view src/libm/k_sin.c @ 4805:de3b3455f8ec

Put the render loop back in its right place, but with delaying functionality to keep it down to roughly 60fps, not eating up all the X11 time.
author Eli Gottlieb <eligottlieb@gmail.com>
date Mon, 19 Jul 2010 00:24:02 -0400
parents dc1eb82ffdaa
children
line wrap: on
line source

/* @(#)k_sin.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_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $";
#endif

/* __kernel_sin( x, y, iy)
 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
 * Input x is assumed to be bounded by ~pi/4 in magnitude.
 * Input y is the tail of x.
 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
 *
 * Algorithm
 *	1. Since sin(-x) = -sin(x), we need only to consider positive x.
 *	2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
 *	3. sin(x) is approximated by a polynomial of degree 13 on
 *	   [0,pi/4]
 *		  	         3            13
 *	   	sin(x) ~ x + S1*x + ... + S6*x
 *	   where
 *
 * 	|sin(x)         2     4     6     8     10     12  |     -58
 * 	|----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
 * 	|  x 					           |
 *
 *	4. sin(x+y) = sin(x) + sin'(x')*y
 *		    ~ sin(x) + (1-x*x/2)*y
 *	   For better accuracy, let
 *		     3      2      2      2      2
 *		r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
 *	   then                   3    2
 *		sin(x) = x + (S1*x + (x *(r-y/2)+y))
 */

#include "math.h"
#include "math_private.h"

#ifdef __STDC__
static const double
#else
static double
#endif
  half = 5.00000000000000000000e-01,    /* 0x3FE00000, 0x00000000 */
    S1 = -1.66666666666666324348e-01,   /* 0xBFC55555, 0x55555549 */
    S2 = 8.33333333332248946124e-03,    /* 0x3F811111, 0x1110F8A6 */
    S3 = -1.98412698298579493134e-04,   /* 0xBF2A01A0, 0x19C161D5 */
    S4 = 2.75573137070700676789e-06,    /* 0x3EC71DE3, 0x57B1FE7D */
    S5 = -2.50507602534068634195e-08,   /* 0xBE5AE5E6, 0x8A2B9CEB */
    S6 = 1.58969099521155010221e-10;    /* 0x3DE5D93A, 0x5ACFD57C */

#ifdef __STDC__
double attribute_hidden
__kernel_sin(double x, double y, int iy)
#else
double attribute_hidden
__kernel_sin(x, y, iy)
     double x, y;
     int iy;                    /* iy=0 if y is zero */
#endif
{
    double z, r, v;
    int32_t ix;
    GET_HIGH_WORD(ix, x);
    ix &= 0x7fffffff;           /* high word of x */
    if (ix < 0x3e400000) {      /* |x| < 2**-27 */
        if ((int) x == 0)
            return x;
    }                           /* generate inexact */
    z = x * x;
    v = z * x;
    r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
    if (iy == 0)
        return x + v * (S1 + z * r);
    else
        return x - ((z * (half * y - v * r) - y) - v * S1);
}