view src/libm/k_sin.c @ 2960:91708bc14aab

It's probably not worth pushing palettized textures. The memory optimization isn't worth the effort on modern hardware with the sorts of games that would be using the SDL 1.3 texture API.
author Sam Lantinga <slouken@libsdl.org>
date Fri, 02 Jan 2009 09:27:36 +0000
parents a98604b691c8
children dc1eb82ffdaa
line wrap: on
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/* @(#)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 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);
}