diff options
Diffstat (limited to 'gsl-1.9/complex')
| -rw-r--r-- | gsl-1.9/complex/ChangeLog | 48 | ||||
| -rw-r--r-- | gsl-1.9/complex/Makefile.am | 15 | ||||
| -rw-r--r-- | gsl-1.9/complex/Makefile.in | 545 | ||||
| -rw-r--r-- | gsl-1.9/complex/TODO | 16 | ||||
| -rw-r--r-- | gsl-1.9/complex/gsl_complex.h | 103 | ||||
| -rw-r--r-- | gsl-1.9/complex/gsl_complex_math.h | 140 | ||||
| -rw-r--r-- | gsl-1.9/complex/math.c | 1007 | ||||
| -rw-r--r-- | gsl-1.9/complex/results.h | 4573 | ||||
| -rw-r--r-- | gsl-1.9/complex/results1.h | 583 | ||||
| -rw-r--r-- | gsl-1.9/complex/results_real.h | 115 | ||||
| -rw-r--r-- | gsl-1.9/complex/test.c | 159 |
11 files changed, 7304 insertions, 0 deletions
diff --git a/gsl-1.9/complex/ChangeLog b/gsl-1.9/complex/ChangeLog new file mode 100644 index 0000000..72edc7d --- /dev/null +++ b/gsl-1.9/complex/ChangeLog @@ -0,0 +1,48 @@ +2003-01-25 Brian Gough <brian.gough@network-theory.co.uk> + + * math.c (gsl_complex_arccsc_real): fixed bug for incorrect sign + of imaginary part when -1<a<0 + +Wed Dec 11 13:17:21 2002 Brian Gough <brian.gough@network-theory.co.uk> + + * math.c (gsl_complex_arg): enforce special case arg(0,0) = 0.0 + +Mon Sep 10 22:57:27 2001 Brian Gough <bjg@network-theory.co.uk> + + * math.c (gsl_complex_div_real gsl_complex_div_real): added + missing functions div_real and div_imag + +Mon Aug 27 18:58:41 2001 Brian Gough <bjg@network-theory.co.uk> + + * test.el: trim the tests down to a more reasonable size + +Thu Aug 9 15:48:48 2001 Brian Gough <bjg@network-theory.co.uk> + + * math.c (gsl_complex_tanh): improve accuracy for large R + +Fri Jul 27 23:29:10 2001 Brian Gough <bjg@network-theory.co.uk> + + * math.c (gsl_complex_cos): avoid returning negative zero for the + imaginary part when the argument is purely real + +Wed Mar 21 14:40:34 2001 Brian Gough <bjg@network-theory.co.uk> + + * gsl_complex.h (GSL_COMPLEX_P): added macro to point to beginning + of complex array within the struct + +Mon Dec 4 12:29:12 2000 Brian Gough <bjg@network-theory.co.uk> + + * math.c (gsl_complex_rect): changed the function gsl_complex_xy + to gsl_complex_rect, since this is more meaningful + +Sun Oct 22 13:55:09 2000 Brian Gough <bjg@network-theory.co.uk> + + * math.c: changed calls to gsl_hypot() to hypot() so that the + system function is used in preference (the configure script will + define hypot to gsl_hypot if hypot is unavailable), similar change + for functions log1p and gsl_log1p also + +Wed Mar 15 11:17:21 2000 Brian Gough <bjg@network-theory.co.uk> + + * gsl_complex.h: moved into complex/ subdirectory from top-level + diff --git a/gsl-1.9/complex/Makefile.am b/gsl-1.9/complex/Makefile.am new file mode 100644 index 0000000..9fd87a9 --- /dev/null +++ b/gsl-1.9/complex/Makefile.am @@ -0,0 +1,15 @@ +noinst_LTLIBRARIES = libgslcomplex.la + +pkginclude_HEADERS = gsl_complex.h gsl_complex_math.h + +#INCLUDES = -I$(top_builddir) -I$(top_srcdir) +INCLUDES = -I$(top_srcdir) + +libgslcomplex_la_SOURCES = math.c + +TESTS = $(check_PROGRAMS) +check_PROGRAMS = test + +test_SOURCES = test.c results.h results1.h results_real.h +test_LDADD = libgslcomplex.la ../err/libgslerr.la ../ieee-utils/libgslieeeutils.la ../err/libgslerr.la ../test/libgsltest.la ../sys/libgslsys.la ../utils/libutils.la + diff --git a/gsl-1.9/complex/Makefile.in b/gsl-1.9/complex/Makefile.in new file mode 100644 index 0000000..2e90920 --- /dev/null +++ b/gsl-1.9/complex/Makefile.in @@ -0,0 +1,545 @@ +# Makefile.in generated by automake 1.9.6 from Makefile.am. +# @configure_input@ + +# Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, +# 2003, 2004, 2005 Free Software Foundation, Inc. +# This Makefile.in is free software; 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This should by +special casing "small" vs "large" arguments as has been done for the +sin,cos,tan versions. + +* Perhaps there is something useful in LCY65 L. A. Lyusternik, +O. A. Chervonenkis, and A. R. Yanpol'skii, Handbook for computing +elementary functions, International Series of Monographs in Pure and +Applied Mathematics, vol. 76, Pergamon Press, Oxford, 1965. + + + diff --git a/gsl-1.9/complex/gsl_complex.h b/gsl-1.9/complex/gsl_complex.h new file mode 100644 index 0000000..f97f5ac --- /dev/null +++ b/gsl-1.9/complex/gsl_complex.h @@ -0,0 +1,103 @@ +/* complex/gsl_complex.h + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman, Brian Gough + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation; either version 2 of the License, or (at + * your option) any later version. + * + * This program is distributed in the hope that it will be useful, but + * WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + * General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. + */ + +#ifndef __GSL_COMPLEX_H__ +#define __GSL_COMPLEX_H__ + +#undef __BEGIN_DECLS +#undef __END_DECLS +#ifdef __cplusplus +# define __BEGIN_DECLS extern "C" { +# define __END_DECLS } +#else +# define __BEGIN_DECLS /* empty */ +# define __END_DECLS /* empty */ +#endif + +__BEGIN_DECLS + + +/* two consecutive built-in types as a complex number */ +typedef double * gsl_complex_packed ; +typedef float * gsl_complex_packed_float ; +typedef long double * gsl_complex_packed_long_double ; + +typedef const double * gsl_const_complex_packed ; +typedef const float * gsl_const_complex_packed_float ; +typedef const long double * gsl_const_complex_packed_long_double ; + + +/* 2N consecutive built-in types as N complex numbers */ +typedef double * gsl_complex_packed_array ; +typedef float * gsl_complex_packed_array_float ; +typedef long double * gsl_complex_packed_array_long_double ; + +typedef const double * gsl_const_complex_packed_array ; +typedef const float * gsl_const_complex_packed_array_float ; +typedef const long double * gsl_const_complex_packed_array_long_double ; + + +/* Yes... this seems weird. Trust us. The point is just that + sometimes you want to make it obvious that something is + an output value. The fact that it lacks a 'const' may not + be enough of a clue for people in some contexts. + */ +typedef double * gsl_complex_packed_ptr ; +typedef float * gsl_complex_packed_float_ptr ; +typedef long double * gsl_complex_packed_long_double_ptr ; + +typedef const double * gsl_const_complex_packed_ptr ; +typedef const float * gsl_const_complex_packed_float_ptr ; +typedef const long