void xkolmog(sf_complex *trace1, sf_complex *trace2)
/*< convert Fourier-domain cross-correlation to minimum-phase >*/
{
int i1;
const double eps=1.e-32;
for (i1=0; i1 < nk; i1++) {
#ifdef SF_HAS_COMPLEX_H
fft1[i1] = clogf(trace1[i1]+eps)/nk;
#else
fft1[i1] = sf_crmul(clogf(sf_cadd(trace1[i1],sf_cmplx(eps,0.))),
1.0/nk);
#endif
}
/* Inverse transform */
kiss_fft(invs,(const kiss_fft_cpx *) fft1, (kiss_fft_cpx *) trace1);
#ifdef SF_HAS_COMPLEX_H
trace1[0] *= 0.5; trace2[0] = trace1[0];
trace1[nk/2] *= 0.5; trace2[nk/2] = trace1[nk/2];
#else
trace1[0] = sf_crmul(trace1[0], 0.5); trace2[0] = trace1[0];
trace1[nk/2] = sf_crmul(trace1[nk/2],0.5); trace2[nk/2] = trace1[nk/2];
#endif
for (i1=1+nk/2; i1 < nk; i1++) {
trace2[nk-i1] = trace1[i1];
trace1[i1] = sf_cmplx(0.,0.);
trace2[i1] = sf_cmplx(0.,0.);
}
/* Fourier transform */
kiss_fft(forw,(const kiss_fft_cpx *) trace1, (kiss_fft_cpx *) fft1);
kiss_fft(forw,(const kiss_fft_cpx *) trace2, (kiss_fft_cpx *) fft2);
for (i1=0; i1 < nk; i1++) {
#ifdef SF_HAS_COMPLEX_H
fft1[i1] = cexpf(fft1[i1])/nk;
fft2[i1] = cexpf(fft2[i1])/nk;
#else
fft1[i1] = sf_crmul(cexpf(fft1[i1]),1./nk);
fft2[i1] = sf_crmul(cexpf(fft2[i1]),1./nk);
#endif
}
/* Inverse transform */
kiss_fft(invs,(const kiss_fft_cpx *) fft1, (kiss_fft_cpx *) trace1);
kiss_fft(invs,(const kiss_fft_cpx *) fft2, (kiss_fft_cpx *) trace2);
for (i1=0; i1 < nk; i1++) {
trace2[i1] = conjf(trace2[i1]);
}
}
float complex sandbox_cacosf(float complex _z)
{
// return based on quadrant
int sign_i = crealf(_z) > 0;
int sign_q = cimagf(_z) > 0;
if (sign_i == sign_q) {
return - _Complex_I*clogf(_z + csqrtf(_z*_z - 1.0f));
} else {
return - _Complex_I*clogf(_z - csqrtf(_z*_z - 1.0f));
}
// should never get to this state
return 0.0f;
}
float complex
catanf (float complex Z)
{
float complex Res;
float complex Tmp;
float x = __real__ Z;
float y = __imag__ Z;
if ( x == 0.0f && (1.0f - fabsf (y)) == 0.0f)
{
errno = ERANGE;
__real__ Res = HUGE_VALF;
__imag__ Res = HUGE_VALF;
}
else if (isinf (hypotf (x, y)))
{
__real__ Res = (x > 0 ? M_PI_2 : -M_PI_2);
__imag__ Res = 0.0f;
}
else
{
__real__ Tmp = - x;
__imag__ Tmp = 1.0f - y;
__real__ Res = x;
__imag__ Res = y + 1.0f;
Tmp = clogf (Res/Tmp);
__real__ Res = - 0.5f * __imag__ Tmp;
__imag__ Res = 0.5f * __real__ Tmp;
}
return Res;
}
float complex casinf(float complex z)
{
float complex w;
float x, y;
x = crealf(z);
y = cimagf(z);
w = CMPLXF(1.0 - (x - y)*(x + y), -2.0*x*y);
return clogf(CMPLXF(-y, x) + csqrtf(w));
}
float complex
cacoshf(float complex z)
{
float complex w;
#if 0 /* does not give the principal value */
w = I * cacosf(z);
#else
w = clogf(z + csqrtf(z + 1) * csqrtf(z - 1));
#endif
return w;
}
ld = ccoshl(ld); TEST_TRACE(C99 7.3.6.5) d = csinh(d); f = csinhf(f); ld = csinhl(ld); TEST_TRACE(C99 7.3.6.6) d = ctanh(d); f = ctanhf(f); ld = ctanhl(ld); TEST_TRACE(C99 7.3.7.1) d = cexp(d); f = cexpf(f); ld = cexpl(ld); TEST_TRACE(C99 7.3.7.2) d = clog(d); f = clogf(f); ld = clogl(ld); TEST_TRACE(C99 7.3.8.1) d = cabs(d); f = cabsf(f); ld = cabsl(ld); TEST_TRACE(C99 7.3.8.2) d = cpow(d, d); f = cpowf(f, f); ld = cpowl(ld, ld); TEST_TRACE(C99 7.3.8.3) d = csqrt(d); f = csqrtf(f); ld = csqrtl(ld); TEST_TRACE(C99 7.3.9.1) d = carg(d);
