[libc++] Optimize lexicographical_compare (llvm#65279)

If the comparison operation is equivalent to < and that is a total order, we know that we can use equality comparison on that type instead to extract some information. Furthermore, if equality comparison on that type is trivial, the user can't observe that we're calling it. So instead of using the user-provided total order, we use std::mismatch, which uses equality comparison (and is vertorized). Additionally, if the type is trivially lexicographically comparable, we can go one step further and use std::memcmp directly instead of calling std::mismatch. Benchmarks: ``` ------------------------------------------------------------------------------------- Benchmark old new ------------------------------------------------------------------------------------- bm_lexicographical_compare<unsigned char>/1 1.17 ns 2.34 ns bm_lexicographical_compare<unsigned char>/2 1.64 ns 2.57 ns bm_lexicographical_compare<unsigned char>/3 2.23 ns 2.58 ns bm_lexicographical_compare<unsigned char>/4 2.82 ns 2.57 ns bm_lexicographical_compare<unsigned char>/5 3.34 ns 2.11 ns bm_lexicographical_compare<unsigned char>/6 3.94 ns 2.21 ns bm_lexicographical_compare<unsigned char>/7 4.56 ns 2.11 ns bm_lexicographical_compare<unsigned char>/8 5.25 ns 2.11 ns bm_lexicographical_compare<unsigned char>/16 9.88 ns 2.11 ns bm_lexicographical_compare<unsigned char>/64 38.9 ns 2.36 ns bm_lexicographical_compare<unsigned char>/512 317 ns 6.54 ns bm_lexicographical_compare<unsigned char>/4096 2517 ns 41.4 ns bm_lexicographical_compare<unsigned char>/32768 20052 ns 488 ns bm_lexicographical_compare<unsigned char>/262144 159579 ns 4409 ns bm_lexicographical_compare<unsigned char>/1048576 640456 ns 20342 ns bm_lexicographical_compare<signed char>/1 1.18 ns 2.37 ns bm_lexicographical_compare<signed char>/2 1.65 ns 2.60 ns bm_lexicographical_compare<signed char>/3 2.23 ns 2.83 ns bm_lexicographical_compare<signed char>/4 2.81 ns 3.06 ns bm_lexicographical_compare<signed char>/5 3.35 ns 3.30 ns bm_lexicographical_compare<signed char>/6 3.90 ns 3.99 ns bm_lexicographical_compare<signed char>/7 4.56 ns 3.78 ns bm_lexicographical_compare<signed char>/8 5.20 ns 4.02 ns bm_lexicographical_compare<signed char>/16 9.80 ns 6.21 ns bm_lexicographical_compare<signed char>/64 39.0 ns 3.16 ns bm_lexicographical_compare<signed char>/512 318 ns 7.58 ns bm_lexicographical_compare<signed char>/4096 2514 ns 47.4 ns bm_lexicographical_compare<signed char>/32768 20096 ns 504 ns bm_lexicographical_compare<signed char>/262144 156617 ns 4146 ns bm_lexicographical_compare<signed char>/1048576 624265 ns 19810 ns bm_lexicographical_compare<int>/1 1.15 ns 2.12 ns bm_lexicographical_compare<int>/2 1.60 ns 2.36 ns bm_lexicographical_compare<int>/3 2.21 ns 2.59 ns bm_lexicographical_compare<int>/4 2.74 ns 2.83 ns bm_lexicographical_compare<int>/5 3.26 ns 3.06 ns bm_lexicographical_compare<int>/6 3.81 ns 4.53 ns bm_lexicographical_compare<int>/7 4.41 ns 4.72 ns bm_lexicographical_compare<int>/8 5.08 ns 2.36 ns bm_lexicographical_compare<int>/16 9.54 ns 3.08 ns bm_lexicographical_compare<int>/64 37.8 ns 4.71 ns bm_lexicographical_compare<int>/512 309 ns 24.6 ns bm_lexicographical_compare<int>/4096 2422 ns 204 ns bm_lexicographical_compare<int>/32768 19362 ns 1947 ns