#include "Python.h"

#ifdef X87_DOUBLE_ROUNDING

/* On x86 platforms using an x87 FPU, this function is called from the

Py_FORCE_DOUBLE macro (defined in pymath.h) to force a floating-point

number out of an 80-bit x87 FPU register and into a 64-bit memory location,

thus rounding from extended precision to double precision. */

double _Py_force_double(double x)

{

volatile double y;

y = x;

return y;

}

#endif

#ifdef HAVE_GCC_ASM_FOR_X87

/* inline assembly for getting and setting the 387 FPU control word on

gcc/x86 */

unsigned short _Py_get_387controlword(void) {

unsigned short cw;

__asm__ __volatile__ ("fnstcw %0" : "=m" (cw));

return cw;

}

void _Py_set_387controlword(unsigned short cw) {

__asm__ __volatile__ ("fldcw %0" : : "m" (cw));

}

#endif

#ifndef HAVE_HYPOT

double hypot(double x, double y)

{

double yx;

x = fabs(x);

y = fabs(y);

if (x < y) {

double temp = x;

x = y;

y = temp;

}

if (x == 0.)

return 0.;

else {

yx = y/x;

return x*sqrt(1.+yx*yx);

}

}

#endif /* HAVE_HYPOT */

#ifndef HAVE_COPYSIGN

double

copysign(double x, double y)

{

/* use atan2 to distinguish -0. from 0. */

if (y > 0. || (y == 0. && atan2(y, -1.) > 0.)) {

return fabs(x);

} else {

return -fabs(x);

}

}

#endif /* HAVE_COPYSIGN */

#ifndef HAVE_ROUND

double

round(double x)

{

double absx, y;

absx = fabs(x);

y = floor(absx);

if (absx - y >= 0.5)

y += 1.0;

return copysign(y, x);

}

#endif /* HAVE_ROUND */

#ifndef HAVE_LOG1P

#include <float.h>

double

log1p(double x)

{

/* For x small, we use the following approach. Let y be the nearest

float to 1+x, then

1+x = y * (1 - (y-1-x)/y)

so log(1+x) = log(y) + log(1-(y-1-x)/y). Since (y-1-x)/y is tiny,

the second term is well approximated by (y-1-x)/y. If abs(x) >=

DBL_EPSILON/2 or the rounding-mode is some form of round-to-nearest

then y-1-x will be exactly representable, and is computed exactly

by (y-1)-x.

If abs(x) < DBL_EPSILON/2 and the rounding mode is not known to be

round-to-nearest then this method is slightly dangerous: 1+x could

be rounded up to 1+DBL_EPSILON instead of down to 1, and in that

case y-1-x will not be exactly representable any more and the

result can be off by many ulps. But this is easily fixed: for a

floating-point number |x| < DBL_EPSILON/2., the closest

floating-point number to log(1+x) is exactly x.

*/

double y;

if (fabs(x) < DBL_EPSILON/2.) {

return x;

} else if (-0.5 <= x && x <= 1.) {

/* WARNING: it's possible than an overeager compiler

will incorrectly optimize the following two lines

to the equivalent of "return log(1.+x)". If this

happens, then results from log1p will be inaccurate

for small x. */

y = 1.+x;

return log(y)-((y-1.)-x)/y;

} else {

/* NaNs and infinities should end up here */

return log(1.+x);

}

}

#endif /* HAVE_LOG1P */

/*

* ====================================================

* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

*

* Developed at SunPro, a Sun Microsystems, Inc. business.

* Permission to use, copy, modify, and distribute this

* software is freely granted, provided that this notice

* is preserved.

* ====================================================

*/

static const double ln2 = 6.93147180559945286227E-01;

static const double two_pow_m28 = 3.7252902984619141E-09; /* 2**-28 */

static const double two_pow_p28 = 268435456.0; /* 2**28 */

static const double zero = 0.0;

/* asinh(x)

* Method :

* Based on

* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]

* we have

* asinh(x) := x if 1+x*x=1,

* := sign(x)*(log(x)+ln2)) for large |x|, else

* := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else

* := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))

*/

#ifndef HAVE_ASINH

double

asinh(double x)

{

double w;

double absx = fabs(x);

if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) {

return x+x;

}

if (absx < two_pow_m28) { /* |x| < 2**-28 */

return x; /* return x inexact except 0 */

}

if (absx > two_pow_p28) { /* |x| > 2**28 */

w = log(absx)+ln2;

}

else if (absx > 2.0) { /* 2 < |x| < 2**28 */

w = log(2.0*absx + 1.0 / (sqrt(x*x + 1.0) + absx));

}

else { /* 2**-28 <= |x| < 2= */

double t = x*x;

w = log1p(absx + t / (1.0 + sqrt(1.0 + t)));

}

return copysign(w, x);

}

#endif /* HAVE_ASINH */

/* acosh(x)

* Method :

* Based on

* acosh(x) = log [ x + sqrt(x*x-1) ]

* we have

* acosh(x) := log(x)+ln2, if x is large; else

* acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else

* acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.

*

* Special cases:

* acosh(x) is NaN with signal if x<1.

* acosh(NaN) is NaN without signal.

*/

#ifndef HAVE_ACOSH

double

acosh(double x)

{

if (Py_IS_NAN(x)) {

return x+x;

}

if (x < 1.) { /* x < 1; return a signaling NaN */

errno = EDOM;

#ifdef Py_NAN

return Py_NAN;

#else

return (x-x)/(x-x);

#endif

}

else if (x >= two_pow_p28) { /* x > 2**28 */

if (Py_IS_INFINITY(x)) {

return x+x;

} else {

return log(x)+ln2; /* acosh(huge)=log(2x) */

}

}

else if (x == 1.) {

return 0.0; /* acosh(1) = 0 */

}

else if (x > 2.) { /* 2 < x < 2**28 */

double t = x*x;

return log(2.0*x - 1.0 / (x + sqrt(t - 1.0)));

}

else { /* 1 < x <= 2 */

double t = x - 1.0;

return log1p(t + sqrt(2.0*t + t*t));

}

}

#endif /* HAVE_ACOSH */

/* atanh(x)

* Method :

* 1.Reduced x to positive by atanh(-x) = -atanh(x)

* 2.For x>=0.5

* 1 2x x

* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)

* 2 1 - x 1 - x

*

* For x<0.5

* atanh(x) = 0.5*log1p(2x+2x*x/(1-x))

*

* Special cases:

* atanh(x) is NaN if |x| >= 1 with signal;

* atanh(NaN) is that NaN with no signal;

*

*/

#ifndef HAVE_ATANH

double

atanh(double x)

{

double absx;

double t;

if (Py_IS_NAN(x)) {

return x+x;

}

absx = fabs(x);

if (absx >= 1.) { /* |x| >= 1 */

errno = EDOM;

#ifdef Py_NAN

return Py_NAN;

#else

return x/zero;

#endif

}

if (absx < two_pow_m28) { /* |x| < 2**-28 */

return x;

}

if (absx < 0.5) { /* |x| < 0.5 */

t = absx+absx;

t = 0.5 * log1p(t + t*absx / (1.0 - absx));

}

else { /* 0.5 <= |x| <= 1.0 */

t = 0.5 * log1p((absx + absx) / (1.0 - absx));

}

return copysign(t, x);

}

#endif /* HAVE_ATANH */