1 | /**
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2 | * @license
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3 | * Copyright Google LLC All Rights Reserved.
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4 | *
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5 | * Use of this source code is governed by an MIT-style license that can be
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6 | * found in the LICENSE file at https://angular.io/license
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7 | */
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8 | /**
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9 | * Represents a big integer using a buffer of its individual digits, with the least significant
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10 | * digit stored at the beginning of the array (little endian).
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11 | *
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12 | * For performance reasons, each instance is mutable. The addition operation can be done in-place
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13 | * to reduce memory pressure of allocation for the digits array.
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14 | */
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15 | export class BigInteger {
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16 | /**
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17 | * Creates a big integer using its individual digits in little endian storage.
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18 | */
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19 | constructor(digits) {
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20 | this.digits = digits;
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21 | }
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22 | static zero() {
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23 | return new BigInteger([0]);
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24 | }
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25 | static one() {
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26 | return new BigInteger([1]);
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27 | }
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28 | /**
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29 | * Creates a clone of this instance.
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30 | */
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31 | clone() {
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32 | return new BigInteger(this.digits.slice());
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33 | }
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34 | /**
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35 | * Returns a new big integer with the sum of `this` and `other` as its value. This does not mutate
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36 | * `this` but instead returns a new instance, unlike `addToSelf`.
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37 | */
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38 | add(other) {
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39 | const result = this.clone();
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40 | result.addToSelf(other);
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41 | return result;
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42 | }
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43 | /**
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44 | * Adds `other` to the instance itself, thereby mutating its value.
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45 | */
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46 | addToSelf(other) {
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47 | const maxNrOfDigits = Math.max(this.digits.length, other.digits.length);
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48 | let carry = 0;
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49 | for (let i = 0; i < maxNrOfDigits; i++) {
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50 | let digitSum = carry;
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51 | if (i < this.digits.length) {
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52 | digitSum += this.digits[i];
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53 | }
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54 | if (i < other.digits.length) {
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55 | digitSum += other.digits[i];
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56 | }
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57 | if (digitSum >= 10) {
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58 | this.digits[i] = digitSum - 10;
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59 | carry = 1;
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60 | }
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61 | else {
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62 | this.digits[i] = digitSum;
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63 | carry = 0;
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64 | }
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65 | }
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66 | // Apply a remaining carry if needed.
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67 | if (carry > 0) {
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68 | this.digits[maxNrOfDigits] = 1;
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69 | }
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70 | }
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71 | /**
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72 | * Builds the decimal string representation of the big integer. As this is stored in
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73 | * little endian, the digits are concatenated in reverse order.
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74 | */
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75 | toString() {
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76 | let res = '';
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77 | for (let i = this.digits.length - 1; i >= 0; i--) {
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78 | res += this.digits[i];
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79 | }
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80 | return res;
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81 | }
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82 | }
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83 | /**
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84 | * Represents a big integer which is optimized for multiplication operations, as its power-of-twos
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85 | * are memoized. See `multiplyBy()` for details on the multiplication algorithm.
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86 | */
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87 | export class BigIntForMultiplication {
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88 | constructor(value) {
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89 | this.powerOfTwos = [value];
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90 | }
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91 | /**
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92 | * Returns the big integer itself.
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93 | */
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94 | getValue() {
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95 | return this.powerOfTwos[0];
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96 | }
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97 | /**
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98 | * Computes the value for `num * b`, where `num` is a JS number and `b` is a big integer. The
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99 | * value for `b` is represented by a storage model that is optimized for this computation.
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100 | *
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101 | * This operation is implemented in N(log2(num)) by continuous halving of the number, where the
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102 | * least-significant bit (LSB) is tested in each iteration. If the bit is set, the bit's index is
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103 | * used as exponent into the power-of-two multiplication of `b`.
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104 | *
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105 | * As an example, consider the multiplication num=42, b=1337. In binary 42 is 0b00101010 and the
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106 | * algorithm unrolls into the following iterations:
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107 | *
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108 | * Iteration | num | LSB | b * 2^iter | Add? | product
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109 | * -----------|------------|------|------------|------|--------
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110 | * 0 | 0b00101010 | 0 | 1337 | No | 0
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111 | * 1 | 0b00010101 | 1 | 2674 | Yes | 2674
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112 | * 2 | 0b00001010 | 0 | 5348 | No | 2674
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113 | * 3 | 0b00000101 | 1 | 10696 | Yes | 13370
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114 | * 4 | 0b00000010 | 0 | 21392 | No | 13370
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115 | * 5 | 0b00000001 | 1 | 42784 | Yes | 56154
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116 | * 6 | 0b00000000 | 0 | 85568 | No | 56154
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117 | *
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118 | * The computed product of 56154 is indeed the correct result.