bm_lexicographical_compare<int>/262144 155727 ns 19793 ns bm_lexicographical_compare<int>/1048576 623614 ns 80180 ns bm_ranges_lexicographical_compare<unsigned char>/1 1.07 ns 2.35 ns bm_ranges_lexicographical_compare<unsigned char>/2 1.72 ns 2.13 ns bm_ranges_lexicographical_compare<unsigned char>/3 2.46 ns 2.12 ns bm_ranges_lexicographical_compare<unsigned char>/4 3.17 ns 2.12 ns bm_ranges_lexicographical_compare<unsigned char>/5 3.86 ns 2.12 ns bm_ranges_lexicographical_compare<unsigned char>/6 4.55 ns 2.12 ns bm_ranges_lexicographical_compare<unsigned char>/7 5.25 ns 2.12 ns bm_ranges_lexicographical_compare<unsigned char>/8 5.95 ns 2.13 ns bm_ranges_lexicographical_compare<unsigned char>/16 11.7 ns 2.13 ns bm_ranges_lexicographical_compare<unsigned char>/64 45.5 ns 2.36 ns bm_ranges_lexicographical_compare<unsigned char>/512 366 ns 6.35 ns bm_ranges_lexicographical_compare<unsigned char>/4096 2886 ns 40.9 ns bm_ranges_lexicographical_compare<unsigned char>/32768 23054 ns 489 ns bm_ranges_lexicographical_compare<unsigned char>/262144 185302 ns 4339 ns bm_ranges_lexicographical_compare<unsigned char>/1048576 741576 ns 19430 ns bm_ranges_lexicographical_compare<signed char>/1 1.10 ns 2.12 ns bm_ranges_lexicographical_compare<signed char>/2 1.66 ns 2.35 ns bm_ranges_lexicographical_compare<signed char>/3 2.23 ns 2.58 ns bm_ranges_lexicographical_compare<signed char>/4 2.82 ns 2.82 ns bm_ranges_lexicographical_compare<signed char>/5 3.34 ns 3.06 ns bm_ranges_lexicographical_compare<signed char>/6 3.92 ns 3.99 ns bm_ranges_lexicographical_compare<signed char>/7 4.64 ns 4.10 ns bm_ranges_lexicographical_compare<signed char>/8 5.21 ns 4.61 ns bm_ranges_lexicographical_compare<signed char>/16 9.79 ns 7.42 ns bm_ranges_lexicographical_compare<signed char>/64 38.9 ns 2.93 ns bm_ranges_lexicographical_compare<signed char>/512 317 ns 7.31 ns bm_ranges_lexicographical_compare<signed char>/4096 2500 ns 47.5 ns bm_ranges_lexicographical_compare<signed char>/32768 19940 ns 496 ns bm_ranges_lexicographical_compare<signed char>/262144 159166 ns 4393 ns bm_ranges_lexicographical_compare<signed char>/1048576 638206 ns 19786 ns bm_ranges_lexicographical_compare<int>/1 1.10 ns 2.12 ns bm_ranges_lexicographical_compare<int>/2 1.64 ns 3.04 ns bm_ranges_lexicographical_compare<int>/3 2.23 ns 2.58 ns bm_ranges_lexicographical_compare<int>/4 2.81 ns 2.81 ns bm_ranges_lexicographical_compare<int>/5 3.35 ns 3.05 ns bm_ranges_lexicographical_compare<int>/6 3.94 ns 4.60 ns bm_ranges_lexicographical_compare<int>/7 4.60 ns 4.81 ns bm_ranges_lexicographical_compare<int>/8 5.19 ns 2.35 ns bm_ranges_lexicographical_compare<int>/16 9.85 ns 2.87 ns bm_ranges_lexicographical_compare<int>/64 38.9 ns 4.70 ns bm_ranges_lexicographical_compare<int>/512 318 ns 24.5 ns bm_ranges_lexicographical_compare<int>/4096 2494 ns 202 ns bm_ranges_lexicographical_compare<int>/32768 20000 ns 1939 ns bm_ranges_lexicographical_compare<int>/262144 160433 ns 19730 ns bm_ranges_lexicographical_compare<int>/1048576 642636 ns 80760 ns ```
banach-space · Aug 7, 2024 · 3366349 · 3366349
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diff --git a/libcxx/docs/ReleaseNotes/20.rst b/libcxx/docs/ReleaseNotes/20.rst
@@ -44,7 +44,8 @@ Implemented Papers
 Improvements and New Features
 -----------------------------
 
