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Optimize log2 with a lookup table (#5236)

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Co-authored-by: Hadrien Croubois <hadrien.croubois@gmail.com>
Co-authored-by: cairo <cairoeth@protonmail.com>
This commit is contained in:
Lohann Paterno Coutinho Ferreira
2024-10-29 16:09:20 +00:00
committed by GitHub
parent 3da7a869aa
commit 448efeea66
1 changed files with 37 additions and 33 deletions
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70
contracts/utils/math/Math.sol
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@ -537,41 +537,45 @@ library Math {
* @dev Return the log in base 2 of a positive value rounded towards zero.
* Returns 0 if given 0.
*/
function log2(uint256 value) internal pure returns (uint256) {
uint256 result = 0;
uint256 exp;
unchecked {
exp = 128 * SafeCast.toUint(value > (1 << 128) - 1);
value >>= exp;
result += exp;
function log2(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;
// If upper 8 bits of 16-bit half set, add 8 to result
r |= SafeCast.toUint((x >> r) > 0xff) << 3;
// If upper 4 bits of 8-bit half set, add 4 to result
r |= SafeCast.toUint((x >> r) > 0xf) << 2;
exp = 64 * SafeCast.toUint(value > (1 << 64) - 1);
value >>= exp;
result += exp;
exp = 32 * SafeCast.toUint(value > (1 << 32) - 1);
value >>= exp;
result += exp;
exp = 16 * SafeCast.toUint(value > (1 << 16) - 1);
value >>= exp;
result += exp;
exp = 8 * SafeCast.toUint(value > (1 << 8) - 1);
value >>= exp;
result += exp;
exp = 4 * SafeCast.toUint(value > (1 << 4) - 1);
value >>= exp;
result += exp;
exp = 2 * SafeCast.toUint(value > (1 << 2) - 1);
value >>= exp;
result += exp;
result += SafeCast.toUint(value > 1);
// Shifts value right by the current result and use it as an index into this lookup table:
//
// | x (4 bits) | index | table[index] = MSB position |
// |------------|---------|-----------------------------|
// | 0000 | 0 | table[0] = 0 |
// | 0001 | 1 | table[1] = 0 |
// | 0010 | 2 | table[2] = 1 |
// | 0011 | 3 | table[3] = 1 |
// | 0100 | 4 | table[4] = 2 |
// | 0101 | 5 | table[5] = 2 |
// | 0110 | 6 | table[6] = 2 |
// | 0111 | 7 | table[7] = 2 |
// | 1000 | 8 | table[8] = 3 |
// | 1001 | 9 | table[9] = 3 |
// | 1010 | 10 | table[10] = 3 |
// | 1011 | 11 | table[11] = 3 |
// | 1100 | 12 | table[12] = 3 |
// | 1101 | 13 | table[13] = 3 |
// | 1110 | 14 | table[14] = 3 |
// | 1111 | 15 | table[15] = 3 |
//
// The lookup table is represented as a 32-byte value with the MSB positions for 0-15 in the last 16 bytes.
assembly ("memory-safe") {
r := or(r, byte(shr(r, x), 0x0000010102020202030303030303030300000000000000000000000000000000))
}
return result;
}
/**