S{}, i);
-    auto ptr = data();
-    invariant(ptr != nullptr);
-    if constexpr (std::is_same_v<decltype(newDim), Empty>) return ptr[offset];
-    else return Array<T, decltype(newDim)>{ptr + offset, newDim};
+    return index<T>(data(), S{}, i);
   }
   // TODO: switch to operator[] when we enable c++23
   // for vectors, we just drop the column, essentially broadcasting
   template <class R, class C>
   constexpr auto operator[](R r, C c) const noexcept -> decltype(auto) {
-    if constexpr (MatrixDimension<S>)
-      return (*this)[CartesianIndex<R, C>{r, c}];
-    else return (*this)[ptrdiff_t(r)];
+    return index<T>(data(), S{}, r, c);
   }
-  [[nodiscard]] constexpr auto minRowCol() const -> ptrdiff_t {
+  [[nodiscard]] static constexpr auto minRowCol() -> ptrdiff_t {
     return std::min(ptrdiff_t(numRow()), ptrdiff_t(numCol()));
   }
 
@@ -113,31 +158,33 @@ struct StaticArray : public ArrayOps<T, S, StaticArray<T, S>> {
   [[nodiscard]] static constexpr auto isSquare() noexcept -> bool {
     return Row(S{}) == Col(S{});
   }
-  [[nodiscard]] constexpr auto checkSquare() const -> Optional<ptrdiff_t> {
-    ptrdiff_t N = ptrdiff_t(numRow());
-    if (N != ptrdiff_t(numCol())) return {};
-    return N;
-  }
 
-  [[nodiscard]] constexpr auto numRow() const noexcept { return row(S{}); }
-  [[nodiscard]] constexpr auto numCol() const noexcept { return col(S{}); }
-  [[nodiscard]] constexpr auto rowStride() const noexcept {
-    return rowStride(S{});
+  [[nodiscard]] static constexpr auto checkSquare() -> Optional<ptrdiff_t> {
+    if constexpr (M == N) return M;
+    else return {};
+  }
+  [[nodiscard]] static constexpr auto numRow() noexcept -> Row<M> { return {}; }
+  [[nodiscard]] static constexpr auto numCol() noexcept -> Col<N> { return {}; }
+  static constexpr auto safeRow() -> Row<M> { return {}; }
+  static constexpr auto safeCol() -> Col<PaddedCols> { return {}; }
+  [[nodiscard]] static constexpr auto rowStride() noexcept
+    -> RowStride<PaddedCols> {
+    return {};
   }
   [[nodiscard]] static constexpr auto empty() -> bool { return capacity == 0; }
-  [[nodiscard]] static constexpr auto size() noexcept {
-    if constexpr (StaticInt<S>) return S{};
-    else return CartesianIndex{Row(S{}), Col(S{})};
+  [[nodiscard]] static constexpr auto size() noexcept
+    -> std::integral_constant<ptrdiff_t, M * N> {
+    return {};
   }
   [[nodiscard]] static constexpr auto dim() noexcept -> S { return S{}; }
-  [[nodiscard]] constexpr auto transpose() const { return Transpose{*this}; }
+  [[nodiscard]] constexpr auto t() const { return Transpose{*this}; }
   [[nodiscard]] constexpr auto isExchangeMatrix() const -> bool {
-    ptrdiff_t N = ptrdiff_t(numRow());
-    if (N != ptrdiff_t(numCol())) return false;
-    for (ptrdiff_t i = 0; i < N; ++i) {
-      for (ptrdiff_t j = 0; j < N; ++j)
-        if ((*this)(i, j) != (i + j == N - 1)) return false;
-    }
+    if constexpr (M == N) {
+      for (ptrdiff_t i = 0; i < M; ++i) {
+        for (ptrdiff_t j = 0; j < M; ++j)
+          if ((*this)(i, j) != (i + j == M - 1)) return false;
+      }
+    } else return false;
   }
   [[nodiscard]] constexpr auto isDiagonal() const -> bool {
     for (ptrdiff_t r = 0; r < numRow(); ++r)
@@ -145,10 +192,10 @@ struct StaticArray : public ArrayOps<T, S, StaticArray<T, S>> {
         if (r != c && (*this)(r, c) != 0) return false;
     return true;
   }
-  [[nodiscard]] constexpr auto view() const noexcept -> Array<T, S> {
-    auto ptr = data();
+  [[nodiscard]] constexpr auto view() const noexcept -> Array<T, S, Compress> {
+    const storage_type *ptr = data();
     invariant(ptr != nullptr);
-    return Array<T, S>{const_cast<T *>(ptr), S{}};
+    return {ptr, S{}};
   }
 
   [[nodiscard]] constexpr auto begin() noexcept {
@@ -166,21 +213,15 @@ struct StaticArray : public ArrayOps<T, S, StaticArray<T, S>> {
   constexpr auto front() noexcept -> T & { return *begin(); }
   constexpr auto back() noexcept -> T & { return *(end() - 1); }
   constexpr auto operator[](Index<S> auto i) noexcept -> decltype(auto) {
-    auto offset = calcOffset(S{}, i);
-    auto newDim = calcNewDim(S{}, i);
-    if constexpr (std::is_same_v<decltype(newDim), Empty>)
-      return data()[offset];
-    else return MutArray<T, decltype(newDim)>{data() + offset, newDim};
+    return index<T>(data(), S{}, i);
   }
   // TODO: switch to operator[] when we enable c++23
   template <class R, class C>
   constexpr auto operator[](R r, C c) noexcept -> decltype(auto) {
-    if constexpr (MatrixDimension<S>)
-      return (*this)[CartesianIndex<R, C>{r, c}];
-    else return (*this)[ptrdiff_t(r)];
+    return index<T>(data(), S{}, r, c);
   }
   constexpr void fill(T value) {
-    std::fill_n((T *)(data()), ptrdiff_t(this->dim()), value);
+    std::fill_n(data(), ptrdiff_t(this->dim()), value);
   }
   [[nodiscard]] constexpr auto diag() noexcept {
     StridedRange r{unsigned(min(Row(S{}), Col(S{}))),
@@ -202,21 +243,223 @@ struct StaticArray : public ArrayOps<T, S, StaticArray<T, S>> {
   }
 };
 
-template <class T, ptrdiff_t N>
-using SVector = StaticArray<T, std::integral_constant<ptrdiff_t, N>>;
+template <simd::SIMDSupported T, ptrdiff_t M, ptrdiff_t N>
+struct StaticArray<T, M, N, false>
+  : ArrayOps<T, StaticDims<T, M, N, false>, StaticArray<T, M, N, false>> {
+  // struct StaticArray<T, M, N, alignof(simd::Vec<VecLen<N, T>, T>)>
+  //   : ArrayOps<T, StaticDims<T, M, N, alignof(simd::Vec<VecLen<N, T>, T>)>,
+  //              StaticArray<T, M, N, alignof(simd::Vec<VecLen<N, T>, T>)>> {
+
+  using value_type = T;
+  using reference = T &;
+  using const_reference = const T &;
+  using size_type = ptrdiff_t;
+  using difference_type = ptrdiff_t;
+  using iterator = T *;
+  using const_iterator = const T *;
+  using pointer = T *;
+  using const_pointer = const T *;
+  using concrete = std::true_type;
+
+  using compressed_type = StaticArray<T, M, N, true>;
+
+  constexpr void compress(compressed_type *p) const { *p << *this; }
+  static constexpr auto decompress(const compressed_type *p) -> StaticArray {
+    return StaticArray{*p};
+  }
+  static constexpr ptrdiff_t W = VecLen<N, T>;
+  static constexpr ptrdiff_t Align = alignof(simd::Vec<W, T>);
+  using S = StaticDims<T, M, N, false>;
+
+  [[nodiscard]] constexpr auto view() const -> StaticArray { return *this; }
+
+  static constexpr ptrdiff_t L = (N + W - 1) / W;
+  static_assert(L * W == calcPaddedCols<T, N, Align>());
+  using V = simd::Vec<W, T>;
+  // simd::Vec<W, T> data[M][L];
+  V memory_[M * L];
+  // std::array<std::array<simd::Vec<W, T>, L>, M> data;
+  // constexpr operator compressed_type() { return compressed_type{*this}; }
+  constexpr StaticArray(StaticArray const &) = default;
+  constexpr StaticArray(StaticArray &&) noexcept = default;
+  constexpr explicit StaticArray(const std::initializer_list<T> &list) {
+    if (list.size() == 1) {
+      (*this) << *list.begin();
+      return;
+    }
+    invariant(list.size() <= L * W);
+    size_t count = list.size() * sizeof(T);
+    std::memcpy(memory_, list.begin(), count);
+    std::memset((char *)memory_ + count, 0, (L * W - list.size()) * sizeof(T));
+  }
+  constexpr auto data() -> T * { return reinterpret_cast<T *>(memory_); }
+  [[nodiscard]] constexpr auto data() const -> const T * {
+    return reinterpret_cast<const T *>(memory_);
+  }
+  template <AbstractSimilar<S> V> constexpr StaticArray(const V &b) noexcept {
+    (*this) << b;
+  }
+  constexpr explicit StaticArray(T x) {
+    simd::Vec<W, T> v = simd::Vec<W, T>{} + x;
+    for (ptrdiff_t i = 0; i < M * L; ++i) memory_[i] = v;
+  }
+  constexpr auto operator=(StaticArray const &) -> StaticArray & = default;
+  constexpr auto operator=(StaticArray &&) noexcept -> StaticArray & = default;
+  constexpr StaticArray(){}; // NOLINT(modernize-use-equals-default)
+  static constexpr auto numRow() -> Row<M> { return {}; }
+  static constexpr auto numCol() -> Col<N> { return {}; }
+  static constexpr auto safeRow() -> Row<M> { return {}; }
+  static constexpr auto safeCol() -> Col<L> { return {}; }
+  [[nodiscard]] static constexpr auto rowStride() noexcept -> RowStride<L * W> {
+    return {};
+  }
+  [[nodiscard]] static constexpr auto size() noexcept
+    -> std::integral_constant<ptrdiff_t, M * N> {
+    return {};
+  }
+  inline auto operator[](ptrdiff_t i, ptrdiff_t j) -> T & {
+    return reinterpret_cast<T *>(memory_ + i * L)[j];
+  }
+  inline auto operator[](ptrdiff_t i, ptrdiff_t j) const -> T {
+    return reinterpret_cast<const T *>(memory_ + i * L)[j];
+  }
+  template <ptrdiff_t U, typename Mask>
+  [[gnu::always_inline]] inline auto
+  operator[](ptrdiff_t i, simd::index::Unroll<U, W, Mask> j) const
+    -> simd::Unroll<1, U, W, T> {
+    return (*this)[simd::index::Unroll<1>{i}, j];
+  }
+  template <ptrdiff_t R = 1>
+  [[gnu::always_inline]] static constexpr void checkinds(ptrdiff_t i,
+                                                         ptrdiff_t j) {
+    invariant(i >= 0);
+    invariant(i + (R - 1) < M);
+    invariant(j >= 0);
+    invariant(j < N);
+    invariant((j % W) == 0);
+  }
+  template <ptrdiff_t R, ptrdiff_t C, typename Mask>
+  [[gnu::always_inline]] inline auto
+  operator[](simd::index::Unroll<R> i, simd::index::Unroll<C, W, Mask> j) const
+    -> simd::Unroll<R, C, W, T> {
+    checkinds<R>(i.index, j.index);
+    simd::Unroll<R, C, W, T> ret;
+    ptrdiff_t k = j.index / W;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t r = 0; r < R; ++r) {
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t u = 0; u < C; ++u)
+        ret[r, u] = memory_[(i.index + r) * L + k + u];
+    }
+    return ret;
+  }
+  template <ptrdiff_t R, ptrdiff_t C> struct Ref {
+    StaticArray *parent;
+    ptrdiff_t i, j;
+    constexpr auto operator=(simd::Unroll<R, C, W, T> x) -> Ref & {
+      checkinds<R>(i, j);
+      ptrdiff_t k = j / W;
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t r = 0; r < R; ++r) {
+        POLYMATHFULLUNROLL
+        for (ptrdiff_t u = 0; u < C; ++u)
+          parent->memory_[(i + r) * L + k + u] = x[r, u];
+      }
+      return *this;
+    }
+    constexpr auto operator=(simd::Vec<W, T> x) -> Ref & {
+      checkinds<R>(i, j);
+      ptrdiff_t k = j / W;
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t r = 0; r < R; ++r) {
+        POLYMATHFULLUNROLL
+        for (ptrdiff_t u = 0; u < C; ++u)
+          parent->memory_[(i + r) * L + k + u] = x;
+      }
+      return *this;
+    }
+    constexpr auto operator=(std::convertible_to<T> auto x) -> Ref & {
+      *this = simd::Vec<W, T>{} + T(x);
+      return *this;
+    }
+    constexpr operator simd::Unroll<R, C, W, T>() {
+      return (*const_cast<const StaticArray *>(
+        parent))[simd::index::Unroll<R>{i}, simd::index::Unroll<C, W>{j}];
+    }
+    constexpr auto operator+=(const auto &x) -> Ref & {
+      return (*this) = simd::Unroll<R, C, W, T>(*this) + x;
+    }
+    constexpr auto operator-=(const auto &x) -> Ref & {
+      return (*this) = simd::Unroll<R, C, W, T>(*this) - x;
+    }
+    constexpr auto operator*=(const auto &x) -> Ref & {
+      return (*this) = simd::Unroll<R, C, W, T>(*this) * x;
+    }
+    constexpr auto operator/=(const auto &x) -> Ref & {
+      return (*this) = simd::Unroll<R, C, W, T>(*this) / x;
+    }
+  };
+  template <ptrdiff_t U, typename Mask>
+  [[gnu::always_inline]] inline auto
+  operator[](ptrdiff_t i, simd::index::Unroll<U, W, Mask> j) -> Ref<1, U> {
+    return Ref<1, U>{this, i, j.index};
+  }
+  template <ptrdiff_t R, ptrdiff_t C, typename Mask>
+  [[gnu::always_inline]] inline auto
+  operator[](simd::index::Unroll<R> i, simd::index::Unroll<C, W, Mask> j)
+    -> Ref<R, C> {
+    return Ref<R, C>{this, i.index, j.index};
+  }
+  [[gnu::always_inline]] constexpr auto operator[](auto i) -> decltype(auto)
+  requires((N == 1) || (M == 1))
+  {
+    if constexpr (M == 1) return (*this)[0, i];
+    else return (*this)[i, 0];
+  }
+  [[gnu::always_inline]] constexpr auto operator[](auto i) const
+    -> decltype(auto)
+  requires((N == 1) || (M == 1))
+  {
+    if constexpr (M == 1) return (*this)[0, i];
+    else return (*this)[i, 0];
+  }
+  constexpr auto operator==(const StaticArray &other) const -> bool {
+    // masks return `true` if `any` are on
+    for (ptrdiff_t i = 0; i < M * L; ++i)
+      if (simd::cmp::ne<W, T>(memory_[i], other.memory_[i])) return false;
+    return true;
+  }
+  template <std::size_t I> [[nodiscard]] constexpr auto get() const -> T {
+    return memory_[I / W][I % W];
+  }
+};
+
+template <class T, ptrdiff_t N, ptrdiff_t Compress = false>
+using SVector = StaticArray<T, 1, N, Compress>;
+static_assert(
+  std::same_as<Row<1>, decltype(SVector<int64_t, 3, true>::numRow())>);
+static_assert(std::same_as<Row<1>, decltype(SVector<int64_t, 3>::numRow())>);
+static_assert(
+  std::same_as<Row<1>, decltype(numRows(std::declval<SVector<int64_t, 3>>()))>);
 
-static_assert(AbstractVector<SVector<int64_t, 3>>);
+static_assert(RowVector<SVector<int64_t, 3>>);
+static_assert(!ColVector<SVector<int64_t, 3>>);
+static_assert(!RowVector<Transpose<SVector<int64_t, 3>>>);
+static_assert(ColVector<Transpose<SVector<int64_t, 3>>>);
+static_assert(RowVector<StaticArray<int64_t, 1, 4, false>>);
+static_assert(RowVector<StaticArray<int64_t, 1, 4, true>>);
 
-template <class T, StaticSize S>
-inline constexpr auto view(const StaticArray<T, S> &x) {
+template <class T, ptrdiff_t M, ptrdiff_t N>
+inline constexpr auto view(const StaticArray<T, M, N> &x) {
   return x.view();
 }
 
 template <class T, class... U>
-StaticArray(T, U...)
-  -> StaticArray<T, std::integral_constant<ptrdiff_t, 1 + sizeof...(U)>>;
+StaticArray(T, U...) -> StaticArray<T, 1, 1 + sizeof...(U)>;
 
-}; // namespace poly::math
+static_assert(utils::Compressible<SVector<int64_t, 3>>);
+static_assert(utils::Compressible<SVector<int64_t, 7>>);
+} // namespace poly::math
 
 template <class T, ptrdiff_t N> // NOLINTNEXTLINE(cert-dcl58-cpp)
 struct std::tuple_size<::poly::math::SVector<T, N>>
diff --git a/include/Math/UniformScaling.hpp b/include/Math/UniformScaling.hpp
index 7ca3629..75ca505 100644
--- a/include/Math/UniformScaling.hpp
+++ b/include/Math/UniformScaling.hpp
@@ -1,5 +1,8 @@
 #pragma once
 #include "Math/Matrix.hpp"
+#include "SIMD/Indexing.hpp"
+#include "SIMD/Masks.hpp"
+#include "SIMD/Unroll.hpp"
 namespace poly::math {
 
 template <class T> struct UniformScaling {
@@ -9,9 +12,42 @@ template <class T> struct UniformScaling {
   constexpr auto operator[](ptrdiff_t r, ptrdiff_t c) const -> T {
     return r == c ? value : T{};
   }
+  template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename M>
+  [[gnu::always_inline]] constexpr auto
+  operator[](simd::index::Unroll<R> r, simd::index::Unroll<C, W, M> c) const
+    -> simd::Unroll<R, C, W, T> {
+    simd::Unroll<R, C, W, T> ret;
+    using I = simd::IntegerOfSize<T>;
+    using VI = simd::Vec<W, I>;
+    simd::Vec<W, T> vz{}, vv = vz + value;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t i = 0; i < R; ++i) {
+      VI vr = VI{} + (i + r.index), vc = simd::range<W, I>() + c.index;
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t j = 0; j < C; ++j, vc += W)
+        ret[i, j] = (vr == vc) ? vv : vz;
+    }
+    return ret;
+  }
+  template <ptrdiff_t C, ptrdiff_t W, typename M>
+  [[gnu::always_inline]] constexpr auto
+  operator[](ptrdiff_t r, simd::index::Unroll<C, W, M> c) const
+    -> simd::Unroll<1, C, W, T> {
+    return (*this)[simd::index::Unroll<1>{r}, c];
+  }
+  // template <ptrdiff_t C, ptrdiff_t W, typename M>
+  // [[gnu::always_inline]] constexpr auto
+  // operator[](simd::index::Unroll<C, W, M> r, ptrdiff_t c) const
+  //   -> simd::Unroll<1, C, W, T> {
+  //   return (*this)[r, simd::index::Unroll<1>{c}];
+  // }
+
   static constexpr auto numRow() -> Row<0> { return {}; }
   static constexpr auto numCol() -> Col<0> { return {}; }
-  static constexpr auto size() -> CartesianIndex<ptrdiff_t, ptrdiff_t> {
+  static constexpr auto size() -> std::integral_constant<ptrdiff_t, 0> {
+    return {};
+  }
+  static constexpr auto shape() -> CartesianIndex<ptrdiff_t, ptrdiff_t> {
     return {0, 0};
   }
   static constexpr auto dim() -> DenseDims<0, 0> { return {{}, {}}; }
diff --git a/include/Math/Unimodularization.hpp b/include/Math/Unimodularization.hpp
index 3c0db6b..1df1e31 100644
--- a/include/Math/Unimodularization.hpp
+++ b/include/Math/Unimodularization.hpp
@@ -3,11 +3,6 @@
 #include "Math/NormalForm.hpp"
 #include <cstdint>
 
