5074 lines
186 KiB
Java
5074 lines
186 KiB
Java
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/*
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* Copyright (c) 1996, 2021, Oracle and/or its affiliates. All rights reserved.
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License version 2 only, as
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* published by the Free Software Foundation. Oracle designates this
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* particular file as subject to the "Classpath" exception as provided
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* by Oracle in the LICENSE file that accompanied this code.
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*
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* This code is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* version 2 for more details (a copy is included in the LICENSE file that
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* accompanied this code).
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*
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* You should have received a copy of the GNU General Public License version
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* 2 along with this work; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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* or visit www.oracle.com if you need additional information or have any
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* questions.
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*/
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/*
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* Portions Copyright (c) 1995 Colin Plumb. All rights reserved.
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*/
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package java.math;
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import java.io.IOException;
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import java.io.InvalidObjectException;
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import java.io.ObjectInputStream;
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import java.io.ObjectOutputStream;
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import java.io.ObjectStreamField;
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import java.io.ObjectStreamException;
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import java.util.Arrays;
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import java.util.Objects;
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import java.util.Random;
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import java.util.concurrent.ThreadLocalRandom;
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import jdk.internal.math.DoubleConsts;
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import jdk.internal.math.FloatConsts;
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import jdk.internal.vm.annotation.IntrinsicCandidate;
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import libcore.math.NativeBN;
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/**
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* Immutable arbitrary-precision integers. All operations behave as if
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* BigIntegers were represented in two's-complement notation (like Java's
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* primitive integer types). BigInteger provides analogues to all of Java's
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* primitive integer operators, and all relevant methods from java.lang.Math.
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* Additionally, BigInteger provides operations for modular arithmetic, GCD
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* calculation, primality testing, prime generation, bit manipulation,
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* and a few other miscellaneous operations.
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*
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* <p>Semantics of arithmetic operations exactly mimic those of Java's integer
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* arithmetic operators, as defined in <i>The Java Language Specification</i>.
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* For example, division by zero throws an {@code ArithmeticException}, and
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* division of a negative by a positive yields a negative (or zero) remainder.
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*
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* <p>Semantics of shift operations extend those of Java's shift operators
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* to allow for negative shift distances. A right-shift with a negative
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* shift distance results in a left shift, and vice-versa. The unsigned
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* right shift operator ({@code >>>}) is omitted since this operation
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* only makes sense for a fixed sized word and not for a
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* representation conceptually having an infinite number of leading
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* virtual sign bits.
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*
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* <p>Semantics of bitwise logical operations exactly mimic those of Java's
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* bitwise integer operators. The binary operators ({@code and},
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* {@code or}, {@code xor}) implicitly perform sign extension on the shorter
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* of the two operands prior to performing the operation.
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*
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* <p>Comparison operations perform signed integer comparisons, analogous to
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* those performed by Java's relational and equality operators.
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*
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* <p>Modular arithmetic operations are provided to compute residues, perform
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* exponentiation, and compute multiplicative inverses. These methods always
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* return a non-negative result, between {@code 0} and {@code (modulus - 1)},
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* inclusive.
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*
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* <p>Bit operations operate on a single bit of the two's-complement
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* representation of their operand. If necessary, the operand is sign-extended
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* so that it contains the designated bit. None of the single-bit
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* operations can produce a BigInteger with a different sign from the
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* BigInteger being operated on, as they affect only a single bit, and the
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* arbitrarily large abstraction provided by this class ensures that conceptually
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* there are infinitely many "virtual sign bits" preceding each BigInteger.
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*
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* <p>For the sake of brevity and clarity, pseudo-code is used throughout the
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* descriptions of BigInteger methods. The pseudo-code expression
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* {@code (i + j)} is shorthand for "a BigInteger whose value is
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* that of the BigInteger {@code i} plus that of the BigInteger {@code j}."
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* The pseudo-code expression {@code (i == j)} is shorthand for
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* "{@code true} if and only if the BigInteger {@code i} represents the same
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* value as the BigInteger {@code j}." Other pseudo-code expressions are
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* interpreted similarly.
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*
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* <p>All methods and constructors in this class throw
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* {@code NullPointerException} when passed
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* a null object reference for any input parameter.
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*
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* BigInteger must support values in the range
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* -2<sup>{@code Integer.MAX_VALUE}</sup> (exclusive) to
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* +2<sup>{@code Integer.MAX_VALUE}</sup> (exclusive)
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* and may support values outside of that range.
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*
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* An {@code ArithmeticException} is thrown when a BigInteger
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* constructor or method would generate a value outside of the
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* supported range.
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*
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* The range of probable prime values is limited and may be less than
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* the full supported positive range of {@code BigInteger}.
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* The range must be at least 1 to 2<sup>500000000</sup>.
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*
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* @implNote
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* In the reference implementation, BigInteger constructors and
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* operations throw {@code ArithmeticException} when the result is out
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* of the supported range of
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* -2<sup>{@code Integer.MAX_VALUE}</sup> (exclusive) to
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* +2<sup>{@code Integer.MAX_VALUE}</sup> (exclusive).
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*
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* @see BigDecimal
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* @jls 4.2.2 Integer Operations
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* @author Josh Bloch
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* @author Michael McCloskey
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* @author Alan Eliasen
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* @author Timothy Buktu
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* @since 1.1
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*/
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public class BigInteger extends Number implements Comparable<BigInteger> {
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/**
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* The signum of this BigInteger: -1 for negative, 0 for zero, or
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* 1 for positive. Note that the BigInteger zero <em>must</em> have
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* a signum of 0. This is necessary to ensures that there is exactly one
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* representation for each BigInteger value.
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*/
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final int signum;
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/**
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* The magnitude of this BigInteger, in <i>big-endian</i> order: the
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* zeroth element of this array is the most-significant int of the
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* magnitude. The magnitude must be "minimal" in that the most-significant
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* int ({@code mag[0]}) must be non-zero. This is necessary to
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* ensure that there is exactly one representation for each BigInteger
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* value. Note that this implies that the BigInteger zero has a
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* zero-length mag array.
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*/
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final int[] mag;
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// The following fields are stable variables. A stable variable's value
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// changes at most once from the default zero value to a non-zero stable
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// value. A stable value is calculated lazily on demand.
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/**
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* One plus the bitCount of this BigInteger. This is a stable variable.
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*
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* @see #bitCount
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*/
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private int bitCountPlusOne;
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/**
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* One plus the bitLength of this BigInteger. This is a stable variable.
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* (either value is acceptable).
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*
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* @see #bitLength()
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*/
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private int bitLengthPlusOne;
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/**
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* Two plus the lowest set bit of this BigInteger. This is a stable variable.
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*
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* @see #getLowestSetBit
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*/
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private int lowestSetBitPlusTwo;
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/**
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* Two plus the index of the lowest-order int in the magnitude of this
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* BigInteger that contains a nonzero int. This is a stable variable. The
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* least significant int has int-number 0, the next int in order of
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* increasing significance has int-number 1, and so forth.
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*
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* <p>Note: never used for a BigInteger with a magnitude of zero.
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*
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* @see #firstNonzeroIntNum()
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*/
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private int firstNonzeroIntNumPlusTwo;
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/**
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* This mask is used to obtain the value of an int as if it were unsigned.
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*/
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static final long LONG_MASK = 0xffffffffL;
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/**
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* This constant limits {@code mag.length} of BigIntegers to the supported
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* range.
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*/
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private static final int MAX_MAG_LENGTH = Integer.MAX_VALUE / Integer.SIZE + 1; // (1 << 26)
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/**
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* Bit lengths larger than this constant can cause overflow in searchLen
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* calculation and in BitSieve.singleSearch method.
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*/
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private static final int PRIME_SEARCH_BIT_LENGTH_LIMIT = 500000000;
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/**
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* The threshold value for using Karatsuba multiplication. If the number
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* of ints in both mag arrays are greater than this number, then
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* Karatsuba multiplication will be used. This value is found
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* experimentally to work well.
