1*25c28e83SPiotr Jasiukajtis /*
2*25c28e83SPiotr Jasiukajtis * CDDL HEADER START
3*25c28e83SPiotr Jasiukajtis *
4*25c28e83SPiotr Jasiukajtis * The contents of this file are subject to the terms of the
5*25c28e83SPiotr Jasiukajtis * Common Development and Distribution License (the "License").
6*25c28e83SPiotr Jasiukajtis * You may not use this file except in compliance with the License.
7*25c28e83SPiotr Jasiukajtis *
8*25c28e83SPiotr Jasiukajtis * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9*25c28e83SPiotr Jasiukajtis * or http://www.opensolaris.org/os/licensing.
10*25c28e83SPiotr Jasiukajtis * See the License for the specific language governing permissions
11*25c28e83SPiotr Jasiukajtis * and limitations under the License.
12*25c28e83SPiotr Jasiukajtis *
13*25c28e83SPiotr Jasiukajtis * When distributing Covered Code, include this CDDL HEADER in each
14*25c28e83SPiotr Jasiukajtis * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15*25c28e83SPiotr Jasiukajtis * If applicable, add the following below this CDDL HEADER, with the
16*25c28e83SPiotr Jasiukajtis * fields enclosed by brackets "[]" replaced with your own identifying
17*25c28e83SPiotr Jasiukajtis * information: Portions Copyright [yyyy] [name of copyright owner]
18*25c28e83SPiotr Jasiukajtis *
19*25c28e83SPiotr Jasiukajtis * CDDL HEADER END
20*25c28e83SPiotr Jasiukajtis */
21*25c28e83SPiotr Jasiukajtis /*
22*25c28e83SPiotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23*25c28e83SPiotr Jasiukajtis */
24*25c28e83SPiotr Jasiukajtis /*
25*25c28e83SPiotr Jasiukajtis * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26*25c28e83SPiotr Jasiukajtis * Use is subject to license terms.
27*25c28e83SPiotr Jasiukajtis */
28*25c28e83SPiotr Jasiukajtis
29*25c28e83SPiotr Jasiukajtis /* INDENT OFF */
30*25c28e83SPiotr Jasiukajtis /*
31*25c28e83SPiotr Jasiukajtis * __k_cos(double x; double y)
32*25c28e83SPiotr Jasiukajtis * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
33*25c28e83SPiotr Jasiukajtis * Input x is assumed to be bounded by ~pi/4 in magnitude.
34*25c28e83SPiotr Jasiukajtis * Input y is the tail of x.
35*25c28e83SPiotr Jasiukajtis *
36*25c28e83SPiotr Jasiukajtis * Accurate Table look-up algorithm by K.C. Ng, May, 1995.
37*25c28e83SPiotr Jasiukajtis *
38*25c28e83SPiotr Jasiukajtis * Algorithm: see __sincos.c
39*25c28e83SPiotr Jasiukajtis */
40*25c28e83SPiotr Jasiukajtis
41*25c28e83SPiotr Jasiukajtis #include "libm.h"
42*25c28e83SPiotr Jasiukajtis
43*25c28e83SPiotr Jasiukajtis static const double sc[] = {
44*25c28e83SPiotr Jasiukajtis /* ONE = */ 1.0,
45*25c28e83SPiotr Jasiukajtis /* NONE = */ -1.0,
46*25c28e83SPiotr Jasiukajtis /*
47*25c28e83SPiotr Jasiukajtis * |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008
48*25c28e83SPiotr Jasiukajtis */
49*25c28e83SPiotr Jasiukajtis /* PP1 = */ -0.166666666666316558867252052378889521480627858683055567,
50*25c28e83SPiotr Jasiukajtis /* PP2 = */ .008333315652997472323564894248466758248475374977974017927,
51*25c28e83SPiotr Jasiukajtis /*
52*25c28e83SPiotr Jasiukajtis * |(sin(x) - (x+p1*x^3+...+p4*x^9)|
53*25c28e83SPiotr Jasiukajtis * |------------------------------ | <= 2^-57.63 for |x| < 0.1953125
54*25c28e83SPiotr Jasiukajtis * | x |
55*25c28e83SPiotr Jasiukajtis */
56*25c28e83SPiotr Jasiukajtis /* P1 = */ -1.666666666666629669805215138920301589656e-0001,
57*25c28e83SPiotr Jasiukajtis /* P2 = */ 8.333333332390951295683993455280336376663e-0003,
58*25c28e83SPiotr Jasiukajtis /* P3 = */ -1.984126237997976692791551778230098403960e-0004,
59*25c28e83SPiotr Jasiukajtis /* P4 = */ 2.753403624854277237649987622848330351110e-0006,
60*25c28e83SPiotr Jasiukajtis /*
