usr/src/lib/libm/common/Q/hypotl.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 __hypotl = hypotl
  31
  32 /*
  33  * long double hypotl(long double x, long double y);
  34  * Method :
  35  *      If z=x*x+y*y has error less than sqrt(2)/2 ulp than sqrt(z) has
  36  *      error less than 1 ulp.
  37  *      So, compute sqrt(x*x+y*y) with some care as follows:
  38  *      Assume x>y>0;
  39  *      1. save and set rounding to round-to-nearest
  40  *      2. if x > 2y  use
  41  *              x1*x1+(y*y+(x2*(x+x2))) for x*x+y*y
  42  *      where x1 = x with lower 64 bits cleared, x2 = x-x1; else
  43  *      3. if x <= 2y use
  44  *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
  45  *      where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1, y1= y with
  46  *      lower 64 bits chopped, y2 = y-y1.
  47  *
  48  *      NOTE: DO NOT remove parenthsis!
  49  *
  50  * Special cases:
  51  *      hypot(x,y) is INF if x or y is +INF or -INF; else
  52  *      hypot(x,y) is NAN if x or y is NAN.
  53  *
  54  * Accuracy:
  55  *      hypot(x,y) returns sqrt(x^2+y^2) with error less than 1 ulps (units
  56  *      in the last place)
  57  */
  58
  59 #include "libm.h"
  60 #include "longdouble.h"
  61
  62 extern enum fp_direction_type __swapRD(enum fp_direction_type);
  63
  64 static const long double zero = 0.0L, one = 1.0L;
  65
  66 long double
  67 hypotl(long double x, long double y) {
  68         int n0, n1, n2, n3;
  69         long double t1, t2, y1, y2, w;
  70         int *px = (int *) &x, *py = (int *) &y;
  71         int *pt1 = (int *) &t1, *py1 = (int *) &y1;
  72         enum fp_direction_type rd;
  73         int j, k, nx, ny, nz;
  74
  75         if ((*(int *) &one) != 0) {     /* determine word ordering */
  76                 n0 = 0;
  77                 n1 = 1;
  78                 n2 = 2;
  79                 n3 = 3;
  80         } else {
  81                 n0 = 3;
  82                 n1 = 2;
  83                 n2 = 1;
  84                 n3 = 0;
  85         }
  86
  87         px[n0] &= 0x7fffffff;   /* clear sign bit of x and y */
  88         py[n0] &= 0x7fffffff;
  89         k = 0x7fff0000;
  90         nx = px[n0] & k;        /* exponent of x and y */
  91         ny = py[n0] & k;
  92         if (ny > nx) {
  93                 w = x;
  94                 x = y;
  95                 y = w;
  96                 nz = ny;
  97                 ny = nx;
  98                 nx = nz;
  99         }                       /* force x > y */
 100         if ((nx - ny) >= 0x00730000)
 101                 return (x + y); /* x/y >= 2**116 */
 102         if (nx < 0x5ff30000 && ny > 0x205b0000) {       /* medium x,y */
 103                 /* save and set RD to Rounding to nearest */
 104                 rd = __swapRD(fp_nearest);
 105                 w = x - y;
 106                 if (w > y) {
 107                         pt1[n0] = px[n0];
 108                         pt1[n1] = px[n1];
 109                         pt1[n2] = pt1[n3] = 0;
 110                         t2 = x - t1;
 111                         x = sqrtl(t1 * t1 - (y * (-y) - t2 * (x + t1)));
 112                 } else {
 113                         x = x + x;
 114                         py1[n0] = py[n0];
 115                         py1[n1] = py[n1];
 116                         py1[n2] = py1[n3] = 0;
 117                         y2 = y - y1;
 118                         pt1[n0] = px[n0];
 119                         pt1[n1] = px[n1];
 120                         pt1[n2] = pt1[n3] = 0;
 121                         t2 = x - t1;
 122                         x = sqrtl(t1 * y1 - (w * (-w) - (t2 * y1 + y2 * x)));
 123                 }
 124                 if (rd != fp_nearest)
 125                         (void) __swapRD(rd);    /* restore rounding mode */
 126                 return (x);
 127         } else {
 128                 if (nx == k || ny == k) {       /* x or y is INF or NaN */
 129                         if (isinfl(x))
 130                                 t2 = x;
 131                         else if (isinfl(y))
 132                                 t2 = y;
 133                         else
 134                                 t2 = x + y;     /* invalid if x or y is sNaN */
 135                         return (t2);
 136                 }
 137                 if (ny == 0) {
 138                         if (y == zero || x == zero)
 139                                 return (x + y);
 140                         t1 = scalbnl(one, 16381);
 141                         x *= t1;
 142                         y *= t1;
 143                         return (scalbnl(one, -16381) * hypotl(x, y));
 144                 }
 145                 j = nx - 0x3fff0000;
 146                 px[n0] -= j;
 147                 py[n0] -= j;
 148                 pt1[n0] = nx;
 149                 pt1[n1] = pt1[n2] = pt1[n3] = 0;
 150                 return (t1 * hypotl(x, y));
 151         }
 152 }