/* * CDDL HEADER START * * The contents of this file are subject to the terms of the * Common Development and Distribution License (the "License"). * You may not use this file except in compliance with the License. * * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE * or http://www.opensolaris.org/os/licensing. * See the License for the specific language governing permissions * and limitations under the License. * * When distributing Covered Code, include this CDDL HEADER in each * file and include the License file at usr/src/OPENSOLARIS.LICENSE. * If applicable, add the following below this CDDL HEADER, with the * fields enclosed by brackets "[]" replaced with your own identifying * information: Portions Copyright [yyyy] [name of copyright owner] * * CDDL HEADER END */ /* * Copyright 2011 Nexenta Systems, Inc. All rights reserved. */ /* * Copyright 2006 Sun Microsystems, Inc. All rights reserved. * Use is subject to license terms. */ #pragma weak __hypot = hypot /* INDENT OFF */ /* * Hypot(x, y) * by K.C. Ng for SUN 4.0 libm, updated 3/11/2003. * Method : * A. When rounding is rounded-to-nearest: * If z = x * x + y * y has error less than sqrt(2) / 2 ulp than * sqrt(z) has error less than 1 ulp. * So, compute sqrt(x*x+y*y) with some care as follows: * Assume x > y > 0; * 1. Check whether save and set rounding to round-to-nearest * 2. if x > 2y use * xh*xh+(y*y+((x-xh)*(x+xh))) for x*x+y*y * where xh = x with lower 32 bits cleared; else * 3. if x <= 2y use * x2h*yh+((x-y)*(x-y)+(x2h*(y-yh)+(x2-x2h)*y)) * where x2 = 2*x, x2h = 2x with lower 32 bits cleared, yh = y with * lower 32 bits chopped. * * B. When rounding is not rounded-to-nearest: * The following (magic) formula will yield an error less than 1 ulp. * z = sqrt(x * x + y * y) * hypot(x, y) = x + (y / ((x + z) / y)) * * NOTE: DO NOT remove parenthsis! * * Special cases: * hypot(x, y) is INF if x or y is +INF or -INF; else * hypot(x, y) is NAN if x or y is NAN. * * Accuracy: * hypot(x, y) returns sqrt(x^2+y^2) with error less than 1 ulps * (units in the last place) */ #include "libm.h" static const double zero = 0.0, onep1u = 1.00000000000000022204e+00, /* 0x3ff00000 1 = 1+2**-52 */ twom53 = 1.11022302462515654042e-16, /* 0x3ca00000 0 = 2**-53 */ twom768 = 6.441148769597133308e-232, /* 2^-768 */ two768 = 1.552518092300708935e+231; /* 2^768 */ /* INDENT ON */ double hypot(double x, double y) { double xh, yh, w, ax, ay; int i, j, nx, ny, ix, iy, iscale = 0; unsigned lx, ly; ix = ((int *) &x)[HIWORD] & ~0x80000000; lx = ((int *) &x)[LOWORD]; iy = ((int *) &y)[HIWORD] & ~0x80000000; ly = ((int *) &y)[LOWORD]; /* * Force ax = |x| ~>~ ay = |y| */ if (iy > ix) { ax = fabs(y); ay = fabs(x); i = ix; ix = iy; iy = i; i = lx; lx = ly; ly = i; } else { ax = fabs(x); ay = fabs(y); } nx = ix >> 20; ny = iy >> 20; j = nx - ny; /* * x >= 2^500 (x*x or y*y may overflow) */ if (nx >= 0x5f3) { if (nx == 0x7ff) { /* inf or NaN, signal of sNaN */ if (((ix - 0x7ff00000) | lx) == 0) return (ax == ay ? ay : ax); else if (((iy - 0x7ff00000) | ly) == 0) return (ay == ax ? ax : ay); else return (ax * ay); /* + -> * for Cheetah */ } else if (j > 32) { /* x >> y */ if (j <= 53) ay *= twom53; ax += ay; if (((int *) &ax)[HIWORD] == 0x7ff00000) ax = _SVID_libm_err(x, y, 4); return (ax); } ax *= twom768; ay *= twom768; iscale = 2; ix -= 768 << 20; iy -= 768 << 20; } /* * y < 2^-450 (x*x or y*y may underflow) */ else if (ny < 0x23d) { if ((ix | lx) == 0) return (ay); if ((iy | ly) == 0) return (ax); if (j > 53) /* x >> y */ return (ax + ay); iscale = 1; ax *= two768; ay *= two768; if (nx == 0) { if (ax == zero) /* guard subnormal flush to zero */ return (ax); ix = ((int *) &ax)[HIWORD]; } else ix += 768 << 20; if (ny == 0) { if (ay == zero) /* guard subnormal flush to zero */ return (ax * twom768); iy = ((int *) &ay)[HIWORD]; } else iy += 768 << 20; j = (ix >> 20) - (iy >> 20); if (j > 32) { /* x >> y */ if (j <= 53) ay *= twom53; return ((ax + ay) * twom768); } } else if (j > 32) { /* x >> y */ if (j <= 53) ay *= twom53; return (ax + ay); } /* * Medium range ax and ay with max{|ax/ay|,|ay/ax|} bounded by 2^32 * First check rounding mode by comparing onep1u*onep1u with onep1u+twom53. * Make sure the computation is done at run-time. */ if (((lx | ly) << 5) == 0) { ay = ay * ay; ax += ay / (ax + sqrt(ax * ax + ay)); } else if (onep1u * onep1u != onep1u + twom53) { /* round-to-zero, positive, negative mode */ /* magic formula with less than an ulp error */ w = sqrt(ax * ax + ay * ay); ax += ay / ((ax + w) / ay); } else { /* round-to-nearest mode */ w = ax - ay; if (w > ay) { ((int *) &xh)[HIWORD] = ix; ((int *) &xh)[LOWORD] = 0; ay = ay * ay + (ax - xh) * (ax + xh); ax = sqrt(xh * xh + ay); } else { ax = ax + ax; ((int *) &xh)[HIWORD] = ix + 0x00100000; ((int *) &xh)[LOWORD] = 0; ((int *) &yh)[HIWORD] = iy; ((int *) &yh)[LOWORD] = 0; ay = w * w + ((ax - xh) * yh + (ay - yh) * ax); ax = sqrt(xh * yh + ay); } } if (iscale > 0) { if (iscale == 1) ax *= twom768; else { ax *= two768; /* must generate side effect here */ if (((int *) &ax)[HIWORD] == 0x7ff00000) ax = _SVID_libm_err(x, y, 4); } } return (ax); }
