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 2006 Sun Microsystems, Inc.  All rights reserved.
  28  * Use is subject to license terms.
  29  */
  30 
  31 #pragma weak __hypot = hypot
  32 
  33 
  34 /*
  35  * Hypot(x, y)
  36  * by K.C. Ng for SUN 4.0 libm, updated 3/11/2003.
  37  * Method :
  38  * A. When rounding is rounded-to-nearest:
  39  *      If z = x * x + y * y has error less than sqrt(2) / 2 ulp than
  40  *      sqrt(z) has error less than 1 ulp.
  41  *      So, compute sqrt(x*x+y*y) with some care as follows:
  42  *      Assume x > y > 0;
  43  *      1. Check whether save and set rounding to round-to-nearest
  44  *      2. if x > 2y  use
  45  *              xh*xh+(y*y+((x-xh)*(x+xh))) for x*x+y*y
  46  *      where xh = x with lower 32 bits cleared;  else
  47  *      3. if x <= 2y use
  48  *              x2h*yh+((x-y)*(x-y)+(x2h*(y-yh)+(x2-x2h)*y))
  49  *      where x2 = 2*x, x2h = 2x with lower 32 bits cleared, yh = y with
  50  *      lower 32 bits chopped.
  51  *
  52  * B. When rounding is not rounded-to-nearest:
  53  *      The following (magic) formula will yield an error less than 1 ulp.
  54  *      z = sqrt(x * x + y * y)
  55  *              hypot(x, y) = x + (y / ((x + z) / y))
  56  *
  57  * NOTE: DO NOT remove parenthsis!
  58  *
  59  * Special cases:
  60  *      hypot(x, y) is INF if x or y is +INF or -INF; else
  61  *      hypot(x, y) is NAN if x or y is NAN.
  62  *
  63  * Accuracy:
  64  *      hypot(x, y) returns sqrt(x^2+y^2) with error less than 1 ulps
  65  *      (units in the last place)
  66  */
  67 
  68 #include "libm.h"
  69 
  70 static const double zero = 0.0,
  71         onep1u = 1.00000000000000022204e+00,    /* 0x3ff00000 1 = 1+2**-52 */
  72         twom53 = 1.11022302462515654042e-16,    /* 0x3ca00000 0 = 2**-53 */
  73         twom768 = 6.441148769597133308e-232,    /* 2^-768 */
  74         two768 = 1.552518092300708935e+231;     /* 2^768 */
  75 
  76 
  77 double
  78 hypot(double x, double y)
  79 {
  80         double xh, yh, w, ax, ay;
  81         int i, j, nx, ny, ix, iy, iscale = 0;
  82         unsigned lx, ly;
  83 
  84         ix = ((int *)&x)[HIWORD] & ~0x80000000;
  85         lx = ((int *)&x)[LOWORD];
  86         iy = ((int *)&y)[HIWORD] & ~0x80000000;
  87         ly = ((int *)&y)[LOWORD];
  88 
  89 /*
  90  * Force ax = |x| ~>~ ay = |y|
  91  */
  92         if (iy > ix) {
  93                 ax = fabs(y);
  94                 ay = fabs(x);
  95                 i = ix;
  96                 ix = iy;
  97                 iy = i;
  98                 i = lx;
  99                 lx = ly;
 100                 ly = i;
 101         } else {
 102                 ax = fabs(x);
 103                 ay = fabs(y);
 104         }
 105 
 106         nx = ix >> 20;
 107         ny = iy >> 20;
 108         j = nx - ny;
 109 
 110 /*
 111  * x >= 2^500 (x*x or y*y may overflow)
 112  */
 113         if (nx >= 0x5f3) {
 114                 if (nx == 0x7ff) {      /* inf or NaN, signal of sNaN */
 115                         if (((ix - 0x7ff00000) | lx) == 0)
 116                                 return (ax == ay ? ay : ax);
 117                         else if (((iy - 0x7ff00000) | ly) == 0)
 118                                 return (ay == ax ? ax : ay);
 119                         else
 120                                 return (ax * ay);       /* + -> * for Cheetah */
 121                 } else if (j > 32) {                 /* x >> y */
 122                         if (j <= 53)
 123                                 ay *= twom53;
 124 
 125                         ax += ay;
 126 
 127                         if (((int *)&ax)[HIWORD] == 0x7ff00000)
 128                                 ax = _SVID_libm_err(x, y, 4);
 129 
 130                         return (ax);
 131                 }
 132 
