276 lines
6.5 KiB
C++
276 lines
6.5 KiB
C++
/* Translated into C++ by SciPy developers in 2024.
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* Original header with Copyright information appears below.
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*/
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/* ndtr.c
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*
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* Normal distribution function
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, ndtr();
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*
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* y = ndtr( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns the area under the Gaussian probability density
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* function, integrated from minus infinity to x:
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*
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* x
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* -
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* 1 | | 2
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* ndtr(x) = --------- | exp( - t /2 ) dt
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* sqrt(2pi) | |
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* -
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* -inf.
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*
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* = ( 1 + erf(z) ) / 2
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* = erfc(z) / 2
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*
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* where z = x/sqrt(2). Computation is via the functions
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* erf and erfc.
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE -13,0 30000 3.4e-14 6.7e-15
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*
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*
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* ERROR MESSAGES:
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*
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* message condition value returned
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* erfc underflow x > 37.519379347 0.0
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*
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*/
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/* erf.c
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*
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* Error function
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, erf();
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*
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* y = erf( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* The integral is
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*
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* x
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* -
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* 2 | | 2
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* erf(x) = -------- | exp( - t ) dt.
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* sqrt(pi) | |
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* -
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* 0
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*
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* For 0 <= |x| < 1, erf(x) = x * P4(x**2)/Q5(x**2); otherwise
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* erf(x) = 1 - erfc(x).
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE 0,1 30000 3.7e-16 1.0e-16
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*
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*/
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/* erfc.c
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*
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* Complementary error function
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, erfc();
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*
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* y = erfc( x );
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*
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*
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*
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* DESCRIPTION:
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*
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*
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* 1 - erf(x) =
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*
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* inf.
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* -
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* 2 | | 2
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* erfc(x) = -------- | exp( - t ) dt
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* sqrt(pi) | |
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* -
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* x
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*
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*
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* For small x, erfc(x) = 1 - erf(x); otherwise rational
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* approximations are computed.
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE 0,26.6417 30000 5.7e-14 1.5e-14
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*/
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/*
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* Cephes Math Library Release 2.2: June, 1992
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* Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
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* Direct inquiries to 30 Frost Street, Cambridge, MA 02140
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*/
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#pragma once
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#include "../config.h"
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#include "const.h"
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#include "polevl.h"
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namespace xsf {
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namespace cephes {
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namespace detail {
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constexpr double ndtr_P[] = {2.46196981473530512524E-10, 5.64189564831068821977E-1, 7.46321056442269912687E0,
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4.86371970985681366614E1, 1.96520832956077098242E2, 5.26445194995477358631E2,
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9.34528527171957607540E2, 1.02755188689515710272E3, 5.57535335369399327526E2};
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constexpr double ndtr_Q[] = {
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/* 1.00000000000000000000E0, */
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1.32281951154744992508E1, 8.67072140885989742329E1, 3.54937778887819891062E2, 9.75708501743205489753E2,
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1.82390916687909736289E3, 2.24633760818710981792E3, 1.65666309194161350182E3, 5.57535340817727675546E2};
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constexpr double ndtr_R[] = {5.64189583547755073984E-1, 1.27536670759978104416E0, 5.01905042251180477414E0,
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6.16021097993053585195E0, 7.40974269950448939160E0, 2.97886665372100240670E0};
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constexpr double ndtr_S[] = {
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/* 1.00000000000000000000E0, */
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2.26052863220117276590E0, 9.39603524938001434673E0, 1.20489539808096656605E1,
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1.70814450747565897222E1, 9.60896809063285878198E0, 3.36907645100081516050E0};
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constexpr double ndtr_T[] = {9.60497373987051638749E0, 9.00260197203842689217E1, 2.23200534594684319226E3,
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7.00332514112805075473E3, 5.55923013010394962768E4};
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constexpr double ndtr_U[] = {
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/* 1.00000000000000000000E0, */
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3.35617141647503099647E1, 5.21357949780152679795E2, 4.59432382970980127987E3, 2.26290000613890934246E4,
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4.92673942608635921086E4};
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constexpr double ndtri_UTHRESH = 37.519379347;
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} // namespace detail
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XSF_HOST_DEVICE inline double erf(double x);
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XSF_HOST_DEVICE inline double erfc(double a) {
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double p, q, x, y, z;
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if (std::isnan(a)) {
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set_error("erfc", SF_ERROR_DOMAIN, NULL);
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return std::numeric_limits<double>::quiet_NaN();
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}
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if (a < 0.0) {
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x = -a;
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} else {
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x = a;
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}
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if (x < 1.0) {
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return 1.0 - erf(a);
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}
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z = -a * a;
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if (z < -detail::MAXLOG) {
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goto under;
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}
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z = std::exp(z);
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if (x < 8.0) {
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p = polevl(x, detail::ndtr_P, 8);
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q = p1evl(x, detail::ndtr_Q, 8);
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} else {
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p = polevl(x, detail::ndtr_R, 5);
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q = p1evl(x, detail::ndtr_S, 6);
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}
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y = (z * p) / q;
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if (a < 0) {
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y = 2.0 - y;
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}
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if (y != 0.0) {
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return y;
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}
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under:
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set_error("erfc", SF_ERROR_UNDERFLOW, NULL);
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if (a < 0) {
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return 2.0;
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} else {
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return 0.0;
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}
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}
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XSF_HOST_DEVICE inline double erf(double x) {
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double y, z;
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if (std::isnan(x)) {
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set_error("erf", SF_ERROR_DOMAIN, NULL);
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return std::numeric_limits<double>::quiet_NaN();
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}
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if (x < 0.0) {
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return -erf(-x);
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}
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if (std::abs(x) > 1.0) {
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return (1.0 - erfc(x));
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}
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z = x * x;
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y = x * polevl(z, detail::ndtr_T, 4) / p1evl(z, detail::ndtr_U, 5);
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return y;
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}
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XSF_HOST_DEVICE inline double ndtr(double a) {
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double x, y, z;
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if (std::isnan(a)) {
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set_error("ndtr", SF_ERROR_DOMAIN, NULL);
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return std::numeric_limits<double>::quiet_NaN();
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}
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x = a * M_SQRT1_2;
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z = std::abs(x);
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if (z < 1.0) {
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y = 0.5 + 0.5 * erf(x);
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} else {
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y = 0.5 * erfc(z);
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if (x > 0) {
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y = 1.0 - y;
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}
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}
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return y;
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}
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} // namespace cephes
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} // namespace xsf
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