/usr/include/bse/bsemath.hh is in libbse-dev 0.7.8-1.
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#ifndef __BSE_MATH_H__
#define __BSE_MATH_H__
#include <bse/bsedefs.hh>
#include <bse/bseieee754.hh> /* provides math.h */
G_BEGIN_DECLS
/* --- constants --- */
/* PI is defined in bseieee754.hh */
#define BSE_1_DIV_PI (0.3183098861837906715377675267450287240689) // 1/pi
#define BSE_PI_DIV_2 (1.570796326794896619231321691639751442099) // pi/2
#define BSE_2_DIV_PI (0.6366197723675813430755350534900574481378) // 2/pi
#define BSE_2_DIV_SQRT_PI (1.128379167095512573896158903121545171688) // 2/sqrt(pi)
#define BSE_2_DIV_LN2 (2.88539008177792681471984936200378427485329) // 2/ln(2)
#define BSE_PI_DIV_4 (0.7853981633974483096156608458198757210493) // pi/4
#define BSE_E (2.718281828459045235360287471352662497757) // e^1
#define BSE_LOG2E (1.442695040888963407359924681001892137427) // log_2(e^1)
#define BSE_LOG10E (0.4342944819032518276511289189166050822944) // log_10(e^1)
#define BSE_LN2 (0.6931471805599453094172321214581765680755) // ln(2)
#define BSE_SQRT2 (1.41421356237309504880168872420969807857) // sqrt(2)
#define BSE_1_DIV_SQRT2 (0.7071067811865475244008443621048490392848) // 1/sqrt(2)
#define BSE_LN4 (1.386294361119890618834464242916353136151) // ln(4)
#define BSE_LN10 (2.302585092994045684017991454684364207601) // ln(10)
#define BSE_LOG2_10 (3.321928094887362347870319429489390175865) // log_2(10)
#define BSE_LOG2POW20_10 (0.1660964047443681173935159714744695087932) // log_2(10)/20
#define BSE_2_POW_1_DIV_12 (1.059463094359295264561825294946341700779) // 2^(1/12)
#define BSE_LN_2_POW_1_DIV_12 (5.776226504666210911810267678818138067296e-2) // ln(2^(1/12))
#define BSE_LN_2_POW_1_DIV_1200_d (5.776226504666210911810267678818138067296e-4) // ln(2^(1/1200))
#define BSE_2_POW_1_DIV_72 (1.009673533228510862192521401118605073603) // 2^(1/72)
#define BSE_LN_2_POW_1_DIV_72 (9.62704417444368485301711279803023011216e-3) // ln(2^(1/72))
#define BSE_DECIBEL20_FACTOR (8.68588963806503655302257837833210164588794) // 20.0 / ln (10.0)
#define BSE_DECIBEL10_FACTOR (4.34294481903251827651128918916605082294397) // 10.0 / ln (10.0)
#define BSE_1_DIV_DECIBEL20_FACTOR (0.1151292546497022842008995727342182103801) // ln (10) / 20
#define BSE_COMPLEX_ONE (bse_complex (1, 0))
/* --- structures --- */
typedef struct {
double re;
double im;
} BseComplex;
/* --- complex numbers --- */
static inline BseComplex bse_complex (double re,
double im);
static inline BseComplex bse_complex_polar (double abs,
double arg);
static inline BseComplex bse_complex_add (BseComplex c1,
BseComplex c2);
static inline BseComplex bse_complex_add3 (BseComplex c1,
BseComplex c2,
BseComplex c3);
static inline BseComplex bse_complex_sub (BseComplex c1,
BseComplex c2);
static inline BseComplex bse_complex_sub3 (BseComplex c1,
BseComplex c2,
BseComplex c3);
static inline BseComplex bse_complex_scale (BseComplex c1,
double scale);
static inline BseComplex bse_complex_mul (BseComplex c1,
BseComplex c2);
static inline BseComplex bse_complex_mul3 (BseComplex c1,
BseComplex c2,
BseComplex c3);
static inline BseComplex bse_complex_div (BseComplex a,
BseComplex b);
static inline BseComplex bse_complex_reciprocal (BseComplex c);
static inline BseComplex bse_complex_sqrt (BseComplex z);
static inline BseComplex bse_complex_conj (BseComplex c); /* {re, -im} */
static inline BseComplex bse_complex_id (BseComplex c);
static inline BseComplex bse_complex_inv (BseComplex c); /* {-re, -im} */
static inline double bse_complex_abs (BseComplex c);
static inline double bse_complex_arg (BseComplex c);
static inline BseComplex bse_complex_sin (BseComplex c);
static inline BseComplex bse_complex_cos (BseComplex c);
static inline BseComplex bse_complex_tan (BseComplex c);
static inline BseComplex bse_complex_sinh (BseComplex c);
