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use peroxide::fuga::{LambertWAccuracyMode::*, *};
use std::f64::consts::{LN_2, PI};
#[test]
fn lambert_w_test() {
assert_eq!(lambert_w0(1.0, Precise), 0.567143290409784);
assert!(nearly_eq(lambert_w0(1.0, Simple), 0.567143290409784));
}
#[test]
fn test_gamma_poles_and_undefined() {
// Gamma(0) approaches infinity
assert!(gamma(0.0).is_infinite());
assert!(gamma(0.0).is_sign_positive());
// Gamma(-0.0) diverges to negative infinity: tgamma(+0.0) is +inf and
// tgamma(-0.0) is -inf in C99, and `z == 0.0` matches both zeros.
assert!(gamma(-0.0).is_infinite());
assert!(gamma(-0.0).is_sign_negative());
// Gamma for negative integers is mathematically undefined (diverges)
assert!(gamma(-1.0).is_nan());
assert!(gamma(-2.0).is_nan());
assert!(gamma(-10.0).is_nan());
// Log-Gamma goes to positive infinity for all poles
assert!(ln_gamma(0.0).is_infinite());
assert!(ln_gamma(-1.0).is_infinite());
assert!(ln_gamma(-10.0).is_infinite());
assert!(ln_gamma(-0.0).is_infinite());
assert!(ln_gamma(-0.0).is_sign_positive());
}
#[test]
fn test_gamma_integer_fast_path() {
// Standard small factorials: Gamma(n) = (n-1)!
assert_eq!(gamma(1.0), 1.0); // 0!
assert_eq!(gamma(2.0), 1.0); // 1!
assert_eq!(gamma(4.0), 6.0); // 3!
assert_eq!(gamma(5.0), 24.0); // 4!
assert_eq!(gamma(10.0), 362_880.0); // 9!
// Wolfram Alpha high-precision check (21!)
// f64 can exactly represent this without precision loss
assert_eq!(gamma(22.0), 51_090_942_171_709_440_000.0);
// Maximum limit of f64 float representation (~171.6)
// Ensure it doesn't panic on overflow, but correctly yields Infinity
assert!(gamma(172.0).is_infinite());
}
#[test]
fn test_gamma_positive_floats() {
let sqrt_pi = PI.sqrt();
// Gamma(0.5) = sqrt(PI)
assert!(nearly_eq(gamma(0.5), sqrt_pi));
// Gamma(1.5) = 0.5 * sqrt(PI)
assert!(nearly_eq(gamma(1.5), 0.5 * sqrt_pi));
// Gamma(2.5) = 1.329340388179...
assert!(nearly_eq(gamma(2.5), 0.75 * sqrt_pi));
}
#[test]
fn test_gamma_negative_floats_reflection() {
let sqrt_pi = PI.sqrt();
// Gamma(-0.5) = -2 * sqrt(PI)
// This validates that .abs() is NOT used on the sine in gamma_approx
assert!(nearly_eq(gamma(-0.5), -2.0 * sqrt_pi));
assert!(gamma(-0.5).is_sign_negative());
// Gamma(-1.5) = (4/3) * sqrt(PI)
assert!(nearly_eq(gamma(-1.5), (4.0 / 3.0) * sqrt_pi));
assert!(gamma(-1.5).is_sign_positive());
// Gamma(-2.5) = -(8/15) * sqrt(PI)
assert!(nearly_eq(gamma(-2.5), -(8.0 / 15.0) * sqrt_pi));
assert!(gamma(-2.5).is_sign_negative());
}
#[test]
fn test_ln_gamma_consistency() {
// ln_gamma(x) should equal ln(|Gamma(x)|) across the board
let test_values = vec![0.5, 1.5, 2.5, 10.5];
for &val in &test_values {
let expected = gamma(val).ln();
let actual = ln_gamma(val);
assert!(
nearly_eq(expected, actual),
"Failed at positive float: val={}, expected={}, actual={}",
val,
expected,
actual
);
}
// Test Negative Floats to ensure `.abs()` prevents NaN
let negative_test_values = vec![-0.5, -1.5, -2.5, -10.5];
for &val in &negative_test_values {
let expected = gamma(val).abs().ln();
let actual = ln_gamma(val);
assert!(
nearly_eq(expected, actual),
"Failed at negative float: val={}, expected={}, actual={}",
val,
expected,
actual
);
}
}
#[test]
fn test_ln_gamma_exact_at_small_integers() {
// Gamma(1) = Gamma(2) = 1, so the log is exactly zero. The Lanczos series on
// its own lands near -5e-12 here, and that leaks into any caller that forms a
// difference of log-gammas, such as a log-space binomial coefficient.
assert_eq!(ln_gamma(1.0), 0.0);
assert_eq!(ln_gamma(2.0), 0.0);
// Reference values computed with mpmath at 40 digits, rounded to f64. The
// tolerance is tight enough to fail if the integer path is removed, since the
// Lanczos series alone is only good to about 4e-13 relative here.
let cases: [(f64, f64); 3] = [
(3.0, LN_2),
(16.0, 27.89927138384089),
(23.0, 48.47118135183523),
];
for &(z, expected) in &cases {
let got = ln_gamma(z);
let rel = (got - expected).abs() / expected.abs();
assert!(
rel < 1e-14,
"ln_gamma({}) = {}, expected {}, relative error {:e}",
z,
got,
expected,
rel
);
}
}
#[test]
fn test_ln_gamma_against_reference() {
// Independent reference values (mpmath, 40 digits, rounded to f64).
// test_ln_gamma_consistency compares ln_gamma against gamma().ln(), which is
// circular for non-integer z >= 0.5 because gamma is ln_gamma(z).exp() there,
// so these pin the actual values instead. Note nearly_eq compares magnitudes
// and cannot catch a sign flip, hence the explicit signed comparison.
let cases: [(f64, f64); 8] = [
(0.5, 0.5723649429247001),
(1.5, -0.12078223763524522),
(2.5, 0.2846828704729192),
(10.5, 13.940625219403763),
(-0.5, 1.2655121234846454),
(-1.5, 0.860047015376481),
(-2.5, -0.056243716497674054),
(-10.5, -15.147270590717842),
];
for &(z, expected) in &cases {
let got = ln_gamma(z);
let tol = 1e-9 * expected.abs().max(1.0);
assert!(
(got - expected).abs() <= tol,
"ln_gamma({}) = {}, expected {} (tolerance {:e})",
z,
got,
expected,
tol
);
}
}