math/s_cexp.c

   1 /* Return value of complex exponential function for double complex value.
   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.
   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 (__glibc_likely (rcls >= FP_ZERO))
  34     {
  35       /* Real part is finite.  */
  36       if (__glibc_likely (icls >= FP_ZERO))
  37         {
  38           /* Imaginary part is finite.  */
  39           const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2);
  40           double sinix, cosix;
  41
  42           if (__glibc_likely (fabs (__imag__ x) > DBL_MIN))
  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           math_check_force_underflow_complex (retval);
  78         }
  79       else
  80         {
  81           /* If the imaginary part is +-inf or NaN and the real part
  82              is not +-inf the result is NaN + iNaN.  */
  83           __real__ retval = __nan ("");
  84           __imag__ retval = __nan ("");
  85
  86           feraiseexcept (FE_INVALID);
  87         }
  88     }
  89   else if (__glibc_likely (rcls == FP_INFINITE))
  90     {
  91       /* Real part is infinite.  */
  92       if (__glibc_likely (icls >= FP_ZERO))
  93         {
  94           /* Imaginary part is finite.  */
  95           double value = signbit (__real__ x) ? 0.0 : HUGE_VAL;
  96
  97           if (icls == FP_ZERO)
  98             {
  99               /* Imaginary part is 0.0.  */
 100               __real__ retval = value;
 101               __imag__ retval = __imag__ x;
 102             }
 103           else
 104             {
 105               double sinix, cosix;
 106
 107               if (__glibc_likely (fabs (__imag__ x) > DBL_MIN))
 108                 {
 109                   __sincos (__imag__ x, &sinix, &cosix);
 110                 }
 111               else
 112                 {
 113                   sinix = __imag__ x;
 114                   cosix = 1.0;
 115                 }
 116
 117               __real__ retval = __copysign (value, cosix);
 118               __imag__ retval = __copysign (value, sinix);
 119             }
 120         }
 121       else if (signbit (__real__ x) == 0)
 122         {
 123           __real__ retval = HUGE_VAL;
 124           __imag__ retval = __nan ("");
 125
 126           if (icls == FP_INFINITE)
 127             feraiseexcept (FE_INVALID);
 128         }
 129       else
 130         {
 131           __real__ retval = 0.0;
 132           __imag__ retval = __copysign (0.0, __imag__ x);
 133         }
 134     }
 135   else
 136     {
 137       /* If the real part is NaN the result is NaN + iNaN unless the
 138          imaginary part is zero.  */
 139       __real__ retval = __nan ("");
 140       if (icls == FP_ZERO)
 141         __imag__ retval = __imag__ x;
 142       else
 143         {
 144           __imag__ retval = __nan ("");
 145
 146           if (rcls != FP_NAN || icls != FP_NAN)
 147             feraiseexcept (FE_INVALID);
 148         }
 149     }
 150
 151   return retval;
 152 }
 153 weak_alias (__cexp, cexp)
 154 #ifdef NO_LONG_DOUBLE
 155 strong_alias (__cexp, __cexpl)
 156 weak_alias (__cexp, cexpl)
 157 #endif