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annotate src/libm/k_cos.c @ 2824:4dba7aa7ea77

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Added slow but complete blit fallback Don't try to RLE encode surfaces that have alpha channel and alpha modulation Don't turn on blending when converting an RGB surface to RGBA format Do turn on blending when converting colorkey to alpha channel
author Sam Lantinga <slouken@libsdl.org>
date Tue, 02 Dec 2008 17:14:04 +0000
parents a98604b691c8
children dc1eb82ffdaa
rev   line source
2756
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 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 }