compiler/stdc/math/s_csqrtf.c

   1 /*-
   2  * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
   3  * All rights reserved.
   4  *
   5  * Redistribution and use in source and binary forms, with or without
   6  * modification, are permitted provided that the following conditions
   7  * are met:
   8  * 1. Redistributions of source code must retain the above copyright
   9  *    notice, this list of conditions and the following disclaimer.
  10  * 2. Redistributions in binary form must reproduce the above copyright
  11  *    notice, this list of conditions and the following disclaimer in the
  12  *    documentation and/or other materials provided with the distribution.
  13  *
  14  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
  15  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  16  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  17  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
  18  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  19  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  20  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  21  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  22  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  23  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  24  * SUCH DAMAGE.
  25  */
  26
  27 //__FBSDID("$FreeBSD: src/lib/msun/src/s_csqrtf.c,v 1.3 2008/08/08 00:15:16 das Exp $");
  28
  29 #include <complex.h>
  30 #include "math.h"
  31
  32 #include "math_private.h"
  33
  34 #ifdef __clang__
  35 /*
  36  * gcc doesn't implement complex multiplication or division correctly,
  37  * so we need to handle infinities specially. We turn on this pragma to
  38  * notify conforming c99 compilers that the fast-but-incorrect code that
  39  * gcc generates is acceptable, since the special cases have already been
  40  * handled.
  41  */
  42 #pragma STDC CX_LIMITED_RANGE   ON
  43 #endif
  44
  45 float complex
  46 csqrtf(float complex z)
  47 {
  48         float a = crealf(z), b = cimagf(z);
  49         double t;
  50
  51         /* Handle special cases. */
  52         if (z == 0)
  53                 return (CMPLXF(0, b));
  54         if (isinf(b))
  55                 return (CMPLXF(INFINITY, b));
  56         if (isnan(a)) {
  57                 t = (b - b) / (b - b);  /* raise invalid if b is not a NaN */
  58                 return (CMPLXF(a, t));  /* return NaN + NaN i */
  59         }
  60         if (isinf(a)) {
  61                 /*
  62                  * csqrtf(inf + NaN i)  = inf +  NaN i
  63                  * csqrtf(inf + y i)    = inf +  0 i
  64                  * csqrtf(-inf + NaN i) = NaN +- inf i
  65                  * csqrtf(-inf + y i)   = 0   +  inf i
  66                  */
  67                 if (signbit(a))
  68                         return (CMPLXF(fabsf(b - b), copysignf(a, b)));
  69                 else
  70                         return (CMPLXF(a, copysignf(b - b, b)));
  71         }
  72         /*
  73          * The remaining special case (b is NaN) is handled just fine by
  74          * the normal code path below.
  75          */
  76
  77         /*
  78          * We compute t in double precision to avoid overflow and to
  79          * provide correct rounding in nearly all cases.
  80          * This is Algorithm 312, CACM vol 10, Oct 1967.
  81          */
  82         if (a >= 0) {
  83                 t = sqrt((a + hypot(a, b)) * 0.5);
  84                 return (CMPLXF(t, b / (2.0 * t)));
  85         } else {
  86                 t = sqrt((-a + hypot(a, b)) * 0.5);
  87                 return (CMPLXF(fabsf(b) / (2.0 * t), copysignf(t, b)));
  88         }
  89 }