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glibc/math/s_ctanhf.c
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/* Complex hyperbole tangent for float. | |
Copyright (C) 1997-2016 Free Software Foundation, Inc. | |
This file is part of the GNU C Library. | |
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. | |
The GNU C Library is free software; you can redistribute it and/or | |
modify it under the terms of the GNU Lesser General Public | |
License as published by the Free Software Foundation; either | |
version 2.1 of the License, or (at your option) any later version. | |
The GNU C Library is distributed in the hope that it will be useful, | |
but WITHOUT ANY WARRANTY; without even the implied warranty of | |
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
Lesser General Public License for more details. | |
You should have received a copy of the GNU Lesser General Public | |
License along with the GNU C Library; if not, see | |
<http://www.gnu.org/licenses/>. */ | |
#include <complex.h> | |
#include <fenv.h> | |
#include <math.h> | |
#include <math_private.h> | |
#include <float.h> | |
__complex__ float | |
__ctanhf (__complex__ float x) | |
{ | |
__complex__ float res; | |
if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x))) | |
{ | |
if (isinf (__real__ x)) | |
{ | |
__real__ res = __copysignf (1.0, __real__ x); | |
if (isfinite (__imag__ x) && fabsf (__imag__ x) > 1.0f) | |
{ | |
float sinix, cosix; | |
__sincosf (__imag__ x, &sinix, &cosix); | |
__imag__ res = __copysignf (0.0f, sinix * cosix); | |
} | |
else | |
__imag__ res = __copysignf (0.0, __imag__ x); | |
} | |
else if (__imag__ x == 0.0) | |
{ | |
res = x; | |
} | |
else | |
{ | |
__real__ res = __nanf (""); | |
__imag__ res = __nanf (""); | |
if (isinf (__imag__ x)) | |
feraiseexcept (FE_INVALID); | |
} | |
} | |
else | |
{ | |
float sinix, cosix; | |
float den; | |
const int t = (int) ((FLT_MAX_EXP - 1) * 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 (fabsf (__imag__ x) > FLT_MIN)) | |
{ | |
__sincosf (__imag__ x, &sinix, &cosix); | |
} | |
else | |
{ | |
sinix = __imag__ x; | |
cosix = 1.0f; | |
} | |
if (fabsf (__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 = __ieee754_expf (2 * t); | |
__real__ res = __copysignf (1.0, __real__ x); | |
__imag__ res = 4 * sinix * cosix; | |
__real__ x = fabsf (__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 /= __ieee754_expf (2 * __real__ x); | |
} | |
else | |
{ | |
float sinhrx, coshrx; | |
if (fabsf (__real__ x) > FLT_MIN) | |
{ | |
sinhrx = __ieee754_sinhf (__real__ x); | |
coshrx = __ieee754_coshf (__real__ x); | |
} | |
else | |
{ | |
sinhrx = __real__ x; | |
coshrx = 1.0f; | |
} | |
if (fabsf (sinhrx) > fabsf (cosix) * FLT_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; | |
} | |
#ifndef __ctanhf | |
weak_alias (__ctanhf, ctanhf) | |
#endif |