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glibc/math/s_ctan.c
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/* Complex tangent function for double. | |
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__ double | |
__ctan (__complex__ double x) | |
{ | |
__complex__ double res; | |
if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x))) | |
{ | |
if (isinf (__imag__ x)) | |
{ | |
if (isfinite (__real__ x) && fabs (__real__ x) > 1.0) | |
{ | |
double sinrx, cosrx; | |
__sincos (__real__ x, &sinrx, &cosrx); | |
__real__ res = __copysign (0.0, sinrx * cosrx); | |
} | |
else | |
__real__ res = __copysign (0.0, __real__ x); | |
__imag__ res = __copysign (1.0, __imag__ x); | |
} | |
else if (__real__ x == 0.0) | |
{ | |
res = x; | |
} | |
else | |
{ | |
__real__ res = __nan (""); | |
__imag__ res = __nan (""); | |
if (isinf (__real__ x)) | |
feraiseexcept (FE_INVALID); | |
} | |
} | |
else | |
{ | |
double sinrx, cosrx; | |
double den; | |
const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2); | |
/* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y)) | |
= (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */ | |
if (__glibc_likely (fabs (__real__ x) > DBL_MIN)) | |
{ | |
__sincos (__real__ x, &sinrx, &cosrx); | |
} | |
else | |
{ | |
sinrx = __real__ x; | |
cosrx = 1.0; | |
} | |
if (fabs (__imag__ x) > t) | |
{ | |
/* Avoid intermediate overflow when the real part of the | |
result may be subnormal. Ignoring negligible terms, the | |
imaginary part is +/- 1, the real part is | |
sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */ | |
double exp_2t = __ieee754_exp (2 * t); | |
__imag__ res = __copysign (1.0, __imag__ x); | |
__real__ res = 4 * sinrx * cosrx; | |
__imag__ x = fabs (__imag__ x); | |
__imag__ x -= t; | |
__real__ res /= exp_2t; | |
if (__imag__ x > t) | |
{ | |
/* Underflow (original imaginary part of x has absolute | |
value > 2t). */ | |
__real__ res /= exp_2t; | |
} | |
else | |
__real__ res /= __ieee754_exp (2 * __imag__ x); | |
} | |
else | |
{ | |
double sinhix, coshix; | |
if (fabs (__imag__ x) > DBL_MIN) | |
{ | |
sinhix = __ieee754_sinh (__imag__ x); | |
coshix = __ieee754_cosh (__imag__ x); | |
} | |
else | |
{ | |
sinhix = __imag__ x; | |
coshix = 1.0; | |
} | |
if (fabs (sinhix) > fabs (cosrx) * DBL_EPSILON) | |
den = cosrx * cosrx + sinhix * sinhix; | |
else | |
den = cosrx * cosrx; | |
__real__ res = sinrx * cosrx / den; | |
__imag__ res = sinhix * coshix / den; | |
} | |
math_check_force_underflow_complex (res); | |
} | |
return res; | |
} | |
weak_alias (__ctan, ctan) | |
#ifdef NO_LONG_DOUBLE | |
strong_alias (__ctan, __ctanl) | |
weak_alias (__ctan, ctanl) | |
#endif |