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1554 lines
50 KiB
Java
1554 lines
50 KiB
Java
/*
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* Copyright 2009 Google Inc.
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*
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* Licensed under the Apache License, Version 2.0 (the "License"); you may not
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* use this file except in compliance with the License. You may obtain a copy of
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* the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
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* License for the specific language governing permissions and limitations under
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* the License.
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*/
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with this
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* work for additional information regarding copyright ownership. The ASF
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* licenses this file to You under the Apache License, Version 2.0 (the
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* "License"); you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
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* License for the specific language governing permissions and limitations under
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* the License.
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*
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* INCLUDES MODIFICATIONS BY RICHARD ZSCHECH AS WELL AS GOOGLE.
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*/
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package java.math;
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import java.io.Serializable;
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import java.util.Random;
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/**
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* This class represents immutable integer numbers of arbitrary length. Large
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* numbers are typically used in security applications and therefore BigIntegers
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* offer dedicated functionality like the generation of large prime numbers or
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* the computation of modular inverse.
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* <p>
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* Since the class was modeled to offer all the functionality as the
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* {@link Integer} class does, it provides even methods that operate bitwise on
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* a two's complement representation of large integers. Note however that the
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* implementations favors an internal representation where magnitude and sign
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* are treated separately. Hence such operations are inefficient and should be
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* discouraged. In simple words: Do NOT implement any bit fields based on
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* BigInteger.
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*/
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public class BigInteger extends Number implements Comparable<BigInteger>,
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Serializable {
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/**
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* The {@code BigInteger} constant 1.
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*/
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public static final BigInteger ONE = new BigInteger(1, 1);
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/* Fields used for the internal representation. */
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/**
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* The {@code BigInteger} constant 10.
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*/
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public static final BigInteger TEN = new BigInteger(1, 10);
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/**
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* The {@code BigInteger} constant 0.
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*/
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public static final BigInteger ZERO = new BigInteger(0, 0);
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/**
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* The {@code BigInteger} constant 0 used for comparison.
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*/
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static final int EQUALS = 0;
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/**
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* The {@code BigInteger} constant 1 used for comparison.
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*/
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static final int GREATER = 1;
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/**
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* The {@code BigInteger} constant -1 used for comparison.
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*/
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static final int LESS = -1;
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/**
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* The {@code BigInteger} constant -1.
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*/
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static final BigInteger MINUS_ONE = new BigInteger(-1, 1);
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/**
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* 2^32.
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*/
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static final double POW32 = 4294967296d;
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/**
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* All the {@code BigInteger} numbers in the range [0,10] are cached.
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*/
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static final BigInteger[] SMALL_VALUES = {
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ZERO, ONE, new BigInteger(1, 2), new BigInteger(1, 3),
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new BigInteger(1, 4), new BigInteger(1, 5), new BigInteger(1, 6),
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new BigInteger(1, 7), new BigInteger(1, 8), new BigInteger(1, 9), TEN};
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static final BigInteger[] TWO_POWS;
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/**
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* This is the serialVersionUID used by the sun implementation.
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*/
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private static final long serialVersionUID = -8287574255936472291L;
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static {
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TWO_POWS = new BigInteger[32];
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for (int i = 0; i < TWO_POWS.length; i++) {
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TWO_POWS[i] = BigInteger.valueOf(1L << i);
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}
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}
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/**
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* Returns a random positive {@code BigInteger} instance in the range [0,
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* 2^(bitLength)-1] which is probably prime. The probability that the returned
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* {@code BigInteger} is prime is beyond (1-1/2^80).
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* <p>
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* <b>Implementation Note:</b> Currently {@code rnd} is ignored.
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*
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* @param bitLength length of the new {@code BigInteger} in bits.
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* @param rnd random generator used to generate the new {@code BigInteger}.
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* @return probably prime random {@code BigInteger} instance.
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* @throws IllegalArgumentException if {@code bitLength < 2}.
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*/
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public static BigInteger probablePrime(int bitLength, Random rnd) {
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return new BigInteger(bitLength, 100, rnd);
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}
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public static BigInteger valueOf(long val) {
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if (val < 0) {
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if (val != -1) {
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return new BigInteger(-1, -val);
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}
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return MINUS_ONE;
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} else if (val <= 10) {
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return SMALL_VALUES[(int) val];
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} else {
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// (val > 10)
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return new BigInteger(1, val);
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}
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}
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static BigInteger getPowerOfTwo(int exp) {
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if (exp < TWO_POWS.length) {
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return TWO_POWS[exp];
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}
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int intCount = exp >> 5;
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int bitN = exp & 31;
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int resDigits[] = new int[intCount + 1];
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resDigits[intCount] = 1 << bitN;
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return new BigInteger(1, intCount + 1, resDigits);
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}
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static BigInteger valueOf(double val) {
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if (val < 0) {
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if (val != -1) {
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return new BigInteger(-1, -val);
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}
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return MINUS_ONE;
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} else if (val <= 10) {
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return SMALL_VALUES[(int) val];
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} else {
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// (val > 10)
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return new BigInteger(1, val);
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}
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}
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/**
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* @see BigInteger#BigInteger(String, int)
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*/
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private static void setFromString(BigInteger bi, String val, int radix) {
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int sign;
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int[] digits;
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int numberLength;
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int stringLength = val.length();
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int startChar;
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int endChar = stringLength;
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if (val.charAt(0) == '-') {
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sign = -1;
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startChar = 1;
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stringLength--;
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} else {
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sign = 1;
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startChar = 0;
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}
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/*
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* We use the following algorithm: split a string into portions of n
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* characters and convert each portion to an integer according to the radix.
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* Then convert an exp(radix, n) based number to binary using the
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* multiplication method. See D. Knuth, The Art of Computer Programming,
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* vol. 2.
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*/
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int charsPerInt = Conversion.digitFitInInt[radix];
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int bigRadixDigitsLength = stringLength / charsPerInt;
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int topChars = stringLength % charsPerInt;
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if (topChars != 0) {
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bigRadixDigitsLength++;
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}
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digits = new int[bigRadixDigitsLength];
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// Get the maximal power of radix that fits in int
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int bigRadix = Conversion.bigRadices[radix - 2];
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// Parse an input string and accumulate the BigInteger's magnitude
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int digitIndex = 0; // index of digits array
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int substrEnd = startChar + ((topChars == 0) ? charsPerInt : topChars);
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int newDigit;
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for (int substrStart = startChar; substrStart < endChar; substrStart = substrEnd, substrEnd = substrStart
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+ charsPerInt) {
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int bigRadixDigit = Integer.parseInt(
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val.substring(substrStart, substrEnd), radix);
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newDigit = Multiplication.multiplyByInt(digits, digitIndex, bigRadix);
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newDigit += Elementary.inplaceAdd(digits, digitIndex, bigRadixDigit);
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digits[digitIndex++] = newDigit;
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}
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numberLength = digitIndex;
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bi.sign = sign;
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bi.numberLength = numberLength;
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bi.digits = digits;
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bi.cutOffLeadingZeroes();
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}
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/**
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* Converts an integral double to an unsigned integer; ie 2^31 will be
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* returned as 0x80000000.
