lib/msun/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
  21 #include "math_private.h"
  22
  23 /*
  24  * Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]:
  25  * |cos(x) - c(x))| < 2**-122.0
  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
  35 static const long double
  36 C1 =  0.04166666666666666666666666666666658424671L,
  37 C2 = -0.001388888888888888888888888888863490893732L,
  38 C3 =  0.00002480158730158730158730158600795304914210L,
  39 C4 = -0.2755731922398589065255474947078934284324e-6L,
  40 C5 =  0.2087675698786809897659225313136400793948e-8L,
  41 C6 = -0.1147074559772972315817149986812031204775e-10L,
  42 C7 =  0.4779477332386808976875457937252120293400e-13L;
  43
  44 static const double
  45 C8 = -0.1561920696721507929516718307820958119868e-15,
  46 C9 =  0.4110317413744594971475941557607804508039e-18,
  47 C10 = -0.8896592467191938803288521958313920156409e-21,
  48 C11 =  0.1601061435794535138244346256065192782581e-23;
  49
  50 long double
  51 __kernel_cosl(long double x, long double y)
  52 {
  53         long double hz,z,r,w;
  54
  55         z  = x*x;
  56         r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+
  57             z*(C8+z*(C9+z*(C10+z*C11))))))))));
  58         hz = 0.5*z;
  59         w  = one-hz;
  60         return w + (((one-w)-hz) + (z*r-x*y));
  61 }