/*
* 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 __sincos = sincos
/* INDENT OFF */
/*
* sincos(x,s,c)
* Accurate Table look-up algorithm by K.C. Ng, 2000.
*
* 1. Reduce x to x>0 by cos(-x)=cos(x), sin(-x)=-sin(x).
* 2. For 0<= x < 8, 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 hence |d|< 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))
*
* Note: for x close to n*pi/2, special treatment is need for either
* sin or cos:
* i in [81, 100] ( pi/2 +-10.5/64 => tiny cos(x) = sin(pi/2-x)
* i in [181,200] ( pi +-10.5/64 => tiny sin(x) = sin(pi-x)
* i in [282,301] ( 3pi/2+-10.5/64 => tiny cos(x) = sin(x-3pi/2)
* i in [382,401] ( 2pi +-10.5/64 => tiny sin(x) = sin(x-2pi)
* i in [483,502] ( 5pi/2+-10.5/64 => tiny cos(x) = sin(5pi/2-x)
*
* 3. For x >= 8.0, use kernel function __rem_pio2 to perform argument
* reduction and call __k_sincos_ to compute sin and cos.
*
* kernel function:
* __rem_pio2 ... argument reduction routine
* __k_sincos_ ... sine and cosine function on [-pi/4,pi/4]
*
* Method.
* Let S and C denote the sin and cos respectively on [-PI/4, +PI/4].
* 1. Assume the argument x is reduced to y1+y2 = x-k*pi/2 in
* [-pi/2 , +pi/2], and let n = k mod 4.
* 2. Let S=S(y1+y2), C=C(y1+y2). Depending on n, we have
*
* n sin(x) cos(x) tan(x)
* ----------------------------------------------------------
* 0 S C S/C
* 1 C -S -C/S
* 2 -S -C S/C
* 3 -C S -C/S
* ----------------------------------------------------------
*
* Special cases:
* Let trig be any of sin, cos, or tan.
* trig(+-INF) is NaN, with signals;
* trig(NaN) is that NaN;
*
* 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,
/* 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,
/* PI_H = */ 3.1415926535897931159979634685,
/* PI_L = */ 1.22464679914735317722606593227425e-16,
/* PI_L0 = */ 1.22464679914558443311283879205095e-16,
/* PI_L1 = */ 1.768744113227140223300005233735517376e-28,
/* PI3O2_H = */ 4.712388980384689673997,
/* PI3O2_L = */ 1.836970198721029765839e-16,
/* PI3O2_L0 = */ 1.836970198720396133587e-16,
/* PI3O2_L1 = */ 6.336322524749201142226e-29,
/* PI2_H = */ 6.2831853071795862319959269370,
/* PI2_L = */ 2.44929359829470635445213186454850e-16,
/* PI2_L0 = */ 2.44929359829116886622567758410190e-16,
/* PI2_L1 = */ 3.537488226454280446600010467471034752e-28,
/* 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 PI_H sc[18]
#define PI_L sc[19]
#define PI_L0 sc[20]
#define PI_L1 sc[21]
#define PI3O2_H sc[22]
#define PI3O2_L sc[23]
#define PI3O2_L0 sc[24]
#define PI3O2_L1 sc[25]
#define PI2_H sc[26]
#define PI2_L sc[27]
#define PI2_L0 sc[28]
#define PI2_L1 sc[29]
#define PI5O2_H sc[30]
#define PI5O2_L sc[31]
#define PI5O2_L0 sc[32]
#define PI5O2_L1 sc[33]
#define PoS(x, z) ((x * z) * (PP1 + z * PP2))
#define PoL(x, z) ((x * z) * ((P1 + z * P2) + (z * z) * (P3 + z * P4)))
extern const double _TBL_sincos[], _TBL_sincosx[];
void
sincos(double x, double *s, double *c) {
double z, y[2], w, t, 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)
