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/* origin: FreeBSD /usr/src/lib/msun/src/s_tan.c */
/*
* ====================================================
* 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.
* ====================================================
*/
/* tan(x)
* Return tangent function of x.
*
* kernel function:
* __tan ... tangent function on [-pi/4,pi/4]
* __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 "libm.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 < 0x3e400000) /* x < 2**-27 */
/* raise inexact if x != 0 */
if ((int)x == 0)
return x;
return __tan(x, z, 1);
}
/* tan(Inf or NaN) is NaN */
if (ix >= 0x7ff00000)
return x - x;
/* argument reduction needed */
n = __rem_pio2(x, y);
return __tan(y[0], y[1], 1 - ((n&1)<<1)); /* n even: 1, n odd: -1 */
}
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