TheRock/rocm-libraries/projects/rocthrust/thrust/random/detail/erfcinv.h

/*
Copyright © 2003-2013 SciPy Developers.
Modifications Copyright© 2019-2025 Advanced Micro Devices, Inc. All rights reserved.
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the
following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following
disclaimer. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the
following disclaimer in the documentation and/or other materials provided with the distribution. Neither the name of
Enthought nor the names of the SciPy Developers may be used to endorse or promote products derived from this software
without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN
IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/

#pragma once

#include <cmath>
#include <limits>

/* sqrt(2pi) */
static double s2pi              = 2.50662827463100050242E0;
static const double one_o_sqrt2 = (1 / sqrt(2.0));

/* approximation for 0 <= |y - 0.5| <= 3/8 */
static double P0[5] = {
  -5.99633501014107895267E1,
  9.80010754185999661536E1,
  -5.66762857469070293439E1,
  1.39312609387279679503E1,
  -1.23916583867381258016E0,
};

static double Q0[8] = {
  /* 1.00000000000000000000E0, */
  1.95448858338141759834E0,
  4.67627912898881538453E0,
  8.63602421390890590575E1,
  -2.25462687854119370527E2,
  2.00260212380060660359E2,
  -8.20372256168333339912E1,
  1.59056225126211695515E1,
  -1.18331621121330003142E0,
};

/* Approximation for interval z = sqrt(-2 log y ) between 2 and 8
 * i.e., y between exp(-2) = .135 and exp(-32) = 1.27e-14.
 */
static double P1[9] = {
  4.05544892305962419923E0,
  3.15251094599893866154E1,
  5.71628192246421288162E1,
  4.40805073893200834700E1,
  1.46849561928858024014E1,
  2.18663306850790267539E0,
  -1.40256079171354495875E-1,
  -3.50424626827848203418E-2,
  -8.57456785154685413611E-4,
};

static double Q1[8] = {
  /*  1.00000000000000000000E0, */
  1.57799883256466749731E1,
  4.53907635128879210584E1,
  4.13172038254672030440E1,
  1.50425385692907503408E1,
  2.50464946208309415979E0,
  -1.42182922854787788574E-1,
  -3.80806407691578277194E-2,
  -9.33259480895457427372E-4,
};

/* Approximation for interval z = sqrt(-2 log y ) between 8 and 64
 * i.e., y between exp(-32) = 1.27e-14 and exp(-2048) = 3.67e-890.
 */

static double P2[9] = {
  3.23774891776946035970E0,
  6.91522889068984211695E0,
  3.93881025292474443415E0,
  1.33303460815807542389E0,
  2.01485389549179081538E-1,
  1.23716634817820021358E-2,
  3.01581553508235416007E-4,
  2.65806974686737550832E-6,
  6.23974539184983293730E-9,
};

static double Q2[8] = {
  /*  1.00000000000000000000E0, */
  6.02427039364742014255E0,
  3.67983563856160859403E0,
  1.37702099489081330271E0,
  2.16236993594496635890E-1,
  1.34204006088543189037E-2,
  3.28014464682127739104E-4,
  2.89247864745380683936E-6,
  6.79019408009981274425E-9,
};

static inline double polevl(double x, double coef[], int N)
{
  double ans;
  int i;
  double* p;

  p   = coef;
  ans = *p++;
  i   = N;

  do
  {
    ans = ans * x + *p++;
  } while (--i);

  return (ans);
}

/*                                                     p1evl() */
/*                                          N
 * Evaluate polynomial when coefficient of x  is 1.0.
 * Otherwise same as polevl.
 */

static inline double p1evl(double x, double coef[], int N)
{
  double ans;
  double* p;
  int i;

  p   = coef;
  ans = x + *p++;
  i   = N - 1;

  do
  {
    ans = ans * x + *p++;
  } while (--i);

  return (ans);
}

static inline double ndtri(double y0)
{
  double x, y, z, y2, x0, x1;
  int code;

  code = 1;
  y    = y0;
  if (y > (1.0 - 0.13533528323661269189))
  { /* 0.135... = exp(-2) */
    y    = 1.0 - y;
    code = 0;
  }

  if (y > 0.13533528323661269189)
  {
    y  = y - 0.5;
    y2 = y * y;
    x  = y + y * (y2 * polevl(y2, P0, 4) / p1evl(y2, Q0, 8));
    x  = x * s2pi;
    return (x);
  }

  x  = sqrt(-2.0 * log(y));
  x0 = x - log(x) / x;

  z = 1.0 / x;
  if (x < 8.0) /* y > exp(-32) = 1.2664165549e-14 */
  {
    x1 = z * polevl(z, P1, 8) / p1evl(z, Q1, 8);
  }
  else
  {
    x1 = z * polevl(z, P2, 8) / p1evl(z, Q2, 8);
  }
  x = x0 - x1;
  if (code != 0)
  {
    x = -x;
  }
  return (x);
}

static inline double erfcinv(double x)
{
  if (x < 0.0 || x > 2.0)
  {
    return std::nan("undefined");
  }
  if (x == 0.0)
  {
    return std::numeric_limits<double>::infinity();
  }
  if (x == 2.0)
  {
    return -std::numeric_limits<double>::infinity();
  }
  return -ndtri(0.5 * x) * one_o_sqrt2;
}