Mercurial > sdl-ios-xcode
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 |
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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); }