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annotate src/libm/k_sin.c @ 3542:97eae5a705f9

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Make sure we fully clip the first point before starting to adjust the second point.
author Sam Lantinga <slouken@libsdl.org>
date Fri, 11 Dec 2009 09:57:54 +0000
parents dc1eb82ffdaa
children
rev   line source
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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 }