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/* @(#)s_tan.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#ifndef lint
static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_tan.c,v 1.10 2005/11/02 14:01:45 bde Exp $";
#endif
/* 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 "math.h"
#include "math_private.h"
double
tan(double x)
{
double y[2],z=0.0;
int32_t n, ix;
/* High word of x. */
GET_HIGH_WORD(ix,x);
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if(ix <= 0x3fe921fb) {
if(ix<0x3e300000) /* x < 2**-28 */
if((int)x==0) return x; /* generate inexact */
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 */
}
}
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