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/* $Id: boost_erf.c,v 1.1 2016/04/14 19:19:05 fukanchi Exp $
* ===========================================================================
*
* This code is ported from the open source C++ library Boost, for which
* the following notice applies:
*
* (C) Copyright John Maddock 2006.
* Use, modification and distribution are subject to the Boost Software
* License, Version 1.0. (See below or copy at
* http://www.boost.org/LICENSE_1_0.txt)
*
* 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.
*
* ===========================================================================
*
* Author (editor, really): Greg Boratyn, NCBI
*
* File Description:
* Error function and complementary error function for normal distribution.
*
* ===========================================================================
*/
#include "boost_erf.h"
#include <math.h>
#define FALSE 0
#define TRUE 1
static double ErfImpl(double z, int invert)
{
if (z < 0) {
if (!invert) {
return -ErfImpl(-z, invert);
}
else if (z < -0.5) {
return 2.0 - ErfImpl(-z, invert);
}
else {
return 1 + ErfImpl(-z, FALSE);
}
}
double result;
/* Big bunch of selection statements now to pick
which implementation to use,
try to put most likely options first: */
if (z < 0.5) {
/* We're going to calculate erf: */
if (z < 1e-10) {
if (z == 0) {
result = 0.0;
}
else {
static const double c = 0.003379167095512573896158903121545171688;
result = z * 1.125 + z * c;
}
}
else {
/* Maximum Deviation Found: 1.561e-17
Expected Error Term: 1.561e-17
Maximum Relative Change in Control Points: 1.155e-04
Max Error found at double precision = 2.961182e-17 */
static const double Y = 1.044948577880859375;
static const double P[] = {0.0834305892146531832907,
-0.338165134459360935041,
-0.0509990735146777432841,
-0.00772758345802133288487,
-0.000322780120964605683831};
static const double Q[] = {1.0,
0.455004033050794024546,
0.0875222600142252549554,
0.00858571925074406212772,
0.000370900071787748000569};
double zz = z * z;
double p = (((P[4] * zz + P[3]) * zz + P[2]) * zz + P[1]) * zz + P[0];
double q = (((Q[4] * zz + Q[3]) * zz + Q[2]) * zz + Q[1]) * zz + Q[0];
result = z * (Y + p / q);
}
}
else if (invert ? (z < 28.0) : (z < 5.8)) {
/* We'll be calculating erfc: */
invert = !invert;
if(z < 1.5) {
/* Maximum Deviation Found: 3.702e-17
Expected Error Term: 3.702e-17
Maximum Relative Change in Control Points: 2.845e-04
Max Error found at double precision = 4.841816e-17 */
static const double Y = 0.405935764312744140625;
static const double P[] = {-0.098090592216281240205,
0.178114665841120341155,
0.191003695796775433986,
0.0888900368967884466578,
0.0195049001251218801359,
0.00180424538297014223957};
static const double Q[] = {1.0,
1.84759070983002217845,
1.42628004845511324508,
0.578052804889902404909,
0.12385097467900864233,
0.0113385233577001411017,
0.337511472483094676155e-5};
double x = z - 0.5;
double p = ((((P[5] * x + P[4]) * x + P[3]) * x + P[2]) * x + P[1]) * x + P[0];
double q = ((((Q[5] * x + Q[4]) * x + Q[3]) * x + Q[2]) * x + Q[1]) * x + Q[0];
result = Y + p / q;
result *= expl(-z * z) / z;
}
else if(z < 2.5) {
/* Max Error found at double precision = 6.599585e-18
Maximum Deviation Found: 3.909e-18
Expected Error Term: 3.909e-18
Maximum Relative Change in Control Points: 9.886e-05 */
static const double Y = 0.50672817230224609375;
static const double P[] = {-0.0243500476207698441272,
0.0386540375035707201728,
0.04394818964209516296,
0.0175679436311802092299,
0.00323962406290842133584,
0.000235839115596880717416};
static const double Q[] = {1.0,
1.53991494948552447182,
0.982403709157920235114,
0.325732924782444448493,
0.0563921837420478160373,
0.00410369723978904575884};
double x = z - 1.5;
double p = ((((P[5] * x + P[4]) * x + P[3]) * x + P[2]) * x + P[1]) * x + P[0];
double q = ((((Q[5] * x + Q[4]) * x + Q[3]) * x + Q[2]) * x + Q[1]) * x + Q[0];
result = Y + p / q;
result *= expl(-z * z) / z;
}
else if(z < 4.5) {
/* Maximum Deviation Found: 1.512e-17
Expected Error Term: 1.512e-17
Maximum Relative Change in Control Points: 2.222e-04
Max Error found at double precision = 2.062515e-17 */
static const double Y = 0.5405750274658203125;
static const double P[] = {0.00295276716530971662634,
0.0137384425896355332126,
0.00840807615555585383007,
0.00212825620914618649141,
0.000250269961544794627958,
0.113212406648847561139e-4};
static const double Q[] = {1.0,
1.04217814166938418171,
0.442597659481563127003,
0.0958492726301061423444,
0.0105982906484876531489,
0.000479411269521714493907};
double x = z - 3.5;
double p = ((((P[5] * x + P[4]) * x + P[3]) * x + P[2]) * x + P[1]) * x + P[0];
double q = ((((Q[5] * x + Q[4]) * x + Q[3]) * x + Q[2]) * x + Q[1]) * x + Q[0];
result = Y + p / q;
result *= expl(-z * z) / z;
}
else {
/* Max Error found at double precision = 2.997958e-17
Maximum Deviation Found: 2.860e-17
Expected Error Term: 2.859e-17
Maximum Relative Change in Control Points: 1.357e-05 */
static const double Y = 0.5579090118408203125;
static const double P[] = {0.00628057170626964891937,
0.0175389834052493308818,
-0.212652252872804219852,
-0.687717681153649930619,
-2.5518551727311523996,
-3.22729451764143718517,
-2.8175401114513378771};
static const double Q[] = {1.0,
2.79257750980575282228,
11.0567237927800161565,
15.930646027911794143,
22.9367376522880577224,
13.5064170191802889145,
5.48409182238641741584};
double x = 1.0 / z;
double p = (((((P[6] * x + P[5]) * x + P[4]) * x + P[3]) * x + P[2]) * x + P[1]) * x + P[0];
double q = (((((Q[6] * x + Q[5]) * x + Q[4]) * x + Q[3]) * x + Q[2]) * x + Q[1]) * x + Q[0];
result = Y + p / q;
result *= expl(-z * z) / z;
}
}
else {
/* Any value of z larger than 28 will underflow to zero: */
result = 0;
invert = !invert;
}
if(invert) {
result = 1 - result;
}
return result;
}
double Erf(double z)
{
return ErfImpl(z, FALSE);
}
double ErfC(double z)
{
return ErfImpl(z, TRUE);
}
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