double * gsl_const_complex_packed_long_double_ptr ; + + +typedef struct + { + long double dat[2]; + } +gsl_complex_long_double; + +typedef struct + { + double dat[2]; + } +gsl_complex; + +typedef struct + { + float dat[2]; + } +gsl_complex_float; + +#define GSL_REAL(z) ((z).dat[0]) +#define GSL_IMAG(z) ((z).dat[1]) +#define GSL_COMPLEX_P(zp) ((zp)->dat) +#define GSL_COMPLEX_P_REAL(zp) ((zp)->dat[0]) +#define GSL_COMPLEX_P_IMAG(zp) ((zp)->dat[1]) +#define GSL_COMPLEX_EQ(z1,z2) (((z1).dat[0] == (z2).dat[0]) && ((z1).dat[1] == (z2).dat[1])) + +#define GSL_SET_COMPLEX(zp,x,y) do {(zp)->dat[0]=(x); (zp)->dat[1]=(y);} while(0) +#define GSL_SET_REAL(zp,x) do {(zp)->dat[0]=(x);} while(0) +#define GSL_SET_IMAG(zp,y) do {(zp)->dat[1]=(y);} while(0) + +#define GSL_SET_COMPLEX_PACKED(zp,n,x,y) do {*((zp)+2*(n))=(x); *((zp)+(2*(n)+1))=(y);} while(0) + +__END_DECLS + +#endif /* __GSL_COMPLEX_H__ */ diff --git a/gsl-1.9/complex/gsl_complex_math.h b/gsl-1.9/complex/gsl_complex_math.h new file mode 100644 index 0000000..8f521a7 --- /dev/null +++ b/gsl-1.9/complex/gsl_complex_math.h @@ -0,0 +1,140 @@ +/* complex/gsl_complex_math.h + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004 Jorma Olavi Tähtinen, Brian Gough + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation; either version 2 of the License, or (at + * your option) any later version. + * + * This program is distributed in the hope that it will be useful, but + * WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + * General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. + */ + +#ifndef __GSL_COMPLEX_MATH_H__ +#define __GSL_COMPLEX_MATH_H__ +#include <gsl/gsl_complex.h> + +#undef __BEGIN_DECLS +#undef __END_DECLS +#ifdef __cplusplus +#define __BEGIN_DECLS extern "C" { +#define __END_DECLS } +#else +#define __BEGIN_DECLS /* empty */ +#define __END_DECLS /* empty */ +#endif + +__BEGIN_DECLS + +/* Complex numbers */ + +gsl_complex gsl_complex_rect (double x, double y); /* r= real+i*imag */ +gsl_complex gsl_complex_polar (double r, double theta); /* r= r e^(i theta) */ + +#ifdef HAVE_INLINE +extern inline gsl_complex +gsl_complex_rect (double x, double y) +{ /* return z = x + i y */ + gsl_complex z; + GSL_SET_COMPLEX (&z, x, y); + return z; +} +#endif + +#define GSL_COMPLEX_ONE (gsl_complex_rect(1.0,0.0)) +#define GSL_COMPLEX_ZERO (gsl_complex_rect(0.0,0.0)) +#define GSL_COMPLEX_NEGONE (gsl_complex_rect(-1.0,0.0)) + +/* Properties of complex numbers */ + +double gsl_complex_arg (gsl_complex z); /* return arg(z), -pi< arg(z) <=+pi */ +double gsl_complex_abs (gsl_complex z); /* return |z| */ +double gsl_complex_abs2 (gsl_complex z); /* return |z|^2 */ +double gsl_complex_logabs (gsl_complex z); /* return log|z| */ + +/* Complex arithmetic operators */ + +gsl_complex gsl_complex_add (gsl_complex a, gsl_complex b); /* r=a+b */ +gsl_complex gsl_complex_sub (gsl_complex a, gsl_complex b); /* r=a-b */ +gsl_complex gsl_complex_mul (gsl_complex a, gsl_complex b); /* r=a*b */ +gsl_complex gsl_complex_div (gsl_complex a, gsl_complex b); /* r=a/b */ + +gsl_complex gsl_complex_add_real (gsl_complex a, double x); /* r=a+x */ +gsl_complex gsl_complex_sub_real (gsl_complex a, double x); /* r=a-x */ +gsl_complex gsl_complex_mul_real (gsl_complex a, double x); /* r=a*x */ +gsl_complex gsl_complex_div_real (gsl_complex a, double x); /* r=a/x */ + +gsl_complex gsl_complex_add_imag (gsl_complex a, double y); /* r=a+iy */ +gsl_complex gsl_complex_sub_imag (gsl_complex a, double y); /* r=a-iy */ +gsl_complex gsl_complex_mul_imag (gsl_complex a, double y); /* r=a*iy */ +gsl_complex gsl_complex_div_imag (gsl_complex a, double y); /* r=a/iy */ + +gsl_complex gsl_complex_conjugate (gsl_complex z); /* r=conj(z) */ +gsl_complex gsl_complex_inverse (gsl_complex a); /* r=1/a */ +gsl_complex gsl_complex_negative (gsl_complex a); /* r=-a */ + +/* Elementary Complex Functions */ + +gsl_complex gsl_complex_sqrt (gsl_complex z); /* r=sqrt(z) */ +gsl_complex gsl_complex_sqrt_real (double x); /* r=sqrt(x) (x<0 ok) */ + +gsl_complex gsl_complex_pow (gsl_complex a, gsl_complex b); /* r=a^b */ +gsl_complex gsl_complex_pow_real (gsl_complex a, double b); /* r=a^b */ + +gsl_complex gsl_complex_exp (gsl_complex a); /* r=exp(a) */ +gsl_complex gsl_complex_log (gsl_complex a); /* r=log(a) (base e) */ +gsl_complex gsl_complex_log10 (gsl_complex a); /* r=log10(a) (base 10) */ +gsl_complex gsl_complex_log_b (gsl_complex a, gsl_complex b); /* r=log_b(a) (base=b) */ + +/* Complex Trigonometric Functions */ + +gsl_complex gsl_complex_sin (gsl_complex a); /* r=sin(a) */ +gsl_complex gsl_complex_cos (gsl_complex a); /* r=cos(a) */ +gsl_complex gsl_complex_sec (gsl_complex a); /* r=sec(a) */ +gsl_complex gsl_complex_csc (gsl_complex a); /* r=csc(a) */ +gsl_complex gsl_complex_tan (gsl_complex a); /* r=tan(a) */ +gsl_complex gsl_complex_cot (gsl_complex a); /* r=cot(a) */ + +/* Inverse Complex Trigonometric Functions */ + +gsl_complex gsl_complex_arcsin (gsl_complex a); /* r=arcsin(a) */ +gsl_complex gsl_complex_arcsin_real (double a); /* r=arcsin(a) */ +gsl_complex gsl_complex_arccos (gsl_complex a); /* r=arccos(a) */ +gsl_complex gsl_complex_arccos_real (double a); /* r=arccos(a) */ +gsl_complex gsl_complex_arcsec (gsl_complex a); /* r=arcsec(a) */ +gsl_complex gsl_complex_arcsec_real (double a); /* r=arcsec(a) */ +gsl_complex gsl_complex_arccsc (gsl_complex a); /* r=arccsc(a) */ +gsl_complex gsl_complex_arccsc_real (double a); /* r=arccsc(a) */ +gsl_complex gsl_complex_arctan (gsl_complex a); /* r=arctan(a) */ +gsl_complex gsl_complex_arccot (gsl_complex a); /* r=arccot(a) */ + +/* Complex Hyperbolic Functions */ + +gsl_complex gsl_complex_sinh (gsl_complex a); /* r=sinh(a) */ +gsl_complex gsl_complex_cosh (gsl_complex a); /* r=coshh(a) */ +gsl_complex gsl_complex_sech (gsl_complex a); /* r=sech(a) */ +gsl_complex gsl_complex_csch (gsl_complex a); /* r=csch(a) */ +gsl_complex gsl_complex_tanh (gsl_complex a); /* r=tanh(a) */ +gsl_complex gsl_complex_coth (gsl_complex a); /* r=coth(a) */ + +/* Inverse Complex Hyperbolic Functions */ + +gsl_complex gsl_complex_arcsinh (gsl_complex a); /* r=arcsinh(a) */ +gsl_complex gsl_complex_arccosh (gsl_complex a); /* r=arccosh(a) */ +gsl_complex gsl_complex_arccosh_real (double a); /* r=arccosh(a) */ +gsl_complex gsl_complex_arcsech (gsl_complex a); /* r=arcsech(a) */ +gsl_complex