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annotate src/libm/k_cos.c @ 3335:b8d313de8a65

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Adam Strzelecki to SDL Since current DirectFB implementation is incomplete for YUV surfaces (actually causes segmentation faults when trying Lock and use YUV planar textures) I decided to fix it a bit. Here's a patch that should make DirectFB properly support YUV both packed and planar (3 planes). (1) Removed SDL_BYTESPERPIXEL at all in favor of DFB_BYTES_PER_PIXEL(SDLToDFBPixelFormat(fmt)) which does return always proper BPP for YUVs too, coz SDL_BYTESPERPIXEL returns incorrect values for FOURCCs (2) Fixed data->pixels allocation for planar YUVs in CreateTexture, it should allocate 150% more space (3) Copy other planes for planar YUVs in UpdateTexture (4) Moved checking if format is supported at all with DirectFB on CreateTexture at the beginning of the code Waiting for comments, -- Adam Strzelecki | nanoant.com
author Sam Lantinga <slouken@libsdl.org>
date Sun, 04 Oct 2009 04:03:37 +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 }