math/s_csinh.c

   1 /* Complex sine hyperbole function for double.
   2    Copyright (C) 1997-2015 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4    Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
   5
   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.
  10
  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.
  15
  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/>.  */
  19
  20 #include <complex.h>
  21 #include <fenv.h>
  22 #include <math.h>
  23 #include <math_private.h>
  24 #include <float.h>
  25
  26 __complex__ double
  27 __csinh (__complex__ double x)
  28 {
  29   __complex__ double retval;
  30   int negate = signbit (__real__ x);
  31   int rcls = fpclassify (__real__ x);
  32   int icls = fpclassify (__imag__ x);
  33
  34   __real__ x = fabs (__real__ x);
  35
  36   if (__glibc_likely (rcls >= FP_ZERO))
  37     {
  38       /* Real part is finite.  */
  39       if (__glibc_likely (icls >= FP_ZERO))
  40         {
  41           /* Imaginary part is finite.  */
  42           const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2);
  43           double sinix, cosix;
  44
  45           if (__glibc_likely (fabs (__imag__ x) > DBL_MIN))
  46             {
  47               __sincos (__imag__ x, &sinix, &cosix);
  48             }
  49           else
  50             {
  51               sinix = __imag__ x;
  52               cosix = 1.0;
  53             }
  54
  55           if (negate)
  56             cosix = -cosix;
  57
  58           if (fabs (__real__ x) > t)
  59             {
  60               double exp_t = __ieee754_exp (t);
  61               double rx = fabs (__real__ x);
  62               if (signbit (__real__ x))
  63                 cosix = -cosix;
  64               rx -= t;
  65               sinix *= exp_t / 2.0;
  66               cosix *= exp_t / 2.0;
  67               if (rx > t)
  68                 {
  69                   rx -= t;
  70                   sinix *= exp_t;
  71                   cosix *= exp_t;
  72                 }
  73               if (rx > t)
  74                 {
  75                   /* Overflow (original real part of x > 3t).  */
  76                   __real__ retval = DBL_MAX * cosix;
  77                   __imag__ retval = DBL_MAX * sinix;
  78                 }
  79               else
  80                 {
  81                   double exp_val = __ieee754_exp (rx);
  82                   __real__ retval = exp_val * cosix;
  83                   __imag__ retval = exp_val * sinix;
  84                 }
  85             }
  86           else
  87             {
  88               __real__ retval = __ieee754_sinh (__real__ x) * cosix;
  89               __imag__ retval = __ieee754_cosh (__real__ x) * sinix;
  90             }
  91
  92           if (fabs (__real__ retval) < DBL_MIN)
  93             {
  94               volatile double force_underflow
  95                 = __real__ retval * __real__ retval;
  96               (void) force_underflow;
  97             }
  98           if (fabs (__imag__ retval) < DBL_MIN)
  99             {
 100               volatile double force_underflow
 101                 = __imag__ retval * __imag__ retval;
 102               (void) force_underflow;
 103             }
 104         }
 105       else
 106         {
 107           if (rcls == FP_ZERO)
 108             {
 109               /* Real part is 0.0.  */
 110               __real__ retval = __copysign (0.0, negate ? -1.0 : 1.0);
 111               __imag__ retval = __nan ("") + __nan ("");
 112
 113               if (icls == FP_INFINITE)
 114                 feraiseexcept (FE_INVALID);
 115             }
 116           else
 117             {
 118               __real__ retval = __nan ("");
 119               __imag__ retval = __nan ("");
 120
 121               feraiseexcept (FE_INVALID);
 122             }
 123         }
 124     }
 125   else if (rcls == FP_INFINITE)
 126     {
 127       /* Real part is infinite.  */
 128       if (__glibc_likely (icls > FP_ZERO))
 129         {
 130           /* Imaginary part is finite.  */
 131           double sinix, cosix;
 132
 133           if (__glibc_likely (fabs (__imag__ x) > DBL_MIN))
 134             {
 135               __sincos (__imag__ x, &sinix, &cosix);
 136             }
 137           else
 138             {
 139               sinix = __imag__ x;
 140               cosix = 1.0;
 141             }
 142
 143           __real__ retval = __copysign (HUGE_VAL, cosix);
 144           __imag__ retval = __copysign (HUGE_VAL, sinix);
 145
 146           if (negate)
 147             __real__ retval = -__real__ retval;
 148         }
 149       else if (icls == FP_ZERO)
 150         {
 151           /* Imaginary part is 0.0.  */
 152           __real__ retval = negate ? -HUGE_VAL : HUGE_VAL;
 153           __imag__ retval = __imag__ x;
 154         }
 155       else
 156         {
 157           /* The addition raises the invalid exception.  */
 158           __real__ retval = HUGE_VAL;
 159           __imag__ retval = __nan ("") + __nan ("");
 160
 161           if (icls == FP_INFINITE)
 162             feraiseexcept (FE_INVALID);
 163         }
 164     }
 165   else
 166     {
 167       __real__ retval = __nan ("");
 168       __imag__ retval = __imag__ x == 0.0 ? __imag__ x : __nan ("");
 169     }
 170
 171   return retval;
 172 }
 173 weak_alias (__csinh, csinh)
 174 #ifdef NO_LONG_DOUBLE
 175 strong_alias (__csinh, __csinhl)
 176 weak_alias (__csinh, csinhl)
 177 #endif