Optimize log256's binary search (#5284)

Author: cairoeth

contracts/utils/math/Math.sol

@@ -644,29 +644,17 @@ library Math {
      *
      * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
      */
-    function log256(uint256 value) internal pure returns (uint256) {
-        uint256 result = 0;
-        uint256 isGt;
-        unchecked {
-            isGt = SafeCast.toUint(value > (1 << 128) - 1);
-            value >>= isGt * 128;
-            result += isGt * 16;
-
-            isGt = SafeCast.toUint(value > (1 << 64) - 1);
-            value >>= isGt * 64;
-            result += isGt * 8;
-
-            isGt = SafeCast.toUint(value > (1 << 32) - 1);
-            value >>= isGt * 32;
-            result += isGt * 4;
-
-            isGt = SafeCast.toUint(value > (1 << 16) - 1);
-            value >>= isGt * 16;
-            result += isGt * 2;
-
-            result += SafeCast.toUint(value > (1 << 8) - 1);
-        }
-        return result;
+    function log256(uint256 x) internal pure returns (uint256 r) {
+        // If value has upper 128 bits set, log2 result is at least 128
+        r = SafeCast.toUint(x > 0xffffffffffffffffffffffffffffffff) << 7;
+        // If upper 64 bits of 128-bit half set, add 64 to result
+        r |= SafeCast.toUint((x >> r) > 0xffffffffffffffff) << 6;
+        // If upper 32 bits of 64-bit half set, add 32 to result
+        r |= SafeCast.toUint((x >> r) > 0xffffffff) << 5;
+        // If upper 16 bits of 32-bit half set, add 16 to result
+        r |= SafeCast.toUint((x >> r) > 0xffff) << 4;
+        // Add 1 if upper 8 bits of 16-bit half set, and divide accumulated result by 8
+        return (r >> 3) | SafeCast.toUint((x >> r) > 0xff);
     }
 
     /**