# code: 9ferno

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```/* derived from /netlib/fdlibm */

/* @(#)s_tan.c 1.3 95/01/18 */
/*
* ====================================================
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/

/* tan(x)
* Return tangent function of x.
*
* kernel function:
*	__kernel_tan		... tangent function on [-pi/4,pi/4]
*	__ieee754_rem_pio2	... argument reduction routine
*
* Method.
*      Let S,C and T denote the sin, cos and tan respectively on
*	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
*	in [-pi/4 , +pi/4], and let n = k mod 4.
*	We have
*
*          n        sin(x)      cos(x)        tan(x)
*     ----------------------------------------------------------
*	    0	       S	   C		 T
*	    1	       C	  -S		-1/T
*	    2	      -S	  -C		 T
*	    3	      -C	   S		-1/T
*     ----------------------------------------------------------
*
* Special cases:
*      Let trig be any of sin, cos, or tan.
*      trig(+-INF)  is NaN, with signals;
*      trig(NaN)    is that NaN;
*
* Accuracy:
*	TRIG(x) returns trig(x) nearly rounded
*/

#include "fdlibm.h"

double tan(double x)
{
double y[2],z=0.0;
int n, ix;

/* High word of x. */
ix = __HI(x);

/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);

/* tan(Inf or NaN) is NaN */
else if (ix>=0x7ff00000) return x-x;		/* NaN */

/* argument reduction needed */
else {
n = __ieee754_rem_pio2(x,y);
return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
-1 -- n odd */
}
}
```