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gcc/libgfortran/intrinsics/c99_functions.c

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/* Implementation of various C99 functions
Copyright (C) 2004, 2009 Free Software Foundation, Inc.
This file is part of the GNU Fortran 95 runtime library (libgfortran).
Libgfortran is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public
License as published by the Free Software Foundation; either
version 3 of the License, or (at your option) any later version.
Libgfortran is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.
You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
<http://www.gnu.org/licenses/>. */
#include "config.h"
#define C99_PROTOS_H WE_DONT_WANT_PROTOS_NOW
#include "libgfortran.h"
/* IRIX's <math.h> declares a non-C99 compliant implementation of cabs,
which takes two floating point arguments instead of a single complex.
If <complex.h> is missing this prevents building of c99_functions.c.
To work around this we redirect cabs{,f,l} calls to __gfc_cabs{,f,l}. */
#if defined(__sgi__) && !defined(HAVE_COMPLEX_H)
#undef HAVE_CABS
#undef HAVE_CABSF
#undef HAVE_CABSL
#define cabs __gfc_cabs
#define cabsf __gfc_cabsf
#define cabsl __gfc_cabsl
#endif
/* Tru64's <math.h> declares a non-C99 compliant implementation of cabs,
which takes two floating point arguments instead of a single complex.
To work around this we redirect cabs{,f,l} calls to __gfc_cabs{,f,l}. */
#ifdef __osf__
#undef HAVE_CABS
#undef HAVE_CABSF
#undef HAVE_CABSL
#define cabs __gfc_cabs
#define cabsf __gfc_cabsf
#define cabsl __gfc_cabsl
#endif
/* On a C99 system "I" (with I*I = -1) should be defined in complex.h;
if not, we define a fallback version here. */
#ifndef I
# if defined(_Imaginary_I)
# define I _Imaginary_I
# elif defined(_Complex_I)
# define I _Complex_I
# else
# define I (1.0fi)
# endif
#endif
/* Prototypes are included to silence -Wstrict-prototypes
-Wmissing-prototypes. */
/* Wrappers for systems without the various C99 single precision Bessel
functions. */
#if defined(HAVE_J0) && ! defined(HAVE_J0F)
#define HAVE_J0F 1
float j0f (float);
float
j0f (float x)
{
return (float) j0 ((double) x);
}
#endif
#if defined(HAVE_J1) && !defined(HAVE_J1F)
#define HAVE_J1F 1
float j1f (float);
float j1f (float x)
{
return (float) j1 ((double) x);
}
#endif
#if defined(HAVE_JN) && !defined(HAVE_JNF)
#define HAVE_JNF 1
float jnf (int, float);
float
jnf (int n, float x)
{
return (float) jn (n, (double) x);
}
#endif
#if defined(HAVE_Y0) && !defined(HAVE_Y0F)
#define HAVE_Y0F 1
float y0f (float);
float
y0f (float x)
{
return (float) y0 ((double) x);
}
#endif
#if defined(HAVE_Y1) && !defined(HAVE_Y1F)
#define HAVE_Y1F 1
float y1f (float);
float
y1f (float x)
{
return (float) y1 ((double) x);
}
#endif
#if defined(HAVE_YN) && !defined(HAVE_YNF)
#define HAVE_YNF 1
float ynf (int, float);
float
ynf (int n, float x)
{
return (float) yn (n, (double) x);
}
#endif
/* Wrappers for systems without the C99 erff() and erfcf() functions. */
#if defined(HAVE_ERF) && !defined(HAVE_ERFF)
#define HAVE_ERFF 1
float erff (float);
float
erff (float x)
{
return (float) erf ((double) x);
}
#endif
#if defined(HAVE_ERFC) && !defined(HAVE_ERFCF)
#define HAVE_ERFCF 1
float erfcf (float);
float
erfcf (float x)
{
return (float) erfc ((double) x);
}
#endif
#ifndef HAVE_ACOSF
#define HAVE_ACOSF 1
float acosf (float x);
float
acosf (float x)
{
return (float) acos (x);
}
#endif
#if HAVE_ACOSH && !HAVE_ACOSHF
float acoshf (float x);
float
acoshf (float x)
{
return (float) acosh ((double) x);
}
#endif
#ifndef HAVE_ASINF
#define HAVE_ASINF 1
float asinf (float x);
float
asinf (float x)
{
return (float) asin (x);
}
#endif
#if HAVE_ASINH && !HAVE_ASINHF
float asinhf (float x);
float
asinhf (float x)
{
return (float) asinh ((double) x);
}
#endif
#ifndef HAVE_ATAN2F
#define HAVE_ATAN2F 1
float atan2f (float y, float x);
float
atan2f (float y, float x)
{
return (float) atan2 (y, x);
}
#endif
#ifndef HAVE_ATANF
#define HAVE_ATANF 1
float atanf (float x);
float
atanf (float x)
{
return (float) atan (x);
}
#endif
#if HAVE_ATANH && !HAVE_ATANHF
float atanhf (float x);
float
atanhf (float x)
{
return (float) atanh ((double) x);
}
#endif
#ifndef HAVE_CEILF
#define HAVE_CEILF 1
float ceilf (float x);
float
ceilf (float x)
{
return (float) ceil (x);
}
#endif
#ifndef HAVE_COPYSIGNF
#define HAVE_COPYSIGNF 1
float copysignf (float x, float y);
float
copysignf (float x, float y)
{
return (float) copysign (x, y);
}
#endif
#ifndef HAVE_COSF
#define HAVE_COSF 1
float cosf (float x);
float
cosf (float x)
{
return (float) cos (x);
}
#endif
#ifndef HAVE_COSHF
#define HAVE_COSHF 1
float coshf (float x);
float
coshf (float x)
{
return (float) cosh (x);
}
#endif
#ifndef HAVE_EXPF
