math/s_cexp_template.c

   1 /* Return value of complex exponential function for a float type.
   2    Copyright (C) 1997-2021 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    <https://www.gnu.org/licenses/>.  */
  19
  20 #include <complex.h>
  21 #include <fenv.h>
  22 #include <math.h>
  23 #include <math_private.h>
  24 #include <math-underflow.h>
  25 #include <float.h>
  26
  27 CFLOAT
  28 M_DECL_FUNC (__cexp) (CFLOAT x)
  29 {
  30   CFLOAT retval;
  31   int rcls = fpclassify (__real__ x);
  32   int icls = fpclassify (__imag__ x);
  33
  34   if (__glibc_likely (rcls >= FP_ZERO))
  35     {
  36       /* Real part is finite.  */
  37       if (__glibc_likely (icls >= FP_ZERO))
  38         {
  39           /* Imaginary part is finite.  */
  40           const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2));
  41           FLOAT sinix, cosix;
  42
  43           if (__glibc_likely (M_FABS (__imag__ x) > M_MIN))
  44             {
  45               M_SINCOS (__imag__ x, &sinix, &cosix);
  46             }
  47           else
  48             {
  49               sinix = __imag__ x;
  50               cosix = 1;
  51             }
  52
  53           if (__real__ x > t)
  54             {
  55               FLOAT exp_t = M_EXP (t);
  56               __real__ x -= t;
  57               sinix *= exp_t;
  58               cosix *= exp_t;
  59               if (__real__ x > t)
  60                 {
  61                   __real__ x -= t;
  62                   sinix *= exp_t;
  63                   cosix *= exp_t;
  64                 }
  65             }
  66           if (__real__ x > t)
  67             {
  68               /* Overflow (original real part of x > 3t).  */
  69               __real__ retval = M_MAX * cosix;
  70               __imag__ retval = M_MAX * sinix;
  71             }
  72           else
  73             {
  74               FLOAT exp_val = M_EXP (__real__ x);
  75               __real__ retval = exp_val * cosix;
  76               __imag__ retval = exp_val * sinix;
  77             }
  78           math_check_force_underflow_complex (retval);
  79         }
  80       else
  81         {
  82           /* If the imaginary part is +-inf or NaN and the real part
  83              is not +-inf the result is NaN + iNaN.  */
  84           __real__ retval = M_NAN;
  85           __imag__ retval = M_NAN;
  86
  87           feraiseexcept (FE_INVALID);
  88         }
  89     }
  90   else if (__glibc_likely (rcls == FP_INFINITE))
  91     {
  92       /* Real part is infinite.  */
  93       if (__glibc_likely (icls >= FP_ZERO))
  94         {
  95           /* Imaginary part is finite.  */
  96           FLOAT value = signbit (__real__ x) ? 0 : M_HUGE_VAL;
  97
  98           if (icls == FP_ZERO)
  99             {
 100               /* Imaginary part is 0.0.  */
 101               __real__ retval = value;
 102               __imag__ retval = __imag__ x;
 103             }
 104           else
 105             {
 106               FLOAT sinix, cosix;
 107
 108               if (__glibc_likely (M_FABS (__imag__ x) > M_MIN))
 109                 {
 110                   M_SINCOS (__imag__ x, &sinix, &cosix);
 111                 }
 112               else
 113                 {
 114                   sinix = __imag__ x;
 115                   cosix = 1;
 116                 }
 117
 118               __real__ retval = M_COPYSIGN (value, cosix);
 119               __imag__ retval = M_COPYSIGN (value, sinix);
 120             }
 121         }
 122       else if (signbit (__real__ x) == 0)
 123         {
 124           __real__ retval = M_HUGE_VAL;
 125           __imag__ retval = __imag__ x - __imag__ x;
 126         }
 127       else
 128         {
 129           __real__ retval = 0;
 130           __imag__ retval = M_COPYSIGN (0, __imag__ x);
 131         }
 132     }
 133   else
 134     {
 135       /* If the real part is NaN the result is NaN + iNaN unless the
 136          imaginary part is zero.  */
 137       __real__ retval = M_NAN;
 138       if (icls == FP_ZERO)
 139         __imag__ retval = __imag__ x;
 140       else
 141         {
 142           __imag__ retval = M_NAN;
 143
 144           if (rcls != FP_NAN || icls != FP_NAN)
 145             feraiseexcept (FE_INVALID);
 146         }
 147     }
 148
 149   return retval;
 150 }
 151 declare_mgen_alias (__cexp, cexp)