xref: /freebsd/lib/msun/src/s_tan.c (revision 953a3198a35204535cc9d450f04da982a4fea59b)
1 /* @(#)s_tan.c 5.1 93/09/24 */
2 /*
3  * ====================================================
4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5  *
6  * Developed at SunPro, a Sun Microsystems, Inc. business.
7  * Permission to use, copy, modify, and distribute this
8  * software is freely granted, provided that this notice
9  * is preserved.
10  * ====================================================
11  */
12 
13 #ifndef lint
14 static char rcsid[] = "$Id: s_tan.c,v 1.1.1.1 1994/08/19 09:39:53 jkh Exp $";
15 #endif
16 
17 /* tan(x)
18  * Return tangent function of x.
19  *
20  * kernel function:
21  *	__kernel_tan		... tangent function on [-pi/4,pi/4]
22  *	__ieee754_rem_pio2	... argument reduction routine
23  *
24  * Method.
25  *      Let S,C and T denote the sin, cos and tan respectively on
26  *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
27  *	in [-pi/4 , +pi/4], and let n = k mod 4.
28  *	We have
29  *
30  *          n        sin(x)      cos(x)        tan(x)
31  *     ----------------------------------------------------------
32  *	    0	       S	   C		 T
33  *	    1	       C	  -S		-1/T
34  *	    2	      -S	  -C		 T
35  *	    3	      -C	   S		-1/T
36  *     ----------------------------------------------------------
37  *
38  * Special cases:
39  *      Let trig be any of sin, cos, or tan.
40  *      trig(+-INF)  is NaN, with signals;
41  *      trig(NaN)    is that NaN;
42  *
43  * Accuracy:
44  *	TRIG(x) returns trig(x) nearly rounded
45  */
46 
47 #include "math.h"
48 #include "math_private.h"
49 
50 #ifdef __STDC__
51 	double tan(double x)
52 #else
53 	double tan(x)
54 	double x;
55 #endif
56 {
57 	double y[2],z=0.0;
58 	int32_t n, ix;
59 
60     /* High word of x. */
61 	GET_HIGH_WORD(ix,x);
62 
63     /* |x| ~< pi/4 */
64 	ix &= 0x7fffffff;
65 	if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
66 
67     /* tan(Inf or NaN) is NaN */
68 	else if (ix>=0x7ff00000) return x-x;		/* NaN */
69 
70     /* argument reduction needed */
71 	else {
72 	    n = __ieee754_rem_pio2(x,y);
73 	    return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
74 							-1 -- n odd */
75 	}
76 }
77