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1 /*
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2 * ====================================================
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3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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4 *
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5 * Developed at SunPro, a Sun Microsystems, Inc. business.
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6 * Permission to use, copy, modify, and distribute this
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7 * software is freely granted, provided that this notice
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8 * is preserved.
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9 * ====================================================
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10 */
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11
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12 #ifndef __vax__
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13 static const unsigned long
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14 B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
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15 B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
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16
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17 static const double
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18 C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
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19 D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
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20 E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
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21 F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
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22 G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
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23
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24 double
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25 cbrtl (double x)
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26 {
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27 long hx;
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28 double r,s,w;
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29 double lt;
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30 unsigned sign;
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31 typedef unsigned unsigned32 __attribute__((mode(SI)));
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32 union {
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33 double t;
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34 unsigned32 pt[2];
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35 } ut, ux;
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36 int n0;
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37
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38 ut.t = 1.0;
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39 n0 = (ut.pt[0] == 0);
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40
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41 ut.t = 0.0;
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42 ux.t = x;
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43
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44 hx = ux.pt[n0]; /* high word of x */
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45 sign=hx&0x80000000; /* sign= sign(x) */
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46 hx ^=sign;
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47 if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
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48 if((hx| ux.pt[1-n0])==0)
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49 return(ux.t); /* cbrt(0) is itself */
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50
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51 ux.pt[n0] = hx;
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52 /* rough cbrt to 5 bits */
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53 if(hx<0x00100000) /* subnormal number */
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54 {ut.pt[n0]=0x43500000; /* set t= 2**54 */
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55 ut.t*=x; ut.pt[n0]=ut.pt[n0]/3+B2;
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56 }
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57 else
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58 ut.pt[n0]=hx/3+B1;
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59
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60 /* new cbrt to 23 bits, may be implemented in single precision */
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61 r=ut.t*ut.t/ux.t;
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62 s=C+r*ut.t;
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63 ut.t*=G+F/(s+E+D/s);
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64
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65 /* chopped to 20 bits and make it larger than cbrt(x) */
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66 ut.pt[1-n0]=0; ut.pt[n0]+=0x00000001;
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67
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68 /* one step newton iteration to 53 bits with error less than 0.667 ulps */
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69 s=ut.t*ut.t; /* t*t is exact */
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70 r=ux.t/s;
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71 w=ut.t+ut.t;
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72 r=(r-ut.t)/(w+r); /* r-s is exact */
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73 ut.t=ut.t+ut.t*r;
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74
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75 /* restore the sign bit */
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76 ut.pt[n0] |= sign;
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77
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78 lt = ut.t;
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79 lt -= (lt - (x/(lt*lt))) * 0.333333333333333333333;
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80 return lt;
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81 }
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82
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83 main ()
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84 {
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85 if ((int) (cbrtl (27.0) + 0.5) != 3)
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86 abort ();
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87
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88 exit (0);
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89 }
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90 #else
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91 main () { exit (0); }
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92 #endif
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