From 3d49038072ce9fe88ac61cb89f5bce65fef8d26f Mon Sep 17 00:00:00 2001
From: Filip Krawczyk <kotmawszy@gmail.com>
Date: Tue, 24 Oct 2023 17:47:53 +0200
Subject: [PATCH] Add fast_pow function

---
 src/utils/bitwise.cairo |  6 +++-
 src/utils/math.cairo    | 61 ++++++++++++++++++++++++++++++++++++++++-
 2 files changed, 65 insertions(+), 2 deletions(-)

diff --git a/src/utils/bitwise.cairo b/src/utils/bitwise.cairo
index 95f2189..ab1f9c8 100644
--- a/src/utils/bitwise.cairo
+++ b/src/utils/bitwise.cairo
@@ -14,7 +14,11 @@ fn left_shift<
     impl TMul: Mul<T>,
     impl TOneable: Oneable<T>,
     impl TCopy: Copy<T>,
-    impl TDrop: Drop<T>
+    impl TDrop: Drop<T>,
+    impl TDiv: Div<T>,
+    impl TRem: Rem<T>,
+    impl TPartialEq: PartialEq<T>,
+    impl TPartialOrd: PartialOrd<T>
 >(
     num: T, shift: T
 ) -> T {
diff --git a/src/utils/math.cairo b/src/utils/math.cairo
index fe25aa0..7a844c5 100644
--- a/src/utils/math.cairo
+++ b/src/utils/math.cairo
@@ -4,7 +4,34 @@ use math::Oneable;
 // @param base The base of the exponentiation
 // @param exp The exponent of the exponentiation
 // @return The exponentiation result
+
 fn pow<
+    T,
+    impl Zeroable: Zeroable<T>,
+    impl TOneable: Oneable<T>,
+    impl TCopy: Copy<T>,
+    impl TDrop: Drop<T>,
+    impl TAdd: Add<T>,
+    impl TSub: Sub<T>,
+    impl TMul: Mul<T>,
+    impl TDiv: Div<T>,
+    impl TRem: Rem<T>,
+    impl TPartialEq: PartialEq<T>,
+    impl TPartialOrd: PartialOrd<T>
+>(
+    mut base: T, mut exp: T
+) -> T {
+    let two = TOneable::one() + TOneable::one();
+    let four = two + two;
+    let sixteen = four * four;
+    if exp < sixteen {
+        slow_pow(base, exp)
+    } else {
+        fast_pow(base, exp)
+    }
+}
+
+fn slow_pow<
     T,
     impl TZeroable: Zeroable<T>,
     impl TSub: Sub<T>,
@@ -18,6 +45,38 @@ fn pow<
     if exp.is_zero() {
         TOneable::one()
     } else {
-        base * pow(base, exp - TOneable::one())
+        base * slow_pow(base, exp - TOneable::one())
+    }
+}
+
+fn fast_pow<
+    T,
+    impl Zeroable: Zeroable<T>,
+    impl TOneable: Oneable<T>,
+    impl TCopy: Copy<T>,
+    impl TDrop: Drop<T>,
+    impl TAdd: Add<T>,
+    impl TSub: Sub<T>,
+    impl TMul: Mul<T>,
+    impl TDiv: Div<T>,
+    impl TRem: Rem<T>,
+    impl TPartialEq: PartialEq<T>
+>(
+    mut base: T, mut exp: T
+) -> T {
+    let mut ans = TOneable::one();
+    loop {
+        if exp.is_zero() {
+            break ans;
+        }
+        let two = TOneable::one() + TOneable::one();
+        let mm = exp % two;
+        if mm == TOneable::one() {
+            ans = ans * base;
+            exp = exp - TOneable::one();
+        } else {
+            base = base * base;
+            exp = exp / two;
+        };
     }
 }