xref: /titanic_51/usr/src/lib/libm/common/LD/__sinl.c (revision 3f1de28d23e9724b017260ef6b282b278b6e38f9)
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 /* INDENT OFF */
31 /*
32  * __k_sinl( long double x;  long double y )
33  * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.785398164
34  * Input x is assumed to be bounded by ~pi/4 in magnitude.
35  * Input y is the tail of x.
36  *
37  * Table look up algorithm
38  *	1. by sin(-x) = -sin(x), need only to consider positive x
39  *	2. if x < 25/128 = [0x3ffc9000,0,0,0] = 0.1953125 , then
40  *	     if x < 2^-57 (hx < 0x3fc60000,0,0,0), return x (inexact if x !=  0)
41  *	     z = x*x;
42  *	     if x <= 1/64 = 2**-6
43  *		sin(x) = x + (y+(x*z)*(p1 + z*p2))
44  *	     else
45  *		sin(x) = x + (y+(x*z)*(p1 + z*(p2 + z*(p3 + z*p4))))
46  *	3. else
47  *		ht = (hx + 0x400)&0x7ffff800	(round x to a break point t)
48  *		lt = 0
49  *		i  = (hy-0x3ffc4000)>>11;	(i<=64)
50  *		x' = (x - t)+y 			(|x'| ~<= 2^-7
51  *	   By
52  *		sin(t+x')
53  *		  = sin(t)cos(x')+cos(t)sin(x')
54  *		  = sin(t)(1+z*(qq1+z*qq2))+[cos(t)]*x*(1+z*(pp1+z*pp2))
55  *		  = sin(t) + [sin(t)]*(z*(qq1+z*qq2))+
56  *				[cos(t)]*x*(1+z*(pp1+z*pp2))
57  *
58  *	   Thus,
59  *		let a= _TBL_sin_hi[i], b = _TBL_sin_lo[i], c= _TBL_cos_hi[i],
60  *		x = (x-t)+y
61  *		z = x*x;
62  *		sin(t+x) = a+(b+ ((c*x)*(1+z*(pp1+z*pp2))+a*(z*(qq1+z*qq2)))
63  */
64 
65 #include "libm.h"
66 
67 #include <sys/isa_defs.h>
68 
69 extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[], _TBL_cosl_hi[];
70 static const long double
71 one	= 1.0,
72 /*
73  * |sin(x) - (x+pp1*x^3+...+ pp5*x^11)| <= 2^-122.32 for |x|<1/64
74  */
75 pp1	= -1.666666666666666666666666666586782940810e-0001L,
76 pp2	=  8.333333333333333333333003723660929317540e-0003L,
77 pp3	= -1.984126984126984076045903483778337804470e-0004L,
78 pp4	=  2.755731922361906641319723106210900949413e-0006L,
79 pp5	= -2.505198398570947019093998469135012057673e-0008L,
80 /*
81  * |(sin(x) - (x+p1*x^3+...+p8*x^17)|
82  * |------------------------------- | <= 2^-116.17 for |x|<0.1953125
83  * |                 x              |
84  */
85 p1	= -1.666666666666666666666666666666211262297e-0001L,
86 p2	=  8.333333333333333333333333301497876908541e-0003L,
87 p3	= -1.984126984126984126984041302881180621922e-0004L,
88 p4	=  2.755731922398589064100587351307269621093e-0006L,
89 p5	= -2.505210838544163129378906953765595393873e-0008L,
90 p6	=  1.605904383643244375050998243778534074273e-0010L,
91 p7	= -7.647162722800685516901456114270824622699e-0013L,
92 p8	=  2.810046428661902961725428841068844462603e-0015L,
93 /*
94  *		     2	         10        -123.84
95  * |cos(x) - (1+qq1*x +...+ qq5*x  )| <= 2        for |x|<=1/128
96  */
97 qq1	= -4.999999999999999999999999999999378373641e-0001L,
98 qq2	=  4.166666666666666666666665478399327703130e-0002L,
99 qq3	= -1.388888888888888888058211230618051613494e-0003L,
100 qq4	=  2.480158730156105377771585658905303111866e-0005L,
101 qq5	= -2.755728099762526325736488376695157008736e-0007L;
102 /* INDENT ON */
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 #if defined(__i386) || defined(__amd64)
111 	XTOI(px, hx);
112 #else
113 	hx = px[0];
114 #endif
115 	ix = hx & 0x7fffffff;
116 	if (ix < 0x3ffc9000) {
117 		if (ix < 0x3fc60000)
118 			if (((int) x) == 0)
119 				return (x);	/* generate inexact */
120 		z = x * x;
121 		t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 + z *
122 			(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 #if defined(__i386) || defined(__amd64)
129 	ITOX(j, pt);
130 #else
131 	pt[0] = j;
132 #endif
133 	if (hx > 0)
134 		x = y - (t - x);
135 	else
136 		x = (-y) - (t + x);
137 	a = _TBL_sinl_hi[i];
138 	z = x * x;
139 	t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
140 	w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z *
141 		pp5)))));
142 	t = _TBL_cosl_hi[i] * w + a * t;
143 	t += _TBL_sinl_lo[i];
144 	if (hx < 0)
145 		return (-a - t);
146 	else
147 		return (a + t);
148 }
149