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