-- TODO
+- The ``lexicographical_compare`` and ``ranges::lexicographical_compare`` algorithms have been optimized for trivially
+  equality comparable types, resulting in a performance improvement of up to 40x.
 
 
 Deprecations and Removals

diff --git a/libcxx/include/__algorithm/comp.h b/libcxx/include/__algorithm/comp.h
@@ -11,6 +11,7 @@
 
 #include <__config>
 #include <__type_traits/desugars_to.h>
+#include <__type_traits/is_integral.h>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #  pragma GCC system_header
@@ -42,7 +43,7 @@ struct __less<void, void> {
 };
 
 template <class _Tp>
-inline const bool __desugars_to_v<__less_tag, __less<>, _Tp, _Tp> = true;
+inline const bool __desugars_to_v<__totally_ordered_less_tag, __less<>, _Tp, _Tp> = is_integral<_Tp>::value;
 
 _LIBCPP_END_NAMESPACE_STD
 

diff --git a/libcxx/include/__algorithm/lexicographical_compare.h b/libcxx/include/__algorithm/lexicographical_compare.h
@@ -10,40 +10,109 @@
 #define _LIBCPP___ALGORITHM_LEXICOGRAPHICAL_COMPARE_H
 
 #include <__algorithm/comp.h>
-#include <__algorithm/comp_ref_type.h>
+#include <__algorithm/min.h>
+#include <__algorithm/mismatch.h>
+#include <__algorithm/simd_utils.h>
+#include <__algorithm/unwrap_iter.h>
 #include <__config>
+#include <__functional/identity.h>
 #include <__iterator/iterator_traits.h>
+#include <__string/constexpr_c_functions.h>
+#include <__type_traits/desugars_to.h>
+#include <__type_traits/invoke.h>
+#include <__type_traits/is_equality_comparable.h>
+#include <__type_traits/is_integral.h>
+#include <__type_traits/is_trivially_lexicographically_comparable.h>
+#include <__type_traits/is_volatile.h>
+
+#ifndef _LIBCPP_HAS_NO_WIDE_CHARACTERS
+#  include <cwchar>
+#endif
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #  pragma GCC system_header
 #endif
 
+_LIBCPP_PUSH_MACROS
+#include <__undef_macros>
+
 _LIBCPP_BEGIN_NAMESPACE_STD
 
-template <class _Compare, class _InputIterator1, class _InputIterator2>
+template <class _Iter1, class _Sent1, class _Iter2, class _Sent2, class _Proj1, class _Proj2, class _Comp>
 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 bool __lexicographical_compare(
-    _InputIterator1 __first1,
-    _InputIterator1 __last1,
-    _InputIterator2 __first2,
-    _InputIterator2 __last2,
-    _Compare __comp) {
-  for (; __first2 != __last2; ++__first1, (void)++__first2) {
-    if (__first1 == __last1 || __comp(*__first1, *__first2))
+    _Iter1 __first1, _Sent1 __last1, _Iter2 __first2, _Sent2 __last2, _Comp& __comp, _Proj1& __proj1, _Proj2& __proj2) {
+  while (__first2 != __last2) {
+    if (__first1 == __last1 ||
+        std::__invoke(__comp, std::__invoke(__proj1, *__first1), std::__invoke(__proj2, *__first2)))
       return true;
-    if (__comp(*__first2, *__first1))
+    if (std::__invoke(__comp, std::__invoke(__proj2, *__first2), std::__invoke(__proj1, *__first1)))
       return false;
+    ++__first1;
+    ++__first2;
   }
   return false;
 }
 
