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/* @(#)s_tan.c 5.1 93/09/24 */
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/*
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 * ====================================================
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 *
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 * Permission to use, copy, modify, and distribute this
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 * software is freely granted, provided that this notice
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 * is preserved.
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 * ====================================================
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 */
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#ifndef lint
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static char rcsid[] = "$\Id: s_tan.c,v 1.2.6.1 1997/02/23 11:03:23 joerg Exp $";
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#endif
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/* tan(x)
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 * Return tangent function of x.
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 *
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 * kernel function:
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 *      __kernel_tan            ... tangent function on [-pi/4,pi/4]
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 *      __ieee754_rem_pio2      ... argument reduction routine
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 *
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 * Method.
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 *      Let S,C and T denote the sin, cos and tan respectively on
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 *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
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 *      in [-pi/4 , +pi/4], and let n = k mod 4.
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 *      We have
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 *
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 *          n        sin(x)      cos(x)        tan(x)
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 *     ----------------------------------------------------------
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 *          0          S           C             T
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 *          1          C          -S            -1/T
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 *          2         -S          -C             T
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 *          3         -C           S            -1/T
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 *     ----------------------------------------------------------
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 *
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 * Special cases:
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 *      Let trig be any of sin, cos, or tan.
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 *      trig(+-INF)  is NaN, with signals;
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 *      trig(NaN)    is that NaN;
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 *
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 * Accuracy:
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 *      TRIG(x) returns trig(x) nearly rounded
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 */
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#include "math.h"
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#include "math_private.h"
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#ifdef __STDC__
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        double __generic_tan(double x)
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#else
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        double __generic_tan(x)
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        double x;
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#endif
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{
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        double y[2],z=0.0;
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        int32_t n, ix;
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    /* High word of x. */
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        GET_HIGH_WORD(ix,x);
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    /* |x| ~< pi/4 */
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        ix &= 0x7fffffff;
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        if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
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    /* tan(Inf or NaN) is NaN */
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        else if (ix>=0x7ff00000) return x-x;            /* NaN */
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    /* argument reduction needed */
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        else {
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            n = __ieee754_rem_pio2(x,y);
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            return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
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                                                        -1 -- n odd */
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        }
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}