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*
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* @param val
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* @return val as an unsigned int
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*/
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private static native int toUnsignedInt(double val) /*-{
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return ~~val;
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}-*/;
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/**
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* The magnitude of this big integer. This array is in little endian order and
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* each "digit" is a 32-bit unsigned integer. For example: {@code 13} is
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* represented as [ 13 ] {@code -13} is represented as [ 13 ] {@code 2^32 +
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* 13} is represented as [ 13, 1 ] {@code 2^64 + 13} is represented as [ 13,
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* 0, 1 ] {@code 2^31} is represented as [ Integer.MIN_VALUE ] The magnitude
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* array may be longer than strictly necessary, which results in additional
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* trailing zeros.
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*
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* <p>TODO(jat): consider changing to 24-bit integers for better performance
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* in browsers.
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*/
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transient int digits[];
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/**
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* The length of this in measured in ints. Can be less than digits.length().
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*/
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transient int numberLength;
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/**
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* The sign of this.
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*/
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transient int sign;
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private transient int firstNonzeroDigit = -2;
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/**
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* Cache for the hash code.
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*/
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private transient int hashCode = 0;
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/**
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* Constructs a new {@code BigInteger} from the given two's complement
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* representation. The most significant byte is the entry at index 0. The most
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* significant bit of this entry determines the sign of the new {@code
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* BigInteger} instance. The given array must not be empty.
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*
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* @param val two's complement representation of the new {@code BigInteger}.
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* @throws NullPointerException if {@code val == null}.
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* @throws NumberFormatException if the length of {@code val} is zero.
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*/
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public BigInteger(byte[] val) {
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if (val.length == 0) {
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// math.12=Zero length BigInteger
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throw new NumberFormatException("Zero length BigInteger"); //$NON-NLS-1$
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}
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if (val[0] < 0) {
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sign = -1;
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putBytesNegativeToIntegers(val);
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} else {
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sign = 1;
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putBytesPositiveToIntegers(val);
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}
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cutOffLeadingZeroes();
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}
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/**
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* Constructs a new {@code BigInteger} instance with the given sign and the
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* given magnitude. The sign is given as an integer (-1 for negative, 0 for
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* zero, 1 for positive). The magnitude is specified as a byte array. The most
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* significant byte is the entry at index 0.
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*
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* @param signum sign of the new {@code BigInteger} (-1 for negative, 0 for
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* zero, 1 for positive).
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* @param magnitude magnitude of the new {@code BigInteger} with the most
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* significant byte first.
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* @throws NullPointerException if {@code magnitude == null}.
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* @throws NumberFormatException if the sign is not one of -1, 0, 1 or if the
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* sign is zero and the magnitude contains non-zero entries.
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*/
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public BigInteger(int signum, byte[] magnitude) {
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if (magnitude == null) {
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throw new NullPointerException();
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}
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if ((signum < -1) || (signum > 1)) {
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// math.13=Invalid signum value
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throw new NumberFormatException("Invalid signum value"); //$NON-NLS-1$
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}
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if (signum == 0) {
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for (byte element : magnitude) {
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if (element != 0) {
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// math.14=signum-magnitude mismatch
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throw new NumberFormatException("signum-magnitude mismatch"); //$NON-NLS-1$
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}
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}
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}
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if (magnitude.length == 0) {
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sign = 0;
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numberLength = 1;
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digits = new int[] {0};
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} else {
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sign = signum;
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putBytesPositiveToIntegers(magnitude);
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cutOffLeadingZeroes();
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}
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}
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/**
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* Constructs a random {@code BigInteger} instance in the range [0,
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* 2^(bitLength)-1] which is probably prime. The probability that the returned
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* {@code BigInteger} is prime is beyond (1-1/2^certainty).
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*
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* @param bitLength length of the new {@code BigInteger} in bits.
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* @param certainty tolerated primality uncertainty.
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* @param rnd is an optional random generator to be used.
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* @throws ArithmeticException if {@code bitLength} < 2.
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*/
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public BigInteger(int bitLength, int certainty, Random rnd) {
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if (bitLength < 2) {
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// math.1C=bitLength < 2
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throw new ArithmeticException("bitLength < 2"); //$NON-NLS-1$
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}
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BigInteger me = Primality.consBigInteger(bitLength, certainty, rnd);
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sign = me.sign;
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numberLength = me.numberLength;
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digits = me.digits;
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}
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/**
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* Constructs a random non-negative {@code BigInteger} instance in the range
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* [0, 2^(numBits)-1].
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*
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* @param numBits maximum length of the new {@code BigInteger} in bits.
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* @param rnd is an optional random generator to be used.
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* @throws IllegalArgumentException if {@code numBits} < 0.
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*/
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public BigInteger(int numBits, Random rnd) {
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if (numBits < 0) {
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// math.1B=numBits must be non-negative
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throw new IllegalArgumentException("numBits must be non-negative"); //$NON-NLS-1$
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}
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if (numBits == 0) {
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sign = 0;
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numberLength = 1;
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digits = new int[] {0};
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} else {
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sign = 1;
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numberLength = (numBits + 31) >> 5;
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digits = new int[numberLength];
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for (int i = 0; i < numberLength; i++) {
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digits[i] = rnd.nextInt();
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}
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// Using only the necessary bits
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digits[numberLength - 1] >>>= (-numBits) & 31;
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cutOffLeadingZeroes();
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}
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}
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/**
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* Constructs a new {@code BigInteger} instance from the string
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* representation. The string representation consists of an optional minus
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* sign followed by a non-empty sequence of decimal digits.
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*
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* @param val string representation of the new {@code BigInteger}.
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* @throws NullPointerException if {@code val == null}.
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* @throws NumberFormatException if {@code val} is not a valid representation
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* of a {@code BigInteger}.
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*/
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public BigInteger(String val) {
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this(val, 10);
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}
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/**
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* Constructs a new {@code BigInteger} instance from the string
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* representation. The string representation consists of an optional minus
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* sign followed by a non-empty sequence of digits in the specified radix. For
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* the conversion the method {@code Character.digit(char, radix)} is used.
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*
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* @param val string representation of the new {@code BigInteger}.
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* @param radix the base to be used for the conversion.
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* @throws NullPointerException if {@code val == null}.
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* @throws NumberFormatException if {@code val} is not a valid representation
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* of a {@code BigInteger} or if {@code radix < Character.MIN_RADIX}
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* or {@code radix > Character.MAX_RADIX}.
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*/
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public BigInteger(String val, int radix) {
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if (val == null) {
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throw new NullPointerException();
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}
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if ((radix < Character.MIN_RADIX) || (radix > Character.MAX_RADIX)) {
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// math.11=Radix out of range
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throw new NumberFormatException("Radix out of range"); //$NON-NLS-1$
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}
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if (val.length() == 0) {
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// math.12=Zero length BigInteger
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throw new NumberFormatException("Zero length BigInteger"); //$NON-NLS-1$
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}
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setFromString(this, val, radix);
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}
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/**
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* Constructs a number which array is of size 1.
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*
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* @param sign the sign of the number
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* @param value the only one digit of array
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*/
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BigInteger(int sign, int value) {
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this.sign = sign;
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numberLength = 1;
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digits = new int[] {value};
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}
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/**
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* Creates a new {@code BigInteger} with the given sign and magnitude. This
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* constructor does not create a copy, so any changes to the reference will
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* affect the new number.
