1746 lines
33 KiB
C
1746 lines
33 KiB
C
/* Implementation of various C99 functions
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Copyright (C) 2004, 2009 Free Software Foundation, Inc.
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This file is part of the GNU Fortran 95 runtime library (libgfortran).
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Libgfortran is free software; you can redistribute it and/or
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modify it under the terms of the GNU General Public
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License as published by the Free Software Foundation; either
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version 3 of the License, or (at your option) any later version.
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Libgfortran is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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Under Section 7 of GPL version 3, you are granted additional
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permissions described in the GCC Runtime Library Exception, version
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3.1, as published by the Free Software Foundation.
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You should have received a copy of the GNU General Public License and
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a copy of the GCC Runtime Library Exception along with this program;
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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#include "config.h"
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#define C99_PROTOS_H WE_DONT_WANT_PROTOS_NOW
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#include "libgfortran.h"
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/* IRIX's <math.h> declares a non-C99 compliant implementation of cabs,
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which takes two floating point arguments instead of a single complex.
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If <complex.h> is missing this prevents building of c99_functions.c.
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To work around this we redirect cabs{,f,l} calls to __gfc_cabs{,f,l}. */
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#if defined(__sgi__) && !defined(HAVE_COMPLEX_H)
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#undef HAVE_CABS
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#undef HAVE_CABSF
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#undef HAVE_CABSL
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#define cabs __gfc_cabs
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#define cabsf __gfc_cabsf
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#define cabsl __gfc_cabsl
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#endif
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/* Tru64's <math.h> declares a non-C99 compliant implementation of cabs,
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which takes two floating point arguments instead of a single complex.
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To work around this we redirect cabs{,f,l} calls to __gfc_cabs{,f,l}. */
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#ifdef __osf__
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#undef HAVE_CABS
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#undef HAVE_CABSF
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#undef HAVE_CABSL
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#define cabs __gfc_cabs
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#define cabsf __gfc_cabsf
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#define cabsl __gfc_cabsl
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#endif
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/* Prototypes to silence -Wstrict-prototypes -Wmissing-prototypes. */
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float cabsf(float complex);
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double cabs(double complex);
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long double cabsl(long double complex);
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float cargf(float complex);
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double carg(double complex);
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long double cargl(long double complex);
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float complex clog10f(float complex);
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double complex clog10(double complex);
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long double complex clog10l(long double complex);
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/* Wrappers for systems without the various C99 single precision Bessel
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functions. */
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#if defined(HAVE_J0) && ! defined(HAVE_J0F)
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#define HAVE_J0F 1
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extern float j0f (float);
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float
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j0f (float x)
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{
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return (float) j0 ((double) x);
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}
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#endif
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#if defined(HAVE_J1) && !defined(HAVE_J1F)
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#define HAVE_J1F 1
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extern float j1f (float);
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float j1f (float x)
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{
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return (float) j1 ((double) x);
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}
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#endif
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#if defined(HAVE_JN) && !defined(HAVE_JNF)
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#define HAVE_JNF 1
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extern float jnf (int, float);
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float
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jnf (int n, float x)
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{
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return (float) jn (n, (double) x);
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}
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#endif
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#if defined(HAVE_Y0) && !defined(HAVE_Y0F)
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#define HAVE_Y0F 1
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extern float y0f (float);
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float
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y0f (float x)
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{
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return (float) y0 ((double) x);
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}
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#endif
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#if defined(HAVE_Y1) && !defined(HAVE_Y1F)
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#define HAVE_Y1F 1
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extern float y1f (float);
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float
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y1f (float x)
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{
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return (float) y1 ((double) x);
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}
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#endif
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#if defined(HAVE_YN) && !defined(HAVE_YNF)
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#define HAVE_YNF 1
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extern float ynf (int, float);
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float
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ynf (int n, float x)
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{
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return (float) yn (n, (double) x);
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}
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#endif
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/* Wrappers for systems without the C99 erff() and erfcf() functions. */
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#if defined(HAVE_ERF) && !defined(HAVE_ERFF)
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#define HAVE_ERFF 1
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extern float erff (float);
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float
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erff (float x)
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{
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return (float) erf ((double) x);
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}
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#endif
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#if defined(HAVE_ERFC) && !defined(HAVE_ERFCF)
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#define HAVE_ERFCF 1
