xref: /freebsd/lib/msun/src/s_cos.c (revision 6580f5c38dd5b01aeeaed16b370f1a12423437f0)
1 /*
2  * ====================================================
3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4  *
5  * Developed at SunPro, a Sun Microsystems, Inc. business.
6  * Permission to use, copy, modify, and distribute this
7  * software is freely granted, provided that this notice
8  * is preserved.
9  * ====================================================
10  */
11 
12 /* cos(x)
13  * Return cosine function of x.
14  *
15  * kernel function:
16  *	__kernel_sin		... sine function on [-pi/4,pi/4]
17  *	__kernel_cos		... cosine function on [-pi/4,pi/4]
18  *	__ieee754_rem_pio2	... argument reduction routine
19  *
20  * Method.
21  *      Let S,C and T denote the sin, cos and tan respectively on
22  *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
23  *	in [-pi/4 , +pi/4], and let n = k mod 4.
24  *	We have
25  *
26  *          n        sin(x)      cos(x)        tan(x)
27  *     ----------------------------------------------------------
28  *	    0	       S	   C		 T
29  *	    1	       C	  -S		-1/T
30  *	    2	      -S	  -C		 T
31  *	    3	      -C	   S		-1/T
32  *     ----------------------------------------------------------
33  *
34  * Special cases:
35  *      Let trig be any of sin, cos, or tan.
36  *      trig(+-INF)  is NaN, with signals;
37  *      trig(NaN)    is that NaN;
38  *
39  * Accuracy:
40  *	TRIG(x) returns trig(x) nearly rounded
41  */
42 
43 #include <float.h>
44 
45 #include "math.h"
46 #define INLINE_REM_PIO2
47 #include "math_private.h"
48 #include "e_rem_pio2.c"
49 
50 double
51 cos(double x)
52 {
53 	double y[2],z=0.0;
54 	int32_t n, ix;
55 
56     /* High word of x. */
57 	GET_HIGH_WORD(ix,x);
58 
59     /* |x| ~< pi/4 */
60 	ix &= 0x7fffffff;
61 	if(ix <= 0x3fe921fb) {
62 	    if(ix<0x3e46a09e)			/* if x < 2**-27 * sqrt(2) */
63 		if(((int)x)==0) return 1.0;	/* generate inexact */
64 	    return __kernel_cos(x,z);
65 	}
66 
67     /* cos(Inf or NaN) is NaN */
68 	else if (ix>=0x7ff00000) return x-x;
69 
70     /* argument reduction needed */
71 	else {
72 	    n = __ieee754_rem_pio2(x,y);
73 	    switch(n&3) {
74 		case 0: return  __kernel_cos(y[0],y[1]);
75 		case 1: return -__kernel_sin(y[0],y[1],1);
76 		case 2: return -__kernel_cos(y[0],y[1]);
77 		default:
78 		        return  __kernel_sin(y[0],y[1],1);
79 	    }
80 	}
81 }
82 
83 #if (LDBL_MANT_DIG == 53)
84 __weak_reference(cos, cosl);
85 #endif
86