Home | History | Annotate | Line # | Download | only in src 
      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 #include <sys/cdefs.h>
     14 #if defined(LIBM_SCCS) && !defined(lint)
     15 __RCSID("$NetBSD: s_tan.c,v 1.11 2024/05/08 01:40:27 riastradh Exp $");
     16 #endif
     17 
     18 /* tan(x)
     19  * Return tangent function of x.
     20  *
     21  * kernel function:
     22  *	__kernel_tan		... tangent function on [-pi/4,pi/4]
     23  *	__ieee754_rem_pio2	... argument reduction routine
     24  *
     25  * Method.
     26  *      Let S,C and T denote the sin, cos and tan respectively on
     27  *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
     28  *	in [-pi/4 , +pi/4], and let n = k mod 4.
     29  *	We have
     30  *
     31  *          n        sin(x)      cos(x)        tan(x)
     32  *     ----------------------------------------------------------
     33  *	    0	       S	   C		 T
     34  *	    1	       C	  -S		-1/T
     35  *	    2	      -S	  -C		 T
     36  *	    3	      -C	   S		-1/T
     37  *     ----------------------------------------------------------
     38  *
     39  * Special cases:
     40  *      Let trig be any of sin, cos, or tan.
     41  *      trig(+-INF)  is NaN, with signals;
     42  *      trig(NaN)    is that NaN;
     43  *
     44  * Accuracy:
     45  *	TRIG(x) returns trig(x) nearly rounded
     46  */
     47 
     48 #include "namespace.h"
     49 #include "math.h"
     50 #include "math_private.h"
     51 
     52 __weak_alias(tan, _tan)
     53 
     54 double
     55 tan(double x)
     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