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*/
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private static final int KARATSUBA_THRESHOLD = 80;
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/**
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* The threshold value for using 3-way Toom-Cook multiplication.
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* If the number of ints in each mag array is greater than the
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* Karatsuba threshold, and the number of ints in at least one of
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* the mag arrays is greater than this threshold, then Toom-Cook
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* multiplication will be used.
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*/
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private static final int TOOM_COOK_THRESHOLD = 240;
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/**
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* The threshold value for using Karatsuba squaring. If the number
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* of ints in the number are larger than this value,
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* Karatsuba squaring will be used. This value is found
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* experimentally to work well.
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*/
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private static final int KARATSUBA_SQUARE_THRESHOLD = 128;
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/**
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* The threshold value for using Toom-Cook squaring. If the number
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* of ints in the number are larger than this value,
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* Toom-Cook squaring will be used. This value is found
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* experimentally to work well.
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*/
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private static final int TOOM_COOK_SQUARE_THRESHOLD = 216;
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/**
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* The threshold value for using Burnikel-Ziegler division. If the number
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* of ints in the divisor are larger than this value, Burnikel-Ziegler
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* division may be used. This value is found experimentally to work well.
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*/
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static final int BURNIKEL_ZIEGLER_THRESHOLD = 80;
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/**
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* The offset value for using Burnikel-Ziegler division. If the number
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* of ints in the divisor exceeds the Burnikel-Ziegler threshold, and the
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* number of ints in the dividend is greater than the number of ints in the
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* divisor plus this value, Burnikel-Ziegler division will be used. This
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* value is found experimentally to work well.
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*/
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static final int BURNIKEL_ZIEGLER_OFFSET = 40;
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/**
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* The threshold value for using Schoenhage recursive base conversion. If
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* the number of ints in the number are larger than this value,
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* the Schoenhage algorithm will be used. In practice, it appears that the
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* Schoenhage routine is faster for any threshold down to 2, and is
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* relatively flat for thresholds between 2-25, so this choice may be
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* varied within this range for very small effect.
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*/
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private static final int SCHOENHAGE_BASE_CONVERSION_THRESHOLD = 20;
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/**
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* The threshold value for using squaring code to perform multiplication
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* of a {@code BigInteger} instance by itself. If the number of ints in
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* the number are larger than this value, {@code multiply(this)} will
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* return {@code square()}.
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*/
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private static final int MULTIPLY_SQUARE_THRESHOLD = 20;
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/**
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* The threshold for using an intrinsic version of
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* implMontgomeryXXX to perform Montgomery multiplication. If the
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* number of ints in the number is more than this value we do not
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* use the intrinsic.
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*/
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private static final int MONTGOMERY_INTRINSIC_THRESHOLD = 512;
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// Constructors
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/**
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* Translates a byte sub-array containing the two's-complement binary
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* representation of a BigInteger into a BigInteger. The sub-array is
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* specified via an offset into the array and a length. The sub-array is
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* assumed to be in <i>big-endian</i> byte-order: the most significant
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* byte is the element at index {@code off}. The {@code val} array is
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* assumed to be unchanged for the duration of the constructor call.
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*
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* An {@code IndexOutOfBoundsException} is thrown if the length of the array
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* {@code val} is non-zero and either {@code off} is negative, {@code len}
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* is negative, or {@code off+len} is greater than the length of
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* {@code val}.
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*
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* @param val byte array containing a sub-array which is the big-endian
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* two's-complement binary representation of a BigInteger.
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* @param off the start offset of the binary representation.
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* @param len the number of bytes to use.
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* @throws NumberFormatException {@code val} is zero bytes long.
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* @throws IndexOutOfBoundsException if the provided array offset and
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* length would cause an index into the byte array to be
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* negative or greater than or equal to the array length.
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* @since 9
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*/
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public BigInteger(byte[] val, int off, int len) {
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if (val.length == 0) {
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throw new NumberFormatException("Zero length BigInteger");
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}
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Objects.checkFromIndexSize(off, len, val.length);
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if (val[off] < 0) {
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mag = makePositive(val, off, len);
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signum = -1;
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} else {
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mag = stripLeadingZeroBytes(val, off, len);
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signum = (mag.length == 0 ? 0 : 1);
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}
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if (mag.length >= MAX_MAG_LENGTH) {
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checkRange();
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}
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||
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}
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||
|
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/**
|
||
|
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* Translates a byte array containing the two's-complement binary
|
||
|
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* representation of a BigInteger into a BigInteger. The input array is
|
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* assumed to be in <i>big-endian</i> byte-order: the most significant
|
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* byte is in the zeroth element. The {@code val} array is assumed to be
|
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* unchanged for the duration of the constructor call.
|
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*
|
||
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* @param val big-endian two's-complement binary representation of a
|
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* BigInteger.
|
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* @throws NumberFormatException {@code val} is zero bytes long.
|
||
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*/
|
||
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public BigInteger(byte[] val) {
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this(val, 0, val.length);
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}
|
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/**
|
||
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* This private constructor translates an int array containing the
|
||
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* two's-complement binary representation of a BigInteger into a
|
||
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* BigInteger. The input array is assumed to be in <i>big-endian</i>
|
||
|
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* int-order: the most significant int is in the zeroth element. The
|
||
|
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* {@code val} array is assumed to be unchanged for the duration of
|
||
|
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* the constructor call.
|
||
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*/
|
||
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private BigInteger(int[] val) {
|
||
|
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if (val.length == 0)
|
||
|
|
throw new NumberFormatException("Zero length BigInteger");
|
||
|
|
|
||
|
|
if (val[0] < 0) {
|
||
|
|
mag = makePositive(val);
|
||
|
|
signum = -1;
|
||
|
|
} else {
|
||
|
|
mag = trustedStripLeadingZeroInts(val);
|
||
|
|
signum = (mag.length == 0 ? 0 : 1);
|
||
|
|
}
|
||
|
|
if (mag.length >= MAX_MAG_LENGTH) {
|
||
|
|
checkRange();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Translates the sign-magnitude representation of a BigInteger into a
|
||
|
|
* BigInteger. The sign is represented as an integer signum value: -1 for
|
||
|
|
* negative, 0 for zero, or 1 for positive. The magnitude is a sub-array of
|
||
|
|
* a byte array in <i>big-endian</i> byte-order: the most significant byte
|
||
|
|
* is the element at index {@code off}. A zero value of the length
|
||
|
|
* {@code len} is permissible, and will result in a BigInteger value of 0,
|
||
|
|
* whether signum is -1, 0 or 1. The {@code magnitude} array is assumed to
|
||
|
|
* be unchanged for the duration of the constructor call.
|
||
|
|
*
|
||
|
|
* An {@code IndexOutOfBoundsException} is thrown if the length of the array
|
||
|
|
* {@code magnitude} is non-zero and either {@code off} is negative,
|
||
|
|
* {@code len} is negative, or {@code off+len} is greater than the length of
|
||
|
|
* {@code magnitude}.
|
||
|
|
*
|
||
|
|
* @param signum signum of the number (-1 for negative, 0 for zero, 1
|
||
|
|
* for positive).
|
||
|
|
* @param magnitude big-endian binary representation of the magnitude of
|
||
|
|
* the number.
|
||
|
|
* @param off the start offset of the binary representation.
|
||
|
|
* @param len the number of bytes to use.
|
||
|
|
* @throws NumberFormatException {@code signum} is not one of the three
|
||
|
|
* legal values (-1, 0, and 1), or {@code signum} is 0 and
|
||
|
|
* {@code magnitude} contains one or more non-zero bytes.
|
||
|
|
* @throws IndexOutOfBoundsException if the provided array offset and
|
||
|
|
* length would cause an index into the byte array to be
|
||
|
|
* negative or greater than or equal to the array length.
