usr/src/lib/libm/common/complex/cexp.c

   1 /*
   2  * CDDL HEADER START
   3  *
   4  * The contents of this file are subject to the terms of the
   5  * Common Development and Distribution License (the "License").
   6  * You may not use this file except in compliance with the License.
   7  *
   8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
   9  * or http://www.opensolaris.org/os/licensing.
  10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21
  22 /*
  23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  24  */
  25 /*
  26  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  27  * Use is subject to license terms.
  28  */
  29
  30 #pragma weak __cexp = cexp
  31
  32 /* INDENT OFF */
  33 /*
  34  * dcomplex cexp(dcomplex z);
  35  *
  36  *  x+iy    x
  37  * e     = e  (cos(y)+i*sin(y))
  38  *
  39  * Over/underflow issue
  40  * --------------------
  41  * exp(x) may be huge but cos(y) or sin(y) may be tiny. So we use
  42  * function __k_cexp(x,&n) to return exp(x) = __k_cexp(x,&n)*2**n.
  43  * Thus if exp(x+iy) = A + Bi and t = __k_cexp(x,&n), then
  44  *         A = t*cos(y)*2**n,   B = t*sin(y)*2**n
  45  *
  46  * Purge off all exceptional arguments:
  47  *      (x,0) --> (exp(x),0)         for all x, include inf and NaN
  48  *      (+inf, y) --> (+inf, NaN)    for inf, nan
  49  *      (-inf, y) --> (+-0, +-0)     for y = inf, nan
  50  *      (x,+-inf/NaN) --> (NaN,NaN)  for finite x
  51  * For all other cases, return
  52  *      (x,y) --> exp(x)*cos(y)+i*exp(x)*sin(y))
  53  *
  54  * Algorithm for out of range x and finite y
  55  *      1. compute exp(x) in factor form (t=__k_cexp(x,&n))*2**n
  56  *      2. compute sincos(y,&s,&c)
  57  *      3. compute t*s+i*(t*c), then scale back to 2**n and return.
  58  */
  59 /* INDENT ON */
  60
  61 #include "libm.h"               /* exp/scalbn/sincos/__k_cexp */
  62 #include "complex_wrapper.h"
  63
  64 static const double zero = 0.0;
  65
  66 dcomplex
  67 cexp(dcomplex z) {
  68         dcomplex ans;
  69         double x, y, t, c, s;
  70         int n, ix, iy, hx, hy, lx, ly;
  71
  72         x = D_RE(z);
  73         y = D_IM(z);
  74         hx = HI_WORD(x);
  75         lx = LO_WORD(x);
  76         hy = HI_WORD(y);
  77         ly = LO_WORD(y);
  78         ix = hx & 0x7fffffff;
  79         iy = hy & 0x7fffffff;
  80         if ((iy | ly) == 0) {   /* y = 0 */
  81                 D_RE(ans) = exp(x);
  82                 D_IM(ans) = y;
  83         } else if (ISINF(ix, lx)) {     /* x is +-inf */
  84                 if (hx < 0) {
  85                         if (iy >= 0x7ff00000) {
  86                                 D_RE(ans) = zero;
  87                                 D_IM(ans) = zero;
  88                         } else {
  89                                 sincos(y, &s, &c);
  90                                 D_RE(ans) = zero * c;
  91                                 D_IM(ans) = zero * s;
  92                         }
  93                 } else {
  94                         if (iy >= 0x7ff00000) {
  95                                 D_RE(ans) = x;
  96                                 D_IM(ans) = y - y;
  97                         } else {
  98                                 (void) sincos(y, &s, &c);
  99                                 D_RE(ans) = x * c;
 100                                 D_IM(ans) = x * s;
 101                         }
 102                 }
 103         } else {
 104                 (void) sincos(y, &s, &c);
 105                 if (ix >= 0x40862E42) { /* |x| > 709.78... ~ log(2**1024) */
 106                         t = __k_cexp(x, &n);
 107                         D_RE(ans) = scalbn(t * c, n);
 108                         D_IM(ans) = scalbn(t * s, n);
 109                 } else {
 110                         t = exp(x);
 111                         D_RE(ans) = t * c;
 112                         D_IM(ans) = t * s;
 113                 }
 114         }
 115         return (ans);
 116 }