gonzui

    1: /*      $OpenBSD: s_csqrt.c,v 1.2 2011/07/08 19:25:31 martynas Exp $ */
    2: /*
    3:  * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
    4:  *
    5:  * Permission to use, copy, modify, and distribute this software for any
    6:  * purpose with or without fee is hereby granted, provided that the above
    7:  * copyright notice and this permission notice appear in all copies.
    8:  *
    9:  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
   10:  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
   11:  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
   12:  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
   13:  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
   14:  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
   15:  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
   16:  */
   17: 
   18: /* LINTLIBRARY */
   19: 
   20: /*                                                      csqrt()
   21:  *
   22:  *      Complex square root
   23:  *
   24:  *
   25:  *
   26:  * SYNOPSIS:
   27:  *
   28:  * double complex csqrt();
   29:  * double complex z, w;
   30:  *
   31:  * w = csqrt (z);
   32:  *
   33:  *
   34:  *
   35:  * DESCRIPTION:
   36:  *
   37:  *
   38:  * If z = x + iy,  r = |z|, then
   39:  *
   40:  *                       1/2
   41:  * Re w  =  [ (r + x)/2 ]   ,
   42:  *
   43:  *                       1/2
   44:  * Im w  =  [ (r - x)/2 ]   .
   45:  *
   46:  * Cancellation error in r-x or r+x is avoided by using the
   47:  * identity  2 Re w Im w  =  y.
   48:  *
   49:  * Note that -w is also a square root of z.  The root chosen
   50:  * is always in the right half plane and Im w has the same sign as y.
   51:  *
   52:  *
   53:  *
   54:  * ACCURACY:
   55:  *
   56:  *                      Relative error:
   57:  * arithmetic   domain     # trials      peak         rms
   58:  *    DEC       -10,+10     25000       3.2e-17     9.6e-18
   59:  *    IEEE      -10,+10   1,000,000     2.9e-16     6.1e-17
   60:  *
   61:  */
   62: 
   63: #include <sys/cdefs.h>
   64: #include <complex.h>
   65: #include <float.h>
   66: #include <math.h>
   67: 
   68: double complex
   69: csqrt(double complex z)
   70: {
   71:         double complex w;
   72:         double x, y, r, t, scale;
   73: 
   74:         x = creal (z);
   75:         y = cimag (z);
   76: 
   77:         if (y == 0.0) {
   78:                 if (x == 0.0) {
   79:                         w = 0.0 + y * I;
   80:                 }
   81:                 else {
   82:                         r = fabs (x);
   83:                         r = sqrt (r);
   84:                         if (x < 0.0) {
   85:                                 w = 0.0 + r * I;
   86:                         }
   87:                         else {
   88:                                 w = r + y * I;
   89:                         }
   90:                 }
   91:                 return (w);
   92:         }
   93:         if (x == 0.0) {
   94:                 r = fabs (y);
   95:                 r = sqrt (0.5*r);
   96:                 if (y > 0)
   97:                         w = r + r * I;
   98:                 else
   99:                         w = r - r * I;
  100:                 return (w);
  101:         }
  102:         /* Rescale to avoid internal overflow or underflow.  */
  103:         if ((fabs(x) > 4.0) || (fabs(y) > 4.0)) {
  104:                 x *= 0.25;
  105:                 y *= 0.25;
  106:                 scale = 2.0;
  107:         }
  108:         else {
  109:                 x *= 1.8014398509481984e16;  /* 2^54 */
  110:                 y *= 1.8014398509481984e16;
  111:                 scale = 7.450580596923828125e-9; /* 2^-27 */
  112: #if 0
  113:                 x *= 4.0;
  114:                 y *= 4.0;
  115:                 scale = 0.5;
  116: #endif
  117:         }
  118:         w = x + y * I;
  119:         r = cabs(w);
  120:         if (x > 0) {
  121:                 t = sqrt(0.5 * r + 0.5 * x);
  122:                 r = scale * fabs((0.5 * y) / t);
  123:                 t *= scale;
  124:         }
  125:         else {
  126:                 r = sqrt( 0.5 * r - 0.5 * x );
  127:                 t = scale * fabs( (0.5 * y) / r );
  128:                 r *= scale;
  129:         }
  130:         if (y < 0)
  131:                 w = t - r * I;
  132:         else
  133:                 w = t + r * I;
  134:         return (w);
  135: }
  136: 
  137: #if     LDBL_MANT_DIG == 53
  138: #ifdef  lint
  139: /* PROTOLIB1 */
  140: long double complex csqrtl(long double complex);
  141: #else   /* lint */
  142: __weak_alias(csqrtl, csqrt);
  143: #endif  /* lint */
  144: #endif  /* LDBL_MANT_DIG == 53 */