Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Improved integer square root. #202

Closed
wants to merge 4 commits into from
Closed

Improved integer square root. #202

Changes from all commits
Commits
Show all changes
4 commits
Select commit Hold shift + click to select a range
8746667
Improved integer square root.
chgorman Jun 29, 2023
fac56e7
Small updates to sqrt.
chgorman Jul 22, 2023
c7ae038
Fixed variable naming.
chgorman Jul 24, 2023
7e69537
Minor improvement.
chgorman Sep 1, 2023
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
34 changes: 23 additions & 11 deletions contracts/libraries/Math.sol
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -7,17 +7,29 @@ library Math {
z = x < y ? x : y;
}

// babylonian method (https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method)
function sqrt(uint y) internal pure returns (uint z) {
if (y > 3) {
z = y;
uint x = y / 2 + 1;
while (x < z) {
z = x;
x = (y / x + x) / 2;
}
} else if (y != 0) {
z = 1;
function sqrt(uint256 x) internal pure returns (uint256) {
unchecked {
if (x <= 1) { return x; }
if (x >= ((1 << 128) - 1)**2) { return (1 << 128) - 1; }
uint256 xAux = x;
uint256 result = 1;
if (xAux >= (1 << 128)) { xAux >>= 128; result = 1 << 64; }
if (xAux >= (1 << 64 )) { xAux >>= 64; result <<= 32; }
if (xAux >= (1 << 32 )) { xAux >>= 32; result <<= 16; }
if (xAux >= (1 << 16 )) { xAux >>= 16; result <<= 8; }
if (xAux >= (1 << 8 )) { xAux >>= 8; result <<= 4; }
if (xAux >= (1 << 4 )) { xAux >>= 4; result <<= 2; }
if (xAux >= (1 << 2 )) { result <<= 1; }
result = (3 * result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
result = (result + x / result) >> 1;
if (result * result <= a) {
return result;
}
return result-1;
}
}