CFLOAT M_DECL_FUNC (__csin) (CFLOAT x) { CFLOAT retval; int negate = signbit (__real__ x); int rcls = fpclassify (__real__ x); int icls = fpclassify (__imag__ x); __real__ x = M_FABS (__real__ x); if (__glibc_likely (icls >= FP_ZERO)) { /* Imaginary part is finite. */ if (__glibc_likely (rcls >= FP_ZERO)) { /* Real part is finite. */ const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2)); FLOAT sinix, cosix; if (__glibc_likely (__real__ x > M_MIN)) { M_SINCOS (__real__ x, &sinix, &cosix); } else { sinix = __real__ x; cosix = 1; } if (negate) sinix = -sinix; if (M_FABS (__imag__ x) > t) { FLOAT exp_t = M_EXP (t); FLOAT ix = M_FABS (__imag__ x); if (signbit (__imag__ x)) cosix = -cosix; ix -= t; sinix *= exp_t / 2; cosix *= exp_t / 2; if (ix > t) { ix -= t; sinix *= exp_t; cosix *= exp_t; } if (ix > t) { /* Overflow (original imaginary part of x > 3t). */ __real__ retval = M_MAX * sinix; __imag__ retval = M_MAX * cosix; } else { FLOAT exp_val = M_EXP (ix); __real__ retval = exp_val * sinix; __imag__ retval = exp_val * cosix; } } else { __real__ retval = M_COSH (__imag__ x) * sinix; __imag__ retval = M_SINH (__imag__ x) * cosix; } math_check_force_underflow_complex (retval); } else { if (icls == FP_ZERO) { /* Imaginary part is 0.0. */ __real__ retval = __real__ x - __real__ x; __imag__ retval = __imag__ x; } else { __real__ retval = M_NAN; __imag__ retval = M_NAN; feraiseexcept (FE_INVALID); } } } else if (icls == FP_INFINITE) { /* Imaginary part is infinite. */ if (rcls == FP_ZERO) { /* Real part is 0.0. */ __real__ retval = M_COPYSIGN (0, negate ? -1 : 1); __imag__ retval = __imag__ x; } else if (rcls > FP_ZERO) { /* Real part is finite. */ FLOAT sinix, cosix; if (__glibc_likely (__real__ x > M_MIN)) { M_SINCOS (__real__ x, &sinix, &cosix); } else { sinix = __real__ x; cosix = 1; } __real__ retval = M_COPYSIGN (M_HUGE_VAL, sinix); __imag__ retval = M_COPYSIGN (M_HUGE_VAL, cosix); if (negate) __real__ retval = -__real__ retval; if (signbit (__imag__ x)) __imag__ retval = -__imag__ retval; } else { __real__ retval = __real__ x - __real__ x; __imag__ retval = M_HUGE_VAL; } } else { if (rcls == FP_ZERO) __real__ retval = M_COPYSIGN (0, negate ? -1 : 1); else __real__ retval = M_NAN; __imag__ retval = M_NAN; } return retval; }
CFLOAT M_DECL_FUNC (__ctanh) (CFLOAT x) { CFLOAT res; if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x))) { if (isinf (__real__ x)) { __real__ res = M_COPYSIGN (1, __real__ x); if (isfinite (__imag__ x) && M_FABS (__imag__ x) > 1) { FLOAT sinix, cosix; M_SINCOS (__imag__ x, &sinix, &cosix); __imag__ res = M_COPYSIGN (0, sinix * cosix); } else __imag__ res = M_COPYSIGN (0, __imag__ x); } else if (__imag__ x == 0) { res = x; } else { __real__ res = M_NAN; __imag__ res = M_NAN; if (isinf (__imag__ x)) feraiseexcept (FE_INVALID); } } else { FLOAT sinix, cosix; FLOAT den; const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2); /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y)) = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */ if (__glibc_likely (M_FABS (__imag__ x) > M_MIN)) { M_SINCOS (__imag__ x, &sinix, &cosix); } else { sinix = __imag__ x; cosix = 1; } if (M_FABS (__real__ x) > t) { /* Avoid intermediate overflow when the imaginary part of the result may be subnormal. Ignoring negligible terms, the real part is +/- 1, the imaginary part is sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */ FLOAT exp_2t = M_EXP (2 * t); __real__ res = M_COPYSIGN (1, __real__ x); __imag__ res = 4 * sinix * cosix; __real__ x = M_FABS (__real__ x); __real__ x -= t; __imag__ res /= exp_2t; if (__real__ x > t) { /* Underflow (original real part of x has absolute value > 2t). */ __imag__ res /= exp_2t; } else __imag__ res /= M_EXP (2 * __real__ x); } else { FLOAT sinhrx, coshrx; if (M_FABS (__real__ x) > M_MIN) { sinhrx = M_SINH (__real__ x); coshrx = M_COSH (__real__ x); } else { sinhrx = __real__ x; coshrx = 1; } if (M_FABS (sinhrx) > M_FABS (cosix) * M_EPSILON) den = sinhrx * sinhrx + cosix * cosix; else den = cosix * cosix; __real__ res = sinhrx * coshrx / den; __imag__ res = sinix * cosix / den; } math_check_force_underflow_complex (res); } return res; }