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annotate src/libm/k_sin.c @ 3415:1756b9569141

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Adam Strzelecki to SDL Actually after my patch commited in r4928 MinGW configure seems to generate broken Makefile due MSYS bash bug. (Attaching cure/patch below) The problem is that: TEST=`echo 'one\\ two\\ three\\'` echo "$TEST" Should echo: one\ two\ three\ Does it on Linux, Mac.. all UNIX but not on MSYS (MinGW) which outputs: one\two\three\ (new lines removed, probably it doesn't like backslashes) Probably this bug should be submitted to MSYS team, but not waiting till MSYS gets it fixed (they have very slow release cycles) here goes simple cure... My patch simply replaces single quoted SED rules where we needed newlien injection with double quoted ones. Tested on Mac, Linux & MinGW. Please review it ASAP coz this may be showstopper for everybody compiling with MinGW.
author Sam Lantinga <slouken@libsdl.org>
date Wed, 28 Oct 2009 04:27:50 +0000
parents dc1eb82ffdaa
children
rev   line source
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1 /* @(#)k_sin.c 5.1 93/09/24 */
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2 /*
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3 * ====================================================
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4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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5 *
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6 * Developed at SunPro, a Sun Microsystems, Inc. business.
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7 * Permission to use, copy, modify, and distribute this
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8 * software is freely granted, provided that this notice
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9 * is preserved.
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10 * ====================================================
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11 */
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12
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13 #if defined(LIBM_SCCS) && !defined(lint)
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14 static const char rcsid[] =
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15 "$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 }