compiler/stdc/math/s_csqrtl.c

   1 /*-
   2  * Copyright (c) 2007-2008 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 #include <float.h>
  28 #include <complex.h>
  29 #include "math.h"
  30
  31 #include "math_private.h"
  32
  33 #ifdef __clang__
  34 /*
  35  * gcc doesn't implement complex multiplication or division correctly,
  36  * so we need to handle infinities specially. We turn on this pragma to
  37  * notify conforming c99 compilers that the fast-but-incorrect code that
  38  * gcc generates is acceptable, since the special cases have already been
  39  * handled.
  40  */
  41 #pragma STDC CX_LIMITED_RANGE   ON
  42 #endif
  43
  44 /*
  45  * We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)).
  46  * Rather than determining the fully precise value at which we might
  47  * overflow, just use a threshold of approximately LDBL_MAX / 4.
  48  */
  49 #if LDBL_MAX_EXP != 0x4000
  50 #error "Unsupported long double format"
  51 #else
  52 #define THRESH  0x1p16382L
  53 #endif
  54
  55 long double complex
  56 csqrtl(long double complex z)
  57 {
  58         long double complex result;
  59         long double a, b;
  60         long double t;
  61         int scale;
  62
  63         a = creall(z);
  64         b = cimagl(z);
  65
  66         /* Handle special cases. */
  67         if (z == 0)
  68                 return (CMPLXL(0, b));
  69         if (isinf(b))
  70                 return (CMPLXL(INFINITY, b));
  71         if (isnan(a)) {
  72                 t = (b - b) / (b - b);  /* raise invalid if b is not a NaN */
  73                 return (CMPLXL(a, t));  /* return NaN + NaN i */
  74         }
  75         if (isinf(a)) {
  76                 /*
  77                  * csqrt(inf + NaN i)  = inf +  NaN i
  78                  * csqrt(inf + y i)    = inf +  0 i
  79                  * csqrt(-inf + NaN i) = NaN +- inf i
  80                  * csqrt(-inf + y i)   = 0   +  inf i
  81                  */
  82                 if (signbit(a))
  83                         return (CMPLXL(fabsl(b - b), copysignl(a, b)));
  84                 else
  85                         return (CMPLXL(a, copysignl(b - b, b)));
  86         }
  87         /*
  88          * The remaining special case (b is NaN) is handled just fine by
  89          * the normal code path below.
  90          */
  91
  92         /* Scale to avoid overflow. */
  93         if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
  94                 a *= 0.25;
  95                 b *= 0.25;
  96                 scale = 1;
  97         } else {
  98                 scale = 0;
  99         }
 100
 101         /* Algorithm 312, CACM vol 10, Oct 1967. */
 102         if (a >= 0) {
 103                 t = sqrtl((a + hypotl(a, b)) * 0.5);
 104                 result = CMPLXL(t, b / (2 * t));
 105         } else {
 106                 t = sqrtl((-a + hypotl(a, b)) * 0.5);
 107                 result = CMPLXL(fabsl(b) / (2 * t), copysignl(t, b));
 108         }
 109
 110         /* Rescale. */
 111         if (scale)
 112                 return (result * 2);
 113         else
 114                 return (result);
 115 }