Use __builtin_fma more in dbl-64 code.
[glibc.git] / math / s_ctanh_template.c
bloba7b7ebc3e2b052a36cb493f7de836f186df6f9aa
1 /* Complex hyperbolic tangent for float types.
2 Copyright (C) 1997-2016 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, see
18 <http://www.gnu.org/licenses/>. */
20 #include <complex.h>
21 #include <fenv.h>
22 #include <math.h>
23 #include <math_private.h>
24 #include <float.h>
26 CFLOAT
27 M_DECL_FUNC (__ctanh) (CFLOAT x)
29 CFLOAT res;
31 if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
33 if (isinf (__real__ x))
35 __real__ res = M_COPYSIGN (1, __real__ x);
36 if (isfinite (__imag__ x) && M_FABS (__imag__ x) > 1)
38 FLOAT sinix, cosix;
39 M_SINCOS (__imag__ x, &sinix, &cosix);
40 __imag__ res = M_COPYSIGN (0, sinix * cosix);
42 else
43 __imag__ res = M_COPYSIGN (0, __imag__ x);
45 else if (__imag__ x == 0)
47 res = x;
49 else
51 __real__ res = M_NAN;
52 __imag__ res = M_NAN;
54 if (isinf (__imag__ x))
55 feraiseexcept (FE_INVALID);
58 else
60 FLOAT sinix, cosix;
61 FLOAT den;
62 const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2);
64 /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
65 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
67 if (__glibc_likely (M_FABS (__imag__ x) > M_MIN))
69 M_SINCOS (__imag__ x, &sinix, &cosix);
71 else
73 sinix = __imag__ x;
74 cosix = 1;
77 if (M_FABS (__real__ x) > t)
79 /* Avoid intermediate overflow when the imaginary part of
80 the result may be subnormal. Ignoring negligible terms,
81 the real part is +/- 1, the imaginary part is
82 sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
83 FLOAT exp_2t = M_EXP (2 * t);
85 __real__ res = M_COPYSIGN (1, __real__ x);
86 __imag__ res = 4 * sinix * cosix;
87 __real__ x = M_FABS (__real__ x);
88 __real__ x -= t;
89 __imag__ res /= exp_2t;
90 if (__real__ x > t)
92 /* Underflow (original real part of x has absolute value
93 > 2t). */
94 __imag__ res /= exp_2t;
96 else
97 __imag__ res /= M_EXP (2 * __real__ x);
99 else
101 FLOAT sinhrx, coshrx;
102 if (M_FABS (__real__ x) > M_MIN)
104 sinhrx = M_SINH (__real__ x);
105 coshrx = M_COSH (__real__ x);
107 else
109 sinhrx = __real__ x;
110 coshrx = 1;
113 if (M_FABS (sinhrx) > M_FABS (cosix) * M_EPSILON)
114 den = sinhrx * sinhrx + cosix * cosix;
115 else
116 den = cosix * cosix;
117 __real__ res = sinhrx * coshrx / den;
118 __imag__ res = sinix * cosix / den;
120 math_check_force_underflow_complex (res);
123 return res;
126 declare_mgen_alias (__ctanh, ctanh)
128 #if M_LIBM_NEED_COMPAT (ctanh)
129 declare_mgen_libm_compat (__ctanh, ctanh)
130 #endif