mirror of https://github.com/python/cpython
248 lines
6.6 KiB
C
248 lines
6.6 KiB
C
#include "Python.h"
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#ifdef X87_DOUBLE_ROUNDING
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/* On x86 platforms using an x87 FPU, this function is called from the
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Py_FORCE_DOUBLE macro (defined in pymath.h) to force a floating-point
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number out of an 80-bit x87 FPU register and into a 64-bit memory location,
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thus rounding from extended precision to double precision. */
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double _Py_force_double(double x)
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{
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volatile double y;
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y = x;
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return y;
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}
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#endif
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#ifndef HAVE_HYPOT
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double hypot(double x, double y)
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{
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double yx;
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x = fabs(x);
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y = fabs(y);
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if (x < y) {
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double temp = x;
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x = y;
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y = temp;
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}
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if (x == 0.)
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return 0.;
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else {
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yx = y/x;
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return x*sqrt(1.+yx*yx);
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}
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}
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#endif /* HAVE_HYPOT */
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#ifndef HAVE_COPYSIGN
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double
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copysign(double x, double y)
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{
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/* use atan2 to distinguish -0. from 0. */
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if (y > 0. || (y == 0. && atan2(y, -1.) > 0.)) {
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return fabs(x);
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} else {
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return -fabs(x);
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}
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}
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#endif /* HAVE_COPYSIGN */
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#ifndef HAVE_LOG1P
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#include <float.h>
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double
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log1p(double x)
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{
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/* For x small, we use the following approach. Let y be the nearest
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float to 1+x, then
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1+x = y * (1 - (y-1-x)/y)
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so log(1+x) = log(y) + log(1-(y-1-x)/y). Since (y-1-x)/y is tiny,
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the second term is well approximated by (y-1-x)/y. If abs(x) >=
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DBL_EPSILON/2 or the rounding-mode is some form of round-to-nearest
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then y-1-x will be exactly representable, and is computed exactly
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by (y-1)-x.
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If abs(x) < DBL_EPSILON/2 and the rounding mode is not known to be
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round-to-nearest then this method is slightly dangerous: 1+x could
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be rounded up to 1+DBL_EPSILON instead of down to 1, and in that
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case y-1-x will not be exactly representable any more and the
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result can be off by many ulps. But this is easily fixed: for a
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floating-point number |x| < DBL_EPSILON/2., the closest
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floating-point number to log(1+x) is exactly x.
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*/
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double y;
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if (fabs(x) < DBL_EPSILON/2.) {
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return x;
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} else if (-0.5 <= x && x <= 1.) {
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/* WARNING: it's possible than an overeager compiler
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will incorrectly optimize the following two lines
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to the equivalent of "return log(1.+x)". If this
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happens, then results from log1p will be inaccurate
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for small x. */
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y = 1.+x;
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return log(y)-((y-1.)-x)/y;
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} else {
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/* NaNs and infinities should end up here */
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return log(1.+x);
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}
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}
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#endif /* HAVE_LOG1P */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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static const double ln2 = 6.93147180559945286227E-01;
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static const double two_pow_m28 = 3.7252902984619141E-09; /* 2**-28 */
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static const double two_pow_p28 = 268435456.0; /* 2**28 */
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static const double zero = 0.0;
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/* asinh(x)
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* Method :
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* Based on
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* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
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* we have
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* asinh(x) := x if 1+x*x=1,
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* := sign(x)*(log(x)+ln2)) for large |x|, else
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* := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
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* := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
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*/
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#ifndef HAVE_ASINH
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double
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asinh(double x)
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{
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double w;
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double absx = fabs(x);
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if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) {
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return x+x;
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}
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if (absx < two_pow_m28) { /* |x| < 2**-28 */
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return x; /* return x inexact except 0 */
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}
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if (absx > two_pow_p28) { /* |x| > 2**28 */
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w = log(absx)+ln2;
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}
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else if (absx > 2.0) { /* 2 < |x| < 2**28 */
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w = log(2.0*absx + 1.0 / (sqrt(x*x + 1.0) + absx));
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}
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else { /* 2**-28 <= |x| < 2= */
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double t = x*x;
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w = log1p(absx + t / (1.0 + sqrt(1.0 + t)));
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}
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return copysign(w, x);
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}
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#endif /* HAVE_ASINH */
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/* acosh(x)
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* Method :
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* Based on
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* acosh(x) = log [ x + sqrt(x*x-1) ]
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* we have
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* acosh(x) := log(x)+ln2, if x is large; else
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* acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
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* acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
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*
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* Special cases:
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* acosh(x) is NaN with signal if x<1.
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* acosh(NaN) is NaN without signal.
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*/
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#ifndef HAVE_ACOSH
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double
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acosh(double x)
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{
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if (Py_IS_NAN(x)) {
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return x+x;
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}
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if (x < 1.) { /* x < 1; return a signaling NaN */
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errno = EDOM;
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#ifdef Py_NAN
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return Py_NAN;
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#else
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return (x-x)/(x-x);
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#endif
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}
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else if (x >= two_pow_p28) { /* x > 2**28 */
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if (Py_IS_INFINITY(x)) {
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return x+x;
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} else {
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return log(x)+ln2; /* acosh(huge)=log(2x) */
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}
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}
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else if (x == 1.) {
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return 0.0; /* acosh(1) = 0 */
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}
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else if (x > 2.) { /* 2 < x < 2**28 */
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double t = x*x;
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return log(2.0*x - 1.0 / (x + sqrt(t - 1.0)));
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}
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else { /* 1 < x <= 2 */
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double t = x - 1.0;
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return log1p(t + sqrt(2.0*t + t*t));
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}
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}
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#endif /* HAVE_ACOSH */
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/* atanh(x)
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* Method :
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* 1.Reduced x to positive by atanh(-x) = -atanh(x)
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* 2.For x>=0.5
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* 1 2x x
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* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
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* 2 1 - x 1 - x
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*
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* For x<0.5
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* atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
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*
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* Special cases:
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* atanh(x) is NaN if |x| >= 1 with signal;
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* atanh(NaN) is that NaN with no signal;
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*
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*/
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#ifndef HAVE_ATANH
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double
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atanh(double x)
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{
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double absx;
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double t;
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if (Py_IS_NAN(x)) {
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return x+x;
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}
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absx = fabs(x);
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if (absx >= 1.) { /* |x| >= 1 */
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errno = EDOM;
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#ifdef Py_NAN
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return Py_NAN;
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#else
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return x/zero;
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#endif
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}
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if (absx < two_pow_m28) { /* |x| < 2**-28 */
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return x;
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}
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if (absx < 0.5) { /* |x| < 0.5 */
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t = absx+absx;
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t = 0.5 * log1p(t + t*absx / (1.0 - absx));
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}
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else { /* 0.5 <= |x| <= 1.0 */
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t = 0.5 * log1p((absx + absx) / (1.0 - absx));
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}
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return copysign(t, x);
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}
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#endif /* HAVE_ATANH */
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