#define HAVE_EXPF 1
float expf (float x);
float
expf (float x)
{
return (float) exp (x);
}
#endif
#ifndef HAVE_FABSF
#define HAVE_FABSF 1
float fabsf (float x);
float
fabsf (float x)
{
return (float) fabs (x);
}
#endif
#ifndef HAVE_FLOORF
#define HAVE_FLOORF 1
float floorf (float x);
float
floorf (float x)
{
return (float) floor (x);
}
#endif
#ifndef HAVE_FMODF
#define HAVE_FMODF 1
float fmodf (float x, float y);
float
fmodf (float x, float y)
{
return (float) fmod (x, y);
}
#endif
#ifndef HAVE_FREXPF
#define HAVE_FREXPF 1
float frexpf (float x, int *exp);
float
frexpf (float x, int *exp)
{
return (float) frexp (x, exp);
}
#endif
#ifndef HAVE_HYPOTF
#define HAVE_HYPOTF 1
float hypotf (float x, float y);
float
hypotf (float x, float y)
{
return (float) hypot (x, y);
}
#endif
#ifndef HAVE_LOGF
#define HAVE_LOGF 1
float logf (float x);
float
logf (float x)
{
return (float) log (x);
}
#endif
#ifndef HAVE_LOG10F
#define HAVE_LOG10F 1
float log10f (float x);
float
log10f (float x)
{
return (float) log10 (x);
}
#endif
#ifndef HAVE_SCALBN
#define HAVE_SCALBN 1
double scalbn (double x, int y);
double
scalbn (double x, int y)
{
#if (FLT_RADIX == 2) && defined(HAVE_LDEXP)
return ldexp (x, y);
#else
return x * pow (FLT_RADIX, y);
#endif
}
#endif
#ifndef HAVE_SCALBNF
#define HAVE_SCALBNF 1
float scalbnf (float x, int y);
float
scalbnf (float x, int y)
{
return (float) scalbn (x, y);
}
#endif
#ifndef HAVE_SINF
#define HAVE_SINF 1
float sinf (float x);
float
sinf (float x)
{
return (float) sin (x);
}
#endif
#ifndef HAVE_SINHF
#define HAVE_SINHF 1
float sinhf (float x);
float
sinhf (float x)
{
return (float) sinh (x);
}
#endif
#ifndef HAVE_SQRTF
#define HAVE_SQRTF 1
float sqrtf (float x);
float
sqrtf (float x)
{
return (float) sqrt (x);
}
#endif
#ifndef HAVE_TANF
#define HAVE_TANF 1
float tanf (float x);
float
tanf (float x)
{
return (float) tan (x);
}
#endif
#ifndef HAVE_TANHF
#define HAVE_TANHF 1
float tanhf (float x);
float
tanhf (float x)
{
return (float) tanh (x);
}
#endif
#ifndef HAVE_TRUNC
#define HAVE_TRUNC 1
double trunc (double x);
double
trunc (double x)
{
if (!isfinite (x))
return x;
if (x < 0.0)
return - floor (-x);
else
return floor (x);
}
#endif
#ifndef HAVE_TRUNCF
#define HAVE_TRUNCF 1
float truncf (float x);
float
truncf (float x)
{
return (float) trunc (x);
}
#endif
#ifndef HAVE_NEXTAFTERF
#define HAVE_NEXTAFTERF 1
/* This is a portable implementation of nextafterf that is intended to be
independent of the floating point format or its in memory representation.
This implementation works correctly with denormalized values. */
float nextafterf (float x, float y);
float
nextafterf (float x, float y)
{
/* This variable is marked volatile to avoid excess precision problems
on some platforms, including IA-32. */
volatile float delta;
float absx, denorm_min;
if (isnan (x) || isnan (y))
return x + y;
if (x == y)
return x;
if (!isfinite (x))
return x > 0 ? __FLT_MAX__ : - __FLT_MAX__;
/* absx = fabsf (x); */
absx = (x < 0.0) ? -x : x;
/* __FLT_DENORM_MIN__ is non-zero iff the target supports denormals. */
if (__FLT_DENORM_MIN__ == 0.0f)
denorm_min = __FLT_MIN__;
else
denorm_min = __FLT_DENORM_MIN__;
if (absx < __FLT_MIN__)
delta = denorm_min;
else
{
float frac;
int exp;
/* Discard the fraction from x. */
frac = frexpf (absx, &exp);
delta = scalbnf (0.5f, exp);
/* Scale x by the epsilon of the representation. By rights we should
have been able to combine this with scalbnf, but some targets don't
get that correct with denormals. */
delta *= __FLT_EPSILON__;
/* If we're going to be reducing the absolute value of X, and doing so
would reduce the exponent of X, then the delta to be applied is
one exponent smaller. */
if (frac == 0.5f && (y < x) == (x > 0))
delta *= 0.5f;
/* If that underflows to zero, then we're back to the minimum. */
if (delta == 0.0f)
delta = denorm_min;
}
if (y < x)
delta = -delta;
return x + delta;
}
#endif
#if !defined(HAVE_POWF) || defined(HAVE_BROKEN_POWF)
#ifndef HAVE_POWF
#define HAVE_POWF 1
#endif
float powf (float x, float y);
float
powf (float x, float y)
{
return (float) pow (x, y);
}
#endif
/* Note that if fpclassify is not defined, then NaN is not handled */
/* Algorithm by Steven G. Kargl. */
#if !defined(HAVE_ROUNDL)
#define HAVE_ROUNDL 1
long double roundl (long double x);
#if defined(HAVE_CEILL)
/* Round to nearest integral value. If the argument is halfway between two
integral values then round away from zero. */
long double
roundl (long double x)
{
long double t;
if (!isfinite (x))
return (x);
if (x >= 0.0)
{
t = ceill (x);
if (t - x > 0.5)
t -= 1.0;
return (t);
}
else
{
t = ceill (-x);
if (t + x > 0.5)
t -= 1.0;
return (-t);
}
}
#else
/* Poor version of roundl for system that don't have ceill. */
long double
