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  #if defined(LIBM_SCCS) && !defined(lint)
14  static char rcsid[] = "$NetBSD: s_tan.c,v 1.7 1995/05/10 20:48:18 jtc 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 "mathP.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  }