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5 | daniel-mar | 1 | package de.viathinksoft.immortable.gen2; |
2 | |||
3 | import java.math.BigInteger; |
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4 | |||
5 | import de.viathinksoft.immortable.gen2.math.CoPrimeExpectedException; |
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6 | import de.viathinksoft.immortable.gen2.math.ImmortableBase; |
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7 | import de.viathinksoft.immortable.gen2.math.MathUtils; |
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8 | import de.viathinksoft.immortable.gen2.math.MathUtils2; |
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9 | |||
10 | /** |
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11 | * Immortable Number Generator (ING) |
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12 | * |
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13 | * @author Daniel Marschall |
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14 | */ |
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15 | |||
16 | public class Immortable { |
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17 | |||
18 | /** |
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19 | * Calculates M5 or M6 |
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20 | * |
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21 | * @param base |
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22 | * @param u |
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23 | * @return |
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24 | */ |
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25 | public static BigInteger M(ImmortableBase base, BigInteger u) { |
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26 | BigInteger p, q; |
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27 | |||
28 | if (base == ImmortableBase.M5) { |
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29 | p = BigInteger.ONE; |
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30 | q = BigInteger.ZERO; |
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31 | } else if (base == ImmortableBase.M6) { |
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32 | p = BigInteger.ZERO; |
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33 | q = BigInteger.ONE; |
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34 | } else { |
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35 | p = null; |
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36 | q = null; |
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37 | } |
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38 | |||
39 | BigInteger a = MathUtils2.pow(new BigInteger("2"), u); |
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40 | BigInteger b = MathUtils2.pow(new BigInteger("5"), u); |
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41 | |||
42 | // To calculate M5: |
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43 | // x = 2^u = a mod 1 |
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44 | // x = 5^u = b mod 0 |
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45 | |||
46 | // To calculate M6: |
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47 | // x = 2^u = a mod 0 |
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48 | // x = 5^u = b mod 1 |
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49 | |||
50 | try { |
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51 | return MathUtils.chineseRemainder(p, a, q, b); |
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52 | } catch (CoPrimeExpectedException e) { |
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53 | // Can never happen since 2^u and 5^u are always coprimes. |
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54 | return null; |
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55 | } |
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56 | } |
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57 | |||
58 | /** |
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59 | * Gets M5(u) |
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60 | * |
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61 | * @param u |
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62 | * Length of number |
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63 | * @return |
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64 | */ |
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65 | public static BigInteger M5(BigInteger u) { |
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66 | return M(ImmortableBase.M5, u); |
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67 | } |
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68 | |||
69 | /** |
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70 | * Gets M6(u) |
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71 | * |
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72 | * @param u |
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73 | * Length of number |
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74 | * @return |
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75 | */ |
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76 | public static BigInteger M6(BigInteger u) { |
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77 | return M(ImmortableBase.M6, u); |
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78 | } |
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79 | |||
80 | /** |
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81 | * Toggles between M5 and M6 base. |
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82 | * |
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83 | * @param cur |
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84 | * Number |
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85 | * @param u |
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86 | * Length of number (because of possible leading zeros) |
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87 | * @return Number in opposide base. |
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7 | daniel-mar | 88 | * @throws Exception |
5 | daniel-mar | 89 | */ |
90 | public static BigInteger toggleBase(BigInteger cur, BigInteger u) |
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7 | daniel-mar | 91 | throws Exception { |
5 | daniel-mar | 92 | // Converts M6(u) <-> M5(u) |
93 | // M6(u) = 1 + 10^u - M5(u) |
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94 | // M5(u) = 1 + 10^u - M6(u) |
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95 | |||
96 | if (u.compareTo(MathUtils2.length(cur)) < 0) { |
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97 | throw new InvalidLengthException(); |
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98 | } |
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99 | |||
100 | return BigInteger.ONE.add(MathUtils2.pow(BigInteger.TEN, u)).subtract(cur); |
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101 | } |
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102 | |||
103 | /** |
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104 | * Toggles between M5 and M6 base. The length of the current number is |
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105 | * assumed (and no leading zero). |
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106 | * |
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107 | * @param cur |
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108 | * @return |
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7 | daniel-mar | 109 | * @throws Exception |
5 | daniel-mar | 110 | */ |
7 | daniel-mar | 111 | public static BigInteger toggleBase(BigInteger cur) throws Exception { |
5 | daniel-mar | 112 | try { |
113 | return toggleBase(cur, MathUtils2.length(cur)); |
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114 | } catch (InvalidLengthException e) { |
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115 | // Should never happen |
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116 | return null; |
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117 | } |
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118 | } |
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6 | daniel-mar | 119 | |
120 | public static boolean isImmortable(BigInteger num) { |
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121 | // Alternativ: nē%10^m == n%10^m |
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122 | return num.pow(2).toString().endsWith(num.toString()); |
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123 | } |
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124 | |||
125 | public static String findNextImmortable(String num) { |
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126 | if (!isImmortable(new BigInteger(num))) { |
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127 | return null; |
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128 | } |
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129 | for (int i=1; i<=9; i++) { |
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130 | String s = i+num; |
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131 | if (isImmortable(new BigInteger(s))) { |
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132 | return s; |
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133 | } |
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134 | } |
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135 | return "0"+num; |
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136 | } |
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5 | daniel-mar | 137 | |
138 | private Immortable() { |
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139 | } |
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140 | |||
141 | } |