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arts/flow/gsl/gslmath.h

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Copy of aRts for Trinity modifications git-svn-id: svn://anonsvn.kde.org/home/kde/branches/trinity/dependencies/arts@1070145 283d02a7-25f6-0310-bc7c-ecb5cbfe19da
15 years ago
/* GSL - Generic Sound Layer
* Copyright (C) 2001 Stefan Westerfeld and Tim Janik
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2 of the License, or (at your option) any later version.
*
* This library 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
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General
* Public License along with this library; if not, write to the
Updated obsolete GPL license addresses to current GPL address git-svn-id: svn://anonsvn.kde.org/home/kde/branches/trinity/dependencies/arts@1070573 283d02a7-25f6-0310-bc7c-ecb5cbfe19da
15 years ago
* Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
* Boston, MA 02110-1301, USA.
Copy of aRts for Trinity modifications git-svn-id: svn://anonsvn.kde.org/home/kde/branches/trinity/dependencies/arts@1070145 283d02a7-25f6-0310-bc7c-ecb5cbfe19da
15 years ago
*/
#ifndef __GSL_MATH_H__
#define __GSL_MATH_H__
#include <gsl/gslieee754.h>
#include <gsl/gsldefs.h>
#include <math.h>
#ifdef __cplusplus
extern "C" {
#endif /* __cplusplus */
/* --- constants --- */
#define GSL_PI (3.1415926535897932384626433832795029 /* pi */)
#define GSL_PI_DIV_2 (1.5707963267948966192313216916397514 /* pi/2 */)
#define GSL_PI_DIV_4 (0.7853981633974483096156608458198757 /* pi/4 */)
#define GSL_1_DIV_PI (0.3183098861837906715377675267450287 /* 1/pi */)
#define GSL_2_DIV_PI (0.6366197723675813430755350534900574 /* 2/pi */)
#define GSL_2_DIV_SQRT_PI (1.1283791670955125738961589031215452 /* 2/sqrt(pi) */)
#define GSL_SQRT2 (1.4142135623730950488016887242096981 /* sqrt(2) */)
#define GSL_1_DIV_SQRT2 (0.7071067811865475244008443621048490 /* 1/sqrt(2) */)
#define GSL_E (2.7182818284590452353602874713526625 /* e */)
#define GSL_LOG2E (1.4426950408889634073599246810018922 /* log_2(e) */)
#define GSL_LOG10E (0.4342944819032518276511289189166051 /* log_10(e) */)
#define GSL_LN2 (0.6931471805599453094172321214581766 /* ln(2) */)
#define GSL_LN10 (2.3025850929940456840179914546843642 /* ln(10) */)
#define GSL_2_POW_1_DIV_12 (1.0594630943592952645618252949463417 /* 2^(1/12) */)
#define GSL_2_POW_1_DIV_72 (1.0096735332285108621925214011186051 /* 2^(1/72) */)
#define GSL_LN_2_POW_1_DIV_12 (0.0577622650466621091181026767881814 /* ln(2^(1/12)) */)
#define GSL_LN_2_POW_1_DIV_72 (0.0096270441744436848530171127980302 /* ln(2^(1/72)) */)
#define GSL_LOG2_10 (3.3219280948873623478703194294893902 /* log_2(10) */)
#define GSL_LOG2POW20_10 (0.1660964047443681173935159714744695 /* log_2(10)/20 */)
/* --- structures --- */
struct _GslComplex
{
double re;
double im;
};
/* --- float/double signbit extraction --- */
#ifdef signbit
# define gsl_float_sign(dblflt) (signbit (dblflt))
#else
# define gsl_float_sign(dblflt) ((dblflt) < -0.0) /* good enough for us */
#endif
/* --- complex numbers --- */
static inline GslComplex gsl_complex (double re,
double im);
static inline GslComplex gsl_complex_polar (double abs,
double arg);
static inline GslComplex gsl_complex_add (GslComplex c1,
GslComplex c2);
static inline GslComplex gsl_complex_add3 (GslComplex c1,
GslComplex c2,
GslComplex c3);
static inline GslComplex gsl_complex_sub (GslComplex c1,
GslComplex c2);