|
||
|
|
* @since 9
|
||
|
|
*/
|
||
|
|
public BigInteger(int signum, byte[] magnitude, int off, int len) {
|
||
|
|
if (signum < -1 || signum > 1) {
|
||
|
|
throw(new NumberFormatException("Invalid signum value"));
|
||
|
|
}
|
||
|
|
Objects.checkFromIndexSize(off, len, magnitude.length);
|
||
|
|
|
||
|
|
// stripLeadingZeroBytes() returns a zero length array if len == 0
|
||
|
|
this.mag = stripLeadingZeroBytes(magnitude, off, len);
|
||
|
|
|
||
|
|
if (this.mag.length == 0) {
|
||
|
|
this.signum = 0;
|
||
|
|
} else {
|
||
|
|
if (signum == 0)
|
||
|
|
throw(new NumberFormatException("signum-magnitude mismatch"));
|
||
|
|
this.signum = signum;
|
||
|
|
}
|
||
|
|
if (mag.length >= MAX_MAG_LENGTH) {
|
||
|
|
checkRange();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Translates the sign-magnitude representation of a BigInteger into a
|
||
|
|
* BigInteger. The sign is represented as an integer signum value: -1 for
|
||
|
|
* negative, 0 for zero, or 1 for positive. The magnitude is a byte array
|
||
|
|
* in <i>big-endian</i> byte-order: the most significant byte is the
|
||
|
|
* zeroth element. A zero-length magnitude array is permissible, and will
|
||
|
|
* result in a BigInteger value of 0, whether signum is -1, 0 or 1. The
|
||
|
|
* {@code magnitude} array is assumed to be unchanged for the duration of
|
||
|
|
* the constructor call.
|
||
|
|
*
|
||
|
|
* @param signum signum of the number (-1 for negative, 0 for zero, 1
|
||
|
|
* for positive).
|
||
|
|
* @param magnitude big-endian binary representation of the magnitude of
|
||
|
|
* the number.
|
||
|
|
* @throws NumberFormatException {@code signum} is not one of the three
|
||
|
|
* legal values (-1, 0, and 1), or {@code signum} is 0 and
|
||
|
|
* {@code magnitude} contains one or more non-zero bytes.
|
||
|
|
*/
|
||
|
|
public BigInteger(int signum, byte[] magnitude) {
|
||
|
|
this(signum, magnitude, 0, magnitude.length);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* A constructor for internal use that translates the sign-magnitude
|
||
|
|
* representation of a BigInteger into a BigInteger. It checks the
|
||
|
|
* arguments and copies the magnitude so this constructor would be
|
||
|
|
* safe for external use. The {@code magnitude} array is assumed to be
|
||
|
|
* unchanged for the duration of the constructor call.
|
||
|
|
*/
|
||
|
|
private BigInteger(int signum, int[] magnitude) {
|
||
|
|
this.mag = stripLeadingZeroInts(magnitude);
|
||
|
|
|
||
|
|
if (signum < -1 || signum > 1)
|
||
|
|
throw(new NumberFormatException("Invalid signum value"));
|
||
|
|
|
||
|
|
if (this.mag.length == 0) {
|
||
|
|
this.signum = 0;
|
||
|
|
} else {
|
||
|
|
if (signum == 0)
|
||
|
|
throw(new NumberFormatException("signum-magnitude mismatch"));
|
||
|
|
this.signum = signum;
|
||
|
|
}
|
||
|
|
if (mag.length >= MAX_MAG_LENGTH) {
|
||
|
|
checkRange();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Translates the String representation of a BigInteger in the
|
||
|
|
* specified radix into a BigInteger. The String representation
|
||
|
|
* consists of an optional minus or plus sign followed by a
|
||
|
|
* sequence of one or more digits in the specified radix. The
|
||
|
|
* character-to-digit mapping is provided by {@link
|
||
|
|
* Character#digit(char, int) Character.digit}. The String may
|
||
|
|
* not contain any extraneous characters (whitespace, for
|
||
|
|
* example).
|
||
|
|
*
|
||
|
|
* @param val String representation of BigInteger.
|
||
|
|
* @param radix radix to be used in interpreting {@code val}.
|
||
|
|
* @throws NumberFormatException {@code val} is not a valid representation
|
||
|
|
* of a BigInteger in the specified radix, or {@code radix} is
|
||
|
|
* outside the range from {@link Character#MIN_RADIX} to
|
||
|
|
* {@link Character#MAX_RADIX}, inclusive.
|
||
|
|
*/
|
||
|
|
public BigInteger(String val, int radix) {
|
||
|
|
int cursor = 0, numDigits;
|
||
|
|
final int len = val.length();
|
||
|
|
|
||
|
|
if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
|
||
|
|
throw new NumberFormatException("Radix out of range");
|
||
|
|
if (len == 0)
|
||
|
|
throw new NumberFormatException("Zero length BigInteger");
|
||
|
|
|
||
|
|
// Check for at most one leading sign
|
||
|
|
int sign = 1;
|
||
|
|
int index1 = val.lastIndexOf('-');
|
||
|
|
int index2 = val.lastIndexOf('+');
|
||
|
|
if (index1 >= 0) {
|
||
|
|
if (index1 != 0 || index2 >= 0) {
|
||
|
|
throw new NumberFormatException("Illegal embedded sign character");
|
||
|
|
}
|
||
|
|
sign = -1;
|
||
|
|
cursor = 1;
|
||
|
|
} else if (index2 >= 0) {
|
||
|
|
if (index2 != 0) {
|
||
|
|
throw new NumberFormatException("Illegal embedded sign character");
|
||
|
|
}
|
||
|
|
cursor = 1;
|
||
|
|
}
|
||
|
|
if (cursor == len)
|
||
|
|
throw new NumberFormatException("Zero length BigInteger");
|
||
|
|
|
||
|
|
// Skip leading zeros and compute number of digits in magnitude
|
||
|
|
while (cursor < len &&
|
||
|
|
Character.digit(val.charAt(cursor), radix) == 0) {
|
||
|
|
cursor++;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (cursor == len) {
|
||
|
|
signum = 0;
|
||
|
|
mag = ZERO.mag;
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
numDigits = len - cursor;
|
||
|
|
signum = sign;
|
||
|
|
|
||
|
|
// Pre-allocate array of expected size. May be too large but can
|
||
|
|
// never be too small. Typically exact.
|
||
|
|
long numBits = ((numDigits * bitsPerDigit[radix]) >>> 10) + 1;
|
||
|
|
if (numBits + 31 >= (1L << 32)) {
|
||
|
|
reportOverflow();
|
||
|
|
}
|
||
|
|
int numWords = (int) (numBits + 31) >>> 5;
|
||
|
|
int[] magnitude = new int[numWords];
|
||
|
|
|
||
|
|
// Process first (potentially short) digit group
|
||
|
|
int firstGroupLen = numDigits % digitsPerInt[radix];
|
||
|
|
if (firstGroupLen == 0)
|
||
|
|
firstGroupLen = digitsPerInt[radix];
|
||
|
|
String group = val.substring(cursor, cursor += firstGroupLen);
|
||
|
|
magnitude[numWords - 1] = Integer.parseInt(group, radix);
|
||
|
|
if (magnitude[numWords - 1] < 0)
|
||
|
|
throw new NumberFormatException("Illegal digit");
|
||
|
|
|
||
|
|
// Process remaining digit groups
|
||
|
|
int superRadix = intRadix[radix];
|
||
|
|
int groupVal = 0;
|
||
|
|
while (cursor < len) {
|
||
|
|
group = val.substring(cursor, cursor += digitsPerInt[radix]);
|
||
|
|
groupVal = Integer.parseInt(group, radix);
|
||
|
|
if (groupVal < 0)
|
||
|
|
throw new NumberFormatException("Illegal digit");
|
||
|
|
destructiveMulAdd(magnitude, superRadix, groupVal);
|
||
|
|
}
|
||
|
|
// Required for cases where the array was overallocated.
|
||
|
|
mag = trustedStripLeadingZeroInts(magnitude);
|
||
|
|
if (mag.length >= MAX_MAG_LENGTH) {
|
||
|
|
checkRange();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
* Constructs a new BigInteger using a char array with radix=10.
|
||
|
|
* Sign is precalculated outside and not allowed in the val. The {@code val}
|
||
|
|
* array is assumed to be unchanged for the duration of the constructor
|
||
|
|
* call.