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*
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* @param signum The sign of the number represented by {@code digits}
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* @param digits The magnitude of the number
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*/
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BigInteger(int signum, int digits[]) {
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if (digits.length == 0) {
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sign = 0;
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numberLength = 1;
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this.digits = new int[] {0};
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} else {
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sign = signum;
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numberLength = digits.length;
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this.digits = digits;
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cutOffLeadingZeroes();
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}
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}
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/**
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* Constructs a number without to create new space. This construct should be
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* used only if the three fields of representation are known.
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*
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* @param sign the sign of the number
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* @param numberLength the length of the internal array
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* @param digits a reference of some array created before
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*/
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BigInteger(int sign, int numberLength, int[] digits) {
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this.sign = sign;
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this.numberLength = numberLength;
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this.digits = digits;
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}
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/**
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* Creates a new {@code BigInteger} whose value is equal to the specified
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* {@code long}.
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*
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* @param sign the sign of the number
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* @param val the value of the new {@code BigInteger}.
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*/
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BigInteger(int sign, long val) {
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// PRE: (val >= 0) && (sign >= -1) && (sign <= 1)
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this.sign = sign;
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if ((val & 0xFFFFFFFF00000000L) == 0) {
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// It fits in one 'int'
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numberLength = 1;
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digits = new int[] {(int) val};
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} else {
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numberLength = 2;
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digits = new int[] {(int) val, (int) (val >> 32)};
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}
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}
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/**
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* Creates a new {@code BigInteger} whose value is equal to the specified
|
|
* {@code double} (which must be an integral value).
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*
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* @param sign the sign of the number
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* @param val the value of the new {@code BigInteger}.
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*/
|
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private BigInteger(int sign, double val) {
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// PRE: (val >= 0) && (sign >= -1) && (sign <= 1)
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|
// ~~ forces coercion to 32 bits
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this.sign = sign;
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if (val < POW32) {
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// It fits in one 'int'
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numberLength = 1;
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|
digits = new int[] { toUnsignedInt(val) };
|
|
} else {
|
|
numberLength = 2;
|
|
digits = new int[] { toUnsignedInt(val % POW32),
|
|
toUnsignedInt(val / POW32)};
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Returns a (new) {@code BigInteger} whose value is the absolute value of
|
|
* {@code this}.
|
|
*
|
|
* @return {@code abs(this)}.
|
|
*/
|
|
public BigInteger abs() {
|
|
return ((sign < 0) ? new BigInteger(1, numberLength, digits) : this);
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is {@code this + val}.
|
|
*
|
|
* @param val value to be added to {@code this}.
|
|
* @return {@code this + val}.
|
|
* @throws NullPointerException if {@code val == null}.
|
|
*/
|
|
public BigInteger add(BigInteger val) {
|
|
return Elementary.add(this, val);
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is {@code this & val}.
|
|
* <p>
|
|
* <b>Implementation Note:</b> Usage of this method is not recommended as the
|
|
* current implementation is not efficient.
|
|
*
|
|
* @param val value to be and'ed with {@code this}.
|
|
* @return {@code this & val}.
|
|
* @throws NullPointerException if {@code val == null}.
|
|
*/
|
|
public BigInteger and(BigInteger val) {
|
|
return Logical.and(this, val);
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is {@code this & ~val}.
|
|
* Evaluating {@code x.andNot(val)} returns the same result as {@code
|
|
* x.and(val.not())}.
|
|
* <p>
|
|
* <b>Implementation Note:</b> Usage of this method is not recommended as the
|
|
* current implementation is not efficient.
|
|
*
|
|
* @param val value to be not'ed and then and'ed with {@code this}.
|
|
* @return {@code this & ~val}.
|
|
* @throws NullPointerException if {@code val == null}.
|
|
*/
|
|
public BigInteger andNot(BigInteger val) {
|
|
return Logical.andNot(this, val);
|
|
}
|
|
|
|
/**
|
|
* Use {@code bitLength(0)} if you want to know the length of the binary value
|
|
* in bits.
|
|
* <p>
|
|
* Returns the number of bits in the binary representation of {@code this}
|
|
* which differ from the sign bit. If {@code this} is positive the result is
|
|
* equivalent to the number of bits set in the binary representation of
|
|
* {@code this}. If {@code this} is negative the result is equivalent to the
|
|
* number of bits set in the binary representation of {@code -this-1}.
|
|
* <p>
|
|
* <b>Implementation Note:</b> Usage of this method is not recommended as the
|
|
* current implementation is not efficient.
|
|
*
|
|
* @return number of bits in the binary representation of {@code this} which
|
|
* differ from the sign bit
|
|
*/
|
|
public int bitCount() {
|
|
return BitLevel.bitCount(this);
|
|
}
|
|
|
|
/**
|
|
* Returns the length of the value's two's complement representation without
|
|
* leading zeros for positive numbers / without leading ones for negative
|
|
* values.
|
|
* <p>
|
|
* The two's complement representation of {@code this} will be at least
|
|
* {@code bitLength() + 1} bits long.
|
|
* <p>
|
|
* The value will fit into an {@code int} if {@code bitLength() < 32} or into
|
|
* a {@code long} if {@code bitLength() < 64}.
|
|
*
|
|
* @return the length of the minimal two's complement representation for
|
|
* {@code this} without the sign bit.
|
|
*/
|
|
public int bitLength() {
|
|
return BitLevel.bitLength(this);
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} which has the same binary representation
|
|
* as {@code this} but with the bit at position n cleared. The result is
|
|
* equivalent to {@code this & ~(2^n)}.
|
|
* <p>
|
|
* <b>Implementation Note:</b> Usage of this method is not recommended as the
|
|
* current implementation is not efficient.
|
|
*
|
|
* @param n position where the bit in {@code this} has to be cleared.
|
|
* @return {@code this & ~(2^n)}.
|
|
* @throws ArithmeticException if {@code n < 0}.
|
|
*/
|
|
public BigInteger clearBit(int n) {
|
|
if (testBit(n)) {
|
|
return BitLevel.flipBit(this, n);
|
|
}
|
|
return this;
|
|
}
|
|
|
|
/**
|
|
* Compares this {@code BigInteger} with {@code val}. Returns one of the three
|
|
* values 1, 0, or -1.
|
|
*
|
|
* @param val value to be compared with {@code this}.
|
|
* @return {@code 1} if {@code this > val}, {@code -1} if {@code this < val} ,
|
|
* {@code 0} if {@code this == val}.
|
|
* @throws NullPointerException if {@code val == null}.
|
|
*/
|
|
public int compareTo(BigInteger val) {
|
|
if (sign > val.sign) {
|
|
return GREATER;
|
|
}
|
|
if (sign < val.sign) {
|
|
return LESS;
|
|
}
|
|
if (numberLength > val.numberLength) {
|
|
return sign;
|
|
}
|
|
if (numberLength < val.numberLength) {
|
|
return -val.sign;
|
|
}
|
|
// Equal sign and equal numberLength
|
|
return (sign * Elementary.compareArrays(digits, val.digits, numberLength));
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is {@code this / divisor}.
|
|
*
|
|
* @param divisor value by which {@code this} is divided.
|
|
* @return {@code this / divisor}.
|
|
* @throws NullPointerException if {@code divisor == null}.