+#if _LIBCPP_STD_VER >= 14
+
+// If the comparison operation is equivalent to < and that is a total order, we know that we can use equality comparison
+// on that type instead to extract some information. Furthermore, if equality comparison on that type is trivial, the
+// user can't observe that we're calling it. So instead of using the user-provided total order, we use std::mismatch,
+// which uses equality comparison (and is vertorized). Additionally, if the type is trivially lexicographically
+// comparable, we can go one step further and use std::memcmp directly instead of calling std::mismatch.
+template <class _Tp,
+          class _Proj1,
+          class _Proj2,
+          class _Comp,
+          __enable_if_t<__desugars_to_v<__totally_ordered_less_tag, _Comp, _Tp, _Tp> && !is_volatile<_Tp>::value &&
+                            __libcpp_is_trivially_equality_comparable<_Tp, _Tp>::value &&
+                            __is_identity<_Proj1>::value && __is_identity<_Proj2>::value,
+                        int> = 0>
+_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 bool
+__lexicographical_compare(_Tp* __first1, _Tp* __last1, _Tp* __first2, _Tp* __last2, _Comp&, _Proj1&, _Proj2&) {
+  if constexpr (__is_trivially_lexicographically_comparable_v<_Tp, _Tp>) {
+    auto __res =
+        std::__constexpr_memcmp(__first1, __first2, __element_count(std::min(__last1 - __first1, __last2 - __first2)));
+    if (__res == 0)
+      return __last1 - __first1 < __last2 - __first2;
+    return __res < 0;
+  }
+#  ifndef _LIBCPP_HAS_NO_WIDE_CHARACTERS
+  else if constexpr (is_same<__remove_cv_t<_Tp>, wchar_t>::value) {
+    auto __res = std::__constexpr_wmemcmp(__first1, __first2, std::min(__last1 - __first1, __last2 - __first2));
+    if (__res == 0)
+      return __last1 - __first1 < __last2 - __first2;
+    return __res < 0;
+  }
+#  endif // _LIBCPP_HAS_NO_WIDE_CHARACTERS
+  else {
+    auto __res = std::mismatch(__first1, __last1, __first2, __last2);
+    if (__res.second == __last2)
+      return false;
+    if (__res.first == __last1)
+      return true;
+    return *__res.first < *__res.second;
+  }
+}
+
+#endif // _LIBCPP_STD_VER >= 14
+
 template <class _InputIterator1, class _InputIterator2, class _Compare>
 _LIBCPP_NODISCARD inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 bool lexicographical_compare(
     _InputIterator1 __first1,
     _InputIterator1 __last1,
     _InputIterator2 __first2,
     _InputIterator2 __last2,
     _Compare __comp) {
-  return std::__lexicographical_compare<__comp_ref_type<_Compare> >(__first1, __last1, __first2, __last2, __comp);
+  __identity __proj;
+  return std::__lexicographical_compare(
+      std::__unwrap_iter(__first1),
+      std::__unwrap_iter(__last1),
+      std::__unwrap_iter(__first2),
+      std::__unwrap_iter(__last2),
+      __comp,
+      __proj,
+      __proj);
 }
 
 template <class _InputIterator1, class _InputIterator2>
@@ -54,4 +123,6 @@ _LIBCPP_NODISCARD inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 boo
 
 _LIBCPP_END_NAMESPACE_STD
 
+_LIBCPP_POP_MACROS
+
 #endif // _LIBCPP___ALGORITHM_LEXICOGRAPHICAL_COMPARE_H
diff --git a/libcxx/include/__algorithm/ranges_lexicographical_compare.h b/libcxx/include/__algorithm/ranges_lexicographical_compare.h
@@ -9,6 +9,8 @@
 #ifndef _LIBCPP___ALGORITHM_RANGES_LEXICOGRAPHICAL_COMPARE_H
 #define _LIBCPP___ALGORITHM_RANGES_LEXICOGRAPHICAL_COMPARE_H
 
