2115 lines
40 KiB
C
2115 lines
40 KiB
C
/* Implementation of various C99 functions
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Copyright (C) 2004-2020 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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/* On a C99 system "I" (with I*I = -1) should be defined in complex.h;
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if not, we define a fallback version here. */
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#ifndef I
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# if defined(_Imaginary_I)
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# define I _Imaginary_I
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# elif defined(_Complex_I)
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# define I _Complex_I
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# else
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# define I (1.0fi)
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# endif
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#endif
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/* Macros to get real and imaginary parts of a complex, and set
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a complex value. */
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#define REALPART(z) (__real__(z))
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#define IMAGPART(z) (__imag__(z))
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#define COMPLEX_ASSIGN(z_, r_, i_) {__real__(z_) = (r_); __imag__(z_) = (i_);}
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/* Prototypes are included to silence -Wstrict-prototypes
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-Wmissing-prototypes. */
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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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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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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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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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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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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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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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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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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 acosf (float x);
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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 acoshf (float x);
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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 asinf (float x);
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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 asinhf (float x);
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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 atan2f (float y, float x);
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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 atanf (float x);
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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 atanhf (float x);
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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 ceilf (float x);
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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 copysignf (float x, float y);
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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 cosf (float x);
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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 coshf (float x);
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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 expf (float x);
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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 fabsf (float x);
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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 floorf (float x);
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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 fmodf (float x, float y);
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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 frexpf (float x, int *exp);
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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 hypotf (float x, float y);
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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 logf (float x);
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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 log10f (float x);
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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 scalbn (double x, int y);
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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 scalbnf (float x, int y);
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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 sinf (float x);
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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 sinhf (float x);
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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 sqrtf (float x);
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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 tanf (float x);
