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 /*
23*25c28e83SPiotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24*25c28e83SPiotr Jasiukajtis */
25*25c28e83SPiotr Jasiukajtis /*
26*25c28e83SPiotr Jasiukajtis * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27*25c28e83SPiotr Jasiukajtis * Use is subject to license terms.
28*25c28e83SPiotr Jasiukajtis */
29*25c28e83SPiotr Jasiukajtis
30*25c28e83SPiotr Jasiukajtis /*
31*25c28e83SPiotr Jasiukajtis * long double __k_sincos(long double x, long double y, long double *c);
32*25c28e83SPiotr Jasiukajtis * kernel sincosl 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 * return sinl(x) with *c = cosl(x)
36*25c28e83SPiotr Jasiukajtis *
37*25c28e83SPiotr Jasiukajtis * Table look up algorithm
38*25c28e83SPiotr Jasiukajtis * see __k_sinl and __k_cosl
39*25c28e83SPiotr Jasiukajtis */
40*25c28e83SPiotr Jasiukajtis
41*25c28e83SPiotr Jasiukajtis #include "libm.h"
42*25c28e83SPiotr Jasiukajtis
43*25c28e83SPiotr Jasiukajtis extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[],
44*25c28e83SPiotr Jasiukajtis _TBL_cosl_hi[], _TBL_cosl_lo[];
45*25c28e83SPiotr Jasiukajtis static const long double
46*25c28e83SPiotr Jasiukajtis one = 1.0L,
47*25c28e83SPiotr Jasiukajtis /*
48*25c28e83SPiotr Jasiukajtis * 3 11 -122.32
49*25c28e83SPiotr Jasiukajtis * |sin(x) - (x+pp1*x +...+ pp5*x )| <= 2 for |x|<1/64
50*25c28e83SPiotr Jasiukajtis */
51*25c28e83SPiotr Jasiukajtis pp1 = -1.666666666666666666666666666586782940810e-0001L,
52*25c28e83SPiotr Jasiukajtis pp2 = +8.333333333333333333333003723660929317540e-0003L,
53*25c28e83SPiotr Jasiukajtis pp3 = -1.984126984126984076045903483778337804470e-0004L,
54*25c28e83SPiotr Jasiukajtis pp4 = +2.755731922361906641319723106210900949413e-0006L,
55*25c28e83SPiotr Jasiukajtis pp5 = -2.505198398570947019093998469135012057673e-0008L,
56*25c28e83SPiotr Jasiukajtis /*
57*25c28e83SPiotr Jasiukajtis * |(sin(x) - (x+p1*x^3+...+p8*x^17)|
58*25c28e83SPiotr Jasiukajtis * |------------------------------- | <= 2^-116.17 for |x|<0.1953125
59*25c28e83SPiotr Jasiukajtis * | x |
60*25c28e83SPiotr Jasiukajtis */
61*25c28e83SPiotr Jasiukajtis p1 = -1.666666666666666666666666666666211262297e-0001L,
62*25c28e83SPiotr Jasiukajtis p2 = +8.333333333333333333333333301497876908541e-0003L,
63*25c28e83SPiotr Jasiukajtis p3 = -1.984126984126984126984041302881180621922e-0004L,
64*25c28e83SPiotr Jasiukajtis p4 = +2.755731922398589064100587351307269621093e-0006L,
65*25c28e83SPiotr Jasiukajtis p5 = -2.505210838544163129378906953765595393873e-0008L,
66*25c28e83SPiotr Jasiukajtis p6 = +1.605904383643244375050998243778534074273e-0010L,
67*25c28e83SPiotr Jasiukajtis p7 = -7.647162722800685516901456114270824622699e-0013L,
68*25c28e83SPiotr Jasiukajtis p8 = +2.810046428661902961725428841068844462603e-0015L,
69*25c28e83SPiotr Jasiukajtis /*
70*25c28e83SPiotr Jasiukajtis * 2 10 -123.84
71*25c28e83SPiotr Jasiukajtis * |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128
72*25c28e83SPiotr Jasiukajtis */
73*25c28e83SPiotr Jasiukajtis qq1 = -4.999999999999999999999999999999378373641e-0001L,
74*25c28e83SPiotr Jasiukajtis qq2 = +4.166666666666666666666665478399327703130e-0002L,
75*25c28e83SPiotr Jasiukajtis qq3 = -1.388888888888888888058211230618051613494e-0003L,
76*25c28e83SPiotr Jasiukajtis qq4 = +2.480158730156105377771585658905303111866e-0005L,
77*25c28e83SPiotr Jasiukajtis qq5 = -2.755728099762526325736488376695157008736e-0007L,
78*25c28e83SPiotr Jasiukajtis /*
79*25c28e83SPiotr Jasiukajtis * 2 16 -117.11
80*25c28e83SPiotr Jasiukajtis * |cos(x) - (1+q1*x + ... + q8*x )| <= 2 for |x|<= 0.15625
81*25c28e83SPiotr Jasiukajtis */