+#include <__algorithm/lexicographical_compare.h>
+#include <__algorithm/unwrap_range.h>
 #include <__config>
 #include <__functional/identity.h>
 #include <__functional/invoke.h>
@@ -33,23 +35,24 @@ _LIBCPP_BEGIN_NAMESPACE_STD
 namespace ranges {
 struct __lexicographical_compare {
   template <class _Iter1, class _Sent1, class _Iter2, class _Sent2, class _Proj1, class _Proj2, class _Comp>
-  _LIBCPP_HIDE_FROM_ABI constexpr static bool __lexicographical_compare_impl(
+  static _LIBCPP_HIDE_FROM_ABI constexpr bool __lexicographical_compare_unwrap(
       _Iter1 __first1,
       _Sent1 __last1,
       _Iter2 __first2,
       _Sent2 __last2,
       _Comp& __comp,
       _Proj1& __proj1,
       _Proj2& __proj2) {
-    while (__first2 != __last2) {
-      if (__first1 == __last1 || std::invoke(__comp, std::invoke(__proj1, *__first1), std::invoke(__proj2, *__first2)))
-        return true;
-      if (std::invoke(__comp, std::invoke(__proj2, *__first2), std::invoke(__proj1, *__first1)))
-        return false;
-      ++__first1;
-      ++__first2;
-    }
-    return false;
+    auto [__first1_un, __last1_un] = std::__unwrap_range(std::move(__first1), std::move(__last1));
+    auto [__first2_un, __last2_un] = std::__unwrap_range(std::move(__first2), std::move(__last2));
+    return std::__lexicographical_compare(
+        std::move(__first1_un),
+        std::move(__last1_un),
+        std::move(__first2_un),
+        std::move(__last2_un),
+        __comp,
+        __proj1,
+        __proj2);
   }
 
   template <input_iterator _Iter1,
@@ -67,7 +70,7 @@ struct __lexicographical_compare {
       _Comp __comp   = {},
       _Proj1 __proj1 = {},
       _Proj2 __proj2 = {}) const {
-    return __lexicographical_compare_impl(
+    return __lexicographical_compare_unwrap(
         std::move(__first1), std::move(__last1), std::move(__first2), std::move(__last2), __comp, __proj1, __proj2);
   }
 
@@ -79,7 +82,7 @@ struct __lexicographical_compare {
                 _Comp = ranges::less>
   [[nodiscard]] _LIBCPP_HIDE_FROM_ABI constexpr bool operator()(
       _Range1&& __range1, _Range2&& __range2, _Comp __comp = {}, _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const {
-    return __lexicographical_compare_impl(
+    return __lexicographical_compare_unwrap(
         ranges::begin(__range1),
         ranges::end(__range1),
         ranges::begin(__range2),

diff --git a/libcxx/include/__algorithm/ranges_minmax.h b/libcxx/include/__algorithm/ranges_minmax.h
@@ -88,7 +88,7 @@ struct __minmax {
     // vectorize the code.
     if constexpr (contiguous_range<_Range> && is_integral_v<_ValueT> &&
                   __is_cheap_to_copy<_ValueT> & __is_identity<_Proj>::value &&
-                  __desugars_to_v<__less_tag, _Comp, _ValueT, _ValueT>) {
+                  __desugars_to_v<__totally_ordered_less_tag, _Comp, _ValueT, _ValueT>) {
       minmax_result<_ValueT> __result = {__r[0], __r[0]};
       for (auto __e : __r) {
         if (__e < __result.min)

diff --git a/libcxx/include/__functional/operations.h b/libcxx/include/__functional/operations.h
@@ -14,6 +14,7 @@
 #include <__functional/binary_function.h>
 #include <__functional/unary_function.h>
 #include <__type_traits/desugars_to.h>
+#include <__type_traits/is_integral.h>
 #include <__utility/forward.h>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
@@ -362,7 +363,7 @@ struct _LIBCPP_TEMPLATE_VIS less : __binary_function<_Tp, _Tp, bool> {
 _LIBCPP_CTAD_SUPPORTED_FOR_TYPE(less);
 
 template <class _Tp>
-inline const bool __desugars_to_v<__less_tag, less<_Tp>, _Tp, _Tp> = true;
+inline const bool __desugars_to_v<__totally_ordered_less_tag, less<_Tp>, _Tp, _Tp> = is_integral<_Tp>::value;
 
