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       1                 :             : /*-
       2                 :             :  * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
       3                 :             :  * All rights reserved.
       4                 :             :  *
       5                 :             :  * Redistribution and use in source and binary forms, with or without
       6                 :             :  * modification, are permitted provided that the following conditions
       7                 :             :  * are met:
       8                 :             :  * 1. Redistributions of source code must retain the above copyright
       9                 :             :  *    notice, this list of conditions and the following disclaimer.
      10                 :             :  * 2. Redistributions in binary form must reproduce the above copyright
      11                 :             :  *    notice, this list of conditions and the following disclaimer in the
      12                 :             :  *    documentation and/or other materials provided with the distribution.
      13                 :             :  *
      14                 :             :  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
      15                 :             :  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
      16                 :             :  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
      17                 :             :  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
      18                 :             :  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
      19                 :             :  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
      20                 :             :  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
      21                 :             :  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
      22                 :             :  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
      23                 :             :  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
      24                 :             :  * SUCH DAMAGE.
      25                 :             :  */
      26                 :             : 
      27                 :             : #include "cdefs-compat.h"
      28                 :             : //__FBSDID("$FreeBSD: src/lib/msun/src/s_cexp.c,v 1.3 2011/10/21 06:27:56 das Exp $");
      29                 :             : 
      30                 :             : #include <openlibm_complex.h>
      31                 :             : #include <openlibm_math.h>
      32                 :             : 
      33                 :             : #include "math_private.h"
      34                 :             : 
      35                 :             : static const u_int32_t
      36                 :             : exp_ovfl  = 0x40862e42,                 /* high bits of MAX_EXP * ln2 ~= 710 */
      37                 :             : cexp_ovfl = 0x4096b8e4;                 /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
      38                 :             : 
      39                 :             : OLM_DLLEXPORT double complex
      40                 :           0 : cexp(double complex z)
      41                 :             : {
      42                 :             :         double x, y, exp_x;
      43                 :             :         u_int32_t hx, hy, lx, ly;
      44                 :             : 
      45                 :           0 :         x = creal(z);
      46                 :           0 :         y = cimag(z);
      47                 :             : 
      48                 :           0 :         EXTRACT_WORDS(hy, ly, y);
      49                 :           0 :         hy &= 0x7fffffff;
      50                 :             : 
      51                 :             :         /* cexp(x + I 0) = exp(x) + I 0 */
      52         [ #  # ]:           0 :         if ((hy | ly) == 0)
      53                 :           0 :                 return (CMPLX(exp(x), y));
      54                 :           0 :         EXTRACT_WORDS(hx, lx, x);
      55                 :             :         /* cexp(0 + I y) = cos(y) + I sin(y) */
      56         [ #  # ]:           0 :         if (((hx & 0x7fffffff) | lx) == 0)
      57                 :           0 :                 return (CMPLX(cos(y), sin(y)));
      58                 :             : 
      59         [ #  # ]:           0 :         if (hy >= 0x7ff00000) {
      60   [ #  #  #  # ]:           0 :                 if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) {
      61                 :             :                         /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
      62                 :           0 :                         return (CMPLX(y - y, y - y));
      63         [ #  # ]:           0 :                 } else if (hx & 0x80000000) {
      64                 :             :                         /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
      65                 :           0 :                         return (CMPLX(0.0, 0.0));
      66                 :             :                 } else {
      67                 :             :                         /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
      68                 :           0 :                         return (CMPLX(x, y - y));
      69                 :             :                 }
      70                 :             :         }
      71                 :             : 
      72   [ #  #  #  # ]:           0 :         if (hx >= exp_ovfl && hx <= cexp_ovfl) {
      73                 :             :                 /*
      74                 :             :                  * x is between 709.7 and 1454.3, so we must scale to avoid
      75                 :             :                  * overflow in exp(x).
      76                 :             :                  */
      77                 :           0 :                 return (__ldexp_cexp(z, 0));
      78                 :             :         } else {
      79                 :             :                 /*
      80                 :             :                  * Cases covered here:
      81                 :             :                  *  -  x < exp_ovfl and exp(x) won't overflow (common case)
      82                 :             :                  *  -  x > cexp_ovfl, so exp(x) * s overflows for all s > 0
      83                 :             :                  *  -  x = +-Inf (generated by exp())
      84                 :             :                  *  -  x = NaN (spurious inexact exception from y)
      85                 :             :                  */
      86                 :           0 :                 exp_x = exp(x);
      87                 :           0 :                 return (CMPLX(exp_x * cos(y), exp_x * sin(y)));
      88                 :             :         }
      89                 :             : }