12116Sjkh/* @(#)s_tan.c 5.1 93/09/24 */
22116Sjkh/*
32116Sjkh * ====================================================
42116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
52116Sjkh *
62116Sjkh * Developed at SunPro, a Sun Microsystems, Inc. business.
72116Sjkh * Permission to use, copy, modify, and distribute this
88870Srgrimes * software is freely granted, provided that this notice
92116Sjkh * is preserved.
102116Sjkh * ====================================================
112116Sjkh */
122116Sjkh
13176385Sbde#include <sys/cdefs.h>
14176385Sbde__FBSDID("$FreeBSD: releng/11.0/lib/msun/src/s_tan.c 218509 2011-02-10 07:37:50Z das $");
152116Sjkh
162116Sjkh/* tan(x)
172116Sjkh * Return tangent function of x.
182116Sjkh *
192116Sjkh * kernel function:
202116Sjkh *	__kernel_tan		... tangent function on [-pi/4,pi/4]
212116Sjkh *	__ieee754_rem_pio2	... argument reduction routine
222116Sjkh *
232116Sjkh * Method.
248870Srgrimes *      Let S,C and T denote the sin, cos and tan respectively on
258870Srgrimes *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
262116Sjkh *	in [-pi/4 , +pi/4], and let n = k mod 4.
272116Sjkh *	We have
282116Sjkh *
292116Sjkh *          n        sin(x)      cos(x)        tan(x)
302116Sjkh *     ----------------------------------------------------------
312116Sjkh *	    0	       S	   C		 T
322116Sjkh *	    1	       C	  -S		-1/T
332116Sjkh *	    2	      -S	  -C		 T
342116Sjkh *	    3	      -C	   S		-1/T
352116Sjkh *     ----------------------------------------------------------
362116Sjkh *
372116Sjkh * Special cases:
382116Sjkh *      Let trig be any of sin, cos, or tan.
392116Sjkh *      trig(+-INF)  is NaN, with signals;
402116Sjkh *      trig(NaN)    is that NaN;
412116Sjkh *
422116Sjkh * Accuracy:
438870Srgrimes *	TRIG(x) returns trig(x) nearly rounded
442116Sjkh */
452116Sjkh
46176360Sdas#include <float.h>
47176360Sdas
482116Sjkh#include "math.h"
49176385Sbde#define INLINE_REM_PIO2
502116Sjkh#include "math_private.h"
51176385Sbde#include "e_rem_pio2.c"
522116Sjkh
5397413Salfreddouble
54117912Spetertan(double x)
552116Sjkh{
562116Sjkh	double y[2],z=0.0;
572116Sjkh	int32_t n, ix;
582116Sjkh
592116Sjkh    /* High word of x. */
602116Sjkh	GET_HIGH_WORD(ix,x);
612116Sjkh
622116Sjkh    /* |x| ~< pi/4 */
632116Sjkh	ix &= 0x7fffffff;
64151969Sbde	if(ix <= 0x3fe921fb) {
65218509Sdas	    if(ix<0x3e400000)			/* x < 2**-27 */
66151969Sbde		if((int)x==0) return x;		/* generate inexact */
67151969Sbde	    return __kernel_tan(x,z,1);
68151969Sbde	}
692116Sjkh
702116Sjkh    /* tan(Inf or NaN) is NaN */
712116Sjkh	else if (ix>=0x7ff00000) return x-x;		/* NaN */
722116Sjkh
732116Sjkh    /* argument reduction needed */
742116Sjkh	else {
752116Sjkh	    n = __ieee754_rem_pio2(x,y);
762116Sjkh	    return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
772116Sjkh							-1 -- n odd */
782116Sjkh	}
792116Sjkh}
80176360Sdas
81176360Sdas#if (LDBL_MANT_DIG == 53)
82176360Sdas__weak_reference(tan, tanl);
83176360Sdas#endif
84