eb647f7d99
PR libfortran/29810 * intrinsics/c99_functions.c (fmodf, fmodl, floorl): New functions. * c99_protos.h (fmodf, fmodl, floorl): New prototypes. * configure.ac: Check for fmodf, fmod and fmodl. * configure: Regenerate. * config.h.in: Regenerate. From-SVN: r119599
1307 lines
24 KiB
C
1307 lines
24 KiB
C
/* Implementation of various C99 functions
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Copyright (C) 2004 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 2 of the License, or (at your option) any later version.
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In addition to the permissions in the GNU General Public License, the
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Free Software Foundation gives you unlimited permission to link the
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compiled version of this file into combinations with other programs,
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and to distribute those combinations without any restriction coming
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from the use of this file. (The General Public License restrictions
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do apply in other respects; for example, they cover modification of
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the file, and distribution when not linked into a combine
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executable.)
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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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You should have received a copy of the GNU General Public
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License along with libgfortran; see the file COPYING. If not,
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write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
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Boston, MA 02110-1301, USA. */
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#include "config.h"
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#include <sys/types.h>
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#include <float.h>
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#include <math.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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return x * pow(FLT_RADIX, y);
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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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#ifndef HAVE_POWF
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#define HAVE_POWF 1
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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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#ifndef HAVE_ROUND
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#define HAVE_ROUND 1
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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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double
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round(double x)
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{
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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 = ceil(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 = ceil(-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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#ifndef HAVE_ROUNDF
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#define HAVE_ROUNDF 1
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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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float
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roundf(float x)
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{
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float 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 = ceilf(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 = ceilf(-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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#ifndef HAVE_LOG10L
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#define HAVE_LOG10L 1
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|
/* log10 function for long double variables. The version provided here
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|
reduces the argument until it fits into a double, then use log10. */
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|
long double
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log10l(long double x)
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|
{
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#if LDBL_MAX_EXP > DBL_MAX_EXP
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if (x > DBL_MAX)
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{
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double val;
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int p2_result = 0;
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if (x > 0x1p16383L) { p2_result += 16383; x /= 0x1p16383L; }
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if (x > 0x1p8191L) { p2_result += 8191; x /= 0x1p8191L; }
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if (x > 0x1p4095L) { p2_result += 4095; x /= 0x1p4095L; }
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if (x > 0x1p2047L) { p2_result += 2047; x /= 0x1p2047L; }
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if (x > 0x1p1023L) { p2_result += 1023; x /= 0x1p1023L; }
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val = log10 ((double) x);
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return (val + p2_result * .30102999566398119521373889472449302L);
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}
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#endif
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#if LDBL_MIN_EXP < DBL_MIN_EXP
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if (x < DBL_MIN)
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{
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double val;
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int p2_result = 0;
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if (x < 0x1p-16380L) { p2_result += 16380; x /= 0x1p-16380L; }
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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
|
|
|