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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 2005 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
/*
* __rem_pio2(x, y) passes back a better-than-double-precision
* approximation to x mod pi/2 in y[0]+y[1] and returns an integer
* congruent mod 8 to the integer part of x/(pi/2).
*
* This implementation tacitly assumes that x is finite and at
* least about pi/4 in magnitude.
*/
#include "libm.h"
extern const int _TBL_ipio2_inf[];
/* INDENT OFF */
/*
* invpio2: 53 bits of 2/pi
* pio2_1: first 33 bit of pi/2
* pio2_1t: pi/2 - pio2_1
* pio2_2: second 33 bit of pi/2
* pio2_2t: pi/2 - pio2_2
* pio2_3: third 33 bit of pi/2
* pio2_3t: pi/2 - pio2_3
*/
static const double
half = 0.5,
invpio2 = 0.636619772367581343075535, /* 2^ -1 * 1.45F306DC9C883 */
pio2_1 = 1.570796326734125614166, /* 2^ 0 * 1.921FB54400000 */
pio2_1t = 6.077100506506192601475e-11, /* 2^-34 * 1.0B4611A626331 */
pio2_2 = 6.077100506303965976596e-11, /* 2^-34 * 1.0B4611A600000 */
pio2_2t = 2.022266248795950732400e-21, /* 2^-69 * 1.3198A2E037073 */
pio2_3 = 2.022266248711166455796e-21, /* 2^-69 * 1.3198A2E000000 */
pio2_3t = 8.478427660368899643959e-32; /* 2^-104 * 1.B839A252049C1 */
/* INDENT ON */
int
__rem_pio2(double x, double *y) {
double w, t, r, fn;
double tx[3];
int e0, i, j, nx, n, ix, hx, lx;
hx = ((int *)&x)[HIWORD];
ix = hx & 0x7fffffff;
if (ix < 0x4002d97c) {
/* |x| < 3pi/4, special case with n=1 */
t = fabs(x) - pio2_1;
if (ix != 0x3ff921fb) { /* 33+53 bit pi is good enough */
y[0] = t - pio2_1t;
y[1] = (t - y[0]) - pio2_1t;
} else { /* near pi/2, use 33+33+53 bit pi */
t -= pio2_2;
y[0] = t - pio2_2t;
y[1] = (t - y[0]) - pio2_2t;
}
if (hx < 0) {
y[0] = -y[0];
y[1] = -y[1];
return (-1);
}
return (1);
}
if (ix <= 0x413921fb) {
/* |x| <= 2^19 pi */
t = fabs(x);
n = (int)(t * invpio2 + half);
fn = (double)n;
r = t - fn * pio2_1;
j = ix >> 20;
w = fn * pio2_1t; /* 1st round good to 85 bit */
y[0] = r - w;
i = j - ((((int *)y)[HIWORD] >> 20) & 0x7ff);
if (i > 16) { /* 2nd iteration (rare) */
/* 2nd round good to 118 bit */
if (i < 35) {
t = r; /* r-fn*pio2_2 may not be exact */
w = fn * pio2_2;
r = t - w;
w = fn * pio2_2t - ((t - r) - w);
y[0] = r - w;
} else {
r -= fn * pio2_2;
w = fn * pio2_2t;
y[0] = r - w;
i = j - ((((int *)y)[HIWORD] >> 20) & 0x7ff);
if (i > 49) {
/* 3rd iteration (extremely rare) */
if (i < 68) {
t = r;
w = fn * pio2_3;
r = t - w;
w = fn * pio2_3t -
((t - r) - w);
y[0] = r - w;
} else {
/*
* 3rd round good to 151 bits;
* covered all possible cases
*/
r -= fn * pio2_3;
w = fn * pio2_3t;
y[0] = r - w;
}
}
}
}
y[1] = (r - y[0]) - w;
if (hx < 0) {
y[0] = -y[0];
y[1] = -y[1];
return (-n);
}
return (n);
}
e0 = (ix >> 20) - 1046; /* e0 = ilogb(x)-23; */
/* break x into three 24 bit pieces */
lx = ((int *)&x)[LOWORD];
i = (lx & 0x1f) << 19;
tx[2] = (double)i;
j = (lx >> 5) & 0xffffff;
tx[1] = (double)j;
tx[0] = (double)((((ix & 0xfffff) | 0x100000) << 3) |
((unsigned)lx >> 29));
nx = 3;
if (i == 0) {
/* skip zero term */
nx--;
if (j == 0)
nx--;
}
n = __rem_pio2m(tx, y, e0, nx, 2, _TBL_ipio2_inf);
if (hx < 0) {
y[0] = -y[0];
y[1] = -y[1];
return (-n);
}
return (n);
}
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