double complex cexp(double complex z) { double x, y, exp_x; uint32_t hx, hy, lx, ly; x = creal(z); y = cimag(z); EXTRACT_WORDS(hy, ly, y); hy &= 0x7fffffff; /* cexp(x + I 0) = exp(x) + I 0 */ if ((hy | ly) == 0) return (CMPLX(exp(x), y)); EXTRACT_WORDS(hx, lx, x); /* cexp(0 + I y) = cos(y) + I sin(y) */ if (((hx & 0x7fffffff) | lx) == 0) return (CMPLX(cos(y), sin(y))); if (hy >= 0x7ff00000) { if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) { /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ return (CMPLX(y - y, y - y)); } else if (hx & 0x80000000) { /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ return (CMPLX(0.0, 0.0)); } else { /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ return (CMPLX(x, y - y)); } } if (hx >= exp_ovfl && hx <= cexp_ovfl) { /* * x is between 709.7 and 1454.3, so we must scale to avoid * overflow in exp(x). */ return (__ldexp_cexp(z, 0)); } else { /* * Cases covered here: * - x < exp_ovfl and exp(x) won't overflow (common case) * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 * - x = +-Inf (generated by exp()) * - x = NaN (spurious inexact exception from y) */ exp_x = exp(x); return (CMPLX(exp_x * cos(y), exp_x * sin(y))); } }
double complex csinh(double complex z) { double x, y, h; int32_t hx, hy, ix, iy, lx, ly; x = creal(z); y = cimag(z); EXTRACT_WORDS(hx, lx, x); EXTRACT_WORDS(hy, ly, y); ix = 0x7fffffff & hx; iy = 0x7fffffff & hy; /* Handle the nearly-non-exceptional cases where x and y are finite. */ if (ix < 0x7ff00000 && iy < 0x7ff00000) { if ((iy | ly) == 0) return CMPLX(sinh(x), y); if (ix < 0x40360000) /* small x: normal case */ return CMPLX(sinh(x) * cos(y), cosh(x) * sin(y)); /* |x| >= 22, so cosh(x) ~= exp(|x|) */ if (ix < 0x40862e42) { /* x < 710: exp(|x|) won't overflow */ h = exp(fabs(x)) * 0.5; return CMPLX(copysign(h, x) * cos(y), h * sin(y)); } else if (ix < 0x4096bbaa) { /* x < 1455: scale to avoid overflow */ z = __ldexp_cexp(CMPLX(fabs(x), y), -1); return CMPLX(creal(z) * copysign(1, x), cimag(z)); } else { /* x >= 1455: the result always overflows */ h = huge * x; return CMPLX(h * cos(y), h * h * sin(y)); } } /* * sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN. * The sign of 0 in the result is unspecified. Choice = normally * the same as dNaN. Raise the invalid floating-point exception. * * sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN). * The sign of 0 in the result is unspecified. Choice = normally * the same as d(NaN). */ if ((ix | lx) == 0 && iy >= 0x7ff00000) return CMPLX(copysign(0, x * (y - y)), y - y); /* * sinh(+-Inf +- I 0) = +-Inf + I +-0. * * sinh(NaN +- I 0) = d(NaN) + I +-0. */ if ((iy | ly) == 0 && ix >= 0x7ff00000) { if (((hx & 0xfffff) | lx) == 0) return CMPLX(x, y); return CMPLX(x, copysign(0, y)); } /* * sinh(x +- I Inf) = dNaN + I dNaN. * Raise the invalid floating-point exception for finite nonzero x. * * sinh(x + I NaN) = d(NaN) + I d(NaN). * Optionally raises the invalid floating-point exception for finite * nonzero x. Choice = don't raise (except for signaling NaNs). */ if (ix < 0x7ff00000 && iy >= 0x7ff00000) return CMPLX(y - y, x * (y - y)); /* * sinh(+-Inf + I NaN) = +-Inf + I d(NaN). * The sign of Inf in the result is unspecified. Choice = normally * the same as d(NaN). * * sinh(+-Inf +- I Inf) = +Inf + I dNaN. * The sign of Inf in the result is unspecified. Choice = always +. * Raise the invalid floating-point exception. * * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y) */ if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) { if (iy >= 0x7ff00000) return CMPLX(x * x, x * (y - y)); return CMPLX(x * cos(y), INFINITY * sin(y)); } /* * sinh(NaN + I NaN) = d(NaN) + I d(NaN). * * sinh(NaN +- I Inf) = d(NaN) + I d(NaN). * Optionally raises the invalid floating-point exception. * Choice = raise. * * sinh(NaN + I y) = d(NaN) + I d(NaN). * Optionally raises the invalid floating-point exception for finite * nonzero y. Choice = don't raise (except for signaling NaNs). */ return CMPLX((x * x) * (y - y), (x + x) * (y - y)); }