roundl (long double x)
{
if (x > DBL_MAX || x < -DBL_MAX)
{
#ifdef HAVE_NEXTAFTERL
static long double prechalf = nexafterl (0.5L, LDBL_MAX);
#else
static long double prechalf = 0.5L;
#endif
return (GFC_INTEGER_LARGEST) (x + (x > 0 ? prechalf : -prechalf));
}
else
/* Use round(). */
return round ((double) x);
}
#endif
#endif
#ifndef HAVE_ROUND
#define HAVE_ROUND 1
/* Round to nearest integral value. If the argument is halfway between two
integral values then round away from zero. */
double round (double x);
double
round (double x)
{
double t;
if (!isfinite (x))
return (x);
if (x >= 0.0)
{
t = floor (x);
if (t - x <= -0.5)
t += 1.0;
return (t);
}
else
{
t = floor (-x);
if (t + x <= -0.5)
t += 1.0;
return (-t);
}
}
#endif
#ifndef HAVE_ROUNDF
#define HAVE_ROUNDF 1
/* Round to nearest integral value. If the argument is halfway between two
integral values then round away from zero. */
float roundf (float x);
float
roundf (float x)
{
float t;
if (!isfinite (x))
return (x);
if (x >= 0.0)
{
t = floorf (x);
if (t - x <= -0.5)
t += 1.0;
return (t);
}
else
{
t = floorf (-x);
if (t + x <= -0.5)
t += 1.0;
return (-t);
}
}
#endif
/* lround{f,,l} and llround{f,,l} functions. */
#if !defined(HAVE_LROUNDF) && defined(HAVE_ROUNDF)
#define HAVE_LROUNDF 1
long int lroundf (float x);
long int
lroundf (float x)
{
return (long int) roundf (x);
}
#endif
#if !defined(HAVE_LROUND) && defined(HAVE_ROUND)
#define HAVE_LROUND 1
long int lround (double x);
long int
lround (double x)
{
return (long int) round (x);
}
#endif
#if !defined(HAVE_LROUNDL) && defined(HAVE_ROUNDL)
#define HAVE_LROUNDL 1
long int lroundl (long double x);
long int
lroundl (long double x)
{
return (long long int) roundl (x);
}
#endif
#if !defined(HAVE_LLROUNDF) && defined(HAVE_ROUNDF)
#define HAVE_LLROUNDF 1
long long int llroundf (float x);
long long int
llroundf (float x)
{
return (long long int) roundf (x);
}
#endif
#if !defined(HAVE_LLROUND) && defined(HAVE_ROUND)
#define HAVE_LLROUND 1
long long int llround (double x);
long long int
llround (double x)
{
return (long long int) round (x);
}
#endif
#if !defined(HAVE_LLROUNDL) && defined(HAVE_ROUNDL)
#define HAVE_LLROUNDL 1
long long int llroundl (long double x);
long long int
llroundl (long double x)
{
return (long long int) roundl (x);
}
#endif
#ifndef HAVE_LOG10L
#define HAVE_LOG10L 1
/* log10 function for long double variables. The version provided here
reduces the argument until it fits into a double, then use log10. */
long double log10l (long double x);
long double
log10l (long double x)
{
#if LDBL_MAX_EXP > DBL_MAX_EXP
if (x > DBL_MAX)
{
double val;
int p2_result = 0;
if (x > 0x1p16383L) { p2_result += 16383; x /= 0x1p16383L; }
if (x > 0x1p8191L) { p2_result += 8191; x /= 0x1p8191L; }
if (x > 0x1p4095L) { p2_result += 4095; x /= 0x1p4095L; }
if (x > 0x1p2047L) { p2_result += 2047; x /= 0x1p2047L; }
if (x > 0x1p1023L) { p2_result += 1023; x /= 0x1p1023L; }
val = log10 ((double) x);
return (val + p2_result * .30102999566398119521373889472449302L);
}
#endif
#if LDBL_MIN_EXP < DBL_MIN_EXP
if (x < DBL_MIN)
{
double val;
int p2_result = 0;
if (x < 0x1p-16380L) { p2_result += 16380; x /= 0x1p-16380L; }
if (x < 0x1p-8189L) { p2_result += 8189; x /= 0x1p-8189L; }
if (x < 0x1p-4093L) { p2_result += 4093; x /= 0x1p-4093L; }
if (x < 0x1p-2045L) { p2_result += 2045; x /= 0x1p-2045L; }
if (x < 0x1p-1021L) { p2_result += 1021; x /= 0x1p-1021L; }
val = fabs (log10 ((double) x));
return (- val - p2_result * .30102999566398119521373889472449302L);
}
#endif
return log10 (x);
}
#endif
#ifndef HAVE_FLOORL
#define HAVE_FLOORL 1
long double floorl (long double x);
long double
floorl (long double x)
{
/* Zero, possibly signed. */
if (x == 0)
return x;
/* Large magnitude. */
if (x > DBL_MAX || x < (-DBL_MAX))
return x;
/* Small positive values. */
if (x >= 0 && x < DBL_MIN)
return 0;
/* Small negative values. */
if (x < 0 && x > (-DBL_MIN))
return -1;
return floor (x);
}
#endif
#ifndef HAVE_FMODL
#define HAVE_FMODL 1
long double fmodl (long double x, long double y);
long double
fmodl (long double x, long double y)
{
if (y == 0.0L)
return 0.0L;
/* Need to check that the result has the same sign as x and magnitude
less than the magnitude of y. */
return x - floorl (x / y) * y;
}
#endif
#if !defined(HAVE_CABSF)
#define HAVE_CABSF 1
float cabsf (float complex z);
float
cabsf (float complex z)
{
return hypotf (REALPART (z), IMAGPART (z));
}
#endif
#if !defined(HAVE_CABS)
#define HAVE_CABS 1
double cabs (double complex z);
double
cabs (double complex z)
{
return hypot (REALPART (z), IMAGPART (z));
}
#endif
#if !defined(HAVE_CABSL) && defined(HAVE_HYPOTL)
#define HAVE_CABSL 1
long double cabsl (long double complex z);
long double
cabsl (long double complex z)
{