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extern float erfcf (float);
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float
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erfcf (float x)
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{
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return (float) erfc ((double) x);
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}
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#endif
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#ifndef HAVE_ACOSF
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#define HAVE_ACOSF 1
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float
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acosf(float x)
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{
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return (float) acos(x);
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}
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#endif
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#if HAVE_ACOSH && !HAVE_ACOSHF
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float
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acoshf (float x)
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{
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return (float) acosh ((double) x);
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}
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#endif
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#ifndef HAVE_ASINF
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#define HAVE_ASINF 1
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float
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asinf(float x)
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{
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return (float) asin(x);
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}
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#endif
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#if HAVE_ASINH && !HAVE_ASINHF
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float
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asinhf (float x)
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{
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return (float) asinh ((double) x);
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}
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#endif
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#ifndef HAVE_ATAN2F
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#define HAVE_ATAN2F 1
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float
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atan2f(float y, float x)
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{
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return (float) atan2(y, x);
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}
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#endif
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#ifndef HAVE_ATANF
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#define HAVE_ATANF 1
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float
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atanf(float x)
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{
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return (float) atan(x);
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}
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#endif
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#if HAVE_ATANH && !HAVE_ATANHF
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float
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atanhf (float x)
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{
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return (float) atanh ((double) x);
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}
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#endif
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#ifndef HAVE_CEILF
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#define HAVE_CEILF 1
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float
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ceilf(float x)
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{
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return (float) ceil(x);
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}
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#endif
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#ifndef HAVE_COPYSIGNF
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#define HAVE_COPYSIGNF 1
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float
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copysignf(float x, float y)
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{
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return (float) copysign(x, y);
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}
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#endif
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#ifndef HAVE_COSF
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#define HAVE_COSF 1
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float
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cosf(float x)
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{
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return (float) cos(x);
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}
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#endif
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#ifndef HAVE_COSHF
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#define HAVE_COSHF 1
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float
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coshf(float x)
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{
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return (float) cosh(x);
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}
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#endif
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#ifndef HAVE_EXPF
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#define HAVE_EXPF 1
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float
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expf(float x)
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{
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return (float) exp(x);
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}
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#endif
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#ifndef HAVE_FABSF
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#define HAVE_FABSF 1
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float
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fabsf(float x)
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{
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return (float) fabs(x);
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}
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#endif
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#ifndef HAVE_FLOORF
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#define HAVE_FLOORF 1
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float
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floorf(float x)
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{
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return (float) floor(x);
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}
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#endif
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#ifndef HAVE_FMODF
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#define HAVE_FMODF 1
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float
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fmodf (float x, float y)
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{
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return (float) fmod (x, y);
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}
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#endif
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#ifndef HAVE_FREXPF
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#define HAVE_FREXPF 1
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float
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frexpf(float x, int *exp)
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{
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return (float) frexp(x, exp);
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}
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#endif
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#ifndef HAVE_HYPOTF
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#define HAVE_HYPOTF 1
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float
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hypotf(float x, float y)
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{
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return (float) hypot(x, y);
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}
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#endif
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#ifndef HAVE_LOGF
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#define HAVE_LOGF 1
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float
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logf(float x)
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{