 133                 ax *= twom768;
 134                 ay *= twom768;
 135                 iscale = 2;
 136                 ix -= 768 << 20;
 137                 iy -= 768 << 20;
 138         }
 139 
 140 /*
 141  * y < 2^-450 (x*x or y*y may underflow)
 142  */
 143         else if (ny < 0x23d) {
 144                 if ((ix | lx) == 0)
 145                         return (ay);
 146 
 147                 if ((iy | ly) == 0)
 148                         return (ax);
 149 
 150                 if (j > 53)          /* x >> y */
 151                         return (ax + ay);
 152 
 153                 iscale = 1;
 154                 ax *= two768;
 155                 ay *= two768;
 156 
 157                 if (nx == 0) {
 158                         if (ax == zero) /* guard subnormal flush to zero */
 159                                 return (ax);
 160 
 161                         ix = ((int *)&ax)[HIWORD];
 162                 } else {
 163                         ix += 768 << 20;
 164                 }
 165 
 166                 if (ny == 0) {
 167                         if (ay == zero) /* guard subnormal flush to zero */
 168                                 return (ax * twom768);
 169 
 170                         iy = ((int *)&ay)[HIWORD];
 171                 } else {
 172                         iy += 768 << 20;
 173                 }
 174 
 175                 j = (ix >> 20) - (iy >> 20);
 176 
 177                 if (j > 32) {                /* x >> y */
 178                         if (j <= 53)
 179                                 ay *= twom53;
 180 
 181                         return ((ax + ay) * twom768);
 182                 }
 183         } else if (j > 32) {         /* x >> y */
 184                 if (j <= 53)
 185                         ay *= twom53;
 186 
 187                 return (ax + ay);
 188         }
 189 
 190 /*
 191  * Medium range ax and ay with max{|ax/ay|,|ay/ax|} bounded by 2^32
 192  * First check rounding mode by comparing onep1u*onep1u with onep1u+twom53.
 193  * Make sure the computation is done at run-time.
 194  */
 195         if (((lx | ly) << 5) == 0) {
 196                 ay = ay * ay;
 197                 ax += ay / (ax + sqrt(ax * ax + ay));
 198         } else if (onep1u * onep1u != onep1u + twom53) {
 199                 /*
 200                  * round-to-zero, positive, negative mode
 201                  * magic formula with less than an ulp error
 202                  */
 203                 w = sqrt(ax * ax + ay * ay);
 204                 ax += ay / ((ax + w) / ay);
 205         } else {
 206                 /* round-to-nearest mode */
 207                 w = ax - ay;
 208 
 209                 if (w > ay) {
 210                         ((int *)&xh)[HIWORD] = ix;
 211                         ((int *)&xh)[LOWORD] = 0;
 212                         ay = ay * ay + (ax - xh) * (ax + xh);
 213                         ax = sqrt(xh * xh + ay);
 214                 } else {
 215                         ax = ax + ax;
 216                         ((int *)&xh)[HIWORD] = ix + 0x00100000;
 217                         ((int *)&xh)[LOWORD] = 0;
 218                         ((int *)&yh)[HIWORD] = iy;
 219                         ((int *)&yh)[LOWORD] = 0;
 220                         ay = w * w + ((ax - xh) * yh + (ay - yh) * ax);
 221                         ax = sqrt(xh * yh + ay);
 222                 }
 223         }
 224 
 225         if (iscale > 0) {
 226                 if (iscale == 1) {
 227                         ax *= twom768;
 228                 } else {
 229                         ax *= two768;   /* must generate side effect here */
 230 
 231                         if (((int *)&ax)[HIWORD] == 0x7ff00000)
 232                                 ax = _SVID_libm_err(x, y, 4);
 233                 }
 234         }
 235 
 236         return (ax);
 237 }