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119 | *
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120 | * The `BigIntForMultiplication` representation for a big integer provides memoized access to the
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121 | * power-of-two values to reduce the workload in computing those values.
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122 | */
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123 | multiplyBy(num) {
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124 | const product = BigInteger.zero();
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125 | this.multiplyByAndAddTo(num, product);
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126 | return product;
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127 | }
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128 | /**
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129 | * See `multiplyBy()` for details. This function allows for the computed product to be added
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130 | * directly to the provided result big integer.
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131 | */
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132 | multiplyByAndAddTo(num, result) {
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133 | for (let exponent = 0; num !== 0; num = num >>> 1, exponent++) {
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134 | if (num & 1) {
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135 | const value = this.getMultipliedByPowerOfTwo(exponent);
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136 | result.addToSelf(value);
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137 | }
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138 | }
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139 | }
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140 | /**
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141 | * Computes and memoizes the big integer value for `this.number * 2^exponent`.
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142 | */
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143 | getMultipliedByPowerOfTwo(exponent) {
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144 | // Compute the powers up until the requested exponent, where each value is computed from its
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145 | // predecessor. This is simple as `this.number * 2^(exponent - 1)` only has to be doubled (i.e.
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146 | // added to itself) to reach `this.number * 2^exponent`.
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147 | for (let i = this.powerOfTwos.length; i <= exponent; i++) {
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148 | const previousPower = this.powerOfTwos[i - 1];
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149 | this.powerOfTwos[i] = previousPower.add(previousPower);
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150 | }
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151 | return this.powerOfTwos[exponent];
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152 | }
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153 | }
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154 | /**
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155 | * Represents an exponentiation operation for the provided base, of which exponents are computed and
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156 | * memoized. The results are represented by a `BigIntForMultiplication` which is tailored for
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157 | * multiplication operations by memoizing the power-of-twos. This effectively results in a matrix
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158 | * representation that is lazily computed upon request.
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159 | */
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160 | export class BigIntExponentiation {
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161 | constructor(base) {
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162 | this.base = base;
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163 | this.exponents = [new BigIntForMultiplication(BigInteger.one())];
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164 | }
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165 | /**
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166 | * Compute the value for `this.base^exponent`, resulting in a big integer that is optimized for
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167 | * further multiplication operations.
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168 | */
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169 | toThePowerOf(exponent) {
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170 | // Compute the results up until the requested exponent, where every value is computed from its
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171 | // predecessor. This is because `this.base^(exponent - 1)` only has to be multiplied by `base`
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172 | // to reach `this.base^exponent`.
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173 | for (let i = this.exponents.length; i <= exponent; i++) {
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174 | const value = this.exponents[i - 1].multiplyBy(this.base);
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175 | this.exponents[i] = new BigIntForMultiplication(value);
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176 | }
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177 | return this.exponents[exponent];
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178 | }
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179 | }
