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1 /*-------------------------------------------------------------------- |
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2 *© Portions copyright (c) 2006 Nokia Corporation. All rights reserved. |
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3 *-------------------------------------------------------------------- |
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4 */ |
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5 /* @(#)k_cos.c 1.3 95/01/18 */ |
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6 /* |
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7 * ==================================================== |
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8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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9 * |
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10 * Developed at SunSoft, a Sun Microsystems, Inc. business. |
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11 * Permission to use, copy, modify, and distribute this |
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12 * software is freely granted, provided that this notice |
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13 * is preserved. |
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14 * ==================================================== |
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15 */ |
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16 #ifndef __SYMBIAN32__ |
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17 #ifndef lint |
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18 static char rcsid[] = "$FreeBSD: src/lib/msun/src/k_cos.c,v 1.8 2005/02/04 18:26:06 das Exp $"; |
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19 #endif |
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20 #endif //__SYMBIAN32__ |
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21 |
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22 /* |
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23 * __kernel_cos( x, y ) |
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24 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 |
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25 * Input x is assumed to be bounded by ~pi/4 in magnitude. |
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26 * Input y is the tail of x. |
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27 * |
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28 * Algorithm |
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29 * 1. Since cos(-x) = cos(x), we need only to consider positive x. |
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30 * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. |
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31 * 3. cos(x) is approximated by a polynomial of degree 14 on |
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32 * [0,pi/4] |
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33 * 4 14 |
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34 * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x |
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35 * where the remez error is |
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36 * |
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37 * | 2 4 6 8 10 12 14 | -58 |
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38 * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 |
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39 * | | |
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40 * |
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41 * 4 6 8 10 12 14 |
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42 * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then |
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43 * cos(x) = 1 - x*x/2 + r |
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44 * since cos(x+y) ~ cos(x) - sin(x)*y |
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45 * ~ cos(x) - x*y, |
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46 * a correction term is necessary in cos(x) and hence |
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47 * cos(x+y) = 1 - (x*x/2 - (r - x*y)) |
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48 * For better accuracy when x > 0.3, let qx = |x|/4 with |
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49 * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. |
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50 * Then |
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51 * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). |
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52 * Note that 1-qx and (x*x/2-qx) is EXACT here, and the |
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53 * magnitude of the latter is at least a quarter of x*x/2, |
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54 * thus, reducing the rounding error in the subtraction. |
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55 */ |
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56 |
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57 #include <math.h> |
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58 #include "math_private.h" |
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59 |
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60 static const double |
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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 double |
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70 __kernel_cos(double x, double y) |
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71 { |
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72 double a,hz,z,r,qx; |
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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; /* ix = |x|'s high word*/ |
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76 if(ix<0x3e400000) { /* if x < 2**27 */ |
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77 if(((int)x)==0) return one; /* generate inexact */ |
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78 } |
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79 z = x*x; |
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80 r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); |
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81 if(ix < 0x3FD33333) /* if |x| < 0.3 */ |
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82 return one - (0.5*z - (z*r - x*y)); |
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83 else { |
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84 if(ix > 0x3fe90000) { /* x > 0.78125 */ |
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85 qx = 0.28125; |
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86 } else { |
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87 INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */ |
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88 } |
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89 hz = 0.5*z-qx; |
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90 a = one-qx; |
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91 return a - (hz - (z*r-x*y)); |
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92 } |
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93 } |