static inline BseComplex bse_complex_cosh (BseComplex c);
static inline BseComplex bse_complex_tanh (BseComplex c);
char* bse_complex_str (BseComplex c);
char* bse_complex_list (uint n_points,
BseComplex *points,
const char *indent);
void bse_complex_gnuplot (const char *file_name,
uint n_points,
BseComplex *points);
/* --- polynomials --- */
/* example, degree=2: 5+2x+7x^2 => a[0..degree] = { 5, 2, 7 } */
static inline void bse_poly_add (uint degree,
double *a, /* a[0..degree] */
double *b);
static inline void bse_poly_sub (uint order,
double *a, /* [0..degree] */
double *b);
static inline void bse_poly_mul (double *p, /* out:[0..aorder+border] */
uint aorder,
const double *a, /* in:[0..aorder] */
uint border,
const double *b); /* in:[0..border] */
static inline void bse_poly_scale (uint order,
double *a, /* [0..degree] */
double scale);
static inline void bse_poly_xscale (uint order,
double *a, /* [0..degree] */
double xscale);
static inline double bse_poly_eval (uint degree,
double *a, /* [0..degree] */
double x);
void bse_poly_complex_roots (uint poly_degree,
double *a, /* [0..degree] (degree+1 elements) */
BseComplex *roots); /* [degree] */
void bse_poly_from_re_roots (uint poly_degree,
double *a, /* [0..degree] */
BseComplex *roots);
void bse_cpoly_from_roots (uint poly_degree,
BseComplex *c, /* [0..degree] */
BseComplex *roots);
static inline void bse_cpoly_mul_monomial (uint degree, /* _new_ degree */
BseComplex *c, /* in:[0..degree-1] out:[0..degree] */
BseComplex root); /* c(x) *= (x^1 - root) */
static inline void bse_cpoly_mul_reciprocal (uint degree, /* _new_ degree */
BseComplex *c, /* in:[0..degree-1] out:[0..degree] */
BseComplex root); /* c(x) *= (1 - root * x^-1) */
static inline void bse_cpoly_mul (BseComplex *p, /* out:[0..aorder+border] */
uint aorder,
BseComplex *a, /* in:[0..aorder] */
uint border,
BseComplex *b); /* in:[0..border] */
gboolean bse_poly2_droots (gdouble roots[2],
gdouble a,
gdouble b,
gdouble c);
char* bse_poly_str (uint degree,
double *a,
const char *var);
char* bse_poly_str1 (uint degree,
double *a,
const char *var);
/* --- transformations --- */
double bse_temp_freq (double kammer_freq,
int semitone_delta);
/* --- miscellaneous --- */
double bse_bit_depth_epsilon (guint n_bits); /* 1..32 */
gint bse_rand_int (void); /* +-G_MAXINT */
gfloat bse_rand_float (void); /* -1.0..1.0 */
gint bse_rand_bool (void); /* random bit */
void bse_float_gnuplot (const char *file_name,
double xstart,
double xstep,
uint n_ypoints,
const float *ypoints);
/* --- implementations --- */
static inline BseComplex
bse_complex (double re,
double im)
{
BseComplex r;
r.re = re;
r.im = im;
return r;
}
static inline BseComplex
bse_complex_polar (double abs,
double arg)
{
return bse_complex (abs * cos (arg), abs * sin (arg));
}
static inline BseComplex
bse_complex_add (BseComplex c1,
BseComplex c2)
{
return bse_complex (c1.re + c2.re, c1.im + c2.im);
}
static inline BseComplex
bse_complex_add3 (BseComplex c1,
BseComplex c2,
BseComplex c3)
{
return bse_complex (c1.re + c2.re + c3.re, c1.im + c2.im + c3.im);
}
static inline BseComplex
bse_complex_sub (BseComplex c1,
BseComplex c2)
{
return bse_complex (c1.re - c2.re, c1.im - c2.im);
}
static inline BseComplex
bse_complex_sub3 (BseComplex c1,
BseComplex c2,
BseComplex c3)
{
return bse_complex (c1.re - c2.re - c3.re, c1.im - c2.im - c3.im);
}
static inline BseComplex
bse_complex_scale (BseComplex c1,
double scale)
{
return bse_complex (c1.re * scale, c1.im * scale);
}
static inline BseComplex
bse_complex_mul (BseComplex c1,
BseComplex c2)
{
return bse_complex (c1.re * c2.re - c1.im * c2.im, c1.re * c2.im + c1.im * c2.re);
}
static inline BseComplex
bse_complex_mul3 (BseComplex c1,
BseComplex c2,