return hypotl (REALPART (z), IMAGPART (z));
}
#endif
#if !defined(HAVE_CARGF)
#define HAVE_CARGF 1
float cargf (float complex z);
float
cargf (float complex z)
{
return atan2f (IMAGPART (z), REALPART (z));
}
#endif
#if !defined(HAVE_CARG)
#define HAVE_CARG 1
double carg (double complex z);
double
carg (double complex z)
{
return atan2 (IMAGPART (z), REALPART (z));
}
#endif
#if !defined(HAVE_CARGL) && defined(HAVE_ATAN2L)
#define HAVE_CARGL 1
long double cargl (long double complex z);
long double
cargl (long double complex z)
{
return atan2l (IMAGPART (z), REALPART (z));
}
#endif
/* exp(z) = exp(a)*(cos(b) + i sin(b)) */
#if !defined(HAVE_CEXPF)
#define HAVE_CEXPF 1
float complex cexpf (float complex z);
float complex
cexpf (float complex z)
{
float a, b;
float complex v;
a = REALPART (z);
b = IMAGPART (z);
COMPLEX_ASSIGN (v, cosf (b), sinf (b));
return expf (a) * v;
}
#endif
#if !defined(HAVE_CEXP)
#define HAVE_CEXP 1
double complex cexp (double complex z);
double complex
cexp (double complex z)
{
double a, b;
double complex v;
a = REALPART (z);
b = IMAGPART (z);
COMPLEX_ASSIGN (v, cos (b), sin (b));
return exp (a) * v;
}
#endif
#if !defined(HAVE_CEXPL) && defined(HAVE_COSL) && defined(HAVE_SINL) && defined(EXPL)
#define HAVE_CEXPL 1
long double complex cexpl (long double complex z);
long double complex
cexpl (long double complex z)
{
long double a, b;
long double complex v;
a = REALPART (z);
b = IMAGPART (z);
COMPLEX_ASSIGN (v, cosl (b), sinl (b));
return expl (a) * v;
}
#endif
/* log(z) = log (cabs(z)) + i*carg(z) */
#if !defined(HAVE_CLOGF)
#define HAVE_CLOGF 1
float complex clogf (float complex z);
float complex
clogf (float complex z)
{
float complex v;
COMPLEX_ASSIGN (v, logf (cabsf (z)), cargf (z));
return v;
}
#endif
#if !defined(HAVE_CLOG)
#define HAVE_CLOG 1
double complex clog (double complex z);
double complex
clog (double complex z)
{
double complex v;
COMPLEX_ASSIGN (v, log (cabs (z)), carg (z));
return v;
}
#endif
#if !defined(HAVE_CLOGL) && defined(HAVE_LOGL) && defined(HAVE_CABSL) && defined(HAVE_CARGL)
#define HAVE_CLOGL 1
long double complex clogl (long double complex z);
long double complex
clogl (long double complex z)
{
long double complex v;
COMPLEX_ASSIGN (v, logl (cabsl (z)), cargl (z));
return v;
}
#endif
/* log10(z) = log10 (cabs(z)) + i*carg(z) */
#if !defined(HAVE_CLOG10F)
#define HAVE_CLOG10F 1
float complex clog10f (float complex z);
float complex
clog10f (float complex z)
{
float complex v;
COMPLEX_ASSIGN (v, log10f (cabsf (z)), cargf (z));
return v;
}
#endif
#if !defined(HAVE_CLOG10)
#define HAVE_CLOG10 1
double complex clog10 (double complex z);
double complex
clog10 (double complex z)
{
double complex v;
COMPLEX_ASSIGN (v, log10 (cabs (z)), carg (z));
return v;
}
#endif
#if !defined(HAVE_CLOG10L) && defined(HAVE_LOG10L) && defined(HAVE_CABSL) && defined(HAVE_CARGL)
#define HAVE_CLOG10L 1
long double complex clog10l (long double complex z);
long double complex
clog10l (long double complex z)
{
long double complex v;
COMPLEX_ASSIGN (v, log10l (cabsl (z)), cargl (z));
return v;
}
#endif
/* pow(base, power) = cexp (power * clog (base)) */
#if !defined(HAVE_CPOWF)
#define HAVE_CPOWF 1
float complex cpowf (float complex base, float complex power);
float complex
cpowf (float complex base, float complex power)
{
return cexpf (power * clogf (base));
}
#endif
#if !defined(HAVE_CPOW)
#define HAVE_CPOW 1
double complex cpow (double complex base, double complex power);
double complex
cpow (double complex base, double complex power)
{
return cexp (power * clog (base));
}
#endif
#if !defined(HAVE_CPOWL) && defined(HAVE_CEXPL) && defined(HAVE_CLOGL)
#define HAVE_CPOWL 1
long double complex cpowl (long double complex base, long double complex power);
long double complex
cpowl (long double complex base, long double complex power)
{
return cexpl (power * clogl (base));
}
#endif
/* sqrt(z). Algorithm pulled from glibc. */
#if !defined(HAVE_CSQRTF)
#define HAVE_CSQRTF 1
float complex csqrtf (float complex z);
float complex
csqrtf (float complex z)
{
float re, im;
float complex v;
re = REALPART (z);
im = IMAGPART (z);
if (im == 0)
{
if (re < 0)
{
COMPLEX_ASSIGN (v, 0, copysignf (sqrtf (-re), im));
}
else
{
COMPLEX_ASSIGN (v, fabsf (sqrtf (re)), copysignf (0, im));
}
}
else if (re == 0)
{
float r;
r = sqrtf (0.5 * fabsf (im));
COMPLEX_ASSIGN (v, r, copysignf (r, im));
}
else
{
float d, r, s;
d = hypotf (re, im);
/* Use the identity 2 Re res Im res = Im x
to avoid cancellation error in d +/- Re x. */
if (re > 0)
{
r = sqrtf (0.5 * d + 0.5 * re);
s = (0.5 * im) / r;
}
else
{
s = sqrtf (0.5 * d - 0.5 * re);
r = fabsf ((0.5 * im) / s);
}
COMPLEX_ASSIGN (v, r, copysignf (s, im));
}
return v;
}
#endif
#if !defined(HAVE_CSQRT)
#define HAVE_CSQRT 1
