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      1 /* s_tanl.c -- long double version of s_tan.c.
      2  * Conversion to IEEE quad long double by Jakub Jelinek, jj (at) ultra.linux.cz.
      3  */
      4 
      5 /* @(#)s_tan.c 5.1 93/09/24 */
      6 /*
      7  * ====================================================
      8  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
      9  *
     10  * Developed at SunPro, a Sun Microsystems, Inc. business.
     11  * Permission to use, copy, modify, and distribute this
     12  * software is freely granted, provided that this notice
     13  * is preserved.
     14  * ====================================================
     15  */
     16 
     17 /* tanq(x)
     18  * Return tangent function of x.
     19  *
     20  * kernel function:
     21  *	__quadmath_kernel_tanq		... tangent function on [-pi/4,pi/4]
     22  *	__quadmath_rem_pio2q	... argument reduction routine
     23  *
     24  * Method.
     25  *      Let S,C and T denote the sin, cos and tan respectively on
     26  *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
     27  *	in [-pi/4 , +pi/4], and let n = k mod 4.
     28  *	We have
     29  *
     30  *          n        sin(x)      cos(x)        tan(x)
     31  *     ----------------------------------------------------------
     32  *	    0	       S	   C		 T
     33  *	    1	       C	  -S		-1/T
     34  *	    2	      -S	  -C		 T
     35  *	    3	      -C	   S		-1/T
     36  *     ----------------------------------------------------------
     37  *
     38  * Special cases:
     39  *      Let trig be any of sin, cos, or tan.
     40  *      trig(+-INF)  is NaN, with signals;
     41  *      trig(NaN)    is that NaN;
     42  *
     43  * Accuracy:
     44  *	TRIG(x) returns trig(x) nearly rounded
     45  */
     46 
     47 #include "quadmath-imp.h"
     48 
     49 __float128 tanq(__float128 x)
     50 {
     51 	__float128 y[2],z=0;
     52 	int64_t n, ix;
     53 
     54     /* High word of x. */
     55 	GET_FLT128_MSW64(ix,x);
     56 
     57     /* |x| ~< pi/4 */
     58 	ix &= 0x7fffffffffffffffLL;
     59 	if(ix <= 0x3ffe921fb54442d1LL) return __quadmath_kernel_tanq(x,z,1);
     60 
     61     /* tanq(Inf or NaN) is NaN */
     62 	else if (ix>=0x7fff000000000000LL) {
     63 	    if (ix == 0x7fff000000000000LL) {
     64 		GET_FLT128_LSW64(n,x);
     65 		if (n == 0)
     66 		    errno = EDOM;
     67 	    }
     68 	    return x-x;		/* NaN */
     69 	}
     70 
     71     /* argument reduction needed */
     72 	else {
     73 	    n = __quadmath_rem_pio2q(x,y);
     74 	    return __quadmath_kernel_tanq(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
     75 							-1 -- n odd */
     76 	}
     77 }
     78