src/libm/k_cos.c
author Ryan C. Gordon <icculus@icculus.org>
Fri, 12 Aug 2016 19:59:00 -0400
changeset 10266 c09f06c4e8c8
parent 6044 35448a5ea044
permissions -rw-r--r--
emscripten: send fake mouse events for touches, like other targets do. (This really should be handled at the higher level and not in the individual targets, but this fixes the immediate bug.)

/* @(#)k_cos.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#if defined(LIBM_SCCS) && !defined(lint)
static const char rcsid[] =
    "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $";
#endif

/*
 * __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 "math_libm.h"
#include "math_private.h"

#ifdef __STDC__
static const double
#else
static double
#endif
  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 */

#ifdef __STDC__
double attribute_hidden
__kernel_cos(double x, double y)
#else
double attribute_hidden
__kernel_cos(x, y)
     double x, y;
#endif
{
    double a, hz, z, r, qx;
    int32_t ix;
    GET_HIGH_WORD(ix, x);
    ix &= 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 {
            INSERT_WORDS(qx, ix - 0x00200000, 0);       /* x/4 */
        }
        hz = 0.5 * z - qx;
        a = one - qx;
        return a - (hz - (z * r - x * y));
    }
}