 #if _LIBCPP_STD_VER >= 14
 template <>
@@ -377,7 +378,7 @@ struct _LIBCPP_TEMPLATE_VIS less<void> {
 };
 
 template <class _Tp>
-inline const bool __desugars_to_v<__less_tag, less<>, _Tp, _Tp> = true;
+inline const bool __desugars_to_v<__totally_ordered_less_tag, less<>, _Tp, _Tp> = is_integral<_Tp>::value;
 #endif
 
 #if _LIBCPP_STD_VER >= 14

diff --git a/libcxx/include/__functional/ranges_operations.h b/libcxx/include/__functional/ranges_operations.h
@@ -100,7 +100,7 @@ template <class _Tp, class _Up>
 inline const bool __desugars_to_v<__equal_tag, ranges::equal_to, _Tp, _Up> = true;
 
 template <class _Tp, class _Up>
-inline const bool __desugars_to_v<__less_tag, ranges::less, _Tp, _Up> = true;
+inline const bool __desugars_to_v<__totally_ordered_less_tag, ranges::less, _Tp, _Up> = true;
 
 #endif // _LIBCPP_STD_VER >= 20
 

diff --git a/libcxx/include/__string/constexpr_c_functions.h b/libcxx/include/__string/constexpr_c_functions.h
@@ -64,13 +64,13 @@ inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 size_t __constexpr_st
   return __builtin_strlen(reinterpret_cast<const char*>(__str));
 }
 
-// Because of __libcpp_is_trivially_lexicographically_comparable we know that comparing the object representations is
+// Because of __is_trivially_lexicographically_comparable_v we know that comparing the object representations is
 // equivalent to a std::memcmp. Since we have multiple objects contiguously in memory, we can call memcmp once instead
 // of invoking it on every object individually.
 template <class _Tp, class _Up>
 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 int
 __constexpr_memcmp(const _Tp* __lhs, const _Up* __rhs, __element_count __n) {
-  static_assert(__libcpp_is_trivially_lexicographically_comparable<_Tp, _Up>::value,
+  static_assert(__is_trivially_lexicographically_comparable_v<_Tp, _Up>,
                 "_Tp and _Up have to be trivially lexicographically comparable");
 
   auto __count = static_cast<size_t>(__n);

diff --git a/libcxx/include/__type_traits/desugars_to.h b/libcxx/include/__type_traits/desugars_to.h
@@ -17,10 +17,21 @@
 
 _LIBCPP_BEGIN_NAMESPACE_STD
 
-// Tags to represent the canonical operations
+// Tags to represent the canonical operations.
+
+// syntactically, the operation is equivalent to calling `a == b`
 struct __equal_tag {};
+
+// syntactically, the operation is equivalent to calling `a + b`
 struct __plus_tag {};
-struct __less_tag {};
+
+// syntactically, the operation is equivalent to calling `a < b`, and these expressions
+// have to be true for any `a` and `b`:
+// - `(a < b) == (b > a)`
+// - `(!(a < b) && !(b < a)) == (a == b)`
+// For example, this is satisfied for std::less on integral types, but also for ranges::less on all types due to
+// additional semantic requirements on that operation.
+struct __totally_ordered_less_tag {};
 
 // This class template is used to determine whether an operation "desugars"
 // (or boils down) to a given canonical operation.

