__sincosl.c revision 25c28e83beb90e7c80452a7c818c5e6f73a07dc8
/*
* 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.
*/
/*
* long double __k_sincos(long double x, long double y, long double *c);
* kernel sincosl 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 sinl(x) with *c = cosl(x)
*
* Table look up algorithm
* see __k_sinl and __k_cosl
*/
#include "libm.h"
extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[],
_TBL_cosl_hi[], _TBL_cosl_lo[];
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,
/*
* |(sin(x) - (x+p1*x^3+...+p8*x^17)|
* |------------------------------- | <= 2^-116.17 for |x|<0.1953125
* | x |
*/
p1 = -1.666666666666666666666666666666211262297e-0001L,
p2 = +8.333333333333333333333333301497876908541e-0003L,
p3 = -1.984126984126984126984041302881180621922e-0004L,
p4 = +2.755731922398589064100587351307269621093e-0006L,
p5 = -2.505210838544163129378906953765595393873e-0008L,
p6 = +1.605904383643244375050998243778534074273e-0010L,
p7 = -7.647162722800685516901456114270824622699e-0013L,
p8 = +2.810046428661902961725428841068844462603e-0015L,
/*
* 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,
/*
* 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;
#define i0 0
long double
__k_sincosl(long double x, long double y, long double *c) {
long double a1, a2, t, t1, t2, 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 (((int) x) == 0) {
*c = one;
return (x);
} /* generate inexact */
z = x * x;
if (ix < 0x3ff80000) {
*c = one + z * (qq1 + z * (qq2 + z * (qq3 +
z * (qq4 + z * qq5))));
t = z * (p1 + z * (p2 + z * (p3 + z * (p4 +
z * (p5 + z * p6)))));
} else {
*c = one + z * (q1 + z * (q2 + z * (q3 + z * (q4 +
z * (q5 + z * (q6 + z * (q7 + z * q8)))))));
t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
z * (p6 + z * (p7 + z * p8)))))));
}
t = y + x * t;
return (x + t);
}
j = (ix + 0x400) & 0x7ffff800;
i = (j - 0x3ffc4000) >> 11;
pt[i0] = j;
if (hx > 0)
x = y - (t - x);
else
x = (-y) - (t + x);
a1 = _TBL_sinl_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)))));
a2 = _TBL_cosl_hi[i];
t2 = _TBL_cosl_lo[i] - (a1 * w - a2 * t);
*c = a2 + t2;
t1 = a2 * w + a1 * t;
t1 += _TBL_sinl_lo[i];
if (hx < 0)
return (-a1 - t1);
else
return (a1 + t1);
}