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#include "__complex.h" // for redupi, MACHEP
#include <complex.h> // for cimag, creal, complex, I, ctan
#include <math.h> // for fabs, HUGE_VAL, cos, cosh, sin, sinh
double _ctans(double complex z)
{
double f, x, x2, y, y2, rn, t;
double d;
x = fabs(2.0 * creal(z));
y = fabs(2.0 * cimag(z));
x = redupi(x);
x = x * x;
y = y * y;
x2 = 1.0;
y2 = 1.0;
f = 1.0;
rn = 0.0;
d = 0.0;
do {
rn += 1.0;
f *= rn;
rn += 1.0;
f *= rn;
x2 *= x;
y2 *= y;
t = y2 + x2;
t /= f;
d += t;
rn += 1.0;
f *= rn;
rn += 1.0;
f *= rn;
x2 *= x;
y2 *= y;
t = y2 - x2;
t /= f;
d += t;
} while (fabs(t / d) > MACHEP);
return d;
}
double complex ctan(double complex z)
{
double d = cos(2.0 * creal(z)) + cosh(2.0 * cimag(z));
if (fabs(d) < 0.25)
d = _ctans(z);
if (d == 0.0) {
return HUGE_VAL + HUGE_VAL * (double complex)I;
}
return sin(2.0 * creal(z)) / d + (sinh(2.0 * cimag(z)) / d) * (double complex)I;
}
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