gsl_complex_arccsch (gsl_complex a); /* r=arccsch(a) */ +gsl_complex gsl_complex_arctanh (gsl_complex a); /* r=arctanh(a) */ +gsl_complex gsl_complex_arctanh_real (double a); /* r=arctanh(a) */ +gsl_complex gsl_complex_arccoth (gsl_complex a); /* r=arccoth(a) */ + +__END_DECLS + +#endif /* __GSL_COMPLEX_MATH_H__ */ diff --git a/gsl-1.9/complex/math.c b/gsl-1.9/complex/math.c new file mode 100644 index 0000000..19df2ac --- /dev/null +++ b/gsl-1.9/complex/math.c @@ -0,0 +1,1007 @@ +/* complex/math.c + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000 Jorma Olavi Tähtinen, Brian Gough + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation; either version 2 of the License, or (at + * your option) any later version. + * + * This program is distributed in the hope that it will be useful, but + * WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + * General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. + */ + +/* Basic complex arithmetic functions + + * Original version by Jorma Olavi Tähtinen <jotahtin@cc.hut.fi> + * + * Modified for GSL by Brian Gough, 3/2000 + */ + +/* The following references describe the methods used in these + * functions, + * + * T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter Tang, + * "Implementing Complex Elementary Functions Using Exception + * Handling", ACM Transactions on Mathematical Software, Volume 20 + * (1994), pp 215-244, Corrigenda, p553 + * + * Hull et al, "Implementing the complex arcsin and arccosine + * functions using exception handling", ACM Transactions on + * Mathematical Software, Volume 23 (1997) pp 299-335 + * + * Abramowitz and Stegun, Handbook of Mathematical Functions, "Inverse + * Circular Functions in Terms of Real and Imaginary Parts", Formulas + * 4.4.37, 4.4.38, 4.4.39 + */ + +#include <config.h> +#include <math.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_complex.h> +#include <gsl/gsl_complex_math.h> + +/********************************************************************** + * Complex numbers + **********************************************************************/ + +#ifndef HIDE_INLINE_STATIC +gsl_complex +gsl_complex_rect (double x, double y) +{ /* return z = x + i y */ + gsl_complex z; + GSL_SET_COMPLEX (&z, x, y); + return z; +} +#endif + +gsl_complex +gsl_complex_polar (double r, double theta) +{ /* return z = r exp(i theta) */ + gsl_complex z; + GSL_SET_COMPLEX (&z, r * cos (theta), r * sin (theta)); + return z; +} + +/********************************************************************** + * Properties of complex numbers + **********************************************************************/ + +double +gsl_complex_arg (gsl_complex z) +{ /* return arg(z), -pi < arg(z) <= +pi */ + double x = GSL_REAL (z); + double y = GSL_IMAG (z); + + if (x == 0.0 && y == 0.0) + { + return 0; + } + + return atan2 (y, x); +} + +double +gsl_complex_abs (gsl_complex z) +{ /* return |z| */ + return hypot (GSL_REAL (z), GSL_IMAG (z)); +} + +double +gsl_complex_abs2 (gsl_complex z) +{ /* return |z|^2 */ + double x = GSL_REAL (z); + double y = GSL_IMAG (z); + + return (x * x + y * y); +} + +double +gsl_complex_logabs (gsl_complex z) +{ /* return log|z| */ + double xabs = fabs (GSL_REAL (z)); + double yabs = fabs (GSL_IMAG (z)); + double max, u; + + if (xabs >= yabs) + { + max = xabs; + u = yabs / xabs; + } + else + { + max = yabs; + u = xabs / yabs; + } + + /* Handle underflow when u is close to 0 */ + + return log (max) + 0.5 * log1p (u * u); +} + + +/*********************************************************************** + * Complex arithmetic operators + ***********************************************************************/ + +gsl_complex +gsl_complex_add (gsl_complex a, gsl_complex b) +{ /* z=a+b */ + double ar = GSL_REAL (a), ai = GSL_IMAG (a); + double br = GSL_REAL (b), bi = GSL_IMAG (b); + + gsl_complex z; + GSL_SET_COMPLEX (&z, ar + br, ai + bi); + return z; +} + +gsl_complex +gsl_complex_add_real (gsl_complex a, double x) +{ /* z=a+x */ + gsl_complex z; + GSL_SET_COMPLEX (&z, GSL_REAL (a) + x, GSL_IMAG (a)); + return z; +} + +gsl_complex +gsl_complex_add_imag (gsl_complex a, double y) +{ /* z=a+iy */ + gsl_complex z; + GSL_SET_COMPLEX (&z, GSL_REAL (a), GSL_IMAG (a) + y); + return z; +} + + +gsl_complex +gsl_complex_sub (gsl_complex a, gsl_complex b) +{ /* z=a-b */ + double ar = GSL_REAL (a), ai = GSL_IMAG (a); + double br = GSL_REAL (b), bi = GSL_IMAG (b); + + gsl_complex z; + GSL_SET_COMPLEX (&z, ar - br, ai - bi); + return z; +} + +gsl_complex +gsl_complex_sub_real (gsl_complex a, double x) +{ /* z=a-x */ + gsl_complex z; + GSL_SET_COMPLEX (&z, GSL_REAL (a) - x, GSL_IMAG (a)); + return z; +} + +gsl_complex +gsl_complex_sub_imag (gsl_complex a, double y) +{ /* z=a-iy */ + gsl_complex z; + GSL_SET_COMPLEX (&z, GSL_REAL (a), GSL_IMAG (a) - y); + return z; +} + +gsl_complex +gsl_complex_mul (gsl_complex a, gsl_complex b) +{ /* z=a*b */ + double ar = GSL_REAL (a), ai = GSL_IMAG (a); + double br = GSL_REAL (b), bi = GSL_IMAG (b); + + gsl_complex z; + GSL_SET_COMPLEX (&z, ar * br - ai * bi, ar * bi + ai * br); + return z; +} + +gsl_complex +gsl_complex_mul_real (gsl_complex a, double x) +{ /* z=a*x */ + gsl_complex z; + GSL_SET_COMPLEX (&z, x * GSL_REAL (a), x * GSL_IMAG (a)); + return z; +} + +gsl_complex +gsl_complex_mul_imag (gsl_complex a, double y) +{ /* z=a*iy */ + gsl_complex z; + GSL_SET_COMPLEX (&z, -y * GSL_IMAG (a), y * GSL_REAL (a)); + return z; +} + +gsl_complex +gsl_complex_div (gsl_complex a, gsl_complex b) +{ /* z=a/b */ + double ar = GSL_REAL (a), ai = GSL_IMAG (a); + double br = GSL_REAL (b), bi = GSL_IMAG (b); + + double s = 1.0 / gsl_complex_abs (b); + + double sbr = s * br; + double sbi = s * bi; + + double zr = (ar * sbr + ai * sbi) * s; + double zi = (ai * sbr - ar * sbi) * s; + + gsl_complex z; + GSL_SET_COMPLEX (&z, zr, zi); + return z; +} + +gsl_complex +gsl_complex_div_real (gsl_complex a, double x) +{ /* z=a/x */ + gsl_complex z; + GSL_SET_COMPLEX (&z, GSL_REAL (a) / x, GSL_IMAG (a) / x); + return z; +} + +gsl_complex +gsl_complex_div_imag (gsl_complex a, double y) +{ /* z=a/(iy) */ + gsl_complex z; + GSL_SET_COMPLEX (&z, GSL_IMAG (a) / y, - GSL_REAL (a) / y); + return z; +} + +gsl_complex +gsl_complex_conjugate (gsl_complex a) +{ /* z=conj(a) */ + gsl_complex z; + GSL_SET_COMPLEX (&z, GSL_REAL (a), -GSL_IMAG (a)); + return