```   1 /*
2  * CDDL HEADER START
3  *
4  * The contents of this file are subject to the terms of the
5  * Common Development and Distribution License (the "License").
6  * You may not use this file except in compliance with the License.
7  *
8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9  * or http://www.opensolaris.org/os/licensing.
10  * See the License for the specific language governing permissions
11  * and limitations under the License.
12  *
13  * When distributing Covered Code, include this CDDL HEADER in each
14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15  * If applicable, add the following below this CDDL HEADER, with the
16  * fields enclosed by brackets "[]" replaced with your own identifying
17  * information: Portions Copyright [yyyy] [name of copyright owner]
18  *
19  * CDDL HEADER END
20  */
21
22 /*
23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
24  */
25 /*
26  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
27  * Use is subject to license terms.
28  */
29
30 /*
31  * long double __k_sinl(long double x, long double y);
32  * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.785398164
33  * Input x is assumed to be bounded by ~pi/4 in magnitude.
34  * Input y is the tail of x.
35  *
36  * Table look up algorithm
37  *      1. by sin(-x) = -sin(x), need only to consider positive x
38  *      2. if x < 25/128 = [0x3ffc9000,0,0,0] = 0.1953125 , then
39  *           if x < 2^-57 (hx < 0x3fc60000,0,0,0), return x (inexact if x !=  0)
40  *           z = x*x;
41  *           if x <= 1/64 = 2**-6
42  *              sin(x) = x + (y+(x*z)*(p1 + z*p2))
43  *           else
44  *              sin(x) = x + (y+(x*z)*(p1 + z*(p2 + z*(p3 + z*p4))))
45  *      3. else
46  *              ht = (hx + 0x400)&0x7ffff800        (round x to a break point t)
47  *              lt = 0
48  *              i  = (hy-0x3ffc4000)>>11; (i<=64)
49  *              x' = (x - t)+y                  (|x'| ~<= 2^-7
50  *         By
51  *              sin(t+x')
52  *                = sin(t)cos(x')+cos(t)sin(x')
53  *                = sin(t)(1+z*(qq1+z*qq2))+[cos(t)]*x*(1+z*(pp1+z*pp2))
54  *                = sin(t) + [sin(t)]*(z*(qq1+z*qq2))+
55  *                              [cos(t)]*x*(1+z*(pp1+z*pp2))
56  *
57  *         Thus,
58  *              let a= _TBL_sin_hi[i], b = _TBL_sin_lo[i], c= _TBL_cos_hi[i],
59  *              x = (x-t)+y
60  *              z = x*x;
61  *              sin(t+x) = a+(b+ ((c*x)*(1+z*(pp1+z*pp2))+a*(z*(qq1+z*qq2)))
62  */
63
64 #include "libm.h"
65
66 extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[], _TBL_cosl_hi[];
67 static const long double
68 one     = 1.0L,
69 /*
70  *                   3           11       -122.32
71  * |sin(x) - (x+pp1*x +...+ pp5*x  )| <= 2        for |x|<1/64
72  */
73         pp1     = -1.666666666666666666666666666586782940810e-0001L,
74         pp2     = +8.333333333333333333333003723660929317540e-0003L,
75         pp3     = -1.984126984126984076045903483778337804470e-0004L,
76         pp4     = +2.755731922361906641319723106210900949413e-0006L,
77         pp5     = -2.505198398570947019093998469135012057673e-0008L,
78 /*
79  * |(sin(x) - (x+p1*x^3+...+p8*x^17)|
80  * |------------------------------- | <= 2^-116.17 for |x|<0.1953125
81  * |                 x              |
82  */
83         p1      = -1.666666666666666666666666666666211262297e-0001L,
84         p2      = +8.333333333333333333333333301497876908541e-0003L,
85         p3      = -1.984126984126984126984041302881180621922e-0004L,
86         p4      = +2.755731922398589064100587351307269621093e-0006L,
87         p5      = -2.505210838544163129378906953765595393873e-0008L,
88         p6      = +1.605904383643244375050998243778534074273e-0010L,
89         p7      = -7.647162722800685516901456114270824622699e-0013L,
90         p8      = +2.810046428661902961725428841068844462603e-0015L,
91 /*
92  *                   2           10        -123.84
93  * |cos(x) - (1+qq1*x +...+ qq5*x  )| <= 2        for |x|<=1/128
94  */
95         qq1     = -4.999999999999999999999999999999378373641e-0001L,
96         qq2     = +4.166666666666666666666665478399327703130e-0002L,
97         qq3     = -1.388888888888888888058211230618051613494e-0003L,
98         qq4     = +2.480158730156105377771585658905303111866e-0005L,
99         qq5     = -2.755728099762526325736488376695157008736e-0007L;
100
101 #define i0      0
102
103 long double
104 __k_sinl(long double x, long double y) {
105         long double a, t, z, w;
106         int *pt = (int *) &t, *px = (int *) &x;
107         int i, j, hx, ix;
108
109         t = 1.0L;
110         hx = px[i0];
111         ix = hx & 0x7fffffff;
112         if (ix < 0x3ffc9000) {
113                 *(3 - i0 + (int *) &t) = -1;        /* one-ulp */
114                 *(2 + (int *) &t) = -1;     /* one-ulp */
115                 *(1 + (int *) &t) = -1;     /* one-ulp */
116                 *(i0 + (int *) &t) -= 1;    /* one-ulp */
117                 if (ix < 0x3fc60000)
118                         if (((int) (x * t)) < 1)
119                                 return (x);     /* inexact and underflow */
120                 z = x * x;
121                 t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
122                         z * (p6 + z * (p7 + z * p8)))))));
123                 t = y + x * t;
124                 return (x + t);
125         }
126         j = (ix + 0x400) & 0x7ffff800;
127         i = (j - 0x3ffc4000) >> 11;
128         pt[i0] = j;
129         if (hx > 0)
130                 x = y - (t - x);
131         else
132                 x = (-y) - (t + x);
133         a = _TBL_sinl_hi[i];
134         z = x * x;
135         t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
136         w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5)))));
137         t = _TBL_cosl_hi[i] * w + a * t;
138         t += _TBL_sinl_lo[i];
139         if (hx < 0)
140                 return (-a - t);
141         else
142                 return (a + t);
143 }
```