src/complex/cexp.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/s_cexp.c */
   2 /*-
   3  * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
   4  * All rights reserved.
   5  *
   6  * Redistribution and use in source and binary forms, with or without
   7  * modification, are permitted provided that the following conditions
   8  * are met:
   9  * 1. Redistributions of source code must retain the above copyright
  10  *    notice, this list of conditions and the following disclaimer.
  11  * 2. Redistributions in binary form must reproduce the above copyright
  12  *    notice, this list of conditions and the following disclaimer in the
  13  *    documentation and/or other materials provided with the distribution.
  14  *
  15  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
  16  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  17  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  18  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
  19  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  20  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  21  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  22  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  23  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  24  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  25  * SUCH DAMAGE.
  26  */
  27
  28 #include "complex_impl.h"
  29
  30 static const uint32_t
  31 exp_ovfl  = 0x40862e42,  /* high bits of MAX_EXP * ln2 ~= 710 */
  32 cexp_ovfl = 0x4096b8e4;  /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
  33
  34 double complex cexp(double complex z)
  35 {
  36         double x, y, exp_x;
  37         uint32_t hx, hy, lx, ly;
  38
  39         x = creal(z);
  40         y = cimag(z);
  41
  42         EXTRACT_WORDS(hy, ly, y);
  43         hy &= 0x7fffffff;
  44
  45         /* cexp(x + I 0) = exp(x) + I 0 */
  46         if ((hy | ly) == 0)
  47                 return CMPLX(exp(x), y);
  48         EXTRACT_WORDS(hx, lx, x);
  49         /* cexp(0 + I y) = cos(y) + I sin(y) */
  50         if (((hx & 0x7fffffff) | lx) == 0)
  51                 return CMPLX(cos(y), sin(y));
  52
  53         if (hy >= 0x7ff00000) {
  54                 if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) {
  55                         /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
  56                         return CMPLX(y - y, y - y);
  57                 } else if (hx & 0x80000000) {
  58                         /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
  59                         return CMPLX(0.0, 0.0);
  60                 } else {
  61                         /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
  62                         return CMPLX(x, y - y);
  63                 }
  64         }
  65
  66         if (hx >= exp_ovfl && hx <= cexp_ovfl) {
  67                 /*
  68                  * x is between 709.7 and 1454.3, so we must scale to avoid
  69                  * overflow in exp(x).
  70                  */
  71                 return __ldexp_cexp(z, 0);
  72         } else {
  73                 /*
  74                  * Cases covered here:
  75                  *  -  x < exp_ovfl and exp(x) won't overflow (common case)
  76                  *  -  x > cexp_ovfl, so exp(x) * s overflows for all s > 0
  77                  *  -  x = +-Inf (generated by exp())
  78                  *  -  x = NaN (spurious inexact exception from y)
  79                  */
  80                 exp_x = exp(x);
  81                 return CMPLX(exp_x * cos(y), exp_x * sin(y));
  82         }
  83 }