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annotate src/libm/k_sin.c @ 2824:4dba7aa7ea77

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Added slow but complete blit fallback Don't try to RLE encode surfaces that have alpha channel and alpha modulation Don't turn on blending when converting an RGB surface to RGBA format Do turn on blending when converting colorkey to alpha channel
author Sam Lantinga <slouken@libsdl.org>
date Tue, 02 Dec 2008 17:14:04 +0000
parents a98604b691c8
children dc1eb82ffdaa
rev   line source
2756
a98604b691c8 Expanded the libm support and put it into a separate directory.
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1 /* @(#)k_sin.c 5.1 93/09/24 */
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2 /*
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3 * ====================================================
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4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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5 *
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6 * Developed at SunPro, a Sun Microsystems, Inc. business.
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7 * Permission to use, copy, modify, and distribute this
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8 * software is freely granted, provided that this notice
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9 * is preserved.
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10 * ====================================================
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11 */
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12
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13 #if defined(LIBM_SCCS) && !defined(lint)
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14 static char rcsid[] = "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $";
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15 #endif
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16
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17 /* __kernel_sin( x, y, iy)
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18 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
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19 * Input x is assumed to be bounded by ~pi/4 in magnitude.
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20 * Input y is the tail of x.
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21 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
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22 *
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23 * Algorithm
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24 * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
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25 * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
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26 * 3. sin(x) is approximated by a polynomial of degree 13 on
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27 * [0,pi/4]
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28 * 3 13
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29 * sin(x) ~ x + S1*x + ... + S6*x
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30 * where
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31 *
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32 * |sin(x) 2 4 6 8 10 12 | -58
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33 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
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34 * | x |
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35 *
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36 * 4. sin(x+y) = sin(x) + sin'(x')*y
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37 * ~ sin(x) + (1-x*x/2)*y
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38 * For better accuracy, let
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39 * 3 2 2 2 2
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40 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
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41 * then 3 2
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42 * sin(x) = x + (S1*x + (x *(r-y/2)+y))
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43 */
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44
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45 #include "math.h"
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46 #include "math_private.h"
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47
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48 #ifdef __STDC__
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49 static const double
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50 #else
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51 static double
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52 #endif
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53 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
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54 S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
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55 S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
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56 S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
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57 S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
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58 S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
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59 S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
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60
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61 #ifdef __STDC__
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62 double attribute_hidden
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63 __kernel_sin(double x, double y, int iy)
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64 #else
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65 double attribute_hidden
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66 __kernel_sin(x, y, iy)
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67 double x, y;
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68 int iy; /* iy=0 if y is zero */
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69 #endif
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70 {
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71 double z, r, v;
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72 int32_t ix;
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73 GET_HIGH_WORD(ix, x);
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74 ix &= 0x7fffffff; /* high word of x */
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75 if (ix < 0x3e400000) { /* |x| < 2**-27 */
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76 if ((int) x == 0)
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77 return x;
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78 } /* generate inexact */
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79 z = x * x;
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80 v = z * x;
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81 r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
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82 if (iy == 0)
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83 return x + v * (S1 + z * r);
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84 else
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85 return x - ((z * (half * y - v * r) - y) - v * S1);
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86 }