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      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[] = "$FreeBSD: src/lib/msun/src/s_tan.c,v 1.10 2005/11/02 14:01:45 bde 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 double
     51 tan(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<0x3e300000)			/* x < 2**-28 */
     63 		if((int)x==0) return x;		/* generate inexact */
     64 	    return __kernel_tan(x,z,1);
     65 	}
     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