Thanks to visit codestin.com
Credit goes to github.com

Skip to content

more accurate sqrt function #129

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

Open
wants to merge 3 commits into
base: master
Choose a base branch
from
Open

more accurate sqrt function #129

Changes from 1 commit
Commits
Show all changes
3 commits
Select commit Hold shift + click to select a range
ed22935
more accurate sqrt function
pascalkuthe May 11, 2024
6178de6
add accuracy testcase
pascalkuthe Dec 14, 2024
c5b8101
add roundtrip tests
pascalkuthe Dec 15, 2024
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
Prev Previous commit
Next Next commit
add accuracy testcase
  • Loading branch information
@pascalkuthe
pascalkuthe authored Dec 14, 2024
commit 6178de61f8fdfb1a934665a7a33393abb7250786
65 changes: 65 additions & 0 deletions src/lib.rs
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -2156,6 +2156,71 @@ pub(crate) mod test {
}
}


#[test]
#[allow(clippy::float_cmp)]
fn test_sqrt_accuract() {
fn naive_sqrt(c: Complex64) -> Complex64 {
let (r, theta) = c.to_polar();
Complex64::from_polar(r.sqrt(), theta / 2.0)
}

#[track_caller]
fn check_sqrt(re: f64, im: f64, exact_sqrt_re: f64, exact_sqrt_im: f64) {
let sqrt = Complex::new(re, im).sqrt();
assert_eq!(sqrt.re, exact_sqrt_re, "real(sqrt(c))e invalid for {re}");
assert_eq!(sqrt.im, exact_sqrt_im, "imag(sqrt(c))e invalid for {re}");
let naive_sqrt = naive_sqrt(Complex::new(re, im));
assert_ne!(naive_sqrt, sqrt, "invalid testcase {re} {im}");
}
// reference values were computed with numpy but are identical
// with musl and glibc, showing that we round correctly both
// in reasonable ranges and extremes cases. All of these tests
// fail with a naive sqrt implementation based on phase shift (this
// is checked as part of the tests).
//
// The testcases were generated by the following python script:
//
// import numpy as np
// vals = [
// (0.1, 0.1),
// (0.1, 1 / 3),
// (1 / 3, 0.1),
// (1 / 3, 1 / 3),
// (1.1, 1e-100),
// (1e-100, 0.1),
// (1e-100, 1.1),
// (1e-100, 1e-100),
// ]
// for re, im in vals:
// reference = np.sqrt(re + im * 1j)
// print(f"check_sqrt({re}, {im}, {reference.real}, {reference.imag});")

check_sqrt(0.1, 0.1, 0.34743442276011566, 0.14391204994250742);
check_sqrt(
0.1,
0.3333333333333333,
0.4732917794361556,
0.3521435907152684,
);
check_sqrt(
0.3333333333333333,
0.1,
0.5836709476652998,
0.08566470577300687,
);
check_sqrt(
0.3333333333333333,
0.3333333333333333,
0.6343255686650054,
0.26274625350107117,
);
check_sqrt(1.1, 1e-100, 1.0488088481701516, 4.767312946227961e-101);
check_sqrt(1e-100, 0.1, 0.22360679774997896, 0.223606797749979);
check_sqrt(1e-100, 1.1, 0.7416198487095663, 0.7416198487095663);
check_sqrt(1e-100, 1e-100, 1.09868411346781e-50, 4.550898605622274e-51);
}

#[test]
fn test_cbrt() {
assert!(close(_0_0i.cbrt(), _0_0i));
Expand Down