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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.
*/
/*
* __k_cosl(long double x, long double y)
* kernel cos 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.
*
* Table look up algorithm
* 1. by cos(-x) = cos(x), we may replace x by |x|
* 2. if x < 25/128 = [0x3ffc4000, 0] = 0.15625 , then
* if x < 2^-57 (hx < 0x3fc60000 0), return 1.0 with inexact if x != 0
* z = x*x;
* if x <= 1/128 = 2**-7 = 0.0078125
* cos(x)=1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))))
* else
* cos(x)=1.0+z*(q1+ ... z*q8)
* 3. else
* ht = (hx + 0x400)&0x7ffff800 (round x to a break point t)
* lt = 0
* i = (hy-0x3ffc4000)>>11; (i<=64)
* x' = (x - t)+y (|x'| ~<= 2^-7
* By
* cos(t+x')
* = cos(t)cos(x')-sin(t)sin(x')
* = cos(t)(1+z*(qq1+z*qq2))-[sin(t)]*x*(1+z*(pp1+z*pp2))
* = cos(t) + [cos(t)]*(z*(qq1+z*qq2))-
* [sin(t)]*x*(1+z*(pp1+z*pp2))
*
* Thus,
* let a= _TBL_cos_hi[i], b = _TBL_cos_lo[i], c= _TBL_sin_hi[i],
* x = (x-t)+y
* z = x*x;
* cos(t+x) = a+(b+ (-c*x*(1+z*(pp1+z*pp2))+a*(z*(qq1+z*qq2)))
*/
#include "libm.h"
extern const long double _TBL_cosl_hi[], _TBL_cosl_lo[], _TBL_sinl_hi[];
static const long double
one = 1.0L,
/*
* 3 11 -122.32
* |sin(x) - (x+pp1*x +...+ pp5*x )| <= 2 for |x|<1/64
*/
pp1 = -1.666666666666666666666666666586782940810e-0001L,
pp2 = +8.333333333333333333333003723660929317540e-0003L,
pp3 = -1.984126984126984076045903483778337804470e-0004L,
pp4 = +2.755731922361906641319723106210900949413e-0006L,
pp5 = -2.505198398570947019093998469135012057673e-0008L,
/*
* 2 16 -117.11
* |cos(x) - (1+q1*x + ... + q8*x )| <= 2 for |x|<= 0.15625
*/
q1 = -4.999999999999999999999999999999756416975e-0001L,
q2 = +4.166666666666666666666666664006066577258e-0002L,
q3 = -1.388888888888888888888877700363937169637e-0003L,
q4 = +2.480158730158730158494468463031814083559e-0005L,
q5 = -2.755731922398586276322819250356005542871e-0007L,
q6 = +2.087675698767424261441959760729854017855e-0009L,
q7 = -1.147074481239662089072452129010790774761e-0011L,
q8 = +4.777761647399651599730663422263531034782e-0014L,
/*
* 2 10 -123.84
* |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128
*/
qq1 = -4.999999999999999999999999999999378373641e-0001L,
qq2 = +4.166666666666666666666665478399327703130e-0002L,
qq3 = -1.388888888888888888058211230618051613494e-0003L,
qq4 = +2.480158730156105377771585658905303111866e-0005L,
qq5 = -2.755728099762526325736488376695157008736e-0007L;
#define i0 0
long double
__k_cosl(long double x, long double y) {
long double a, t, z, w;
int *pt = (int *) &t, *px = (int *) &x;
int i, j, hx, ix;
t = 1.0L;
hx = px[i0];
ix = hx & 0x7fffffff;
if (ix < 0x3ffc4000) {
if (ix < 0x3fc60000)
if ((i = (int) x) == 0)
return (one); /* generate inexact */
z = x * x;
if (ix < 0x3ff80000) /* 0.0078125 */
return one + z * (qq1 + z * (qq2 + z * (qq3 +
z * (qq4 + z * qq5))));
else
return one + z * (q1 + z * (q2 + z * (q3 +
z * (q4 + z * (q5 + z * (q6 + z * (q7 +
z * q8)))))));
}
j = (ix + 0x400) & 0x7ffff800;
i = (j - 0x3ffc4000) >> 11;
pt[i0] = j;
if (hx > 0)
x = y - (t - x);
else
x = (-y) - (t + x);
a = _TBL_cosl_hi[i];
z = x * x;
t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5)))));
t = _TBL_cosl_lo[i] - (_TBL_sinl_hi[i] * w - a * t);
return (a + t);
}
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