newlib/libm/ld128/k_cosl.c

   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 __FBSDID("$FreeBSD$");
  16
  17 /*
  18  * ld128 version of k_cos.c.  See ../src/k_cos.c for most comments.
  19  */
  20 #include <math.h>
  21 #include "../ld/math_private.h"
  22
  23 /*
  24  * Domain [-0.7854, 0.7854], range ~[-1.17e-39, 1.19e-39]:
  25  * |cos(x) - c(x))| < 2**-129.3
  26  *
  27  * 113-bit precision requires more care than 64-bit precision, since
  28  * simple methods give a minimax polynomial with coefficient for x^2
  29  * that is 1 ulp below 0.5, but we want it to be precisely 0.5.  See
  30  * ../ld80/k_cosl.c for more details.
  31  */
  32 static const double
  33 one = 1.0;
  34 static const long double
  35 C1 =  4.16666666666666666666666666666666667e-02L,
  36 C2 = -1.38888888888888888888888888888888834e-03L,
  37 C3 =  2.48015873015873015873015873015446795e-05L,
  38 C4 = -2.75573192239858906525573190949988493e-07L,
  39 C5 =  2.08767569878680989792098886701451072e-09L,
  40 C6 = -1.14707455977297247136657111139971865e-11L,
  41 C7 =  4.77947733238738518870113294139830239e-14L,
  42 C8 = -1.56192069685858079920640872925306403e-16L,
  43 C9 =  4.11031762320473354032038893429515732e-19L,
  44 C10= -8.89679121027589608738005163931958096e-22L,
  45 C11=  1.61171797801314301767074036661901531e-24L,
  46 C12= -2.46748624357670948912574279501044295e-27L;
  47
  48 long double
  49 __kernel_cosl(long double x, long double y)
  50 {
  51         long double hz,z,r,w;
  52
  53         z  = x*x;
  54         r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+
  55             z*(C8+z*(C9+z*(C10+z*(C11+z*C12)))))))))));
  56         hz = 0.5*z;
  57         w  = one-hz;
  58         return w + (((one-w)-hz) + (z*r-x*y));
  59 }