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annotate src/libm/k_cos.c @ 4593:3892fe2f6537

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Fixed so many things. See the changelog listed below. 1. Use SDL_X11_HAVE_XRENDER to check for RENDER at runtime. 2. Added lots of comments. 3. Added checks and lots of calls to SDL_SetError(). 4. Fixed X11_CreateTexture() so that the pixmap and image created are for the format specified by the user and not the window format. This is only for the RENDER case. 5. The above change required that functions to convert SDL pixel format enums to Visuals and XRenderPictFormats be added. 6. Fixed lots of 'style' issues.
author Sunny Sachanandani <sunnysachanandani@gmail.com>
date Sat, 17 Jul 2010 15:38:24 +0530
parents dc1eb82ffdaa
children
rev   line source
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a98604b691c8 Expanded the libm support and put it into a separate directory.
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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 }