float complex
cpowf (float complex base, float complex power)
{
return cexpf (power * clogf (base));
}
complex float
cacosf (complex float z)
{
return -I*clogf (z + I*csqrtf (1.0f-z*z));
}
int main() {
unsigned int n=32; // number of tests
unsigned int d=2; // number items per line
// data arrays
float complex z[n];
float complex test[n];
unsigned int i;
float complex err_max = 0.0f;
for (i=0; i<n; i++) {
// generate random complex number
z[i] = 4.0f*(2.0f*sandbox_randf() - 1.0f) +
4.0f*(2.0f*sandbox_randf() - 1.0f) * _Complex_I;
test[i] = clogf(z[i]);
float complex logz_hat = sandbox_clogf(z[i]);
float complex err = test[i] - logz_hat;
printf("%3u: z=%6.2f+j%6.2f, log(z)=%6.2f+j%6.2f (%6.2f+j%6.2f) e=%12.4e\n",
i,
crealf(z[i]), cimagf(z[i]),
crealf(test[i]), cimagf(test[i]),
crealf(logz_hat), cimagf(logz_hat),
cabsf(err));
if ( cabsf(err) > cabsf(err_max) )
err_max = err;
}
printf("maximum error: %12.4e;\n", cabsf(err_max));
//
// print autotest lines
//
printf("\n");
printf(" float complex z[%u] = {\n ", n);
for (i=0; i<n; i++) {
printf("%12.4e+_Complex_I*%12.4e", crealf(z[i]), cimagf(z[i]));
if ( i == n-1)
printf(" ");
else if ( ((i+1)%d)==0 )
printf(",\n ");
else
printf(", ");
}
printf("};\n");
printf("\n");
printf(" float complex test[%u] = {\n ", n);
for (i=0; i<n; i++) {
printf("%12.4e+_Complex_I*%12.4e", crealf(test[i]), cimagf(test[i]));
if ( i == n-1)
printf(" ");
else if ( ((i+1)%d)==0 )
printf(",\n ");
else
printf(", ");
}
printf("};\n");
printf("done.\n");
return 0;
}
float complex sandbox_catanf(float complex _z)
{
return 0.5f*_Complex_I*clogf( (1.0f-_Complex_I*_z)/(1.0f+_Complex_I*_z) );
}
complex float
catanhf (complex float z)
{
return clogf ((1.0f+z)/(1.0f-z))/2.0f;
}
complex float
cacoshf (complex float z)
{
return clogf (z + csqrtf (z-1.0f) * csqrtf (z+1.0f));
}
complex float
casinhf (complex float z)
{
return clogf (z + csqrtf (z*z+1.0f));
}
complex float
catanf (complex float z)
{
return I*clogf ((I+z)/(I-z))/2.0f;
}
/* pow(base, power) = cexp (power * clog (base)) */
GFC_COMPLEX_4
cpowf (GFC_COMPLEX_4 base, GFC_COMPLEX_4 power)
{
return cexpf (power * clogf (base));
}
float complex
casinf(float complex z)
{
float complex w;
float complex ca, ct, zz, z2;
float x, y;
x = crealf(z);
y = cimagf(z);
#if 0 /* MD: test is incorrect, casin(>1) is defined */
if (y == 0.0f) {
if (fabsf(x) > 1.0) {
w = M_PI_2 + 0.0f * I;
#if 0
mtherr ("casin", DOMAIN);
#endif
} else {
w = asinf(x) + 0.0f * I;
}
return w;
}
#endif
/* Power series expansion */
/*
b = cabsf(z);
if( b < 0.125 )
{
z2.r = (x - y) * (x + y);
z2.i = 2.0 * x * y;
cn = 1.0;
n = 1.0;
ca.r = x;
ca.i = y;
sum.r = x;
sum.i = y;
do
{
ct.r = z2.r * ca.r - z2.i * ca.i;
ct.i = z2.r * ca.i + z2.i * ca.r;
ca.r = ct.r;
ca.i = ct.i;
cn *= n;
n += 1.0;
cn /= n;
n += 1.0;
b = cn/n;
ct.r *= b;
ct.i *= b;
sum.r += ct.r;
sum.i += ct.i;
b = fabsf(ct.r) + fabsf(ct.i);
}
while( b > MACHEP );
w->r = sum.r;
w->i = sum.i;
return;
}
*/
ca = x + y * I;
ct = ca * I;
/* sqrt( 1 - z*z) */
/* cmul( &ca, &ca, &zz ) */
/*x * x - y * y */
zz = (x - y) * (x + y) + (2.0f * x * y) * I;
zz = 1.0f - crealf(zz) - cimagf(zz) * I;