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return (float) log(x);
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}
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#endif
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#ifndef HAVE_LOG10F
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#define HAVE_LOG10F 1
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float
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log10f(float x)
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{
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return (float) log10(x);
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}
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#endif
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#ifndef HAVE_SCALBN
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#define HAVE_SCALBN 1
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double
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scalbn(double x, int y)
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{
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#if (FLT_RADIX == 2) && defined(HAVE_LDEXP)
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return ldexp (x, y);
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#else
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return x * pow(FLT_RADIX, y);
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#endif
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}
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#endif
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#ifndef HAVE_SCALBNF
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#define HAVE_SCALBNF 1
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float
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scalbnf(float x, int y)
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{
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return (float) scalbn(x, y);
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}
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#endif
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#ifndef HAVE_SINF
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#define HAVE_SINF 1
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float
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sinf(float x)
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{
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return (float) sin(x);
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}
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#endif
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#ifndef HAVE_SINHF
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#define HAVE_SINHF 1
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float
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sinhf(float x)
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{
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return (float) sinh(x);
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}
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#endif
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#ifndef HAVE_SQRTF
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#define HAVE_SQRTF 1
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float
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sqrtf(float x)
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{
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return (float) sqrt(x);
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}
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#endif
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#ifndef HAVE_TANF
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#define HAVE_TANF 1
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float
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tanf(float x)
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{
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return (float) tan(x);
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}
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#endif
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#ifndef HAVE_TANHF
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#define HAVE_TANHF 1
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float
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tanhf(float x)
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{
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return (float) tanh(x);
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}
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#endif
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#ifndef HAVE_TRUNC
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#define HAVE_TRUNC 1
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double
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trunc(double x)
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{
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if (!isfinite (x))
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return x;
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if (x < 0.0)
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return - floor (-x);
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else
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return floor (x);
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}
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#endif
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#ifndef HAVE_TRUNCF
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#define HAVE_TRUNCF 1
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float
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truncf(float x)
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{
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return (float) trunc (x);
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}
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#endif
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#ifndef HAVE_NEXTAFTERF
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#define HAVE_NEXTAFTERF 1
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/* This is a portable implementation of nextafterf that is intended to be
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independent of the floating point format or its in memory representation.
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This implementation works correctly with denormalized values. */
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float
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nextafterf(float x, float y)
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{
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/* This variable is marked volatile to avoid excess precision problems
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on some platforms, including IA-32. */
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volatile float delta;
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float absx, denorm_min;
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if (isnan(x) || isnan(y))
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return x + y;
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if (x == y)
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return x;
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if (!isfinite (x))
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return x > 0 ? __FLT_MAX__ : - __FLT_MAX__;
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/* absx = fabsf (x); */
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absx = (x < 0.0) ? -x : x;
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/* __FLT_DENORM_MIN__ is non-zero iff the target supports denormals. */
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if (__FLT_DENORM_MIN__ == 0.0f)
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denorm_min = __FLT_MIN__;
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else
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denorm_min = __FLT_DENORM_MIN__;
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if (absx < __FLT_MIN__)
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delta = denorm_min;
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else
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{
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float frac;
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int exp;
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/* Discard the fraction from x. */
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frac = frexpf (absx, &exp);
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delta = scalbnf (0.5f, exp);
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/* Scale x by the epsilon of the representation. By rights we should
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have been able to combine this with scalbnf, but some targets don't
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get that correct with denormals. */
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delta *= __FLT_EPSILON__;
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/* If we're going to be reducing the absolute value of X, and doing so
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would reduce the exponent of X, then the delta to be applied is
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one exponent smaller. */
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if (frac == 0.5f && (y < x) == (x > 0))
