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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 #include <sys/cdefs.h>
     14 __FBSDID("$FreeBSD$");
     15 
     16 /* tan(x)
     17  * Return tangent function of x.
     18  *
     19  * kernel function:
     20  *	__kernel_tan		... tangent function on [-pi/4,pi/4]
     21  *	__ieee754_rem_pio2	... argument reduction routine
     22  *
     23  * Method.
     24  *      Let S,C and T denote the sin, cos and tan respectively on
     25  *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
     26  *	in [-pi/4 , +pi/4], and let n = k mod 4.
     27  *	We have
     28  *
     29  *          n        sin(x)      cos(x)        tan(x)
     30  *     ----------------------------------------------------------
     31  *	    0	       S	   C		 T
     32  *	    1	       C	  -S		-1/T
     33  *	    2	      -S	  -C		 T
     34  *	    3	      -C	   S		-1/T
     35  *     ----------------------------------------------------------
     36  *
     37  * Special cases:
     38  *      Let trig be any of sin, cos, or tan.
     39  *      trig(+-INF)  is NaN, with signals;
     40  *      trig(NaN)    is that NaN;
     41  *
     42  * Accuracy:
     43  *	TRIG(x) returns trig(x) nearly rounded
     44  */
     45 
     46 #include <float.h>
     47 
     48 #include "math.h"
     49 #define INLINE_REM_PIO2
     50 #include "math_private.h"
     51 #include "e_rem_pio2.c"
     52 
     53 double
     54 tan(double x)
     55 {
     56 	double y[2],z=0.0;
     57 	int32_t n, ix;
     58 
     59     /* High word of x. */
     60 	GET_HIGH_WORD(ix,x);
     61 
     62     /* |x| ~< pi/4 */
     63 	ix &= 0x7fffffff;
     64 	if(ix <= 0x3fe921fb) {
     65 	    if(ix<0x3e400000)			/* x < 2**-27 */
     66 		if((int)x==0) return x;		/* generate inexact */
     67 	    return __kernel_tan(x,z,1);
     68 	}
     69 
     70     /* tan(Inf or NaN) is NaN */
     71 	else if (ix>=0x7ff00000) return x-x;		/* NaN */
     72 
     73     /* argument reduction needed */
     74 	else {
     75 	    n = __ieee754_rem_pio2(x,y);
     76 	    return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
     77 							-1 -- n odd */
     78 	}
     79 }
     80 
     81 #if (LDBL_MANT_DIG == 53)
     82 __weak_reference(tan, tanl);
     83 #endif
     84