From db6ebd82e8b36c3ec0106b62b39d76c37ec57bee Mon Sep 17 00:00:00 2001
From: Shramee Srivastav <shramee.srivastav@gmail.com>
Date: Wed, 15 May 2024 22:12:01 +0530
Subject: [PATCH] optimise mod_pow (#301)

<!--- Please provide a general summary of your changes in the title
above -->

## Pull Request type

<!-- Please try to limit your pull request to one type; submit multiple
pull requests if needed. -->

Please check the type of change your PR introduces:

- [ ] Bugfix
- [ ] Feature
- [ ] Code style update (formatting, renaming)
- [x] Refactoring (no functional changes, no API changes)
- [ ] Build-related changes
- [ ] Documentation content changes
- [ ] Other (please describe):

## What is the current behavior?

```diff
running 3 tests
- test alexandria_math::tests::mod_arithmetics_test::pow_mod_1_test ... ok (gas usage est.: 28413612)
+ test alexandria_math::tests::mod_arithmetics_test::pow_mod_1_test ... ok (gas usage est.: 27142740)
- test alexandria_math::tests::mod_arithmetics_test::pow_mod_2_test ... ok (gas usage est.: 28413612)
+ test alexandria_math::tests::mod_arithmetics_test::pow_mod_2_test ... ok (gas usage est.: 27142740)
- test alexandria_math::tests::mod_arithmetics_test::pow_mod_test ... ok (gas usage est.: 28443352)
+ test alexandria_math::tests::mod_arithmetics_test::pow_mod_test ... ok (gas usage est.: 27173670)
```
Issue Number: N/A

## What is the new behavior?

No changes in functionality, just slightly faster `pow_mod`.
## Does this introduce a breaking change?

- [ ] Yes
- [x] No
---
 src/math/src/mod_arithmetics.cairo | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/src/math/src/mod_arithmetics.cairo b/src/math/src/mod_arithmetics.cairo
index 26a429eb..d424c417 100644
--- a/src/math/src/mod_arithmetics.cairo
+++ b/src/math/src/mod_arithmetics.cairo
@@ -95,12 +95,11 @@ pub fn div_mod(a: u256, b: u256, mod_non_zero: NonZero<u256>) -> u256 {
 pub fn pow_mod(mut base: u256, mut pow: u256, mod_non_zero: NonZero<u256>) -> u256 {
     let mut result: u256 = 1;
     while (pow != 0) {
-        if ((pow & 1) > 0) {
+        let (q, r) = DivRem::div_rem(pow, 2);
+        if r == 1 {
             result = mult_mod(result, base, mod_non_zero);
         }
-
-        pow = pow / 2;
-
+        pow = q;
         base = mult_mod(base, base, mod_non_zero);
     };