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      1 /* From: @(#)k_cos.c 1.3 95/01/18 */
      2 /*
      3  * ====================================================
      4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
      5  * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
      6  *
      7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
      8  * Permission to use, copy, modify, and distribute this
      9  * software is freely granted, provided that this notice
     10  * is preserved.
     11  * ====================================================
     12  */
     13 
     14 #include <sys/cdefs.h>
     15 /*
     16  * ld128 version of k_cos.c.  See ../src/k_cos.c for most comments.
     17  */
     18 
     19 #include "math_private.h"
     20 
     21 /*
     22  * Domain [-0.7854, 0.7854], range ~[-1.17e-39, 1.19e-39]:
     23  * |cos(x) - c(x))| < 2**-129.3
     24  *
     25  * 113-bit precision requires more care than 64-bit precision, since
     26  * simple methods give a minimax polynomial with coefficient for x^2
     27  * that is 1 ulp below 0.5, but we want it to be precisely 0.5.  See
     28  * ../ld80/k_cosl.c for more details.
     29  */
     30 static const double
     31 one = 1.0;
     32 static const long double
     33 C1 =  4.16666666666666666666666666666666667e-02L,
     34 C2 = -1.38888888888888888888888888888888834e-03L,
     35 C3 =  2.48015873015873015873015873015446795e-05L,
     36 C4 = -2.75573192239858906525573190949988493e-07L,
     37 C5 =  2.08767569878680989792098886701451072e-09L,
     38 C6 = -1.14707455977297247136657111139971865e-11L,
     39 C7 =  4.77947733238738518870113294139830239e-14L,
     40 C8 = -1.56192069685858079920640872925306403e-16L,
     41 C9 =  4.11031762320473354032038893429515732e-19L,
     42 C10= -8.89679121027589608738005163931958096e-22L,
     43 C11=  1.61171797801314301767074036661901531e-24L,
     44 C12= -2.46748624357670948912574279501044295e-27L;
     45 
     46 long double
     47 __kernel_cosl(long double x, long double y)
     48 {
     49 	long double hz,z,r,w;
     50 
     51 	z  = x*x;
     52 	r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+
     53 	    z*(C8+z*(C9+z*(C10+z*(C11+z*C12)))))))))));
     54 	hz = 0.5*z;
     55 	w  = one-hz;
     56 	return w + (((one-w)-hz) + (z*r-x*y));
     57 }
     58