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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 /* @(#)s_cbrt.c 5.1 93/09/24 */ |
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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 SunPro, 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/s_cbrt.c,v 1.7 2002/05/28 18:15:04 alfred Exp $"; |
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19 #endif |
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20 #endif //__SYMBIAN32__ |
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21 |
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22 #include <math.h> |
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23 #include "math_private.h" |
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24 |
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25 /* cbrt(x) |
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26 * Return cube root of x |
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27 */ |
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28 static const u_int32_t |
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29 B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ |
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30 B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ |
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31 |
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32 static const double |
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33 C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ |
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34 D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ |
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35 E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ |
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36 F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ |
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37 G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ |
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38 |
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39 EXPORT_C double |
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40 cbrt(double x) |
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41 { |
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42 int32_t hx; |
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43 double r,s,t=0.0,w; |
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44 u_int32_t sign; |
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45 u_int32_t high,low; |
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46 |
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47 GET_HIGH_WORD(hx,x); |
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48 sign=hx&0x80000000; /* sign= sign(x) */ |
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49 hx ^=sign; |
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50 if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ |
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51 GET_LOW_WORD(low,x); |
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52 if((hx|low)==0) |
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53 return(x); /* cbrt(0) is itself */ |
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54 |
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55 SET_HIGH_WORD(x,hx); /* x <- |x| */ |
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56 /* rough cbrt to 5 bits */ |
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57 if(hx<0x00100000) /* subnormal number */ |
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58 {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */ |
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59 t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2); |
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60 } |
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61 else |
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62 SET_HIGH_WORD(t,hx/3+B1); |
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63 |
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64 |
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65 /* new cbrt to 23 bits, may be implemented in single precision */ |
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66 r=t*t/x; |
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67 s=C+r*t; |
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68 t*=G+F/(s+E+D/s); |
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69 |
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70 /* chopped to 20 bits and make it larger than cbrt(x) */ |
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71 GET_HIGH_WORD(high,t); |
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72 INSERT_WORDS(t,high+0x00000001,0); |
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73 |
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74 |
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75 /* one step newton iteration to 53 bits with error less than 0.667 ulps */ |
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76 s=t*t; /* t*t is exact */ |
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77 r=x/s; |
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78 w=t+t; |
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79 r=(r-t)/(w+r); /* r-s is exact */ |
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80 t=t+t*r; |
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81 |
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82 /* retore the sign bit */ |
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83 GET_HIGH_WORD(high,t); |
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84 SET_HIGH_WORD(t,high|sign); |
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85 return(t); |
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86 } |