z; +} + +gsl_complex +gsl_complex_negative (gsl_complex a) +{ /* z=-a */ + gsl_complex z; + GSL_SET_COMPLEX (&z, -GSL_REAL (a), -GSL_IMAG (a)); + return z; +} + +gsl_complex +gsl_complex_inverse (gsl_complex a) +{ /* z=1/a */ + double s = 1.0 / gsl_complex_abs (a); + + gsl_complex z; + GSL_SET_COMPLEX (&z, (GSL_REAL (a) * s) * s, -(GSL_IMAG (a) * s) * s); + return z; +} + +/********************************************************************** + * Elementary complex functions + **********************************************************************/ + +gsl_complex +gsl_complex_sqrt (gsl_complex a) +{ /* z=sqrt(a) */ + gsl_complex z; + + if (GSL_REAL (a) == 0.0 && GSL_IMAG (a) == 0.0) + { + GSL_SET_COMPLEX (&z, 0, 0); + } + else + { + double x = fabs (GSL_REAL (a)); + double y = fabs (GSL_IMAG (a)); + double w; + + if (x >= y) + { + double t = y / x; + w = sqrt (x) * sqrt (0.5 * (1.0 + sqrt (1.0 + t * t))); + } + else + { + double t = x / y; + w = sqrt (y) * sqrt (0.5 * (t + sqrt (1.0 + t * t))); + } + + if (GSL_REAL (a) >= 0.0) + { + double ai = GSL_IMAG (a); + GSL_SET_COMPLEX (&z, w, ai / (2.0 * w)); + } + else + { + double ai = GSL_IMAG (a); + double vi = (ai >= 0) ? w : -w; + GSL_SET_COMPLEX (&z, ai / (2.0 * vi), vi); + } + } + + return z; +} + +gsl_complex +gsl_complex_sqrt_real (double x) +{ /* z=sqrt(x) */ + gsl_complex z; + + if (x >= 0) + { + GSL_SET_COMPLEX (&z, sqrt (x), 0.0); + } + else + { + GSL_SET_COMPLEX (&z, 0.0, sqrt (-x)); + } + + return z; +} + +gsl_complex +gsl_complex_exp (gsl_complex a) +{ /* z=exp(a) */ + double rho = exp (GSL_REAL (a)); + double theta = GSL_IMAG (a); + + gsl_complex z; + GSL_SET_COMPLEX (&z, rho * cos (theta), rho * sin (theta)); + return z; +} + +gsl_complex +gsl_complex_pow (gsl_complex a, gsl_complex b) +{ /* z=a^b */ + gsl_complex z; + + if (GSL_REAL (a) == 0 && GSL_IMAG (a) == 0.0) + { + GSL_SET_COMPLEX (&z, 0.0, 0.0); + } + else + { + double logr = gsl_complex_logabs (a); + double theta = gsl_complex_arg (a); + + double br = GSL_REAL (b), bi = GSL_IMAG (b); + + double rho = exp (logr * br - bi * theta); + double beta = theta * br + bi * logr; + + GSL_SET_COMPLEX (&z, rho * cos (beta), rho * sin (beta)); + } + + return z; +} + +gsl_complex +gsl_complex_pow_real (gsl_complex a, double b) +{ /* z=a^b */ + gsl_complex z; + + if (GSL_REAL (a) == 0 && GSL_IMAG (a) == 0) + { + GSL_SET_COMPLEX (&z, 0, 0); + } + else + { + double logr = gsl_complex_logabs (a); + double theta = gsl_complex_arg (a); + double rho = exp (logr * b); + double beta = theta * b; + GSL_SET_COMPLEX (&z, rho * cos (beta), rho * sin (beta)); + } + + return z; +} + +gsl_complex +gsl_complex_log (gsl_complex a) +{ /* z=log(a) */ + double logr = gsl_complex_logabs (a); + double theta = gsl_complex_arg (a); + + gsl_complex z; + GSL_SET_COMPLEX (&z, logr, theta); + return z; +} + +gsl_complex +gsl_complex_log10 (gsl_complex a) +{ /* z = log10(a) */ + return gsl_complex_mul_real (gsl_complex_log (a), 1 / log (10.)); +} + +gsl_complex +gsl_complex_log_b (gsl_complex a, gsl_complex b) +{ + return gsl_complex_div (gsl_complex_log (a), gsl_complex_log (b)); +} + +/*********************************************************************** + * Complex trigonometric functions + ***********************************************************************/ + +gsl_complex +gsl_complex_sin (gsl_complex a) +{ /* z = sin(a) */ + double R = GSL_REAL (a), I = GSL_IMAG (a); + + gsl_complex z; + + if (I == 0.0) + { + /* avoid returing negative zero (-0.0) for the imaginary part */ + + GSL_SET_COMPLEX (&z, sin (R), 0.0); + } + else + { + GSL_SET_COMPLEX (&z, sin (R) * cosh (I), cos (R) * sinh (I)); + } + + return z; +} + +gsl_complex +gsl_complex_cos (gsl_complex a) +{ /* z = cos(a) */ + double R = GSL_REAL (a), I = GSL_IMAG (a); + + gsl_complex z; + + if (I == 0.0) + { + /* avoid returing negative zero (-0.0) for the imaginary part */ + + GSL_SET_COMPLEX (&z, cos (R), 0.0); + } + else + { + GSL_SET_COMPLEX (&z, cos (R) * cosh (I), sin (R) * sinh (-I)); + } + + return z; +} + +gsl_complex +gsl_complex_tan (gsl_complex a) +{ /* z = tan(a) */ + double R = GSL_REAL (a), I = GSL_IMAG (a); + + gsl_complex z; + + if (fabs (I) < 1) + { + double D = pow (cos (R), 2.0) + pow (sinh (I), 2.0); + + GSL_SET_COMPLEX (&z, 0.5 * sin (2 * R) / D, 0.5 * sinh (2 * I) / D); + } + else + { + double u = exp (-I); + double C = 2 * u / (1 - pow (u, 2.0)); + double D = 1 + pow (cos (R), 2.0) * pow (C, 2.0); + + double S = pow (C, 2.0); + double T = 1.0 / tanh (I); + + GSL_SET_COMPLEX (&z, 0.5 * sin (2 * R) * S / D, T / D); + } + + return z; +} + +gsl_complex +gsl_complex_sec (gsl_complex a) +{ /* z = sec(a) */ + gsl_complex z = gsl_complex_cos (a); + return gsl_complex_inverse (z); +} + +gsl_complex +gsl_complex_csc (gsl_complex a) +{ /* z = csc(a) */ + gsl_complex z = gsl_complex_sin (a); + return gsl_complex_inverse(z); +} + + +gsl_complex +gsl_complex_cot (gsl_complex a) +{ /* z = cot(a) */ + gsl_complex z = gsl_complex_tan (a); + return gsl_complex_inverse (z); +} + +/********************************************************************** + * Inverse Complex Trigonometric Functions + **********************************************************************/ + +gsl_complex +gsl_complex_arcsin (gsl_complex a) +{ /* z = arcsin(a) */ + double R = GSL_REAL (a), I = GSL_IMAG (a); + gsl_complex z; + + if (I == 0) + { + z = gsl_complex_arcsin_real (R); + } + else + { + double x = fabs (R), y = fabs (I); + double r = hypot (x + 1, y), s = hypot (x - 1, y); + double A = 0.5 * (r + s); + double B = x / A; + double y2 = y * y; + + double real, imag; + + const double A_crossover = 1.5, B_crossover = 0.6417; + + if (B <= B_crossover) + { + real = asin (B); + } + else + { + if (x <= 1) + { + double D = 0.5 * (A + x) * (y2 / (r + x + 1) + (s + (1 - x))); + real = atan (x / sqrt (D)); + } + else + { + double Apx = A + x; + double D = 0.5 * (Apx / (r + x + 1) + Apx / (s + (x - 1))); + real = atan (x / (y * sqrt (D))); + } + } + + if (A <= A_crossover) + { + double Am1; + + if (x < 1) + { + Am1 = 0.5 * (y2 / (r + (x + 1)) + y2 / (s + (1 - x))); + } + else + { + Am1 = 0.5 * (y2 / (r + (x + 1)) + (s + (x - 1))); + } + + imag = log1p (Am1 + sqrt (Am1 * (A + 1))); + } + else + { + imag = log (A + sqrt (A * A - 1)); + } + + GSL_SET_COMPLEX (&z, (R >= 0) ? real : -real, (I >= 0) ? imag : -imag); + } + + return z; +} + +gsl_complex +gsl_complex_arcsin_real (double a) +{ /* z = arcsin(a) */ + gsl_complex z; + + if (fabs (a) <= 1.0) + { + GSL_SET_COMPLEX (&z, asin (a), 0.0); + } + else + { + if (a < 0.0) + { + GSL_SET_COMPLEX (&z, -M_PI_2, acosh (-a)); + } + else + { + GSL_SET_COMPLEX (&z, M_PI_2, -acosh (a)); + } + } + + return z; +} + +gsl_complex +gsl_complex_arccos (gsl_complex a) +{ /* z = arccos(a) */ + double R = GSL_REAL (a), I = GSL_IMAG (a); + gsl_complex z; + + if (I == 0) + { + z = gsl_complex_arccos_real (R); + } + else + { + double x = fabs (R), y = fabs (I); + double r = hypot (x + 1, y), s = hypot (x - 1, y); + double A = 0.5 * (r + s); + double B = x / A; + double y2 = y * y; + + double real, imag; + + const double A_crossover = 1.5, B_crossover = 0.6417; + + if (B <= B_crossover) + { + real = acos (B); + } + else + { + if (x <= 1) + { + double D = 0.5 * (A + x) * (y2 / (r + x + 1) + (s + (1 - x))); + real = atan (sqrt (D) / x); + } + else + { + double Apx = A + x; + double D = 0.5 * (Apx / (r + x + 1) + Apx / (s + (x - 1))); + real = atan ((y * sqrt (D)) / x); + } + } + + if (A <= A_crossover) + { + double Am1; + + if (x < 1) + { + Am1 = 0.5 * (y2 / (r + (x + 1)) + y2 / (s + (1 - x))); + } + else + { + Am1 = 0.5 * (y2 / (r + (x + 1)) + (s + (x - 1))); + } + + imag = log1p (Am1 + sqrt (Am1 * (A + 1))); + } + else + { + imag = log (A + sqrt (A * A - 1)); + } + + GSL_SET_COMPLEX (&z, (R >= 0) ? real : M_PI - real, (I >= 0) ? -imag : imag); + } + + return z; +} + +gsl_complex +gsl_complex_arccos_real (double a) +{ /* z = arccos(a) */ + gsl_complex z; + + if (fabs (a) <= 1.0) + { + GSL_SET_COMPLEX (&z, acos (a), 0); + } + else + { + if (a < 0.0) + { + GSL_SET_COMPLEX (&z, M_PI, -acosh (-a)); + } + else + { + GSL_SET_COMPLEX (&z, 0, acosh (a)); + } + } + + return z; +} + +gsl_complex +gsl_complex_arctan (gsl_complex a) +{ /* z = arctan(a) */ + double R = GSL_REAL (a), I = GSL_IMAG (a); + gsl_complex z; + + if (I == 0) + { + GSL_SET_COMPLEX (&z, atan (R), 0); + } + else + { + /* FIXME: This is a naive implementation which does not fully + take into account cancellation errors, overflow, underflow + etc. It would benefit from the Hull et al treatment. */ + + double r = hypot (R, I); + + double imag; + + double u = 2 * I / (1 + r * r); + + /* FIXME: the following cross-over should be optimized but 0.1 + seems to work ok */ + + if (fabs (u) < 0.1) + { + imag = 0.25 * (log1p (u) - log1p (-u)); + } + else + { + double A = hypot (R, I + 1); + double B = hypot (R, I - 1); + imag = 0.5 * log (A / B); + } + + if (R == 0) + { + if (I > 1) + { + GSL_SET_COMPLEX (&z, M_PI_2, imag); + } + else if (I < -1) + { + GSL_SET_COMPLEX (&z, -M_PI_2, imag); + } + else + { + GSL_SET_COMPLEX (&z, 0, imag); + }; + } + else + { + GSL_SET_COMPLEX (&z, 0.5 * atan2 (2 * R, ((1 + r) * (1 - r))), imag); + } + } + + return z; +} + +gsl_complex +gsl_complex_arcsec (gsl_complex a) +{ /* z = arcsec(a) */ + gsl_complex z = gsl_complex_inverse (a); + return gsl_complex_arccos (z); +} + +gsl_complex +gsl_complex_arcsec_real (double a) +{ /* z = arcsec(a) */ + gsl_complex z; + + if (a <= -1.0 || a >= 1.0) + { + GSL_SET_COMPLEX (&z, acos (1 / a), 0.0); + } + else + { + if (a >= 0.0) + { + GSL_SET_COMPLEX (&z, 0, acosh (1 / a)); + } + else + { + GSL_SET_COMPLEX (&z, M_PI, -acosh (-1 / a)); + } + } + + return z; +} + +gsl_complex +gsl_complex_arccsc (gsl_complex a) +{ /* z = arccsc(a) */ + gsl_complex z = gsl_complex_inverse (a); + return gsl_complex_arcsin (z); +} + +gsl_complex +gsl_complex_arccsc_real (double a) +{ /* z = arccsc(a) */ + gsl_complex z; + + if (a <= -1.0 || a >= 1.0) + { + GSL_SET_COMPLEX (&z, asin (1 / a), 0.0); + } + else + { + if (a >= 0.0) + { + GSL_SET_COMPLEX (&z, M_PI_2, -acosh (1 / a)); + } + else + { + GSL_SET_COMPLEX (&z, -M_PI_2, acosh (-1 / a)); + } + } + + return z; +} + +gsl_complex +gsl_complex_arccot (gsl_complex a) +{ /* z = arccot(a) */ + gsl_complex z; + + if (GSL_REAL (a) == 0.0 && GSL_IMAG (a) == 0.0) + { + GSL_SET_COMPLEX (&z, M_PI_2, 0); + } + else + { + z = gsl_complex_inverse (a); + z = gsl_complex_arctan (z); + } + + return z; +} + +/********************************************************************** + * Complex Hyperbolic Functions + **********************************************************************/ + +gsl_complex +gsl_complex_sinh (gsl_complex a) +{ /* z = sinh(a) */ + double R = GSL_REAL (a), I = GSL_IMAG (a); + + gsl_complex z; + GSL_SET_COMPLEX (&z, sinh (R) * cos (I), cosh (R) * sin (I)); + return z; +} + +gsl_complex +gsl_complex_cosh (gsl_complex a) +{ /* z = cosh(a) */ + double R = GSL_REAL (a), I = GSL_IMAG (a); + + gsl_complex z; + GSL_SET_COMPLEX (&z, cosh (R) * cos (I), sinh (R) * sin (I)); + return z; +} + +gsl_complex +gsl_complex_tanh (gsl_complex a) +{ /* z = tanh(a) */ + double R = GSL_REAL (a), I = GSL_IMAG (a); + + gsl_complex z; + + if (fabs(R) < 1.0) + { + double D = pow (cos (I), 2.0) + pow (sinh (R), 2.0); + + GSL_SET_COMPLEX (&z, sinh (R) * cosh (R) / D, 0.5 * sin (2 * I) / D); + } + else + { + double D = pow (cos (I), 2.0) + pow (sinh (R), 2.0); + double F = 1 + pow (cos (I) / sinh (R), 2.0); + + GSL_SET_COMPLEX (&z, 1.0 / (tanh (R) * F), 0.5 * sin (2 * I) / D); + } + + return z; +} + +gsl_complex +gsl_complex_sech (gsl_complex a) +{ /* z = sech(a) */ + gsl_complex z = gsl_complex_cosh (a); + return gsl_complex_inverse (z); +} + +gsl_complex +gsl_complex_csch (gsl_complex a) +{ /* z = csch(a) */ + gsl_complex z = gsl_complex_sinh (a); + return gsl_complex_inverse (z); +} + +gsl_complex +gsl_complex_coth (gsl_complex a) +{ /* z = coth(a) */ + gsl_complex z = gsl_complex_tanh (a); + return gsl_complex_inverse (z); +} + +/********************************************************************** + * Inverse Complex Hyperbolic Functions + **********************************************************************/ + +gsl_complex +gsl_complex_arcsinh (gsl_complex a) +{ /* z = arcsinh(a) */ + gsl_complex z = gsl_complex_mul_imag(a, 1.0); + z = gsl_complex_arcsin (z); + z = gsl_complex_mul_imag (z, -1.0); + return z; +} + +gsl_complex +gsl_complex_arccosh (gsl_complex a) +{ /* z = arccosh(a) */ + gsl_complex z = gsl_complex_arccos (a); + z = gsl_complex_mul_imag (z, GSL_IMAG(z) > 0 ? -1.0 : 1.0); + return z; +} + +gsl_complex +gsl_complex_arccosh_real (double a) +{ /* z = arccosh(a) */ + gsl_complex