/*
Adapted from: https://github.com/compute-io/erfcinv/blob/aa116e23883839359e310ad41a7c42f72815fc1e/lib/number.js

The MIT License (MIT)

Copyright (c) 2014-2015 The Compute.io Authors. All rights reserved.

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.


Boost Software License - Version 1.0 - August 17th, 2003

Permission is hereby granted, free of charge, to any person or organization obtaining a copy of the software and accompanying documentation covered by this license (the "Software") to use, reproduce, display, distribute, execute, and transmit the Software, and to prepare derivative works of the Software, and to permit third-parties to whom the Software is furnished to do so, all subject to the following:

The copyright notices in the Software and this entire statement, including the above license grant, this restriction and the following disclaimer, must be included in all copies of the Software, in whole or in part, and all derivative works of the Software, unless such copies or derivative works are solely in the form of machine-executable object code generated by a source language processor.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/

/* eslint-disable no-loss-of-precision */

// Coefficients for erfcinv on [0, 0.5]:
const Y1 = 8.91314744949340820313e-2;
const P1 = [
  -5.38772965071242932965e-3, 8.22687874676915743155e-3,
  2.19878681111168899165e-2, -3.65637971411762664006e-2,
  -1.26926147662974029034e-2, 3.34806625409744615033e-2,
  -8.36874819741736770379e-3, -5.08781949658280665617e-4,
];
const Q1 = [
  8.86216390456424707504e-4, -2.33393759374190016776e-3,
  7.95283687341571680018e-2, -5.27396382340099713954e-2,
  -7.1228902341542847553e-1, 6.62328840472002992063e-1, 1.56221558398423026363,
  -1.56574558234175846809, -9.70005043303290640362e-1, 1,
];

// Coefficients for erfcinv for 0.5 > 1-x >= 0:
const Y2 = 2.249481201171875;
const P2 = [
  -3.67192254707729348546, 2.11294655448340526258e1, 1.7445385985570866523e1,
  -4.46382324441786960818e1, -1.88510648058714251895e1,
  1.76447298408374015486e1, 8.37050328343119927838, 1.05264680699391713268e-1,
  -2.02433508355938759655e-1,
];
const Q2 = [
  1.72114765761200282724, -2.26436933413139721736e1, 1.08268667355460159008e1,
  4.85609213108739935468e1, -2.01432634680485188801e1,
  -2.86608180499800029974e1, 3.9713437953343869095, 6.24264124854247537712, 1,
];

// Coefficients for erfcinv for sqrt( -log(1-x)):
const Y3 = 8.07220458984375e-1;
const P3 = [
  -6.81149956853776992068e-10, 2.85225331782217055858e-8,
  -6.79465575181126350155e-7, 2.14558995388805277169e-3,
  2.90157910005329060432e-2, 1.42869534408157156766e-1,
  3.37785538912035898924e-1, 3.87079738972604337464e-1,
  1.17030156341995252019e-1, -1.63794047193317060787e-1,
  -1.31102781679951906451e-1,
];
const Q3 = [
  1.105924229346489121e-2, 1.52264338295331783612e-1, 8.48854343457902036425e-1,
  2.59301921623620271374, 4.77846592945843778382, 5.38168345707006855425,
  3.46625407242567245975, 1,
];

const Y4 = 9.3995571136474609375e-1;
const P4 = [
  2.66339227425782031962e-12, -2.30404776911882601748e-10,
  4.60469890584317994083e-6, 1.57544617424960554631e-4,
  1.87123492819559223345e-3, 9.50804701325919603619e-3,
  1.85573306514231072324e-2, -2.22426529213447927281e-3,
  -3.50353787183177984712e-2,
];
const Q4 = [
  7.64675292302794483503e-5, 2.63861676657015992959e-3,
  3.41589143670947727934e-2, 2.20091105764131249824e-1,
  7.62059164553623404043e-1, 1.3653349817554063097, 1,
];

const Y5 = 9.8362827301025390625e-1;
const P5 = [
  9.9055709973310326855e-17, -2.81128735628831791805e-14,
  4.62596163522878599135e-9, 4.49696789927706453732e-7,
  1.49624783758342370182e-5, 2.09386317487588078668e-4,
  1.05628862152492910091e-3, -1.12951438745580278863e-3,
  -1.67431005076633737133e-2,
];
const Q5 = [
  2.82243172016108031869e-7, 2.75335474764726041141e-5,
  9.64011807005165528527e-4, 1.60746087093676504695e-2,
  1.38151865749083321638e-1, 5.91429344886417493481e-1, 1,
];

/**
 * Polyval.
 * @param c - Array of Number.
 * @param x - Number.
 * @returns Number.
 */
function polyval(c: number[], x: number): number {
  let p = 0;
  for (const coef of c) {
    p = p * x + coef;
  }
  return p;
}

/**
 * Calculates a rational approximation.
 * @private
 * @param x - Number.
 * @param v - Number.
 * @param P - Array of polynomial coefficients.
 * @param Q - Array of polynomial coefficients.
 * @param Y - Number.
 * @returns Rational approximation.
 */
function calc(
  x: number,
  v: number,
  P: number[],
  Q: number[],
  Y: number,
): number {
  const s = x - v;
  const r = polyval(P, s) / polyval(Q, s);
  return Y * x + r * x;
}

/**
 * Evaluates the complementary inverse error function for an input value.
 * @private
 * @param x - Input value.
 * @returns Evaluated complementary inverse error function.
 */
export default function erfcinv(x: number): number {
  let sign = false;
  let val;
  let q;
  let g;
  let r;

  // [1] Special cases...

  // NaN:
  if (Number.isNaN(x)) {
    return Number.NaN;
  }
  // x not on the interval: [0,2]
  if (x < 0 || x > 2) {
    throw new RangeError(
      `erfcinv()::invalid input argument. Value must be on the interval [0,2]. Value: \`${x}\`.`,
    );
  }
  if (x === 0) {
    return Number.POSITIVE_INFINITY;
  }
  if (x === 2) {
    return Number.NEGATIVE_INFINITY;
  }
  if (x === 1) {
    return 0;
  }
  // [2] Get the sign and make use of `erfc` reflection formula: `erfc(-z)=2 - erfc(z)`...
  if (x > 1) {
    q = 2 - x;
    x = 1 - q;
    sign = true;
  } else {
    q = x;
    x = 1 - x;
  }
  // [3] |x| <= 0.5
  if (x <= 0.5) {
    g = x * (x + 10);
    r = polyval(P1, x) / polyval(Q1, x);
    val = g * Y1 + g * r;
    return sign ? -val : val;
  }

  // [4] 1-|x| >= 0.25
  if (q >= 0.25) {
    g = Math.sqrt(-2 * Math.log(q));
    q = q - 0.25;
    r = polyval(P2, q) / polyval(Q2, q);
    val = g / (Y2 + r);
    return sign ? -val : val;
  }
  q = Math.sqrt(-Math.log(q));

  // [5] q < 3
  if (q < 3) {
    return calc(q, 1.125, P3, Q3, Y3);
  }
  // [6] q < 6
  if (q < 6) {
    return calc(q, 3, P4, Q4, Y4);
  }
  // Note that the smallest number in JavaScript is 5e-324. Math.sqrt( -Math.log( 5e-324 ) ) ~27.2844
  return calc(q, 6, P5, Q5, Y5);

  // Note that in the boost library, they are able to go to much smaller values, as 128 bit long doubles support ~1e-5000; something which JavaScript does not natively support.
}