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/*
* 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.
*/
#if defined(ELFOBJ)
#pragma weak hypot = __hypot
#endif
/* 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);
}
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