|
||
|
|
*/
|
||
|
|
BigInteger(char[] val, int sign, int len) {
|
||
|
|
int cursor = 0, numDigits;
|
||
|
|
|
||
|
|
// Skip leading zeros and compute number of digits in magnitude
|
||
|
|
while (cursor < len && Character.digit(val[cursor], 10) == 0) {
|
||
|
|
cursor++;
|
||
|
|
}
|
||
|
|
if (cursor == len) {
|
||
|
|
signum = 0;
|
||
|
|
mag = ZERO.mag;
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
numDigits = len - cursor;
|
||
|
|
signum = sign;
|
||
|
|
// Pre-allocate array of expected size
|
||
|
|
int numWords;
|
||
|
|
if (len < 10) {
|
||
|
|
numWords = 1;
|
||
|
|
} else {
|
||
|
|
long numBits = ((numDigits * bitsPerDigit[10]) >>> 10) + 1;
|
||
|
|
if (numBits + 31 >= (1L << 32)) {
|
||
|
|
reportOverflow();
|
||
|
|
}
|
||
|
|
numWords = (int) (numBits + 31) >>> 5;
|
||
|
|
}
|
||
|
|
int[] magnitude = new int[numWords];
|
||
|
|
|
||
|
|
// Process first (potentially short) digit group
|
||
|
|
int firstGroupLen = numDigits % digitsPerInt[10];
|
||
|
|
if (firstGroupLen == 0)
|
||
|
|
firstGroupLen = digitsPerInt[10];
|
||
|
|
magnitude[numWords - 1] = parseInt(val, cursor, cursor += firstGroupLen);
|
||
|
|
|
||
|
|
// Process remaining digit groups
|
||
|
|
while (cursor < len) {
|
||
|
|
int groupVal = parseInt(val, cursor, cursor += digitsPerInt[10]);
|
||
|
|
destructiveMulAdd(magnitude, intRadix[10], groupVal);
|
||
|
|
}
|
||
|
|
mag = trustedStripLeadingZeroInts(magnitude);
|
||
|
|
if (mag.length >= MAX_MAG_LENGTH) {
|
||
|
|
checkRange();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// Create an integer with the digits between the two indexes
|
||
|
|
// Assumes start < end. The result may be negative, but it
|
||
|
|
// is to be treated as an unsigned value.
|
||
|
|
private int parseInt(char[] source, int start, int end) {
|
||
|
|
int result = Character.digit(source[start++], 10);
|
||
|
|
if (result == -1)
|
||
|
|
throw new NumberFormatException(new String(source));
|
||
|
|
|
||
|
|
for (int index = start; index < end; index++) {
|
||
|
|
int nextVal = Character.digit(source[index], 10);
|
||
|
|
if (nextVal == -1)
|
||
|
|
throw new NumberFormatException(new String(source));
|
||
|
|
result = 10*result + nextVal;
|
||
|
|
}
|
||
|
|
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
// bitsPerDigit in the given radix times 1024
|
||
|
|
// Rounded up to avoid underallocation.
|
||
|
|
private static long bitsPerDigit[] = { 0, 0,
|
||
|
|
1024, 1624, 2048, 2378, 2648, 2875, 3072, 3247, 3402, 3543, 3672,
|
||
|
|
3790, 3899, 4001, 4096, 4186, 4271, 4350, 4426, 4498, 4567, 4633,
|
||
|
|
4696, 4756, 4814, 4870, 4923, 4975, 5025, 5074, 5120, 5166, 5210,
|
||
|
|
5253, 5295};
|
||
|
|
|
||
|
|
// Multiply x array times word y in place, and add word z
|
||
|
|
private static void destructiveMulAdd(int[] x, int y, int z) {
|
||
|
|
// Perform the multiplication word by word
|
||
|
|
long ylong = y & LONG_MASK;
|
||
|
|
long zlong = z & LONG_MASK;
|
||
|
|
int len = x.length;
|
||
|
|
|
||
|
|
long product = 0;
|
||
|
|
long carry = 0;
|
||
|
|
for (int i = len-1; i >= 0; i--) {
|
||
|
|
product = ylong * (x[i] & LONG_MASK) + carry;
|
||
|
|
x[i] = (int)product;
|
||
|
|
carry = product >>> 32;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Perform the addition
|
||
|
|
long sum = (x[len-1] & LONG_MASK) + zlong;
|
||
|
|
x[len-1] = (int)sum;
|
||
|
|
carry = sum >>> 32;
|
||
|
|
for (int i = len-2; i >= 0; i--) {
|
||
|
|
sum = (x[i] & LONG_MASK) + carry;
|
||
|
|
x[i] = (int)sum;
|
||
|
|
carry = sum >>> 32;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Translates the decimal String representation of a BigInteger
|
||
|
|
* into a BigInteger. The String representation consists of an
|
||
|
|
* optional minus or plus sign followed by a sequence of one or
|
||
|
|
* more decimal digits. The character-to-digit mapping is
|
||
|
|
* provided by {@link Character#digit(char, int)
|
||
|
|
* Character.digit}. The String may not contain any extraneous
|
||
|
|
* characters (whitespace, for example).
|
||
|
|
*
|
||
|
|
* @param val decimal String representation of BigInteger.
|
||
|
|
* @throws NumberFormatException {@code val} is not a valid representation
|
||
|
|
* of a BigInteger.
|
||
|
|
*/
|
||
|
|
public BigInteger(String val) {
|
||
|
|
this(val, 10);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Constructs a randomly generated BigInteger, uniformly distributed over
|
||
|
|
* the range 0 to (2<sup>{@code numBits}</sup> - 1), inclusive.
|
||
|
|
* The uniformity of the distribution assumes that a fair source of random
|
||
|
|
* bits is provided in {@code rnd}. Note that this constructor always
|
||
|
|
* constructs a non-negative BigInteger.
|
||
|
|
*
|
||
|
|
* @param numBits maximum bitLength of the new BigInteger.
|
||
|
|
* @param rnd source of randomness to be used in computing the new
|
||
|
|
* BigInteger.
|
||
|
|
* @throws IllegalArgumentException {@code numBits} is negative.
|
||
|
|
* @see #bitLength()
|
||
|
|
*/
|
||
|
|
public BigInteger(int numBits, Random rnd) {
|
||
|
|
byte[] magnitude = randomBits(numBits, rnd);
|
||
|
|
|
||
|
|
try {
|
||
|
|
// stripLeadingZeroBytes() returns a zero length array if len == 0
|
||
|
|
this.mag = stripLeadingZeroBytes(magnitude, 0, magnitude.length);
|
||
|
|
|
||
|
|
if (this.mag.length == 0) {
|
||
|
|
this.signum = 0;
|
||
|
|
} else {
|
||
|
|
this.signum = 1;
|
||
|
|
}
|
||
|
|
if (mag.length >= MAX_MAG_LENGTH) {
|
||
|
|
checkRange();
|
||
|
|
}
|
||
|
|
} finally {
|
||
|
|
Arrays.fill(magnitude, (byte)0);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
private static byte[] randomBits(int numBits, Random rnd) {
|
||
|
|
if (numBits < 0)
|
||
|
|
throw new IllegalArgumentException("numBits must be non-negative");
|
||
|
|
int numBytes = (int)(((long)numBits+7)/8); // avoid overflow
|
||
|
|
byte[] randomBits = new byte[numBytes];
|
||
|
|
|
||
|
|
// Generate random bytes and mask out any excess bits
|
||
|
|
if (numBytes > 0) {
|
||
|
|
rnd.nextBytes(randomBits);
|
||
|
|
int excessBits = 8*numBytes - numBits;
|
||
|
|
randomBits[0] &= (1 << (8-excessBits)) - 1;
|
||
|
|
}
|
||
|
|
return randomBits;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Constructs a randomly generated positive BigInteger that is probably
|
||
|
|
* prime, with the specified bitLength.
