Reduce gas usage of pow by about 15 percent. (#7013)

corelib/src/num/traits/ops/pow.cairo

@@ -40,16 +40,42 @@ mod mul_based {
         type Output = T;
 
         const fn pow(self: T, exp: usize) -> T {
-            let (tail_exp, head_exp) = DivRem::div_rem(exp, 2);
-            let tail_result = if tail_exp == 0 {
+            if exp == 0 {
                 H::one()
             } else {
-                Self::pow(H::mul(self, self), tail_exp)
-            };
+                pow_non_zero_exp(self, exp)
+            }
+        }
+    }
+
+    /// Equivalent of `PowByMul::pow` but assumes `exp` is non zero.
+    const fn pow_non_zero_exp<T, impl H: ConstPowHelper<T>, +Copy<T>, +Drop<T>>(
+        base: T, exp: usize,
+    ) -> T {
+        let (tail_exp, head_exp) = DivRem::div_rem(exp, 2);
+        if head_exp == 0 {
+            pow_non_zero_exp(H::mul(base, base), tail_exp)
+        } else {
+            pow_given_sqrt_base(base, tail_exp, base)
+        }
+    }
+
+    /// Returns `(sqrt_base * sqrt_base).pow(exp) * acc`.
+    ///
+    /// Receives the square root of the base to avoid overflow if the squaring is not required for
+    /// the calculation (mostly when `exp` is 0).
+    const fn pow_given_sqrt_base<T, impl H: ConstPowHelper<T>, +Copy<T>, +Drop<T>>(
+        sqrt_base: T, exp: usize, acc: T,
+    ) -> T {
+        if exp == 0 {
+            acc
+        } else {
+            let (tail_exp, head_exp) = DivRem::div_rem(exp, 2);
+            let base = H::mul(sqrt_base, sqrt_base);
             if head_exp == 0 {
-                tail_result
+                H::mul(pow_non_zero_exp(H::mul(base, base), tail_exp), acc)
             } else {
-                H::mul(tail_result, self)
+                pow_given_sqrt_base(base, tail_exp, H::mul(base, acc))
             }
         }
     }