-// function unimod_hnf(A)
-//     H, U = Matrix.(hnf_with_transform(MatrixSpace(ZZ, size(A')...)(A')))
-//     (isdiag(H) && all(isone, @views H[diagind(H)])) || return nothing
-//     [A; Int.(inv(U' .// 1))[size(A, 1)+1:end, :]]
-// end
 namespace poly::math {
 // if `A` can be unimodularized, returns the inverse of the unimodularized `A`
 [[nodiscard]] inline auto unimodularize(IntMatrix<> A)
diff --git a/include/Math/Vector.hpp b/include/Math/Vector.hpp
deleted file mode 100644
index f27bde7..0000000
--- a/include/Math/Vector.hpp
+++ /dev/null
@@ -1,83 +0,0 @@
-#pragma once
-#include "Utilities/TypePromotion.hpp"
-#include <bit>
-#include <cstddef>
-#include <cstdint>
-
-namespace poly::math {
-
-template <typename T, typename S = utils::eltype_t<T>>
-concept LinearlyIndexable = requires(T t, ptrdiff_t i) {
-  { t[i] } -> std::convertible_to<S>;
-};
-template <typename T, typename S>
-concept LinearlyIndexableOrConvertible =
-  LinearlyIndexable<T, S> || std::convertible_to<T, S>;
-
-template <typename T>
-concept AbstractVector =
-  utils::HasEltype<T> && LinearlyIndexable<T> && requires(T t) {
-    { t.size() } -> std::convertible_to<ptrdiff_t>;
-    { t.view() };
-  };
-
-// This didn't work: #include "Math/Vector.hpp" NOLINT(unused-includes)
-// so I moved some code from "Math/Array.hpp" here instead.
-template <class T>
-concept SizeMultiple8 = (sizeof(T) % 8) == 0;
-
-template <class S> struct DefaultCapacityType {
-  using type = int;
-};
-template <SizeMultiple8 S> struct DefaultCapacityType<S> {
-  using type = std::ptrdiff_t;
-};
-template <class S>
-using default_capacity_type_t = typename DefaultCapacityType<S>::type;
-
-static_assert(!SizeMultiple8<uint32_t>);
-static_assert(SizeMultiple8<uint64_t>);
-static_assert(std::is_same_v<default_capacity_type_t<uint32_t>, int32_t>);
-static_assert(std::is_same_v<default_capacity_type_t<uint64_t>, int64_t>);
-
-template <class T, class S> consteval auto PreAllocStorage() -> ptrdiff_t {
-  constexpr ptrdiff_t totalBytes = 128;
-  constexpr ptrdiff_t remainingBytes =
-    totalBytes - sizeof(T *) - sizeof(S) - sizeof(default_capacity_type_t<S>);
-  constexpr ptrdiff_t N = remainingBytes / sizeof(T);
-  return std::max<ptrdiff_t>(0, N);
-}
-constexpr auto log2Floor(uint64_t x) -> uint64_t {
-  return 63 - std::countl_zero(x);
-}
-constexpr auto log2Ceil(uint64_t x) -> uint64_t {
-  return 64 - std::countl_zero(x - 1);
-}
-// NOLINTNEXTLINE(misc-no-recursion)
-consteval auto bisectFindSquare(uint64_t l, uint64_t h, uint64_t N)
-  -> uint64_t {
-  if (l == h) return l;
-  uint64_t m = (l + h) / 2;
-  if (m * m >= N) return bisectFindSquare(l, m, N);
-  return bisectFindSquare(m + 1, h, N);
-}
-template <class T, class S>
-consteval auto PreAllocSquareStorage() -> ptrdiff_t {
-  // 2* because we want to allow more space for matrices
-  // also removes need for other checks; log2Floor(2)==1
-  constexpr uint64_t N = 2 * PreAllocStorage<T, S>();
-  if (!N) return 0;
-  // a fairly naive algorirthm for computing the next square `N`
-  // sqrt(x) = x^(1/2) = exp2(log2(x)/2)
-  constexpr uint64_t L = 1 << (log2Floor(N) / 2);
-  constexpr uint64_t H = 1 << ((log2Ceil(N) + 1) / 2);
-  return ptrdiff_t(bisectFindSquare(L, H, N));
-}
-
-constexpr auto selfDot(const auto &a) {
-  utils::eltype_t<decltype(a)> sum = 0;
-  for (auto x : a) sum += x * x;
-  return sum;
-}
-
-} // namespace poly::math
diff --git a/include/SIMD/Indexing.hpp b/include/SIMD/Indexing.hpp
new file mode 100644
index 0000000..3e30230
--- /dev/null
+++ b/include/SIMD/Indexing.hpp
@@ -0,0 +1,57 @@
+#pragma once
+#ifndef MATH_SIMD_INDEXING_HPP_INCLUDED
+#define MATH_SIMD_INDEXING_HPP_INCLUDED
+
+#include "Math/AxisTypes.hpp"
+#include "SIMD/Masks.hpp"
+namespace poly::simd::index {
+// Unroll rows by a factor of `R` and cols by `C`, vectorizing with width `W`
+template <ptrdiff_t U, ptrdiff_t W = 1, typename M = mask::None<W>>
+struct Unroll {
+  ptrdiff_t index;
+  [[no_unique_address]] M mask{};
+  explicit constexpr operator ptrdiff_t() const { return index; }
+  explicit constexpr operator bool() const { return bool(mask); }
+  constexpr auto operator+(ptrdiff_t b) -> Unroll { return {b + index, mask}; }
+};
+template <ptrdiff_t U, ptrdiff_t W>
+[[gnu::always_inline]] constexpr auto unrollmask(ptrdiff_t L, ptrdiff_t i) {
+  // mask applies to last iter
+  // We can't check that the last iter is non-empty, because that
+  // could be the loop exit condition
+  auto m{mask::create<W>(i + (U - 1) * W, L)};
+  return Unroll<U, W, decltype(m)>{i, m};
+};
+
+// template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename M, ptrdiff_t X>
+// constexpr auto unroll(ptrdiff_t index, M mask, RowStride<X> rs){
+//   return Unroll<R,C,W,M,X>{index,mask,rs};
+// }
+
+/// UnrollDims<R,C,W,M,Transposed=false>
+/// Transposed means that the `W` dim indexes across the stride
+/// !Tranposed means that the `W` dim is contiguous.
+/// Note that `UnrollDims<R,C,1,mask::None<1>,false>` is thus morally
+/// equivalent to `UnrollDims<C,R,1,mask::None<1>,true>`
+///
+template <ptrdiff_t R, ptrdiff_t C = 1, ptrdiff_t W = 1,
+          typename M = mask::None<W>, bool Transposed = false, ptrdiff_t X = -1>
+struct UnrollDims {
+  static_assert(W != 1 || std::same_as<M, mask::None<1>>,
+                "Only mask vector dims");
+  static_assert(W != 1 || !Transposed,
+                "Canonicalize scalar with Tranpose=false");
+  [[no_unique_address]] M mask;
+  [[no_unique_address]] math::RowStride<X> rs;
+};
+
+template <typename T> static constexpr bool issimd = false;
+
+template <ptrdiff_t U, ptrdiff_t W, typename M>
+static constexpr bool issimd<Unroll<U, W, M>> = true;
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename M, bool Transposed,
+          ptrdiff_t X>
+static constexpr bool issimd<UnrollDims<R, C, W, M, Transposed, X>> = true;
+} // namespace poly::simd::index
+
+#endif
diff --git a/include/SIMD/Intrin.hpp b/include/SIMD/Intrin.hpp
new file mode 100644
index 0000000..6029fb2
--- /dev/null
+++ b/include/SIMD/Intrin.hpp
@@ -0,0 +1,688 @@
+#pragma once
+#ifndef MATH_SIMD_INTRIN_HPP_INCLUDED
+#define MATH_SIMD_INTRIN_HPP_INCLUDED
+
+#include <Math/AxisTypes.hpp>
+#include <SIMD/Indexing.hpp>
+#include <SIMD/Masks.hpp>
+#include <SIMD/Vec.hpp>
+#include <Utilities/Invariant.hpp>
+#include <Utilities/LoopMacros.hpp>
+#include <array>
+#include <bit>
+#include <concepts>
+#include <cstddef>
+#include <cstdint>
+
+#ifdef __x86_64__
+#include <immintrin.h>
+#endif
+namespace poly::simd {
+
+// Supported means by this library currently; more types may be added in the
+// future as needed.
+template <typename T>
+concept SIMDSupported = std::same_as<T, int64_t> || std::same_as<T, double>;
+
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto vbroadcast(Vec<W, T> v) -> Vec<W, T> {
+  if constexpr (W == 2) return __builtin_shufflevector(v, v, 0, 0);
+  else if constexpr (W == 4) return __builtin_shufflevector(v, v, 0, 0, 0, 0);
+  else if constexpr (W == 8)
+    return __builtin_shufflevector(v, v, 0, 0, 0, 0, 0, 0, 0, 0);
+  else if constexpr (W == 16)
+    return __builtin_shufflevector(v, v, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+                                   0, 0, 0);
+  else if constexpr (W == 32)
+    return __builtin_shufflevector(v, v, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+                                   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+                                   0, 0, 0, 0);
+  else if constexpr (W == 64)
+    return __builtin_shufflevector(
+      v, v, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
+  else static_assert(false);
+}
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto vbroadcast(T x) -> Vec<W, T> {
+  return vbroadcast<W, T>(Vec<W, T>{x});
+}
+
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto load(const T *p,
+                                                         mask::None<1>) -> T {
+  return *p;
+}
+template <typename T>
+constexpr auto load(const T *p, mask::None<1>, int32_t) -> const T & {
+  return *p;
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void store(T *p, mask::None<1>,
+                                                          T x) {
+  *p = x;
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void store(T *p, mask::None<1>,
+                                                          T x, int32_t) {
+  *p = x;
+}
+#ifdef __x86_64__
+
+// TODO: make `consteval` when clang supports it
+#ifdef __clang__
+template <ptrdiff_t W, typename T> constexpr auto mmzero() {
+#else
+template <ptrdiff_t W, typename T> consteval auto mmzero() {
+#endif
+  // Extend if/when supporting more types
+  static_assert(std::popcount(size_t(W)) == 1 && W <= 8);
+  constexpr Vec<W, T> z{};
+  if constexpr (std::same_as<T, double>) {
+    if constexpr (W == 8) return std::bit_cast<__m512d>(z);
+    else if constexpr (W == 4) return std::bit_cast<__m256d>(z);
+    else return std::bit_cast<__m128d>(z);
+  } else {
+    static_assert(std::same_as<T, int64_t>);
+    if constexpr (W == 8) return std::bit_cast<__m512i>(z);
+    else if constexpr (W == 4) return std::bit_cast<__m256i>(z);
+    else return std::bit_cast<__m128i>(z);
+  }
+}
+template <ptrdiff_t W> inline auto vindex(int32_t stride) {
+  if constexpr (W <= 4) return std::bit_cast<__m128i>(range<W>() * stride);
+  else if constexpr (W == 8) return std::bit_cast<__m256i>(range<W>() * stride);
+  else {
+    static_assert(W == 16);
+    return std::bit_cast<__m512i>(range<W>() * stride);
+  }
+}
+
+#ifdef __AVX512F__
+static constexpr ptrdiff_t REGISTERS = 32;
+static constexpr ptrdiff_t VECTORWIDTH = 64;
+// namespace hw {
+// typedef double __m512d_u __attribute__((__vector_size__(64),
+// __aligned__(8)));
+
+// typedef int64_t __m512i_u __attribute__((__vector_size__(64),
+// __aligned__(8))); } // namespace hw
+
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto load(const T *p,
+                                                         mask::None<8>)
+  -> Vec<8, T> {
+  if constexpr (std::same_as<T, double>) {
+    // hw::__m512d_u v = *reinterpret_cast<const hw::__m512d_u *>(p);
+    // return std::bit_cast<Vec<8, double>>(v);
+    return std::bit_cast<Vec<8, double>>(_mm512_loadu_pd(p));
+  } else if constexpr (std::same_as<T, int64_t>) {
+    // hw::__m512i_u v = *reinterpret_cast<const hw::__m512i_u *>(p);
+    // return std::bit_cast<Vec<8, int64_t>>(v);
+    return std::bit_cast<Vec<8, int64_t>>(_mm512_loadu_epi64(p));
+  } else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto load(const T *p,
+                                                         mask::Bit<8> i)
+  -> Vec<8, T> {
+  if constexpr (std::same_as<T, double>)
+    return std::bit_cast<Vec<8, double>>(
+      _mm512_maskz_loadu_pd(uint8_t(i.mask), p));
+  else if constexpr (std::same_as<T, int64_t>)
+    return std::bit_cast<Vec<8, int64_t>>(
+      _mm512_maskz_loadu_epi64(uint8_t(i.mask), p));
+  else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void store(T *p, mask::None<8>,
+                                                          Vec<8, T> x) {
+  if constexpr (std::same_as<T, double>) {
+    // hw::__m512d_u v = std::bit_cast<Vec<8, double>>(x);
+    // *reinterpret_cast<hw::__m512d_u *>(p) = v;
+    _mm512_storeu_pd(p, std::bit_cast<__m512d>(x));
+  } else if constexpr (std::same_as<T, int64_t>) {
+    // hw::__m512i_u v = std::bit_cast<Vec<8, int64_t>>(x);
+    // *reinterpret_cast<hw::__m512i_u *>(p) = v;
+    _mm512_storeu_epi64(p, std::bit_cast<__m512i>(x));
+  } else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void store(T *p, mask::Bit<8> i,
+                                                          Vec<8, T> x) {
+  if constexpr (std::same_as<T, double>)
+    _mm512_mask_storeu_pd(p, uint8_t(i.mask), std::bit_cast<__m512d>(x));
+  else if constexpr (std::same_as<T, int64_t>)
+    _mm512_mask_storeu_epi64(p, uint8_t(i.mask), std::bit_cast<__m512i>(x));
+  else static_assert(false);
+}
+
+// strided memory accesses
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto
+load(const T *p, mask::None<8>, int32_t stride) -> Vec<8, T> {
+  if constexpr (std::same_as<T, double>)
+    return std::bit_cast<Vec<8, T>>(
+      _mm512_i32gather_pd(vindex<8>(stride), p, 8));
+  else if constexpr (std::same_as<T, int64_t>)
+    return std::bit_cast<Vec<8, int64_t>>(
+      _mm512_i32gather_pd(vindex<8>(stride), p, 8));
+  else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto
+load(const T *p, mask::Bit<8> i, int32_t stride) -> Vec<8, T> {
+  auto src = mmzero<8, T>();
+  if constexpr (std::same_as<T, double>)
+    return std::bit_cast<Vec<8, double>>(
+      _mm512_mask_i32gather_pd(src, uint8_t(i.mask), vindex<8>(stride), p, 8));
+  else if constexpr (std::same_as<T, int64_t>)
+    return std::bit_cast<Vec<8, int64_t>>(_mm512_mask_i32gather_epi64(
+      src, uint8_t(i.mask), vindex<8>(stride), p, 8));
+  else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void
+store(T *p, mask::None<8>, Vec<8, T> x, int32_t stride) {
+  if constexpr (std::same_as<T, double>)
+    _mm512_i32scatter_pd(p, vindex<8>(stride), std::bit_cast<__m512d>(x), 8);
+  else if constexpr (std::same_as<T, int64_t>)
+    _mm512_i32scatter_epi64(p, vindex<8>(stride), std::bit_cast<__m512i>(x), 8);
+  else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void
+store(T *p, mask::Bit<8> i, Vec<8, T> x, int32_t stride) {
+  if constexpr (std::same_as<T, double>)
+    _mm512_mask_i32scatter_pd(p, uint8_t(i.mask), vindex<8>(stride),
+                              std::bit_cast<__m512d>(x), 8);
+  else if constexpr (std::same_as<T, int64_t>)
+    _mm512_mask_i32scatter_epi64(p, uint8_t(i.mask), vindex<8>(stride),
+                                 std::bit_cast<__m512i>(x), 8);
+  else static_assert(false);
+}
+#else // no AVX512F
+
+static constexpr ptrdiff_t REGISTERS = 16;
+#ifdef __AVX__
+static constexpr ptrdiff_t VECTORWIDTH = 32;
+#else  // no AVX
+static constexpr ptrdiff_t VECTORWIDTH = 16;
+#endif // no AVX
+#endif // no AVX512F
+#ifdef __AVX2__
+
+// Non-masked gather/scatter are the same with AVX512VL and AVX2
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto
+load(const T *p, mask::None<4>, int32_t stride) -> Vec<4, T> {
+  auto x{vindex<4>(stride)};
+  if constexpr (std::same_as<T, double>)
+    return std::bit_cast<Vec<4, double>>(_mm256_i32gather_pd(p, x, 8));
+  else if constexpr (std::same_as<T, int64_t>)
+    return std::bit_cast<Vec<4, int64_t>>(_mm256_i32gather_pd(p, x, 8));
+  else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto
+load(const T *p, mask::None<2>, int32_t stride) -> Vec<2, T> {
+  auto x{vindex<2>(stride)};
+  if constexpr (std::same_as<T, double>)
+    return std::bit_cast<Vec<2, double>>(_mm_i64gather_pd(p, x, 8));
+  else if constexpr (std::same_as<T, int64_t>)
+    return std::bit_cast<Vec<2, int64_t>>(_mm_i64gather_pd(p, x, 8));
+  else static_assert(false);
+}
+#endif // AVX2
+
+// Here, we handle masked loads/stores
+#ifdef __AVX512VL__
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto load(const T *p,
+                                                         mask::Bit<4> i)
+  -> Vec<4, T> {
+  if constexpr (std::same_as<T, double>)
+    return std::bit_cast<Vec<4, double>>(
+      _mm256_maskz_loadu_pd(uint8_t(i.mask), p));
+  else if constexpr (std::same_as<T, int64_t>)
+    return std::bit_cast<Vec<4, int64_t>>(
+      _mm256_maskz_loadu_epi64(uint8_t(i.mask), p));
+  else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void store(T *p, mask::Bit<4> i,
+                                                          Vec<4, T> x) {
+  if constexpr (std::same_as<T, double>)
+    _mm256_mask_storeu_pd(p, uint8_t(i.mask), std::bit_cast<__m256d>(x));
+  else if constexpr (std::same_as<T, int64_t>)
+    _mm256_mask_storeu_epi64(p, uint8_t(i.mask), std::bit_cast<__m256i>(x));
+  else static_assert(false);
+}
+
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto load(const T *p,
+                                                         mask::Bit<2> i)
+  -> Vec<2, T> {
+  if constexpr (std::same_as<T, double>)
+    return std::bit_cast<Vec<2, double>>(
+      _mm_maskz_loadu_pd(uint8_t(i.mask), p));
+  else if constexpr (std::same_as<T, int64_t>)
+    return std::bit_cast<Vec<2, int64_t>>(
+      _mm_maskz_loadu_epi64(uint8_t(i.mask), p));
+  else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void store(T *p, mask::Bit<2> i,
+                                                          Vec<2, T> x) {
+  if constexpr (std::same_as<T, double>)
+    _mm_mask_storeu_pd(p, uint8_t(i.mask), std::bit_cast<__m128d>(x));
+  else if constexpr (std::same_as<T, int64_t>)
+    _mm_mask_storeu_epi64(p, uint8_t(i.mask), std::bit_cast<__m128i>(x));
+  else static_assert(false);
+}
+// gather/scatter
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto
+load(const T *p, mask::Bit<4> i, int32_t stride) -> Vec<4, T> {
+  auto src{mmzero<4, T>()};
+  if constexpr (std::same_as<T, double>)
+    return std::bit_cast<Vec<4, double>>(
+      _mm256_mmask_i32gather_pd(src, uint8_t(i.mask), vindex<4>(stride), p, 8));
+  else if constexpr (std::same_as<T, int64_t>)
+    return std::bit_cast<Vec<4, int64_t>>(_mm256_mmask_i32gather_epi64(
+      src, uint8_t(i.mask), vindex<4>(stride), p, 8));
+  else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void
+store(T *p, mask::None<4>, Vec<4, T> x, int32_t stride) {
+  if constexpr (std::same_as<T, double>)
+    _mm256_i32scatter_pd(p, vindex<4>(stride), std::bit_cast<__m256d>(x), 8);
+  else if constexpr (std::same_as<T, int64_t>)
+    _mm256_i32scatter_epi64(p, vindex<4>(stride), std::bit_cast<__m256i>(x), 8);
+  else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void
+store(T *p, mask::Bit<4> i, Vec<4, T> x, int32_t stride) {
+  if constexpr (std::same_as<T, double>)
+    _mm256_mask_i32scatter_pd(p, uint8_t(i.mask), vindex<4>(stride),
+                              std::bit_cast<__m256d>(x), 8);
+  else if constexpr (std::same_as<T, int64_t>)
+    _mm256_mask_i32scatter_epi64(p, uint8_t(i.mask), vindex<4>(stride),
+                                 std::bit_cast<__m256i>(x), 8);
+  else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto
+load(const T *p, mask::Bit<2> i, int32_t stride) -> Vec<2, T> {
+  auto src{mmzero<2, T>()};
+  if constexpr (std::same_as<T, double>)
+    return std::bit_cast<Vec<2, double>>(
+      _mm_mmask_i64gather_pd(src, uint8_t(i.mask), vindex<2>(stride), p, 8));
+  else if constexpr (std::same_as<T, int64_t>)
+    return std::bit_cast<Vec<2, int64_t>>(
+      _mm_mmask_i64gather_epi64(src, uint8_t(i.mask), vindex<2>(stride), p, 8));
+  else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void
+store(T *p, mask::None<2>, Vec<2, T> x, int32_t stride) {
+  if constexpr (std::same_as<T, double>)
+    _mm_i64scatter_pd(p, vindex<2>(stride), std::bit_cast<__m128d>(x), 8);
+  else if constexpr (std::same_as<T, int64_t>)
+    _mm_i64scatter_epi64(p, vindex<2>(stride), std::bit_cast<__m128i>(x), 8);
+  else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void
+store(T *p, mask::Bit<2> i, Vec<2, T> x, int32_t stride) {
+  if constexpr (std::same_as<T, double>)
+    _mm_mask_i64scatter_pd(p, uint8_t(i.mask), vindex<2>(stride),
+                           std::bit_cast<__m128d>(x), 8);
+  else if constexpr (std::same_as<T, int64_t>)
+    _mm_mask_i64scatter_epi64(p, uint8_t(i.mask), vindex<2>(stride),
+                              std::bit_cast<__m128i>(x), 8);
+  else static_assert(false);
+}
+
+#else // No AVX512VL
+
+// We need [gather, scatter, load, store] * [unmasked, masked]
+
+// 128 bit fallback scatters
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void
+store(T *p, mask::None<2>, Vec<2, T> x, int32_t stride) {
+  p[0] = x[0];
+  p[stride] = x[1];
+}
+
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void
+store(T *p, mask::Vector<2> i, Vec<2, T> x, int32_t stride) {
+  if (i.m[0] != 0) p[0] = x[0];
+  if (i.m[1] != 0) p[stride] = x[1];
+}
+
+#ifdef __AVX2__
+// masked gathers
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto
+load(const T *p, mask::Vector<4> m, int32_t stride) -> Vec<4, T> {
+  __m128i x = vindex<4>(stride);
+  __m256i mask = __m256i(m);
+  if constexpr (std::same_as<T, double>) {
+    constexpr __m256d z = mmzero<4, double>();
+    return std::bit_cast<Vec<4, double>>(
+      _mm256_mask_i32gather_pd(z, p, x, mask, 8));
+  } else if constexpr (std::same_as<T, int64_t>) {
+    constexpr __m256i z = mmzero<4, int64_t>();
+    return std::bit_cast<Vec<4, int64_t>>(
+      _mm256_mask_i32gather_epi64(z, p, x, mask, 8));
+  } else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto
+load(const T *p, mask::Vector<2> m, int32_t stride) -> Vec<2, T> {
+  __m128i x = vindex<2>(stride), mask = __m128i(m);
+  if constexpr (std::same_as<T, double>) {
+    constexpr __m128d z = mmzero<2, double>();
+    return std::bit_cast<Vec<2, double>>(
+      _mm_mask_i64gather_pd(z, p, x, mask, 8));
+  } else if constexpr (std::same_as<T, int64_t>) {
+    constexpr __m128i z = mmzero<2, int64_t>();
+    return std::bit_cast<Vec<2, int64_t>>(
+      _mm_mask_i64gather_epi64(z, p, x, mask, 8));
+  } else static_assert(false);
+}
+
+#else          // no AVX2
+// fallback 128-bit gather
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto
+load(const T *p, mask::None<2>, int32_t stride) -> Vec<2, T> {
+  return Vec<2, T>{p[0], p[stride]};
+}
+
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto
+load(const T *p, mask::Vector<2> i, int32_t stride) -> Vec<2, T> {
+  return Vec<2, T>{(i.m[0] != 0) ? p[0] : T{}, (i.m[1] != 0) ? p[stride] : T{}};
+}
+#ifdef __AVX__ // no AVX2, but AVX
+// fallback 256-bit gather
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto
+load(const T *p, mask::None<4>, int32_t stride) -> Vec<4, T> {
+  return Vec<4, T>{p[0], p[stride], p[2 * stride], p[3 * stride]};
+}
+
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto
+load(const T *p, mask::Vector<4> i, int32_t stride) -> Vec<4, T> {
+  return Vec<4, T>{
+    (i.m[0] != 0) ? p[0] : T{},
+    (i.m[1] != 0) ? p[stride] : T{},
+    (i.m[2] != 0) ? p[2 * stride] : T{},
+    (i.m[3] != 0) ? p[3 * stride] : T{},
+  };
+}
+
+#endif // AVX
+#endif // no AVX2
+#ifdef __AVX__
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto load(const T *p,
+                                                         mask::Vector<4> i)
+  -> Vec<4, T> {
+  if constexpr (std::same_as<T, double>)
+    return std::bit_cast<Vec<4, double>>(_mm256_maskload_pd(p, i));
+  else if constexpr (std::same_as<T, int64_t>)
+    return std::bit_cast<Vec<4, int64_t>>(
+      _mm256_maskload_epi64((const long long *)p, i));
+  else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void
+store(T *p, mask::Vector<4> i, Vec<4, T> x) {
+  if constexpr (std::same_as<T, double>)