diff --git a/libcxx/include/__type_traits/is_trivially_lexicographically_comparable.h b/libcxx/include/__type_traits/is_trivially_lexicographically_comparable.h
@@ -16,6 +16,7 @@
 #include <__type_traits/remove_cv.h>
 #include <__type_traits/void_t.h>
 #include <__utility/declval.h>
+#include <cstddef>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #  pragma GCC system_header
@@ -40,13 +41,22 @@ _LIBCPP_BEGIN_NAMESPACE_STD
 // unsigned integer types with sizeof(T) > 1: depending on the endianness, the LSB might be the first byte to be
 //                                            compared. This means that when comparing unsigned(129) and unsigned(2)
 //                                            using memcmp(), the result would be that 2 > 129.
-//                                            TODO: Do we want to enable this on big-endian systems?
+
+template <class _Tp>
+inline const bool __is_std_byte_v = false;
+
+#if _LIBCPP_STD_VER >= 17
+template <>
+inline const bool __is_std_byte_v<byte> = true;
+#endif
 
 template <class _Tp, class _Up>
-struct __libcpp_is_trivially_lexicographically_comparable
-    : integral_constant<bool,
-                        is_same<__remove_cv_t<_Tp>, __remove_cv_t<_Up> >::value && sizeof(_Tp) == 1 &&
-                            is_unsigned<_Tp>::value> {};
+inline const bool __is_trivially_lexicographically_comparable_v =
+    is_same<__remove_cv_t<_Tp>, __remove_cv_t<_Up> >::value &&
+#ifdef _LIBCPP_LITTLE_ENDIAN
+    sizeof(_Tp) == 1 &&
+#endif
+    (is_unsigned<_Tp>::value || __is_std_byte_v<_Tp>);
 
 _LIBCPP_END_NAMESPACE_STD
 

diff --git a/libcxx/test/benchmarks/CMakeLists.txt b/libcxx/test/benchmarks/CMakeLists.txt
@@ -114,6 +114,7 @@ set(BENCHMARK_TESTS
     algorithms/find.bench.cpp
     algorithms/fill.bench.cpp
     algorithms/for_each.bench.cpp
+    algorithms/lexicographical_compare.bench.cpp
     algorithms/lower_bound.bench.cpp
     algorithms/make_heap.bench.cpp
     algorithms/make_heap_then_sort_heap.bench.cpp

diff --git a/libcxx/test/benchmarks/algorithms/lexicographical_compare.bench.cpp b/libcxx/test/benchmarks/algorithms/lexicographical_compare.bench.cpp
@@ -0,0 +1,44 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include <algorithm>
+#include <benchmark/benchmark.h>
+#include <vector>
+
+// Benchmarks the worst case: check the whole range just to find out that they compare equal
+template <class T>
+static void bm_lexicographical_compare(benchmark::State& state) {
+  std::vector<T> vec1(state.range(), '1');
+  std::vector<T> vec2(state.range(), '1');
+
+  for (auto _ : state) {
+    benchmark::DoNotOptimize(vec1);
+    benchmark::DoNotOptimize(vec2);
+    benchmark::DoNotOptimize(std::lexicographical_compare(vec1.begin(), vec1.end(), vec2.begin(), vec2.end()));
+  }
+}
+BENCHMARK(bm_lexicographical_compare<unsigned char>)->DenseRange(1, 8)->Range(16, 1 << 20);
+BENCHMARK(bm_lexicographical_compare<signed char>)->DenseRange(1, 8)->Range(16, 1 << 20);
+BENCHMARK(bm_lexicographical_compare<int>)->DenseRange(1, 8)->Range(16, 1 << 20);
+
+template <class T>
+static void bm_ranges_lexicographical_compare(benchmark::State& state) {
+  std::vector<T> vec1(state.range(), '1');
+  std::vector<T> vec2(state.range(), '1');
+
+  for (auto _ : state) {
+    benchmark::DoNotOptimize(vec1);
+    benchmark::DoNotOptimize(vec2);
+    benchmark::DoNotOptimize(std::ranges::lexicographical_compare(vec1.begin(), vec1.end(), vec2.begin(), vec2.end()));
+  }
+}
+BENCHMARK(bm_ranges_lexicographical_compare<unsigned char>)->DenseRange(1, 8)->Range(16, 1 << 20);
+BENCHMARK(bm_ranges_lexicographical_compare<signed char>)->DenseRange(1, 8)->Range(16, 1 << 20);
+BENCHMARK(bm_ranges_lexicographical_compare<int>)->DenseRange(1, 8)->Range(16, 1 << 20);
+
+BENCHMARK_MAIN();