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  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  23  */
  24 /*
  25  * Copyright 2005 Sun Microsystems, Inc.  All rights reserved.
  26  * Use is subject to license terms.
  27  */
  28 
  29 #pragma weak cabs = __cabs
  30 
  31 #include "libm_synonyms.h"
  32 #include <math.h>
  33 #include "complex_wrapper.h"
  34 
  35 /*
  36  * If C were the only standard we cared about, cabs could just call
  37  * hypot.  Unfortunately, various other standards say that hypot must
  38  * call matherr and/or set errno to ERANGE when the result overflows.
  39  * Since cabs should do neither of these things, we have to either
  40  * make hypot a wrapper on another internal function or duplicate
  41  * the hypot implementation here.  I've chosen to do the latter.
  42  */
  43 
  44 static const double
  45         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         nx = ix >> 20;
  81         ny = iy >> 20;
  82         j  = nx - ny;
  83 
  84         if (nx >= 0x5f3) {
  85                 /* x >= 2^500 (x*x or y*y may overflow) */
  86                 if (nx == 0x7ff) {
  87                         /* inf or NaN, signal of sNaN */
  88                         if (((ix - 0x7ff00000) | lx) == 0)
  89                                 return ((ax == ay)? ay : ax);
  90                         else if (((iy - 0x7ff00000) | ly) == 0)
  91                                 return ((ay == ax)? ax : ay);
  92                         else
  93                                 return (ax * ay);
  94                 } else if (j > 32) {
  95                         /* x >> y */
  96                         if (j <= 53)
  97                                 ay *= twom53;
  98                         ax += ay;
  99                         return (ax);
 100                 }
 101                 ax *= twom768;
 102                 ay *= twom768;
 103                 iscale = 2;
 104                 ix -= 768 << 20;
 105                 iy -= 768 << 20;
 106         } else if (ny < 0x23d) {
 107                 /* y < 2^-450 (x*x or y*y may underflow) */
 108                 if ((ix | lx) == 0)
 109                         return (ay);
 110                 if ((iy | ly) == 0)
 111                         return (ax);
 112                 if (j > 53)          /* x >> y */
 113                         return (ax + ay);
 114                 iscale = 1;
 115                 ax *= two768;
 116                 ay *= two768;
 117                 if (nx == 0) {
 118                         if (ax == zero) /* guard subnormal flush to zero */
 119                                 return (ax);
 120                         ix = ((int *)&ax)[HIWORD];
 121                 } else {
 122                         ix += 768 << 20;
 123                 }
 124                 if (ny == 0) {
 125                         if (ay == zero) /* guard subnormal flush to zero */
 126                                 return (ax * twom768);
 127                         iy = ((int *)&ay)[HIWORD];
 128                 } else {
 129                         iy += 768 << 20;
 130                 }
 131                 j = (ix >> 20) - (iy >> 20);
 132                 if (j > 32) {
 133                         /* x >> y */
 134                         if (j <= 53)
 135                                 ay *= twom53;
 136                         return ((ax + ay) * twom768);
 137                 }
 138         } else if (j > 32) {
 139                 /* x >> y */
 140                 if (j <= 53)
 141                         ay *= twom53;
 142                 return (ax + ay);
 143         }
 144 
 145         /*
 146          * Medium range ax and ay with max{|ax/ay|,|ay/ax|} bounded by 2^32.
 147          * First check rounding mode by comparing onep1u*onep1u with onep1u
 148          * + twom53.  Make sure the computation is done at run-time.
 149          */
 150         if (((lx | ly) << 5) == 0) {
 151                 ay = ay * ay;
 152                 ax += ay / (ax + sqrt(ax * ax + ay));
 153         } else if (onep1u * onep1u != onep1u + twom53) {
 154                 /* round-to-zero, positive, negative mode */
 155                 /* magic formula with less than an ulp error */
 156                 w = sqrt(ax * ax + ay * ay);
 157                 ax += ay / ((ax + w) / ay);
 158         } else {
 159                 /* round-to-nearest mode */
 160                 w = ax - ay;
 161                 if (w > ay) {
 162                         ((int *)&xh)[HIWORD] = ix;
 163                         ((int *)&xh)[LOWORD] = 0;
 164                         ay = ay * ay + (ax - xh) * (ax + xh);
 165                         ax = sqrt(xh * xh + ay);
 166                 } else {
 167                         ax = ax + ax;
 168                         ((int *)&xh)[HIWORD] = ix + 0x00100000;
 169                         ((int *)&xh)[LOWORD] = 0;
 170                         ((int *)&yh)[HIWORD] = iy;
 171                         ((int *)&yh)[LOWORD] = 0;
 172                         ay = w * w + ((ax - xh) * yh + (ay - yh) * ax);
 173                         ax = sqrt(xh * yh + ay);
 174                 }
 175         }
 176         if (iscale > 0) {
 177                 if (iscale == 1)
 178                         ax *= twom768;
 179                 else
 180                         ax *= two768;   /* must generate side effect here */
 181         }
 182         return (ax);
 183 }