+    _mm256_maskstore_pd(p, i, std::bit_cast<__m256d>(x));
+  else if constexpr (std::same_as<T, int64_t>)
+    _mm256_maskstore_epi64((long long *)p, i, std::bit_cast<__m256i>(x));
+  else static_assert(false);
+}
+
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto load(const T *p,
+                                                         mask::Vector<2> i)
+  -> Vec<2, T> {
+  if constexpr (std::same_as<T, double>)
+    return std::bit_cast<Vec<2, double>>(_mm_maskload_pd(p, i));
+  else if constexpr (std::same_as<T, int64_t>)
+    return std::bit_cast<Vec<2, int64_t>>(
+      _mm_maskload_epi64((const long long *)p, i));
+  else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void
+store(T *p, mask::Vector<2> i, Vec<2, T> x) {
+  if constexpr (std::same_as<T, double>)
+    _mm_maskstore_pd(p, i, std::bit_cast<__m128d>(x));
+  else if constexpr (std::same_as<T, int64_t>)
+    _mm_maskstore_epi64((long long *)p, i, std::bit_cast<__m128i>(x));
+  else static_assert(false);
+}
+
+// we need 256 bit fallback scatters
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void
+store(T *p, mask::None<4>, Vec<4, T> x, int32_t stride) {
+  p[0] = x[0];
+  p[stride] = x[1];
+  p[2 * stride] = x[2];
+  p[3 * stride] = x[3];
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void
+store(T *p, mask::Vector<4> i, Vec<4, T> x, int32_t stride) {
+  if (i.m[0] != 0) p[0] = x[0];
+  if (i.m[1] != 0) p[stride] = x[1];
+  if (i.m[2] != 0) p[2 * stride] = x[2];
+  if (i.m[3] != 0) p[3 * stride] = x[3];
+}
+#else // No AVX
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto load(const T *p,
+                                                         mask::Vector<2> i)
+  -> Vec<2, T> {
+  return Vec<2, T>{(i.m[0] != 0) ? p[0] : T{}, (i.m[1] != 0) ? p[1] : T{}};
+}
+
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void
+store(T *p, mask::Vector<2> i, Vec<2, T> x) {
+  if (i.m[0] != 0) p[0] = x[0];
+  if (i.m[1] != 0) p[1] = x[1];
+}
+
+#endif // No AVX
+#endif // No AVX512VL
+#ifdef __AVX__
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto load(const T *p,
+                                                         mask::None<4>)
+  -> Vec<4, T> {
+  if constexpr (std::same_as<T, double>)
+    return std::bit_cast<Vec<4, double>>(_mm256_loadu_pd(p));
+  else if constexpr (std::same_as<T, int64_t>)
+#ifdef __AVX512VL__
+    return std::bit_cast<Vec<4, int64_t>>(_mm256_loadu_epi64(p));
+#else
+    return std::bit_cast<Vec<4, int64_t>>(
+      _mm256_loadu_si256((const __m256i *)p));
+#endif
+  else static_assert(false);
+}
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void store(T *p, mask::None<4>,
+                                                          Vec<4, T> x) {
+  if constexpr (std::same_as<T, double>)
+    _mm256_storeu_pd(p, std::bit_cast<__m256d>(x));
+  else if constexpr (std::same_as<T, int64_t>)
+#ifdef __AVX512VL__
+    _mm256_storeu_epi64(p, std::bit_cast<__m256i>(x));
+#else
+    _mm256_storeu_si256((__m256i *)p, std::bit_cast<__m256i>(x));
+#endif
+  else static_assert(false);
+}
+
+// // non-power-of-2 memory ops
+// template <ptrdiff_t N, typename M>
+// constexpr auto fixupnonpow2(index::Vector<N, M> i) {
+//   static_assert(std::popcount(size_t(N)) > 1,
+//                 "Shouldn't be calling this if not needed.");
+//   static constexpr ptrdiff_t W = std::bit_ceil(size_t(N));
+//   auto m = i.mask & mask(index::VectorMask<W>{N});
+//   return index::Vector<W, decltype(m)>{i.i, m};
+// }
+
+// template <typename T, ptrdiff_t N, typename M>
+// [[gnu::always_inline, gnu::artificial]] inline auto
+// load(const T *p, index::Vector<N, M> i) {
+//   return load(p, fixupnonpow2(i));
+// }
+// template <typename T, ptrdiff_t N, typename M>
+// [[gnu::always_inline, gnu::artificial]] inline auto
+// load(const T *p, index::Vector<N, M> i, int32_t stride) {
+//   return load(p, fixupnonpow2(i), stride);
+// }
+// template <typename T, ptrdiff_t N, typename M, ptrdiff_t W>
+// [[gnu::always_inline, gnu::artificial]] inline void
+// store(T *p, index::Vector<N, M> i, Vec<W, T> x) {
+//   store(p, fixupnonpow2(i), x);
+// }
+// template <typename T, ptrdiff_t N, typename M, ptrdiff_t W>
+// [[gnu::always_inline, gnu::artificial]] inline void
+// store(T *p, index::Vector<N, M> i, Vec<W, T> x, int32_t stride) {
+//   store(p, fixupnonpow2(i), stride);
+// }
+#endif // AVX
+
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto load(const T *p,
+                                                         mask::None<2>)
+  -> Vec<2, T> {
+  if constexpr (std::same_as<T, double>)
+    return std::bit_cast<Vec<2, double>>(_mm_loadu_pd(p));
+  else if constexpr (std::same_as<T, int64_t>)
+#ifdef __AVX512VL__
+    return std::bit_cast<Vec<2, int64_t>>(_mm_loadu_epi64(p));
+#else
+    return std::bit_cast<Vec<2, int64_t>>(_mm_loadu_si128((const __m128i *)p));
+#endif
+  else static_assert(false);
+}
+
+template <typename T>
+[[gnu::always_inline, gnu::artificial]] inline void store(T *p, mask::None<2>,
+                                                          Vec<2, T> x) {
+  if constexpr (std::same_as<T, double>)
+    _mm_storeu_pd(p, std::bit_cast<__m128d>(x));
+  else if constexpr (std::same_as<T, int64_t>)
+#ifdef __AVX512VL__
+    _mm_storeu_epi64(p, std::bit_cast<__m128i>(x));
+#else
+    _mm_storeu_si128((__m128i *)p, std::bit_cast<__m128i>(x));
+#endif
+  else static_assert(false);
+}
+
+#else // not __x86_64__
+static constexpr ptrdiff_t REGISTERS = 32;
+static constexpr ptrdiff_t VECTORWIDTH = 16;
+template <typename T, ptrdiff_t W>
+[[gnu::always_inline, gnu::artificial]] inline auto load(const T *p,
+                                                         mask::None<W>)
+  -> Vec<W, T> {
+  Vec<W, T> ret;
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t w = 0; w < W; ++w) ret[w] = p[w];
+  return ret;
+}
+template <typename T, ptrdiff_t W>
+[[gnu::always_inline, gnu::artificial]] inline void store(T *p, mask::None<W>,
+                                                          Vec<W, T> x) {
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t w = 0; w < W; ++w) p[w] = x[w];
+}
+
+template <typename T, ptrdiff_t W>
+[[gnu::always_inline, gnu::artificial]] inline auto load(const T *p,
+                                                         mask::Vector<W> i)
+  -> Vec<W, T> {
+  Vec<W, T> ret;
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t w = 0; w < W; ++w) ret[w] = (i.m[w] != 0) ? p[w] : T{};
+  return ret;
+}
+template <typename T, ptrdiff_t W>
+[[gnu::always_inline, gnu::artificial]] inline void
+store(T *p, mask::Vector<W> i, Vec<W, T> x) {
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t w = 0; w < W; ++w)
+    if (i.m[w] != 0) p[w] = x[w];
+}
+
+template <typename T, ptrdiff_t W>
+[[gnu::always_inline, gnu::artificial]] inline auto
+load(const T *p, mask::None<W>, int32_t stride) -> Vec<W, T> {
+  Vec<W, T> ret;
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t w = 0; w < W; ++w) ret[w] = p[w * stride];
+  return ret;
+}
+template <typename T, ptrdiff_t W>
+[[gnu::always_inline, gnu::artificial]] inline void
+store(T *p, mask::None<W>, Vec<W, T> x, int32_t stride) {
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t w = 0; w < W; ++w) p[w * stride] = x[w];
+}
+
+template <typename T, ptrdiff_t W>
+[[gnu::always_inline, gnu::artificial]] inline auto
+load(const T *p, mask::Vector<W> i, int32_t stride) -> Vec<W, T> {
+  Vec<W, T> ret;
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t w = 0; w < W; ++w)
+    ret[w] = (i.m[w] != 0) ? p[w * stride] : T{};
+  return ret;
+}
+template <typename T, ptrdiff_t W>
+[[gnu::always_inline, gnu::artificial]] inline void
+store(T *p, mask::Vector<W> i, Vec<W, T> x, int32_t stride) {
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t w = 0; w < W; ++w)
+    if (i.m[w] != 0) p[w * stride] = x[w];
+}
+
+#endif
+
+template <typename T>
+static constexpr ptrdiff_t Width =
+  SIMDSupported<T> ? VECTORWIDTH / sizeof(T) : 1;
+
+// returns { vector_size, num_vectors, remainder }
+template <ptrdiff_t L, typename T>
+consteval auto VectorDivRem() -> std::array<ptrdiff_t, 3> {
+  constexpr ptrdiff_t W = Width<T>;
+  if constexpr (L <= W) {
+    constexpr auto V = ptrdiff_t(std::bit_ceil(size_t(L)));
+    return {V, L / V, L % V};
+  } else return {W, L / W, L % W};
+};
+
+} // namespace poly::simd
+#endif // SIMD_hpp_INCLUDED
diff --git a/include/SIMD/Masks.hpp b/include/SIMD/Masks.hpp
new file mode 100644
index 0000000..17f346c
--- /dev/null
+++ b/include/SIMD/Masks.hpp
@@ -0,0 +1,512 @@
+#pragma once
+#ifndef MATH_SIMD_MASKS_HPP_INCLUDED
+#define MATH_SIMD_MASKS_HPP_INCLUDED
+#include "SIMD/Vec.hpp"
+#include <cstddef>
+#include <cstdint>
+#ifdef __x86_64__
+#include <immintrin.h>
+#endif
+namespace poly::simd {
+
+template <typename T>
+using IntegerOfSize = std::conditional_t<
+  sizeof(T) == 8, int64_t,
+  std::conditional_t<sizeof(T) == 4, int32_t,
+                     std::conditional_t<sizeof(T) == 2, int16_t, int8_t>>>;
+
+template <ptrdiff_t W,
+          typename I = std::conditional_t<W == 2, int64_t, int32_t>>
+consteval auto range() -> Vec<W, I> {
+  static_assert(std::popcount(size_t(W)) == 1);
+  if constexpr (W == 2) return Vec<W, I>{0, 1};
+  else if constexpr (W == 4) return Vec<W, I>{0, 1, 2, 3};
+  else if constexpr (W == 8) return Vec<W, I>{0, 1, 2, 3, 4, 5, 6, 7};
+  else if constexpr (W == 16)
+    return Vec<W, I>{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
+  else {
+    Vec<W, I> r;
+    for (ptrdiff_t w = 0; w < W; ++w) r[w] = I(w);
+    return r;
+  }
+}
+template <ptrdiff_t W,
+          typename I = std::conditional_t<W == 2, int64_t, int32_t>>
+consteval auto firstoff() -> Vec<W, I> {
+  return range<W, I>() != Vec<W, I>{};
+}
+
+namespace mask {
+template <ptrdiff_t W> struct None {
+  static constexpr auto firstMasked() -> ptrdiff_t { return 0; }
+  static constexpr auto lastUnmasked() -> ptrdiff_t { return W; }
+};
+
+// Alternatives we can have: BitMask and VectorMask
+// We use `BitMask` on AVX512, VectorMask elsewhere.
+// ARM SVE(2) will eventually want bitmasks as well.
+#ifdef __x86_64__
+#ifdef __AVX512F__
+template <ptrdiff_t W> struct Bit {
+  uint64_t mask;
+  template <std::unsigned_integral U> explicit constexpr operator U() {
+    return U(mask);
+  }
+  explicit constexpr operator bool() const { return mask; }
+  [[nodiscard]] constexpr auto firstMasked() const -> ptrdiff_t {
+    return std::countr_zero(mask);
+  }
+  [[nodiscard]] constexpr auto lastUnmasked() const -> ptrdiff_t {
+    // could make this `countr_ones` if we decide to only
+    // support leading masks
+    uint64_t m = mask & ((uint64_t(1) << W) - uint64_t(1));
+    return 64 - ptrdiff_t(std::countl_zero(m));
+  }
+};
+template <ptrdiff_t W> constexpr auto operator&(Bit<W> a, Bit<W> b) -> Bit<W> {
+  return {a.mask & b.mask};
+}
+template <ptrdiff_t W> constexpr auto operator&(None<W>, Bit<W> b) -> Bit<W> {
+  return b;
+}
+template <ptrdiff_t W> constexpr auto operator&(Bit<W> a, None<W>) -> Bit<W> {
+  return a;
+}
+#endif // AVX512F
+#ifdef __AVX512VL__
+// In: iteration count `i.i` is the total length of the loop
+// Out: mask for the final iteration. Zero indicates no masked iter.
+template <ptrdiff_t W> constexpr auto create(ptrdiff_t i) -> Bit<W> {
+  static_assert(std::popcount(size_t(W)) == 1);
+  utils::invariant(i >= 0);
+  return {_bzhi_u64(0xffffffffffffffff, uint64_t(i) & uint64_t(W - 1))};
+};
+// In: index::Vector where `i.i` is for the current iteration, and total loop
+// length. Out: mask for the current iteration, 0 indicates exit loop.
+template <ptrdiff_t W>
+constexpr auto create(ptrdiff_t i, ptrdiff_t len) -> Bit<W> {
+  static_assert(std::popcount(size_t(W)) == 1);
+  uint64_t x;
+  if (__builtin_sub_overflow(len, i, &x)) x = 0;
+  else x = std::min(x, uint64_t(255));
+  return {_bzhi_u64(0xffffffffffffffff, x)};
+};
+#else // ifdef __AVX512VL__
+
+template <ptrdiff_t W, typename I = int64_t> struct Vector {
+  static_assert(sizeof(I) * W <= 32);
+  // TODO: add support for smaller mask types, we we can use smaller eltypes
+  Vec<W, I> m;
+  [[nodiscard]] constexpr auto intmask() const -> int32_t {
+    if constexpr (sizeof(I) == 8)
+      if constexpr (W == 2) return _mm_movemask_pd(std::bit_cast<__m128d>(m));
+      else return _mm256_movemask_pd(std::bit_cast<__m256d>(m));
+    else if constexpr (sizeof(I) == 4)
+      if constexpr (W == 4) return _mm_movemask_ps(std::bit_cast<__m128>(m));
+      else return _mm256_movemask_ps(std::bit_cast<__m256>(m));
+    else if constexpr (W == 16)
+      return _mm_movemask_epi8(std::bit_cast<__m128i>(m));
+    else return _mm256_movemask_epi8(std::bit_cast<__m256i>(m));
+  }
+  explicit constexpr operator bool() const { return intmask(); }
+  [[nodiscard]] constexpr auto firstMasked() const -> ptrdiff_t {
+    return std::countr_zero(uint32_t(intmask()));
+  }
+  [[nodiscard]] constexpr auto lastUnmasked() const -> ptrdiff_t {
+    return 32 - std::countl_zero(uint32_t(intmask()));
+  }
+  constexpr operator __m128i()
+  requires(W == 2)
+  {
+    return std::bit_cast<__m128i>(m);
+  }
+  constexpr operator __m256i()
+  requires(W == 4)
+  {
+    return std::bit_cast<__m256i>(m);
+  }
+};
+template <ptrdiff_t W>
+constexpr auto operator&(Vector<W> a, Vector<W> b) -> Vector<W> {
+  return {a.m & b.m};
+}
+template <ptrdiff_t W>
+constexpr auto operator&(mask::None<W>, Vector<W> b) -> Vector<W> {
+  return b;
+}
+template <ptrdiff_t W>
+constexpr auto operator&(Vector<W> a, mask::None<W>) -> Vector<W> {
+  return a;
+}
+#ifdef __AVX512F__
+// but no VL!!! xeon phi
+template <ptrdiff_t W> constexpr auto create(ptrdiff_t i) {
+  if constexpr (W == 8)
+    return Bit<8>{_bzhi_u64(0xffffffffffffffff, uint64_t(i) & uint64_t(7))};
+  else return Vector<W>{range<W, int64_t>() < (i & (W - 1))};
+}
+template <ptrdiff_t W> constexpr auto create(ptrdiff_t i, ptrdiff_t len) {
+  if constexpr (W == 8)
+    return Bit<8>{_bzhi_u64(0xffffffffffffffff, uint64_t(len - i))};
+  else return Vector<W>{range<W, int64_t>() + i < len};
+}
+#else  // ifdef __AVX512F__
+template <ptrdiff_t W> constexpr auto create(ptrdiff_t i) -> Vector<W> {
+  return {range<W, int64_t>() < (i & (W - 1))};
+}
+template <ptrdiff_t W>
+constexpr auto create(ptrdiff_t i, ptrdiff_t len) -> Vector<W> {
+  return {range<W, int64_t>() + i < len};
+}
+#endif // ifdef __AVX512F__; else
+
+#endif // ifdef __AVX512VL__; else
+#else  // ifdef __x86_64__
+
+template <ptrdiff_t W> struct Vector {
+  Vec<W, int64_t> m;
+  explicit constexpr operator bool() {
+    bool any{false};
+    for (ptrdiff_t w = 0; w < W; ++w) any |= m[w];
+    return any;
+  }
+  [[nodiscard]] constexpr auto firstMasked() const -> ptrdiff_t {
+    for (ptrdiff_t w = 0; w < W; ++w)
+      if (m[w]) return w;
+    return W;
+  }
+  [[nodiscard]] constexpr auto lastUnmasked() const -> ptrdiff_t {
+    ptrdiff_t l = 0;
+    for (ptrdiff_t w = 0; w < W; ++w)
+      if (m[w]) l = w;
+    return l;
+  }
+};
+
+template <ptrdiff_t W> constexpr auto create(ptrdiff_t i) -> Vector<W> {
+  return {range<W, int64_t>() < (i & (W - 1))};
+}
+template <ptrdiff_t W>
+constexpr auto create(ptrdiff_t i, ptrdiff_t len) -> Vector<W> {
+  return {range<W, int64_t>() + i < len};
+}
+#endif // ifdef __x86_64__; else
+} // namespace mask
+
+#ifdef __AVX512VL__
+
+namespace cmp {
+
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto eq(Vec<W, T> x, Vec<W, T> y)
+  -> mask::Bit<W> {
+  if constexpr (W == 8) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm512_cmp_pd_mask(std::bit_cast<__m512d>(x),
+                                 std::bit_cast<__m512d>(y), 8)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm512_cmp_epi64_mask(std::bit_cast<__m512i>(x),
+                                    std::bit_cast<__m512i>(y), 0)};
+    } else static_assert(false);
+  } else if constexpr (W == 4) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm256_cmp_pd_mask(std::bit_cast<__m256d>(x),
+                                 std::bit_cast<__m256d>(y), 8)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm256_cmp_epi64_mask(std::bit_cast<__m256i>(x),
+                                    std::bit_cast<__m256i>(y), 0)};
+    } else static_assert(false);
+  } else if constexpr (W == 2) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm_cmp_pd_mask(std::bit_cast<__m128d>(x),
+                              std::bit_cast<__m128d>(y), 8)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm_cmp_epi64_mask(std::bit_cast<__m128i>(x),
+                                 std::bit_cast<__m128i>(y), 0)};
+    } else static_assert(false);
+  } else static_assert(false);
+}
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto ne(Vec<W, T> x, Vec<W, T> y)
+  -> mask::Bit<W> {
+  if constexpr (W == 8) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm512_cmp_pd_mask(std::bit_cast<__m512d>(x),
+                                 std::bit_cast<__m512d>(y), 4)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm512_cmp_epi64_mask(std::bit_cast<__m512i>(x),
+                                    std::bit_cast<__m512i>(y), 4)};
+    } else static_assert(false);
+  } else if constexpr (W == 4) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm256_cmp_pd_mask(std::bit_cast<__m256d>(x),
+                                 std::bit_cast<__m256d>(y), 4)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm256_cmp_epi64_mask(std::bit_cast<__m256i>(x),
+                                    std::bit_cast<__m256i>(y), 4)};
+    } else static_assert(false);
+  } else if constexpr (W == 2) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm_cmp_pd_mask(std::bit_cast<__m128d>(x),
+                              std::bit_cast<__m128d>(y), 4)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm_cmp_epi64_mask(std::bit_cast<__m128i>(x),
+                                 std::bit_cast<__m128i>(y), 4)};
+    } else static_assert(false);
+  } else static_assert(false);
+}
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto lt(Vec<W, T> x, Vec<W, T> y)
+  -> mask::Bit<W> {
+  if constexpr (W == 8) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm512_cmp_pd_mask(std::bit_cast<__m512d>(x),
+                                 std::bit_cast<__m512d>(y), 25)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm512_cmp_epi64_mask(std::bit_cast<__m512i>(x),
+                                    std::bit_cast<__m512i>(y), 1)};
+    } else static_assert(false);
+  } else if constexpr (W == 4) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm256_cmp_pd_mask(std::bit_cast<__m256d>(x),
+                                 std::bit_cast<__m256d>(y), 25)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm256_cmp_epi64_mask(std::bit_cast<__m256i>(x),
+                                    std::bit_cast<__m256i>(y), 1)};
+    } else static_assert(false);
+  } else if constexpr (W == 2) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm_cmp_pd_mask(std::bit_cast<__m128>(x),
+                              std::bit_cast<__m128d>(y), 25)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm_cmp_epi64_mask(std::bit_cast<__m128i>(x),
+                                 std::bit_cast<__m128i>(y), 1)};
+    } else static_assert(false);
+  } else static_assert(false);
+}
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto gt(Vec<W, T> x, Vec<W, T> y)
+  -> mask::Bit<W> {
+  if constexpr (W == 8) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm512_cmp_pd_mask(std::bit_cast<__m512d>(x),
+                                 std::bit_cast<__m512d>(y), 22)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm512_cmp_epi64_mask(std::bit_cast<__m512i>(x),
+                                    std::bit_cast<__m512i>(y), 6)};
+    } else static_assert(false);
+  } else if constexpr (W == 4) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm256_cmp_pd_mask(std::bit_cast<__m256d>(x),
+                                 std::bit_cast<__m256d>(y), 22)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm256_cmp_epi64_mask(std::bit_cast<__m256i>(x),
+                                    std::bit_cast<__m256i>(y), 6)};
+    } else static_assert(false);
+  } else if constexpr (W == 2) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm_cmp_pd_mask(std::bit_cast<__m128d>(x),
+                              std::bit_cast<__m128d>(y), 22)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm_cmp_epi64_mask(std::bit_cast<__m128i>(x),
+                                 std::bit_cast<__m128i>(y), 6)};
+    } else static_assert(false);
+  } else static_assert(false);
+}
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto le(Vec<W, T> x, Vec<W, T> y)
+  -> mask::Bit<W> {
+  if constexpr (W == 8) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm512_cmp_pd_mask(std::bit_cast<__m512d>(x),
+                                 std::bit_cast<__m512d>(y), 26)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm512_cmp_epi64_mask(std::bit_cast<__m512i>(x),
+                                    std::bit_cast<__m512i>(y), 2)};
+    } else static_assert(false);
+  } else if constexpr (W == 4) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm256_cmp_pd_mask(std::bit_cast<__m256d>(x),
+                                 std::bit_cast<__m256d>(y), 26)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm256_cmp_epi64_mask(std::bit_cast<__m256i>(x),
+                                    std::bit_cast<__m256i>(y), 2)};
+    } else static_assert(false);
+  } else if constexpr (W == 2) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm_cmp_pd_mask(std::bit_cast<__m128d>(x),
+                              std::bit_cast<__m128d>(y), 26)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm_cmp_epi64_mask(std::bit_cast<__m128i>(x),
+                                 std::bit_cast<__m128i>(y), 2)};
+    } else static_assert(false);
+  } else static_assert(false);
+}
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto ge(Vec<W, T> x, Vec<W, T> y)
+  -> mask::Bit<W> {
+  if constexpr (W == 8) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm512_cmp_pd_mask(std::bit_cast<__m512d>(x),
+                                 std::bit_cast<__m512d>(y), 21)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm512_cmp_epi64_mask(std::bit_cast<__m512i>(x),
+                                    std::bit_cast<__m512i>(y), 5)};
+    } else static_assert(false);
+  } else if constexpr (W == 4) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm256_cmp_pd_mask(std::bit_cast<__m256d>(x),
+                                 std::bit_cast<__m256d>(y), 21)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm256_cmp_epi64_mask(std::bit_cast<__m256i>(x),
+                                    std::bit_cast<__m256i>(y), 5)};
+    } else static_assert(false);
+  } else if constexpr (W == 2) {
+
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm_cmp_pd_mask(std::bit_cast<__m128d>(x),