|
|
* @throws ArithmeticException if {@code divisor == 0}.
|
|
*/
|
|
public BigInteger divide(BigInteger divisor) {
|
|
if (divisor.sign == 0) {
|
|
// math.17=BigInteger divide by zero
|
|
throw new ArithmeticException("BigInteger divide by zero"); //$NON-NLS-1$
|
|
}
|
|
int divisorSign = divisor.sign;
|
|
if (divisor.isOne()) {
|
|
return ((divisor.sign > 0) ? this : this.negate());
|
|
}
|
|
int thisSign = sign;
|
|
int thisLen = numberLength;
|
|
int divisorLen = divisor.numberLength;
|
|
if (thisLen + divisorLen == 2) {
|
|
long val = (digits[0] & 0xFFFFFFFFL) / (divisor.digits[0] & 0xFFFFFFFFL);
|
|
if (thisSign != divisorSign) {
|
|
val = -val;
|
|
}
|
|
return valueOf(val);
|
|
}
|
|
int cmp = ((thisLen != divisorLen) ? ((thisLen > divisorLen) ? 1 : -1)
|
|
: Elementary.compareArrays(digits, divisor.digits, thisLen));
|
|
if (cmp == EQUALS) {
|
|
return ((thisSign == divisorSign) ? ONE : MINUS_ONE);
|
|
}
|
|
if (cmp == LESS) {
|
|
return ZERO;
|
|
}
|
|
int resLength = thisLen - divisorLen + 1;
|
|
int resDigits[] = new int[resLength];
|
|
int resSign = ((thisSign == divisorSign) ? 1 : -1);
|
|
if (divisorLen == 1) {
|
|
Division.divideArrayByInt(resDigits, digits, thisLen, divisor.digits[0]);
|
|
} else {
|
|
Division.divide(resDigits, resLength, digits, thisLen, divisor.digits,
|
|
divisorLen);
|
|
}
|
|
BigInteger result = new BigInteger(resSign, resLength, resDigits);
|
|
result.cutOffLeadingZeroes();
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* Returns a {@code BigInteger} array which contains {@code this / divisor} at
|
|
* index 0 and {@code this % divisor} at index 1.
|
|
*
|
|
* @param divisor value by which {@code this} is divided.
|
|
* @return {@code [this / divisor, this % divisor]}.
|
|
* @throws NullPointerException if {@code divisor == null}.
|
|
* @throws ArithmeticException if {@code divisor == 0}.
|
|
* @see #divide
|
|
* @see #remainder
|
|
*/
|
|
public BigInteger[] divideAndRemainder(BigInteger divisor) {
|
|
int divisorSign = divisor.sign;
|
|
if (divisorSign == 0) {
|
|
// math.17=BigInteger divide by zero
|
|
throw new ArithmeticException("BigInteger divide by zero"); //$NON-NLS-1$
|
|
}
|
|
int divisorLen = divisor.numberLength;
|
|
int[] divisorDigits = divisor.digits;
|
|
if (divisorLen == 1) {
|
|
return Division.divideAndRemainderByInteger(this, divisorDigits[0],
|
|
divisorSign);
|
|
}
|
|
// res[0] is a quotient and res[1] is a remainder:
|
|
int[] thisDigits = digits;
|
|
int thisLen = numberLength;
|
|
int cmp = (thisLen != divisorLen) ? ((thisLen > divisorLen) ? 1 : -1)
|
|
: Elementary.compareArrays(thisDigits, divisorDigits, thisLen);
|
|
if (cmp < 0) {
|
|
return new BigInteger[] {ZERO, this};
|
|
}
|
|
int thisSign = sign;
|
|
int quotientLength = thisLen - divisorLen + 1;
|
|
int remainderLength = divisorLen;
|
|
int quotientSign = ((thisSign == divisorSign) ? 1 : -1);
|
|
int quotientDigits[] = new int[quotientLength];
|
|
int remainderDigits[] = Division.divide(quotientDigits, quotientLength,
|
|
thisDigits, thisLen, divisorDigits, divisorLen);
|
|
BigInteger result0 = new BigInteger(quotientSign, quotientLength,
|
|
quotientDigits);
|
|
BigInteger result1 = new BigInteger(thisSign, remainderLength,
|
|
remainderDigits);
|
|
result0.cutOffLeadingZeroes();
|
|
result1.cutOffLeadingZeroes();
|
|
return new BigInteger[] {result0, result1};
|
|
}
|
|
|
|
/**
|
|
* Returns this {@code BigInteger} as an double value. If {@code this} is too
|
|
* big to be represented as an double, then {@code Double.POSITIVE_INFINITY}
|
|
* or {@code Double.NEGATIVE_INFINITY} is returned. Note, that not all
|
|
* integers x in the range [-Double.MAX_VALUE, Double.MAX_VALUE] can be
|
|
* represented as a double. The double representation has a mantissa of length
|
|
* 53. For example, 2^53+1 = 9007199254740993 is returned as double
|
|
* 9007199254740992.0.
|
|
*
|
|
* @return this {@code BigInteger} as a double value
|
|
*/
|
|
@Override
|
|
public double doubleValue() {
|
|
return Double.parseDouble(this.toString());
|
|
}
|
|
|
|
/**
|
|
* Returns {@code true} if {@code x} is a BigInteger instance and if this
|
|
* instance is equal to this {@code BigInteger}.
|
|
*
|
|
* @param x object to be compared with {@code this}.
|
|
* @return true if {@code x} is a BigInteger and {@code this == x}, {@code
|
|
* false} otherwise.
|
|
*/
|
|
@Override
|
|
public boolean equals(Object x) {
|
|
if (this == x) {
|
|
return true;
|
|
}
|
|
if (x instanceof BigInteger) {
|
|
BigInteger x1 = (BigInteger) x;
|
|
return sign == x1.sign && numberLength == x1.numberLength
|
|
&& equalsArrays(x1.digits);
|
|
}
|
|
return false;
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} which has the same binary representation
|
|
* as {@code this} but with the bit at position n flipped. The result is
|
|
* equivalent to {@code this ^ 2^n}.
|
|
* <p>
|
|
* <b>Implementation Note:</b> Usage of this method is not recommended as the
|
|
* current implementation is not efficient.
|
|
*
|
|
* @param n position where the bit in {@code this} has to be flipped.
|
|
* @return {@code this ^ 2^n}.
|
|
* @throws ArithmeticException if {@code n < 0}.
|
|
*/
|
|
public BigInteger flipBit(int n) {
|
|
if (n < 0) {
|
|
// math.15=Negative bit address
|
|
throw new ArithmeticException("Negative bit address"); //$NON-NLS-1$
|
|
}
|
|
return BitLevel.flipBit(this, n);
|
|
}
|
|
|
|
/**
|
|
* Returns this {@code BigInteger} as an float value. If {@code this} is too
|
|
* big to be represented as an float, then {@code Float.POSITIVE_INFINITY} or
|
|
* {@code Float.NEGATIVE_INFINITY} is returned. Note, that not all integers x
|
|
* in the range [-Float.MAX_VALUE, Float.MAX_VALUE] can be represented as a
|
|
* float. The float representation has a mantissa of length 24. For example,
|
|
* 2^24+1 = 16777217 is returned as float 16777216.0.
|
|
*
|
|
* @return this {@code BigInteger} as a float value.