61*25c28e83SPiotr Jasiukajtis * |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d)
62*25c28e83SPiotr Jasiukajtis */
63*25c28e83SPiotr Jasiukajtis /* QQ1 = */ -0.4999999999975492381842911981948418542742729,
64*25c28e83SPiotr Jasiukajtis /* QQ2 = */ 0.041666542904352059294545209158357640398771740,
65*25c28e83SPiotr Jasiukajtis /*
66*25c28e83SPiotr Jasiukajtis * |cos(x) - (1+q1*x^2+...+q4*x^8)| <= 2^-55.86 for |x| <= 0.1640625 (10.5/64)
67*25c28e83SPiotr Jasiukajtis */
68*25c28e83SPiotr Jasiukajtis /* Q1 = */ -0.5,
69*25c28e83SPiotr Jasiukajtis /* Q2 = */ 4.166666666500350703680945520860748617445e-0002,
70*25c28e83SPiotr Jasiukajtis /* Q3 = */ -1.388888596436972210694266290577848696006e-0003,
71*25c28e83SPiotr Jasiukajtis /* Q4 = */ 2.478563078858589473679519517892953492192e-0005,
72*25c28e83SPiotr Jasiukajtis };
73*25c28e83SPiotr Jasiukajtis /* INDENT ON */
74*25c28e83SPiotr Jasiukajtis
75*25c28e83SPiotr Jasiukajtis #define ONE sc[0]
76*25c28e83SPiotr Jasiukajtis #define NONE sc[1]
77*25c28e83SPiotr Jasiukajtis #define PP1 sc[2]
78*25c28e83SPiotr Jasiukajtis #define PP2 sc[3]
79*25c28e83SPiotr Jasiukajtis #define P1 sc[4]
80*25c28e83SPiotr Jasiukajtis #define P2 sc[5]
81*25c28e83SPiotr Jasiukajtis #define P3 sc[6]
82*25c28e83SPiotr Jasiukajtis #define P4 sc[7]
83*25c28e83SPiotr Jasiukajtis #define QQ1 sc[8]
84*25c28e83SPiotr Jasiukajtis #define QQ2 sc[9]
85*25c28e83SPiotr Jasiukajtis #define Q1 sc[10]
86*25c28e83SPiotr Jasiukajtis #define Q2 sc[11]
87*25c28e83SPiotr Jasiukajtis #define Q3 sc[12]
88*25c28e83SPiotr Jasiukajtis #define Q4 sc[13]
89*25c28e83SPiotr Jasiukajtis
90*25c28e83SPiotr Jasiukajtis extern const double _TBL_sincos[], _TBL_sincosx[];
91*25c28e83SPiotr Jasiukajtis
92*25c28e83SPiotr Jasiukajtis double
__k_cos(double x,double y)93*25c28e83SPiotr Jasiukajtis __k_cos(double x, double y) {
94*25c28e83SPiotr Jasiukajtis double z, w, s, v, p, q;
95*25c28e83SPiotr Jasiukajtis int i, j, n, hx, ix;
96*25c28e83SPiotr Jasiukajtis
97*25c28e83SPiotr Jasiukajtis hx = ((int *)&x)[HIWORD];
98*25c28e83SPiotr Jasiukajtis ix = hx & ~0x80000000;
99*25c28e83SPiotr Jasiukajtis
100*25c28e83SPiotr Jasiukajtis if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */
101*25c28e83SPiotr Jasiukajtis if (ix < 0x3e400000) /* |x| < 2**-27 */
102*25c28e83SPiotr Jasiukajtis if ((int)x == 0)
103*25c28e83SPiotr Jasiukajtis return (ONE);
104*25c28e83SPiotr Jasiukajtis z = x * x;
105*25c28e83SPiotr Jasiukajtis if (ix < 0x3f800000) /* |x| < 0.008 */
106*25c28e83SPiotr Jasiukajtis q = z * (QQ1 + z * QQ2);
107*25c28e83SPiotr Jasiukajtis else
108*25c28e83SPiotr Jasiukajtis q = z * ((Q1 + z * Q2) + (z * z) * (Q3 + z * Q4));
109*25c28e83SPiotr Jasiukajtis return (ONE + q);
110*25c28e83SPiotr Jasiukajtis } else { /* 0.164062500 < |x| < ~pi/4 */
111*25c28e83SPiotr Jasiukajtis n = ix >> 20;
112*25c28e83SPiotr Jasiukajtis i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n);
113*25c28e83SPiotr Jasiukajtis j = i - 10;
114*25c28e83SPiotr Jasiukajtis if (hx < 0)
115*25c28e83SPiotr Jasiukajtis v = -y - (_TBL_sincosx[j] + x);
116*25c28e83SPiotr Jasiukajtis else
117*25c28e83SPiotr Jasiukajtis v = y - (_TBL_sincosx[j] - x);
118*25c28e83SPiotr Jasiukajtis s = v * v;
119*25c28e83SPiotr Jasiukajtis j <<= 1;
120*25c28e83SPiotr Jasiukajtis w = _TBL_sincos[j];
121*25c28e83SPiotr Jasiukajtis z = _TBL_sincos[j+1];
122*25c28e83SPiotr Jasiukajtis p = s * (PP1 + s * PP2);
123*25c28e83SPiotr Jasiukajtis q = s * (QQ1 + s * QQ2);
124*25c28e83SPiotr Jasiukajtis p = v + v * p;
125*25c28e83SPiotr Jasiukajtis return (z - (w * p - z * q));
126*25c28e83SPiotr Jasiukajtis }
127*25c28e83SPiotr Jasiukajtis }
128