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+/* 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
+ * Free Software Foundation, Inc., 59 Temple Place, Suite 330,
+ * Boston, MA 02111-1307, USA.
+ */
+#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: */
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