static inline GslComplex gsl_complex_sub3 (GslComplex c1,
GslComplex c2,
GslComplex c3);
static inline GslComplex gsl_complex_scale (GslComplex c1,
double scale);
static inline GslComplex gsl_complex_mul (GslComplex c1,
GslComplex c2);
static inline GslComplex gsl_complex_mul3 (GslComplex c1,
GslComplex c2,
GslComplex c3);
static inline GslComplex gsl_complex_div (GslComplex a,
GslComplex b);
static inline GslComplex gsl_complex_reciprocal (GslComplex c);
static inline GslComplex gsl_complex_sqrt (GslComplex z);
static inline GslComplex gsl_complex_conj (GslComplex c); /* {re, -im} */
static inline GslComplex gsl_complex_id (GslComplex c);
static inline GslComplex gsl_complex_inv (GslComplex c); /* {-re, -im} */
static inline double gsl_complex_abs (GslComplex c);
static inline double gsl_complex_arg (GslComplex c);
static inline GslComplex gsl_complex_sin (GslComplex c);
static inline GslComplex gsl_complex_cos (GslComplex c);
static inline GslComplex gsl_complex_tan (GslComplex c);
static inline GslComplex gsl_complex_sinh (GslComplex c);
static inline GslComplex gsl_complex_cosh (GslComplex c);
static inline GslComplex gsl_complex_tanh (GslComplex c);
char* gsl_complex_str (GslComplex c);
char* gsl_complex_list (unsigned int n_points,
GslComplex *points,
const char *indent);
void gsl_complex_gnuplot (const char *file_name,
unsigned int n_points,
GslComplex *points);
/* --- polynomials --- */
/* example, degree=2: 5+2x+7x^2 => a[0..degree] = { 5, 2, 7 } */
static inline void gsl_poly_add (unsigned int degree,
double *a, /* a[0..degree] */
double *b);
static inline void gsl_poly_sub (unsigned int order,
double *a, /* [0..degree] */
double *b);
static inline void gsl_poly_mul (double *p, /* out:[0..aorder+border] */
unsigned int aorder,
const double *a, /* in:[0..aorder] */
unsigned int border,
const double *b); /* in:[0..border] */
static inline void gsl_poly_scale (unsigned int order,
double *a, /* [0..degree] */
double scale);
static inline void gsl_poly_xscale (unsigned int order,
double *a, /* [0..degree] */
double xscale);
static inline double gsl_poly_eval (unsigned int degree,
double *a, /* [0..degree] */
double x);
void gsl_poly_complex_roots (unsigned int poly_degree,
double *a, /* [0..degree] (degree+1 elements) */
GslComplex *roots); /* [degree] */
void gsl_poly_from_re_roots (unsigned int poly_degree,
double *a, /* [0..degree] */
GslComplex *roots);
void gsl_cpoly_from_roots (unsigned int poly_degree,
GslComplex *c, /* [0..degree] */
GslComplex *roots);
static inline void gsl_cpoly_mul_monomial (unsigned int degree, /* _new_ degree */
GslComplex *c, /* in:[0..degree-1] out:[0..degree] */
GslComplex root); /* c(x) *= (x^1 - root) */
static inline void gsl_cpoly_mul_reciprocal (unsigned int degree, /* _new_ degree */
GslComplex *c, /* in:[0..degree-1] out:[0..degree] */
GslComplex root); /* c(x) *= (1 - root * x^-1) */
static inline void gsl_cpoly_mul (GslComplex *p, /* out:[0..aorder+border] */
unsigned int aorder,
GslComplex *a, /* in:[0..aorder] */
unsigned int border,
GslComplex *b); /* in:[0..border] */
char* gsl_poly_str (unsigned int degree,
double *a,
const char *var);
char* gsl_poly_str1 (unsigned int degree,
double *a,
const char *var);
/* --- transformations --- */
double gsl_temp_freq (double kammer_freq,
int halftone_delta);
/* --- miscellaneous --- */
double gsl_bit_depth_epsilon (guint n_bits); /* 1..32 */
/* --- ellipses --- */
double gsl_ellip_rf (double x,
