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annotate src/libm/k_sin.c @ 3197:434ce3242e1c

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Alexei Tereschenko Why not to use hardware vertex processing instead of software one if it is available in D3D render driver? With hardware processing testsprite2 runs three times faster on all videocards which I could test.
author Sam Lantinga <slouken@libsdl.org>
date Tue, 16 Jun 2009 14:34:15 +0000
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_sin.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_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $";
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16 #endif
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17
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18 /* __kernel_sin( x, y, iy)
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19 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
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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 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
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23 *
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24 * Algorithm
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25 * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
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26 * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
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27 * 3. sin(x) is approximated by a polynomial of degree 13 on
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28 * [0,pi/4]
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29 * 3 13
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30 * sin(x) ~ x + S1*x + ... + S6*x
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31 * where
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32 *
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33 * |sin(x) 2 4 6 8 10 12 | -58
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34 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
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35 * | x |
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36 *
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37 * 4. sin(x+y) = sin(x) + sin'(x')*y
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38 * ~ sin(x) + (1-x*x/2)*y
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39 * For better accuracy, let
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40 * 3 2 2 2 2
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41 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
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42 * then 3 2
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43 * sin(x) = x + (S1*x + (x *(r-y/2)+y))
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44 */
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45
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46 #include "math.h"
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47 #include "math_private.h"
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48
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49 #ifdef __STDC__
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50 static const double
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51 #else
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52 static double
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53 #endif
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54 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
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55 S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
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56 S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
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57 S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
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58 S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
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59 S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
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60 S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
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61
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62 #ifdef __STDC__
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63 double attribute_hidden
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64 __kernel_sin(double x, double y, int iy)
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65 #else
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66 double attribute_hidden
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67 __kernel_sin(x, y, iy)
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68 double x, y;
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69 int iy; /* iy=0 if y is zero */
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70 #endif
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71 {
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72 double z, r, v;
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73 int32_t ix;
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74 GET_HIGH_WORD(ix, x);
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75 ix &= 0x7fffffff; /* high word of x */
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76 if (ix < 0x3e400000) { /* |x| < 2**-27 */
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77 if ((int) x == 0)
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78 return x;
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79 } /* generate inexact */
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80 z = x * x;
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81 v = z * x;
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82 r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
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83 if (iy == 0)
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84 return x + v * (S1 + z * r);
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85 else
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86 return x - ((z * (half * y - v * r) - y) - v * S1);
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87 }