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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 tanhf (float x);
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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 trunc (double x);
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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 truncf (float x);
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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 nextafterf (float x, float y);
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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 powf (float x, float y);
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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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#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 round (double x);
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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 = 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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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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|
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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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long double roundl (long double x);
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|
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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
|
|
long double prechalf = nextafterl (0.5L, LDBL_MAX);
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#else
|
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static long double prechalf = 0.5L;
|
|
#endif
|
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return (GFC_INTEGER_LARGEST) (x + (x > 0 ? prechalf : -prechalf));
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}
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|
else
|
|
/* Use round(). */
|
|
return round ((double) x);
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}
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|
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#endif
|
|
#endif
|
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|
|
#ifndef HAVE_ROUNDF
|
|
#define HAVE_ROUNDF 1
|
|
/* Round to nearest integral value. If the argument is halfway between two
|
|
integral values then round away from zero. */
|
|
float roundf (float x);
|
|
|
|
float
|
|
roundf (float x)
|
|
{
|
|
float t;
|
|
if (!isfinite (x))
|
|
return (x);
|
|
|
|
if (x >= 0.0)
|
|
{
|
|
t = floorf (x);
|
|
if (t - x <= -0.5)
|
|
t += 1.0;
|
|
return (t);
|
|
}
|
|
else
|
|
{
|
|
t = floorf (-x);
|
|
if (t + x <= -0.5)
|
|
t += 1.0;
|
|
return (-t);
|
|
}
|
|
}
|
|
#endif
|
|
|
|
|
|
/* lround{f,,l} and llround{f,,l} functions. */
|
|
|
|
#if !defined(HAVE_LROUNDF) && defined(HAVE_ROUNDF)
|
|
#define HAVE_LROUNDF 1
|
|
long int lroundf (float x);
|
|
|
|
long int
|
|
lroundf (float x)
|
|
{
|
|
return (long int) roundf (x);
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_LROUND) && defined(HAVE_ROUND)
|
|
#define HAVE_LROUND 1
|
|
long int lround (double x);
|
|
|
|
long int
|
|
lround (double x)
|
|
{
|
|
return (long int) round (x);
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_LROUNDL) && defined(HAVE_ROUNDL)
|
|
#define HAVE_LROUNDL 1
|
|
long int lroundl (long double x);
|
|
|
|
long int
|
|
lroundl (long double x)
|
|
{
|
|
return (long long int) roundl (x);
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_LLROUNDF) && defined(HAVE_ROUNDF)
|
|
#define HAVE_LLROUNDF 1
|
|
long long int llroundf (float x);
|
|
|
|
long long int
|
|
llroundf (float x)
|
|
{
|
|
return (long long int) roundf (x);
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_LLROUND) && defined(HAVE_ROUND)
|
|
#define HAVE_LLROUND 1
|
|
long long int llround (double x);
|
|
|
|
long long int
|
|
llround (double x)
|
|
{
|
|
return (long long int) round (x);
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_LLROUNDL) && defined(HAVE_ROUNDL)
|
|
#define HAVE_LLROUNDL 1
|
|
long long int llroundl (long double x);
|
|
|
|
long long int
|
|
llroundl (long double x)
|
|
{
|
|
return (long long int) roundl (x);
|
|
}
|
|
#endif
|
|
|
|
|
|
#ifndef HAVE_LOG10L
|
|
#define HAVE_LOG10L 1
|
|
/* log10 function for long double variables. The version provided here
|
|
reduces the argument until it fits into a double, then use log10. */
|
|
long double log10l (long double x);
|
|
|
|
long double
|
|
log10l (long double x)
|
|
{
|
|
#if LDBL_MAX_EXP > DBL_MAX_EXP
|
|
if (x > DBL_MAX)
|
|
{
|
|
double val;
|
|
int p2_result = 0;
|
|
if (x > 0x1p16383L) { p2_result += 16383; x /= 0x1p16383L; }
|
|
if (x > 0x1p8191L) { p2_result += 8191; x /= 0x1p8191L; }
|
|
if (x > 0x1p4095L) { p2_result += 4095; x /= 0x1p4095L; }
|
|
if (x > 0x1p2047L) { p2_result += 2047; x /= 0x1p2047L; }
|
|
if (x > 0x1p1023L) { p2_result += 1023; x /= 0x1p1023L; }
|
|
val = log10 ((double) x);
|
|
return (val + p2_result * .30102999566398119521373889472449302L);
|
|
}
|
|
#endif
|
|
#if LDBL_MIN_EXP < DBL_MIN_EXP
|
|
if (x < DBL_MIN)
|
|
{
|
|
double val;
|
|
int p2_result = 0;
|
|
if (x < 0x1p-16380L) { p2_result += 16380; x /= 0x1p-16380L; }
|
|
if (x < 0x1p-8189L) { p2_result += 8189; x /= 0x1p-8189L; }
|
|
if (x < 0x1p-4093L) { p2_result += 4093; x /= 0x1p-4093L; }
|
|
if (x < 0x1p-2045L) { p2_result += 2045; x /= 0x1p-2045L; }
|
|
if (x < 0x1p-1021L) { p2_result += 1021; x /= 0x1p-1021L; }
|
|
val = fabs (log10 ((double) x));
|
|
return (- val - p2_result * .30102999566398119521373889472449302L);
