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