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annotate src/libm/k_cos.c @ 3070:3e3724fb829e

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Fixed bug #681 Description From Philipp 2009-01-16 20:50:01 (-) [reply] The File test/README from the svn says this: testgl A very simple example of using OpenGL with SDL testgl2 Improved version of testgl It is actually exchanged. testgl.c is the improved version right now and testgl2.c the simple one.
author Sam Lantinga <slouken@libsdl.org>
date Tue, 17 Feb 2009 05:44:49 +0000
parents a98604b691c8
children dc1eb82ffdaa
rev   line source
2756
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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 char rcsid[] = "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $";
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15 #endif
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16
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17 /*
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18 * __kernel_cos( x, y )
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19 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
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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 *
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23 * Algorithm
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24 * 1. Since cos(-x) = cos(x), we need only to consider positive x.
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25 * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
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26 * 3. cos(x) is approximated by a polynomial of degree 14 on
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27 * [0,pi/4]
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28 * 4 14
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29 * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
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30 * where the remez error is
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31 *
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32 * | 2 4 6 8 10 12 14 | -58
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33 * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
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34 * | |
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35 *
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36 * 4 6 8 10 12 14
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37 * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
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38 * cos(x) = 1 - x*x/2 + r
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39 * since cos(x+y) ~ cos(x) - sin(x)*y
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40 * ~ cos(x) - x*y,
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41 * a correction term is necessary in cos(x) and hence
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42 * cos(x+y) = 1 - (x*x/2 - (r - x*y))
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43 * For better accuracy when x > 0.3, let qx = |x|/4 with
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44 * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
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45 * Then
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46 * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
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47 * Note that 1-qx and (x*x/2-qx) is EXACT here, and the
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48 * magnitude of the latter is at least a quarter of x*x/2,
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49 * thus, reducing the rounding error in the subtraction.
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50 */
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51
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52 #include "math.h"
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53 #include "math_private.h"
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54
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55 #ifdef __STDC__
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56 static const double
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57 #else
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58 static double
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59 #endif
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60 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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61 C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
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62 C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
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63 C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
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64 C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
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65 C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
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66 C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
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67
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68 #ifdef __STDC__
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69 double attribute_hidden
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70 __kernel_cos(double x, double y)
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71 #else
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72 double attribute_hidden
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73 __kernel_cos(x, y)
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74 double x, y;
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75 #endif
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76 {
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77 double a, hz, z, r, qx;
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78 int32_t ix;
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79 GET_HIGH_WORD(ix, x);
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80 ix &= 0x7fffffff; /* ix = |x|'s high word */
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81 if (ix < 0x3e400000) { /* if x < 2**27 */
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82 if (((int) x) == 0)
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83 return one; /* generate inexact */
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84 }
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85 z = x * x;
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86 r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6)))));
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87 if (ix < 0x3FD33333) /* if |x| < 0.3 */
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88 return one - (0.5 * z - (z * r - x * y));
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89 else {
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90 if (ix > 0x3fe90000) { /* x > 0.78125 */
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91 qx = 0.28125;
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92 } else {
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93 INSERT_WORDS(qx, ix - 0x00200000, 0); /* x/4 */
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94 }
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95 hz = 0.5 * z - qx;
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96 a = one - qx;
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97 return a - (hz - (z * r - x * y));
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98 }
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99 }