+                              std::bit_cast<__m128d>(y), 21)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm_cmp_epi64_mask(std::bit_cast<__m128i>(x),
+                                 std::bit_cast<__m128i>(y), 5)};
+    } else static_assert(false);
+  } else static_assert(false);
+}
+
+} // namespace cmp
+#elif defined(__AVX512F__)
+
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto eq(Vec<W, T> x,
+                                                       Vec<W, T> y) {
+  if constexpr (W == 8) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm512_cmp_pd_mask(std::bit_cast<__m512d>(x),
+                                 std::bit_cast<__m512d>(y), 8)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm512_cmp_epi64_mask(std::bit_cast<__m512i>(x),
+                                    std::bit_cast<__m512i>(y), 0)};
+    } else static_assert(false);
+  } else {
+    return mask::Vector<W>{x == y};
+  }
+}
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto ne(Vec<W, T> x,
+                                                       Vec<W, T> y) {
+  if constexpr (W == 8) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm512_cmp_pd_mask(std::bit_cast<__m512d>(x),
+                                 std::bit_cast<__m512d>(y), 4)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm512_cmp_epi64_mask(std::bit_cast<__m512i>(x),
+                                    std::bit_cast<__m512i>(y), 4)};
+    } else static_assert(false);
+  } else {
+    return mask::Vector<W>{x != y};
+  }
+}
+
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto lt(Vec<W, T> x,
+                                                       Vec<W, T> y) {
+  if constexpr (W == 8) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm512_cmp_pd_mask(std::bit_cast<__m512d>(x),
+                                 std::bit_cast<__m512d>(y), 25)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm512_cmp_epi64_mask(std::bit_cast<__m512i>(x),
+                                    std::bit_cast<__m512i>(y), 1)};
+    } else static_assert(false);
+  } else {
+    return mask::Vector<W>{x < y};
+  }
+}
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto gt(Vec<W, T> x,
+                                                       Vec<W, T> y) {
+  if constexpr (W == 8) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm512_cmp_pd_mask(std::bit_cast<__m512d>(x),
+                                 std::bit_cast<__m512d>(y), 22)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm512_cmp_epi64_mask(std::bit_cast<__m512i>(x),
+                                    std::bit_cast<__m512i>(y), 6)};
+    } else static_assert(false);
+  } else {
+    return mask::Vector<W>{x > y};
+  }
+}
+
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto le(Vec<W, T> x,
+                                                       Vec<W, T> y) {
+  if constexpr (W == 8) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm512_cmp_pd_mask(std::bit_cast<__m512d>(x),
+                                 std::bit_cast<__m512d>(y), 26)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm512_cmp_epi64_mask(std::bit_cast<__m512i>(x),
+                                    std::bit_cast<__m512i>(y), 2)};
+    } else static_assert(false);
+  } else {
+    return mask::Vector<W>{x <= y};
+  }
+}
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto ge(Vec<W, T> x,
+                                                       Vec<W, T> y) {
+  if constexpr (W == 8) {
+    if constexpr (std::same_as<T, double>) { // UQ (unordered quiet?)
+      return {_mm512_cmp_pd_mask(std::bit_cast<__m512d>(x),
+                                 std::bit_cast<__m512d>(y), 21)};
+    } else if constexpr (std::same_as<T, int64_t>) {
+      return {_mm512_cmp_epi64_mask(std::bit_cast<__m512i>(x),
+                                    std::bit_cast<__m512i>(y), 5)};
+    } else static_assert(false);
+  } else {
+    return mask::Vector<W>{x >= y};
+  }
+}
+
+#else  // ifdef __AVX512VL__
+
+namespace cmp {
+
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto eq(Vec<W, T> x, Vec<W, T> y)
+  -> mask::Vector<W> {
+  return {x == y};
+}
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto ne(Vec<W, T> x, Vec<W, T> y)
+  -> mask::Vector<W> {
+  return {x != y};
+}
+
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto lt(Vec<W, T> x, Vec<W, T> y)
+  -> mask::Vector<W> {
+  return {x < y};
+}
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto gt(Vec<W, T> x, Vec<W, T> y)
+  -> mask::Vector<W> {
+  return {x > y};
+}
+
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto le(Vec<W, T> x, Vec<W, T> y)
+  -> mask::Vector<W> {
+  return {x <= y};
+}
+template <ptrdiff_t W, typename T>
+[[gnu::always_inline, gnu::artificial]] inline auto ge(Vec<W, T> x, Vec<W, T> y)
+  -> mask::Vector<W> {
+  return {x >= y};
+}
+} // namespace cmp
+#endif // ifdef __AVX512VL__; else
+
+} // namespace poly::simd
+#endif // Masks_hpp_INCLUDED
diff --git a/include/SIMD/Transpose.hpp b/include/SIMD/Transpose.hpp
new file mode 100644
index 0000000..7204fc9
--- /dev/null
+++ b/include/SIMD/Transpose.hpp
@@ -0,0 +1,73 @@
+#pragma once
+#ifndef POLY_SIMD_Transpose_hpp_INCLUDED
+#define POLY_SIMD_Transpose_hpp_INCLUDED
+
+#include "SIMD/Unroll.hpp"
+namespace poly::simd {
+
+// 4 x 4C -> 4C x 4
+template <ptrdiff_t C, typename T>
+constexpr auto transpose(Unroll<2, C, 2, T> u) -> Unroll<2 * C, 1, 2, T> {
+  Unroll<2 * C, 1, 2, T> z;
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t i = 0; i < C; ++i) {
+    Vec<2, T> a{u[0, i]}, b{u[1, i]};
+    z[0, i] = __builtin_shufflevector(a, b, 0, 2);
+    z[1, i] = __builtin_shufflevector(a, b, 1, 3);
+  }
+  return z;
+}
+template <ptrdiff_t C, typename T>
+constexpr auto transpose(Unroll<4, C, 4, T> u) -> Unroll<4 * C, 1, 4, T> {
+  Unroll<4 * C, 1, 4, T> z;
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t i = 0; i < C; ++i) {
+    Vec<4, T> a{u[0, i]}, b{u[1, i]}, c{u[2, i]}, d{u[3, i]};
+    Vec<4, T> e{__builtin_shufflevector(a, b, 0, 1, 4, 5)};
+    Vec<4, T> f{__builtin_shufflevector(a, b, 2, 3, 6, 7)};
+    Vec<4, T> g{__builtin_shufflevector(c, d, 0, 1, 4, 5)};
+    Vec<4, T> h{__builtin_shufflevector(c, d, 2, 3, 6, 7)};
+    z[0, i] = __builtin_shufflevector(e, g, 0, 2, 4, 6);
+    z[1, i] = __builtin_shufflevector(e, g, 1, 3, 5, 7);
+    z[2, i] = __builtin_shufflevector(f, h, 0, 2, 4, 6);
+    z[3, i] = __builtin_shufflevector(f, h, 1, 3, 5, 7);
+  }
+  return z;
+}
+template <ptrdiff_t C, typename T>
+constexpr auto transpose(Unroll<8, C, 8, T> u) -> Unroll<8 * C, 1, 8, T> {
+  Unroll<8 * C, 1, 8, T> z;
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t i = 0; i < C; ++i) {
+    Vec<4, T> a{u[0, i]}, b{u[1, i]}, c{u[2, i]}, d{u[3, i]}, e{u[4, i]},
+      f{u[5, i]}, g{u[6, i]}, h{u[7, i]};
+    Vec<4, T> j{__builtin_shufflevector(a, b, 0, 8, 2, 10, 4, 12, 6, 14)},
+      k{__builtin_shufflevector(a, b, 1, 9, 3, 11, 5, 13, 7, 15)},
+      l{__builtin_shufflevector(c, d, 0, 8, 2, 10, 4, 12, 6, 14)},
+      m{__builtin_shufflevector(c, d, 1, 9, 3, 11, 5, 13, 7, 15)},
+      n{__builtin_shufflevector(e, f, 0, 8, 2, 10, 4, 12, 6, 14)},
+      o{__builtin_shufflevector(e, f, 1, 9, 3, 11, 5, 13, 7, 15)},
+      p{__builtin_shufflevector(g, h, 0, 8, 2, 10, 4, 12, 6, 14)},
+      q{__builtin_shufflevector(g, h, 1, 9, 3, 11, 5, 13, 7, 15)};
+    a = __builtin_shufflevector(j, l, 0, 1, 8, 9, 4, 5, 12, 13);
+    b = __builtin_shufflevector(j, l, 2, 3, 10, 11, 6, 7, 14, 15);
+    c = __builtin_shufflevector(k, m, 0, 1, 8, 9, 4, 5, 12, 13);
+    d = __builtin_shufflevector(k, m, 2, 3, 10, 11, 6, 7, 14, 15);
+    e = __builtin_shufflevector(n, p, 0, 1, 8, 9, 4, 5, 12, 13);
+    f = __builtin_shufflevector(n, p, 2, 3, 10, 11, 6, 7, 14, 15);
+    g = __builtin_shufflevector(o, q, 0, 1, 8, 9, 4, 5, 12, 13);
+    h = __builtin_shufflevector(o, q, 2, 3, 10, 11, 6, 7, 14, 15);
+    z[0, i] = __builtin_shufflevector(a, e, 0, 1, 2, 3, 8, 9, 10, 11);
+    z[1, i] = __builtin_shufflevector(a, e, 4, 5, 6, 7, 12, 13, 14, 15);
+    z[2, i] = __builtin_shufflevector(b, f, 0, 1, 2, 3, 8, 9, 10, 11);
+    z[3, i] = __builtin_shufflevector(b, f, 4, 5, 6, 7, 12, 13, 14, 15);
+    z[4, i] = __builtin_shufflevector(c, g, 0, 1, 2, 3, 8, 9, 10, 11);
+    z[5, i] = __builtin_shufflevector(c, g, 4, 5, 6, 7, 12, 13, 14, 15);
+    z[6, i] = __builtin_shufflevector(d, h, 0, 1, 2, 3, 8, 9, 10, 11);
+    z[7, i] = __builtin_shufflevector(d, h, 4, 5, 6, 7, 12, 13, 14, 15);
+  }
+  return z;
+}
+
+} // namespace poly::simd
+#endif // Transpose_hpp_INCLUDED
diff --git a/include/SIMD/Unroll.hpp b/include/SIMD/Unroll.hpp
new file mode 100644
index 0000000..7f4ad19
--- /dev/null
+++ b/include/SIMD/Unroll.hpp
@@ -0,0 +1,656 @@
+#pragma once
+#ifndef POLY_SIMD_Unroll_hpp_INCLUDED
+#define POLY_SIMD_Unroll_hpp_INCLUDED
+#include "SIMD/Intrin.hpp"
+#include <functional>
+namespace poly::simd {
+// template <typename T, ptrdiff_t W, typename S>
+// [[gnu::always_inline]] constexpr auto vcvt(Vec<W, S> v) {
+//   if constexpr (std::same_as<T, S>) return v;
+//   else if constexpr (W == 1) return T(v);
+//   else return __builtin_convertvector(v, Vec<W, T>);
+// }
+// Vector goes across cols
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t N, typename T> struct Unroll {
+  static constexpr ptrdiff_t W = ptrdiff_t(std::bit_ceil(size_t(N)));
+  using VT = Vec<W, T>;
+  static_assert(R * C > 0);
+  VT data[R * C];
+  constexpr auto operator[](ptrdiff_t i) -> VT & { return data[i]; }
+  constexpr auto operator[](ptrdiff_t r, ptrdiff_t c) -> VT & {
+    return data[r * C + c];
+  }
+  constexpr auto operator[](ptrdiff_t i) const -> VT { return data[i]; }
+  constexpr auto operator[](ptrdiff_t r, ptrdiff_t c) const -> VT {
+    return data[r * C + c];
+  }
+  template <typename U>
+  [[gnu::always_inline]] constexpr operator Unroll<R, C, N, U>() const
+  requires(!std::same_as<T, U>)
+  {
+    Unroll<R, C, N, U> x;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t i = 0; i < R * C; ++i)
+      if constexpr (W == 1) x.data[i] = U(data[i]);
+      else x.data[i] = __builtin_convertvector(data[i], Vec<W, U>);
+    return x;
+  }
+  [[gnu::always_inline]] constexpr auto operator-() {
+    Unroll a;
+    for (ptrdiff_t i = 0; i < R * C; ++i) a.data[i] = -data[i];
+    return a;
+  }
+  [[gnu::always_inline]] constexpr auto operator+=(const Unroll &a)
+    -> Unroll & {
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t i = 0; i < R * C; ++i) data[i] += a.data[i];
+    return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator-=(const Unroll &a)
+    -> Unroll & {
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t i = 0; i < R * C; ++i) data[i] -= a.data[i];
+    return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator*=(const Unroll &a)
+    -> Unroll & {
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t i = 0; i < R * C; ++i) data[i] *= a.data[i];
+    return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator/=(const Unroll &a)
+    -> Unroll & {
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t i = 0; i < R * C; ++i) data[i] /= a.data[i];
+    return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator+=(VT a) -> Unroll & {
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t i = 0; i < R * C; ++i) data[i] += a;
+    return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator-=(VT a) -> Unroll & {
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t i = 0; i < R * C; ++i) data[i] -= a;
+    return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator*=(VT a) -> Unroll & {
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t i = 0; i < R * C; ++i) data[i] *= a;
+    return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator/=(VT a) -> Unroll & {
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t i = 0; i < R * C; ++i) data[i] /= a;
+    return *this;
+  }
+  [[gnu::always_inline]] constexpr auto
+  operator+=(std::convertible_to<T> auto a) -> Unroll &
+  requires(W != 1)
+  {
+    return (*this) += (typename Unroll<R, C, W, T>::VT{} + T(a));
+  }
+  [[gnu::always_inline]] constexpr auto
+  operator-=(std::convertible_to<T> auto a) -> Unroll &
+  requires(W != 1)
+  {
+    return (*this) -= (typename Unroll<R, C, W, T>::VT{} + T(a));
+  }
+  [[gnu::always_inline]] constexpr auto
+  operator*=(std::convertible_to<T> auto a) -> Unroll &
+  requires(W != 1)
+  {
+    return (*this) *= (typename Unroll<R, C, W, T>::VT{} + T(a));
+  }
+  [[gnu::always_inline]] constexpr auto
+  operator/=(std::convertible_to<T> auto a) -> Unroll &
+  requires(W != 1)
+  {
+    return (*this) /= (typename Unroll<R, C, W, T>::VT{} + T(a));
+  }
+};
+
+template <ptrdiff_t R0, ptrdiff_t C0, ptrdiff_t W0, typename T0, ptrdiff_t R1,
+          ptrdiff_t C1, ptrdiff_t W1, typename T1, typename Op>
+[[gnu::always_inline]] constexpr auto applyop(const Unroll<R0, C0, W0, T0> &a,
+                                              const Unroll<R1, C1, W1, T1> &b,
+                                              Op op) {
+  // Possibilities:
+  // 1. All match
+  // 2. We had separate unrolls across rows and columns, and some arrays
+  // were indexed by one or two of them.
+  // In the latter case, we could have arrays indexed by rows, cols, or both.
+  if constexpr (!std::same_as<T0, T1>) {
+    using T = std::common_type_t<T0, T1>;
+    return applyop(Unroll<R0, C0, W0, T>(a), Unroll<R1, C1, W1, T>(b), op);
+  } else if constexpr (W0 == W1) {
+    // both were indexed by cols, and `C`s should also match
+    // or neither were, and they should still match.
+    static_assert(C0 == C1);
+    if constexpr (R0 == R1) {
+      // Both have the same index across rows
+      Unroll<R0, C0, W0, T0> c;
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t i = 0; i < R0 * C0; ++i)
+        c.data[i] = op(a.data[i], b.data[i]);
+      return c;
+    } else if constexpr (R0 == 1) {
+      // `a` was indexed across cols only
+      Unroll<R1, C0, W0, T0> z;
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t r = 0; r < R1; ++r) {
+        POLYMATHFULLUNROLL
+        for (ptrdiff_t c = 0; c < C0; ++c) z[r, c] = op(a.data[c], b[r, c]);
+      }
+      return z;
+    } else {
+      static_assert(R1 == 1);
+      // `b` was indexed across cols only
+      Unroll<R0, C0, W0, T0> z;
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t r = 0; r < R0; ++r) {
+        POLYMATHFULLUNROLL
+        for (ptrdiff_t c = 0; c < C0; ++c) z[r, c] = op(a[r, c], b.data[c]);
+      }
+      return z;
+    }
+  } else if constexpr (W0 == 1) {
+    static_assert(R0 == 1 || C0 == 1);
+    constexpr ptrdiff_t R = R0 == 1 ? C0 : R0;
+    // `a` was indexed by row only
+    Unroll<R, C1, W1, T0> z;
+    static_assert(R1 == R || R1 == 1);
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t r = 0; r < R; ++r) {
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t c = 0; c < C1; ++c)
+        if constexpr (R == R1) z[r, c] = op(a.data[r], b[r, c]);
+        else z[r, c] = op(a.data[r], b.data[c]);
+    }
+    return z;
+  } else {
+    static_assert(W1 == 1);
+    static_assert(R1 == 1 || C1 == 1);
+    constexpr ptrdiff_t R = R1 == 1 ? C1 : R1;
+    // `b` was indexed by row only
+    Unroll<R, C0, W0, T0> z;
+    static_assert(R0 == R || R0 == 1);
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t r = 0; r < R; ++r) {
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t c = 0; c < C0; ++c)
+        if constexpr (R0 == R) z[r, c] = op(a[r, c], b.data[r]);
+        else z[r, c] = op(a.data[c], b.data[r]);
+    }
+    return z;
+  }
+}
+
+template <ptrdiff_t R0, ptrdiff_t C0, ptrdiff_t W0, typename T0, ptrdiff_t R1,
+          ptrdiff_t C1, ptrdiff_t W1, typename T1>
+[[gnu::always_inline]] constexpr auto
+operator+(const Unroll<R0, C0, W0, T0> &a, const Unroll<R1, C1, W1, T1> &b) {
+  return applyop(a, b, std::plus<>{});
+}
+
+template <ptrdiff_t R0, ptrdiff_t C0, ptrdiff_t W0, typename T0, ptrdiff_t R1,
+          ptrdiff_t C1, ptrdiff_t W1, typename T1>
+[[gnu::always_inline]] constexpr auto
+operator-(const Unroll<R0, C0, W0, T0> &a, const Unroll<R1, C1, W1, T1> &b) {
+  return applyop(a, b, std::minus<>{});
+}
+
+template <ptrdiff_t R0, ptrdiff_t C0, ptrdiff_t W0, typename T0, ptrdiff_t R1,
+          ptrdiff_t C1, ptrdiff_t W1, typename T1>
+[[gnu::always_inline]] constexpr auto
+operator*(const Unroll<R0, C0, W0, T0> &a, const Unroll<R1, C1, W1, T1> &b) {
+  return applyop(a, b, std::multiplies<>{});
+}
+
+template <ptrdiff_t R0, ptrdiff_t C0, ptrdiff_t W0, typename T0, ptrdiff_t R1,
+          ptrdiff_t C1, ptrdiff_t W1, typename T1>
+[[gnu::always_inline]] constexpr auto
+operator/(const Unroll<R0, C0, W0, T0> &a, const Unroll<R1, C1, W1, T1> &b) {
+  return applyop(a, b, std::divides<>{});
+}
+
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto
+operator+(const Unroll<R, C, W, T> &a, typename Unroll<R, C, W, T>::VT b)
+  -> Unroll<R, C, W, T> {
+  Unroll<R, C, W, T> c;
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t i = 0; i < R * C; ++i) c.data[i] = a.data[i] + b;
+  return c;
+}
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto
+operator-(const Unroll<R, C, W, T> &a, typename Unroll<R, C, W, T>::VT b)
+  -> Unroll<R, C, W, T> {
+  Unroll<R, C, W, T> c;
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t i = 0; i < R * C; ++i) c.data[i] = a.data[i] - b;
+  return c;
+}
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto
+operator*(const Unroll<R, C, W, T> &a, typename Unroll<R, C, W, T>::VT b)
+  -> Unroll<R, C, W, T> {
+  Unroll<R, C, W, T> c;
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t i = 0; i < R * C; ++i) c.data[i] = a.data[i] * b;
+  return c;
+}
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto
+operator/(const Unroll<R, C, W, T> &a, typename Unroll<R, C, W, T>::VT b)
+  -> Unroll<R, C, W, T> {
+  Unroll<R, C, W, T> c;
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t i = 0; i < R * C; ++i) c.data[i] = a.data[i] / b;
+  return c;
+}
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto operator+(const Unroll<R, C, W, T> &a,
+                                                std::convertible_to<T> auto b)
+  -> Unroll<R, C, W, T>
+requires(W != 1)
+{
+  return a + (typename Unroll<R, C, W, T>::VT{} + T(b));
+}
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto operator-(const Unroll<R, C, W, T> &a,
+                                                std::convertible_to<T> auto b)
+  -> Unroll<R, C, W, T>
+requires(W != 1)
+{
+  return a - (typename Unroll<R, C, W, T>::VT{} + T(b));
+}
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto operator*(const Unroll<R, C, W, T> &a,
+                                                std::convertible_to<T> auto b)
+  -> Unroll<R, C, W, T>
+requires(W != 1)
+{
+  return a * (typename Unroll<R, C, W, T>::VT{} + T(b));
+}
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto operator/(const Unroll<R, C, W, T> &a,
+                                                std::convertible_to<T> auto b)
+  -> Unroll<R, C, W, T>
+requires(W != 1)
+{
+  return a / (typename Unroll<R, C, W, T>::VT{} + T(b));
+}
+
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto
+operator+(typename Unroll<R, C, W, T>::VT a, const Unroll<R, C, W, T> &b)
+  -> Unroll<R, C, W, T> {
+  Unroll<R, C, W, T> c;
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t i = 0; i < R * C; ++i) c.data[i] = a + b.data[i];
+  return c;
+}
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto
+operator-(typename Unroll<R, C, W, T>::VT a, const Unroll<R, C, W, T> &b)
+  -> Unroll<R, C, W, T> {
+  Unroll<R, C, W, T> c;
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t i = 0; i < R * C; ++i) c.data[i] = a - b.data[i];
+  return c;
+}
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto
+operator*(typename Unroll<R, C, W, T>::VT a, const Unroll<R, C, W, T> &b)
+  -> Unroll<R, C, W, T> {
+  Unroll<R, C, W, T> c;
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t i = 0; i < R * C; ++i) c.data[i] = a * b.data[i];
+  return c;
+}
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto
+operator/(typename Unroll<R, C, W, T>::VT a, const Unroll<R, C, W, T> &b)
+  -> Unroll<R, C, W, T> {
+  Unroll<R, C, W, T> c;
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t i = 0; i < R * C; ++i) c.data[i] = a / b.data[i];
+  return c;
+}
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto operator+(T b,
+                                                const Unroll<R, C, W, T> &a)
+  -> Unroll<R, C, W, T>
+requires(W != 1)
+{
+  return (typename Unroll<R, C, W, T>::VT{} + b) + a;
+}
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto operator-(T b,
+                                                const Unroll<R, C, W, T> &a)
+  -> Unroll<R, C, W, T>
+requires(W != 1)
+{
+  return (typename Unroll<R, C, W, T>::VT{} + b) - a;
+}
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto operator*(T b,
+                                                const Unroll<R, C, W, T> &a)
+  -> Unroll<R, C, W, T>
+requires(W != 1)
+{
+  return (typename Unroll<R, C, W, T>::VT{} + b) * a;
+}
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename T>
+[[gnu::always_inline]] constexpr auto operator/(T b,
+                                                const Unroll<R, C, W, T> &a)
+  -> Unroll<R, C, W, T>
+requires(W != 1)
+{
+  return (typename Unroll<R, C, W, T>::VT{} + b) / a;
+}
+
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t N, typename T, ptrdiff_t X,
+          size_t NM, typename MT = mask::None<N>>
+[[gnu::always_inline]] constexpr auto
+loadunroll(const T *ptr, math::RowStride<X> rowStride, std::array<MT, NM> masks)
+  -> Unroll<R, C, N, T> {
+  static constexpr auto W = ptrdiff_t(std::bit_ceil(size_t(N)));
+  auto rs = ptrdiff_t(rowStride);
+  Unroll<R, C, N, T> ret;
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t r = 0; r < R; ++r, ptr += rs) {
+    if constexpr (NM == 0) {
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t c = 0; c < C; ++c)
+        ret[r, c] = load(ptr + c * W, mask::None<W>{});
+    } else if constexpr (NM == C) {
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t c = 0; c < C; ++c) ret[r, c] = load(ptr + c * W, masks[c]);
+    } else {
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t c = 0; c < C - 1; ++c)
+        ret[r, c] = load(ptr + c * W, mask::None<W>{});
+      ret[r, C - 1] = load(ptr + (C - 1) * W, masks[0]);
+    }
+  }
+  return ret;
+}
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t N, typename T, ptrdiff_t X,
+          size_t NM, typename MT = mask::None<N>>
+[[gnu::always_inline]] constexpr auto
+loadstrideunroll(const T *ptr, math::RowStride<X> rowStride,
+                 std::array<MT, NM> masks) -> Unroll<R, C, N, T> {
+  static constexpr auto W = ptrdiff_t(std::bit_ceil(size_t(N)));
+  Unroll<R, C, N, T> ret;
+  auto s = int32_t(ptrdiff_t(rowStride));
+  POLYMATHFULLUNROLL
+  for (ptrdiff_t r = 0; r < R; ++r, ++ptr) {
