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[/] [openrisc/] [trunk/] [gnu-src/] [newlib-1.18.0/] [newlib/] [libm/] [math/] [k_cos.c] - Blame information for rev 207

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1 207 jeremybenn
 
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/* @(#)k_cos.c 5.1 93/09/24 */
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/*
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 * ====================================================
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 *
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 * Permission to use, copy, modify, and distribute this
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 * software is freely granted, provided that this notice
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 * is preserved.
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 * ====================================================
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 */
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/*
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 * __kernel_cos( x,  y )
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 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
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 * Input x is assumed to be bounded by ~pi/4 in magnitude.
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 * Input y is the tail of x.
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 *
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 * Algorithm
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 *      1. Since cos(-x) = cos(x), we need only to consider positive x.
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 *      2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
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 *      3. cos(x) is approximated by a polynomial of degree 14 on
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 *         [0,pi/4]
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 *                                       4            14
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 *              cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
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 *         where the remez error is
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 *
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 *      |              2     4     6     8     10    12     14 |     -58
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 *      |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
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 *      |                                                      |
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 *
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 *                     4     6     8     10    12     14
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 *      4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
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 *             cos(x) = 1 - x*x/2 + r
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 *         since cos(x+y) ~ cos(x) - sin(x)*y
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 *                        ~ cos(x) - x*y,
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 *         a correction term is necessary in cos(x) and hence
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 *              cos(x+y) = 1 - (x*x/2 - (r - x*y))
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 *         For better accuracy when x > 0.3, let qx = |x|/4 with
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 *         the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
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 *         Then
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 *              cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
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 *         Note that 1-qx and (x*x/2-qx) is EXACT here, and the
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 *         magnitude of the latter is at least a quarter of x*x/2,
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 *         thus, reducing the rounding error in the subtraction.
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 */
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#include "fdlibm.h"
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#ifndef _DOUBLE_IS_32BITS
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#ifdef __STDC__
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static const double
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#else
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static double
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#endif
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one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
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C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
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C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
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C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
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C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
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C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
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#ifdef __STDC__
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        double __kernel_cos(double x, double y)
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#else
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        double __kernel_cos(x, y)
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        double x,y;
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#endif
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{
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        double a,hz,z,r,qx;
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        __int32_t ix;
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        GET_HIGH_WORD(ix,x);
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        ix &= 0x7fffffff;                       /* ix = |x|'s high word*/
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        if(ix<0x3e400000) {                     /* if x < 2**27 */
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            if(((int)x)==0) return one;          /* generate inexact */
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        }
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        z  = x*x;
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        r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
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        if(ix < 0x3FD33333)                     /* if |x| < 0.3 */
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            return one - (0.5*z - (z*r - x*y));
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        else {
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            if(ix > 0x3fe90000) {               /* x > 0.78125 */
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                qx = 0.28125;
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            } else {
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                INSERT_WORDS(qx,ix-0x00200000,0);        /* x/4 */
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            }
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            hz = 0.5*z-qx;
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            a  = one-qx;
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            return a - (hz - (z*r-x*y));
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        }
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}
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#endif /* defined(_DOUBLE_IS_32BITS) */

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