double y,
double z);
double gsl_ellip_F (double phi,
double ak);
double gsl_ellip_sn (double u,
double emmc);
double gsl_ellip_asn (double y,
double emmc);
GslComplex gsl_complex_ellip_asn (GslComplex y,
GslComplex emmc);
GslComplex gsl_complex_ellip_sn (GslComplex u,
GslComplex emmc);
/* --- implementations --- */
static inline GslComplex
gsl_complex (double re,
double im)
{
GslComplex r;
r.re = re;
r.im = im;
return r;
}
static inline GslComplex
gsl_complex_polar (double abs,
double arg)
{
return gsl_complex (abs * cos (arg), abs * sin (arg));
}
static inline GslComplex
gsl_complex_add (GslComplex c1,
GslComplex c2)
{
return gsl_complex (c1.re + c2.re, c1.im + c2.im);
}
static inline GslComplex
gsl_complex_add3 (GslComplex c1,
GslComplex c2,
GslComplex c3)
{
return gsl_complex (c1.re + c2.re + c3.re, c1.im + c2.im + c3.im);
}
static inline GslComplex
gsl_complex_sub (GslComplex c1,
GslComplex c2)
{
return gsl_complex (c1.re - c2.re, c1.im - c2.im);
}
static inline GslComplex
gsl_complex_sub3 (GslComplex c1,
GslComplex c2,
GslComplex c3)
{
return gsl_complex (c1.re - c2.re - c3.re, c1.im - c2.im - c3.im);
}
static inline GslComplex
gsl_complex_scale (GslComplex c1,
double scale)
{
return gsl_complex (c1.re * scale, c1.im * scale);
}
static inline GslComplex
gsl_complex_mul (GslComplex c1,
GslComplex c2)
{
return gsl_complex (c1.re * c2.re - c1.im * c2.im, c1.re * c2.im + c1.im * c2.re);
}
static inline GslComplex
gsl_complex_mul3 (GslComplex c1,
GslComplex c2,
GslComplex c3)
{
double aec = c1.re * c2.re * c3.re;
double bde = c1.im * c2.im * c3.re;
double adf = c1.re * c2.im * c3.im;
double bcf = c1.im * c2.re * c3.im;
double ade = c1.re * c2.im * c3.re;
double bce = c1.im * c2.re * c3.re;
double acf = c1.re * c2.re * c3.im;
double bdf = c1.im * c2.im * c3.im;
return gsl_complex (aec - bde - adf - bcf, ade + bce + acf - bdf);
}
static inline GslComplex
gsl_complex_div (GslComplex a,
GslComplex b)
{
GslComplex c;
if (fabs (b.re) >= fabs (b.im))
{
double r = b.im / b.re, den = b.re + r * b.im;
c.re = (a.re + r * a.im) / den;
c.im = (a.im - r * a.re) / den;
}
else
{
double r = b.re / b.im, den = b.im + r * b.re;
c.re = (a.re * r + a.im) / den;
c.im = (a.im * r - a.re) / den;
}
return c;
}
static inline GslComplex
gsl_complex_reciprocal (GslComplex c)
{
if (fabs (c.re) >= fabs (c.im))
{
double r = c.im / c.re, den = c.re + r * c.im;
c.re = 1. / den;
c.im = - r / den;
}
else
{
double r = c.re / c.im, den = c.im + r * c.re;
c.re = r / den;
c.im = - 1. / den;
}
return c;
}
static inline GslComplex
gsl_complex_sqrt (GslComplex z)
{
if (z.re == 0.0 && z.im == 0.0)
return z;
else
{
GslComplex c;
double w, x = fabs (z.re), y = fabs (z.im);
if (x >= y)
{
double r = y / x;
w = sqrt (x) * sqrt (0.5 * (1.0 + sqrt (1.0 + r * r)));
}
else
{
double r = x / y;
w = sqrt (y) * sqrt (0.5 * (r + sqrt (1.0 + r * r)));
}
if (z.re >= 0.0)
{
c.re = w;
c.im = z.im / (2.0 * w);
}
else
{
c.im = z.im >= 0 ? w : -w;
c.re = z.im / (2.0 * c.im);
}
return c;
}
}
static inline GslComplex
gsl_complex_conj (GslComplex c)
{
return gsl_complex (c.re, -c.im);
}
static inline GslComplex
gsl_complex_inv (GslComplex c)
{
return gsl_complex (-c.re, -c.im);
}
static inline GslComplex
gsl_complex_id (GslComplex c)
{
return c;
}
static inline double
gsl_complex_abs (GslComplex c)
{
/* compute (a^2 + b^2)^(1/2) without destructive underflow or overflow */
double absa = fabs (c.re), absb = fabs (c.im);
return (absa > absb ?