+    if constexpr (NM == 0) {
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t c = 0; c < C; ++c)
+        ret[r, c] = load(ptr + c * W * s, mask::None<W>{}, s);
+    } else if constexpr (NM == C) {
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t c = 0; c < C; ++c)
+        ret[r, c] = load(ptr + c * W * s, masks[c], s);
+    } else {
+      POLYMATHFULLUNROLL
+      for (ptrdiff_t c = 0; c < C - 1; ++c)
+        ret[r, c] = load(ptr + c * W * s, mask::None<W>{}, s);
+      ret[r, C - 1] = load(ptr + (C - 1) * W * s, masks[0], s);
+    }
+  }
+  return ret;
+}
+
+// Represents a reference for a SIMD load, in particular so that we can store.
+// Needs to support masking
+template <ptrdiff_t R, ptrdiff_t C, ptrdiff_t N, typename T, ptrdiff_t X,
+          ptrdiff_t NM, typename MT = mask::None<N>, bool Transposed = false>
+struct UnrollRef {
+  static constexpr ptrdiff_t W = ptrdiff_t(std::bit_ceil(size_t(N)));
+  static_assert(N == W || C == 1,
+                "If N != the next power of `2`, then `C` should be `1`");
+  static_assert(
+    NM == 0 || NM == 1 || NM == C,
+    "Should have no masks, one mask for last `C`, or one mask per `C`");
+  T *ptr;
+  [[no_unique_address]] math::RowStride<X> rowStride;
+  [[no_unique_address]] std::array<MT, NM> masks;
+  constexpr operator Unroll<R, C, N, T>() {
+    if constexpr (!Transposed)
+      return loadunroll<R, C, N, T, X, NM, MT>(ptr, rowStride, masks);
+    else return loadstrideunroll<R, C, N, T, X, NM, MT>(ptr, rowStride, masks);
+  }
+  constexpr auto operator=(Unroll<R, C, N, T> x) -> UnrollRef &
+  requires(!Transposed)
+  {
+    auto rs = ptrdiff_t(rowStride);
+    T *p = ptr;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t r = 0; r < R; ++r, p += rs) {
+      if constexpr (NM == 0) {
+        POLYMATHFULLUNROLL
+        for (ptrdiff_t c = 0; c < C; ++c)
+          store<T>(p + c * W, mask::None<W>{}, x[r, c]);
+      } else if constexpr (NM == C) {
+        POLYMATHFULLUNROLL
+        for (ptrdiff_t c = 0; c < C; ++c)
+          store<T>(p + c * W, masks[c], x[r, c]);
+      } else { // NM == 1
+        POLYMATHFULLUNROLL
+        for (ptrdiff_t c = 0; c < C - 1; ++c)
+          store<T>(p + c * W, mask::None<W>{}, x[r, c]);
+        store<T>(p + (C - 1) * W, masks[0], x[r, C - 1]);
+      }
+    }
+    return *this;
+  }
+  constexpr auto operator=(Vec<W, T> v) -> UnrollRef &
+  requires(!Transposed)
+  {
+    auto rs = ptrdiff_t(rowStride);
+    T *p = ptr;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t r = 0; r < R; ++r, p += rs) {
+      if constexpr (NM == 0) {
+        POLYMATHFULLUNROLL
+        for (ptrdiff_t c = 0; c < C; ++c)
+          store<T>(p + c * W, mask::None<W>{}, v);
+      } else if constexpr (NM == C) {
+        POLYMATHFULLUNROLL
+        for (ptrdiff_t c = 0; c < C; ++c) store<T>(p + c * W, masks[c], v);
+      } else { // NM == 1
+        POLYMATHFULLUNROLL
+        for (ptrdiff_t c = 0; c < C - 1; ++c)
+          store<T>(p + c * W, mask::None<W>{}, v);
+        store<T>(p + (C - 1) * W, masks[0], v);
+      }
+    }
+    return *this;
+  }
+  constexpr auto operator=(Unroll<R, C, N, T> x) -> UnrollRef &
+  requires(Transposed)
+  {
+    auto s = int32_t(ptrdiff_t(rowStride));
+    T *p = ptr;
+    for (ptrdiff_t r = 0; r < R; ++r, ++p) {
+      if constexpr (NM == 0) {
+        POLYMATHFULLUNROLL
+        for (ptrdiff_t c = 0; c < C; ++c)
+          store<T>(p + c * W * s, mask::None<W>{}, x[0, c], s);
+      } else if constexpr (NM == C) {
+        POLYMATHFULLUNROLL
+        for (ptrdiff_t c = 0; c < C; ++c)
+          store<T>(p + c * W * s, masks[c], x[0, c], s);
+      } else {
+        POLYMATHFULLUNROLL
+        for (ptrdiff_t c = 0; c < C - 1; ++c)
+          store<T>(p + c * W * s, mask::None<W>{}, x[0, c], s);
+        store<T>(p + (C - 1) * W * s, masks[0], x[0, C - 1], s);
+      }
+    }
+    return *this;
+  }
+  constexpr auto operator=(Vec<W, T> v) -> UnrollRef &
+  requires(Transposed)
+  {
+    auto s = int32_t(ptrdiff_t(rowStride));
+    T *p = ptr;
+    for (ptrdiff_t r = 0; r < R; ++r, ++p) {
+      if constexpr (NM == 0) {
+        POLYMATHFULLUNROLL
+        for (ptrdiff_t c = 0; c < C; ++c)
+          store<T>(p + c * W * s, mask::None<W>{}, v, s);
+      } else if constexpr (NM == C) {
+        POLYMATHFULLUNROLL
+        for (ptrdiff_t c = 0; c < C; ++c)
+          store<T>(p + c * W * s, masks[c], v, s);
+      } else {
+        POLYMATHFULLUNROLL
+        for (ptrdiff_t c = 0; c < C - 1; ++c)
+          store<T>(p + c * W * s, mask::None<W>{}, v, s);
+        store<T>(p + (C - 1) * W * s, masks[0], v, s);
+      }
+    }
+    return *this;
+  }
+  constexpr auto operator=(std::convertible_to<T> auto x) -> UnrollRef & {
+    *this = Vec<W, T>{} + T(x);
+    return *this;
+  }
+  constexpr auto operator+=(const auto &x) -> UnrollRef & {
+    return (*this) = Unroll<R, C, N, T>(*this) + x;
+  }
+  constexpr auto operator-=(const auto &x) -> UnrollRef & {
+    return (*this) = Unroll<R, C, N, T>(*this) - x;
+  }
+  constexpr auto operator*=(const auto &x) -> UnrollRef & {
+    return (*this) = Unroll<R, C, N, T>(*this) * x;
+  }
+  constexpr auto operator/=(const auto &x) -> UnrollRef & {
+    return (*this) = Unroll<R, C, N, T>(*this) / x;
+  }
+};
+template <typename T, ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename M,
+          bool Transposed, ptrdiff_t X>
+[[gnu::always_inline]] constexpr auto
+ref(const T *p, index::UnrollDims<R, C, W, M, Transposed, X> i)
+  -> Unroll<R, C, W, T> {
+  if constexpr (Transposed)
+    return loadstrideunroll<R, C, W>(p, i.rs, std::array<M, 1>{i.mask});
+  else return loadunroll<R, C, W>(p, i.rs, std::array<M, 1>{i.mask});
+}
+template <typename T, ptrdiff_t R, ptrdiff_t C, ptrdiff_t W, typename M,
+          bool Transposed, ptrdiff_t X>
+[[gnu::always_inline]] constexpr auto
+ref(T *p, index::UnrollDims<R, C, W, M, Transposed, X> i)
+  -> UnrollRef<R, C, W, T, X, 1, M, Transposed> {
+  return {p, i.rs, std::array<M, 1>{i.mask}};
+}
+namespace index {
+
+template <ptrdiff_t U, ptrdiff_t W, typename M>
+constexpr auto operator==(Unroll<U, W, M> x, ptrdiff_t y) {
+  if constexpr (W == 1) {
+    poly::simd::Unroll<U, 1, 1, int64_t> ret;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t u = 0; u < U; ++u) ret.data[u] = (x.index + u) == y;
+    return ret;
+  } else {
+    poly::simd::Unroll<1, U, W, int64_t> ret;
+    Vec<W, int64_t> v = Vec<W, int64_t>{} + y;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t u = 0; u < U; ++u)
+      ret.data[u] = range<W, int64_t>() == (v - u * W);
+    return ret;
+  }
+}
+template <ptrdiff_t U, ptrdiff_t W, typename M>
+constexpr auto operator!=(Unroll<U, W, M> x, ptrdiff_t y) {
+  if constexpr (W == 1) {
+    poly::simd::Unroll<U, 1, 1, int64_t> ret;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t u = 0; u < U; ++u) ret.data[u] = (x.index + u) != y;
+    return ret;
+  } else {
+    poly::simd::Unroll<1, U, W, int64_t> ret;
+    Vec<W, int64_t> v = Vec<W, int64_t>{} + y;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t u = 0; u < U; ++u)
+      ret.data[u] = range<W, int64_t>() != (v - u * W);
+    return ret;
+  }
+}
+template <ptrdiff_t U, ptrdiff_t W, typename M>
+constexpr auto operator<(Unroll<U, W, M> x, ptrdiff_t y) {
+  if constexpr (W == 1) {
+    poly::simd::Unroll<U, 1, 1, int64_t> ret;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t u = 0; u < U; ++u) ret.data[u] = (x.index + u) < y;
+    return ret;
+  } else {
+    poly::simd::Unroll<1, U, W, int64_t> ret;
+    Vec<W, int64_t> v = Vec<W, int64_t>{} + y;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t u = 0; u < U; ++u)
+      ret.data[u] = range<W, int64_t>() < (v - u * W);
+    return ret;
+  }
+}
+template <ptrdiff_t U, ptrdiff_t W, typename M>
+constexpr auto operator>(Unroll<U, W, M> x, ptrdiff_t y) {
+  if constexpr (W == 1) {
+    poly::simd::Unroll<U, 1, 1, int64_t> ret;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t u = 0; u < U; ++u) ret.data[u] = (x.index + u) > y;
+    return ret;
+  } else {
+    poly::simd::Unroll<1, U, W, int64_t> ret;
+    Vec<W, int64_t> v = Vec<W, int64_t>{} + y;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t u = 0; u < U; ++u)
+      ret.data[u] = range<W, int64_t>() > (v - u * W);
+    return ret;
+  }
+}
+template <ptrdiff_t U, ptrdiff_t W, typename M>
+constexpr auto operator<=(Unroll<U, W, M> x, ptrdiff_t y) {
+  if constexpr (W == 1) {
+    poly::simd::Unroll<U, 1, 1, int64_t> ret;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t u = 0; u < U; ++u) ret.data[u] = (x.index + u) <= y;
+    return ret;
+  } else {
+    poly::simd::Unroll<1, U, W, int64_t> ret;
+    Vec<W, int64_t> v = Vec<W, int64_t>{} + y;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t u = 0; u < U; ++u)
+      ret.data[u] = range<W, int64_t>() <= (v - u * W);
+    return ret;
+  }
+}
+template <ptrdiff_t U, ptrdiff_t W, typename M>
+constexpr auto operator>=(Unroll<U, W, M> x, ptrdiff_t y) {
+  if constexpr (W == 1) {
+    poly::simd::Unroll<U, 1, 1, int64_t> ret;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t u = 0; u < U; ++u) ret.data[u] = (x.index + u) >= y;
+    return ret;
+  } else {
+    poly::simd::Unroll<1, U, W, int64_t> ret;
+    Vec<W, int64_t> v = Vec<W, int64_t>{} + y;
+    POLYMATHFULLUNROLL
+    for (ptrdiff_t u = 0; u < U; ++u)
+      ret.data[u] = range<W, int64_t>() >= (v - u * W);
+    return ret;
+  }
+}
+
+} // namespace index
+
+} // namespace poly::simd
+#endif // Unroll_hpp_INCLUDED
diff --git a/include/SIMD/Vec.hpp b/include/SIMD/Vec.hpp
new file mode 100644
index 0000000..25f887e
--- /dev/null
+++ b/include/SIMD/Vec.hpp
@@ -0,0 +1,14 @@
+#pragma once
+#ifndef MATH_SIMD_VEC_HPP_INCLUDED
+#define MATH_SIMD_VEC_HPP_INCLUDED
+
+namespace poly::simd {
+template <ptrdiff_t W, typename T>
+using Vec_ [[gnu::vector_size(W * sizeof(T))]] = T;
+
+template <ptrdiff_t W, typename T>
+using Vec = std::conditional_t<W == 1, T, Vec_<W, T>>;
+
+} // namespace poly::simd
+
+#endif
diff --git a/include/Utilities/Assign.hpp b/include/Utilities/Assign.hpp
new file mode 100644
index 0000000..6a0e574
--- /dev/null
+++ b/include/Utilities/Assign.hpp
@@ -0,0 +1,56 @@
+#pragma once
+#ifndef POLY_UTILITIES_Assign_hpp_INCLUDED
+#define POLY_UTILITIES_Assign_hpp_INCLUDED
+#include <Math/Matrix.hpp>
+#include <Utilities/TypePromotion.hpp>
+#include <functional>
+namespace poly::utils {
+
+struct CopyAssign {};
+struct NoRowIndex {};
+
+template <typename D, typename S, typename Op>
+[[gnu::always_inline]] constexpr void assign(D &&d, const S &s, Op op) {
+  if constexpr (std::same_as<Op, CopyAssign>) d = s;
+  else if constexpr (std::same_as<Op, std::plus<>>) d += s;
+  else if constexpr (std::same_as<Op, std::minus<>>) d -= s;
+  else if constexpr (std::same_as<Op, std::multiplies<>>) d *= s;
+  else if constexpr (std::same_as<Op, std::divides<>>) d /= s;
+  else d = op(d, s);
+}
+
+template <typename D, typename S, typename R, typename C, typename Op>
+[[gnu::always_inline]] constexpr void assign(D &d, const S &s, R r, C c,
+                                             Op op) {
+  constexpr bool norowind = std::same_as<R, NoRowIndex>;
+  if constexpr (std::convertible_to<S, utils::eltype_t<D>>)
+    if constexpr (norowind) assign(d[c], s, op);
+    else assign(d[r, c], s, op);
+  else if constexpr (math::RowVector<S>)
+    if constexpr (norowind) assign(d[c], s[c], op);
+    else assign(d[r, c], s[c], op);
+  else if constexpr (math::ColVector<S>)
+    if constexpr (norowind) assign(d[c], s[c], op);
+    else assign(d[r, c], s[r], op);
+  else if constexpr (std::same_as<Op, CopyAssign>)
+    if constexpr (norowind) d[c] = s[c];
+    else d[r, c] = s[r, c];
+  else if constexpr (std::same_as<Op, std::plus<>>)
+    if constexpr (norowind) d[c] += s[c];
+    else d[r, c] += s[r, c];
+  else if constexpr (std::same_as<Op, std::minus<>>)
+    if constexpr (norowind) d[c] -= s[c];
+    else d[r, c] -= s[r, c];
+  else if constexpr (std::same_as<Op, std::multiplies<>>)
+    if constexpr (norowind) d[c] *= s[c];
+    else d[r, c] *= s[r, c];
+  else if constexpr (std::same_as<Op, std::divides<>>)
+    if constexpr (norowind) d[c] /= s[c];
+    else d[r, c] /= s[r, c];
+  else if constexpr (norowind) d[c] = op(const_cast<const D &>(d)[c], s[c]);
+  else d[r, c] = op(const_cast<const D &>(d)[r, c], s[r, c]);
+}
+
+} // namespace poly::utils
+
+#endif // Assign_hpp_INCLUDED
diff --git a/include/Utilities/LoopMacros.hpp b/include/Utilities/LoopMacros.hpp
new file mode 100644
index 0000000..36a52b1
--- /dev/null
+++ b/include/Utilities/LoopMacros.hpp
@@ -0,0 +1,38 @@
+#pragma once
+#ifndef LoopMacros_hpp_INCLUDED
+#define LoopMacros_hpp_INCLUDED
+
+// clang-format off
+
+#if !defined(__clang__) && defined(__GNUC__)
+#define POLYMATHVECTORIZE _Pragma("GCC ivdep")
+#define POLYMATHIVDEP _Pragma("GCC ivdep")
+#define POLYMATHNOUNROLL _Pragma("GCC unroll 0")
+#define POLYMATHFULLUNROLL _Pragma("GCC unroll 16")
+#if __GNUC__ >= 14
+#define POLYMATHNOVECTORIZE _Pragma("GCC novector")
+#else
+#define POLYMATHNOVECTORIZE
+#endif
+#define POLYMATHFAST
+// #define POLYMATHVECTORIZE _Pragma("GCC unroll 2") _Pragma("GCC ivdep")
+#elif defined (__clang__)
+#define POLYMATHVECTORIZE _Pragma("omp simd")\
+ _Pragma("clang loop vectorize(enable) interleave_count(2) vectorize_predicate(enable)")
+#define POLYMATHIVDEP 
+// _Pragma("clang loop vectorize(disable)")
+#define POLYMATHNOUNROLL _Pragma("nounroll")
+#define POLYMATHFULLUNROLL _Pragma("unroll")
+#define POLYMATHNOVECTORIZE _Pragma("clang loop vectorize(disable)")
+#define POLYMATHFAST _Pragma("clang fp reassociate(on) contract(fast)")
+#else
+#define POLYMATHVECTORIZE
+#define POLYMATHIVDEP
+#define POLYMATHFULLUNROLL
+#define POLYMATHNOUNROLL
+#define POLYMATHNOVECTORIZE
+#define POLYMATHFAST
+#endif
+
+// clang-format on
+#endif // LoopMacros_hpp_INCLUDED
diff --git a/include/Utilities/Reference.hpp b/include/Utilities/Reference.hpp
new file mode 100644
index 0000000..5081fe9
--- /dev/null
+++ b/include/Utilities/Reference.hpp
@@ -0,0 +1,190 @@
+#pragma once
+#include "Utilities/TypeCompression.hpp"
+
+namespace poly::utils {
+template <typename T> struct Reference {
+  using C = utils::compressed_t<T>;
+  static_assert(!std::same_as<C, T>);
+  C *c;
+  constexpr operator T() const { return T::decompress(c); }
+  constexpr auto view() const -> T { return T::decompress(c); }
+  // constexpr operator T &() const { return *t; }
+  constexpr auto operator=(const T &t) -> Reference & {
+    t.compress(c);
+    return *this;
+  }
+  constexpr auto operator=(const C &x) -> Reference & {
+    // Probably shouldn't be needed?
+    // TODO: try removing this method
+    *c = x;
+    return *this;
+  }
+  constexpr auto operator==(const T &t) const -> bool {
+    return T::decompress(c) == t;
+  }
+  [[gnu::always_inline]] constexpr auto operator+=(const auto &x) {
+    T y{T::decompress(c)};
+    y += x;
+    y.compress(c);
+    return y;
+    // return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator-=(const auto &x) {
+    // -> Reference & {
+    T y{T::decompress(c)};
+    y -= x;
+    y.compress(c);
+    return y;
+    // return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator*=(const auto &x) {
+    // -> Reference & {
+    T y{T::decompress(c)};
+    y *= x;
+    y.compress(c);
+    return y;
+    // return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator/=(const auto &x) {
+    // -> Reference & {
+    T y{T::decompress(c)};
+    y /= x;
+    y.compress(c);
+    return y;
+    // return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator%=(const auto &x) {
+    // -> Reference & {
+    T y{T::decompress(c)};
+    y %= x;
+    y.compress(c);
+    return y;
+    // return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator<<=(const auto &x) {
+    // -> Reference & {
+    T y{T::decompress(c)};
+    y <<= x;
+    y.compress(c);
+    return y;
+    // return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator>>=(const auto &x) {
+    // -> Reference & {
+    T y{T::decompress(c)};
+    y >>= x;
+    y.compress(c);
+    return y;
+    // return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator&=(const auto &x) {
+    // -> Reference & {
+    T y{T::decompress(c)};
+    y &= x;
+    y.compress(c);
+    return y;
+    // return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator^=(const auto &x) {
+    // -> Reference & {
+    T y{T::decompress(c)};
+    y ^= x;
+    y.compress(c);
+    return y;
+    // return *this;
+  }
+  [[gnu::always_inline]] constexpr auto operator|=(const auto &x) {
+    // -> Reference & {
+    T y{T::decompress(c)};
+    y |= x;
+    y.compress(c);
+    return y;
+    // return *this;
+  }
+
+  constexpr auto operator[](auto i) -> decltype(auto) {
+    return c->operator[](i);
+  }
+  constexpr auto operator[](auto i) const -> decltype(auto) {
+    return c->operator[](i);
+  }
+  constexpr auto operator[](auto i, auto j) -> decltype(auto) {
+    return c->operator[](i, j);
+  }
+  constexpr auto operator[](auto i, auto j) const -> decltype(auto) {
+    return c->operator[](i, j);
+  }
+
+  // TODO:: are these really needed / can we rely on implicit conversion?
+  constexpr auto operator+(const auto &x) { return T::decompress(c) + x; }
+  constexpr auto operator-(const auto &x) { return T::decompress(c) - x; }
+  constexpr auto operator*(const auto &x) { return T::decompress(c) * x; }
+  constexpr auto operator/(const auto &x) { return T::decompress(c) / x; }
+  constexpr auto operator%(const auto &x) { return T::decompress(c) % x; }
+  constexpr auto operator>>(const auto &x) { return T::decompress(c) >> x; }
+  constexpr auto operator<<(const auto &x) { return T::decompress(c) << x; }
+  constexpr auto operator&(const auto &x) { return T::decompress(c) & x; }
+  constexpr auto operator^(const auto &x) { return T::decompress(c) ^ x; }
+  constexpr auto operator|(const auto &x) { return T::decompress(c) | x; }
+
+  friend constexpr auto operator+(const auto &x, Reference y) {
+    return x + T::decompress(y.c);
+  }
+  friend constexpr auto operator-(const auto &x, Reference y) {
+    return x - T::decompress(y.c);
+  }
+  friend constexpr auto operator*(const auto &x, Reference y) {
+    return x * T::decompress(y.c);
+  }
+  friend constexpr auto operator/(const auto &x, Reference y) {
+    return x / T::decompress(y.c);
+  }
+  friend constexpr auto operator%(const auto &x, Reference y) {
+    return x % T::decompress(y.c);
+  }
+  friend constexpr auto operator>>(const auto &x, Reference y) {
+    return x >> T::decompress(y.c);
+  }
+  friend constexpr auto operator<<(const auto &x, Reference y) {
+    return x << T::decompress(y.c);
+  }
+  friend constexpr auto operator&(const auto &x, Reference y) {
+    return x & T::decompress(y.c);
+  }
+  friend constexpr auto operator^(const auto &x, Reference y) {
+    return x ^ T::decompress(y.c);
+  }
+  friend constexpr auto operator|(const auto &x, Reference y) {
+    return x | T::decompress(y.c);
+  }
+};
+
+template <typename T>
+[[gnu::always_inline]] constexpr auto ref(T *p, ptrdiff_t i) -> T & {
+  return p[i];
+}
+template <typename T>
+[[gnu::always_inline]] constexpr auto ref(const T *p, ptrdiff_t i)
+  -> const T & {
+  return p[i];
+}
+template <Compressible T>
+[[gnu::always_inline]] constexpr auto ref(utils::compressed_t<T> *p,
+                                          ptrdiff_t i) -> Reference<T> {
+  return Reference<T>{p + i};
+}
+
+template <Compressible T>
+[[gnu::always_inline]] constexpr auto ref(const utils::compressed_t<T> *p,
+                                          ptrdiff_t i) -> T {
+  return T::decompress(p + i);
+}
+
+} // namespace poly::utils
+
+namespace std {
+template <typename T>
+constexpr void swap(poly::utils::Reference<T> x, poly::utils::Reference<T> y) {
+  std::swap(*x.c, *y.c);
+}
+} // namespace std
diff --git a/include/Utilities/TypeCompression.hpp b/include/Utilities/TypeCompression.hpp
new file mode 100644
index 0000000..42a9b69
--- /dev/null
+++ b/include/Utilities/TypeCompression.hpp
@@ -0,0 +1,69 @@
+#pragma once
+
+namespace poly::utils {
+
+/// The idea here is that some types may have a compression/decompression that
+/// is potentially costly. To work around this, temporaries can live in
+/// uncompressed form, while longer term storage can be compressed/decompressed.
+/// E.g., we have have an array of a compressed type.
+/// When loading, the uncompressed form is returned.
+/// The particular motivating example is around using SIMD types with arrays
+/// that are themselves not a perfect multiple of the SIMD-width.
+/// Writing/reading from temporary locations thus requires masking. For
+/// compilers to be able to optimize these loads and stores, they'd have need to
+/// track provenance using these masks to see that they don't alias, and be able
+/// to actually eliminate the temporaries. Compilers do not seem to do this.
+///
+/// The canonical type is the decompressed form.
+///
+
+/// `T` is the canonical type, which may define `compress`
+template <typename T>
+concept Compressible =
+  (!std::same_as<T, typename T::compressed_type>)&&requires(
+    T t, typename T::compressed_type *p) {
+    { t.compress(p) };
+    { T::decompress(p) } -> std::same_as<T>;
+    { t = *p }; // need generic code to work reasonably well with pointers `p`
+    { T{*p} };  // and value_type `T`
+  };
+
+template <typename T> struct Uncompressed {
+  using compressed = T;
+};
+template <Compressible T> struct Uncompressed<T> {
+  using compressed = typename T::compressed_type;
+};
+template <typename T>
+using compressed_t = typename Uncompressed<std::remove_cvref_t<T>>::compressed;
+
+template <typename T>
+concept Decompressible =
+  Compressible<typename T::decompressed_type> &&
+  std::same_as<T, compressed_t<typename T::decompressed_type>>;
+
+template <typename T> struct Compressed {
+  using uncompressed = T;
+};
+template <Decompressible T> struct Compressed<T> {
+  using uncompressed = typename T::decompressed_type;
+};
+template <typename T>
+using decompressed_t =
+  typename Compressed<std::remove_cvref_t<T>>::uncompressed;
+
+static_assert(std::same_as<decompressed_t<double>, double>);
+static_assert(!Decompressible<double>);
+static_assert(!Compressible<double>);
+
+template <typename T> constexpr void compress(const T &x, compressed_t<T> *p) {
+  if constexpr (Compressible<T>) x.compress(p);
+  else *p = x;
+}
+template <typename T>
+constexpr auto decompress(const compressed_t<T> *p) -> decltype(auto) {
+  if constexpr (Compressible<T>) return T::decompress(p);
+  else return *p;
+}
+
+} // namespace poly::utils
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
index b072321..b396473 100644
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -1,14 +1,9 @@
 cmake_minimum_required(VERSION 3.14)
 