double complex csqrt (double complex z);
double complex
csqrt (double complex z)
{
double re, im;
double complex v;
re = REALPART (z);
im = IMAGPART (z);
if (im == 0)
{
if (re < 0)
{
COMPLEX_ASSIGN (v, 0, copysign (sqrt (-re), im));
}
else
{
COMPLEX_ASSIGN (v, fabs (sqrt (re)), copysign (0, im));
}
}
else if (re == 0)
{
double r;
r = sqrt (0.5 * fabs (im));
COMPLEX_ASSIGN (v, r, copysign (r, im));
}
else
{
double d, r, s;
d = hypot (re, im);
/* Use the identity 2 Re res Im res = Im x
to avoid cancellation error in d +/- Re x. */
if (re > 0)
{
r = sqrt (0.5 * d + 0.5 * re);
s = (0.5 * im) / r;
}
else
{
s = sqrt (0.5 * d - 0.5 * re);
r = fabs ((0.5 * im) / s);
}
COMPLEX_ASSIGN (v, r, copysign (s, im));
}
return v;
}
#endif
#if !defined(HAVE_CSQRTL) && defined(HAVE_COPYSIGNL) && defined(HAVE_SQRTL) && defined(HAVE_FABSL) && defined(HAVE_HYPOTL)
#define HAVE_CSQRTL 1
long double complex csqrtl (long double complex z);
long double complex
csqrtl (long double complex z)
{
long double re, im;
long double complex v;
re = REALPART (z);
im = IMAGPART (z);
if (im == 0)
{
if (re < 0)
{
COMPLEX_ASSIGN (v, 0, copysignl (sqrtl (-re), im));
}
else
{
COMPLEX_ASSIGN (v, fabsl (sqrtl (re)), copysignl (0, im));
}
}
else if (re == 0)
{
long double r;
r = sqrtl (0.5 * fabsl (im));
COMPLEX_ASSIGN (v, copysignl (r, im), r);
}
else
{
long double d, r, s;
d = hypotl (re, im);
/* Use the identity 2 Re res Im res = Im x
to avoid cancellation error in d +/- Re x. */
if (re > 0)
{
r = sqrtl (0.5 * d + 0.5 * re);
s = (0.5 * im) / r;
}
else
{
s = sqrtl (0.5 * d - 0.5 * re);
r = fabsl ((0.5 * im) / s);
}
COMPLEX_ASSIGN (v, r, copysignl (s, im));
}
return v;
}
#endif
/* sinh(a + i b) = sinh(a) cos(b) + i cosh(a) sin(b) */
#if !defined(HAVE_CSINHF)
#define HAVE_CSINHF 1
float complex csinhf (float complex a);
float complex
csinhf (float complex a)
{
float r, i;
float complex v;
r = REALPART (a);
i = IMAGPART (a);
COMPLEX_ASSIGN (v, sinhf (r) * cosf (i), coshf (r) * sinf (i));
return v;
}
#endif
#if !defined(HAVE_CSINH)
#define HAVE_CSINH 1
double complex csinh (double complex a);
double complex
csinh (double complex a)
{
double r, i;
double complex v;
r = REALPART (a);
i = IMAGPART (a);
COMPLEX_ASSIGN (v, sinh (r) * cos (i), cosh (r) * sin (i));
return v;
}
#endif
#if !defined(HAVE_CSINHL) && defined(HAVE_COSL) && defined(HAVE_COSHL) && defined(HAVE_SINL) && defined(HAVE_SINHL)
#define HAVE_CSINHL 1
long double complex csinhl (long double complex a);
long double complex
csinhl (long double complex a)
{
long double r, i;
long double complex v;
r = REALPART (a);
i = IMAGPART (a);
COMPLEX_ASSIGN (v, sinhl (r) * cosl (i), coshl (r) * sinl (i));
return v;
}
#endif
/* cosh(a + i b) = cosh(a) cos(b) + i sinh(a) sin(b) */
#if !defined(HAVE_CCOSHF)
#define HAVE_CCOSHF 1
float complex ccoshf (float complex a);
float complex
ccoshf (float complex a)
{
float r, i;
float complex v;
r = REALPART (a);
i = IMAGPART (a);
COMPLEX_ASSIGN (v, coshf (r) * cosf (i), sinhf (r) * sinf (i));
return v;
}
#endif
#if !defined(HAVE_CCOSH)
#define HAVE_CCOSH 1
double complex ccosh (double complex a);
double complex
ccosh (double complex a)
{
double r, i;
double complex v;
r = REALPART (a);
i = IMAGPART (a);
COMPLEX_ASSIGN (v, cosh (r) * cos (i), sinh (r) * sin (i));
return v;
}
#endif
#if !defined(HAVE_CCOSHL) && defined(HAVE_COSL) && defined(HAVE_COSHL) && defined(HAVE_SINL) && defined(HAVE_SINHL)
#define HAVE_CCOSHL 1
long double complex ccoshl (long double complex a);
long double complex
ccoshl (long double complex a)
{
long double r, i;
long double complex v;
r = REALPART (a);
i = IMAGPART (a);
COMPLEX_ASSIGN (v, coshl (r) * cosl (i), sinhl (r) * sinl (i));
return v;
}
#endif
/* tanh(a + i b) = (tanh(a) + i tan(b)) / (1 + i tanh(a) tan(b)) */
#if !defined(HAVE_CTANHF)
#define HAVE_CTANHF 1
float complex ctanhf (float complex a);
float complex
ctanhf (float complex a)
{
float rt, it;
float complex n, d;
rt = tanhf (REALPART (a));
it = tanf (IMAGPART (a));
COMPLEX_ASSIGN (n, rt, it);
COMPLEX_ASSIGN (d, 1, rt * it);
return n / d;
}
#endif
#if !defined(HAVE_CTANH)
#define HAVE_CTANH 1
double complex ctanh (double complex a);
double complex
ctanh (double complex a)
{
double rt, it;
double complex n, d;
rt = tanh (REALPART (a));
it = tan (IMAGPART (a));
COMPLEX_ASSIGN (n, rt, it);
COMPLEX_ASSIGN (d, 1, rt * it);
return n / d;
}
#endif
#if !defined(HAVE_CTANHL) && defined(HAVE_TANL) && defined(HAVE_TANHL)
#define HAVE_CTANHL 1
long double complex ctanhl (long double complex a);
long double complex
ctanhl (long double complex a)
{
long double rt, it;
long double complex n, d;
rt = tanhl (REALPART (a));
it = tanl (IMAGPART (a));
COMPLEX_ASSIGN (n, rt, it);
COMPLEX_ASSIGN (d, 1, rt * it);
return n / d;
}
#endif