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The addition operation can be done in-place\n * to reduce memory pressure of allocation for the digits array.\n */\nexport class BigInteger {\n  static zero(): BigInteger {\n    return new BigInteger([0]);\n  }\n\n  static one(): BigInteger {\n    return new BigInteger([1]);\n  }\n\n  /**\n   * Creates a big integer using its individual digits in little endian storage.\n   */\n  private constructor(private readonly digits: number[]) {}\n\n  /**\n   * Creates a clone of this instance.\n   */\n  clone(): BigInteger {\n    return new BigInteger(this.digits.slice());\n  }\n\n  /**\n   * Returns a new big integer with the sum of `this` and `other` as its value. This does not mutate\n   * `this` but instead returns a new instance, unlike `addToSelf`.\n   */\n  add(other: BigInteger): BigInteger {\n    const result = this.clone();\n    result.addToSelf(other);\n    return result;\n  }\n\n  /**\n   * Adds `other` to the instance itself, thereby mutating its value.\n   */\n  addToSelf(other: BigInteger): void {\n    const maxNrOfDigits = Math.max(this.digits.length, other.digits.length);\n    let carry = 0;\n    for (let i = 0; i < maxNrOfDigits; i++) {\n      let digitSum = carry;\n      if (i < this.digits.length) {\n        digitSum += this.digits[i];\n      }\n      if (i < other.digits.length) {\n        digitSum += other.digits[i];\n      }\n\n      if (digitSum >= 10) {\n        this.digits[i] = digitSum - 10;\n        carry = 1;\n      } else {\n        this.digits[i] = digitSum;\n        carry = 0;\n      }\n    }\n\n    // Apply a remaining carry if needed.\n    if (carry > 0) {\n      this.digits[maxNrOfDigits] = 1;\n    }\n  }\n\n  /**\n   * Builds the decimal string representation of the big integer. As this is stored in\n   * little endian, the digits are concatenated in reverse order.\n   */\n  toString(): string {\n    let res = '';\n    for (let i = this.digits.length - 1; i >= 0; i--) {\n      res += this.digits[i];\n    }\n    return res;\n  }\n}\n\n/**\n * Represents a big integer which is optimized for multiplication operations, as its power-of-twos\n * are memoized. See `multiplyBy()` for details on the multiplication algorithm.\n */\nexport class BigIntForMultiplication {\n  /**\n   * Stores all memoized power-of-twos, where each index represents `this.number * 2^index`.\n   */\n  private readonly powerOfTwos: BigInteger[];\n\n  constructor(value: BigInteger) {\n    this.powerOfTwos = [value];\n  }\n\n  /**\n   * Returns the big integer itself.\n   */\n  getValue(): BigInteger {\n    return this.powerOfTwos[0];\n  }\n\n  /**\n   * Computes the value for `num * b`, where `num` is a JS number and `b` is a big integer. The\n   * value for `b` is represented by a storage model that is optimized for this computation.\n   *\n   * This operation is implemented in N(log2(num)) by continuous halving of the number, where the\n   * least-significant bit (LSB) is tested in each iteration. If the bit is set, the bit's index is\n   * used as exponent into the power-of-two multiplication of `b`.\n   *\n   * As an example, consider the multiplication num=42, b=1337. In binary 42 is 0b00101010 and the\n   * algorithm unrolls into the following iterations:\n   *\n   *  Iteration | num        | LSB  | b * 2^iter | Add? | product\n   * -----------|------------|------|------------|------|--------\n   *  0         | 0b00101010 | 0    | 1337       | No   | 0\n   *  1         | 0b00010101 | 1    | 2674       | Yes  | 2674\n   *  2         | 0b00001010 | 0    | 5348       | No   | 2674\n   *  3         | 0b00000101 | 1    | 10696      | Yes  | 13370\n   *  4         | 0b00000010 | 0    | 21392      | No   | 13370\n   *  5         | 0b00000001 | 1    | 42784      | Yes  | 56154\n   *  6         | 0b00000000 | 0    | 85568      | No   | 56154\n   *\n   * The computed product of 56154 is indeed the correct result.\n   *\n   * The `BigIntForMultiplication` representation for a big integer provides memoized access to the\n   * power-of-two values to reduce the workload in computing those values.\n   */\n  multiplyBy(num: number): BigInteger {\n    const product = BigInteger.zero();\n    this.multiplyByAndAddTo(num, product);\n    return product;\n  }\n\n  /**\n   * See `multiplyBy()` for details. This function allows for the computed product to be added\n   * directly to the provided result big integer.\n   */\n  multiplyByAndAddTo(num: number, result: BigInteger): void {\n    for (let exponent = 0; num !== 0; num = num >>> 1, exponent++) {\n      if (num & 1) {\n        const value = this.getMultipliedByPowerOfTwo(exponent);\n        result.addToSelf(value);\n      }\n    }\n  }\n\n  /**\n   * Computes and memoizes the big integer value for `this.number * 2^exponent`.\n   */\n  private getMultipliedByPowerOfTwo(exponent: number): BigInteger {\n    // Compute the powers up until the requested exponent, where each value is computed from its\n    // predecessor. This is simple as `this.number * 2^(exponent - 1)` only has to be doubled (i.e.\n    // added to itself) to reach `this.number * 2^exponent`.\n    for (let i = this.powerOfTwos.length; i <= exponent; i++) {\n      const previousPower = this.powerOfTwos[i - 1];\n      this.powerOfTwos[i] = previousPower.add(previousPower);\n    }\n    return this.powerOfTwos[exponent];\n  }\n}\n\n/**\n * Represents an exponentiation operation for the provided base, of which exponents are computed and\n * memoized. The results are represented by a `BigIntForMultiplication` which is tailored for\n * multiplication operations by memoizing the power-of-twos. This effectively results in a matrix\n * representation that is lazily computed upon request.\n */\nexport class BigIntExponentiation {\n  private readonly exponents = [new BigIntForMultiplication(BigInteger.one())];\n\n  constructor(private readonly base: number) {}\n\n  /**\n   * Compute the value for `this.base^exponent`, resulting in a big integer that is optimized for\n   * further multiplication operations.\n   */\n  toThePowerOf(exponent: number): BigIntForMultiplication {\n    // Compute the results up until the requested exponent, where every value is computed from its\n    // predecessor. This is because `this.base^(exponent - 1)` only has to be multiplied by `base`\n    // to reach `this.base^exponent`.\n    for (let i = this.exponents.length; i <= exponent; i++) {\n      const value = this.exponents[i - 1].multiplyBy(this.base);\n      this.exponents[i] = new BigIntForMultiplication(value);\n    }\n    return this.exponents[exponent];\n  }\n}\n"]} |
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