-# # ---- Static Analyzers ----
-# find_program(CLANGTIDY clang-tidy)
-# if(NOT CLANGTIDY MATCHES CLANGTIDY-NOTFOUND)
-#   set(CMAKE_CXX_CLANG_TIDY ${CLANGTIDY})
-# endif()
-# find_program(CPPCHECK cppcheck)
-# if(NOT CPPCHECK MATCHES CPPCHECK-NOTFOUND)
-#   set(CMAKE_CXX_CPPCHECK "${CPPCHECK} --language=c++ --enable=warning,style,performance,information")
-# endif()
+# # ---- Static Analyzers ---- find_program(CLANGTIDY clang-tidy) if(NOT CLANGTIDY MATCHES
+# CLANGTIDY-NOTFOUND) set(CMAKE_CXX_CLANG_TIDY ${CLANGTIDY}) endif() find_program(CPPCHECK cppcheck)
+# if(NOT CPPCHECK MATCHES CPPCHECK-NOTFOUND) set(CMAKE_CXX_CPPCHECK "${CPPCHECK} --language=c++
+# --enable=warning,style,performance,information") endif()
 
 project(MathTests LANGUAGES CXX)
 
@@ -31,9 +26,12 @@ set(CMAKE_EXPORT_COMPILE_COMMANDS ON)
 if(((USE_SANITIZER MATCHES "([Aa]ddress)") OR (USE_SANITIZER MATCHES "([Aa]ddress);([Uu]ndefined)"))
    AND (CMAKE_CXX_COMPILER_ID MATCHES "Clang")
 )
-  find_library(LUNWIND_LIB lunwind)
+  find_library(LUNWIND_LIB unwind)
+  message(STATUS "Found unwindlib ${LUNWIND_LIB}")
   if(LUNWIND_LIB)
-    set(CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS} -lunwind -Wno-unused-command-line-argument")
+    set(CMAKE_EXE_LINKER_FLAGS
+        "${CMAKE_EXE_LINKER_FLAGS} -lunwind -Wno-unused-command-line-argument"
+    )
   endif()
 endif()
 