/* sin(a + i b) = sin(a) cosh(b) + i cos(a) sinh(b) */
#if !defined(HAVE_CSINF)
#define HAVE_CSINF 1
float complex csinf (float complex a);
float complex
csinf (float complex a)
{
float r, i;
float complex v;
r = REALPART (a);
i = IMAGPART (a);
COMPLEX_ASSIGN (v, sinf (r) * coshf (i), cosf (r) * sinhf (i));
return v;
}
#endif
#if !defined(HAVE_CSIN)
#define HAVE_CSIN 1
double complex csin (double complex a);
double complex
csin (double complex a)
{
double r, i;
double complex v;
r = REALPART (a);
i = IMAGPART (a);
COMPLEX_ASSIGN (v, sin (r) * cosh (i), cos (r) * sinh (i));
return v;
}
#endif
#if !defined(HAVE_CSINL) && defined(HAVE_COSL) && defined(HAVE_COSHL) && defined(HAVE_SINL) && defined(HAVE_SINHL)
#define HAVE_CSINL 1
long double complex csinl (long double complex a);
long double complex
csinl (long double complex a)
{
long double r, i;
long double complex v;
r = REALPART (a);
i = IMAGPART (a);
COMPLEX_ASSIGN (v, sinl (r) * coshl (i), cosl (r) * sinhl (i));
return v;
}
#endif
/* cos(a + i b) = cos(a) cosh(b) - i sin(a) sinh(b) */
#if !defined(HAVE_CCOSF)
#define HAVE_CCOSF 1
float complex ccosf (float complex a);
float complex
ccosf (float complex a)
{
float r, i;
float complex v;
r = REALPART (a);
i = IMAGPART (a);
COMPLEX_ASSIGN (v, cosf (r) * coshf (i), - (sinf (r) * sinhf (i)));
return v;
}
#endif
#if !defined(HAVE_CCOS)
#define HAVE_CCOS 1
double complex ccos (double complex a);
double complex
ccos (double complex a)
{
double r, i;
double complex v;
r = REALPART (a);
i = IMAGPART (a);
COMPLEX_ASSIGN (v, cos (r) * cosh (i), - (sin (r) * sinh (i)));
return v;
}
#endif
#if !defined(HAVE_CCOSL) && defined(HAVE_COSL) && defined(HAVE_COSHL) && defined(HAVE_SINL) && defined(HAVE_SINHL)
#define HAVE_CCOSL 1
long double complex ccosl (long double complex a);
long double complex
ccosl (long double complex a)
{
long double r, i;
long double complex v;
r = REALPART (a);
i = IMAGPART (a);
COMPLEX_ASSIGN (v, cosl (r) * coshl (i), - (sinl (r) * sinhl (i)));
return v;
}
#endif
/* tan(a + i b) = (tan(a) + i tanh(b)) / (1 - i tan(a) tanh(b)) */
#if !defined(HAVE_CTANF)
#define HAVE_CTANF 1
float complex ctanf (float complex a);
float complex
ctanf (float complex a)
{
float rt, it;
float complex n, d;
rt = tanf (REALPART (a));
it = tanhf (IMAGPART (a));
COMPLEX_ASSIGN (n, rt, it);
COMPLEX_ASSIGN (d, 1, - (rt * it));
return n / d;
}
#endif
#if !defined(HAVE_CTAN)
#define HAVE_CTAN 1
double complex ctan (double complex a);
double complex
ctan (double complex a)
{
double rt, it;
double complex n, d;
rt = tan (REALPART (a));
it = tanh (IMAGPART (a));
COMPLEX_ASSIGN (n, rt, it);
COMPLEX_ASSIGN (d, 1, - (rt * it));
return n / d;
}
#endif
#if !defined(HAVE_CTANL) && defined(HAVE_TANL) && defined(HAVE_TANHL)
#define HAVE_CTANL 1
long double complex ctanl (long double complex a);
long double complex
ctanl (long double complex a)
{
long double rt, it;
long double complex n, d;
rt = tanl (REALPART (a));
it = tanhl (IMAGPART (a));
COMPLEX_ASSIGN (n, rt, it);
COMPLEX_ASSIGN (d, 1, - (rt * it));
return n / d;
}
#endif
/* Complex ASIN. Returns wrongly NaN for infinite arguments.
Algorithm taken from Abramowitz & Stegun. */
#if !defined(HAVE_CASINF) && defined(HAVE_CLOGF) && defined(HAVE_CSQRTF)
#define HAVE_CASINF 1
complex float casinf (complex float z);
complex float
casinf (complex float z)
{
return -I*clogf (I*z + csqrtf (1.0f-z*z));
}
#endif
#if !defined(HAVE_CASIN) && defined(HAVE_CLOG) && defined(HAVE_CSQRT)
#define HAVE_CASIN 1
complex double casin (complex double z);
complex double
casin (complex double z)
{
return -I*clog (I*z + csqrt (1.0-z*z));
}
#endif
#if !defined(HAVE_CASINL) && defined(HAVE_CLOGL) && defined(HAVE_CSQRTL)
#define HAVE_CASINL 1
complex long double casinl (complex long double z);
complex long double
casinl (complex long double z)
{
return -I*clogl (I*z + csqrtl (1.0L-z*z));
}
#endif
/* Complex ACOS. Returns wrongly NaN for infinite arguments.
Algorithm taken from Abramowitz & Stegun. */
#if !defined(HAVE_CACOSF) && defined(HAVE_CLOGF) && defined(HAVE_CSQRTF)
#define HAVE_CACOSF 1
complex float cacosf (complex float z);
complex float
cacosf (complex float z)
{
return -I*clogf (z + I*csqrtf (1.0f-z*z));
}
#endif
#if !defined(HAVE_CACOS) && defined(HAVE_CLOG) && defined(HAVE_CSQRT)
#define HAVE_CACOS 1
complex double cacos (complex double z);
complex double
cacos (complex double z)
{
return -I*clog (z + I*csqrt (1.0-z*z));
}
#endif
#if !defined(HAVE_CACOSL) && defined(HAVE_CLOGL) && defined(HAVE_CSQRTL)
#define HAVE_CACOSL 1
complex long double cacosl (complex long double z);
complex long double
cacosl (complex long double z)
{
return -I*clogl (z + I*csqrtl (1.0L-z*z));
}
#endif
/* Complex ATAN. Returns wrongly NaN for infinite arguments.
