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 } 211