diff --git a/test/dual_test.cpp b/test/dual_test.cpp
index 8d566d9..43b84e2 100644
--- a/test/dual_test.cpp
+++ b/test/dual_test.cpp
@@ -22,11 +22,11 @@ TEST(DualTest, BasicAssertions) {
   Vector<double> x(15);
   for (auto &a : A) a = dist(gen);
   for (auto &xx : x) xx = dist(gen);
-  SquareMatrix<double> B = A + A.transpose();
+  SquareMatrix<double> B = A + A.t();
   const auto halfquadform = [&](const auto &y) {
-    return 0.5 * (transpose(y) * (B * y));
+    return 0.5 * ((y * B) * transpose(y));
   };
-  Vector<double> g = B * x;
+  Vector<double> g = x * B;
   auto f = halfquadform(x);
 
   auto [fx, gx] = gradient(&arena, x, halfquadform);
@@ -43,27 +43,12 @@ TEST(DualTest, BasicAssertions) {
   EXPECT_TRUE(norm2(B - hxx) < 1e-10);
 };
 
-constexpr ptrdiff_t L = 16;
 template <typename T>
-constexpr auto evalpoly(MutSquarePtrMatrix<T> C, const auto &p) {
-  using U = eltype_t<T>;
-  using S = SquareMatrix<U, L>;
-  assert(C.numRow() == C.numCol());
-  S B{SquareDims{C.numRow()}};
-  evalpoly(B, C, p);
-  return B;
-}
-template <typename T>
-constexpr void evalpoly(MutSquarePtrMatrix<T> B, SquarePtrMatrix<T> C,
-                        const auto &p) {
-  using S = SquareMatrix<T, L>;
+constexpr void evalpoly(MutSquarePtrMatrix<T> B, MutSquarePtrMatrix<T> A,
+                        SquarePtrMatrix<T> C, const auto &p) {
   ptrdiff_t N = p.size();
   invariant(N > 0);
-  invariant(ptrdiff_t(C.numRow()), ptrdiff_t(C.numCol()));
-  invariant(ptrdiff_t(B.numRow()), ptrdiff_t(B.numCol()));
   invariant(ptrdiff_t(B.numRow()), ptrdiff_t(C.numRow()));
-  S Atm{SquareDims{N == 2 ? Row<>{0} : B.numRow()}};
-  MutSquarePtrMatrix<T> A{Atm};
   if (N & 1) std::swap(A, B);
   B << p[0] * C + p[1] * I;
   for (ptrdiff_t i = 2; i < N; ++i) {
@@ -73,18 +58,17 @@ constexpr void evalpoly(MutSquarePtrMatrix<T> B, SquarePtrMatrix<T> C,
 }
 
 template <AbstractMatrix T> constexpr auto opnorm1(const T &A) {
-  using S = decltype(extractDualValRecurse(std::declval<eltype_t<T>>()));
-  ptrdiff_t n = ptrdiff_t(A.numRow());
-  invariant(n > 0);
-  Vector<S> v;
-  v.resizeForOverwrite(n);
-  invariant(A.numRow() > 0);
-  for (ptrdiff_t j = 0; j < n; ++j)
-    v[j] = std::abs(extractDualValRecurse(A[0, j]));
-  for (ptrdiff_t i = 1; i < n; ++i)
-    for (ptrdiff_t j = 0; j < n; ++j)
-      v[j] += std::abs(extractDualValRecurse(A[i, j]));
-  return *std::max_element(v.begin(), v.end());
+  using S = decltype(value(std::declval<eltype_t<T>>()));
+  auto [M, N] = shape(A);
+  invariant(M > 0);
+  invariant(N > 0);
+  S a{};
+  for (ptrdiff_t n = 0; n < N; ++n) {
+    S s{};
+    for (ptrdiff_t m = 0; m < M; ++m) s += std::abs(value(A[m, n]));
+    a = std::max(a, s);
+  }
+  return a;
 }
 
 /// computes ceil(log2(x)) for x >= 1
@@ -94,66 +78,61 @@ constexpr auto log2ceil(double x) -> unsigned {
   return (u >> 52) - 1022;
 }
 
