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 (the "License").
   6  * You may not use this file except in compliance with the License.
   7  *
   8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
   9  * or http://www.opensolaris.org/os/licensing.
  10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21 
  22 /*
  23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  24  */
  25 
  26 /*
  27  * Copyright 2005 Sun Microsystems, Inc.  All rights reserved.
  28  * Use is subject to license terms.
  29  */
  30 
  31 #pragma weak __cabs = cabs
  32 
  33 #include <math.h>
  34 #include "complex_wrapper.h"
  35 
  36 /*
  37  * If C were the only standard we cared about, cabs could just call
  38  * hypot.  Unfortunately, various other standards say that hypot must
  39  * call matherr and/or set errno to ERANGE when the result overflows.
  40  * Since cabs should do neither of these things, we have to either
  41  * make hypot a wrapper on another internal function or duplicate
  42  * the hypot implementation here.  I've chosen to do the latter.
  43  */
  44 
  45 static const double zero = 0.0,
  46         onep1u = 1.00000000000000022204e+00,    /* 0x3ff00000 1 = 1+2**-52 */
  47         twom53 = 1.11022302462515654042e-16,    /* 0x3ca00000 0 = 2**-53 */
  48         twom768 = 6.441148769597133308e-232,    /* 2^-768 */
  49         two768 = 1.552518092300708935e+231;     /* 2^768 */
  50 
  51 double
  52 cabs(dcomplex z)
  53 {
  54         double x, y, xh, yh, w, ax, ay;
  55         int i, j, nx, ny, ix, iy, iscale = 0;
  56         unsigned lx, ly;
  57 
  58         x = D_RE(z);
  59         y = D_IM(z);
  60 
  61         ix = ((int *)&x)[HIWORD] & ~0x80000000;
  62         lx = ((int *)&x)[LOWORD];
  63         iy = ((int *)&y)[HIWORD] & ~0x80000000;
  64         ly = ((int *)&y)[LOWORD];
  65 
  66         /* force ax = |x| ~>~ ay = |y| */
  67         if (iy > ix) {
  68                 ax = fabs(y);
  69                 ay = fabs(x);
  70                 i = ix;
  71                 ix = iy;
  72                 iy = i;
  73                 i = lx;
  74                 lx = ly;
  75                 ly = i;
  76         } else {
  77                 ax = fabs(x);
  78                 ay = fabs(y);
  79         }
  80 
  81         nx = ix >> 20;
  82         ny = iy >> 20;
  83         j = nx - ny;
  84 
  85         if (nx >= 0x5f3) {
  86                 /* x >= 2^500 (x*x or y*y may overflow) */
  87                 if (nx == 0x7ff) {
  88                         /* inf or NaN, signal of sNaN */
  89                         if (((ix - 0x7ff00000) | lx) == 0)
  90                                 return ((ax == ay) ? ay : ax);
  91                         else if (((iy - 0x7ff00000) | ly) == 0)
  92                                 return ((ay == ax) ? ax : ay);
  93                         else
  94                                 return (ax * ay);
  95                 } else if (j > 32) {
  96                         /* x >> y */
  97                         if (j <= 53)
  98                                 ay *= twom53;
  99 
 100                         ax += ay;
 101                         return (ax);
 102                 }
 103 
 104                 ax *= twom768;
 105                 ay *= twom768;
 106                 iscale = 2;
 107                 ix -= 768 << 20;
 108                 iy -= 768 << 20;
 109         } else if (ny < 0x23d) {
 110                 /* y < 2^-450 (x*x or y*y may underflow) */
 111                 if ((ix | lx) == 0)
 112                         return (ay);
 113 
 114                 if ((iy | ly) == 0)
 115                         return (ax);
 116 
 117                 if (j > 53)          /* x >> y */
 118                         return (ax + ay);
 119 
 120                 iscale = 1;
 121                 ax *= two768;
 122                 ay *= two768;
 123 
 124                 if (nx == 0) {
 125                         if (ax == zero) /* guard subnormal flush to zero */
 126                                 return (ax);
 127 
 128                         ix = ((int *)&ax)[HIWORD];
 129                 } else {
 130                         ix += 768 << 20;
 131                 }
 132 
 133                 if (ny == 0) {
 134                         if (ay == zero) /* guard subnormal flush to zero */
 135                                 return (ax * twom768);
 136 
 137                         iy = ((int *)&ay)[HIWORD];
 138                 } else {
 139                         iy += 768 << 20;
 140                 }
 141 
 142                 j = (ix >> 20) - (iy >> 20);
 143 
 144                 if (j > 32) {
 145                         /* x >> y */
 146                         if (j <= 53)
 147                                 ay *= twom53;
 148 
 149                         return ((ax + ay) * twom768);
 150                 }
 151         } else if (j > 32) {
 152                 /* x >> y */
 153                 if (j <= 53)
 154                         ay *= twom53;
 155 
 156                 return (ax + ay);
 157         }
 158 
 159         /*
 160          * Medium range ax and ay with max{|ax/ay|,|ay/ax|} bounded by 2^32.
 161          * First check rounding mode by comparing onep1u*onep1u with onep1u
 162          * + twom53.  Make sure the computation is done at run-time.
 163          */
 164         if (((lx | ly) << 5) == 0) {
 165                 ay = ay * ay;
 166                 ax += ay / (ax + sqrt(ax * ax + ay));
 167         } else if (onep1u * onep1u != onep1u + twom53) {
 168                 /*
 169                  * round-to-zero, positive, negative mode
 170                  * magic formula with less than an ulp error
 171                  */
 172                 w = sqrt(ax * ax + ay * ay);
 173                 ax += ay / ((ax + w) / ay);
 174         } else {
 175                 /* round-to-nearest mode */
 176                 w = ax - ay;
 177 
 178                 if (w > ay) {
 179                         ((int *)&xh)[HIWORD] = ix;
 180                         ((int *)&xh)[LOWORD] = 0;
 181                         ay = ay * ay + (ax - xh) * (ax + xh);
 182                         ax = sqrt(xh * xh + ay);
 183                 } else {
 184                         ax = ax + ax;
 185                         ((int *)&xh)[HIWORD] = ix + 0x00100000;
 186                         ((int *)&xh)[LOWORD] = 0;
 187                         ((int *)&yh)[HIWORD] = iy;
 188                         ((int *)&yh)[LOWORD] = 0;
 189                         ay = w * w + ((ax - xh) * yh + (ay - yh) * ax);
 190                         ax = sqrt(xh * yh + ay);
 191                 }
 192         }
 193 
 194         if (iscale > 0) {
 195                 if (iscale == 1)
 196                         ax *= twom768;
 197                 else
 198                         ax *= two768;   /* must generate side effect here */
 199         }
 200 
 201         return (ax);
 202 }