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delta *= 0.5f;
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/* If that underflows to zero, then we're back to the minimum. */
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if (delta == 0.0f)
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delta = denorm_min;
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}
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if (y < x)
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delta = -delta;
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return x + delta;
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}
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#endif
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#if !defined(HAVE_POWF) || defined(HAVE_BROKEN_POWF)
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#ifndef HAVE_POWF
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#define HAVE_POWF 1
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#endif
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float
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powf(float x, float y)
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{
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return (float) pow(x, y);
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}
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#endif
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/* Note that if fpclassify is not defined, then NaN is not handled */
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/* Algorithm by Steven G. Kargl. */
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#if !defined(HAVE_ROUNDL)
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#define HAVE_ROUNDL 1
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#if defined(HAVE_CEILL)
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/* Round to nearest integral value. If the argument is halfway between two
|
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integral values then round away from zero. */
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long double
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roundl(long double x)
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{
|
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long double t;
|
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if (!isfinite (x))
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return (x);
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if (x >= 0.0)
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{
|
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t = ceill(x);
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if (t - x > 0.5)
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t -= 1.0;
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return (t);
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}
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else
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{
|
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t = ceill(-x);
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if (t + x > 0.5)
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t -= 1.0;
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return (-t);
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}
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}
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#else
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/* Poor version of roundl for system that don't have ceill. */
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long double
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roundl(long double x)
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{
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if (x > DBL_MAX || x < -DBL_MAX)
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{
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#ifdef HAVE_NEXTAFTERL
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static long double prechalf = nexafterl (0.5L, LDBL_MAX);
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#else
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static long double prechalf = 0.5L;
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#endif
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return (GFC_INTEGER_LARGEST) (x + (x > 0 ? prechalf : -prechalf));
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}
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else
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/* Use round(). */
|
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return round((double) x);
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}
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#endif
|
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#endif
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#ifndef HAVE_ROUND
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#define HAVE_ROUND 1
|
|
/* Round to nearest integral value. If the argument is halfway between two
|
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integral values then round away from zero. */
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|
|
double
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round(double x)
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|
{
|
|
double t;
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if (!isfinite (x))
|
|
return (x);
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|
|
if (x >= 0.0)
|
|
{
|
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t = floor(x);
|
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if (t - x <= -0.5)
|
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t += 1.0;
|
|
return (t);
|
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}
|
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else
|
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{
|
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t = floor(-x);
|
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if (t + x <= -0.5)
|
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t += 1.0;
|
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return (-t);
|
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}
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}
|
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#endif
|
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|
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#ifndef HAVE_ROUNDF
|
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#define HAVE_ROUNDF 1
|
|
/* Round to nearest integral value. If the argument is halfway between two
|
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integral values then round away from zero. */
|
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|
|
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)
|
|
{
|
|
return (long int) roundf (x);
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_LROUND) && defined(HAVE_ROUND)
|
|
#define HAVE_LROUND 1
|
|
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)
|
|
{
|
|
return (long long int) roundl (x);
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_LLROUNDF) && defined(HAVE_ROUNDF)
|
|
#define HAVE_LLROUNDF 1
|
|
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)
|
|
{
|
|
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)
|
|
{
|
|
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)
|
|
{
|
|
#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)
|
|
{
|
|
/* 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)
|
|
{
|
|
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)
|
|
{
|
|
return hypotf (REALPART (z), IMAGPART (z));
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CABS)
|
|
#define HAVE_CABS 1
|
|
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)
|
|
{
|
|
return hypotl (REALPART (z), IMAGPART (z));
|
|
}
|
|
#endif
|
|
|
|
|
|
#if !defined(HAVE_CARGF)
|
|
#define HAVE_CARGF 1
|
|
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)
|
|
{
|
|
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)
|
|
{
|
|
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 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 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 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 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 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 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 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 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 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)
|
|
{
|
|
return cexpf (power * clogf (base));
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CPOW)
|
|
#define HAVE_CPOW 1
|
|
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)
|
|
{
|
|
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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
|
|
|
|
|
|
#if !defined(HAVE_TGAMMA)
|
|
#define HAVE_TGAMMA 1
|
|
|
|
extern 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
|
|
|
|
extern 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
|
|
extern float tgammaf (float);
|
|
|
|
float
|
|
tgammaf (float x)
|
|
{
|
|
return (float) tgamma ((double) x);
|
|
}
|
|
#endif
|
|
|
|
#if defined(HAVE_LGAMMA) && !defined(HAVE_LGAMMAF)
|
|
#define HAVE_LGAMMAF 1
|
|
extern float lgammaf (float);
|
|
|
|
float
|
|
lgammaf (float x)
|
|
{
|
|
return (float) lgamma ((double) x);
|
|
}
|
|
#endif
|