|
|
}
|
|
#endif
|
|
return log10 (x);
|
|
}
|
|
#endif
|
|
|
|
|
|
#ifndef HAVE_FLOORL
|
|
#define HAVE_FLOORL 1
|
|
long double floorl (long double x);
|
|
|
|
long double
|
|
floorl (long double x)
|
|
{
|
|
/* Zero, possibly signed. */
|
|
if (x == 0)
|
|
return x;
|
|
|
|
/* Large magnitude. */
|
|
if (x > DBL_MAX || x < (-DBL_MAX))
|
|
return x;
|
|
|
|
/* Small positive values. */
|
|
if (x >= 0 && x < DBL_MIN)
|
|
return 0;
|
|
|
|
/* Small negative values. */
|
|
if (x < 0 && x > (-DBL_MIN))
|
|
return -1;
|
|
|
|
return floor (x);
|
|
}
|
|
#endif
|
|
|
|
|
|
#ifndef HAVE_FMODL
|
|
#define HAVE_FMODL 1
|
|
long double fmodl (long double x, long double y);
|
|
|
|
long double
|
|
fmodl (long double x, long double y)
|
|
{
|
|
if (y == 0.0L)
|
|
return 0.0L;
|
|
|
|
/* Need to check that the result has the same sign as x and magnitude
|
|
less than the magnitude of y. */
|
|
return x - floorl (x / y) * y;
|
|
}
|
|
#endif
|
|
|
|
|
|
#if !defined(HAVE_CABSF)
|
|
#define HAVE_CABSF 1
|
|
float cabsf (float complex z);
|
|
|
|
float
|
|
cabsf (float complex z)
|
|
{
|
|
return hypotf (REALPART (z), IMAGPART (z));
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CABS)
|
|
#define HAVE_CABS 1
|
|
double cabs (double complex z);
|
|
|
|
double
|
|
cabs (double complex z)
|
|
{
|
|
return hypot (REALPART (z), IMAGPART (z));
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CABSL) && defined(HAVE_HYPOTL)
|
|
#define HAVE_CABSL 1
|
|
long double cabsl (long double complex z);
|
|
|
|
long double
|
|
cabsl (long double complex z)
|
|
{
|
|
return hypotl (REALPART (z), IMAGPART (z));
|
|
}
|
|
#endif
|
|
|
|
|
|
#if !defined(HAVE_CARGF)
|
|
#define HAVE_CARGF 1
|
|
float cargf (float complex z);
|
|
|
|
float
|
|
cargf (float complex z)
|
|
{
|
|
return atan2f (IMAGPART (z), REALPART (z));
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CARG)
|
|
#define HAVE_CARG 1
|
|
double carg (double complex z);
|
|
|
|
double
|
|
carg (double complex z)
|
|
{
|
|
return atan2 (IMAGPART (z), REALPART (z));
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CARGL) && defined(HAVE_ATAN2L)
|
|
#define HAVE_CARGL 1
|
|
long double cargl (long double complex z);
|
|
|
|
long double
|
|
cargl (long double complex z)
|
|
{
|
|
return atan2l (IMAGPART (z), REALPART (z));
|
|
}
|
|
#endif
|
|
|
|
|
|
/* exp(z) = exp(a)*(cos(b) + i sin(b)) */
|
|
#if !defined(HAVE_CEXPF)
|
|
#define HAVE_CEXPF 1
|
|
float complex cexpf (float complex z);
|
|
|
|
float complex
|
|
cexpf (float complex z)
|
|
{
|
|
float a, b;
|
|
float complex v;
|
|
|
|
a = REALPART (z);
|
|
b = IMAGPART (z);
|
|
COMPLEX_ASSIGN (v, cosf (b), sinf (b));
|
|
return expf (a) * v;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CEXP)
|
|
#define HAVE_CEXP 1
|
|
double complex cexp (double complex z);
|
|
|
|
double complex
|
|
cexp (double complex z)
|
|
{
|
|
double a, b;
|
|
double complex v;
|
|
|
|
a = REALPART (z);
|
|
b = IMAGPART (z);
|
|
COMPLEX_ASSIGN (v, cos (b), sin (b));
|
|
return exp (a) * v;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CEXPL) && defined(HAVE_COSL) && defined(HAVE_SINL) && defined(HAVE_EXPL)
|
|
#define HAVE_CEXPL 1
|
|
long double complex cexpl (long double complex z);
|
|
|
|
long double complex
|
|
cexpl (long double complex z)
|
|
{
|
|
long double a, b;
|
|
long double complex v;
|
|
|
|
a = REALPART (z);
|
|
b = IMAGPART (z);
|
|
COMPLEX_ASSIGN (v, cosl (b), sinl (b));
|
|
return expl (a) * v;
|
|
}
|
|
#endif
|
|
|
|
|
|
/* log(z) = log (cabs(z)) + i*carg(z) */
|
|
#if !defined(HAVE_CLOGF)
|
|
#define HAVE_CLOGF 1
|
|
float complex clogf (float complex z);
|
|
|
|
float complex
|
|
clogf (float complex z)
|
|
{
|
|
float complex v;
|
|
|
|
COMPLEX_ASSIGN (v, logf (cabsf (z)), cargf (z));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CLOG)
|
|
#define HAVE_CLOG 1
|
|
double complex clog (double complex z);
|
|
|
|
double complex
|
|
clog (double complex z)
|
|
{
|
|
double complex v;
|
|
|
|
COMPLEX_ASSIGN (v, log (cabs (z)), carg (z));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CLOGL) && defined(HAVE_LOGL) && defined(HAVE_CABSL) && defined(HAVE_CARGL)
|
|
#define HAVE_CLOGL 1
|
|
long double complex clogl (long double complex z);
|
|
|
|
long double complex
|
|
clogl (long double complex z)
|
|
{
|
|
long double complex v;
|
|
|
|
COMPLEX_ASSIGN (v, logl (cabsl (z)), cargl (z));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
|
|
/* log10(z) = log10 (cabs(z)) + i*carg(z) */
|
|
#if !defined(HAVE_CLOG10F)
|
|
#define HAVE_CLOG10F 1
|
|
float complex clog10f (float complex z);
|
|
|
|
float complex
|
|
clog10f (float complex z)
|
|
{
|
|
float complex v;
|
|
|
|
COMPLEX_ASSIGN (v, log10f (cabsf (z)), cargf (z));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CLOG10)
|
|
#define HAVE_CLOG10 1
|
|
double complex clog10 (double complex z);
|
|
|
|
double complex
|
|
clog10 (double complex z)
|
|
{
|
|
double complex v;
|
|
|
|
COMPLEX_ASSIGN (v, log10 (cabs (z)), carg (z));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CLOG10L) && defined(HAVE_LOG10L) && defined(HAVE_CABSL) && defined(HAVE_CARGL)
|
|
#define HAVE_CLOG10L 1
|
|
long double complex clog10l (long double complex z);
|
|
|
|
long double complex
|
|
clog10l (long double complex z)
|
|
{
|
|
long double complex v;
|
|
|
|
COMPLEX_ASSIGN (v, log10l (cabsl (z)), cargl (z));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
|
|
/* pow(base, power) = cexp (power * clog (base)) */
|
|
#if !defined(HAVE_CPOWF)
|
|
#define HAVE_CPOWF 1
|
|
float complex cpowf (float complex base, float complex power);
|
|
|
|
float complex
|
|
cpowf (float complex base, float complex power)
|
|
{
|
|
return cexpf (power * clogf (base));
