feat: fast_exp (#809)

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## Pull request type

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

## What is the current behavior?

<!-- Please describe the current behavior that you are modifying,
or link to a relevant issue. -->

Resolves #700 

## What is the new behavior?

src/kakarot/instructions/stop_and_math_operations.cairo

@@ -31,7 +31,7 @@ from kakarot.model import model
 from kakarot.execution_context import ExecutionContext
 from kakarot.stack import Stack
 from kakarot.errors import Errors
-from utils.uint256 import uint256_exp, uint256_signextend
+from utils.uint256 import uint256_fast_exp, uint256_signextend
 
 // @title Stop and Math operations opcodes.
 // @notice Math operations gathers Arithmetic and Comparison operations
@@ -241,7 +241,7 @@ namespace StopAndMathOperations {
         let range_check_ptr = [ap - 2];
         let popped = cast([ap - 1], Uint256*);
 
-        let result = uint256_exp(popped[0], popped[1]);
+        let result = uint256_fast_exp(popped[0], popped[1]);
 
         tempvar bitwise_ptr = cast([fp - 4], BitwiseBuiltin*);
         tempvar range_check_ptr = range_check_ptr;

src/utils/uint256.cairo

@@ -1,31 +1,31 @@
 from starkware.cairo.common.uint256 import (
     Uint256,
     uint256_eq,
-    uint256_le,
     uint256_sub,
     uint256_mul,
-    uint256_add,
-    uint256_pow2,
     uint256_unsigned_div_rem,
+    uint256_le,
+    uint256_pow2,
+    uint256_add,
 )
 from starkware.cairo.common.bool import FALSE
 
 // @notice Internal exponentiation of two 256-bit integers.
 // @dev The result is modulo 2^256.
-// @param a The base.
-// @param b The exponent.
+// @param value - The base.
+// @param exponent - The exponent.
 // @return The result of the exponentiation.
-func uint256_exp{range_check_ptr}(a: Uint256, b: Uint256) -> Uint256 {
-    let one_uint = Uint256(1, 0);
-    let zero_uint = Uint256(0, 0);
+func uint256_exp{range_check_ptr}(value: Uint256, exponent: Uint256) -> Uint256 {
+    let one = Uint256(1, 0);
+    let zero = Uint256(0, 0);
 
-    let (is_b_zero) = uint256_eq(b, zero_uint);
-    if (is_b_zero != FALSE) {
-        return one_uint;
+    let (exponent_is_zero) = uint256_eq(exponent, zero);
+    if (exponent_is_zero != FALSE) {
+        return one;
     }
-    let (b_minus_one) = uint256_sub(b, one_uint);
-    let pow = uint256_exp(a, b_minus_one);
-    let (res, _) = uint256_mul(a, pow);
+    let (exponent_minus_one) = uint256_sub(exponent, one);
+    let pow = uint256_exp(value, exponent_minus_one);
+    let (res, _) = uint256_mul(value, pow);
     return res;
 }
 
@@ -56,3 +56,38 @@ func uint256_signextend{range_check_ptr}(x: Uint256, byte_num: Uint256) -> Uint2
     let (value, _) = uint256_add(value, padding);
     return value;
 }
+
+// @notice Internal fast exponentiation of two 256-bit integers.
+// @dev The result is modulo 2^256.
+// @param value - The base.
+// @param exponent - The exponent.
+// @return The result of the exponentiation.
+func uint256_fast_exp{range_check_ptr}(value: Uint256, exponent: Uint256) -> Uint256 {
+    alloc_locals;
+
+    let one = Uint256(1, 0);
+    let zero = Uint256(0, 0);
+
+    let (exponent_is_zero) = uint256_eq(exponent, zero);
+    if (exponent_is_zero != FALSE) {
+        return one;
+    }
+
+    let (exponent_is_one) = uint256_eq(exponent, one);
+    if (exponent_is_one != FALSE) {
+        return value;
+    }
+
+    let (half_exponent, is_odd) = uint256_unsigned_div_rem(exponent, Uint256(2, 0));
+    let pow = uint256_fast_exp(value, half_exponent);
+
+    if (is_odd.low != FALSE) {
+        let (res, _) = uint256_mul(pow, pow);
+        let (res, _) = uint256_mul(res, value);
+        return res;
+    }
+
+    let pow = uint256_fast_exp(value, half_exponent);
+    let (res, _) = uint256_mul(pow, pow);
+    return res;
+}

tests/src/kakarot/instructions/test_stop_and_math_operations.py

@@ -37,6 +37,12 @@ class TestMathOperations:
                 (Opcodes.MULMOD, [3, 2, 2], (3 * 2) % 2),
                 (Opcodes.EXP, [3, 2], (3**2)),
                 (Opcodes.EXP, [3, 1], (3**1)),
+                (Opcodes.EXP, [3, 0], (3**0)),
+                (
+                    Opcodes.EXP,
+                    [0xFF, 0x11],
+                    (0xFF**0x11),
+                ),
                 (
                     Opcodes.SIGNEXTEND,
                     [