math/s_cexp.c

   1 /* Return value of complex exponential function for double complex value.
   2    Copyright (C) 1997-2012 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         }
  78       else
  79         {
  80           /* If the imaginary part is +-inf or NaN and the real part
  81              is not +-inf the result is NaN + iNaN.  */
  82           __real__ retval = __nan ("");
  83           __imag__ retval = __nan ("");
  84
  85           feraiseexcept (FE_INVALID);
  86         }
  87     }
  88   else if (__builtin_expect (rcls == FP_INFINITE, 1))
  89     {
  90       /* Real part is infinite.  */
  91       if (__builtin_expect (icls >= FP_ZERO, 1))
  92         {
  93           /* Imaginary part is finite.  */
  94           double value = signbit (__real__ x) ? 0.0 : HUGE_VAL;
  95
  96           if (icls == FP_ZERO)
  97             {
  98               /* Imaginary part is 0.0.  */
  99               __real__ retval = value;
 100               __imag__ retval = __imag__ x;
 101             }
 102           else
 103             {
 104               double sinix, cosix;
 105
 106               if (__builtin_expect (icls != FP_SUBNORMAL, 1))
 107                 {
 108                   __sincos (__imag__ x, &sinix, &cosix);
 109                 }
 110               else
 111                 {
 112                   sinix = __imag__ x;
 113                   cosix = 1.0;
 114                 }
 115
 116               __real__ retval = __copysign (value, cosix);
 117               __imag__ retval = __copysign (value, sinix);
 118             }
 119         }
 120       else if (signbit (__real__ x) == 0)
 121         {
 122           __real__ retval = HUGE_VAL;
 123           __imag__ retval = __nan ("");
 124
 125           if (icls == FP_INFINITE)
 126             feraiseexcept (FE_INVALID);
 127         }
 128       else
 129         {
 130           __real__ retval = 0.0;
 131           __imag__ retval = __copysign (0.0, __imag__ x);
 132         }
 133     }
 134   else
 135     {
 136       /* If the real part is NaN the result is NaN + iNaN.  */
 137       __real__ retval = __nan ("");
 138       __imag__ retval = __nan ("");
 139
 140       if (rcls != FP_NAN || icls != FP_NAN)
 141         feraiseexcept (FE_INVALID);
 142     }
 143
 144   return retval;
 145 }
 146 weak_alias (__cexp, cexp)
 147 #ifdef NO_LONG_DOUBLE
 148 strong_alias (__cexp, __cexpl)
 149 weak_alias (__cexp, cexpl)
 150 #endif