|
|
*/
|
|
@Override
|
|
public float floatValue() {
|
|
return Float.parseFloat(this.toString());
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is greatest common divisor of
|
|
* {@code this} and {@code val}. If {@code this==0} and {@code val==0} then
|
|
* zero is returned, otherwise the result is positive.
|
|
*
|
|
* @param val value with which the greatest common divisor is computed.
|
|
* @return {@code gcd(this, val)}.
|
|
* @throws NullPointerException if {@code val == null}.
|
|
*/
|
|
public BigInteger gcd(BigInteger val) {
|
|
BigInteger val1 = this.abs();
|
|
BigInteger val2 = val.abs();
|
|
// To avoid a possible division by zero
|
|
if (val1.signum() == 0) {
|
|
return val2;
|
|
} else if (val2.signum() == 0) {
|
|
return val1;
|
|
}
|
|
|
|
// Optimization for small operands
|
|
// (op2.bitLength() < 64) and (op1.bitLength() < 64)
|
|
if (((val1.numberLength == 1) || ((val1.numberLength == 2) && (val1.digits[1] > 0)))
|
|
&& (val2.numberLength == 1 || (val2.numberLength == 2 && val2.digits[1] > 0))) {
|
|
return BigInteger.valueOf(Division.gcdBinary(val1.longValue(),
|
|
val2.longValue()));
|
|
}
|
|
|
|
return Division.gcdBinary(val1.copy(), val2.copy());
|
|
}
|
|
|
|
/**
|
|
* Returns the position of the lowest set bit in the two's complement
|
|
* representation of this {@code BigInteger}. If all bits are zero (this=0)
|
|
* then -1 is returned as result.
|
|
* <p>
|
|
* <b>Implementation Note:</b> Usage of this method is not recommended as the
|
|
* current implementation is not efficient.
|
|
*
|
|
* @return position of lowest bit if {@code this != 0}, {@code -1} otherwise
|
|
*/
|
|
public int getLowestSetBit() {
|
|
if (sign == 0) {
|
|
return -1;
|
|
}
|
|
// (sign != 0) implies that exists some non zero digit
|
|
int i = getFirstNonzeroDigit();
|
|
return ((i << 5) + Integer.numberOfTrailingZeros(digits[i]));
|
|
}
|
|
|
|
/**
|
|
* Returns a hash code for this {@code BigInteger}.
|
|
*
|
|
* @return hash code for {@code this}.
|
|
*/
|
|
@Override
|
|
public int hashCode() {
|
|
if (hashCode != 0) {
|
|
return hashCode;
|
|
}
|
|
for (int i = 0; i < digits.length; i++) {
|
|
hashCode = (hashCode * 33 + (digits[i] & 0xffffffff));
|
|
}
|
|
hashCode = hashCode * sign;
|
|
return hashCode;
|
|
}
|
|
|
|
/**
|
|
* Returns this {@code BigInteger} as an int value. If {@code this} is too big
|
|
* to be represented as an int, then {@code this} % 2^32 is returned.
|
|
*
|
|
* @return this {@code BigInteger} as an int value.
|
|
*/
|
|
@Override
|
|
public int intValue() {
|
|
return (sign * digits[0]);
|
|
}
|
|
|
|
/**
|
|
* Tests whether this {@code BigInteger} is probably prime. If {@code true} is
|
|
* returned, then this is prime with a probability beyond (1-1/2^certainty).
|
|
* If {@code false} is returned, then this is definitely composite. If the
|
|
* argument {@code certainty} <= 0, then this method returns true.
|
|
*
|
|
* @param certainty tolerated primality uncertainty.
|
|
* @return {@code true}, if {@code this} is probably prime, {@code false}
|
|
* otherwise.
|
|
*/
|
|
public boolean isProbablePrime(int certainty) {
|
|
return Primality.isProbablePrime(abs(), certainty);
|
|
}
|
|
|
|
/**
|
|
* Returns this {@code BigInteger} as an long value. If {@code this} is too
|
|
* big to be represented as an long, then {@code this} % 2^64 is returned.
|
|
*
|
|
* @return this {@code BigInteger} as a long value.
|
|
*/
|
|
@Override
|
|
public long longValue() {
|
|
long value = (numberLength > 1) ? (((long) digits[1]) << 32)
|
|
| (digits[0] & 0xFFFFFFFFL) : (digits[0] & 0xFFFFFFFFL);
|
|
return (sign * value);
|
|
}
|
|
|
|
/**
|
|
* Returns the maximum of this {@code BigInteger} and {@code val}.
|
|
*
|
|
* @param val value to be used to compute the maximum with {@code this}
|
|
* @return {@code max(this, val)}
|
|
* @throws NullPointerException if {@code val == null}
|
|
*/
|
|
public BigInteger max(BigInteger val) {
|
|
return ((this.compareTo(val) == GREATER) ? this : val);
|
|
}
|
|
|
|
/**
|
|
* Returns the minimum of this {@code BigInteger} and {@code val}.
|
|
*
|
|
* @param val value to be used to compute the minimum with {@code this}.
|
|
* @return {@code min(this, val)}.
|
|
* @throws NullPointerException if {@code val == null}.
|
|
*/
|
|
public BigInteger min(BigInteger val) {
|
|
return ((this.compareTo(val) == LESS) ? this : val);
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is {@code this mod m}. The
|
|
* modulus {@code m} must be positive. The result is guaranteed to be in the
|
|
* interval {@code [0, m)} (0 inclusive, m exclusive). The behavior of this
|
|
* function is not equivalent to the behavior of the % operator defined for
|
|
* the built-in {@code int}'s.
|
|
*
|
|
* @param m the modulus.
|
|
* @return {@code this mod m}.
|
|
* @throws NullPointerException if {@code m == null}.
|
|
* @throws ArithmeticException if {@code m < 0}.
|
|
*/
|
|
public BigInteger mod(BigInteger m) {
|
|
if (m.sign <= 0) {
|
|
// math.18=BigInteger: modulus not positive
|
|
throw new ArithmeticException("BigInteger: modulus not positive"); //$NON-NLS-1$
|
|
}
|
|
BigInteger rem = remainder(m);
|
|
return ((rem.sign < 0) ? rem.add(m) : rem);
|
|
}
|
|
|
|
// @Override
|
|
// public double doubleValue() {
|
|
// return Conversion.bigInteger2Double(this);
|
|
// }
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is {@code 1/this mod m}. The
|
|
* modulus {@code m} must be positive. The result is guaranteed to be in the
|
|
* interval {@code [0, m)} (0 inclusive, m exclusive). If {@code this} is not
|
|
* relatively prime to m, then an exception is thrown.
|
|
*
|
|
* @param m the modulus.
|
|
* @return {@code 1/this mod m}.
|
|
* @throws NullPointerException if {@code m == null}
|
|
* @throws ArithmeticException if {@code m < 0 or} if {@code this} is not
|
|
* relatively prime to {@code m}
|
|
*/
|
|
public BigInteger modInverse(BigInteger m) {
|
|
if (m.sign <= 0) {
|
|
// math.18=BigInteger: modulus not positive
|
|
throw new ArithmeticException("BigInteger: modulus not positive"); //$NON-NLS-1$
|
|
}
|
|
// If both are even, no inverse exists
|
|
if (!(testBit(0) || m.testBit(0))) {
|
|
// math.19=BigInteger not invertible.
