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annotate src/libm/k_cos.c @ 4525:3abf0b9cafad

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pelya 2010-07-12 03:53:48 PDT In function GLES_RenderCopy() in SDL_renderer_gles.c:819 there is one memcpy() that can be avoided if we're updating whole texture. Because of that the SDL 1.3 in compatibility mode is working even slower than software rendering in SDL 1.2.
author Sam Lantinga <slouken@libsdl.org>
date Wed, 14 Jul 2010 07:31:35 -0700
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 }