|
||
|
|
*
|
||
|
|
* @apiNote It is recommended that the {@link #probablePrime probablePrime}
|
||
|
|
* method be used in preference to this constructor unless there
|
||
|
|
* is a compelling need to specify a certainty.
|
||
|
|
*
|
||
|
|
* @param bitLength bitLength of the returned BigInteger.
|
||
|
|
* @param certainty a measure of the uncertainty that the caller is
|
||
|
|
* willing to tolerate. The probability that the new BigInteger
|
||
|
|
* represents a prime number will exceed
|
||
|
|
* (1 - 1/2<sup>{@code certainty}</sup>). The execution time of
|
||
|
|
* this constructor is proportional to the value of this parameter.
|
||
|
|
* @param rnd source of random bits used to select candidates to be
|
||
|
|
* tested for primality.
|
||
|
|
* @throws ArithmeticException {@code bitLength < 2} or {@code bitLength} is too large.
|
||
|
|
* @see #bitLength()
|
||
|
|
*/
|
||
|
|
public BigInteger(int bitLength, int certainty, Random rnd) {
|
||
|
|
BigInteger prime;
|
||
|
|
|
||
|
|
if (bitLength < 2)
|
||
|
|
throw new ArithmeticException("bitLength < 2");
|
||
|
|
prime = (bitLength < SMALL_PRIME_THRESHOLD
|
||
|
|
? smallPrime(bitLength, certainty, rnd)
|
||
|
|
: largePrime(bitLength, certainty, rnd));
|
||
|
|
signum = 1;
|
||
|
|
mag = prime.mag;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Minimum size in bits that the requested prime number has
|
||
|
|
// before we use the large prime number generating algorithms.
|
||
|
|
// The cutoff of 95 was chosen empirically for best performance.
|
||
|
|
private static final int SMALL_PRIME_THRESHOLD = 95;
|
||
|
|
|
||
|
|
// Certainty required to meet the spec of probablePrime
|
||
|
|
private static final int DEFAULT_PRIME_CERTAINTY = 100;
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a positive BigInteger that is probably prime, with the
|
||
|
|
* specified bitLength. The probability that a BigInteger returned
|
||
|
|
* by this method is composite does not exceed 2<sup>-100</sup>.
|
||
|
|
*
|
||
|
|
* @param bitLength bitLength of the returned BigInteger.
|
||
|
|
* @param rnd source of random bits used to select candidates to be
|
||
|
|
* tested for primality.
|
||
|
|
* @return a BigInteger of {@code bitLength} bits that is probably prime
|
||
|
|
* @throws ArithmeticException {@code bitLength < 2} or {@code bitLength} is too large.
|
||
|
|
* @see #bitLength()
|
||
|
|
* @since 1.4
|
||
|
|
*/
|
||
|
|
public static BigInteger probablePrime(int bitLength, Random rnd) {
|
||
|
|
if (bitLength < 2)
|
||
|
|
throw new ArithmeticException("bitLength < 2");
|
||
|
|
|
||
|
|
return (bitLength < SMALL_PRIME_THRESHOLD ?
|
||
|
|
smallPrime(bitLength, DEFAULT_PRIME_CERTAINTY, rnd) :
|
||
|
|
largePrime(bitLength, DEFAULT_PRIME_CERTAINTY, rnd));
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Find a random number of the specified bitLength that is probably prime.
|
||
|
|
* This method is used for smaller primes, its performance degrades on
|
||
|
|
* larger bitlengths.
|
||
|
|
*
|
||
|
|
* This method assumes bitLength > 1.
|
||
|
|
*/
|
||
|
|
private static BigInteger smallPrime(int bitLength, int certainty, Random rnd) {
|
||
|
|
int magLen = (bitLength + 31) >>> 5;
|
||
|
|
int temp[] = new int[magLen];
|
||
|
|
int highBit = 1 << ((bitLength+31) & 0x1f); // High bit of high int
|
||
|
|
int highMask = (highBit << 1) - 1; // Bits to keep in high int
|
||
|
|
|
||
|
|
while (true) {
|
||
|
|
// Construct a candidate
|
||
|
|
for (int i=0; i < magLen; i++)
|
||
|
|
temp[i] = rnd.nextInt();
|
||
|
|
temp[0] = (temp[0] & highMask) | highBit; // Ensure exact length
|
||
|
|
if (bitLength > 2)
|
||
|
|
temp[magLen-1] |= 1; // Make odd if bitlen > 2
|
||
|
|
|
||
|
|
BigInteger p = new BigInteger(temp, 1);
|
||
|
|
|
||
|
|
// Do cheap "pre-test" if applicable
|
||
|
|
if (bitLength > 6) {
|
||
|
|
long r = p.remainder(SMALL_PRIME_PRODUCT).longValue();
|
||
|
|
if ((r%3==0) || (r%5==0) || (r%7==0) || (r%11==0) ||
|
||
|
|
(r%13==0) || (r%17==0) || (r%19==0) || (r%23==0) ||
|
||
|
|
(r%29==0) || (r%31==0) || (r%37==0) || (r%41==0))
|
||
|
|
continue; // Candidate is composite; try another
|
||
|
|
}
|
||
|
|
|
||
|
|
// All candidates of bitLength 2 and 3 are prime by this point
|
||
|
|
if (bitLength < 4)
|
||
|
|
return p;
|
||
|
|
|
||
|
|
// Do expensive test if we survive pre-test (or it's inapplicable)
|
||
|
|
if (p.primeToCertainty(certainty, rnd))
|
||
|
|
return p;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
private static final BigInteger SMALL_PRIME_PRODUCT
|
||
|
|
= valueOf(3L*5*7*11*13*17*19*23*29*31*37*41);
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Find a random number of the specified bitLength that is probably prime.
|
||
|
|
* This method is more appropriate for larger bitlengths since it uses
|
||
|
|
* a sieve to eliminate most composites before using a more expensive
|
||
|
|
* test.
|
||
|
|
*/
|
||
|
|
private static BigInteger largePrime(int bitLength, int certainty, Random rnd) {
|
||
|
|
BigInteger p;
|
||
|
|
p = new BigInteger(bitLength, rnd).setBit(bitLength-1);
|
||
|
|
p.mag[p.mag.length-1] &= 0xfffffffe;
|
||
|
|
|
||
|
|
// Use a sieve length likely to contain the next prime number
|
||
|
|
int searchLen = getPrimeSearchLen(bitLength);
|
||
|
|
BitSieve searchSieve = new BitSieve(p, searchLen);
|
||
|
|
BigInteger candidate = searchSieve.retrieve(p, certainty, rnd);
|
||
|
|
|
||
|
|
while ((candidate == null) || (candidate.bitLength() != bitLength)) {
|
||
|
|
p = p.add(BigInteger.valueOf(2*searchLen));
|
||
|
|
if (p.bitLength() != bitLength)
|
||
|
|
p = new BigInteger(bitLength, rnd).setBit(bitLength-1);
|
||
|
|
p.mag[p.mag.length-1] &= 0xfffffffe;
|
||
|
|
searchSieve = new BitSieve(p, searchLen);
|
||
|
|
candidate = searchSieve.retrieve(p, certainty, rnd);
|
||
|
|
}
|
||
|
|
return candidate;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the first integer greater than this {@code BigInteger} that
|
||
|
|
* is probably prime. The probability that the number returned by this
|
||
|
|
* method is composite does not exceed 2<sup>-100</sup>. This method will
|
||
|
|
* never skip over a prime when searching: if it returns {@code p}, there
|
||
|
|
* is no prime {@code q} such that {@code this < q < p}.
|
||
|
|
*
|
||
|
|
* @return the first integer greater than this {@code BigInteger} that
|
||
|
|
* is probably prime.
|
||
|
|
* @throws ArithmeticException {@code this < 0} or {@code this} is too large.
