src/complex/csqrtf.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/s_csqrtf.c */
   2 /*-
   3  * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
   4  * All rights reserved.
   5  *
   6  * Redistribution and use in source and binary forms, with or without
   7  * modification, are permitted provided that the following conditions
   8  * are met:
   9  * 1. Redistributions of source code must retain the above copyright
  10  *    notice, this list of conditions and the following disclaimer.
  11  * 2. Redistributions in binary form must reproduce the above copyright
  12  *    notice, this list of conditions and the following disclaimer in the
  13  *    documentation and/or other materials provided with the distribution.
  14  *
  15  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
  16  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  17  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  18  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
  19  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  20  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  21  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  22  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  23  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  24  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  25  * SUCH DAMAGE.
  26  */
  27
  28 #include "complex_impl.h"
  29
  30 /*
  31  * gcc doesn't implement complex multiplication or division correctly,
  32  * so we need to handle infinities specially. We turn on this pragma to
  33  * notify conforming c99 compilers that the fast-but-incorrect code that
  34  * gcc generates is acceptable, since the special cases have already been
  35  * handled.
  36  */
  37 #pragma STDC CX_LIMITED_RANGE ON
  38
  39 float complex csqrtf(float complex z)
  40 {
  41         float a = crealf(z), b = cimagf(z);
  42         double t;
  43
  44         /* Handle special cases. */
  45         if (z == 0)
  46                 return CMPLXF(0, b);
  47         if (isinf(b))
  48                 return CMPLXF(INFINITY, b);
  49         if (isnan(a)) {
  50                 t = (b - b) / (b - b);  /* raise invalid if b is not a NaN */
  51                 return CMPLXF(a, t);  /* return NaN + NaN i */
  52         }
  53         if (isinf(a)) {
  54                 /*
  55                  * csqrtf(inf + NaN i)  = inf +  NaN i
  56                  * csqrtf(inf + y i)    = inf +  0 i
  57                  * csqrtf(-inf + NaN i) = NaN +- inf i
  58                  * csqrtf(-inf + y i)   = 0   +  inf i
  59                  */
  60                 if (signbit(a))
  61                         return CMPLXF(fabsf(b - b), copysignf(a, b));
  62                 else
  63                         return CMPLXF(a, copysignf(b - b, b));
  64         }
  65         /*
  66          * The remaining special case (b is NaN) is handled just fine by
  67          * the normal code path below.
  68          */
  69
  70         /*
  71          * We compute t in double precision to avoid overflow and to
  72          * provide correct rounding in nearly all cases.
  73          * This is Algorithm 312, CACM vol 10, Oct 1967.
  74          */
  75         if (a >= 0) {
  76                 t = sqrt((a + hypot(a, b)) * 0.5);
  77                 return CMPLXF(t, b / (2.0 * t));
  78         } else {
  79                 t = sqrt((-a + hypot(a, b)) * 0.5);
  80                 return CMPLXF(fabsf(b) / (2.0 * t), copysignf(t, b));
  81         }
  82 }