82*25c28e83SPiotr Jasiukajtis q1 = -4.999999999999999999999999999999756416975e-0001L,
83*25c28e83SPiotr Jasiukajtis q2 = +4.166666666666666666666666664006066577258e-0002L,
84*25c28e83SPiotr Jasiukajtis q3 = -1.388888888888888888888877700363937169637e-0003L,
85*25c28e83SPiotr Jasiukajtis q4 = +2.480158730158730158494468463031814083559e-0005L,
86*25c28e83SPiotr Jasiukajtis q5 = -2.755731922398586276322819250356005542871e-0007L,
87*25c28e83SPiotr Jasiukajtis q6 = +2.087675698767424261441959760729854017855e-0009L,
88*25c28e83SPiotr Jasiukajtis q7 = -1.147074481239662089072452129010790774761e-0011L,
89*25c28e83SPiotr Jasiukajtis q8 = +4.777761647399651599730663422263531034782e-0014L;
90*25c28e83SPiotr Jasiukajtis
91*25c28e83SPiotr Jasiukajtis #define i0 0
92*25c28e83SPiotr Jasiukajtis
93*25c28e83SPiotr Jasiukajtis long double
__k_sincosl(long double x,long double y,long double * c)94*25c28e83SPiotr Jasiukajtis __k_sincosl(long double x, long double y, long double *c) {
95*25c28e83SPiotr Jasiukajtis long double a1, a2, t, t1, t2, z, w;
96*25c28e83SPiotr Jasiukajtis int *pt = (int *) &t, *px = (int *) &x;
97*25c28e83SPiotr Jasiukajtis int i, j, hx, ix;
98*25c28e83SPiotr Jasiukajtis
99*25c28e83SPiotr Jasiukajtis t = 1.0L;
100*25c28e83SPiotr Jasiukajtis hx = px[i0];
101*25c28e83SPiotr Jasiukajtis ix = hx & 0x7fffffff;
102*25c28e83SPiotr Jasiukajtis if (ix < 0x3ffc4000) {
103*25c28e83SPiotr Jasiukajtis if (ix < 0x3fc60000)
104*25c28e83SPiotr Jasiukajtis if (((int) x) == 0) {
105*25c28e83SPiotr Jasiukajtis *c = one;
106*25c28e83SPiotr Jasiukajtis return (x);
107*25c28e83SPiotr Jasiukajtis } /* generate inexact */
108*25c28e83SPiotr Jasiukajtis z = x * x;
109*25c28e83SPiotr Jasiukajtis
110*25c28e83SPiotr Jasiukajtis if (ix < 0x3ff80000) {
111*25c28e83SPiotr Jasiukajtis *c = one + z * (qq1 + z * (qq2 + z * (qq3 +
112*25c28e83SPiotr Jasiukajtis z * (qq4 + z * qq5))));
113*25c28e83SPiotr Jasiukajtis t = z * (p1 + z * (p2 + z * (p3 + z * (p4 +
114*25c28e83SPiotr Jasiukajtis z * (p5 + z * p6)))));
115*25c28e83SPiotr Jasiukajtis } else {
116*25c28e83SPiotr Jasiukajtis *c = one + z * (q1 + z * (q2 + z * (q3 + z * (q4 +
117*25c28e83SPiotr Jasiukajtis z * (q5 + z * (q6 + z * (q7 + z * q8)))))));
118*25c28e83SPiotr Jasiukajtis t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
119*25c28e83SPiotr Jasiukajtis z * (p6 + z * (p7 + z * p8)))))));
120*25c28e83SPiotr Jasiukajtis }
121*25c28e83SPiotr Jasiukajtis
122*25c28e83SPiotr Jasiukajtis t = y + x * t;
123*25c28e83SPiotr Jasiukajtis return (x + t);
124*25c28e83SPiotr Jasiukajtis }
125*25c28e83SPiotr Jasiukajtis j = (ix + 0x400) & 0x7ffff800;
126*25c28e83SPiotr Jasiukajtis i = (j - 0x3ffc4000) >> 11;
127*25c28e83SPiotr Jasiukajtis pt[i0] = j;
128*25c28e83SPiotr Jasiukajtis if (hx > 0)
129*25c28e83SPiotr Jasiukajtis x = y - (t - x);
130*25c28e83SPiotr Jasiukajtis else
131*25c28e83SPiotr Jasiukajtis x = (-y) - (t + x);
132*25c28e83SPiotr Jasiukajtis a1 = _TBL_sinl_hi[i];
133*25c28e83SPiotr Jasiukajtis z = x * x;
134*25c28e83SPiotr Jasiukajtis t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
135*25c28e83SPiotr Jasiukajtis w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5)))));
136*25c28e83SPiotr Jasiukajtis a2 = _TBL_cosl_hi[i];
137*25c28e83SPiotr Jasiukajtis t2 = _TBL_cosl_lo[i] - (a1 * w - a2 * t);
138*25c28e83SPiotr Jasiukajtis *c = a2 + t2;
139*25c28e83SPiotr Jasiukajtis t1 = a2 * w + a1 * t;
140*25c28e83SPiotr Jasiukajtis t1 += _TBL_sinl_lo[i];
141*25c28e83SPiotr Jasiukajtis if (hx < 0)
142*25c28e83SPiotr Jasiukajtis return (-a1 - t1);
143*25c28e83SPiotr Jasiukajtis else
144*25c28e83SPiotr Jasiukajtis return (a1 + t1);
145*25c28e83SPiotr Jasiukajtis }
146