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pub(crate) use _statistics::module_def;

#[pymodule]

mod _statistics {

use crate::vm::{PyResult, VirtualMachine, function::ArgIntoFloat};

// See https://github.com/python/cpython/blob/6846d6712a0894f8e1a91716c11dd79f42864216/Modules/_statisticsmodule.c#L28-L120

#[allow(

clippy::excessive_precision,

reason = "constants are kept at CPython precision"

)]

fn normal_dist_inv_cdf(p: f64, mu: f64, sigma: f64) -> Option<f64> {

if p <= 0.0 || p >= 1.0 {

return None;

}

let q = p - 0.5;

if q.abs() <= 0.425 {

let r = 0.180625 - q * q;

// Hash sum-55.8831928806149014439

let num = (((((((2.5090809287301226727e+3 * r + 3.3430575583588128105e+4) * r

+ 6.7265770927008700853e+4)

* r

+ 4.5921953931549871457e+4)

* r

+ 1.3731693765509461125e+4)

* r

+ 1.9715909503065514427e+3)

* r

+ 1.3314166789178437745e+2)

* r

+ 3.3871328727963666080e+0)

* q;

let den = ((((((5.2264952788528545610e+3 * r + 2.8729085735721942674e+4) * r

+ 3.9307895800092710610e+4)

* r

+ 2.1213794301586595867e+4)

* r

+ 5.3941960214247511077e+3)

* r

+ 6.8718700749205790830e+2)

* r

+ 4.2313330701600911252e+1)

* r

+ 1.0;

if den == 0.0 {

return None;

}

let x = num / den;

return Some(mu + (x * sigma));

}

let r = if q <= 0.0 { p } else { 1.0 - p };

if r <= 0.0 || r >= 1.0 {

return None;

}

let r = (-(r.ln())).sqrt();

let num;

let den;

#[allow(

clippy::excessive_precision,

reason = "piecewise polynomial coefficients match CPython"

)]

if r <= 5.0 {

let r = r - 1.6;

// Hash sum-49.33206503301610289036

num = ((((((7.74545014278341407640e-4 * r + 2.27238449892691845833e-2) * r

+ 2.41780725177450611770e-1)

* r

+ 1.27045825245236838258e+0)

* r

+ 3.64784832476320460504e+0)

* r

+ 5.76949722146069140550e+0)

* r

+ 4.63033784615654529590e+0)

* r

+ 1.42343711074968357734e+0;

den = ((((((1.05075007164441684324e-9 * r + 5.47593808499534494600e-4) * r

+ 1.51986665636164571966e-2)

* r

+ 1.48103976427480074590e-1)

* r

+ 6.89767334985100004550e-1)

* r

+ 1.67638483018380384940e+0)

* r

+ 2.05319162663775882187e+0)

* r

+ 1.0;

} else {

let r = r - 5.0;

// Hash sum-47.52583317549289671629

num = ((((((2.01033439929228813265e-7 * r + 2.71155556874348757815e-5) * r

+ 1.24266094738807843860e-3)

* r

+ 2.65321895265761230930e-2)

* r

+ 2.96560571828504891230e-1)

* r

+ 1.78482653991729133580e+0)

* r

+ 5.46378491116411436990e+0)

* r

+ 6.65790464350110377720e+0;

den = ((((((2.04426310338993978564e-15 * r + 1.42151175831644588870e-7) * r

+ 1.84631831751005468180e-5)

* r

+ 7.86869131145613259100e-4)

* r

+ 1.48753612908506148525e-2)

* r

+ 1.36929880922735805310e-1)

* r

+ 5.99832206555887937690e-1)

* r

+ 1.0;

}

if den == 0.0 {

return None;

}

let mut x = num / den;

if q < 0.0 {

x = -x;

}

Some(mu + (x * sigma))

}

#[pyfunction]

fn _normal_dist_inv_cdf(

p: ArgIntoFloat,

mu: ArgIntoFloat,

sigma: ArgIntoFloat,

vm: &VirtualMachine,

) -> PyResult<f64> {

normal_dist_inv_cdf(p.into_float(), mu.into_float(), sigma.into_float())

.ok_or_else(|| vm.new_value_error("inv_cdf undefined for these parameters"))

}

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