Mercurial > flash_v2
diff packages/language/c/libm/current/src/double/internal/k_cos.c @ 0:3111d98ba7b3 ecos-v1_1-release
Initial commit of eCos version 1.1
| author | jlarmour |
|---|---|
| date | Tue, 11 May 1999 11:16:07 +0000 |
| parents | |
| children | 443894e2e912 |
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new file mode 100644 --- /dev/null +++ b/packages/language/c/libm/current/src/double/internal/k_cos.c @@ -0,0 +1,138 @@ +//=========================================================================== +// +// k_cos.c +// +// Part of the standard mathematical function library +// +//=========================================================================== +//####COPYRIGHTBEGIN#### +// +// ------------------------------------------- +// The contents of this file are subject to the Cygnus eCos Public License +// Version 1.0 (the "License"); you may not use this file except in +// compliance with the License. You may obtain a copy of the License at +// http://sourceware.cygnus.com/ecos +// +// Software distributed under the License is distributed on an "AS IS" +// basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See the +// License for the specific language governing rights and limitations under +// the License. +// +// The Original Code is eCos - Embedded Cygnus Operating System, released +// September 30, 1998. +// +// The Initial Developer of the Original Code is Cygnus. Portions created +// by Cygnus are Copyright (C) 1998 Cygnus Solutions. All Rights Reserved. +// ------------------------------------------- +// +//####COPYRIGHTEND#### +//=========================================================================== +//#####DESCRIPTIONBEGIN#### +// +// Author(s): jlarmour@cygnus.co.uk +// Contributors: jlarmour@cygnus.co.uk +// Date: 1998-02-13 +// Purpose: +// Description: +// Usage: +// +//####DESCRIPTIONEND#### +// +//=========================================================================== + +// CONFIGURATION + +#include <pkgconf/libm.h> // Configuration header + +// Include the Math library? +#ifdef CYGPKG_LIBM + +// Derived from code with the following copyright + + +/* @(#)k_cos.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * __kernel_cos( x, y ) + * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * + * Algorithm + * 1. Since cos(-x) = cos(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. + * 3. cos(x) is approximated by a polynomial of degree 14 on + * [0,pi/4] + * 4 14 + * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x + * where the remez error is + * + * | 2 4 6 8 10 12 14 | -58 + * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 + * | | + * + * 4 6 8 10 12 14 + * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then + * cos(x) = 1 - x*x/2 + r + * since cos(x+y) ~ cos(x) - sin(x)*y + * ~ cos(x) - x*y, + * a correction term is necessary in cos(x) and hence + * cos(x+y) = 1 - (x*x/2 - (r - x*y)) + * For better accuracy when x > 0.3, let qx = |x|/4 with + * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. + * Then + * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). + * Note that 1-qx and (x*x/2-qx) is EXACT here, and the + * magnitude of the latter is at least a quarter of x*x/2, + * thus, reducing the rounding error in the subtraction. + */ + +#include "mathincl/fdlibm.h" + +static const double +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ +C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ +C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ +C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ +C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ +C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ + + double __kernel_cos(double x, double y) +{ + double a,hz,z,r,qx; + int ix; + ix = CYG_LIBM_HI(x)&0x7fffffff; /* ix = |x|'s high word*/ + if(ix<0x3e400000) { /* if x < 2**27 */ + if(((int)x)==0) return one; /* generate inexact */ + } + z = x*x; + r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); + if(ix < 0x3FD33333) /* if |x| < 0.3 */ + return one - (0.5*z - (z*r - x*y)); + else { + if(ix > 0x3fe90000) { /* x > 0.78125 */ + qx = 0.28125; + } else { + CYG_LIBM_HI(qx) = ix-0x00200000; /* x/4 */ + CYG_LIBM_LO(qx) = 0; + } + hz = 0.5*z-qx; + a = one-qx; + return a - (hz - (z*r-x*y)); + } +} + +#endif // ifdef CYGPKG_LIBM + +// EOF k_cos.c
