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annotate src/libm/k_sin.c @ 3409:c8f580ebc96a

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Adam Strzelecki to SDL Sending a patch for fullscreen Mac OS X SDL 1.3 (SVN) Cocoa mouse position handling. In fullscreen mouse coordinates should be relative to SCREEN not to the window, which doesn't really occupy fullscreen. Without this patch mouse position (especially Y) was totally incorrect (shifted) in fullscreen.
author Sam Lantinga <slouken@libsdl.org>
date Thu, 22 Oct 2009 04:46:11 +0000
parents dc1eb82ffdaa
children
rev   line source
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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 const char rcsid[] =
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15 "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $";
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16 #endif
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17
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18 /* __kernel_sin( x, y, iy)
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19 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
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20 * Input x is assumed to be bounded by ~pi/4 in magnitude.
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21 * Input y is the tail of x.
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22 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
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23 *
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24 * Algorithm
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25 * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
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26 * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
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27 * 3. sin(x) is approximated by a polynomial of degree 13 on
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28 * [0,pi/4]
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29 * 3 13
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30 * sin(x) ~ x + S1*x + ... + S6*x
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31 * where
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32 *
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33 * |sin(x) 2 4 6 8 10 12 | -58
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34 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
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35 * | x |
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36 *
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37 * 4. sin(x+y) = sin(x) + sin'(x')*y
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38 * ~ sin(x) + (1-x*x/2)*y
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39 * For better accuracy, let
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40 * 3 2 2 2 2
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41 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
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42 * then 3 2
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43 * sin(x) = x + (S1*x + (x *(r-y/2)+y))
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44 */
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45
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46 #include "math.h"
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47 #include "math_private.h"
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48
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49 #ifdef __STDC__
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50 static const double
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51 #else
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52 static double
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53 #endif
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54 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
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55 S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
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56 S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
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57 S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
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58 S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
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59 S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
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60 S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
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61
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62 #ifdef __STDC__
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63 double attribute_hidden
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64 __kernel_sin(double x, double y, int iy)
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65 #else
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66 double attribute_hidden
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67 __kernel_sin(x, y, iy)
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68 double x, y;
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69 int iy; /* iy=0 if y is zero */
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70 #endif
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71 {
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72 double z, r, v;
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73 int32_t ix;
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74 GET_HIGH_WORD(ix, x);
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75 ix &= 0x7fffffff; /* high word of x */
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76 if (ix < 0x3e400000) { /* |x| < 2**-27 */
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77 if ((int) x == 0)
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78 return x;
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79 } /* generate inexact */
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80 z = x * x;
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81 v = z * x;
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82 r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
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83 if (iy == 0)
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84 return x + v * (S1 + z * r);
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85 else
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86 return x - ((z * (half * y - v * r) - y) - v * S1);
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87 }