|
|
throw new ArithmeticException("BigInteger not invertible."); //$NON-NLS-1$
|
|
}
|
|
if (m.isOne()) {
|
|
return ZERO;
|
|
}
|
|
|
|
// From now on: (m > 1)
|
|
BigInteger res = Division.modInverseMontgomery(abs().mod(m), m);
|
|
if (res.sign == 0) {
|
|
// math.19=BigInteger not invertible.
|
|
throw new ArithmeticException("BigInteger not invertible."); //$NON-NLS-1$
|
|
}
|
|
|
|
res = ((sign < 0) ? m.subtract(res) : res);
|
|
return res;
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is {@code this^exponent mod m}
|
|
* . The modulus {@code m} must be positive. The result is guaranteed to be in
|
|
* the interval {@code [0, m)} (0 inclusive, m exclusive). If the exponent is
|
|
* negative, then {@code this.modInverse(m)^(-exponent) mod m)} is computed.
|
|
* The inverse of this only exists if {@code this} is relatively prime to m,
|
|
* otherwise an exception is thrown.
|
|
*
|
|
* @param exponent the exponent.
|
|
* @param m the modulus.
|
|
* @return {@code this^exponent mod val}.
|
|
* @throws NullPointerException if {@code m == null} or {@code exponent ==
|
|
* null}.
|
|
* @throws ArithmeticException if {@code m < 0} or if {@code exponent<0} and
|
|
* this is not relatively prime to {@code m}.
|
|
*/
|
|
public BigInteger modPow(BigInteger exponent, BigInteger m) {
|
|
if (m.sign <= 0) {
|
|
// math.18=BigInteger: modulus not positive
|
|
throw new ArithmeticException("BigInteger: modulus not positive"); //$NON-NLS-1$
|
|
}
|
|
BigInteger base = this;
|
|
|
|
if (m.isOne() | (exponent.sign > 0 & base.sign == 0)) {
|
|
return BigInteger.ZERO;
|
|
}
|
|
if (base.sign == 0 && exponent.sign == 0) {
|
|
return BigInteger.ONE;
|
|
}
|
|
if (exponent.sign < 0) {
|
|
base = modInverse(m);
|
|
exponent = exponent.negate();
|
|
}
|
|
// From now on: (m > 0) and (exponent >= 0)
|
|
BigInteger res = (m.testBit(0)) ? Division.oddModPow(base.abs(), exponent,
|
|
m) : Division.evenModPow(base.abs(), exponent, m);
|
|
if ((base.sign < 0) && exponent.testBit(0)) {
|
|
// -b^e mod m == ((-1 mod m) * (b^e mod m)) mod m
|
|
res = m.subtract(BigInteger.ONE).multiply(res).mod(m);
|
|
}
|
|
// else exponent is even, so base^exp is positive
|
|
return res;
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is {@code this * val}.
|
|
*
|
|
* @param val value to be multiplied with {@code this}.
|
|
* @return {@code this * val}.
|
|
* @throws NullPointerException if {@code val == null}.
|
|
*/
|
|
public BigInteger multiply(BigInteger val) {
|
|
// This let us to throw NullPointerException when val == null
|
|
if (val.sign == 0) {
|
|
return ZERO;
|
|
}
|
|
if (sign == 0) {
|
|
return ZERO;
|
|
}
|
|
return Multiplication.multiply(this, val);
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is the {@code -this}.
|
|
*
|
|
* @return {@code -this}.
|
|
*/
|
|
public BigInteger negate() {
|
|
return ((sign == 0) ? this : new BigInteger(-sign, numberLength, digits));
|
|
}
|
|
|
|
/**
|
|
* Returns the smallest integer x > {@code this} which is probably prime as a
|
|
* {@code BigInteger} instance. The probability that the returned {@code
|
|
* BigInteger} is prime is beyond (1-1/2^80).
|
|
*
|
|
* @return smallest integer > {@code this} which is robably prime.
|
|
* @throws ArithmeticException if {@code this < 0}.
|
|
*/
|
|
public BigInteger nextProbablePrime() {
|
|
if (sign < 0) {
|
|
// math.1A=start < 0: {0}
|
|
throw new ArithmeticException("start < 0: " + this); //$NON-NLS-1$
|
|
}
|
|
return Primality.nextProbablePrime(this);
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is {@code ~this}. The result
|
|
* of this operation is {@code -this-1}.
|
|
* <p>
|
|
* <b>Implementation Note:</b> Usage of this method is not recommended as the
|
|
* current implementation is not efficient.
|
|
*
|
|
* @return {@code ~this}.
|
|
*/
|
|
public BigInteger not() {
|
|
return Logical.not(this);
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is {@code this | val}.
|
|
* <p>
|
|
* <b>Implementation Note:</b> Usage of this method is not recommended as the
|
|
* current implementation is not efficient.
|
|
*
|
|
* @param val value to be or'ed with {@code this}.
|
|
* @return {@code this | val}.
|
|
* @throws NullPointerException if {@code val == null}.
|
|
*/
|
|
public BigInteger or(BigInteger val) {
|
|
return Logical.or(this, val);
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is {@code this ^ exp}.
|
|
*
|
|
* @param exp exponent to which {@code this} is raised.
|
|
* @return {@code this ^ exp}.
|
|
* @throws ArithmeticException if {@code exp < 0}.
|
|
*/
|
|
public BigInteger pow(int exp) {
|
|
if (exp < 0) {
|
|
// math.16=Negative exponent
|
|
throw new ArithmeticException("Negative exponent"); //$NON-NLS-1$
|
|
}
|
|
if (exp == 0) {
|
|
return ONE;
|
|
} else if (exp == 1 || equals(ONE) || equals(ZERO)) {
|
|
return this;
|
|
}
|
|
|
|
// if even take out 2^x factor which we can
|
|
// calculate by shifting.
|
|
if (!testBit(0)) {
|
|
int x = 1;
|
|
while (!testBit(x)) {
|
|
x++;
|
|
}
|
|
return getPowerOfTwo(x * exp).multiply(this.shiftRight(x).pow(exp));
|
|
}
|
|
return Multiplication.pow(this, exp);
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is {@code this % divisor}.
|
|
* Regarding signs this methods has the same behavior as the % operator on
|
|
* int's, i.e. the sign of the remainder is the same as the sign of this.
|
|
*
|
|
* @param divisor value by which {@code this} is divided.
|
|
* @return {@code this % divisor}.
|
|
* @throws NullPointerException if {@code divisor == null}.
|
|
* @throws ArithmeticException if {@code divisor == 0}.