BseComplex 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 bse_complex (aec - bde - adf - bcf, ade + bce + acf - bdf);
}
static inline BseComplex
bse_complex_div (BseComplex a,
BseComplex b)
{
BseComplex 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 BseComplex
bse_complex_reciprocal (BseComplex 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 BseComplex
bse_complex_sqrt (BseComplex z)
{
if (z.re == 0.0 && z.im == 0.0)
return z;
else
{
BseComplex 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 BseComplex
bse_complex_conj (BseComplex c)
{
return bse_complex (c.re, -c.im);
}
static inline BseComplex
bse_complex_inv (BseComplex c)
{
return bse_complex (-c.re, -c.im);
}
static inline BseComplex
bse_complex_id (BseComplex c)
{
return c;
}
static inline double
bse_complex_abs (BseComplex 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
bse_complex_arg (BseComplex c)
{
double a = atan2 (c.im, c.re);
return a;
}
static inline BseComplex
bse_complex_sin (BseComplex c)
{
return bse_complex (sin (c.re) * cosh (c.im), cos (c.re) * sinh (c.im));
}
static inline BseComplex
bse_complex_cos (BseComplex c)
{
return bse_complex (cos (c.re) * cosh (c.im), - sin (c.re) * sinh (c.im));
}
static inline BseComplex
bse_complex_tan (BseComplex c)
{
return bse_complex_div (bse_complex (tan (c.re), tanh (c.im)),
bse_complex (1.0, -tan (c.re) * tanh (c.im)));
}
static inline BseComplex
bse_complex_sinh (BseComplex c)
{
return bse_complex (sinh (c.re) * cos (c.im), cosh (c.re) * sin (c.im));
}
static inline BseComplex
bse_complex_cosh (BseComplex c)
{
return bse_complex (cosh (c.re) * cos (c.im), sinh (c.re) * sin (c.im));
}
static inline BseComplex
bse_complex_tanh (BseComplex c)
{
return bse_complex_div (bse_complex_sinh (c),
bse_complex_cosh (c));
}
static inline void
bse_poly_add (uint degree,
double *a,
double *b)
{
uint i;
for (i = 0; i <= degree; i++)
a[i] += b[i];
}
static inline void
bse_poly_sub (uint degree,
double *a,
double *b)
{
uint i;
for (i = 0; i <= degree; i++)
a[i] -= b[i];
}
static inline void
bse_poly_mul (double *p, /* out:[0..aorder+border] */
uint aorder,
const double *a, /* in:[0..aorder] */
uint border,
const double *b) /* in:[0..border] */
{
uint i;
for (i = aorder + border; i > 0; i--)
{
uint 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
bse_cpoly_mul_monomial (uint degree,
BseComplex *c,
BseComplex root)
{
uint j;
c[degree] = c[degree - 1];
for (j = degree - 1; j >= 1; j--)
c[j] = bse_complex_sub (c[j - 1], bse_complex_mul (c[j], root));
c[0] = bse_complex_mul (c[0], bse_complex_inv (root));
}
static inline void
bse_cpoly_mul_reciprocal (uint degree,
BseComplex *c,
BseComplex root)
{
uint j;
c[degree] = bse_complex_mul (c[degree - 1], bse_complex_inv (root));
for (j = degree - 1; j >= 1; j--)
c[j] = bse_complex_sub (c[j], bse_complex_mul (c[j - 1], root));
/* c[0] = c[0]; */
}
static inline void
bse_cpoly_mul (BseComplex *p, /* [0..aorder+border] */
uint aorder,
BseComplex *a,
uint border,
BseComplex *b)
{
uint i;
for (i = aorder + border; i > 0; i--)
{
BseComplex t;
uint j;
t = bse_complex (0, 0);
for (j = i - MIN (i, border); j <= MIN (aorder, i); j++)
t = bse_complex_add (t, bse_complex_mul (a[j], b[i - j]));
p[i] = t;
}
p[0] = bse_complex_mul (a[0], b[0]);
}
static inline void
bse_poly_scale (uint degree,
double *a,
double scale)
{
uint i;
for (i = 0; i <= degree; i++)
a[i] *= scale;
}
static inline void
bse_poly_xscale (uint degree,
double *a,
double xscale)
{
double scale = xscale;
uint i;
for (i = 1; i <= degree; i++)
{
a[i] *= scale;
scale *= xscale;
}
}
static inline double
bse_poly_eval (uint degree,
double *a,
double x)
{
double sum = a[degree];
while (degree--)
sum = sum * x + a[degree];
return sum;
}
G_END_DECLS
#endif /* __BSE_MATH_H__ */ /* vim: set ts=8 sw=2 sts=2: */
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