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annotate src/libm/k_cos.c @ 4426:1bceff8f008f

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Fixed bug #943 Ozkan Sezer 2010-02-06 12:31:06 PST Hi: Here are some small fixes for compiling SDL against mingw-w64. (see http://mingw-w64.sourceforge.net/ . Despite the name, it supports both win32 and win64.) src/audio/windx5/directx.h and src/video/windx5/directx.h (both SDL-1.2 and SDL-1.3.) I get compilation errors about some union not having a member named u1 and alike, because of other system headers being included before this one and them already defining DUMMYUNIONNAME and stuff. This header probably assumes that those stuff are defined in windef.h, but mingw-w64 headers define them in _mingw.h. Easily fixed by moving NONAMELESSUNION definition to the top of the file. src/thread/win32/SDL_systhread.c (both SDL-1.2 and SDL-1.3.) : The __GNUC__ case for pfnSDL_CurrentBeginThread is 32-bit centric because _beginthreadex returns uintptr_t, not unsigned long which is 32 bits in win64. Changing the return type to uintptr_t fixes it. video/SDL_blit.h (and configure.in) (SDL-1.3-only) : MinGW-w64 uses msvcrt version of _aligned_malloc and _aligned_free and they are defined in intrin.h (similar to VC). Adding proper ifdefs fixes it. (Notes about macros to check: __MINGW32__ is defined for both mingw.org and for mingw-w64 for both win32 and win64, __MINGW64__ is only defined for _WIN64, so __MINGW64__ can't be used to detect mingw-w64: including _mingw.h and then checking for __MINGW64_VERSION_MAJOR does the trick.) SDL_win32video.h (SDL-1.3-only) : Tweaked the VINWER definition and location in order to avoid multiple redefinition warnings. Hope these are useful. Thanks.
author Sam Lantinga <slouken@libsdl.org>
date Wed, 10 Mar 2010 15:02:58 +0000
parents dc1eb82ffdaa
children
rev   line source
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1 /* @(#)k_cos.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_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $";
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16 #endif
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17
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18 /*
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19 * __kernel_cos( x, y )
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20 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
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21 * Input x is assumed to be bounded by ~pi/4 in magnitude.
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22 * Input y is the tail of x.
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23 *
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24 * Algorithm
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25 * 1. Since cos(-x) = cos(x), we need only to consider positive x.
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26 * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
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27 * 3. cos(x) is approximated by a polynomial of degree 14 on
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28 * [0,pi/4]
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29 * 4 14
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30 * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
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31 * where the remez error is
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32 *
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33 * | 2 4 6 8 10 12 14 | -58
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34 * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
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35 * | |
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36 *
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37 * 4 6 8 10 12 14
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38 * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
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39 * cos(x) = 1 - x*x/2 + r
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40 * since cos(x+y) ~ cos(x) - sin(x)*y
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41 * ~ cos(x) - x*y,
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42 * a correction term is necessary in cos(x) and hence
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43 * cos(x+y) = 1 - (x*x/2 - (r - x*y))
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44 * For better accuracy when x > 0.3, let qx = |x|/4 with
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45 * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
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46 * Then
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47 * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
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48 * Note that 1-qx and (x*x/2-qx) is EXACT here, and the
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49 * magnitude of the latter is at least a quarter of x*x/2,
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50 * thus, reducing the rounding error in the subtraction.
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51 */
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52
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53 #include "math.h"
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54 #include "math_private.h"
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55
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56 #ifdef __STDC__
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57 static const double
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58 #else
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59 static double
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60 #endif
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61 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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62 C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
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63 C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
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64 C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
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65 C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
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66 C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
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67 C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
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68
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69 #ifdef __STDC__
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70 double attribute_hidden
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71 __kernel_cos(double x, double y)
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72 #else
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73 double attribute_hidden
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74 __kernel_cos(x, y)
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75 double x, y;
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76 #endif
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77 {
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78 double a, hz, z, r, qx;
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79 int32_t ix;
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80 GET_HIGH_WORD(ix, x);
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81 ix &= 0x7fffffff; /* ix = |x|'s high word */
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82 if (ix < 0x3e400000) { /* if x < 2**27 */
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83 if (((int) x) == 0)
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84 return one; /* generate inexact */
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85 }
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86 z = x * x;
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87 r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6)))));
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88 if (ix < 0x3FD33333) /* if |x| < 0.3 */
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89 return one - (0.5 * z - (z * r - x * y));
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90 else {
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91 if (ix > 0x3fe90000) { /* x > 0.78125 */
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92 qx = 0.28125;
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93 } else {
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94 INSERT_WORDS(qx, ix - 0x00200000, 0); /* x/4 */
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95 }
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96 hz = 0.5 * z - qx;
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97 a = one - qx;
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98 return a - (hz - (z * r - x * y));
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99 }
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100 }