complex_float complex_cot(complex_float c1){
// this is 1/tan = 1/(sin/cos) = cos/sin
complex_float cpx_sin = complex_sin(c1);
complex_float cpx_cos = complex_cos(c1);
complex_float r = complex_div(cpx_cos,cpx_sin);
return r;
}
void
complex_gamma (complex_t *dst, complex_t const *src)
{
if (complex_real_p (src)) {
complex_init (dst, gnm_gamma (src->re), 0);
} else if (src->re < 0) {
/* Gamma(z) = pi / (sin(pi*z) * Gamma(-z+1)) */
complex_t a, b, mz;
complex_init (&mz, -src->re, -src->im);
complex_fact (&a, &mz);
complex_init (&b,
M_PIgnum * gnm_fmod (src->re, 2),
M_PIgnum * src->im);
/* Hmm... sin overflows when b.im is large. */
complex_sin (&b, &b);
complex_mul (&a, &a, &b);
complex_init (&b, M_PIgnum, 0);
complex_div (dst, &b, &a);
} else {
complex_t zmh, zmhd2, zmhpg, f, f2, p, q, pq;
int i;
i = G_N_ELEMENTS(lanczos_num) - 1;
complex_init (&p, lanczos_num[i], 0);
complex_init (&q, lanczos_denom[i], 0);
while (--i >= 0) {
complex_mul (&p, &p, src);
p.re += lanczos_num[i];
complex_mul (&q, &q, src);
q.re += lanczos_denom[i];
}
complex_div (&pq, &p, &q);
complex_init (&zmh, src->re - 0.5, src->im);
complex_init (&zmhpg, zmh.re + lanczos_g, zmh.im);
complex_init (&zmhd2, zmh.re * 0.5, zmh.im * 0.5);
complex_pow (&f, &zmhpg, &zmhd2);
zmh.re = -zmh.re; zmh.im = -zmh.im;
complex_exp (&f2, &zmh);
complex_mul (&f2, &f, &f2);
complex_mul (&f2, &f2, &f);
complex_mul (dst, &f2, &pq);
}
}
void sinc(double x, double y) {
if (x == 0.0 && y == 0.0) {
resultR = 1.0; resultI = 0;
}
else {
if (x != 0.0 || y != 0.0) {
complex_sin(M_PI*x, M_PI*y);
division(resultR, resultI, M_PI*x, M_PI*y);
}
else {
if (rasf > 0.0) {
printf("\nError in function domain.\n\n ==> For normalized sinc function the valid domain is [-INF, INF].\n\n");
printf(" ==> Your function argument: ");
complexNumber(x, y);
}
}
}
}
/* do the iterations
* if binary is true, check halfplane of last iteration.
* if demrange is non zero, estimate lower bound of dist(c, M)
*
* DEM - Distance Estimator Method
* Based on Peitgen & Saupe's "The Science of Fractal Images"
*
* ALPHA - level sets of closest return.
* INDEX - index of ALPHA.
* Based on Peitgen & Richter's "The Beauty of Fractals" (Fig 33,34)
*
* LYAPUNOV - lyapunov exponent estimate
* Based on an idea by Jan Thor
*
*/
static int
reps(complex c, double p, int r, Bool binary, interior_t interior, double demrange, Bool zpow, Bool zsin)
{
int rep;
int escaped = 0;
complex t;
int escape = (int) ((demrange == 0) ? ESCAPE :
ESCAPE*ESCAPE*ESCAPE*ESCAPE); /* 2 more iterations */
complex t1;
complex dt;
double L = 0.0;
double l2;
double dl2 = 1.0;
double alpha2 = ESCAPE;
int index = 0;
#if defined(USE_LOG)
double log_top = log((double) r);
#endif
t = c;
dt.real = 1; dt.imag = 0;
for (rep = 0; rep < r; rep++) {
t1 = t;
ipow(&t, (int) p);
add(&t, c);
if (zpow)
add(&t, complex_pow(t1, t1));
if (zsin)
add(&t, complex_sin(t1));
l2 = t.real * t.real + t.imag * t.imag;
if (l2 <= alpha2) {
alpha2 = l2;
index = rep;
}
if (l2 >= escape) {
escaped = 1;
break;
} else if (interior == LYAPUNOV) {
/* Crude estimate of Lyapunov exponent. The stronger the
attractor, the more negative the exponent will be. */
/* n=N
L = lim 1/N * Sum log(abs(dx(n+1)/dx(n)))/ln(2)
N->inf n=1
*/
L += log(sqrt(l2));
}
if (demrange){
/* compute dt/dc
* p-1
* dt = p * t * dt + 1
* k+1 k k
*/
/* Note this is incorrect for zpow or zsin, but a correct
implementation is too slow to be useful. */
dt.real *= p; dt.imag *= p;
if(p > 2) ipow(&t1, (int) (p - 1));
mult(&dt, t1);
dt.real += 1;
dl2 = dt.real * dt.real + dt.imag * dt.imag;
if (dl2 >= 1e300) {
escaped = 2;
break;
}
}
}
if (escaped) {
if(demrange) {
double mt = sqrt(t1.real * t1.real + t1.imag * t1.imag);
/* distance estimate */
double dist = 0.5 * mt * log(mt) / sqrt(dl2);
/* scale for viewing. Allow black when showing interior. */
rep = (int) (((interior > NONE)?0:1) + 10*r*dist/demrange);
if(rep > r-1) rep = r-1; /* chop into color range */
}
if(binary && t.imag > 0)
rep = (r + rep / 2) % r; /* binary decomp */
#ifdef USE_LOG
if ( rep > 0 )
rep = (int) (r * log((double) rep)/log_top); /* Log Scale */
#endif
return rep;
} else if (interior == LYAPUNOV) {
return -(int)(L/M_LN2) % r;
} else if (interior == INDEX) {
return 1 + index;
} else if (interior == ALPHA) {
return (int) (r * sqrt(alpha2));
} else
return r;
}
complex_float complex_tan(complex_float c1){
complex_float cpx_sin = complex_sin(c1);
complex_float cpx_cos = complex_cos(c1);
complex_float r = complex_div( cpx_sin, cpx_cos );
return r;
}
complex_float complex_csc(complex_float c1){
// this is 1/sin
complex_float cpx_sin = complex_sin(c1);
complex_float r = complex_div(complex_make(1.0f),cpx_sin);
return r;
}
