Merge pull request #270 from BillXu2000/benchmark_inv

Add modular multiplicative inverse benchmark

benchmarks/core/mod_inv.bril

@@ -0,0 +1,90 @@
+# ARGS: 46, 10007
+@main(n: int, p: int) {
+  v0: int = const 2;
+  two: int = id v0;
+  v1: int = id p;
+  v2: int = id two;
+  v3: int = sub v1 v2;
+  m: int = id v3;
+  v4: int = const 1;
+  ans: int = id v4;
+  v5: int = id n;
+  a: int = id v5;
+  v7: int = const 1;
+  i: int = id v7;
+.for.cond.6:
+  v8: int = id m;
+  v9: int = const 0;
+  v10: bool = gt v8 v9;
+  br v10 .for.body.6 .for.end.6;
+.for.body.6:
+  v12: int = id m;
+  v13: int = id m;
+  v14: int = id two;
+  v15: int = div v13 v14;
+  v16: int = id two;
+  v17: int = mul v15 v16;
+  v18: bool = eq v12 v17;
+  br v18 .then.11 .else.11;
+.then.11:
+  jmp .endif.11;
+.else.11:
+  v19: int = id ans;
+  v20: int = id a;
+  v21: int = mul v19 v20;
+  v22: int = id p;
+  v23: int = call @mod v21 v22;
+  ans: int = id v23;
+.endif.11:
+  v24: int = id a;
+  v25: int = id a;
+  v26: int = mul v24 v25;
+  v27: int = id p;
+  v28: int = call @mod v26 v27;
+  a: int = id v28;
+  v29: int = id m;
+  v30: int = id two;
+  v31: int = div v29 v30;
+  m: int = id v31;
+  jmp .for.cond.6;
+.for.end.6:
+  v32: int = id ans;
+  print v32;
+  v33: int = const 0;
+}
+@mod(n: int, p: int): int {
+  v0: int = id n;
+  v1: int = id n;
+  v2: int = id p;
+  v3: int = div v1 v2;
+  v4: int = id p;
+  v5: int = mul v3 v4;
+  v6: int = sub v0 v5;
+  ret v6;
+}
+
+# ts2bril inv.ts | bril2txt | tail +3 | sed -E 's/float/int/g' | sed -E 's/fgt/gt/g' > inv.bril
+# generated by typescript code below:
+#
+# function main(n: bigint, p: bigint) {
+#   var two: bigint = 2;
+#   var m: bigint = p - two;
+#   var ans: bigint = 1;
+#   var a: bigint = n;
+#   for (let i = 1; m > 0; m = m / two) {
+#     if (m == m / two * two) {
+#     }
+#     else {
+#       ans = mod(ans * a, p);
+#     }
+#     a = mod(a * a, p);
+#   }
+#   console.log(ans);
+# }
+# 
+# function mod(n: bigint, p: bigint): bigint {
+#   return n - n / p * p;
+# }
+#
+
+

benchmarks/core/mod_inv.out

@@ -0,0 +1 @@
+2393

benchmarks/core/mod_inv.prof

@@ -0,0 +1 @@
+total_dyn_inst: 558

docs/tools/bench.md

@@ -36,6 +36,7 @@ The current benchmarks are:
 * `mat-inv` : Calculates the inverse of a 3x3 matrix and prints it out.
 * `mat-mul`: Multiplies two `nxn` matrices using the [naive][matmul] matrix multiplication algorithm. The matrices are randomly generated using a [linear congruential generator][rng].
 * `max-subarray`: solution to the classic Maximum Subarray problem.
+* `mod_inv`: Calculates the [modular inverse][modinv] of `n` under to a prime modulus p.
 * `newton`: Calculate the square root of 99,999 using the [newton method][newton]
 * `n_root`: Calculate nth root of a float using newton's method.
 * `orders`: Compute the order ord(u) for each u in a cyclic group [<Zn,+>][cgroup] of integers modulo *n* under the group operation + (modulo *n*). Set the second argument *is_lcm* to true if you would like to compute the orders using the lowest common multiple and otherwise the program will use the greatest common divisor.
@@ -88,4 +89,5 @@ Credit for several of these benchmarks goes to Alexa VanHattum and Gregory Yaune
 [palindrome]: https://en.wikipedia.org/wiki/Palindrome
 [hanoi]: https://en.wikipedia.org/wiki/Tower_of_Hanoi
 [euler]: https://en.wikipedia.org/wiki/E_(mathematical_constant)
-[totient]: https://en.wikipedia.org/wiki/Euler's_totient_function
+[modinv]: https://en.wikipedia.org/wiki/Modular_multiplicative_inverse
+[totient]: https://en.wikipedia.org/wiki/Euler's_totient_function