absb == 0.0 ? absa :
absa * sqrt (1.0 + (absb / absa) * (absb / absa)) :
absb == 0.0 ? 0.0 :
absb * sqrt (1.0 + (absa / absb) * (absa / absb)));
}
static inline double
gsl_complex_arg (GslComplex c)
{
double a = atan2 (c.im, c.re);
return a;
}
static inline GslComplex
gsl_complex_sin (GslComplex c)
{
return gsl_complex (sin (c.re) * cosh (c.im), cos (c.re) * sinh (c.im));
}
static inline GslComplex
gsl_complex_cos (GslComplex c)
{
return gsl_complex (cos (c.re) * cosh (c.im), - sin (c.re) * sinh (c.im));
}
static inline GslComplex
gsl_complex_tan (GslComplex c)
{
return gsl_complex_div (gsl_complex (tan (c.re), tanh (c.im)),
gsl_complex (1.0, -tan (c.re) * tanh (c.im)));
}
static inline GslComplex
gsl_complex_sinh (GslComplex c)
{
return gsl_complex (sinh (c.re) * cos (c.im), cosh (c.re) * sin (c.im));
}
static inline GslComplex
gsl_complex_cosh (GslComplex c)
{
return gsl_complex (cosh (c.re) * cos (c.im), sinh (c.re) * sin (c.im));
}
static inline GslComplex
gsl_complex_tanh (GslComplex c)
{
return gsl_complex_div (gsl_complex_sinh (c),
gsl_complex_cosh (c));
}
static inline void
gsl_poly_add (unsigned int degree,
double *a,
double *b)
{
unsigned int i;
for (i = 0; i <= degree; i++)
a[i] += b[i];
}
static inline void
gsl_poly_sub (unsigned int degree,
double *a,
double *b)
{
unsigned int i;
for (i = 0; i <= degree; i++)
a[i] -= b[i];
}
static inline void
gsl_poly_mul (double *p, /* out:[0..aorder+border] */
unsigned int aorder,
const double *a, /* in:[0..aorder] */
unsigned int border,
const double *b) /* in:[0..border] */
{
unsigned int i;
for (i = aorder + border; i > 0; i--)
{
unsigned int j;
double t = 0;
for (j = i - MIN (border, i); j <= MIN (aorder, i); j++)
t += a[j] * b[i - j];
p[i] = t;
}
p[0] = a[0] * b[0];
}
static inline void
gsl_cpoly_mul_monomial (unsigned int degree,
GslComplex *c,
GslComplex root)
{
unsigned int j;
c[degree] = c[degree - 1];
for (j = degree - 1; j >= 1; j--)
c[j] = gsl_complex_sub (c[j - 1], gsl_complex_mul (c[j], root));
c[0] = gsl_complex_mul (c[0], gsl_complex_inv (root));
}
static inline void
gsl_cpoly_mul_reciprocal (unsigned int degree,
GslComplex *c,
GslComplex root)
{
unsigned int j;
c[degree] = gsl_complex_mul (c[degree - 1], gsl_complex_inv (root));
for (j = degree - 1; j >= 1; j--)
c[j] = gsl_complex_sub (c[j], gsl_complex_mul (c[j - 1], root));
/* c[0] = c[0]; */
}
static inline void
gsl_cpoly_mul (GslComplex *p, /* [0..aorder+border] */
unsigned int aorder,
GslComplex *a,
unsigned int border,
GslComplex *b)
{
unsigned int i;
for (i = aorder + border; i > 0; i--)
{
GslComplex t;
unsigned int j;
t = gsl_complex (0, 0);
for (j = i - MIN (i, border); j <= MIN (aorder, i); j++)
t = gsl_complex_add (t, gsl_complex_mul (a[j], b[i - j]));
p[i] = t;
}
p[0] = gsl_complex_mul (a[0], b[0]);
}
static inline void
gsl_poly_scale (unsigned int degree,
double *a,
double scale)
{
unsigned int i;
for (i = 0; i <= degree; i++)
a[i] *= scale;
}
static inline void
gsl_poly_xscale (unsigned int degree,
double *a,
double xscale)
{
double scale = xscale;
unsigned int i;
for (i = 1; i <= degree; i++)
{
a[i] *= scale;
scale *= xscale;
}
}
static inline double
gsl_poly_eval (unsigned int degree,
double *a,
double x)
{
double sum = a[degree];
while (degree--)
sum = sum * x + a[degree];
return sum;
}
#ifdef __cplusplus
}
#endif /* __cplusplus */
#endif /* __GSL_MATH_H__ */ /* vim: set ts=8 sw=2 sts=2: */