|
||
|
|
* @since 1.5
|
||
|
|
*/
|
||
|
|
public BigInteger nextProbablePrime() {
|
||
|
|
if (this.signum < 0)
|
||
|
|
throw new ArithmeticException("start < 0: " + this);
|
||
|
|
|
||
|
|
// Handle trivial cases
|
||
|
|
if ((this.signum == 0) || this.equals(ONE))
|
||
|
|
return TWO;
|
||
|
|
|
||
|
|
BigInteger result = this.add(ONE);
|
||
|
|
|
||
|
|
// Fastpath for small numbers
|
||
|
|
if (result.bitLength() < SMALL_PRIME_THRESHOLD) {
|
||
|
|
|
||
|
|
// Ensure an odd number
|
||
|
|
if (!result.testBit(0))
|
||
|
|
result = result.add(ONE);
|
||
|
|
|
||
|
|
while (true) {
|
||
|
|
// Do cheap "pre-test" if applicable
|
||
|
|
if (result.bitLength() > 6) {
|
||
|
|
long r = result.remainder(SMALL_PRIME_PRODUCT).longValue();
|
||
|
|
if ((r%3==0) || (r%5==0) || (r%7==0) || (r%11==0) ||
|
||
|
|
(r%13==0) || (r%17==0) || (r%19==0) || (r%23==0) ||
|
||
|
|
(r%29==0) || (r%31==0) || (r%37==0) || (r%41==0)) {
|
||
|
|
result = result.add(TWO);
|
||
|
|
continue; // Candidate is composite; try another
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// All candidates of bitLength 2 and 3 are prime by this point
|
||
|
|
if (result.bitLength() < 4)
|
||
|
|
return result;
|
||
|
|
|
||
|
|
// The expensive test
|
||
|
|
if (result.primeToCertainty(DEFAULT_PRIME_CERTAINTY, null))
|
||
|
|
return result;
|
||
|
|
|
||
|
|
result = result.add(TWO);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// Start at previous even number
|
||
|
|
if (result.testBit(0))
|
||
|
|
result = result.subtract(ONE);
|
||
|
|
|
||
|
|
// Looking for the next large prime
|
||
|
|
int searchLen = getPrimeSearchLen(result.bitLength());
|
||
|
|
|
||
|
|
while (true) {
|
||
|
|
BitSieve searchSieve = new BitSieve(result, searchLen);
|
||
|
|
BigInteger candidate = searchSieve.retrieve(result,
|
||
|
|
DEFAULT_PRIME_CERTAINTY, null);
|
||
|
|
if (candidate != null)
|
||
|
|
return candidate;
|
||
|
|
result = result.add(BigInteger.valueOf(2 * searchLen));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
private static int getPrimeSearchLen(int bitLength) {
|
||
|
|
if (bitLength > PRIME_SEARCH_BIT_LENGTH_LIMIT + 1) {
|
||
|
|
throw new ArithmeticException("Prime search implementation restriction on bitLength");
|
||
|
|
}
|
||
|
|
return bitLength / 20 * 64;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns {@code true} if this BigInteger is probably prime,
|
||
|
|
* {@code false} if it's definitely composite.
|
||
|
|
*
|
||
|
|
* This method assumes bitLength > 2.
|
||
|
|
*
|
||
|
|
* @param certainty a measure of the uncertainty that the caller is
|
||
|
|
* willing to tolerate: if the call returns {@code true}
|
||
|
|
* the probability that this BigInteger is prime exceeds
|
||
|
|
* {@code (1 - 1/2<sup>certainty</sup>)}. The execution time of
|
||
|
|
* this method is proportional to the value of this parameter.
|
||
|
|
* @return {@code true} if this BigInteger is probably prime,
|
||
|
|
* {@code false} if it's definitely composite.
|
||
|
|
*/
|
||
|
|
boolean primeToCertainty(int certainty, Random random) {
|
||
|
|
int rounds = 0;
|
||
|
|
int n = (Math.min(certainty, Integer.MAX_VALUE-1)+1)/2;
|
||
|
|
|
||
|
|
// The relationship between the certainty and the number of rounds
|
||
|
|
// we perform is given in the draft standard ANSI X9.80, "PRIME
|
||
|
|
// NUMBER GENERATION, PRIMALITY TESTING, AND PRIMALITY CERTIFICATES".
|
||
|
|
int sizeInBits = this.bitLength();
|
||
|
|
if (sizeInBits < 100) {
|
||
|
|
rounds = 50;
|
||
|
|
rounds = n < rounds ? n : rounds;
|
||
|
|
return passesMillerRabin(rounds, random);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (sizeInBits < 256) {
|
||
|
|
rounds = 27;
|
||
|
|
} else if (sizeInBits < 512) {
|
||
|
|
rounds = 15;
|
||
|
|
} else if (sizeInBits < 768) {
|
||
|
|
rounds = 8;
|
||
|
|
} else if (sizeInBits < 1024) {
|
||
|
|
rounds = 4;
|
||
|
|
} else {
|
||
|
|
rounds = 2;
|
||
|
|
}
|
||
|
|
rounds = n < rounds ? n : rounds;
|
||
|
|
|
||
|
|
return passesMillerRabin(rounds, random) && passesLucasLehmer();
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns true iff this BigInteger is a Lucas-Lehmer probable prime.
|
||
|
|
*
|
||
|
|
* The following assumptions are made:
|
||
|
|
* This BigInteger is a positive, odd number.
|
||
|
|
*/
|
||
|
|
private boolean passesLucasLehmer() {
|
||
|
|
BigInteger thisPlusOne = this.add(ONE);
|
||
|
|
|
||
|
|
// Step 1
|
||
|
|
int d = 5;
|
||
|
|
while (jacobiSymbol(d, this) != -1) {
|
||
|
|
// 5, -7, 9, -11, ...
|
||
|
|
d = (d < 0) ? Math.abs(d)+2 : -(d+2);
|
||
|
|
}
|
||
|
|
|
||
|
|
// Step 2
|
||
|
|
BigInteger u = lucasLehmerSequence(d, thisPlusOne, this);
|
||
|
|
|
||
|
|
// Step 3
|
||
|
|
return u.mod(this).equals(ZERO);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Computes Jacobi(p,n).
|
||
|
|
* Assumes n positive, odd, n>=3.
|
||
|
|
*/
|
||
|
|
private static int jacobiSymbol(int p, BigInteger n) {
|
||
|
|
if (p == 0)
|
||
|
|
return 0;
|
||
|
|
|
||
|
|
// Algorithm and comments adapted from Colin Plumb's C library.
|
||
|
|
int j = 1;
|
||
|
|
int u = n.mag[n.mag.length-1];
|
||
|
|
|
||
|
|
// Make p positive
|
||
|
|
if (p < 0) {
|
||
|
|
p = -p;
|
||
|
|
int n8 = u & 7;
|
||
|
|
if ((n8 == 3) || (n8 == 7))
|
||
|
|
j = -j; // 3 (011) or 7 (111) mod 8
|
||
|
|
}
|
||
|
|
|
||
|
|
// Get rid of factors of 2 in p
|
||
|
|
while ((p & 3) == 0)
|
||
|
|
p >>= 2;
|
||
|
|
if ((p & 1) == 0) {
|
||
|
|
p >>= 1;
|
||
|
|
if (((u ^ (u>>1)) & 2) != 0)
|
||
|
|
j = -j; // 3 (011) or 5 (101) mod 8
|
||
|
|
}
|
||
|
|
if (p == 1)
|
||
|
|
return j;
|
||
|
|
// Then, apply quadratic reciprocity
|
||
|
|
if ((p & u & 2) != 0) // p = u = 3 (mod 4)?
|
||
|
|
j = -j;
|
||
|
|
// And reduce u mod p
|
||
|
|
u = n.mod(BigInteger.valueOf(p)).intValue();
|
||
|
|
|
||
|
|
// Now compute Jacobi(u,p), u < p
|
||
|
|
while (u != 0) {
|
||
|
|
while ((u & 3) == 0)
|
||
|
|
u >>= 2;
|
||
|
|
if ((u & 1) == 0) {
|
||
|
|
u >>= 1;
|
||
|
|
if (((p ^ (p>>1)) & 2) != 0)
|
||
|
|
j = -j; // 3 (011) or 5 (101) mod 8
|
||
|
|
}
|
||
|
|
if (u == 1)
|
||
|
|
return j;
|
||
|
|
// Now both u and p are odd, so use quadratic reciprocity
|
||
|
|
assert (u < p);
|
||
|
|
int t = u; u = p; p = t;
|
||
|
|
if ((u & p & 2) != 0) // u = p = 3 (mod 4)?
