inline Complex PlasmaDispersion(Complex z) {
static const double SQRT_PI = 1.7724538509055160272981674833411451;
Complex Z;
Complex z2 = z*z;
// sometimes imaginary part is too high, due to test functions, limit
if(cimag(z) > 25.) z = creal(z) + 25.I;
// Use asymptotic expansions for large values |z| >> 1
// See definition in NRL Plasma Formulary
if(creal(z*z) > 100) {
const double x = creal(z);
const double y = cimag(z);
const double sigma = (y > 0.) ? 0 : (( y == 0) ? 1. : 2.);
Complex z4 = z2*z2;
Complex z6 = z4*z2;
Z = 1.0I * SQRT_PI * sigma * cexp(-z2) - 1./z * ( 1. + 1./(2.*z2) + 3./(4.*z4) + 15./(8.*z6));
}
else Z = 1.0I * SQRT_PI * cexp(- z2) * cerfc(- 1.0I * z);
return Z;
};
int main(void)
{
const int n = 50000000;
{
float re, im, rer, imr;
re = 0.5, im = 0.5;
cerff(re, im, &rer, &imr);
printf("cerf (%21.14e,%21.14e) = (%21.14e, %21.14e)\n", re, im, rer, imr);
cerfcf(re, im, &rer, &imr);
printf("cerfc(%21.14e,%21.14e) = (%21.14e, %21.14e)\n", re, im, rer, imr);
re = -0.5, im = 0.5;
cerff(re, im, &rer, &imr);
printf("cerf (%21.14e,%21.14e) = (%21.14e, %21.14e)\n", re, im, rer, imr);
cerfcf(re, im, &rer, &imr);
printf("cerfc(%21.14e,%21.14e) = (%21.14e, %21.14e)\n", re, im, rer, imr);
double t0 = clock();
for (int i=0; i < n; i++) cerff(re, im, &rer, &imr);
double t1 = clock();
printf("cerff: %.3f Mcalls/sec\n", n/((t1-t0)/CLOCKS_PER_SEC)/1000000);
}
{
double re, im, rer, imr;
re = 0.5, im = 0.5;
cerf(re, im, &rer, &imr);
printf("cerf (%21.14e,%21.14e) = (%21.14e, %21.14e)\n", re, im, rer, imr);
cerfc(re, im, &rer, &imr);
printf("cerfc(%21.14e,%21.14e) = (%21.14e, %21.14e)\n", re, im, rer, imr);
re = -0.5, im = 0.5;
cerf(re, im, &rer, &imr);
printf("cerf (%21.14e,%21.14e) = (%21.14e, %21.14e)\n", re, im, rer, imr);
cerfc(re, im, &rer, &imr);
printf("cerfc(%21.14e,%21.14e) = (%21.14e, %21.14e)\n", re, im, rer, imr);
double t0 = clock();
for (int i=0; i < n; i++) cerf(re, im, &rer, &imr);
double t1 = clock();
printf("cerf: %.3f Mcalls/sec\n", n/((t1-t0)/CLOCKS_PER_SEC)/1000000);
}
}