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CPOW)
|
|
#define HAVE_CPOW 1
|
|
double complex cpow (double complex base, double complex power);
|
|
|
|
double complex
|
|
cpow (double complex base, double complex power)
|
|
{
|
|
return cexp (power * clog (base));
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CPOWL) && defined(HAVE_CEXPL) && defined(HAVE_CLOGL)
|
|
#define HAVE_CPOWL 1
|
|
long double complex cpowl (long double complex base, long double complex power);
|
|
|
|
long double complex
|
|
cpowl (long double complex base, long double complex power)
|
|
{
|
|
return cexpl (power * clogl (base));
|
|
}
|
|
#endif
|
|
|
|
|
|
/* sqrt(z). Algorithm pulled from glibc. */
|
|
#if !defined(HAVE_CSQRTF)
|
|
#define HAVE_CSQRTF 1
|
|
float complex csqrtf (float complex z);
|
|
|
|
float complex
|
|
csqrtf (float complex z)
|
|
{
|
|
float re, im;
|
|
float complex v;
|
|
|
|
re = REALPART (z);
|
|
im = IMAGPART (z);
|
|
if (im == 0)
|
|
{
|
|
if (re < 0)
|
|
{
|
|
COMPLEX_ASSIGN (v, 0, copysignf (sqrtf (-re), im));
|
|
}
|
|
else
|
|
{
|
|
COMPLEX_ASSIGN (v, fabsf (sqrtf (re)), copysignf (0, im));
|
|
}
|
|
}
|
|
else if (re == 0)
|
|
{
|
|
float r;
|
|
|
|
r = sqrtf (0.5 * fabsf (im));
|
|
|
|
COMPLEX_ASSIGN (v, r, copysignf (r, im));
|
|
}
|
|
else
|
|
{
|
|
float d, r, s;
|
|
|
|
d = hypotf (re, im);
|
|
/* Use the identity 2 Re res Im res = Im x
|
|
to avoid cancellation error in d +/- Re x. */
|
|
if (re > 0)
|
|
{
|
|
r = sqrtf (0.5 * d + 0.5 * re);
|
|
s = (0.5 * im) / r;
|
|
}
|
|
else
|
|
{
|
|
s = sqrtf (0.5 * d - 0.5 * re);
|
|
r = fabsf ((0.5 * im) / s);
|
|
}
|
|
|
|
COMPLEX_ASSIGN (v, r, copysignf (s, im));
|
|
}
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CSQRT)
|
|
#define HAVE_CSQRT 1
|
|
double complex csqrt (double complex z);
|
|
|
|
double complex
|
|
csqrt (double complex z)
|
|
{
|
|
double re, im;
|
|
double complex v;
|
|
|
|
re = REALPART (z);
|
|
im = IMAGPART (z);
|
|
if (im == 0)
|
|
{
|
|
if (re < 0)
|
|
{
|
|
COMPLEX_ASSIGN (v, 0, copysign (sqrt (-re), im));
|
|
}
|
|
else
|
|
{
|
|
COMPLEX_ASSIGN (v, fabs (sqrt (re)), copysign (0, im));
|
|
}
|
|
}
|
|
else if (re == 0)
|
|
{
|
|
double r;
|
|
|
|
r = sqrt (0.5 * fabs (im));
|
|
|
|
COMPLEX_ASSIGN (v, r, copysign (r, im));
|
|
}
|
|
else
|
|
{
|
|
double d, r, s;
|
|
|
|
d = hypot (re, im);
|
|
/* Use the identity 2 Re res Im res = Im x
|
|
to avoid cancellation error in d +/- Re x. */
|
|
if (re > 0)
|
|
{
|
|
r = sqrt (0.5 * d + 0.5 * re);
|
|
s = (0.5 * im) / r;
|
|
}
|
|
else
|
|
{
|
|
s = sqrt (0.5 * d - 0.5 * re);
|
|
r = fabs ((0.5 * im) / s);
|
|
}
|
|
|
|
COMPLEX_ASSIGN (v, r, copysign (s, im));
|
|
}
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CSQRTL) && defined(HAVE_COPYSIGNL) && defined(HAVE_SQRTL) && defined(HAVE_FABSL) && defined(HAVE_HYPOTL)
|
|
#define HAVE_CSQRTL 1
|
|
long double complex csqrtl (long double complex z);
|
|
|
|
long double complex
|
|
csqrtl (long double complex z)
|
|
{
|
|
long double re, im;
|
|
long double complex v;
|
|
|
|
re = REALPART (z);
|
|
im = IMAGPART (z);
|
|
if (im == 0)
|
|
{
|
|
if (re < 0)
|
|
{
|
|
COMPLEX_ASSIGN (v, 0, copysignl (sqrtl (-re), im));
|
|
}
|
|
else
|
|
{
|
|
COMPLEX_ASSIGN (v, fabsl (sqrtl (re)), copysignl (0, im));
|
|
}
|
|
}
|
|
else if (re == 0)
|
|
{
|
|
long double r;
|
|
|
|
r = sqrtl (0.5 * fabsl (im));
|
|
|
|
COMPLEX_ASSIGN (v, copysignl (r, im), r);
|
|
}
|
|
else
|
|
{
|
|
long double d, r, s;
|
|
|
|
d = hypotl (re, im);
|
|
/* Use the identity 2 Re res Im res = Im x
|
|
to avoid cancellation error in d +/- Re x. */
|
|
if (re > 0)
|
|
{
|
|
r = sqrtl (0.5 * d + 0.5 * re);
|
|
s = (0.5 * im) / r;
|
|
}
|
|
else
|
|
{
|
|
s = sqrtl (0.5 * d - 0.5 * re);
|
|
r = fabsl ((0.5 * im) / s);
|
|
}
|
|
|
|
COMPLEX_ASSIGN (v, r, copysignl (s, im));
|
|
}
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
|
|
/* sinh(a + i b) = sinh(a) cos(b) + i cosh(a) sin(b) */
|
|
#if !defined(HAVE_CSINHF)
|
|
#define HAVE_CSINHF 1
|
|
float complex csinhf (float complex a);
|
|
|
|
float complex
|
|
csinhf (float complex a)
|
|
{
|
|
float r, i;
|
|
float complex v;
|
|
|
|
r = REALPART (a);
|
|
i = IMAGPART (a);
|
|
COMPLEX_ASSIGN (v, sinhf (r) * cosf (i), coshf (r) * sinf (i));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CSINH)
|
|
#define HAVE_CSINH 1
|
|
double complex csinh (double complex a);
|
|
|
|
double complex
|
|
csinh (double complex a)
|
|
{
|
|
double r, i;
|
|
double complex v;
|
|
|
|
r = REALPART (a);
|
|
i = IMAGPART (a);
|
|
COMPLEX_ASSIGN (v, sinh (r) * cos (i), cosh (r) * sin (i));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CSINHL) && defined(HAVE_COSL) && defined(HAVE_COSHL) && defined(HAVE_SINL) && defined(HAVE_SINHL)
|
|
#define HAVE_CSINHL 1
|
|
long double complex csinhl (long double complex a);
|
|
|
|
long double complex
|
|
csinhl (long double complex a)
|
|
{
|
|
long double r, i;
|
|
long double complex v;
|
|
|
|
r = REALPART (a);
|
|
i = IMAGPART (a);
|
|
COMPLEX_ASSIGN (v, sinhl (r) * cosl (i), coshl (r) * sinl (i));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
|
|
/* cosh(a + i b) = cosh(a) cos(b) + i sinh(a) sin(b) */
|
|
#if !defined(HAVE_CCOSHF)
|
|
#define HAVE_CCOSHF 1
|
|
float complex ccoshf (float complex a);
|
|
|
|
float complex
|
|
ccoshf (float complex a)
|
|
{
|
|
float r, i;
|
|
float complex v;
|
|
|
|
r = REALPART (a);
|
|
i = IMAGPART (a);
|
|
COMPLEX_ASSIGN (v, coshf (r) * cosf (i), sinhf (r) * sinf (i));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CCOSH)
|
|
#define HAVE_CCOSH 1
|
|
double complex ccosh (double complex a);
|
|
|
|
double complex
|
|
ccosh (double complex a)
|
|
{
|
|
double r, i;
|
|
double complex v;
|
|
|
|
