newlib/libm/complex/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 <sys/cdefs.h>
  28 #if 0
  29 __FBSDID("$FreeBSD: head/lib/msun/src/s_csqrtl.c 181402 2008-08-08 00:15:16Z das $");
  30 #else
  31 __RCSID("$NetBSD: csqrtl.c,v 1.2 2014/10/11 00:43:51 christos Exp $");
  32 #endif
  33
  34 #include <complex.h>
  35 #include <float.h>
  36 #include <math.h>
  37 #include <stdbool.h>
  38 /*
  39  * gcc doesn't implement complex multiplication or division correctly,
  40  * so we need to handle infinities specially. We turn on this pragma to
  41  * notify conforming c99 compilers that the fast-but-incorrect code that
  42  * gcc generates is acceptable, since the special cases have already been
  43  * handled.
  44  */
  45 // #pragma      STDC CX_LIMITED_RANGE   ON
  46
  47 /* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */
  48 #define THRESH  (LDBL_MAX / 2.414213562373095048801688724209698L)
  49
  50 #define cpackl(r, i) ((r) + (i) * I)
  51
  52 /* On platforms where long double is as wide as double.  */
  53 #ifdef _LDBL_EQ_DBL
  54 long double complex
  55 csqrtl(long double complex z)
  56 {
  57         long double complex result;
  58         long double a, b;
  59         long double t;
  60         bool scale;
  61
  62         a = creall(z);
  63         b = cimagl(z);
  64
  65         /* Handle special cases. */
  66         if (z == 0.0L)
  67                 return (cpackl(0.0L, b));
  68         if (isinf(b))
  69                 return (cpackl(INFINITY, b));
  70         if (isnan(a)) {
  71                 t = (b - b) / (b - b);  /* raise invalid if b is not a NaN */
  72                 return (cpackl(a, t));  /* return NaN + NaN i */
  73         }
  74         if (isinf(a)) {
  75                 /*
  76                  * csqrt(inf + NaN i)  = inf +  NaN i
  77                  * csqrt(inf + y i)    = inf +  0 i
  78                  * csqrt(-inf + NaN i) = NaN +- inf i
  79                  * csqrt(-inf + y i)   = 0   +  inf i
  80                  */
  81                 if (signbit(a))
  82                         return (cpackl(fabsl(b - b), copysignl(a, b)));
  83                 else
  84                         return (cpackl(a, copysignl(b - b, b)));
  85         }
  86         /*
  87          * The remaining special case (b is NaN) is handled just fine by
  88          * the normal code path below.
  89          */
  90
  91         /* Scale to avoid overflow. */
  92         if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
  93                 a *= 0.25L;
  94                 b *= 0.25L;
  95                 scale = true;
  96         } else {
  97                 scale = false;
  98         }
  99
 100         /* Algorithm 312, CACM vol 10, Oct 1967. */
 101         if (a >= 0L) {
 102                 t = sqrtl((a + hypotl(a, b)) * 0.5L);
 103                 result = cpackl(t, b / (2.0L * t));
 104         } else {
 105                 t = sqrtl((-a + hypotl(a, b)) * 0.5L);
 106                 result = cpackl(fabsl(b) / (2.0L * t), copysignl(t, b));
 107         }
 108
 109         /* Rescale. */
 110         if (scale)
 111                 return (result * 2.0L);
 112         else
 113                 return (result);
 114 }
 115 #endif