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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.
*/
/* INDENT OFF */
/*
* double __k_sincos(double x, double y, double *c);
* kernel sincos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
* return sin(x) with *c = cos(x)
*
* Accurate Table look-up algorithm by K.C. Ng, May, 1995.
*
* 1. Reduce x to x>0 by sin(-x)=-sin(x),cos(-x)=cos(x).
* 2. For 0<= x < pi/4, let i = (64*x chopped)-10. Let d = x - a[i], where
* a[i] is a double that is close to (i+10.5)/64 and such that
* sin(a[i]) and cos(a[i]) is close to a double (with error less
* than 2**-8 ulp). Then
* cos(x) = cos(a[i]+d) = cos(a[i])cos(d) - sin(a[i])*sin(d)
* = TBL_cos_a[i]*(1+QQ1*d^2+QQ2*d^4) -
* TBL_sin_a[i]*(d+PP1*d^3+PP2*d^5)
* = TBL_cos_a[i] + (TBL_cos_a[i]*d^2*(QQ1+QQ2*d^2) -
* TBL_sin_a[i]*(d+PP1*d^3+PP2*d^5))
* sin(x) = sin(a[i]+d) = sin(a[i])cos(d) + cos(a[i])*sin(d)
* = TBL_sin_a[i]*(1+QQ1*d^2+QQ2*d^4) +
* TBL_cos_a[i]*(d+PP1*d^3+PP2*d^5)
* = TBL_sin_a[i] + (TBL_sin_a[i]*d^2*(QQ1+QQ2*d^2) +
* TBL_cos_a[i]*(d+PP1*d^3+PP2*d^5))
*
* For |y| less than 10.5/64 = 0.1640625, use
* sin(y) = y + y^3*(p1+y^2*(p2+y^2*(p3+y^2*p4)))
* cos(y) = 1 + y^2*(q1+y^2*(q2+y^2*(q3+y^2*q4)))
*
* For |y| less than 0.008, use
* sin(y) = y + y^3*(pp1+y^2*pp2)
* cos(y) = 1 + y^2*(qq1+y^2*qq2)
*
* Accuracy:
* TRIG(x) returns trig(x) nearly rounded (less than 1 ulp)
*/
#include "libm.h"
static const double sc[] = {
/* ONE = */ 1.0,
/* NONE = */ -1.0,
/*
* |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008
*/
/* PP1 = */ -0.166666666666316558867252052378889521480627858683055567,
/* PP2 = */ .008333315652997472323564894248466758248475374977974017927,
/*
* |(sin(x) - (x+p1*x^3+...+p4*x^9)|
* |------------------------------ | <= 2^-57.63 for |x| < 0.1953125
* | x |
*/
/* P1 = */ -1.666666666666629669805215138920301589656e-0001,
/* P2 = */ 8.333333332390951295683993455280336376663e-0003,
/* P3 = */ -1.984126237997976692791551778230098403960e-0004,
/* P4 = */ 2.753403624854277237649987622848330351110e-0006,
/*
* |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d)
*/
/* QQ1 = */ -0.4999999999975492381842911981948418542742729,
/* QQ2 = */ 0.041666542904352059294545209158357640398771740,
/*
* |cos(x) - (1+q1*x^2+...+q4*x^8)| <= 2^-55.86 for |x| <= 0.1640625 (10.5/64)
*/
/* Q1 = */ -0.5,
/* Q2 = */ 4.166666666500350703680945520860748617445e-0002,
/* Q3 = */ -1.388888596436972210694266290577848696006e-0003,
/* Q4 = */ 2.478563078858589473679519517892953492192e-0005,
};
/* INDENT ON */
#define ONE sc[0]
#define NONE sc[1]
#define PP1 sc[2]
#define PP2 sc[3]
#define P1 sc[4]
#define P2 sc[5]
#define P3 sc[6]
#define P4 sc[7]
#define QQ1 sc[8]
#define QQ2 sc[9]
#define Q1 sc[10]
#define Q2 sc[11]
#define Q3 sc[12]
#define Q4 sc[13]
extern const double _TBL_sincos[], _TBL_sincosx[];
double
__k_sincos(double x, double y, double *c) {
double z, w, s, v, p, q;
int i, j, n, hx, ix;
hx = ((int *)&x)[HIWORD];
ix = hx & ~0x80000000;
if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */
if (ix < 0x3e400000) { /* |x| < 2**-27 */
if ((int)x == 0)
*c = ONE;
return (x + y);
} else {
z = x * x;
if (ix < 0x3f800000) { /* |x| < 0.008 */
q = z * (QQ1 + z * QQ2);
p = (x * z) * (PP1 + z * PP2) + y;
} else {
q = z * ((Q1 + z * Q2) + (z * z) * (Q3 +
z * Q4));
p = (x * z) * ((P1 + z * P2) + (z * z) * (P3 +
z * P4)) + y;
}
*c = ONE + q;
return (x + p);
}
} else { /* 0.164062500 < |x| < ~pi/4 */
n = ix >> 20;
i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n);
j = i - 10;
if (hx < 0)
v = -y - (_TBL_sincosx[j] + x);
else
v = y - (_TBL_sincosx[j] - x);
s = v * v;
j <<= 1;
w = _TBL_sincos[j];
z = _TBL_sincos[j+1];
p = s * (PP1 + s * PP2);
q = s * (QQ1 + s * QQ2);
p = v + v * p;
*c = z - (w * p - z * q);
s = w * q + z * p;
return ((hx >= 0)? w + s : -(w + s));
}
}
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