r = REALPART (a);
|
|
i = IMAGPART (a);
|
|
COMPLEX_ASSIGN (v, cosh (r) * cos (i), sinh (r) * sin (i));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CCOSHL) && defined(HAVE_COSL) && defined(HAVE_COSHL) && defined(HAVE_SINL) && defined(HAVE_SINHL)
|
|
#define HAVE_CCOSHL 1
|
|
long double complex ccoshl (long double complex a);
|
|
|
|
long double complex
|
|
ccoshl (long double complex a)
|
|
{
|
|
long double r, i;
|
|
long double complex v;
|
|
|
|
r = REALPART (a);
|
|
i = IMAGPART (a);
|
|
COMPLEX_ASSIGN (v, coshl (r) * cosl (i), sinhl (r) * sinl (i));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
|
|
/* tanh(a + i b) = (tanh(a) + i tan(b)) / (1 + i tanh(a) tan(b)) */
|
|
#if !defined(HAVE_CTANHF)
|
|
#define HAVE_CTANHF 1
|
|
float complex ctanhf (float complex a);
|
|
|
|
float complex
|
|
ctanhf (float complex a)
|
|
{
|
|
float rt, it;
|
|
float complex n, d;
|
|
|
|
rt = tanhf (REALPART (a));
|
|
it = tanf (IMAGPART (a));
|
|
COMPLEX_ASSIGN (n, rt, it);
|
|
COMPLEX_ASSIGN (d, 1, rt * it);
|
|
|
|
return n / d;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CTANH)
|
|
#define HAVE_CTANH 1
|
|
double complex ctanh (double complex a);
|
|
double complex
|
|
ctanh (double complex a)
|
|
{
|
|
double rt, it;
|
|
double complex n, d;
|
|
|
|
rt = tanh (REALPART (a));
|
|
it = tan (IMAGPART (a));
|
|
COMPLEX_ASSIGN (n, rt, it);
|
|
COMPLEX_ASSIGN (d, 1, rt * it);
|
|
|
|
return n / d;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CTANHL) && defined(HAVE_TANL) && defined(HAVE_TANHL)
|
|
#define HAVE_CTANHL 1
|
|
long double complex ctanhl (long double complex a);
|
|
|
|
long double complex
|
|
ctanhl (long double complex a)
|
|
{
|
|
long double rt, it;
|
|
long double complex n, d;
|
|
|
|
rt = tanhl (REALPART (a));
|
|
it = tanl (IMAGPART (a));
|
|
COMPLEX_ASSIGN (n, rt, it);
|
|
COMPLEX_ASSIGN (d, 1, rt * it);
|
|
|
|
return n / d;
|
|
}
|
|
#endif
|
|
|
|
|
|
/* sin(a + i b) = sin(a) cosh(b) + i cos(a) sinh(b) */
|
|
#if !defined(HAVE_CSINF)
|
|
#define HAVE_CSINF 1
|
|
float complex csinf (float complex a);
|
|
|
|
float complex
|
|
csinf (float complex a)
|
|
{
|
|
float r, i;
|
|
float complex v;
|
|
|
|
r = REALPART (a);
|
|
i = IMAGPART (a);
|
|
COMPLEX_ASSIGN (v, sinf (r) * coshf (i), cosf (r) * sinhf (i));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CSIN)
|
|
#define HAVE_CSIN 1
|
|
double complex csin (double complex a);
|
|
|
|
double complex
|
|
csin (double complex a)
|
|
{
|
|
double r, i;
|
|
double complex v;
|
|
|
|
r = REALPART (a);
|
|
i = IMAGPART (a);
|
|
COMPLEX_ASSIGN (v, sin (r) * cosh (i), cos (r) * sinh (i));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CSINL) && defined(HAVE_COSL) && defined(HAVE_COSHL) && defined(HAVE_SINL) && defined(HAVE_SINHL)
|
|
#define HAVE_CSINL 1
|
|
long double complex csinl (long double complex a);
|
|
|
|
long double complex
|
|
csinl (long double complex a)
|
|
{
|
|
long double r, i;
|
|
long double complex v;
|
|
|
|
r = REALPART (a);
|
|
i = IMAGPART (a);
|
|
COMPLEX_ASSIGN (v, sinl (r) * coshl (i), cosl (r) * sinhl (i));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
|
|
/* cos(a + i b) = cos(a) cosh(b) - i sin(a) sinh(b) */
|
|
#if !defined(HAVE_CCOSF)
|
|
#define HAVE_CCOSF 1
|
|
float complex ccosf (float complex a);
|
|
|
|
float complex
|
|
ccosf (float complex a)
|
|
{
|
|
float r, i;
|
|
float complex v;
|
|
|
|
r = REALPART (a);
|
|
i = IMAGPART (a);
|
|
COMPLEX_ASSIGN (v, cosf (r) * coshf (i), - (sinf (r) * sinhf (i)));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CCOS)
|
|
#define HAVE_CCOS 1
|
|
double complex ccos (double complex a);
|
|
|
|
double complex
|
|
ccos (double complex a)
|
|
{
|
|
double r, i;
|
|
double complex v;
|
|
|
|
r = REALPART (a);
|
|
i = IMAGPART (a);
|
|
COMPLEX_ASSIGN (v, cos (r) * cosh (i), - (sin (r) * sinh (i)));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CCOSL) && defined(HAVE_COSL) && defined(HAVE_COSHL) && defined(HAVE_SINL) && defined(HAVE_SINHL)
|
|
#define HAVE_CCOSL 1
|
|
long double complex ccosl (long double complex a);
|
|
|
|
long double complex
|
|
ccosl (long double complex a)
|
|
{
|
|
long double r, i;
|
|
long double complex v;
|
|
|
|
r = REALPART (a);
|
|
i = IMAGPART (a);
|
|
COMPLEX_ASSIGN (v, cosl (r) * coshl (i), - (sinl (r) * sinhl (i)));
|
|
return v;
|
|
}
|
|
#endif
|
|
|
|
|
|
/* tan(a + i b) = (tan(a) + i tanh(b)) / (1 - i tan(a) tanh(b)) */
|
|
#if !defined(HAVE_CTANF)
|
|
#define HAVE_CTANF 1
|
|
float complex ctanf (float complex a);
|
|
|
|
float complex
|
|
ctanf (float complex a)
|
|
{
|
|
float rt, it;
|
|
float complex n, d;
|
|
|
|
rt = tanf (REALPART (a));
|
|
it = tanhf (IMAGPART (a));
|
|
COMPLEX_ASSIGN (n, rt, it);
|
|
COMPLEX_ASSIGN (d, 1, - (rt * it));
|
|
|
|
return n / d;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CTAN)
|
|
#define HAVE_CTAN 1
|
|
double complex ctan (double complex a);
|
|
|
|
double complex
|
|
ctan (double complex a)
|
|
{
|
|
double rt, it;
|
|
double complex n, d;
|
|
|
|
rt = tan (REALPART (a));
|
|
it = tanh (IMAGPART (a));
|
|
COMPLEX_ASSIGN (n, rt, it);
|
|
COMPLEX_ASSIGN (d, 1, - (rt * it));
|
|
|
|
return n / d;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CTANL) && defined(HAVE_TANL) && defined(HAVE_TANHL)
|
|
#define HAVE_CTANL 1
|
|
long double complex ctanl (long double complex a);
|
|
|
|
long double complex
|
|
ctanl (long double complex a)
|
|
{
|
|
long double rt, it;
|
|
long double complex n, d;
|
|
|
|
rt = tanl (REALPART (a));
|
|
it = tanhl (IMAGPART (a));
|
|
COMPLEX_ASSIGN (n, rt, it);
|
|
COMPLEX_ASSIGN (d, 1, - (rt * it));
|
|
|
|
return n / d;
|
|
}
|
|
#endif
|
|
|
|
|
|
/* Complex ASIN. Returns wrongly NaN for infinite arguments.