Algorithm taken from Abramowitz & Stegun. */
#if !defined(HAVE_CATANF) && defined(HAVE_CLOGF)
#define HAVE_CACOSF 1
complex float catanf (complex float z);
complex float
catanf (complex float z)
{
return I*clogf ((I+z)/(I-z))/2.0f;
}
#endif
#if !defined(HAVE_CATAN) && defined(HAVE_CLOG)
#define HAVE_CACOS 1
complex double catan (complex double z);
complex double
catan (complex double z)
{
return I*clog ((I+z)/(I-z))/2.0;
}
#endif
#if !defined(HAVE_CATANL) && defined(HAVE_CLOGL)
#define HAVE_CACOSL 1
complex long double catanl (complex long double z);
complex long double
catanl (complex long double z)
{
return I*clogl ((I+z)/(I-z))/2.0L;
}
#endif
/* Complex ASINH. Returns wrongly NaN for infinite arguments.
Algorithm taken from Abramowitz & Stegun. */
#if !defined(HAVE_CASINHF) && defined(HAVE_CLOGF) && defined(HAVE_CSQRTF)
#define HAVE_CASINHF 1
complex float casinhf (complex float z);
complex float
casinhf (complex float z)
{
return clogf (z + csqrtf (z*z+1.0f));
}
#endif
#if !defined(HAVE_CASINH) && defined(HAVE_CLOG) && defined(HAVE_CSQRT)
#define HAVE_CASINH 1
complex double casinh (complex double z);
complex double
casinh (complex double z)
{
return clog (z + csqrt (z*z+1.0));
}
#endif
#if !defined(HAVE_CASINHL) && defined(HAVE_CLOGL) && defined(HAVE_CSQRTL)
#define HAVE_CASINHL 1
complex long double casinhl (complex long double z);
complex long double
casinhl (complex long double z)
{
return clogl (z + csqrtl (z*z+1.0L));
}
#endif
/* Complex ACOSH. Returns wrongly NaN for infinite arguments.
Algorithm taken from Abramowitz & Stegun. */
#if !defined(HAVE_CACOSHF) && defined(HAVE_CLOGF) && defined(HAVE_CSQRTF)
#define HAVE_CACOSHF 1
complex float cacoshf (complex float z);
complex float
cacoshf (complex float z)
{
return clogf (z + csqrtf (z-1.0f) * csqrtf (z+1.0f));
}
#endif
#if !defined(HAVE_CACOSH) && defined(HAVE_CLOG) && defined(HAVE_CSQRT)
#define HAVE_CACOSH 1
complex double cacosh (complex double z);
complex double
cacosh (complex double z)
{
return clog (z + csqrt (z-1.0) * csqrt (z+1.0));
}
#endif
#if !defined(HAVE_CACOSHL) && defined(HAVE_CLOGL) && defined(HAVE_CSQRTL)
#define HAVE_CACOSHL 1
complex long double cacoshl (complex long double z);
complex long double
cacoshl (complex long double z)
{
return clogl (z + csqrtl (z-1.0L) * csqrtl (z+1.0L));
}
#endif
/* Complex ATANH. Returns wrongly NaN for infinite arguments.
Algorithm taken from Abramowitz & Stegun. */
#if !defined(HAVE_CATANHF) && defined(HAVE_CLOGF)
#define HAVE_CATANHF 1
complex float catanhf (complex float z);
complex float
catanhf (complex float z)
{
return clogf ((1.0f+z)/(1.0f-z))/2.0f;
}
#endif
#if !defined(HAVE_CATANH) && defined(HAVE_CLOG)
#define HAVE_CATANH 1
complex double catanh (complex double z);
complex double
catanh (complex double z)
{
return clog ((1.0+z)/(1.0-z))/2.0;
}
#endif
#if !defined(HAVE_CATANHL) && defined(HAVE_CLOGL)
#define HAVE_CATANHL 1
complex long double catanhl (complex long double z);
complex long double
catanhl (complex long double z)
{
return clogl ((1.0L+z)/(1.0L-z))/2.0L;
}
#endif
#if !defined(HAVE_TGAMMA)
#define HAVE_TGAMMA 1
double tgamma (double);
/* Fallback tgamma() function. Uses the algorithm from
http://www.netlib.org/specfun/gamma and references therein. */
#undef SQRTPI
#define SQRTPI 0.9189385332046727417803297
#undef PI
#define PI 3.1415926535897932384626434
double
tgamma (double x)
{
int i, n, parity;
double fact, res, sum, xden, xnum, y, y1, ysq, z;
static double p[8] = {
-1.71618513886549492533811e0, 2.47656508055759199108314e1,
-3.79804256470945635097577e2, 6.29331155312818442661052e2,
8.66966202790413211295064e2, -3.14512729688483675254357e4,
-3.61444134186911729807069e4, 6.64561438202405440627855e4 };
static double q[8] = {
-3.08402300119738975254353e1, 3.15350626979604161529144e2,
-1.01515636749021914166146e3, -3.10777167157231109440444e3,
2.25381184209801510330112e4, 4.75584627752788110767815e3,
-1.34659959864969306392456e5, -1.15132259675553483497211e5 };
static double c[7] = { -1.910444077728e-03,
8.4171387781295e-04, -5.952379913043012e-04,
7.93650793500350248e-04, -2.777777777777681622553e-03,
8.333333333333333331554247e-02, 5.7083835261e-03 };
static const double xminin = 2.23e-308;
static const double xbig = 171.624;
static const double xnan = __builtin_nan ("0x0"), xinf = __builtin_inf ();
static double eps = 0;
if (eps == 0)
eps = nextafter (1., 2.) - 1.;
parity = 0;
fact = 1;
n = 0;
y = x;
if (__builtin_isnan (x))
return x;
if (y <= 0)
{
y = -x;
y1 = trunc (y);
res = y - y1;
if (res != 0)
{
if (y1 != trunc (y1*0.5l)*2)
parity = 1;
fact = -PI / sin (PI*res);
y = y + 1;
}
else
return x == 0 ? copysign (xinf, x) : xnan;
}
if (y < eps)
{
if (y >= xminin)
res = 1 / y;
else
return xinf;
}
else if (y < 13)
{
y1 = y;
if (y < 1)
{
z = y;
y = y + 1;
}
else
{
n = (int)y - 1;
y = y - n;
z = y - 1;
}
xnum = 0;
xden = 1;
for (i = 0; i < 8; i++)
{
