1 | |
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2 | /* @(#)s_cbrt.c 5.1 93/09/24 */ |
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3 | /* |
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4 | * ==================================================== |
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5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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6 | * |
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7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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8 | * Permission to use, copy, modify, and distribute this |
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9 | * software is freely granted, provided that this notice |
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10 | * is preserved. |
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11 | * ==================================================== |
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12 | * |
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13 | */ |
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14 | |
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15 | #include <libm/fdlibm.h> |
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16 | |
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17 | /* cbrt(x) |
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18 | * Return cube root of x |
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19 | */ |
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20 | #ifdef __STDC__ |
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21 | static const unsigned |
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22 | #else |
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23 | static unsigned |
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24 | #endif |
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25 | B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ |
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26 | B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ |
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27 | |
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28 | #ifdef __STDC__ |
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29 | static const double |
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30 | #else |
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31 | static double |
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32 | #endif |
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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 | #ifdef __STDC__ |
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40 | double cbrt(double x) |
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41 | #else |
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42 | double cbrt(x) |
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43 | double x; |
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44 | #endif |
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45 | { |
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46 | double one = 1.0; |
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47 | int n0,hx; |
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48 | double r,s,t=0.0,w; |
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49 | unsigned *pt = (unsigned *) &t, sign; |
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50 | |
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51 | |
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52 | n0 = ((*(int*)&one)>>29)^1; /* index of high word */ |
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53 | hx = *( n0 + (int*)&x); /* high word of x */ |
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54 | sign=hx&0x80000000; /* sign= sign(x) */ |
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55 | hx ^=sign; |
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56 | if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ |
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57 | if((hx|*(1-n0+(int*)&x))==0) |
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58 | return(x); /* cbrt(0) is itself */ |
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59 | |
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60 | *(n0+(int*)&x) = hx; /* x <- |x| */ |
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61 | /* rough cbrt to 5 bits */ |
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62 | if(hx<0x00100000) /* subnormal number */ |
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63 | {pt[n0]=0x43500000; /* set t= 2**54 */ |
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64 | t*=x; pt[n0]=pt[n0]/3+B2; |
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65 | } |
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66 | else |
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67 | pt[n0]=hx/3+B1; |
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68 | |
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69 | |
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70 | /* new cbrt to 23 bits, may be implemented in single precision */ |
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71 | r=t*t/x; |
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72 | s=C+r*t; |
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73 | t*=G+F/(s+E+D/s); |
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74 | |
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75 | /* chopped to 20 bits and make it larger than cbrt(x) */ |
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76 | pt[1-n0]=0; pt[n0]+=0x00000001; |
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77 | |
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78 | |
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79 | /* one step newton iteration to 53 bits with error less than 0.667 ulps */ |
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80 | s=t*t; /* t*t is exact */ |
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81 | r=x/s; |
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82 | w=t+t; |
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83 | r=(r-t)/(w+r); /* r-s is exact */ |
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84 | t=t+t*r; |
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85 | |
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86 | /* retore the sign bit */ |
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87 | pt[n0] |= sign; |
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88 | return(t); |
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89 | } |
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