lib/libm/complex/csqrtf.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 float complex
  36 csqrtf(float complex z)
  37 {
  38         float complex w;
  39         float x, y, r, t, scale;
  40
  41         x = crealf (z);
  42         y = cimagf (z);
  43
  44         if (y == 0.0f) {
  45                 if (x < 0.0f) {
  46                         w = 0.0f + sqrtf(-x) * I;
  47                         return w;
  48                 } else if (x == 0.0f) {
  49                         return (0.0f + y * I);
  50                 } else {
  51                         w = sqrtf(x) + y * I;
  52                         return w;
  53                 }
  54         }
  55
  56         if (x == 0.0f) {
  57                 r = fabsf(y);
  58                 r = sqrtf(0.5f * r);
  59                 if (y > 0)
  60                         w = r + r * I;
  61                 else
  62                         w = r - r * I;
  63                 return w;
  64         }
  65
  66         /* Rescale to avoid internal overflow or underflow.  */
  67         if ((fabsf(x) > 4.0f) || (fabsf(y) > 4.0f)) {
  68                 x *= 0.25f;
  69                 y *= 0.25f;
  70                 scale = 2.0f;
  71         } else {
  72 #if 1
  73                 x *= 6.7108864e7f; /* 2^26 */
  74                 y *= 6.7108864e7f;
  75                 scale = 1.220703125e-4f; /* 2^-13 */
  76 #else
  77                 x *= 4.0f;
  78                 y *= 4.0f;
  79                 scale = 0.5f;
  80 #endif
  81         }
  82         w = x + y * I;
  83         r = cabsf(w);
  84         if( x > 0 ) {
  85                 t = sqrtf(0.5f * r + 0.5f * x);
  86                 r = scale * fabsf((0.5f * y) / t);
  87                 t *= scale;
  88         } else {
  89                 r = sqrtf(0.5f * r - 0.5f * x);
  90                 t = scale * fabsf((0.5f * y) / r);
  91                 r *= scale;
  92         }
  93
  94         if (y < 0)
  95                 w = t - r * I;
  96         else
  97                 w = t + r * I;
  98         return w;
  99 }