math/s_cexp.c

   1 /* Return value of complex exponential function for double complex value.
   2    Copyright (C) 1997-2013 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 __cexp (__complex__ double x)
  28 {
  29   __complex__ double retval;
  30   int rcls = fpclassify (__real__ x);
  31   int icls = fpclassify (__imag__ x);
  32
  33   if (__builtin_expect (rcls >= FP_ZERO, 1))
  34     {
  35       /* Real part is finite.  */
  36       if (__builtin_expect (icls >= FP_ZERO, 1))
  37         {
  38           /* Imaginary part is finite.  */
  39           const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2);
  40           double sinix, cosix;
  41
  42           if (__builtin_expect (icls != FP_SUBNORMAL, 1))
  43             {
  44               __sincos (__imag__ x, &sinix, &cosix);
  45             }
  46           else
  47             {
  48               sinix = __imag__ x;
  49               cosix = 1.0;
  50             }
  51
  52           if (__real__ x > t)
  53             {
  54               double exp_t = __ieee754_exp (t);
  55               __real__ x -= t;
  56               sinix *= exp_t;
  57               cosix *= exp_t;
  58               if (__real__ x > t)
  59                 {
  60                   __real__ x -= t;
  61                   sinix *= exp_t;
  62                   cosix *= exp_t;
  63                 }
  64             }
  65           if (__real__ x > t)
  66             {
  67               /* Overflow (original real part of x > 3t).  */
  68               __real__ retval = DBL_MAX * cosix;
  69               __imag__ retval = DBL_MAX * sinix;
  70             }
  71           else
  72             {
  73               double exp_val = __ieee754_exp (__real__ x);
  74               __real__ retval = exp_val * cosix;
  75               __imag__ retval = exp_val * sinix;
  76             }
  77           if (fabs (__real__ retval) < DBL_MIN)
  78             {
  79               volatile double force_underflow
  80                 = __real__ retval * __real__ retval;
  81               (void) force_underflow;
  82             }
  83           if (fabs (__imag__ retval) < DBL_MIN)
  84             {
  85               volatile double force_underflow
  86                 = __imag__ retval * __imag__ retval;
  87               (void) force_underflow;
  88             }
  89         }
  90       else
  91         {
  92           /* If the imaginary part is +-inf or NaN and the real part
  93              is not +-inf the result is NaN + iNaN.  */
  94           __real__ retval = __nan ("");
  95           __imag__ retval = __nan ("");
  96
  97           feraiseexcept (FE_INVALID);
  98         }
  99     }
 100   else if (__builtin_expect (rcls == FP_INFINITE, 1))
 101     {
 102       /* Real part is infinite.  */
 103       if (__builtin_expect (icls >= FP_ZERO, 1))
 104         {
 105           /* Imaginary part is finite.  */
 106           double value = signbit (__real__ x) ? 0.0 : HUGE_VAL;
 107
 108           if (icls == FP_ZERO)
 109             {
 110               /* Imaginary part is 0.0.  */
 111               __real__ retval = value;
 112               __imag__ retval = __imag__ x;
 113             }
 114           else
 115             {
 116               double sinix, cosix;
 117
 118               if (__builtin_expect (icls != FP_SUBNORMAL, 1))
 119                 {
 120                   __sincos (__imag__ x, &sinix, &cosix);
 121                 }
 122               else
 123                 {
 124                   sinix = __imag__ x;
 125                   cosix = 1.0;
 126                 }
 127
 128               __real__ retval = __copysign (value, cosix);
 129               __imag__ retval = __copysign (value, sinix);
 130             }
 131         }
 132       else if (signbit (__real__ x) == 0)
 133         {
 134           __real__ retval = HUGE_VAL;
 135           __imag__ retval = __nan ("");
 136
 137           if (icls == FP_INFINITE)
 138             feraiseexcept (FE_INVALID);
 139         }
 140       else
 141         {
 142           __real__ retval = 0.0;
 143           __imag__ retval = __copysign (0.0, __imag__ x);
 144         }
 145     }
 146   else
 147     {
 148       /* If the real part is NaN the result is NaN + iNaN unless the
 149          imaginary part is zero.  */
 150       __real__ retval = __nan ("");
 151       if (icls == FP_ZERO)
 152         __imag__ retval = __imag__ x;
 153       else
 154         {
 155           __imag__ retval = __nan ("");
 156
 157           if (rcls != FP_NAN || icls != FP_NAN)
 158             feraiseexcept (FE_INVALID);
 159         }
 160     }
 161
 162   return retval;
 163 }
 164 weak_alias (__cexp, cexp)
 165 #ifdef NO_LONG_DOUBLE
 166 strong_alias (__cexp, __cexpl)
 167 weak_alias (__cexp, cexpl)
 168 #endif