src/libm/k_cos.c
changeset 2756 a98604b691c8
child 3162 dc1eb82ffdaa
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/libm/k_cos.c	Mon Sep 15 06:33:23 2008 +0000
     1.3 @@ -0,0 +1,99 @@
     1.4 +/* @(#)k_cos.c 5.1 93/09/24 */
     1.5 +/*
     1.6 + * ====================================================
     1.7 + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     1.8 + *
     1.9 + * Developed at SunPro, a Sun Microsystems, Inc. business.
    1.10 + * Permission to use, copy, modify, and distribute this
    1.11 + * software is freely granted, provided that this notice
    1.12 + * is preserved.
    1.13 + * ====================================================
    1.14 + */
    1.15 +
    1.16 +#if defined(LIBM_SCCS) && !defined(lint)
    1.17 +static char rcsid[] = "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $";
    1.18 +#endif
    1.19 +
    1.20 +/*
    1.21 + * __kernel_cos( x,  y )
    1.22 + * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
    1.23 + * Input x is assumed to be bounded by ~pi/4 in magnitude.
    1.24 + * Input y is the tail of x.
    1.25 + *
    1.26 + * Algorithm
    1.27 + *	1. Since cos(-x) = cos(x), we need only to consider positive x.
    1.28 + *	2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
    1.29 + *	3. cos(x) is approximated by a polynomial of degree 14 on
    1.30 + *	   [0,pi/4]
    1.31 + *		  	                 4            14
    1.32 + *	   	cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
    1.33 + *	   where the remez error is
    1.34 + *
    1.35 + * 	|              2     4     6     8     10    12     14 |     -58
    1.36 + * 	|cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
    1.37 + * 	|    					               |
    1.38 + *
    1.39 + * 	               4     6     8     10    12     14
    1.40 + *	4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
    1.41 + *	       cos(x) = 1 - x*x/2 + r
    1.42 + *	   since cos(x+y) ~ cos(x) - sin(x)*y
    1.43 + *			  ~ cos(x) - x*y,
    1.44 + *	   a correction term is necessary in cos(x) and hence
    1.45 + *		cos(x+y) = 1 - (x*x/2 - (r - x*y))
    1.46 + *	   For better accuracy when x > 0.3, let qx = |x|/4 with
    1.47 + *	   the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
    1.48 + *	   Then
    1.49 + *		cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
    1.50 + *	   Note that 1-qx and (x*x/2-qx) is EXACT here, and the
    1.51 + *	   magnitude of the latter is at least a quarter of x*x/2,
    1.52 + *	   thus, reducing the rounding error in the subtraction.
    1.53 + */
    1.54 +
    1.55 +#include "math.h"
    1.56 +#include "math_private.h"
    1.57 +
    1.58 +#ifdef __STDC__
    1.59 +static const double
    1.60 +#else
    1.61 +static double
    1.62 +#endif
    1.63 +  one = 1.00000000000000000000e+00,     /* 0x3FF00000, 0x00000000 */
    1.64 +    C1 = 4.16666666666666019037e-02,    /* 0x3FA55555, 0x5555554C */
    1.65 +    C2 = -1.38888888888741095749e-03,   /* 0xBF56C16C, 0x16C15177 */
    1.66 +    C3 = 2.48015872894767294178e-05,    /* 0x3EFA01A0, 0x19CB1590 */
    1.67 +    C4 = -2.75573143513906633035e-07,   /* 0xBE927E4F, 0x809C52AD */
    1.68 +    C5 = 2.08757232129817482790e-09,    /* 0x3E21EE9E, 0xBDB4B1C4 */
    1.69 +    C6 = -1.13596475577881948265e-11;   /* 0xBDA8FAE9, 0xBE8838D4 */
    1.70 +
    1.71 +#ifdef __STDC__
    1.72 +double attribute_hidden
    1.73 +__kernel_cos(double x, double y)
    1.74 +#else
    1.75 +double attribute_hidden
    1.76 +__kernel_cos(x, y)
    1.77 +     double x, y;
    1.78 +#endif
    1.79 +{
    1.80 +    double a, hz, z, r, qx;
    1.81 +    int32_t ix;
    1.82 +    GET_HIGH_WORD(ix, x);
    1.83 +    ix &= 0x7fffffff;           /* ix = |x|'s high word */
    1.84 +    if (ix < 0x3e400000) {      /* if x < 2**27 */
    1.85 +        if (((int) x) == 0)
    1.86 +            return one;         /* generate inexact */
    1.87 +    }
    1.88 +    z = x * x;
    1.89 +    r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6)))));
    1.90 +    if (ix < 0x3FD33333)        /* if |x| < 0.3 */
    1.91 +        return one - (0.5 * z - (z * r - x * y));
    1.92 +    else {
    1.93 +        if (ix > 0x3fe90000) {  /* x > 0.78125 */
    1.94 +            qx = 0.28125;
    1.95 +        } else {
    1.96 +            INSERT_WORDS(qx, ix - 0x00200000, 0);       /* x/4 */
    1.97 +        }
    1.98 +        hz = 0.5 * z - qx;
    1.99 +        a = one - qx;
   1.100 +        return a - (hz - (z * r - x * y));
   1.101 +    }
   1.102 +}