xnum = (xnum + p[i]) * z;
xden = xden * z + q[i];
}
res = xnum / xden + 1;
if (y1 < y)
res = res / y1;
else if (y1 > y)
for (i = 1; i <= n; i++)
{
res = res * y;
y = y + 1;
}
}
else
{
if (y < xbig)
{
ysq = y * y;
sum = c[6];
for (i = 0; i < 6; i++)
sum = sum / ysq + c[i];
sum = sum/y - y + SQRTPI;
sum = sum + (y - 0.5) * log (y);
res = exp (sum);
}
else
return x < 0 ? xnan : xinf;
}
if (parity)
res = -res;
if (fact != 1)
res = fact / res;
return res;
}
#endif
#if !defined(HAVE_LGAMMA)
#define HAVE_LGAMMA 1
double lgamma (double);
/* Fallback lgamma() function. Uses the algorithm from
http://www.netlib.org/specfun/algama and references therein,
except for negative arguments (where netlib would return +Inf)
where we use the following identity:
lgamma(y) = log(pi/(|y*sin(pi*y)|)) - lgamma(-y)
*/
double
lgamma (double y)
{
#undef SQRTPI
#define SQRTPI 0.9189385332046727417803297
#undef PI
#define PI 3.1415926535897932384626434
#define PNT68 0.6796875
#define D1 -0.5772156649015328605195174
#define D2 0.4227843350984671393993777
#define D4 1.791759469228055000094023
static double p1[8] = {
4.945235359296727046734888e0, 2.018112620856775083915565e2,
2.290838373831346393026739e3, 1.131967205903380828685045e4,
2.855724635671635335736389e4, 3.848496228443793359990269e4,
2.637748787624195437963534e4, 7.225813979700288197698961e3 };
static double q1[8] = {
6.748212550303777196073036e1, 1.113332393857199323513008e3,
7.738757056935398733233834e3, 2.763987074403340708898585e4,
5.499310206226157329794414e4, 6.161122180066002127833352e4,
3.635127591501940507276287e4, 8.785536302431013170870835e3 };
static double p2[8] = {
4.974607845568932035012064e0, 5.424138599891070494101986e2,
1.550693864978364947665077e4, 1.847932904445632425417223e5,
1.088204769468828767498470e6, 3.338152967987029735917223e6,
5.106661678927352456275255e6, 3.074109054850539556250927e6 };
static double q2[8] = {
1.830328399370592604055942e2, 7.765049321445005871323047e3,
1.331903827966074194402448e5, 1.136705821321969608938755e6,
5.267964117437946917577538e6, 1.346701454311101692290052e7,
1.782736530353274213975932e7, 9.533095591844353613395747e6 };
static double p4[8] = {
1.474502166059939948905062e4, 2.426813369486704502836312e6,
1.214755574045093227939592e8, 2.663432449630976949898078e9,
2.940378956634553899906876e10, 1.702665737765398868392998e11,
4.926125793377430887588120e11, 5.606251856223951465078242e11 };
static double q4[8] = {
2.690530175870899333379843e3, 6.393885654300092398984238e5,
4.135599930241388052042842e7, 1.120872109616147941376570e9,
1.488613728678813811542398e10, 1.016803586272438228077304e11,
3.417476345507377132798597e11, 4.463158187419713286462081e11 };
static double c[7] = {
-1.910444077728e-03, 8.4171387781295e-04,
-5.952379913043012e-04, 7.93650793500350248e-04,
-2.777777777777681622553e-03, 8.333333333333333331554247e-02,
5.7083835261e-03 };
static double xbig = 2.55e305, xinf = __builtin_inf (), eps = 0,
frtbig = 2.25e76;
int i;
double corr, res, xden, xm1, xm2, xm4, xnum, ysq;
if (eps == 0)
eps = __builtin_nextafter (1., 2.) - 1.;
if ((y > 0) && (y <= xbig))
{
if (y <= eps)
res = -log (y);
else if (y <= 1.5)
{
if (y < PNT68)
{
corr = -log (y);
xm1 = y;
}
else
{
corr = 0;
xm1 = (y - 0.5) - 0.5;
}
if ((y <= 0.5) || (y >= PNT68))
{
xden = 1;
xnum = 0;
for (i = 0; i < 8; i++)
{
xnum = xnum*xm1 + p1[i];
xden = xden*xm1 + q1[i];
}
res = corr + (xm1 * (D1 + xm1*(xnum/xden)));
}
else
{
xm2 = (y - 0.5) - 0.5;
xden = 1;
xnum = 0;
for (i = 0; i < 8; i++)
{
xnum = xnum*xm2 + p2[i];
xden = xden*xm2 + q2[i];
}
res = corr + xm2 * (D2 + xm2*(xnum/xden));
}
}
else if (y <= 4)
{
xm2 = y - 2;
xden = 1;
xnum = 0;
for (i = 0; i < 8; i++)
{
xnum = xnum*xm2 + p2[i];
xden = xden*xm2 + q2[i];
}
res = xm2 * (D2 + xm2*(xnum/xden));
}
else if (y <= 12)
{
xm4 = y - 4;
xden = -1;
xnum = 0;
for (i = 0; i < 8; i++)
{
xnum = xnum*xm4 + p4[i];
xden = xden*xm4 + q4[i];
}
res = D4 + xm4*(xnum/xden);
}
else
{
res = 0;
if (y <= frtbig)
{
res = c[6];
ysq = y * y;
for (i = 0; i < 6; i++)
res = res / ysq + c[i];
}
res = res/y;
corr = log (y);
res = res + SQRTPI - 0.5*corr;
res = res + y*(corr-1);
}
}
else if (y < 0 && __builtin_floor (y) != y)
{
/* lgamma(y) = log(pi/(|y*sin(pi*y)|)) - lgamma(-y)
For abs(y) very close to zero, we use a series expansion to
the first order in y to avoid overflow. */
if (y > -1.e-100)
res = -2 * log (fabs (y)) - lgamma (-y);
else
res = log (PI / fabs (y * sin (PI * y))) - lgamma (-y);
}
else
res = xinf;
return res;
}
#endif
#if defined(HAVE_TGAMMA) && !defined(HAVE_TGAMMAF)
#define HAVE_TGAMMAF 1
float tgammaf (float);
float
tgammaf (float x)
{
return (float) tgamma ((double) x);
}
#endif
#if defined(HAVE_LGAMMA) && !defined(HAVE_LGAMMAF)
#define HAVE_LGAMMAF 1
float lgammaf (float);
float
lgammaf (float x)
{
return (float) lgamma ((double) x);
}
#endif
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