|
||
|
|
j = -j;
|
||
|
|
// Now u >= p, so it can be reduced
|
||
|
|
u %= p;
|
||
|
|
}
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
private static BigInteger lucasLehmerSequence(int z, BigInteger k, BigInteger n) {
|
||
|
|
BigInteger d = BigInteger.valueOf(z);
|
||
|
|
BigInteger u = ONE; BigInteger u2;
|
||
|
|
BigInteger v = ONE; BigInteger v2;
|
||
|
|
|
||
|
|
for (int i=k.bitLength()-2; i >= 0; i--) {
|
||
|
|
u2 = u.multiply(v).mod(n);
|
||
|
|
|
||
|
|
v2 = v.square().add(d.multiply(u.square())).mod(n);
|
||
|
|
if (v2.testBit(0))
|
||
|
|
v2 = v2.subtract(n);
|
||
|
|
|
||
|
|
v2 = v2.shiftRight(1);
|
||
|
|
|
||
|
|
u = u2; v = v2;
|
||
|
|
if (k.testBit(i)) {
|
||
|
|
u2 = u.add(v).mod(n);
|
||
|
|
if (u2.testBit(0))
|
||
|
|
u2 = u2.subtract(n);
|
||
|
|
|
||
|
|
u2 = u2.shiftRight(1);
|
||
|
|
v2 = v.add(d.multiply(u)).mod(n);
|
||
|
|
if (v2.testBit(0))
|
||
|
|
v2 = v2.subtract(n);
|
||
|
|
v2 = v2.shiftRight(1);
|
||
|
|
|
||
|
|
u = u2; v = v2;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return u;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns true iff this BigInteger passes the specified number of
|
||
|
|
* Miller-Rabin tests. This test is taken from the DSA spec (NIST FIPS
|
||
|
|
* 186-2).
|
||
|
|
*
|
||
|
|
* The following assumptions are made:
|
||
|
|
* This BigInteger is a positive, odd number greater than 2.
|
||
|
|
* iterations<=50.
|
||
|
|
*/
|
||
|
|
private boolean passesMillerRabin(int iterations, Random rnd) {
|
||
|
|
// Find a and m such that m is odd and this == 1 + 2**a * m
|
||
|
|
BigInteger thisMinusOne = this.subtract(ONE);
|
||
|
|
BigInteger m = thisMinusOne;
|
||
|
|
int a = m.getLowestSetBit();
|
||
|
|
m = m.shiftRight(a);
|
||
|
|
|
||
|
|
// Do the tests
|
||
|
|
if (rnd == null) {
|
||
|
|
rnd = ThreadLocalRandom.current();
|
||
|
|
}
|
||
|
|
for (int i=0; i < iterations; i++) {
|
||
|
|
// Generate a uniform random on (1, this)
|
||
|
|
BigInteger b;
|
||
|
|
do {
|
||
|
|
b = new BigInteger(this.bitLength(), rnd);
|
||
|
|
} while (b.compareTo(ONE) <= 0 || b.compareTo(this) >= 0);
|
||
|
|
|
||
|
|
int j = 0;
|
||
|
|
BigInteger z = b.modPow(m, this);
|
||
|
|
while (!((j == 0 && z.equals(ONE)) || z.equals(thisMinusOne))) {
|
||
|
|
if (j > 0 && z.equals(ONE) || ++j == a)
|
||
|
|
return false;
|
||
|
|
z = z.modPow(TWO, this);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* This internal constructor differs from its public cousin
|
||
|
|
* with the arguments reversed in two ways: it assumes that its
|
||
|
|
* arguments are correct, and it doesn't copy the magnitude array.
|
||
|
|
*/
|
||
|
|
BigInteger(int[] magnitude, int signum) {
|
||
|
|
this.signum = (magnitude.length == 0 ? 0 : signum);
|
||
|
|
this.mag = magnitude;
|
||
|
|
if (mag.length >= MAX_MAG_LENGTH) {
|
||
|
|
checkRange();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* This private constructor is for internal use and assumes that its
|
||
|
|
* arguments are correct. The {@code magnitude} array is assumed to be
|
||
|
|
* unchanged for the duration of the constructor call.
|
||
|
|
*/
|
||
|
|
private BigInteger(byte[] magnitude, int signum) {
|
||
|
|
this.signum = (magnitude.length == 0 ? 0 : signum);
|
||
|
|
this.mag = stripLeadingZeroBytes(magnitude, 0, magnitude.length);
|
||
|
|
if (mag.length >= MAX_MAG_LENGTH) {
|
||
|
|
checkRange();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Throws an {@code ArithmeticException} if the {@code BigInteger} would be
|
||
|
|
* out of the supported range.
|
||
|
|
*
|
||
|
|
* @throws ArithmeticException if {@code this} exceeds the supported range.
|
||
|
|
*/
|
||
|
|
private void checkRange() {
|
||
|
|
if (mag.length > MAX_MAG_LENGTH || mag.length == MAX_MAG_LENGTH && mag[0] < 0) {
|
||
|
|
reportOverflow();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
private static void reportOverflow() {
|
||
|
|
throw new ArithmeticException("BigInteger would overflow supported range");
|
||
|
|
}
|
||
|
|
|
||
|
|
//Static Factory Methods
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is equal to that of the
|
||
|
|
* specified {@code long}.
|
||
|
|
*
|
||
|
|
* @apiNote This static factory method is provided in preference
|
||
|
|
* to a ({@code long}) constructor because it allows for reuse of
|
||
|
|
* frequently used BigIntegers.
|
||
|
|
*
|
||
|
|
* @param val value of the BigInteger to return.
|
||
|
|
* @return a BigInteger with the specified value.
|
||
|
|
*/
|
||
|
|
public static BigInteger valueOf(long val) {
|
||
|
|
// If -MAX_CONSTANT < val < MAX_CONSTANT, return stashed constant
|
||
|
|
if (val == 0)
|
||
|
|
return ZERO;
|
||
|
|
if (val > 0 && val <= MAX_CONSTANT)
|
||
|
|
return posConst[(int) val];
|
||
|
|
else if (val < 0 && val >= -MAX_CONSTANT)
|
||
|
|
return negConst[(int) -val];
|
||
|
|
|
||
|
|
return new BigInteger(val);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Constructs a BigInteger with the specified value, which may not be zero.
|
||
|
|
*/
|
||
|
|
private BigInteger(long val) {
|
||
|
|
if (val < 0) {
|
||
|
|
val = -val;
|
||
|
|
signum = -1;
|
||
|
|
} else {
|
||
|
|
signum = 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
int highWord = (int)(val >>> 32);
|
||
|
|
if (highWord == 0) {
|
||
|
|
mag = new int[1];
|
||
|
|
mag[0] = (int)val;
|
||
|
|
} else {
|
||
|
|
mag = new int[2];
|
||
|
|
mag[0] = highWord;
|
||
|
|
mag[1] = (int)val;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger with the given two's complement representation.
|
||
|
|
* Assumes that the input array will not be modified (the returned
|
||
|
|
* BigInteger will reference the input array if feasible).
|
||
|
|
*/
|
||
|
|
private static BigInteger valueOf(int val[]) {
|
||
|
|
return (val[0] > 0 ? new BigInteger(val, 1) : new BigInteger(val));
|
||
|
|
}
|
||
|
|
|
||
|
|
// Constants
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Initialize static constant array when class is loaded.
|
||
|
|
*/
|
||
|
|
private static final int MAX_CONSTANT = 16;
|
||
|
|
private static final BigInteger[] posConst = new BigInteger[MAX_CONSTANT+1];
|
||
|
|
private static final BigInteger[] negConst = new BigInteger[MAX_CONSTANT+1];
|
||
|
|
|
||
|
|
/**
|
||
|
|
* The cache of powers of each radix. This allows us to not have to
|
||
|
|
* recalculate powers of radix^(2^n) more than once. This speeds
|
||
|
|
* Schoenhage recursive base conversion significantly.