|
|
*/
|
|
public BigInteger remainder(BigInteger divisor) {
|
|
if (divisor.sign == 0) {
|
|
// math.17=BigInteger divide by zero
|
|
throw new ArithmeticException("BigInteger divide by zero"); //$NON-NLS-1$
|
|
}
|
|
int thisLen = numberLength;
|
|
int divisorLen = divisor.numberLength;
|
|
if (((thisLen != divisorLen) ? ((thisLen > divisorLen) ? 1 : -1)
|
|
: Elementary.compareArrays(digits, divisor.digits, thisLen)) == LESS) {
|
|
return this;
|
|
}
|
|
int resLength = divisorLen;
|
|
int resDigits[] = new int[resLength];
|
|
if (resLength == 1) {
|
|
resDigits[0] = Division.remainderArrayByInt(digits, thisLen,
|
|
divisor.digits[0]);
|
|
} else {
|
|
int qLen = thisLen - divisorLen + 1;
|
|
resDigits = Division.divide(null, qLen, digits, thisLen, divisor.digits,
|
|
divisorLen);
|
|
}
|
|
BigInteger result = new BigInteger(sign, resLength, resDigits);
|
|
result.cutOffLeadingZeroes();
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} which has the same binary representation
|
|
* as {@code this} but with the bit at position n set. The result is
|
|
* equivalent to {@code this | 2^n}.
|
|
* <p>
|
|
* <b>Implementation Note:</b> Usage of this method is not recommended as the
|
|
* current implementation is not efficient.
|
|
*
|
|
* @param n position where the bit in {@code this} has to be set.
|
|
* @return {@code this | 2^n}.
|
|
* @throws ArithmeticException if {@code n < 0}.
|
|
*/
|
|
public BigInteger setBit(int n) {
|
|
if (!testBit(n)) {
|
|
return BitLevel.flipBit(this, n);
|
|
}
|
|
return this;
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is {@code this << n}. The
|
|
* result is equivalent to {@code this * 2^n} if n >= 0. The shift distance
|
|
* may be negative which means that {@code this} is shifted right. The result
|
|
* then corresponds to {@code floor(this / 2^(-n))}.
|
|
* <p>
|
|
* <b>Implementation Note:</b> Usage of this method on negative values is not
|
|
* recommended as the current implementation is not efficient.
|
|
*
|
|
* @param n shift distance.
|
|
* @return {@code this << n} if {@code n >= 0}; {@code this >> (-n)}.
|
|
* otherwise
|
|
*/
|
|
public BigInteger shiftLeft(int n) {
|
|
if ((n == 0) || (sign == 0)) {
|
|
return this;
|
|
}
|
|
return ((n > 0) ? BitLevel.shiftLeft(this, n) : BitLevel.shiftRight(this,
|
|
-n));
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is {@code this >> n}. For
|
|
* negative arguments, the result is also negative. The shift distance may be
|
|
* negative which means that {@code this} is shifted left.
|
|
* <p>
|
|
* <b>Implementation Note:</b> Usage of this method on negative values is not
|
|
* recommended as the current implementation is not efficient.
|
|
*
|
|
* @param n shift distance
|
|
* @return {@code this >> n} if {@code n >= 0}; {@code this << (-n)} otherwise
|
|
*/
|
|
public BigInteger shiftRight(int n) {
|
|
if ((n == 0) || (sign == 0)) {
|
|
return this;
|
|
}
|
|
return ((n > 0) ? BitLevel.shiftRight(this, n) : BitLevel.shiftLeft(this,
|
|
-n));
|
|
}
|
|
|
|
/**
|
|
* Returns the sign of this {@code BigInteger}.
|
|
*
|
|
* @return {@code -1} if {@code this < 0}, {@code 0} if {@code this == 0},
|
|
* {@code 1} if {@code this > 0}.
|
|
*/
|
|
public int signum() {
|
|
return sign;
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is {@code this - val}.
|
|
*
|
|
* @param val value to be subtracted from {@code this}.
|
|
* @return {@code this - val}.
|
|
* @throws NullPointerException if {@code val == null}.
|
|
*/
|
|
public BigInteger subtract(BigInteger val) {
|
|
return Elementary.subtract(this, val);
|
|
}
|
|
|
|
/**
|
|
* Tests whether the bit at position n in {@code this} is set. The result is
|
|
* equivalent to {@code this & (2^n) != 0}.
|
|
* <p>
|
|
* <b>Implementation Note:</b> Usage of this method is not recommended as the
|
|
* current implementation is not efficient.
|
|
*
|
|
* @param n position where the bit in {@code this} has to be inspected.
|
|
* @return {@code this & (2^n) != 0}.
|
|
* @throws ArithmeticException if {@code n < 0}.
|
|
*/
|
|
public boolean testBit(int n) {
|
|
if (n == 0) {
|
|
return ((digits[0] & 1) != 0);
|
|
}
|
|
if (n < 0) {
|
|
// math.15=Negative bit address
|
|
throw new ArithmeticException("Negative bit address"); //$NON-NLS-1$
|
|
}
|
|
int intCount = n >> 5;
|
|
if (intCount >= numberLength) {
|
|
return (sign < 0);
|
|
}
|
|
int digit = digits[intCount];
|
|
n = (1 << (n & 31)); // int with 1 set to the needed position
|
|
if (sign < 0) {
|
|
int firstNonZeroDigit = getFirstNonzeroDigit();
|
|
if (intCount < firstNonZeroDigit) {
|
|
return false;
|
|
} else if (firstNonZeroDigit == intCount) {
|
|
digit = -digit;
|
|
} else {
|
|
digit = ~digit;
|
|
}
|
|
}
|
|
return ((digit & n) != 0);
|
|
}
|
|
|
|
/**
|
|
* Returns the two's complement representation of this BigInteger in a byte
|
|
* array.
|
|
*
|
|
* @return two's complement representation of {@code this}.
|
|
*/
|
|
public byte[] toByteArray() {
|
|
if (this.sign == 0) {
|
|
return new byte[] {0};
|
|
}
|
|
BigInteger temp = this;
|
|
int bitLen = bitLength();
|
|
int iThis = getFirstNonzeroDigit();
|
|
int bytesLen = (bitLen >> 3) + 1;
|
|
/*
|
|
* Puts the little-endian int array representing the magnitude of this
|
|
* BigInteger into the big-endian byte array.
|
|
*/
|
|
byte[] bytes = new byte[bytesLen];
|
|
int firstByteNumber = 0;
|
|
int highBytes;
|
|
int digitIndex = 0;
|
|
int bytesInInteger = 4;
|
|
int digit;
|
|
int hB;
|
|
|
|
if (bytesLen - (numberLength << 2) == 1) {
|
|
bytes[0] = (byte) ((sign < 0) ? -1 : 0);
|
|
highBytes = 4;
|
|
firstByteNumber++;
|
|
} else {
|
|
hB = bytesLen & 3;
|
|
highBytes = (hB == 0) ? 4 : hB;
|
|
}
|
|
|
|
digitIndex = iThis;
|
|
bytesLen -= iThis << 2;
|
|
|
|
if (sign < 0) {
|
|
digit = -temp.digits[digitIndex];
|
|
digitIndex++;
|
|
if (digitIndex == numberLength) {
|
|
bytesInInteger = highBytes;
|
|
}
|
|
for (int i = 0; i < bytesInInteger; i++, digit >>= 8) {
|
|
bytes[--bytesLen] = (byte) digit;
|
|
}
|
|
while (bytesLen > firstByteNumber) {
|
|
digit = ~temp.digits[digitIndex];
|
|
digitIndex++;
|
|
if (digitIndex == numberLength) {
|
|
bytesInInteger = highBytes;
|
|
}
|
|
for (int i = 0; i < bytesInInteger; i++, digit >>= 8) {
|
|
bytes[--bytesLen] = (byte) digit;
|
|
}
|
|
}
|
|
} else {
|
|
while (bytesLen > firstByteNumber) {
|
|
digit = temp.digits[digitIndex];
|
|
digitIndex++;
|
|
if (digitIndex == numberLength) {
|
|
bytesInInteger = highBytes;
|
|
}
|
|
for (int i = 0; i < bytesInInteger; i++, digit >>= 8) {
|
|
bytes[--bytesLen] = (byte) digit;
|
|
}
|
|
}
|
|
}
|
|
return bytes;
|
|
}
|
|
|
|
/**
|
|
* Returns a string representation of this {@code BigInteger} in decimal form.