*c = ONE;
*s = x;
} else {
z = x * x;
if (ix < 0x3f800000) { /* |x| < 0.008 */
q = z * (QQ1 + z * QQ2);
p = PoS(x, z);
} else {
q = z * ((Q1 + z * Q2) + (z * z) *
(Q3 + z * Q4));
p = PoL(x, z);
}
*c = ONE + q;
*s = x + p;
}
return;
}
n = ix >> 20;
i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n);
j = i - 10;
if (n < 0x402) { /* |x| < 8 */
x = fabs(x);
v = x - _TBL_sincosx[j];
t = v * v;
w = _TBL_sincos[(j<<1)];
z = _TBL_sincos[(j<<1)+1];
p = v + PoS(v, t);
q = t * (QQ1 + t * QQ2);
if ((((j - 81) ^ (j - 101)) |
((j - 282) ^ (j - 302)) |
((j - 483) ^ (j - 503)) |
((j - 181) ^ (j - 201)) |
((j - 382) ^ (j - 402))) < 0) {
if (j <= 101) {
/* near pi/2, cos(x) = sin(pi/2-x) */
t = w * q + z * p;
*s = (hx >= 0)? w + t : -w - t;
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;
*c = x + PIO2_L1;
} else {
z = x * x;
if (((ix - 0x3ff92000) >> 12) == 0) {
/* |pi/2-x|<2**-8 */
w = PIO2_L + PoS(x, z);
} else {
w = PIO2_L + PoL(x, z);
}
*c = p + w;
}
} else if (j <= 201) {
/* near pi, sin(x) = sin(pi-x) */
*c = z - (w * p - z * q);
p = PI_H - x;
i = ix - 0x400921fb;
x = p + PI_L;
if ((i | ((lx - 0x54442D00) &
0xffffff00)) == 0) {
/* very close to pi */
x = p + PI_L0;
*s = (hx >= 0)? x + PI_L1 :
-(x + PI_L1);
} else {
z = x * x;
if (((ix - 0x40092000) >> 11) == 0) {
/* |pi-x|<2**-8 */
w = PI_L + PoS(x, z);
} else {
w = PI_L + PoL(x, z);
}
*s = (hx >= 0)? p + w : -p - w;
}
} else if (j <= 302) {
/* near 3/2pi, cos(x)=sin(x-3/2pi) */
t = w * q + z * p;
*s = (hx >= 0)? w + t : -w - t;
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;
*c = x - PI3O2_L1;
} else {
z = x * x;
if (((ix - 0x4012D800) >> 9) == 0) {
/* |3/2pi-x|<2**-8 */
w = PoS(x, z) - PI3O2_L;
} else {
w = PoL(x, z) - PI3O2_L;
}
*c = p + w;
}
} else if (j <= 402) {
/* near 2pi, sin(x)=sin(x-2pi) */
*c = z - (w * p - z * q);
p = x - PI2_H;
i = ix - 0x401921fb;
x = p - PI2_L;
if ((i | ((lx - 0x54442D00) &
0xffffff00)) == 0) {
/* very close to 2pi */
x = p - PI2_L0;
*s = (hx >= 0)? x - PI2_L1 :
-(x - PI2_L1);
} else {
z = x * x;
if (((ix - 0x40192000) >> 10) == 0) {
/* |x-2pi|<2**-8 */
w = PoS(x, z) - PI2_L;
} else {
w = PoL(x, z) - PI2_L;
}
*s = (hx >= 0)? p + w : -p - w;
}
} else {
/* near 5pi/2, cos(x) = sin(5pi/2-x) */
t = w * q + z * p;
*s = (hx >= 0)? w + t : -w - t;
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;
*c = x + PI5O2_L1;
} else {
z = x * x;
if (((ix - 0x401F6A7A) >> 7) == 0) {
/* |5pi/2-x|<2**-8 */
w = PI5O2_L + PoS(x, z);
} else {
w = PI5O2_L + PoL(x, z);
}
*c = p + w;
}
}
} else {
*c = z - (w * p - z * q);
t = w * q + z * p;
*s = (hx >= 0)? w + t : -w - t;
}
return;
}
if (ix >= 0x7ff00000) {
*s = *c = x / x;
return;
}
/* argument reduction needed */
n = __rem_pio2(x, y);
switch (n & 3) {
case 0:
*s = __k_sincos(y[0], y[1], c);
break;
case 1:
*c = -__k_sincos(y[0], y[1], s);
break;
case 2:
*s = -__k_sincos(y[0], y[1], c);
*c = -*c;
break;
default:
*c = __k_sincos(y[0], y[1], s);
*s = -*s;
}
}