z; + + if (a >= 1) + { + GSL_SET_COMPLEX (&z, acosh (a), 0); + } + else + { + if (a >= -1.0) + { + GSL_SET_COMPLEX (&z, 0, acos (a)); + } + else + { + GSL_SET_COMPLEX (&z, acosh (-a), M_PI); + } + } + + return z; +} + +gsl_complex +gsl_complex_arctanh (gsl_complex a) +{ /* z = arctanh(a) */ + if (GSL_IMAG (a) == 0.0) + { + return gsl_complex_arctanh_real (GSL_REAL (a)); + } + else + { + gsl_complex z = gsl_complex_mul_imag(a, 1.0); + z = gsl_complex_arctan (z); + z = gsl_complex_mul_imag (z, -1.0); + return z; + } +} + +gsl_complex +gsl_complex_arctanh_real (double a) +{ /* z = arctanh(a) */ + gsl_complex z; + + if (a > -1.0 && a < 1.0) + { + GSL_SET_COMPLEX (&z, atanh (a), 0); + } + else + { + GSL_SET_COMPLEX (&z, atanh (1 / a), (a < 0) ? M_PI_2 : -M_PI_2); + } + + return z; +} + +gsl_complex +gsl_complex_arcsech (gsl_complex a) +{ /* z = arcsech(a); */ + gsl_complex t = gsl_complex_inverse (a); + return gsl_complex_arccosh (t); +} + +gsl_complex +gsl_complex_arccsch (gsl_complex a) +{ /* z = arccsch(a) */ + gsl_complex t = gsl_complex_inverse (a); + return gsl_complex_arcsinh (t); +} + +gsl_complex +gsl_complex_arccoth (gsl_complex a) +{ /* z = arccoth(a) */ + gsl_complex t = gsl_complex_inverse (a); + return gsl_complex_arctanh (t); +} diff --git a/gsl-1.9/complex/results.h b/gsl-1.9/complex/results.h new file mode 100644 index 0000000..a8eafee --- /dev/null +++ b/gsl-1.9/complex/results.h @@ -0,0 +1,4573 @@ + {FN (sqrt), ARG(0.0e+00,0.0e+00), RES(0e0, 0.0)}, + {FN (sqrt), ARG(0.0e+00,1.19209289550781250e-07), RES(2.44140625e-4, 2.44140625e-4)}, + {FN (sqrt), ARG(0.0e+00,-1.19209289550781250e-07), RES(2.44140625e-4, -2.44140625e-4)}, + {FN (sqrt), ARG(0.0e+00,5.0e-01), RES(5e-1, 5e-1)}, + {FN (sqrt), ARG(0.0e+00,-5.0e-01), RES(5e-1, -5e-1)}, + {FN (sqrt), ARG(0.0e+00,1.0e+00), RES(7.0710678118654752440e-1, 7.0710678118654752440e-1)}, + {FN (sqrt), ARG(0.0e+00,-1.0e+00), RES(7.0710678118654752440e-1, -7.0710678118654752440e-1)}, + {FN (sqrt), ARG(0.0e+00,2.0e+00), RES(1, 1)}, + {FN (sqrt), ARG(0.0e+00,-2.0e+00), RES(1, -1)}, + {FN (sqrt), ARG(0.0e+00,8.3886080e+06), RES(2048, 2048)}, + {FN (sqrt), ARG(0.0e+00,-8.3886080e+06), RES(2048, -2048)}, + {FN (sqrt), ARG(1.19209289550781250e-07,0.0e+00), RES(3.4526698300124390840e-4, 0.0)}, + {FN (sqrt), ARG(-1.19209289550781250e-07,0.0e+00), RES(0, 3.4526698300124390840e-4)}, + {FN (sqrt), ARG(1.19209289550781250e-07,1.19209289550781250e-07), RES(3.7933934912842707699e-4, 1.5712750315077700799e-4)}, + {FN (sqrt), ARG(1.19209289550781250e-07,-1.19209289550781250e-07), RES(3.7933934912842707699e-4, -1.5712750315077700799e-4)}, + {FN (sqrt), ARG(-1.19209289550781250e-07,1.19209289550781250e-07), RES(1.5712750315077700799e-4, 3.7933934912842707699e-4)}, + {FN (sqrt), ARG(-1.19209289550781250e-07,-1.19209289550781250e-07), RES(1.5712750315077700799e-4, -3.7933934912842707699e-4)}, + {FN (sqrt), ARG(1.19209289550781250e-07,5.0e-01), RES(5.0000005960464832810e-1, 4.9999994039535877732e-1)}, + {FN (sqrt), ARG(1.19209289550781250e-07,-5.0e-01), RES(5.0000005960464832810e-1, -4.9999994039535877732e-1)}, + {FN (sqrt), ARG(-1.19209289550781250e-07,5.0e-01), RES(4.9999994039535877732e-1, 5.0000005960464832810e-1)}, + {FN (sqrt), ARG(-1.19209289550781250e-07,-5.0e-01), RES(4.9999994039535877732e-1, -5.0000005960464832810e-1)}, + {FN (sqrt), ARG(1.19209289550781250e-07,1.0e+00), RES(7.0710682333339729137e-1, 7.0710673903970026958e-1)}, + {FN (sqrt), ARG(1.19209289550781250e-07,-1.0e+00), RES(7.0710682333339729137e-1, -7.0710673903970026958e-1)}, + {FN (sqrt), ARG(-1.19209289550781250e-07,1.0e+00), RES(7.0710673903970026958e-1, 7.0710682333339729137e-1)}, + {FN (sqrt), ARG(-1.19209289550781250e-07,-1.0e+00), RES(7.0710673903970026958e-1, -7.0710682333339729137e-1)}, + {FN (sqrt), ARG(1.19209289550781250e-07,2.0e+00), RES(1.0000000298023228318e0, 9.9999997019767805639e-1)}, + {FN (sqrt), ARG(1.19209289550781250e-07,-2.0e+00), RES(1.0000000298023228318e0, -9.9999997019767805639e-1)}, + {FN (sqrt), ARG(-1.19209289550781250e-07,2.0e+00), RES(9.9999997019767805639e-1, 1.0000000298023228318e0)}, + {FN (sqrt), ARG(-1.19209289550781250e-07,-2.0e+00), RES(9.9999997019767805639e-1, -1.0000000298023228318e0)}, + {FN (sqrt), ARG(1.19209289550781250e-07,8.3886080e+06), RES(2.0480000000000145519e3, 2.0479999999999854481e3)}, + {FN (sqrt), ARG(1.19209289550781250e-07,-8.3886080e+06), RES(2.0480000000000145519e3, -2.0479999999999854481e3)}, + {FN (sqrt), ARG(-1.19209289550781250e-07,8.3886080e+06), RES(2.0479999999999854481e3, 2.0480000000000145519e3)}, + {FN (sqrt), ARG(-1.19209289550781250e-07,-8.3886080e+06), RES(2.0479999999999854481e3, -2.0480000000000145519e3)}, + {FN (sqrt), ARG(5.0e-01,0.0e+00), RES(7.0710678118654752440e-1, 0.0)}, + {FN (sqrt), ARG(-5.0e-01,0.0e+00), RES(0, 7.0710678118654752440e-1)}, + {FN (sqrt), ARG(5.0e-01,1.19209289550781250e-07), RES(7.0710678118655254870e-1, 8.4293697021787464631e-8)}, + {FN (sqrt), ARG(5.0e-01,-1.19209289550781250e-07), RES(7.0710678118655254870e-1, -8.4293697021787464631e-8)}, + {FN (sqrt), ARG(-5.0e-01,1.19209289550781250e-07), RES(8.4293697021787464631e-8, 7.0710678118655254870e-1)}, + {FN (sqrt), ARG(-5.0e-01,-1.19209289550781250e-07), RES(8.4293697021787464631e-8, -7.0710678118655254870e-1)}, + {FN (sqrt), ARG(5.0e-01,5.0e-01), RES(7.7688698701501865367e-1, 3.2179712645279131237e-1)}, + {FN (sqrt), ARG(5.0e-01,-5.0e-01), RES(7.7688698701501865367e-1, -3.2179712645279131237e-1)}, + {FN (sqrt), ARG(-5.0e-01,5.0e-01), RES(3.2179712645279131237e-1, 7.7688698701501865367e-1)}, + {FN (sqrt), ARG(-5.0e-01,-5.0e-01), RES(3.2179712645279131237e-1, -7.7688698701501865367e-1)}, + {FN (sqrt), ARG(5.0e-01,1.0e+00), RES(8.9945371997393363613e-1, 5.5589297025142117199e-1)}, + {FN (sqrt), ARG(5.0e-01,-1.0e+00), RES(8.9945371997393363613e-1, -5.5589297025142117199e-1)}, + {FN (sqrt), ARG(-5.0e-01,1.0e+00), RES(5.5589297025142117199e-1, 8.9945371997393363613e-1)}, + {FN (sqrt), ARG(-5.0e-01,-1.0e+00), RES(5.5589297025142117199e-1, -8.9945371997393363613e-1)}, + {FN (sqrt), ARG(5.0e-01,2.0e+00), RES(1.1317139242778694103e0, 8.8361553087551326576e-1)}, + {FN (sqrt), ARG(5.0e-01,-2.0e+00), RES(1.1317139242778694103e0, -8.8361553087551326576e-1)}, + {FN (sqrt), ARG(-5.0e-01,2.0e+00), RES(8.8361553087551326576e-1, 1.1317139242778694103e0)}, + {FN (sqrt), ARG(-5.0e-01,-2.0e+00), RES(8.8361553087551326576e-1, -1.1317139242778694103e0)}, + {FN (sqrt), ARG(5.0e-01,8.3886080e+06), RES(2.0480000610351571595e3, 2.0479999389648446595e3)}, + {FN (sqrt), ARG(5.0e-01,-8.3886080e+06), RES(2.0480000610351571595e3, -2.0479999389648446595e3)}, + {FN (sqrt), ARG(-5.0e-01,8.3886080e+06), RES(2.0479999389648446595e3, 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RES(2.4293413587832283909e-1, -1.0290855136357461252e0)}, + {FN (sqrt), ARG(1.0e+00,1.0e+00), RES(1.0986841134678099660e0, 4.5508986056222734130e-1)}, + {FN (sqrt), ARG(1.0e+00,-1.0e+00), RES(1.0986841134678099660e0, -4.5508986056222734130e-1)}, + {FN (sqrt), ARG(-1.0e+00,1.0e+00), RES(4.5508986056222734130e-1, 1.0986841134678099660e0)}, + {FN (sqrt), ARG(-1.0e+00,-1.0e+00), RES(4.5508986056222734130e-1, -1.0986841134678099660e0)}, + {FN (sqrt), ARG(1.0e+00,2.0e+00), RES(1.2720196495140689643e0, 7.8615137775742328607e-1)}, + {FN (sqrt), ARG(1.0e+00,-2.0e+00), RES(1.2720196495140689643e0, -7.8615137775742328607e-1)}, + {FN (sqrt), ARG(-1.0e+00,2.0e+00), RES(7.8615137775742328607e-1, 1.2720196495140689643e0)}, + {FN (sqrt), ARG(-1.0e+00,-2.0e+00), RES(7.8615137775742328607e-1, -1.2720196495140689643e0)}, + {FN (sqrt), ARG(1.0e+00,8.3886080e+06), RES(2.0480001220703161380e3, 2.0479998779296911380e3)}, + {FN (sqrt), ARG(1.0e+00,-8.3886080e+06), RES(2.0480001220703161380e3, 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+ {FN (sqrt), ARG(-2.0e+00,5.0e-01), RES(1.7543205637629383228e-1, 1.4250531240639470060e0)}, + {FN (sqrt), ARG(-2.0e+00,-5.0e-01), RES(1.7543205637629383228e-1, -1.4250531240639470060e0)}, + {FN (sqrt), ARG(2.0e+00,1.0e+00), RES(1.4553466902253548081e0, 3.4356074972251246414e-1)}, + {FN (sqrt), ARG(2.0e+00,-1.0e+00), RES(1.4553466902253548081e0, -3.4356074972251246414e-1)}, + {FN (sqrt), ARG(-2.0e+00,1.0e+00), RES(3.4356074972251246414e-1, 1.4553466902253548081e0)}, + {FN (sqrt), ARG(-2.0e+00,-1.0e+00), RES(3.4356074972251246414e-1, -1.4553466902253548081e0)}, + {FN (sqrt), ARG(2.0e+00,2.0e+00), RES(1.5537739740300373073e0, 6.4359425290558262474e-1)}, + {FN (sqrt), ARG(2.0e+00,-2.0e+00), RES(1.5537739740300373073e0, -6.4359425290558262474e-1)}, + {FN (sqrt), ARG(-2.0e+00,2.0e+00), RES(6.4359425290558262474e-1, 1.5537739740300373073e0)}, + {FN (sqrt), ARG(-2.0e+00,-2.0e+00), RES(6.4359425290558262474e-1, -1.5537739740300373073e0)}, + {FN (sqrt), ARG(2.0e+00,8.3886080e+06), RES(2.0480002441406395519e3, 2.0479997558593895519e3)}, + {FN (sqrt), ARG(2.0e+00,-8.3886080e+06), RES(2.0480002441406395519e3, -2.0479997558593895519e3)}, + {FN (sqrt), ARG(-2.0e+00,8.3886080e+06), RES(2.0479997558593895519e3, 2.0480002441406395519e3)}, + {FN (sqrt), ARG(-2.0e+00,-8.3886080e+06), RES(2.0479997558593895519e3, -2.0480002441406395519e3)}, + {FN (sqrt), ARG(8.3886080e+06,0.0e+00), RES(2.8963093757400986599e3, 0.0)}, + {FN (sqrt), ARG(-8.3886080e+06,0.0e+00), RES(0, 2.8963093757400986599e3)}, + {FN (sqrt), ARG(8.3886080e+06,1.19209289550781250e-07), RES(2.8963093757400986599e3, 2.0579515874459976458e-11)}, + {FN (sqrt), ARG(8.3886080e+06,-1.19209289550781250e-07), RES(2.8963093757400986599e3, -2.0579515874459976458e-11)}, + {FN (sqrt), ARG(-8.3886080e+06,1.19209289550781250e-07), RES(2.0579515874459976458e-11, 2.8963093757400986599e3)}, + {FN (sqrt), ARG(-8.3886080e+06,-1.19209289550781250e-07), RES(2.0579515874459976458e-11, -2.8963093757400986599e3)}, + {FN (sqrt), ARG(8.3886080e+06,5.0e-01), RES(2.8963093757400999462e3, 8.6316745750310938767e-5)}, + {FN (sqrt), ARG(8.3886080e+06,-5.0e-01), RES(2.8963093757400999462e3, -8.6316745750310938767e-5)}, + {FN (sqrt), ARG(-8.3886080e+06,5.0e-01), RES(8.6316745750310938767e-5, 2.8963093757400999462e3)}, + {FN (sqrt), ARG(-8.3886080e+06,-5.0e-01), RES(8.6316745750310938767e-5, -2.8963093757400999462e3)}, + {FN (sqrt), ARG(8.3886080e+06,1.0e+00), RES(2.8963093757401038048e3, 1.7263349150062164754e-4)}, + {FN (sqrt), ARG(8.3886080e+06,-1.0e+00), RES(2.8963093757401038048e3, -1.7263349150062164754e-4)}, + {FN (sqrt), ARG(-8.3886080e+06,1.0e+00), RES(1.7263349150062164754e-4, 2.8963093757401038048e3)}, + {FN (sqrt), ARG(-8.3886080e+06,-1.0e+00), RES(1.7263349150062164754e-4, -2.8963093757401038048e3)}, + {FN (sqrt), ARG(8.3886080e+06,2.0e+00), RES(2.8963093757401192395e3, 3.4526698300124145513e-4)}, + {FN (sqrt), ARG(8.3886080e+06,-2.0e+00), RES(2.8963093757401192395e3, -3.4526698300124145513e-4)}, + {FN 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(arccosh_real), -1.19209289550781250e-07, RES(0, 1.570796446004186170e0)}, + {FN (arccosh_real), 0.0e+00, RES(0, 1.5707963267948966192e0)}, + {FN (arccosh_real), 1.19209289550781250e-07, RES(0, 1.5707962075856070684e0)}, + {FN (arccosh_real), 3.45266983001243932001e-04, RES(0, 1.5704510598050355363e0)}, + {FN (arccosh_real), 1.250e-01, RES(0, 1.4454684956268312224e0)}, + {FN (arccosh_real), 5.0e-01, RES(0, 1.0471975511965977462e0)}, + {FN (arccosh_real), 7.50e-01, RES(0, 7.2273424781341561118e-1)}, + {FN (arccosh_real), 1.0e+00, RES(0e0, 0.0)}, + {FN (arccosh_real), 2.0e+00, RES(1.3169578969248167086e0, 0.0)}, + {FN (arccosh_real), 1.0e+01, RES(2.9932228461263808979e0, 0.0)}, + {FN (arctanh_real), -1.0e+01, RES(-1.0033534773107558064e-1, 1.5707963267948966192e0)}, + {FN (arctanh_real), -2.0e+00, RES(-5.4930614433405484570e-1, 1.5707963267948966192e0)}, + {FN (arctanh_real), -7.50e-01, RES(-9.7295507452765665255e-1, 0.0)}, + {FN (arctanh_real), -5.0e-01, RES(-5.4930614433405484570e-1, 0.0)}, + {FN (arctanh_real), -1.250e-01, RES(-1.2565721414045303884e-1, 0.0)}, + {FN (arctanh_real), -3.45266983001243932001e-04, RES(-3.4526699672092216295e-4, 0.0)}, + {FN (arctanh_real), -1.19209289550781250e-07, RES(-1.1920928955078181469e-7, 0.0)}, + {FN (arctanh_real), 0.0e+00, RES(0e0, 0.0)}, + {FN (arctanh_real), 1.19209289550781250e-07, RES(1.1920928955078181469e-7, 0.0)}, + {FN (arctanh_real), 3.45266983001243932001e-04, RES(3.4526699672092216295e-4, 0.0)}, + {FN (arctanh_real), 1.250e-01, RES(1.2565721414045303884e-1, 0.0)}, + {FN (arctanh_real), 5.0e-01, RES(5.4930614433405484570e-1, 0.0)}, + {FN (arctanh_real), 7.50e-01, RES(9.7295507452765665255e-1, 0.0)}, + {FN (arctanh_real), 2.0e+00, RES(5.4930614433405484570e-1, -1.5707963267948966192e0)}, + {FN (arctanh_real), 1.0e+01, RES(1.0033534773107558064e-1, -1.5707963267948966192e0)}, + {FN (arccsc_real), -1.0e+01, RES(-1.0016742116155979635e-1, 