cos.c revision ddc0e0b53c661f6e439e3b7072b3ef353eadb4af
/*
* 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.
*/
#pragma weak __cos = cos
/* INDENT OFF */
/*
* cos(x)
* Accurate Table look-up algorithm by K.C. Ng, May, 1995.
*
* Algorithm: see sincos.c
*/
#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,
/* Q1 = */ -0.5,
/* Q2 = */ 4.166666666500350703680945520860748617445e-0002,
/* Q3 = */ -1.388888596436972210694266290577848696006e-0003,
/* Q4 = */ 2.478563078858589473679519517892953492192e-0005,
/* PIO2_H = */ 1.570796326794896557999,
/* PIO2_L = */ 6.123233995736765886130e-17,
/* PIO2_L0 = */ 6.123233995727922165564e-17,
/* PIO2_L1 = */ 8.843720566135701120255e-29,
/* PI3O2_H = */ 4.712388980384689673997,
/* PI3O2_L = */ 1.836970198721029765839e-16,
/* PI3O2_L0 = */ 1.836970198720396133587e-16,
/* PI3O2_L1 = */ 6.336322524749201142226e-29,
/* PI5O2_H = */ 7.853981633974482789995,
/* PI5O2_L = */ 3.061616997868382943065e-16,
/* PI5O2_L0 = */ 3.061616997861941598865e-16,
/* PI5O2_L1 = */ 6.441344200433640781982e-28,
};
/* INDENT ON */
#define ONE sc[0]
#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]
#define PIO2_H sc[14]
#define PIO2_L sc[15]
#define PIO2_L0 sc[16]
#define PIO2_L1 sc[17]
#define PI3O2_H sc[18]
#define PI3O2_L sc[19]
#define PI3O2_L0 sc[20]
#define PI3O2_L1 sc[21]
#define PI5O2_H sc[22]
#define PI5O2_L sc[23]
#define PI5O2_L0 sc[24]
#define PI5O2_L1 sc[25]
extern const double _TBL_sincos[], _TBL_sincosx[];
double
cos(double x) {
double z, y[2], w, s, v, p, q;
int i, j, n, hx, ix, lx;
hx = ((int *)&x)[HIWORD];
lx = ((int *)&x)[LOWORD];
ix = hx & ~0x80000000;
if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */
if (ix < 0x3e400000) { /* |x| < 2**-27 */
if ((int)x == 0)
return (ONE);
}
z = x * x;
if (ix < 0x3f800000) /* |x| < 0.008 */
w = z * (QQ1 + z * QQ2);
else
w = z * ((Q1 + z * Q2) + (z * z) * (Q3 + z * Q4));
return (ONE + w);
}
/* for 0.164062500 < x < M, */
n = ix >> 20;
if (n < 0x402) { /* x < 8 */
i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n);
j = i - 10;
x = fabs(x);
v = x - _TBL_sincosx[j];
if (((j - 81) ^ (j - 101)) < 0) {
/* near pi/2, cos(pi/2-x)=sin(x) */
p = PIO2_H - x;
i = ix - 0x3ff921fb;
x = p + PIO2_L;
if ((i | ((lx - 0x54442D00) & 0xffffff00)) == 0) {
/* very close to pi/2 */
x = p + PIO2_L0;
return (x + PIO2_L1);
}
z = x * x;
if (((ix - 0x3ff92000) >> 12) == 0) {
/* |pi/2-x|<2**-8 */
w = PIO2_L + (z * x) * (PP1 + z * PP2);
} else {
w = PIO2_L + (z * x) * ((P1 + z * P2) +
(z * z) * (P3 + z * P4));
}
return (p + w);
}
s = v * v;
if (((j - 282) ^ (j - 302)) < 0) {
/* near 3/2pi, cos(x-3/2pi)=sin(x) */
p = x - PI3O2_H;
i = ix - 0x4012D97C;
x = p - PI3O2_L;
if ((i | ((lx - 0x7f332100) & 0xffffff00)) == 0) {
/* very close to 3/2pi */
x = p - PI3O2_L0;
return (x - PI3O2_L1);
}
z = x * x;
if (((ix - 0x4012D800) >> 9) == 0) {
/* |x-3/2pi|<2**-8 */
w = (z * x) * (PP1 + z * PP2) - PI3O2_L;
} else {
w = (z * x) * ((P1 + z * P2) + (z * z)
* (P3 + z * P4)) - PI3O2_L;
}
return (p + w);
}
if (((j - 483) ^ (j - 503)) < 0) {
/* near 5pi/2, cos(5pi/2-x)=sin(x) */
p = PI5O2_H - x;
i = ix - 0x401F6A7A;
x = p + PI5O2_L;
if ((i | ((lx - 0x29553800) & 0xffffff00)) == 0) {
/* very close to pi/2 */
x = p + PI5O2_L0;
return (x + PI5O2_L1);
}
z = x * x;
if (((ix - 0x401F6A7A) >> 7) == 0) {
/* |pi/2-x|<2**-8 */
w = PI5O2_L + (z * x) * (PP1 + z * PP2);
} else {
w = PI5O2_L + (z * x) * ((P1 + z * P2) +
(z * z) * (P3 + z * P4));
}
return (p + w);
}
j <<= 1;
w = _TBL_sincos[j];
z = _TBL_sincos[j+1];
p = v + (v * s) * (PP1 + s * PP2);
q = s * (QQ1 + s * QQ2);
return (z - (w * p - z * q));
}
if (ix >= 0x7ff00000) /* cos(Inf or NaN) is NaN */
return (x / x);
/* argument reduction needed */
n = __rem_pio2(x, y);
switch (n & 3) {
case 0:
return (__k_cos(y[0], y[1]));
case 1:
return (-__k_sin(y[0], y[1]));
case 2:
return (-__k_cos(y[0], y[1]));
default:
return (__k_sin(y[0], y[1]));
}
}