|
|
Algorithm taken from Abramowitz & Stegun. */
|
|
|
|
#if !defined(HAVE_CASINF) && defined(HAVE_CLOGF) && defined(HAVE_CSQRTF)
|
|
#define HAVE_CASINF 1
|
|
complex float casinf (complex float z);
|
|
|
|
complex float
|
|
casinf (complex float z)
|
|
{
|
|
return -I*clogf (I*z + csqrtf (1.0f-z*z));
|
|
}
|
|
#endif
|
|
|
|
|
|
#if !defined(HAVE_CASIN) && defined(HAVE_CLOG) && defined(HAVE_CSQRT)
|
|
#define HAVE_CASIN 1
|
|
complex double casin (complex double z);
|
|
|
|
complex double
|
|
casin (complex double z)
|
|
{
|
|
return -I*clog (I*z + csqrt (1.0-z*z));
|
|
}
|
|
#endif
|
|
|
|
|
|
#if !defined(HAVE_CASINL) && defined(HAVE_CLOGL) && defined(HAVE_CSQRTL)
|
|
#define HAVE_CASINL 1
|
|
complex long double casinl (complex long double z);
|
|
|
|
complex long double
|
|
casinl (complex long double z)
|
|
{
|
|
return -I*clogl (I*z + csqrtl (1.0L-z*z));
|
|
}
|
|
#endif
|
|
|
|
|
|
/* Complex ACOS. Returns wrongly NaN for infinite arguments.
|
|
Algorithm taken from Abramowitz & Stegun. */
|
|
|
|
#if !defined(HAVE_CACOSF) && defined(HAVE_CLOGF) && defined(HAVE_CSQRTF)
|
|
#define HAVE_CACOSF 1
|
|
complex float cacosf (complex float z);
|
|
|
|
complex float
|
|
cacosf (complex float z)
|
|
{
|
|
return -I*clogf (z + I*csqrtf (1.0f-z*z));
|
|
}
|
|
#endif
|
|
|
|
|
|
#if !defined(HAVE_CACOS) && defined(HAVE_CLOG) && defined(HAVE_CSQRT)
|
|
#define HAVE_CACOS 1
|
|
complex double cacos (complex double z);
|
|
|
|
complex double
|
|
cacos (complex double z)
|
|
{
|
|
return -I*clog (z + I*csqrt (1.0-z*z));
|
|
}
|
|
#endif
|
|
|
|
|
|
#if !defined(HAVE_CACOSL) && defined(HAVE_CLOGL) && defined(HAVE_CSQRTL)
|
|
#define HAVE_CACOSL 1
|
|
complex long double cacosl (complex long double z);
|
|
|
|
complex long double
|
|
cacosl (complex long double z)
|
|
{
|
|
return -I*clogl (z + I*csqrtl (1.0L-z*z));
|
|
}
|
|
#endif
|
|
|
|
|
|
/* Complex ATAN. Returns wrongly NaN for infinite arguments.
|
|
Algorithm taken from Abramowitz & Stegun. */
|
|
|
|
#if !defined(HAVE_CATANF) && defined(HAVE_CLOGF)
|
|
#define HAVE_CACOSF 1
|
|
complex float catanf (complex float z);
|
|
|
|
complex float
|
|
catanf (complex float z)
|
|
{
|
|
return I*clogf ((I+z)/(I-z))/2.0f;
|
|
}
|
|
#endif
|
|
|
|
|
|
#if !defined(HAVE_CATAN) && defined(HAVE_CLOG)
|
|
#define HAVE_CACOS 1
|
|
complex double catan (complex double z);
|
|
|
|
complex double
|
|
catan (complex double z)
|
|
{
|
|
return I*clog ((I+z)/(I-z))/2.0;
|
|
}
|
|
#endif
|
|
|
|
|
|
#if !defined(HAVE_CATANL) && defined(HAVE_CLOGL)
|
|
#define HAVE_CACOSL 1
|
|
complex long double catanl (complex long double z);
|
|
|
|
complex long double
|
|
catanl (complex long double z)
|
|
{
|
|
return I*clogl ((I+z)/(I-z))/2.0L;
|
|
}
|
|
#endif
|
|
|
|
|
|
/* Complex ASINH. Returns wrongly NaN for infinite arguments.
|
|
Algorithm taken from Abramowitz & Stegun. */
|
|
|
|
#if !defined(HAVE_CASINHF) && defined(HAVE_CLOGF) && defined(HAVE_CSQRTF)
|
|
#define HAVE_CASINHF 1
|
|
complex float casinhf (complex float z);
|
|
|
|
complex float
|
|
casinhf (complex float z)
|
|
{
|
|
return clogf (z + csqrtf (z*z+1.0f));
|
|
}
|
|
#endif
|
|
|
|
|
|
#if !defined(HAVE_CASINH) && defined(HAVE_CLOG) && defined(HAVE_CSQRT)
|
|
#define HAVE_CASINH 1
|
|
complex double casinh (complex double z);
|
|
|
|
complex double
|
|
casinh (complex double z)
|
|
{
|
|
return clog (z + csqrt (z*z+1.0));
|
|
}
|
|
#endif
|
|
|
|
|
|
#if !defined(HAVE_CASINHL) && defined(HAVE_CLOGL) && defined(HAVE_CSQRTL)
|
|
#define HAVE_CASINHL 1
|
|
complex long double casinhl (complex long double z);
|
|
|
|
complex long double
|
|
casinhl (complex long double z)
|
|
{
|
|
return clogl (z + csqrtl (z*z+1.0L));
|
|
}
|
|
#endif
|
|
|
|
|
|
/* Complex ACOSH. Returns wrongly NaN for infinite arguments.