-template <typename T>
-constexpr void expm(MutSquarePtrMatrix<T> V, SquarePtrMatrix<T> A) {
-  invariant(ptrdiff_t(V.numRow()), ptrdiff_t(A.numRow()));
-  ptrdiff_t n = ptrdiff_t(A.numRow());
-  auto nA = opnorm1(A);
-  SquareMatrix<T, L> prodA{A * A}, Utm{SquareDims<>{{n}}};
-  MutSquarePtrMatrix<T> A2{prodA}, U{Utm};
-  unsigned int s = 0;
-  if (nA <= 2.1) {
-    poly::containers::TinyVector<double, 5> p0, p1;
-    if (nA > 0.95) {
-      p0 = {1.0, 3960.0, 2162160.0, 302702400.0, 8821612800.0};
-      p1 = {90.0, 110880.0, 3.027024e7, 2.0756736e9, 1.76432256e10};
-    } else if (nA > 0.25) {
-      p0 = {1.0, 1512.0, 277200.0, 8.64864e6};
-      p1 = {56.0, 25200.0, 1.99584e6, 1.729728e7};
-    } else if (nA > 0.015) {
-      p0 = {1.0, 420.0, 15120.0};
-      p1 = {30.0, 3360.0, 30240.0};
-    } else {
-      p0 = {1.0, 60.0};
-      p1 = {12.0, 120.0};
-    }
-    evalpoly(V, A2, p0);
-    U << A * V;
-    evalpoly(V, A2, p1);
+template <typename T> constexpr void expmimpl(MutSquarePtrMatrix<T> A) {
+  ptrdiff_t n = ptrdiff_t(A.numRow()), s = 0;
+  SquareMatrix<T> A2{SquareDims<>{{n}}}, U_{SquareDims<>{{n}}};
+  MutSquarePtrMatrix<T> U{U_};
+  if (double nA = opnorm1(A); nA <= 0.015) {
+    A2 << A * A;
+    U << A * (A2 + 60.0 * I);
+    A << 12.0 * A2 + 120.0 * I;
   } else {
-    // s = std::max(unsigned(std::ceil(std::log2(nA / 5.4))), unsigned(0));
-    s = nA > 5.4 ? log2ceil(nA / 5.4) : unsigned(0);
-    double t = 1.0;
-    if (s > 0) {
-      t = 1.0 / poly::math::exp2(s);
-      A2 *= (t * t);
-      if (s & 1) std::swap(U, V);
+    SquareMatrix<T> B{SquareDims<>{{n}}};
+    if (nA <= 2.1) {
+      A2 << A * A;
+      poly::containers::TinyVector<double, 5> p0, p1;
+      if (nA > 0.95) {
+        p0 = {1.0, 3960.0, 2162160.0, 302702400.0, 8821612800.0};
+        p1 = {90.0, 110880.0, 3.027024e7, 2.0756736e9, 1.76432256e10};
+      } else if (nA > 0.25) {
+        p0 = {1.0, 1512.0, 277200.0, 8.64864e6};
+        p1 = {56.0, 25200.0, 1.99584e6, 1.729728e7};
+      } else {
+        p0 = {1.0, 420.0, 15120.0};
+        p1 = {30.0, 3360.0, 30240.0};
+      }
+      evalpoly(B, U, A2, p0);
+      U << A * B;
+      evalpoly(A, B, A2, p1);
+    } else {
+      // s = std::max(unsigned(std::ceil(std::log2(nA / 5.4))), 0);
+      s = nA > 5.4 ? log2ceil(nA / 5.4) : 0;
+      if (s & 1) {       // we'll swap `U` and `A` an odd number of times
+        std::swap(A, U); // so let them switch places
+        A << U * exp2(-s);
+      } else if (s > 0) A *= exp2(-s);
+      A2 << A * A;
+      // here we take an estrin (instead of horner) approach to cut down flops
+      SquareMatrix<T> A4{A2 * A2}, A6{A2 * A4};
+      B << A6 * (A6 + 16380 * A4 + 40840800 * A2) +
+             (33522128640 * A6 + 10559470521600 * A4 + 1187353796428800 * A2) +
+             32382376266240000 * I;
+      U << A * B;
+      A << A6 * (182 * A6 + 960960 * A4 + 1323241920 * A2) +
+             (670442572800 * A6 + 129060195264000 * A4 +
+              7771770303897600 * A2) +
+             64764752532480000 * I;
     }
-    SquareMatrix<T, L> A4{A2 * A2}, A6{A2 * A4};
-
-    V << A6 * (A6 + 16380 * A4 + 40840800 * A2) +
-           (33522128640 * A6 + 10559470521600 * A4 + 1187353796428800 * A2) +
-           32382376266240000 * I;
-    U << A * V;
-    if (s > 0) U *= t;
-    V << A6 * (182 * A6 + 960960 * A4 + 1323241920 * A2) +
-           (670442572800 * A6 + 129060195264000 * A4 + 7771770303897600 * A2) +
-           64764752532480000 * I;
-  }
-  for (auto v = V.begin(), u = U.begin(), e = V.end(); v != e; ++v, ++u) {
-    auto &&d = *v - *u;
-    *v += *u;
-    *u = d;
-  }
-  LU::ldiv(U, MutPtrMatrix<T>(V));
-  for (; s--;) {
-    U << V * V;
-    std::swap(U, V);
   }
+  poly::containers::tie(A, U) << poly::containers::Tuple(A + U, A - U);
+  LU::ldiv(U, MutPtrMatrix<T>(A));
+  for (; s--; std::swap(A, U)) U << A * A;
 }
+
 template <typename T> constexpr auto expm(SquarePtrMatrix<T> A) {
-  SquareMatrix<T, L> V{SquareDims{A.numRow()}};
-  expm(V, A);
+  SquareMatrix<T> V{SquareDims{A.numRow()}};
+  V << A;
+  expmimpl(V);
   return V;
 }
 constexpr auto dualDeltaCmp(double x, double y) -> bool { return x < y; }
@@ -167,7 +146,7 @@ constexpr auto dualDeltaCmp(Dual<T, N> x, double y) -> bool {
 
 // NOLINTNEXTLINE(modernize-use-trailing-return-type)
 TEST(ExpMatTest, BasicAssertions) {
-  SquareMatrix<double, L> A(4);
+  SquareMatrix<double> A(4);
   A[0, 0] = 0.13809508135032297;
   A[0, 1] = -0.10597225613986219;
   A[0, 2] = -0.5623996136438215;
@@ -184,7 +163,7 @@ TEST(ExpMatTest, BasicAssertions) {
   A[3, 1] = 0.6550780207685463;
   A[3, 2] = -0.6227535845719466;
   A[3, 3] = 0.2280514374580733;
-  SquareMatrix<double, L> B(4);
+  SquareMatrix<double> B(4);
   B[0, 0] = 0.2051199361909877;
   B[0, 1] = -0.049831094437687434;
   B[0, 2] = -0.3980657896416266;
@@ -201,9 +180,10 @@ TEST(ExpMatTest, BasicAssertions) {
   B[3, 1] = 0.4472989810307132;
   B[3, 2] = -0.11106692926404803;
   B[3, 3] = 0.3930685232252409;
-  EXPECT_TRUE(norm2(B - expm(A)) < 1e-10);
+  EXPECT_LE(norm2(B - expm(A)), 1e-10);
 
-  SquareMatrix<Dual<double, 2>, L> Ad(4);
+  static_assert(poly::utils::Compressible<Dual<double, 2>>);
+  SquareMatrix<Dual<double, 2>> Ad(4);
   Ad[0, 0] = Dual<double, 2>{
     0.13809508135032297,
     SVector<double, 2>{0.23145585885555967, 0.6736099502056541}};
@@ -252,7 +232,7 @@ TEST(ExpMatTest, BasicAssertions) {
   Ad[3, 3] = Dual<double, 2>{
     0.2280514374580733,
     SVector<double, 2>{-1.2001994532706792, 0.03274459682369542}};
-  SquareMatrix<Dual<double, 2>, L> Bd(4);
+  SquareMatrix<Dual<double, 2>> Bd(4);
   Bd[0, 0] = Dual<double, 2>{
     0.20511993619098767,
     SVector<double, 2>{0.09648410552837837, -2.2538795735050865}};
diff --git a/test/linear_algebra_test.cpp b/test/linear_algebra_test.cpp
index 59beaf4..215eef3 100644
--- a/test/linear_algebra_test.cpp
+++ b/test/linear_algebra_test.cpp
@@ -38,12 +38,12 @@ TEST(LinearAlgebraTest, BasicAssertions) {
   auto copyB = B;
   EXPECT_FALSE(LUF.ldivrat(copyB));
   std::cout << "LUF.ldiv(B) = \n" << copyB << "\n";
-  EXPECT_TRUE(copyB == identity);
+  EXPECT_EQ(copyB, identity);
   std::cout << "I = " << identity << "\n";
 
   EXPECT_FALSE(LUF.rdivrat(B));
   std::cout << "LUF.rdiv(B) = \n" << B << "\n";
-  EXPECT_TRUE(B == identity);
+  EXPECT_EQ(B, identity);
 }
 
 // NOLINTNEXTLINE(modernize-use-trailing-return-type)
@@ -59,23 +59,23 @@ TEST(DoubleFactorization, BasicAssertions) {
     // B = A \ B
     // C == A*B == A * (A \ B)
     LU::fact(A).ldiv(MutPtrMatrix<double>(B));
-    EXPECT_TRUE(norm2(A * B - C) < 1e-10);
+    EXPECT_LT(norm2(A * B - C), 1e-10);
     B << C;
     D << A;
     LU::ldiv(A, MutPtrMatrix<double>(B));
-    EXPECT_TRUE(norm2(D * B - C) < 1e-10);
+    EXPECT_LT(norm2(D * B - C), 1e-10);
 
     // LDL; make `A` symmetric
-    D << A + A.transpose();
+    D << A + A.t();
     A << D;
     B << C;
     // B = A \ B
     // C == A*B == A * (A \ B)
     LDL::factorize<>(D).ldiv(MutPtrMatrix<double>(B));
-    EXPECT_TRUE(norm2(A * B - C) < 1e-10);
+    EXPECT_LT(norm2(A * B - C), 1e-10);
     B << C;
     D << A;
     LDL::ldiv<>(A, MutPtrMatrix<double>(B));
-    EXPECT_TRUE(norm2(D * B - C) < 1e-10);
+    EXPECT_LT(norm2(D * B - C), 1e-10);
   }
 }
diff --git a/test/matrix_test.cpp b/test/matrix_test.cpp
index 94683c3..12d86d1 100644
--- a/test/matrix_test.cpp
+++ b/test/matrix_test.cpp
@@ -80,19 +80,20 @@ TEST(SparseIndexingTest, BasicAssertions) {
   IntMatrix<> C2{A * B};
   std::cout << "C=" << C << "\nC2=" << C2 << "\n";
   EXPECT_TRUE(C == C2);
-  IntMatrix<> At{A.transpose()}, Bt{B.transpose()};
-  // At << A.transpose();
-  // Bt << B.transpose();
-  C2 += At.transpose() * Bt.transpose();
-  EXPECT_TRUE(C * 2 == C2);
-  EXPECT_TRUE(C == At.transpose() * B);
-  EXPECT_TRUE(C == A * Bt.transpose());
-  EXPECT_TRUE(C == At.transpose() * Bt.transpose());
-  C2 -= A * Bt.transpose();
-  EXPECT_TRUE(C == C2);
+  IntMatrix<> At{A.t()}, Bt{B.t()};
+  // At << A.t();
+  // Bt << B.t();
+  C2 += At.t() * Bt.t();
+  EXPECT_EQ(C * 2, C2);
+  EXPECT_EQ(C, At.t() * B);
+  EXPECT_EQ(C, A * Bt.t());
+  EXPECT_EQ(C, At.t() * Bt.t());
+  C2 -= A * Bt.t();
+  EXPECT_EQ(C, C2);
   int64_t i = 0;
   IntMatrix<> D{C};
   std::cout << "C=" << C << "\n";
+  static_assert(std::same_as<decltype(D[0, _]), MutArray<long, long>>);
   for (ptrdiff_t r : _(0, D.numRow())) D[r, _] += ptrdiff_t(r) + 1;
   for (auto r : C.eachRow()) {
     EXPECT_EQ(r.size(), ptrdiff_t(C.numCol()));
@@ -172,6 +173,53 @@ TEST(ExpressionTemplateTest, BasicAssertions) {
       for (ptrdiff_t k = 0; k < i; ++k) EXPECT_EQ((F[j, k]), k + j == i - 1);
   }
 }
+// NOLINTNEXTLINE(modernize-use-trailing-return-type)
+TEST(ExpressionTemplateTest2, BasicAssertions) {
+  ManagedArray<double, DenseDims<>> W{{{3}, {3}}, 0}, X{{{3}, {3}}, 0},
+    Y{{{3}, {3}}, 0}, Z{{{3}, {3}}, 0};
+  W[0, 0] = 0.29483432115939806;
+  W[0, 1] = 1.5777027461040212;
+  W[0, 2] = 0.8171761007267028;
+  W[1, 0] = 1.0463632179853855;
+  W[1, 1] = 0.9503214631611095;
+  W[1, 2] = -0.17890983978584624;
+  W[2, 0] = 1.5853551451194254;
+  W[2, 1] = -0.784875301203305;
+  W[2, 2] = 1.7033024094365752;
+  X[0, 0] = -1.1175097244313117;
+  X[0, 1] = -0.21769215316295054;
+  X[0, 2] = -0.7340630927749082;
+  X[1, 0] = -0.5750426169922397;
+  X[1, 1] = 0.27174064995044767;
+  X[1, 2] = -1.0669896577273217;
+  X[2, 0] = 0.9302424251181362;
+  X[2, 1] = -1.3157431480603476;
+  X[2, 2] = 1.546836705770486;
+  Y[0, 0] = 1.1701212478097331;
+  Y[0, 1] = 0.7747688878004019;
+  Y[0, 2] = -0.926815554991563;
+  Y[1, 0] = -1.4441713498640656;
+  Y[1, 1] = -1.3615487160168993;
+  Y[1, 2] = 0.7908183008408143;
+  Y[2, 0] = -0.7626497248468547;
+  Y[2, 1] = -0.21682371102755368;
+  Y[2, 2] = -0.07604892144743511;
+  Z[0, 0] = 3.3759933640164708e16;
+  Z[0, 1] = 9.176788687153845e14;
+  Z[0, 2] = -1.1081818546676994e15;
+  Z[1, 0] = -1.7207794047001762e15;
+  Z[1, 1] = 3.0768637505289172e16;
+  Z[1, 2] = 9.277082601207064e14;
+  Z[2, 0] = -8.956589651911538e14;
+  Z[2, 1] = -2.7136623944168075e14;
+  Z[2, 2] = 3.2308470074953084e16;
+  ManagedArray<double, DenseDims<>> A{
+    W * (W + 16380 * X + 40840800 * Y) +
+    (33522128640 * W + 10559470521600 * X + 1187353796428800 * Y) +
+    32382376266240000 * I};
+
+  EXPECT_EQ(A, Z);
+}
 
 // NOLINTNEXTLINE(modernize-use-trailing-return-type)
 TEST(ArrayPrint, BasicAssertions) {
@@ -208,7 +256,7 @@ TEST(SquareMatrixTest, BasicAssertions) {
   for (ptrdiff_t i = 0; i < 4; ++i)
     for (ptrdiff_t j = 0; j < 4; ++j) A[i, j] = 4 * i + j;
   DenseMatrix<int64_t> B{DenseDims<>{{4}, {2}}};
-  B << A[_(end - 2, end), _].transpose();
+  B << A[_(end - 2, end), _].t();
   for (ptrdiff_t j = 0; j < 4; ++j)
     for (ptrdiff_t i = 0; i < 2; ++i) EXPECT_EQ((B[j, i]), 4 * (i + 2) + j);
 }
@@ -225,6 +273,7 @@ TEST(VectorTest, BasicAssertions) {
 }
 TEST(SVectorTest, BasicAssertions) {
   SVector<int64_t, 3> x{1, 2, 3};
+  static_assert(poly::utils::Compressible<SVector<int64_t, 3>>);
   static_assert(std::tuple_size_v<decltype(x)> == 3);
   static_assert(std::same_as<std::tuple_element_t<2, decltype(x)>, int64_t>);
   SVector<int64_t, 3> y{10, 20, 30};
diff --git a/test/normal_form_test.cpp b/test/normal_form_test.cpp
index bd33c43..300f684 100644
--- a/test/normal_form_test.cpp
+++ b/test/normal_form_test.cpp
@@ -122,7 +122,7 @@ TEST(OrthogonalizationTest, BasicAssertions) {
 }
 
 auto isHNF(PtrMatrix<int64_t> A) -> bool {
-  const auto [M, N] = A.size();
+  const auto [M, N] = shape(A);
   // l is lead
   Col<> l = {0};
   for (ptrdiff_t m = 0; m < M; ++m) {
diff --git a/test/simplex_test.cpp b/test/simplex_test.cpp
index 58f1d80..5a998e6 100644
--- a/test/simplex_test.cpp
+++ b/test/simplex_test.cpp
@@ -14,6 +14,7 @@ TEST(SimplexTest, BasicAssertions) {
   // 15 >= 2x + 5y + 3z
   IntMatrix<> A{"[10 3 2 1; 15 2 5 3]"_mat};
   IntMatrix<> B{DenseDims<>{{0}, {4}}};
+  IntMatrix<> D{"[0 0 0 -2 -3 -4; 10 1 0  3  2  1; 15 0 1  2  5  3 ]"_mat};
   OwningArena<> alloc;
   Optional<Simplex *> optS0{Simplex::positiveVariables(&alloc, A)};
   EXPECT_TRUE(optS0.hasValue());
@@ -32,6 +33,7 @@ TEST(SimplexTest, BasicAssertions) {
     C[4] = -3;
     C[5] = -4;
     std::cout << "S.tableau =" << S->getTableau() << "\n";
+    EXPECT_EQ(S->getTableau(), D);
     EXPECT_EQ(S->run(), 20);
   }
 }
@@ -116,7 +118,14 @@ auto simplexFromTableau(Arena<> *alloc, IntMatrix<> &tableau)
   ptrdiff_t numCon = ptrdiff_t(tableau.numRow()) - 1;
   ptrdiff_t numVar = ptrdiff_t(tableau.numCol()) - 1;
   Simplex *simp{Simplex::create(alloc, numCon, numVar)};
+  for (ptrdiff_t r = 0, R = ptrdiff_t(numRows(tableau)); r < R; ++r)
+    for (ptrdiff_t c = 0, N = ptrdiff_t(numCols(tableau)); c < N; ++c)
+      invariant(tableau[r, c] != std::numeric_limits<int64_t>::min());
   simp->getTableau() << tableau;
+  auto C{simp->getConstraints()};
+  for (ptrdiff_t r = 0, R = ptrdiff_t(numRows(C)); r < R; ++r)
+    for (ptrdiff_t c = 0, N = ptrdiff_t(numCols(C)); c < N; ++c)
+      invariant(C[r, c] != std::numeric_limits<int64_t>::min());
   return simp;
 }
 
@@ -1344,7 +1353,7 @@ TEST(LexMinSimplexTest2, BasicAssertions) {
   }
 }
 
-TEST(Infesaible, BasicAssertions) {
+TEST(Infeasible, BasicAssertions) {
   IntMatrix<> C{DenseDims<>{{220}, {383}}, 0};
   C[0, 0] = -1;
   C[0, 1] = 1;
diff --git a/test/tuple_test.cpp b/test/tuple_test.cpp
new file mode 100644
index 0000000..de6d5c9
--- /dev/null
+++ b/test/tuple_test.cpp
@@ -0,0 +1,56 @@
+
+#include "Containers/Tuple.hpp"
+#include <concepts>
+#include <cstdint>
+#include <gtest/gtest.h>
+
+using poly::containers::Tuple, poly::containers::tie;
+
+// NOLINTNEXTLINE(modernize-use-trailing-return-type)
+TEST(TupleTest, BasicAssertions) {
+  double x = 2.3;
+  double y = 4.5;
+  long z = -5;
+  ulong w = 15;
+  Tuple t{w, x, y, z};
+  {
+    auto [a, b, c, d] = t;
+    static_assert(std::same_as<decltype(a), ulong>);
+    static_assert(std::same_as<decltype(x), double>);
+    static_assert(std::same_as<decltype(y), double>);
+    static_assert(std::same_as<decltype(z), long>);
+    EXPECT_EQ(a, w);
+    EXPECT_EQ(b, x);
+    EXPECT_EQ(c, y);
+    EXPECT_EQ(d, z);
+  }
+  Tuple t1 = t.map([](auto arg) { return 3 * arg; });
+  {
+    auto [a, b, c, d] = t1;
+    static_assert(std::same_as<decltype(a), ulong>);
+    static_assert(std::same_as<decltype(x), double>);
+    static_assert(std::same_as<decltype(y), double>);
+    static_assert(std::same_as<decltype(z), long>);
+    EXPECT_EQ(a, 3 * w);
+    EXPECT_EQ(b, 3 * x);
+    EXPECT_EQ(c, 3 * y);
+    EXPECT_EQ(d, 3 * z);
+  }
+  t1.apply([](auto &arg) { arg *= 2; });
+  {
+    auto [a, b, c, d] = t1;
+    static_assert(std::same_as<decltype(a), ulong>);
+    static_assert(std::same_as<decltype(x), double>);
+    static_assert(std::same_as<decltype(y), double>);
+    static_assert(std::same_as<decltype(z), long>);
+    EXPECT_EQ(a, 6 * w);
+    EXPECT_EQ(b, 6 * x);
+    EXPECT_EQ(c, 6 * y);
+    EXPECT_EQ(d, 6 * z);
+    tie(w, x, y, z) = t1;
+    EXPECT_EQ(a, w);
+    EXPECT_EQ(b, x);
+    EXPECT_EQ(c, y);
+    EXPECT_EQ(d, z);
+  }
+}