1 
2 /* @(#)s_tan.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 /*
16 
17 FUNCTION
18         <<tan>>, <<tanf>>---tangent
19 
20 INDEX
21 tan
22 INDEX
23 tanf
24 
25 ANSI_SYNOPSIS
26         #include <math.h>
27         double tan(double <[x]>);
28         float tanf(float <[x]>);
29 
30 TRAD_SYNOPSIS
31         #include <math.h>
32         double tan(<[x]>)
33         double <[x]>;
34 
35         float tanf(<[x]>)
36         float <[x]>;
37 
38 
39 DESCRIPTION
40 <<tan>> computes the tangent of the argument <[x]>.
41 Angles are specified in radians.
42 
43 <<tanf>> is identical, save that it takes and returns <<float>> values.
44 
45 RETURNS
46 The tangent of <[x]> is returned.
47 
48 PORTABILITY
49 <<tan>> is ANSI. <<tanf>> is an extension.
50 */
51 
52 /* tan(x)
53  * Return tangent function of x.
54  *
55  * kernel function:
56  *	__kernel_tan		... tangent function on [-pi/4,pi/4]
57  *	__ieee754_rem_pio2	... argument reduction routine
58  *
59  * Method.
60  *      Let S,C and T denote the sin, cos and tan respectively on
61  *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
62  *	in [-pi/4 , +pi/4], and let n = k mod 4.
63  *	We have
64  *
65  *          n        sin(x)      cos(x)        tan(x)
66  *     ----------------------------------------------------------
67  *	    0	       S	   C		 T
68  *	    1	       C	  -S		-1/T
69  *	    2	      -S	  -C		 T
70  *	    3	      -C	   S		-1/T
71  *     ----------------------------------------------------------
72  *
73  * Special cases:
74  *      Let trig be any of sin, cos, or tan.
75  *      trig(+-INF)  is NaN, with signals;
76  *      trig(NaN)    is that NaN;
77  *
78  * Accuracy:
79  *	TRIG(x) returns trig(x) nearly rounded
80  */
81 
82 #include "fdlibm.h"
83 
84 #ifndef _DOUBLE_IS_32BITS
85 
86 #ifdef __STDC__
tan(double x)87 	double tan(double x)
88 #else
89 	double tan(x)
90 	double x;
91 #endif
92 {
93 	double y[2],z=0.0;
94 	int32_t n,ix;
95 
96     /* High word of x. */
97 	GET_HIGH_WORD(ix,x);
98 
99     /* |x| ~< pi/4 */
100 	ix &= 0x7fffffff;
101 	if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
102 
103     /* tan(Inf or NaN) is NaN */
104 	else if (ix>=0x7ff00000) return x-x;		/* NaN */
105 
106     /* argument reduction needed */
107 	else {
108 	    n = __ieee754_rem_pio2(x,y);
109 	    return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
110 							-1 -- n odd */
111 	}
112 }
113 
114 #endif /* _DOUBLE_IS_32BITS */
115