|
|
Algorithm taken from Abramowitz & Stegun. */
|
|
|
|
#if !defined(HAVE_CACOSHF) && defined(HAVE_CLOGF) && defined(HAVE_CSQRTF)
|
|
#define HAVE_CACOSHF 1
|
|
complex float cacoshf (complex float z);
|
|
|
|
complex float
|
|
cacoshf (complex float z)
|
|
{
|
|
return clogf (z + csqrtf (z-1.0f) * csqrtf (z+1.0f));
|
|
}
|
|
#endif
|
|
|
|
|
|
#if !defined(HAVE_CACOSH) && defined(HAVE_CLOG) && defined(HAVE_CSQRT)
|
|
#define HAVE_CACOSH 1
|
|
complex double cacosh (complex double z);
|
|
|
|
complex double
|
|
cacosh (complex double z)
|
|
{
|
|
return clog (z + csqrt (z-1.0) * csqrt (z+1.0));
|
|
}
|
|
#endif
|
|
|
|
|
|
#if !defined(HAVE_CACOSHL) && defined(HAVE_CLOGL) && defined(HAVE_CSQRTL)
|
|
#define HAVE_CACOSHL 1
|
|
complex long double cacoshl (complex long double z);
|
|
|
|
complex long double
|
|
cacoshl (complex long double z)
|
|
{
|
|
return clogl (z + csqrtl (z-1.0L) * csqrtl (z+1.0L));
|
|
}
|
|
#endif
|
|
|
|
|
|
/* Complex ATANH. Returns wrongly NaN for infinite arguments.
|
|
Algorithm taken from Abramowitz & Stegun. */
|
|
|
|
#if !defined(HAVE_CATANHF) && defined(HAVE_CLOGF)
|
|
#define HAVE_CATANHF 1
|
|
complex float catanhf (complex float z);
|
|
|
|
complex float
|
|
catanhf (complex float z)
|
|
{
|
|
return clogf ((1.0f+z)/(1.0f-z))/2.0f;
|
|
}
|
|
#endif
|
|
|
|
|
|
#if !defined(HAVE_CATANH) && defined(HAVE_CLOG)
|
|
#define HAVE_CATANH 1
|
|
complex double catanh (complex double z);
|
|
|
|
complex double
|
|
catanh (complex double z)
|
|
{
|
|
return clog ((1.0+z)/(1.0-z))/2.0;
|
|
}
|
|
#endif
|
|
|
|
#if !defined(HAVE_CATANHL) && defined(HAVE_CLOGL)
|
|
#define HAVE_CATANHL 1
|
|
complex long double catanhl (complex long double z);
|
|
|
|
complex long double
|
|
catanhl (complex long double z)
|
|
{
|
|
return clogl ((1.0L+z)/(1.0L-z))/2.0L;
|
|
}
|
|
#endif
|
|
|
|
|
|
#if !defined(HAVE_TGAMMA)
|
|
#define HAVE_TGAMMA 1
|
|
double tgamma (double);
|
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/* Fallback tgamma() function. Uses the algorithm from
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http://www.netlib.org/specfun/gamma and references therein. */
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#undef SQRTPI
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#define SQRTPI 0.9189385332046727417803297
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#undef PI
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#define PI 3.1415926535897932384626434
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double
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tgamma (double x)
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{
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int i, n, parity;
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double fact, res, sum, xden, xnum, y, y1, ysq, z;
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static double p[8] = {
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-1.71618513886549492533811e0, 2.47656508055759199108314e1,
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-3.79804256470945635097577e2, 6.29331155312818442661052e2,
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8.66966202790413211295064e2, -3.14512729688483675254357e4,
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-3.61444134186911729807069e4, 6.64561438202405440627855e4 };
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static double q[8] = {
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-3.08402300119738975254353e1, 3.15350626979604161529144e2,
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-1.01515636749021914166146e3, -3.10777167157231109440444e3,
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2.25381184209801510330112e4, 4.75584627752788110767815e3,
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-1.34659959864969306392456e5, -1.15132259675553483497211e5 };
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static double c[7] = { -1.910444077728e-03,
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8.4171387781295e-04, -5.952379913043012e-04,
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7.93650793500350248e-04, -2.777777777777681622553e-03,
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8.333333333333333331554247e-02, 5.7083835261e-03 };
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static const double xminin = 2.23e-308;
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static const double xbig = 171.624;
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static const double xnan = __builtin_nan ("0x0"), xinf = __builtin_inf ();
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static double eps = 0;
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if (eps == 0)
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eps = nextafter (1., 2.) - 1.;
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parity = 0;
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fact = 1;
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n = 0;
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y = x;
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if (isnan (x))
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return x;
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if (y <= 0)
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{
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y = -x;
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y1 = trunc (y);
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res = y - y1;
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if (res != 0)
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{
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if (y1 != trunc (y1*0.5l)*2)
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parity = 1;
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fact = -PI / sin (PI*res);
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y = y + 1;
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}
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else
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return x == 0 ? copysign (xinf, x) : xnan;
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}
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if (y < eps)
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{
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if (y >= xminin)
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res = 1 / y;
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else
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return xinf;
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}
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else if (y < 13)
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{
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y1 = y;
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if (y < 1)
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{
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z = y;
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y = y + 1;
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}
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else
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{
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n = (int)y - 1;
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y = y - n;
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z = y - 1;
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}
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xnum = 0;
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xden = 1;
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for (i = 0; i < 8; i++)
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{
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xnum = (xnum + p[i]) * z;
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xden = xden * z + q[i];
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}
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res = xnum / xden + 1;
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if (y1 < y)
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res = res / y1;
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else if (y1 > y)
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for (i = 1; i <= n; i++)
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{
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res = res * y;
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y = y + 1;
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}
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}
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else
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{
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if (y < xbig)
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{
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ysq = y * y;
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sum = c[6];
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for (i = 0; i < 6; i++)
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sum = sum / ysq + c[i];
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sum = sum/y - y + SQRTPI;
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sum = sum + (y - 0.5) * log (y);
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res = exp (sum);
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}
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else
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return x < 0 ? xnan : xinf;
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}
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if (parity)
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res = -res;
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if (fact != 1)
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res = fact / res;
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return res;
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}
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#endif
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#if !defined(HAVE_LGAMMA)
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#define HAVE_LGAMMA 1
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double lgamma (double);
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/* Fallback lgamma() function. Uses the algorithm from
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http://www.netlib.org/specfun/algama and references therein,
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except for negative arguments (where netlib would return +Inf)
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where we use the following identity:
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lgamma(y) = log(pi/(|y*sin(pi*y)|)) - lgamma(-y)
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*/
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double
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lgamma (double y)
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{
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#undef SQRTPI
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#define SQRTPI 0.9189385332046727417803297
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#undef PI
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#define PI 3.1415926535897932384626434
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#define PNT68 0.6796875
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#define D1 -0.5772156649015328605195174
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#define D2 0.4227843350984671393993777
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#define D4 1.791759469228055000094023
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static double p1[8] = {
