usr/src/lib/libc/i386/fp/_D_cplx_div.c

   1 /*
   2  * CDDL HEADER START
   3  *
   4  * The contents of this file are subject to the terms of the
   5  * Common Development and Distribution License, Version 1.0 only
   6  * (the "License").  You may not use this file except in compliance
   7  * with the License.
   8  *
   9  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
  10  * or http://www.opensolaris.org/os/licensing.
  11  * See the License for the specific language governing permissions
  12  * and limitations under the License.
  13  *
  14  * When distributing Covered Code, include this CDDL HEADER in each
  15  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  16  * If applicable, add the following below this CDDL HEADER, with the
  17  * fields enclosed by brackets "[]" replaced with your own identifying
  18  * information: Portions Copyright [yyyy] [name of copyright owner]
  19  *
  20  * CDDL HEADER END
  21  */
  22 /*
  23  * Copyright 2004 Sun Microsystems, Inc.  All rights reserved.
  24  * Use is subject to license terms.
  25  */
  26
  27 #pragma ident   "%Z%%M% %I%     %E% SMI"
  28
  29 /*
  30  * _D_cplx_div(z, w) returns z / w with infinities handled according
  31  * to C99.
  32  *
  33  * If z and w are both finite and w is nonzero, _D_cplx_div(z, w)
  34  * delivers the complex quotient q according to the usual formula:
  35  * let a = Re(z), b = Im(z), c = Re(w), and d = Im(w); then q = x +
  36  * I * y where x = (a * c + b * d) / r and y = (b * c - a * d) / r
  37  * with r = c * c + d * d.  This implementation computes intermediate
  38  * results in extended precision to avoid premature underflow or over-
  39  * flow.
  40  *
  41  * If z is neither NaN nor zero and w is zero, or if z is infinite
  42  * and w is finite and nonzero, _D_cplx_div delivers an infinite
  43  * result.  If z is finite and w is infinite, _D_cplx_div delivers
  44  * a zero result.
  45  *
  46  * If z and w are both zero or both infinite, or if either z or w is
  47  * a complex NaN, _D_cplx_div delivers NaN + I * NaN.  C99 doesn't
  48  * specify these cases.
  49  *
  50  * This implementation can raise spurious invalid operation, inexact,
  51  * and division-by-zero exceptions.  C99 allows this.
  52  *
  53  * Warning: Do not attempt to "optimize" this code by removing multi-
  54  * plications by zero.
  55  */
  56
  57 #if !defined(i386) && !defined(__i386) && !defined(__amd64)
  58 #error This code is for x86 only
  59 #endif
  60
  61 static union {
  62         int     i;
  63         float   f;
  64 } inf = {
  65         0x7f800000
  66 };
  67
  68 /*
  69  * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
  70  */
  71 static int
  72 testinf(double x)
  73 {
  74         union {
  75                 int     i[2];
  76                 double  d;
  77         } xx;
  78
  79         xx.d = x;
  80         return (((((xx.i[1] << 1) - 0xffe00000) | xx.i[0]) == 0)?
  81                 (1 | (xx.i[1] >> 31)) : 0);
  82 }
  83
  84 double _Complex
  85 _D_cplx_div(double _Complex z, double _Complex w)
  86 {
  87         double _Complex v;
  88         union {
  89                 int     i[2];
  90                 double  d;
  91         } cc, dd;
  92         double          a, b, c, d;
  93         long double     r, x, y;
  94         int             i, j, recalc;
  95
  96         /*
  97          * The following is equivalent to
  98          *
  99          *  a = creal(z); b = cimag(z);
 100          *  c = creal(w); d = cimag(w);
 101          */
 102         /* LINTED alignment */
 103         a = ((double *)&z)[0];
 104         /* LINTED alignment */
 105         b = ((double *)&z)[1];
 106         /* LINTED alignment */
 107         c = ((double *)&w)[0];
 108         /* LINTED alignment */
 109         d = ((double *)&w)[1];
 110
 111         r = (long double)c * c + (long double)d * d;
 112
 113         if (r == 0.0f) {
 114                 /* w is zero; multiply z by 1/Re(w) - I * Im(w) */
 115                 c = 1.0f / c;
 116                 i = testinf(a);
 117                 j = testinf(b);
 118                 if (i | j) { /* z is infinite */
 119                         a = i;
 120                         b = j;
 121                 }
 122                 /* LINTED alignment */
 123                 ((double *)&v)[0] = a * c + b * d;
 124                 /* LINTED alignment */
 125                 ((double *)&v)[1] = b * c - a * d;
 126                 return (v);
 127         }
 128
 129         r = 1.0f / r;
 130         x = ((long double)a * c + (long double)b * d) * r;
 131         y = ((long double)b * c - (long double)a * d) * r;
 132
 133         if (x != x && y != y) {
 134                 /*
 135                  * Both x and y are NaN, so z and w can't both be finite
 136                  * and nonzero.  Since we handled the case w = 0 above,
 137                  * the only cases to check here are when one of z or w
 138                  * is infinite.
 139                  */
 140                 r = 1.0f;
 141                 recalc = 0;
 142                 i = testinf(a);
 143                 j = testinf(b);
 144                 if (i | j) { /* z is infinite */
 145                         /* "factor out" infinity */
 146                         a = i;
 147                         b = j;
 148                         r = inf.f;
 149                         recalc = 1;
 150                 }
 151                 i = testinf(c);
 152                 j = testinf(d);
 153                 if (i | j) { /* w is infinite */
 154                         /*
 155                          * "factor out" infinity, being careful to preserve
 156                          * signs of finite values
 157                          */
 158                         cc.d = c;
 159                         dd.d = d;
 160                         c = i? i : ((cc.i[1] < 0)? -0.0f : 0.0f);
 161                         d = j? j : ((dd.i[1] < 0)? -0.0f : 0.0f);
 162                         r *= 0.0f;
 163                         recalc = 1;
 164                 }
 165                 if (recalc) {
 166                         x = ((long double)a * c + (long double)b * d) * r;
 167                         y = ((long double)b * c - (long double)a * d) * r;
 168                 }
 169         }
 170
 171         /*
 172          * The following is equivalent to
 173          *
 174          *  return x + I * y;
 175          */
 176         /* LINTED alignment */
 177         ((double *)&v)[0] = (double)x;
 178         /* LINTED alignment */
 179         ((double *)&v)[1] = (double)y;
 180         return (v);
 181 }