0.0)}, + {FN (arccsc_real), -2.0e+00, RES(-5.2359877559829887308e-1, 0.0)}, + {FN (arccsc_real), -1.0e+00, RES(-1.5707963267948966192e0, 0.0)}, + {FN (arccsc_real), -7.50e-01, RES(-1.5707963267948966192e0, 7.9536546122390563053e-1)}, + {FN (arccsc_real), -5.0e-01, RES(-1.5707963267948966192e0, 1.3169578969248167086e0)}, + {FN (arccsc_real), -1.250e-01, RES(-1.5707963267948966192e0, 2.7686593833135738327e0)}, + {FN (arccsc_real), -3.45266983001243932001e-04, RES(-1.5707963267948966192e0, 8.6643397271969925794e0)}, + {FN (arccsc_real), -1.19209289550781250e-07, RES(-1.5707963267948966192e0, 1.6635532333438683873e1)}, + {FN (arccsc_real), 1.19209289550781250e-07, RES(1.5707963267948966192e0, -1.6635532333438683873e1)}, + {FN (arccsc_real), 3.45266983001243932001e-04, RES(1.5707963267948966192e0, -8.6643397271969925794e0)}, + {FN (arccsc_real), 1.250e-01, RES(1.5707963267948966192e0, -2.7686593833135738327e0)}, + {FN (arccsc_real), 5.0e-01, RES(1.5707963267948966192e0, -1.3169578969248167086e0)}, + {FN (arccsc_real), 7.50e-01, RES(1.5707963267948966192e0, -7.9536546122390563053e-1)}, + {FN (arccsc_real), 1.0e+00, RES(1.5707963267948966192e0, 0.0)}, + {FN (arccsc_real), 2.0e+00, RES(5.2359877559829887308e-1, 0.0)}, + {FN (arccsc_real), 1.0e+01, RES(1.0016742116155979635e-1, 0.0)}, + {FN (arcsec_real), -1.0e+01, RES(1.6709637479564564156e0, 0.0)}, + {FN (arcsec_real), -2.0e+00, RES(2.0943951023931954923e0, 0.0)}, + {FN (arcsec_real), -1.0e+00, RES(3.1415926535897932385e0, 0.0)}, + {FN (arcsec_real), -7.50e-01, RES(3.1415926535897932385e0, -7.9536546122390563053e-1)}, + {FN (arcsec_real), -5.0e-01, RES(3.1415926535897932385e0, -1.3169578969248167086e0)}, + {FN (arcsec_real), -1.250e-01, RES(3.1415926535897932385e0, -2.7686593833135738327e0)}, + {FN (arcsec_real), -3.45266983001243932001e-04, RES(3.1415926535897932385e0, -8.6643397271969925794e0)}, + {FN (arcsec_real), -1.19209289550781250e-07, RES(3.1415926535897932385e0, -1.6635532333438683873e1)}, + {FN (arcsec_real), 1.19209289550781250e-07, RES(0, 1.6635532333438683873e1)}, + {FN (arcsec_real), 3.45266983001243932001e-04, RES(0, 8.6643397271969925794e0)}, + {FN (arcsec_real), 1.250e-01, RES(0, 2.7686593833135738327e0)}, + {FN (arcsec_real), 5.0e-01, RES(0, 1.3169578969248167086e0)}, + {FN (arcsec_real), 7.50e-01, RES(0, 7.9536546122390563053e-1)}, + {FN (arcsec_real), 1.0e+00, RES(0e0, 0.0)}, + {FN (arcsec_real), 2.0e+00, RES(1.0471975511965977462e0, 0.0)}, + {FN (arcsec_real), 1.0e+01, RES(1.4706289056333368229e0, 0.0)}, diff --git a/gsl-1.9/complex/test.c b/gsl-1.9/complex/test.c new file mode 100644 index 0000000..7eb31cf --- /dev/null +++ b/gsl-1.9/complex/test.c @@ -0,0 +1,159 @@ +/* complex/test.c + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000 Brian Gough + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation; either version 2 of the License, or (at + * your option) any later version. + * + * This program is distributed in the hope that it will be useful, but + * WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + * General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. + */ + +#include <config.h> +#include <stdlib.h> +#include <stdio.h> +#include <gsl/gsl_ieee_utils.h> +#include <gsl/gsl_test.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_complex.h> +#include <gsl/gsl_complex_math.h> + +struct f +{ + char *name; + double (*f) (gsl_complex z); + double x; + double y; + double fx; + double fy; +}; + +struct fz +{ + char *name; + gsl_complex (*f) (gsl_complex z); + double x; + double y; + double fx; + double fy; +}; + +struct freal +{ + char *name; + gsl_complex (*f) (double x); + double x; + double fx; + double fy; +}; + + +#define FN(x) "gsl_complex_" #x, gsl_complex_ ## x +#define ARG(x,y) x, y +#define RES(x,y) x, y + +struct f list[] = +{ +#include "results1.h" + {"", 0, 0, 0, 0, 0} +}; + + +struct fz listz[] = +{ +#include "results.h" + {"", 0, 0, 0, 0, 0} +}; + +struct freal listreal[] = +{ +#include "results_real.h" + {"", 0, 0, 0, 0} +}; + + +int +main (void) +{ + size_t i = 0; + + gsl_ieee_env_setup(); + + + for (i = 0 ; i < 10; i++) + { + double r = (i - 5.0) * 0.3 ; + double t = 2.0 * M_PI * i / 5 ; + double x = r * cos(t), y = r * sin(t) ; + gsl_complex z = gsl_complex_polar (r, t) ; + gsl_test_rel (GSL_REAL(z), x, 10 * GSL_DBL_EPSILON, "gsl_complex_polar real part at (r=%g,t=%g)", r, t); + + gsl_test_rel (GSL_IMAG(z), y, 10 * GSL_DBL_EPSILON, "gsl_complex_polar imag part at (r=%g,t=%g)", r, t); + } + + i = 0; + + while (list[i].f) + { + struct f t = list[i]; + gsl_complex z = gsl_complex_rect (t.x, t.y); + double f = (t.f) (z); + gsl_test_rel (f, t.fx, 10 * GSL_DBL_EPSILON, "%s at (%g,%g)", t.name, t.x, t.y); + i++; + } + + i = 0; + + while (listz[i].f) + { + struct fz t = listz[i]; + gsl_complex z = gsl_complex_rect (t.x, t.y); + gsl_complex fz = (t.f) (z); + double fx = GSL_REAL (fz), fy = GSL_IMAG (fz); + +#ifdef DEBUG + printf("x = "); gsl_ieee_fprintf_double (stdout, &t.x); printf("\n"); + printf("y = "); gsl_ieee_fprintf_double (stdout, &t.y); printf("\n"); + printf("fx = "); gsl_ieee_fprintf_double (stdout, &fx); printf("\n"); + printf("ex = "); gsl_ieee_fprintf_double (stdout, &t.fx); printf("\n"); + printf("fy = "); gsl_ieee_fprintf_double (stdout, &fy); printf("\n"); + printf("ey = "); gsl_ieee_fprintf_double (stdout, &t.fy); printf("\n"); +#endif + + gsl_test_rel (fx, t.fx, 10 * GSL_DBL_EPSILON, "%s real part at (%g,%g)", t.name, t.x, t.y); + gsl_test_rel (fy, t.fy, 10 * GSL_DBL_EPSILON, "%s imag part at (%g,%g)", t.name, t.x, t.y); + i++; + } + + + i = 0; + + while (listreal[i].f) + { + struct freal t = listreal[i]; + gsl_complex fz = (t.f) (t.x); + double fx = GSL_REAL (fz), fy = GSL_IMAG (fz); + +#ifdef DEBUG + printf("x = "); gsl_ieee_fprintf_double (stdout, &t.x); printf("\n"); + printf("fx = "); gsl_ieee_fprintf_double (stdout, &fx); printf("\n"); + printf("ex = "); gsl_ieee_fprintf_double (stdout, &t.fx); printf("\n"); + printf("fy = "); gsl_ieee_fprintf_double (stdout, &fy); printf("\n"); + printf("ey = "); gsl_ieee_fprintf_double (stdout, &t.fy); printf("\n"); +#endif + + gsl_test_rel (fx, t.fx, 10 * GSL_DBL_EPSILON, "%s real part at (%g,0)", t.name, t.x); + gsl_test_rel (fy, t.fy, 10 * GSL_DBL_EPSILON, "%s imag part at (%g,0)", t.name, t.x); + i++; + } + + exit (gsl_test_summary ()); +} |