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4.945235359296727046734888e0, 2.018112620856775083915565e2,
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2.290838373831346393026739e3, 1.131967205903380828685045e4,
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2.855724635671635335736389e4, 3.848496228443793359990269e4,
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2.637748787624195437963534e4, 7.225813979700288197698961e3 };
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static double q1[8] = {
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6.748212550303777196073036e1, 1.113332393857199323513008e3,
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7.738757056935398733233834e3, 2.763987074403340708898585e4,
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5.499310206226157329794414e4, 6.161122180066002127833352e4,
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3.635127591501940507276287e4, 8.785536302431013170870835e3 };
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static double p2[8] = {
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4.974607845568932035012064e0, 5.424138599891070494101986e2,
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1.550693864978364947665077e4, 1.847932904445632425417223e5,
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1.088204769468828767498470e6, 3.338152967987029735917223e6,
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5.106661678927352456275255e6, 3.074109054850539556250927e6 };
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static double q2[8] = {
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1.830328399370592604055942e2, 7.765049321445005871323047e3,
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1.331903827966074194402448e5, 1.136705821321969608938755e6,
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5.267964117437946917577538e6, 1.346701454311101692290052e7,
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1.782736530353274213975932e7, 9.533095591844353613395747e6 };
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static double p4[8] = {
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1.474502166059939948905062e4, 2.426813369486704502836312e6,
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1.214755574045093227939592e8, 2.663432449630976949898078e9,
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2.940378956634553899906876e10, 1.702665737765398868392998e11,
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4.926125793377430887588120e11, 5.606251856223951465078242e11 };
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static double q4[8] = {
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2.690530175870899333379843e3, 6.393885654300092398984238e5,
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4.135599930241388052042842e7, 1.120872109616147941376570e9,
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1.488613728678813811542398e10, 1.016803586272438228077304e11,
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3.417476345507377132798597e11, 4.463158187419713286462081e11 };
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static double c[7] = {
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-1.910444077728e-03, 8.4171387781295e-04,
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-5.952379913043012e-04, 7.93650793500350248e-04,
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-2.777777777777681622553e-03, 8.333333333333333331554247e-02,
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5.7083835261e-03 };
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static double xbig = 2.55e305, xinf = __builtin_inf (), eps = 0,
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frtbig = 2.25e76;
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int i;
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double corr, res, xden, xm1, xm2, xm4, xnum, ysq;
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if (eps == 0)
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eps = __builtin_nextafter (1., 2.) - 1.;
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if ((y > 0) && (y <= xbig))
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{
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if (y <= eps)
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res = -log (y);
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else if (y <= 1.5)
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{
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if (y < PNT68)
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{
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corr = -log (y);
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xm1 = y;
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}
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else
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{
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corr = 0;
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xm1 = (y - 0.5) - 0.5;
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}
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if ((y <= 0.5) || (y >= PNT68))
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{
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xden = 1;
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xnum = 0;
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for (i = 0; i < 8; i++)
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{
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xnum = xnum*xm1 + p1[i];
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xden = xden*xm1 + q1[i];
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}
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res = corr + (xm1 * (D1 + xm1*(xnum/xden)));
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}
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else
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{
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xm2 = (y - 0.5) - 0.5;
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xden = 1;
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xnum = 0;
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for (i = 0; i < 8; i++)
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{
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xnum = xnum*xm2 + p2[i];
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xden = xden*xm2 + q2[i];
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}
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res = corr + xm2 * (D2 + xm2*(xnum/xden));
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}
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}
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else if (y <= 4)
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{
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xm2 = y - 2;
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xden = 1;
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xnum = 0;
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for (i = 0; i < 8; i++)
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{
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xnum = xnum*xm2 + p2[i];
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xden = xden*xm2 + q2[i];
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}
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res = xm2 * (D2 + xm2*(xnum/xden));
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}
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else if (y <= 12)
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{
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xm4 = y - 4;
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xden = -1;
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xnum = 0;
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for (i = 0; i < 8; i++)
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{
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xnum = xnum*xm4 + p4[i];
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xden = xden*xm4 + q4[i];
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}
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res = D4 + xm4*(xnum/xden);
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}
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else
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{
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res = 0;
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if (y <= frtbig)
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{
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res = c[6];
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ysq = y * y;
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for (i = 0; i < 6; i++)
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res = res / ysq + c[i];
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}
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res = res/y;
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corr = log (y);
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res = res + SQRTPI - 0.5*corr;
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res = res + y*(corr-1);
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}
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}
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else if (y < 0 && __builtin_floor (y) != y)
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{
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/* lgamma(y) = log(pi/(|y*sin(pi*y)|)) - lgamma(-y)
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For abs(y) very close to zero, we use a series expansion to
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the first order in y to avoid overflow. */
|
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if (y > -1.e-100)
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res = -2 * log (fabs (y)) - lgamma (-y);
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else
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res = log (PI / fabs (y * sin (PI * y))) - lgamma (-y);
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}
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else
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res = xinf;
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|
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return res;
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}
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#endif
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#if defined(HAVE_TGAMMA) && !defined(HAVE_TGAMMAF)
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#define HAVE_TGAMMAF 1
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float tgammaf (float);
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float
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tgammaf (float x)
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{
|
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return (float) tgamma ((double) x);
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}
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#endif
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#if defined(HAVE_LGAMMA) && !defined(HAVE_LGAMMAF)
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#define HAVE_LGAMMAF 1
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float lgammaf (float);
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float
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lgammaf (float x)
|
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{
|
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return (float) lgamma ((double) x);
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}
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#endif
|