|
|
*
|
|
* @return a string representation of {@code this} in decimal form.
|
|
*/
|
|
@Override
|
|
public String toString() {
|
|
return Conversion.toDecimalScaledString(this, 0);
|
|
}
|
|
|
|
/**
|
|
* Returns a string containing a string representation of this {@code
|
|
* BigInteger} with base radix. If {@code radix} is less than
|
|
* {@link Character#MIN_RADIX} or greater than {@link Character#MAX_RADIX}
|
|
* then a decimal representation is returned. The characters of the string
|
|
* representation are generated with method {@link Character#forDigit}.
|
|
*
|
|
* @param radix base to be used for the string representation.
|
|
* @return a string representation of this with radix 10.
|
|
*/
|
|
public String toString(int radix) {
|
|
return Conversion.bigInteger2String(this, radix);
|
|
}
|
|
|
|
/**
|
|
* Returns a new {@code BigInteger} whose value is {@code this ^ val}.
|
|
* <p>
|
|
* <b>Implementation Note:</b> Usage of this method is not recommended as the
|
|
* current implementation is not efficient.
|
|
*
|
|
* @param val value to be xor'ed with {@code this}
|
|
* @return {@code this ^ val}
|
|
* @throws NullPointerException if {@code val == null}
|
|
*/
|
|
public BigInteger xor(BigInteger val) {
|
|
return Logical.xor(this, val);
|
|
}
|
|
|
|
/*
|
|
* Returns a copy of the current instance to achieve immutability
|
|
*/
|
|
BigInteger copy() {
|
|
int[] copyDigits = new int[numberLength];
|
|
System.arraycopy(digits, 0, copyDigits, 0, numberLength);
|
|
return new BigInteger(sign, numberLength, copyDigits);
|
|
}
|
|
|
|
/* Private Methods */
|
|
|
|
/**
|
|
* Decreases {@code numberLength} if there are zero high elements.
|
|
*/
|
|
final void cutOffLeadingZeroes() {
|
|
while ((numberLength > 0) && (digits[--numberLength] == 0)) {
|
|
// Empty
|
|
}
|
|
if (digits[numberLength++] == 0) {
|
|
sign = 0;
|
|
}
|
|
}
|
|
|
|
boolean equalsArrays(final int[] b) {
|
|
int i;
|
|
for (i = numberLength - 1; (i >= 0) && (digits[i] == b[i]); i--) {
|
|
// Empty
|
|
}
|
|
return i < 0;
|
|
}
|
|
|
|
int getFirstNonzeroDigit() {
|
|
if (firstNonzeroDigit == -2) {
|
|
int i;
|
|
if (this.sign == 0) {
|
|
i = -1;
|
|
} else {
|
|
for (i = 0; digits[i] == 0; i++) {
|
|
// Empty
|
|
}
|
|
}
|
|
firstNonzeroDigit = i;
|
|
}
|
|
return firstNonzeroDigit;
|
|
}
|
|
|
|
/**
|
|
* Tests if {@code this.abs()} is equals to {@code ONE}.
|
|
*/
|
|
boolean isOne() {
|
|
return ((numberLength == 1) && (digits[0] == 1));
|
|
}
|
|
|
|
BigInteger shiftLeftOneBit() {
|
|
return (sign == 0) ? this : BitLevel.shiftLeftOneBit(this);
|
|
}
|
|
|
|
void unCache() {
|
|
firstNonzeroDigit = -2;
|
|
}
|
|
|
|
/**
|
|
* Puts a big-endian byte array into a little-endian applying two complement.
|
|
*/
|
|
private void putBytesNegativeToIntegers(byte[] byteValues) {
|
|
int bytesLen = byteValues.length;
|
|
int highBytes = bytesLen & 3;
|
|
numberLength = (bytesLen >> 2) + ((highBytes == 0) ? 0 : 1);
|
|
digits = new int[numberLength];
|
|
int i = 0;
|
|
// Setting the sign
|
|
digits[numberLength - 1] = -1;
|
|
// Put bytes to the int array starting from the end of the byte array
|
|
while (bytesLen > highBytes) {
|
|
digits[i] = (byteValues[--bytesLen] & 0xFF)
|
|
| (byteValues[--bytesLen] & 0xFF) << 8
|
|
| (byteValues[--bytesLen] & 0xFF) << 16
|
|
| (byteValues[--bytesLen] & 0xFF) << 24;
|
|
if (digits[i] != 0) {
|
|
digits[i] = -digits[i];
|
|
firstNonzeroDigit = i;
|
|
i++;
|
|
while (bytesLen > highBytes) {
|
|
digits[i] = (byteValues[--bytesLen] & 0xFF)
|
|
| (byteValues[--bytesLen] & 0xFF) << 8
|
|
| (byteValues[--bytesLen] & 0xFF) << 16
|
|
| (byteValues[--bytesLen] & 0xFF) << 24;
|
|
digits[i] = ~digits[i];
|
|
i++;
|
|
}
|
|
break;
|
|
}
|
|
i++;
|
|
}
|
|
if (highBytes != 0) {
|
|
// Put the first bytes in the highest element of the int array
|
|
if (firstNonzeroDigit != -2) {
|
|
for (int j = 0; j < bytesLen; j++) {
|
|
digits[i] = (digits[i] << 8) | (byteValues[j] & 0xFF);
|
|
}
|
|
digits[i] = ~digits[i];
|
|
} else {
|
|
for (int j = 0; j < bytesLen; j++) {
|
|
digits[i] = (digits[i] << 8) | (byteValues[j] & 0xFF);
|
|
}
|
|
digits[i] = -digits[i];
|
|
}
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Puts a big-endian byte array into a little-endian int array.
|
|
*/
|
|
private void putBytesPositiveToIntegers(byte[] byteValues) {
|
|
int bytesLen = byteValues.length;
|
|
int highBytes = bytesLen & 3;
|
|
numberLength = (bytesLen >> 2) + ((highBytes == 0) ? 0 : 1);
|
|
digits = new int[numberLength];
|
|
int i = 0;
|
|
// Put bytes to the int array starting from the end of the byte array
|
|
while (bytesLen > highBytes) {
|
|
digits[i++] = (byteValues[--bytesLen] & 0xFF)
|
|
| (byteValues[--bytesLen] & 0xFF) << 8
|
|
| (byteValues[--bytesLen] & 0xFF) << 16
|
|
| (byteValues[--bytesLen] & 0xFF) << 24;
|
|
}
|
|
// Put the first bytes in the highest element of the int array
|
|
for (int j = 0; j < bytesLen; j++) {
|
|
digits[i] = (digits[i] << 8) | (byteValues[j] & 0xFF);
|
|
}
|
|
}
|
|
}
|