lib/libm/complex/csqrt.c

   1 /* $NetBSD$ */
   2
   3 /*-
   4  * Copyright (c) 2007 The NetBSD Foundation, Inc.
   5  * All rights reserved.
   6  *
   7  * This code is derived from software written by Stephen L. Moshier.
   8  * It is redistributed by the NetBSD Foundation by permission of the author.
   9  *
  10  * Redistribution and use in source and binary forms, with or without
  11  * modification, are permitted provided that the following conditions
  12  * are met:
  13  * 1. Redistributions of source code must retain the above copyright
  14  *    notice, this list of conditions and the following disclaimer.
  15  * 2. Redistributions in binary form must reproduce the above copyright
  16  *    notice, this list of conditions and the following disclaimer in the
  17  *    documentation and/or other materials provided with the distribution.
  18  *
  19  * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
  20  * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
  21  * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  22  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
  23  * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
  24  * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
  25  * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
  26  * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  27  * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  28  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  29  * POSSIBILITY OF SUCH DAMAGE.
  30  */
  31
  32 #include <complex.h>
  33 #include <math.h>
  34
  35 double complex
  36 csqrt(double complex z)
  37 {
  38         double complex w;
  39         double x, y, r, t, scale;
  40
  41         x = creal (z);
  42         y = cimag (z);
  43
  44         if (y == 0.0) {
  45                 if (x == 0.0) {
  46                         w = 0.0 + y * I;
  47                 } else {
  48                         r = fabs(x);
  49                         r = sqrt(r);
  50                         if (x < 0.0) {
  51                                 w = 0.0 + r * I;
  52                         } else {
  53                                 w = r + y * I;
  54                         }
  55                 }
  56                 return w;
  57         }
  58         if (x == 0.0) {
  59                 r = fabs(y);
  60                 r = sqrt(0.5 * r);
  61                 if (y > 0)
  62                         w = r + r * I;
  63                 else
  64                         w = r - r * I;
  65                 return w;
  66         }
  67         /* Rescale to avoid internal overflow or underflow.  */
  68         if ((fabs(x) > 4.0) || (fabs(y) > 4.0)) {
  69                 x *= 0.25;
  70                 y *= 0.25;
  71                 scale = 2.0;
  72         } else {
  73 #if 1
  74                 x *= 1.8014398509481984e16;  /* 2^54 */
  75                 y *= 1.8014398509481984e16;
  76                 scale = 7.450580596923828125e-9; /* 2^-27 */
  77 #else
  78                 x *= 4.0;
  79                 y *= 4.0;
  80                 scale = 0.5;
  81 #endif
  82         }
  83         w = x + y * I;
  84         r = cabs(w);
  85         if (x > 0) {
  86                 t = sqrt(0.5 * r + 0.5 * x);
  87                 r = scale * fabs((0.5 * y) / t );
  88                 t *= scale;
  89         } else {
  90                 r = sqrt(0.5 * r - 0.5 * x);
  91                 t = scale * fabs((0.5 * y) / r);
  92                 r *= scale;
  93         }
  94         if (y < 0)
  95                 w = t - r * I;
  96         else
  97                 w = t + r * I;
  98         return w;
  99 }