z2 = csqrtf(zz);
zz = ct + z2;
zz = clogf(zz);
/* multiply by 1/i = -i */
w = zz * (-1.0f * I);
return w;
}
void
docomplexf (void)
{
#ifndef NO_FLOAT
complex float ca, cb, cc;
float f1;
ca = 1.0 + 1.0 * I;
cb = 1.0 - 1.0 * I;
f1 = cabsf (ca);
fprintf (stdout, "cabsf : %f\n", f1);
cc = cacosf (ca);
fprintf (stdout, "cacosf : %f %fi\n", crealf (cc),
cimagf (cc));
cc = cacoshf (ca);
fprintf (stdout, "cacoshf: %f %fi\n", crealf (cc),
cimagf (cc));
f1 = cargf (ca);
fprintf (stdout, "cargf : %f\n", f1);
cc = casinf (ca);
fprintf (stdout, "casinf : %f %fi\n", crealf (cc),
cimagf (cc));
cc = casinhf (ca);
fprintf (stdout, "casinhf: %f %fi\n", crealf (cc),
cimagf (cc));
cc = catanf (ca);
fprintf (stdout, "catanf : %f %fi\n", crealf (cc),
cimagf (cc));
cc = catanhf (ca);
fprintf (stdout, "catanhf: %f %fi\n", crealf (cc),
cimagf (cc));
cc = ccosf (ca);
fprintf (stdout, "ccosf : %f %fi\n", crealf (cc),
cimagf (cc));
cc = ccoshf (ca);
fprintf (stdout, "ccoshf : %f %fi\n", crealf (cc),
cimagf (cc));
cc = cexpf (ca);
fprintf (stdout, "cexpf : %f %fi\n", crealf (cc),
cimagf (cc));
f1 = cimagf (ca);
fprintf (stdout, "cimagf : %f\n", f1);
cc = clogf (ca);
fprintf (stdout, "clogf : %f %fi\n", crealf (cc),
cimagf (cc));
cc = conjf (ca);
fprintf (stdout, "conjf : %f %fi\n", crealf (cc),
cimagf (cc));
cc = cpowf (ca, cb);
fprintf (stdout, "cpowf : %f %fi\n", crealf (cc),
cimagf (cc));
cc = cprojf (ca);
fprintf (stdout, "cprojf : %f %fi\n", crealf (cc),
cimagf (cc));
f1 = crealf (ca);
fprintf (stdout, "crealf : %f\n", f1);
cc = csinf (ca);
fprintf (stdout, "csinf : %f %fi\n", crealf (cc),
cimagf (cc));
cc = csinhf (ca);
fprintf (stdout, "csinhf : %f %fi\n", crealf (cc),
cimagf (cc));
cc = csqrtf (ca);
fprintf (stdout, "csqrtf : %f %fi\n", crealf (cc),
cimagf (cc));
cc = ctanf (ca);
fprintf (stdout, "ctanf : %f %fi\n", crealf (cc),
cimagf (cc));
cc = ctanhf (ca);
fprintf (stdout, "ctanhf : %f %fi\n", crealf (cc),
cimagf (cc));
#endif
}
float complex
casinf(float complex z)
{
float complex w;
float x, y;
static float complex ca, ct, zz, z2;
/*
float cn, n;
static float a, b, s, t, u, v, y2;
static cmplxf sum;
*/
x = crealf(z);
y = cimagf(z);
#if 0
if(y == 0.0f) {
if(fabsf(x) > 1.0f) {
w = (float)M_PI_2 + 0.0f * I;
/*mtherr( "casinf", DOMAIN );*/
}
else {
w = asinf (x) + 0.0f * I;
}
return (w);
}
#endif
/* Power series expansion */
/*
b = cabsf(z);
if(b < 0.125) {
z2.r = (x - y) * (x + y);
z2.i = 2.0 * x * y;
cn = 1.0;
n = 1.0;
ca.r = x;
ca.i = y;
sum.r = x;
sum.i = y;
do {
ct.r = z2.r * ca.r - z2.i * ca.i;
ct.i = z2.r * ca.i + z2.i * ca.r;
ca.r = ct.r;
ca.i = ct.i;
cn *= n;
n += 1.0;
cn /= n;
n += 1.0;
b = cn/n;
ct.r *= b;
ct.i *= b;
sum.r += ct.r;
sum.i += ct.i;
b = fabsf(ct.r) + fabsf(ct.i);
}
while(b > MACHEPF);
w->r = sum.r;
w->i = sum.i;
return;
}
*/
ca = x + y * I;
ct = ca * I; /* iz */
/* sqrt( 1 - z*z) */
/* cmul( &ca, &ca, &zz ) */
/*x * x - y * y */
zz = (x - y) * (x + y) + (2.0f * x * y) * I;
zz = 1.0f - crealf(zz) - cimagf(zz) * I;
z2 = csqrtf (zz);
zz = ct + z2;
zz = clogf (zz);
/* multiply by 1/i = -i */
w = zz * (-1.0f * I);
return (w);
}
complex float
casinf (complex float z)
{
return -I*clogf (I*z + csqrtf (1.0f-z*z));
}