1 
2 /* @(#)s_sin.c 5.1 93/09/24 */
3 /*
4  * ====================================================
5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6  *
7  * Developed at SunPro, a Sun Microsystems, Inc. business.
8  * Permission to use, copy, modify, and distribute this
9  * software is freely granted, provided that this notice
10  * is preserved.
11  * ====================================================
12  */
13 
14 /*
15 FUNCTION
16         <<sin>>, <<sinf>>, <<cos>>, <<cosf>>---sine or cosine
17 INDEX
18 sin
19 INDEX
20 sinf
21 INDEX
22 cos
23 INDEX
24 cosf
25 ANSI_SYNOPSIS
26         #include <math.h>
27         double sin(double <[x]>);
28         float  sinf(float <[x]>);
29         double cos(double <[x]>);
30         float cosf(float <[x]>);
31 
32 TRAD_SYNOPSIS
33         #include <math.h>
34         double sin(<[x]>)
35         double <[x]>;
36         float  sinf(<[x]>)
37         float <[x]>;
38 
39         double cos(<[x]>)
40         double <[x]>;
41         float cosf(<[x]>)
42         float <[x]>;
43 
44 DESCRIPTION
45 	<<sin>> and <<cos>> compute (respectively) the sine and cosine
46 	of the argument <[x]>.  Angles are specified in radians.
47 
48 	<<sinf>> and <<cosf>> are identical, save that they take and
49 	return <<float>> values.
50 
51 
52 RETURNS
53 	The sine or cosine of <[x]> is returned.
54 
55 PORTABILITY
56 	<<sin>> and <<cos>> are ANSI C.
57 	<<sinf>> and <<cosf>> are extensions.
58 
59 QUICKREF
60 	sin ansi pure
61 	sinf - pure
62 */
63 
64 /* sin(x)
65  * Return sine function of x.
66  *
67  * kernel function:
68  *	__kernel_sin		... sine function on [-pi/4,pi/4]
69  *	__kernel_cos		... cose function on [-pi/4,pi/4]
70  *	__ieee754_rem_pio2	... argument reduction routine
71  *
72  * Method.
73  *      Let S,C and T denote the sin, cos and tan respectively on
74  *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
75  *	in [-pi/4 , +pi/4], and let n = k mod 4.
76  *	We have
77  *
78  *          n        sin(x)      cos(x)        tan(x)
79  *     ----------------------------------------------------------
80  *	    0	       S	   C		 T
81  *	    1	       C	  -S		-1/T
82  *	    2	      -S	  -C		 T
83  *	    3	      -C	   S		-1/T
84  *     ----------------------------------------------------------
85  *
86  * Special cases:
87  *      Let trig be any of sin, cos, or tan.
88  *      trig(+-INF)  is NaN, with signals;
89  *      trig(NaN)    is that NaN;
90  *
91  * Accuracy:
92  *	TRIG(x) returns trig(x) nearly rounded
93  */
94 
95 #include "fdlibm.h"
96 
97 #ifndef _DOUBLE_IS_32BITS
98 
99 #ifdef __STDC__
sin(double x)100 	double sin(double x)
101 #else
102 	double sin(x)
103 	double x;
104 #endif
105 {
106 	double y[2],z=0.0;
107 	int32_t n,ix;
108 
109     /* High word of x. */
110 	GET_HIGH_WORD(ix,x);
111 
112     /* |x| ~< pi/4 */
113 	ix &= 0x7fffffff;
114 	if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
115 
116     /* sin(Inf or NaN) is NaN */
117 	else if (ix>=0x7ff00000) return x-x;
118 
119     /* argument reduction needed */
120 	else {
121 	    n = __ieee754_rem_pio2(x,y);
122 	    switch(n&3) {
123 		case 0: return  __kernel_sin(y[0],y[1],1);
124 		case 1: return  __kernel_cos(y[0],y[1]);
125 		case 2: return -__kernel_sin(y[0],y[1],1);
126 		default:
127 			return -__kernel_cos(y[0],y[1]);
128 	    }
129 	}
130 }
131 
132 #endif /* _DOUBLE_IS_32BITS */
133