|
||
|
|
*/
|
||
|
|
private static volatile BigInteger[][] powerCache;
|
||
|
|
|
||
|
|
/** The cache of logarithms of radices for base conversion. */
|
||
|
|
private static final double[] logCache;
|
||
|
|
|
||
|
|
/** The natural log of 2. This is used in computing cache indices. */
|
||
|
|
private static final double LOG_TWO = Math.log(2.0);
|
||
|
|
|
||
|
|
static {
|
||
|
|
assert 0 < KARATSUBA_THRESHOLD
|
||
|
|
&& KARATSUBA_THRESHOLD < TOOM_COOK_THRESHOLD
|
||
|
|
&& TOOM_COOK_THRESHOLD < Integer.MAX_VALUE
|
||
|
|
&& 0 < KARATSUBA_SQUARE_THRESHOLD
|
||
|
|
&& KARATSUBA_SQUARE_THRESHOLD < TOOM_COOK_SQUARE_THRESHOLD
|
||
|
|
&& TOOM_COOK_SQUARE_THRESHOLD < Integer.MAX_VALUE :
|
||
|
|
"Algorithm thresholds are inconsistent";
|
||
|
|
|
||
|
|
for (int i = 1; i <= MAX_CONSTANT; i++) {
|
||
|
|
int[] magnitude = new int[1];
|
||
|
|
magnitude[0] = i;
|
||
|
|
posConst[i] = new BigInteger(magnitude, 1);
|
||
|
|
negConst[i] = new BigInteger(magnitude, -1);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
* Initialize the cache of radix^(2^x) values used for base conversion
|
||
|
|
* with just the very first value. Additional values will be created
|
||
|
|
* on demand.
|
||
|
|
*/
|
||
|
|
powerCache = new BigInteger[Character.MAX_RADIX+1][];
|
||
|
|
logCache = new double[Character.MAX_RADIX+1];
|
||
|
|
|
||
|
|
for (int i=Character.MIN_RADIX; i <= Character.MAX_RADIX; i++) {
|
||
|
|
powerCache[i] = new BigInteger[] { BigInteger.valueOf(i) };
|
||
|
|
logCache[i] = Math.log(i);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* The BigInteger constant zero.
|
||
|
|
*
|
||
|
|
* @since 1.2
|
||
|
|
*/
|
||
|
|
public static final BigInteger ZERO = new BigInteger(new int[0], 0);
|
||
|
|
|
||
|
|
/**
|
||
|
|
* The BigInteger constant one.
|
||
|
|
*
|
||
|
|
* @since 1.2
|
||
|
|
*/
|
||
|
|
public static final BigInteger ONE = valueOf(1);
|
||
|
|
|
||
|
|
/**
|
||
|
|
* The BigInteger constant two.
|
||
|
|
*
|
||
|
|
* @since 9
|
||
|
|
*/
|
||
|
|
public static final BigInteger TWO = valueOf(2);
|
||
|
|
|
||
|
|
/**
|
||
|
|
* The BigInteger constant -1. (Not exported.)
|
||
|
|
*/
|
||
|
|
private static final BigInteger NEGATIVE_ONE = valueOf(-1);
|
||
|
|
|
||
|
|
/**
|
||
|
|
* The BigInteger constant ten.
|
||
|
|
*
|
||
|
|
* @since 1.5
|
||
|
|
*/
|
||
|
|
public static final BigInteger TEN = valueOf(10);
|
||
|
|
|
||
|
|
// Arithmetic Operations
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this + val)}.
|
||
|
|
*
|
||
|
|
* @param val value to be added to this BigInteger.
|
||
|
|
* @return {@code this + val}
|
||
|
|
*/
|
||
|
|
public BigInteger add(BigInteger val) {
|
||
|
|
if (val.signum == 0)
|
||
|
|
return this;
|
||
|
|
if (signum == 0)
|
||
|
|
return val;
|
||
|
|
if (val.signum == signum)
|
||
|
|
return new BigInteger(add(mag, val.mag), signum);
|
||
|
|
|
||
|
|
int cmp = compareMagnitude(val);
|
||
|
|
if (cmp == 0)
|
||
|
|
return ZERO;
|
||
|
|
int[] resultMag = (cmp > 0 ? subtract(mag, val.mag)
|
||
|
|
: subtract(val.mag, mag));
|
||
|
|
resultMag = trustedStripLeadingZeroInts(resultMag);
|
||
|
|
|
||
|
|
return new BigInteger(resultMag, cmp == signum ? 1 : -1);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Package private methods used by BigDecimal code to add a BigInteger
|
||
|
|
* with a long. Assumes val is not equal to INFLATED.
|
||
|
|
*/
|
||
|
|
BigInteger add(long val) {
|
||
|
|
if (val == 0)
|
||
|
|
return this;
|
||
|
|
if (signum == 0)
|
||
|
|
return valueOf(val);
|
||
|
|
if (Long.signum(val) == signum)
|
||
|
|
return new BigInteger(add(mag, Math.abs(val)), signum);
|
||
|
|
int cmp = compareMagnitude(val);
|
||
|
|
if (cmp == 0)
|
||
|
|
return ZERO;
|
||
|
|
int[] resultMag = (cmp > 0 ? subtract(mag, Math.abs(val)) : subtract(Math.abs(val), mag));
|
||
|
|
resultMag = trustedStripLeadingZeroInts(resultMag);
|
||
|
|
return new BigInteger(resultMag, cmp == signum ? 1 : -1);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Adds the contents of the int array x and long value val. This
|
||
|
|
* method allocates a new int array to hold the answer and returns
|
||
|
|
* a reference to that array. Assumes x.length > 0 and val is
|
||
|
|
* non-negative
|
||
|
|
*/
|
||
|
|
private static int[] add(int[] x, long val) {
|
||
|
|
int[] y;
|
||
|
|
long sum = 0;
|
||
|
|
int xIndex = x.length;
|
||
|
|
int[] result;
|
||
|
|
int highWord = (int)(val >>> 32);
|
||
|
|
if (highWord == 0) {
|
||
|
|
result = new int[xIndex];
|
||
|
|
sum = (x[--xIndex] & LONG_MASK) + val;
|
||
|
|
result[xIndex] = (int)sum;
|
||
|
|
} else {
|
||
|
|
if (xIndex == 1) {
|
||
|
|
result = new int[2];
|
||
|
|
sum = val + (x[0] & LONG_MASK);
|
||
|
|
result[1] = (int)sum;
|
||
|
|
result[0] = (int)(sum >>> 32);
|
||
|
|
return result;
|
||
|
|
} else {
|
||
|
|
result = new int[xIndex];
|
||
|
|
sum = (x[--xIndex] & LONG_MASK) + (val & LONG_MASK);
|
||
|
|
result[xIndex] = (int)sum;
|
||
|
|
sum = (x[--xIndex] & LONG_MASK) + (highWord & LONG_MASK) + (sum >>> 32);
|
||
|
|
result[xIndex] = (int)sum;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// Copy remainder of longer number while carry propagation is required
|
||
|
|
boolean carry = (sum >>> 32 != 0);
|
||
|
|
while (xIndex > 0 && carry)
|
||
|
|
carry = ((result[--xIndex] = x[xIndex] + 1) == 0);
|
||
|
|
// Copy remainder of longer number
|
||
|
|
while (xIndex > 0)
|
||
|
|
result[--xIndex] = x[xIndex];
|
||
|
|
// Grow result if necessary
|
||
|
|
if (carry) {
|
||
|
|
int bigger[] = new int[result.length + 1];
|
||
|
|
System.arraycopy(result, 0, bigger, 1, result.length);
|
||
|
|
bigger[0] = 0x01;
|
||
|
|
return bigger;
|
||
|
|
}
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Adds the contents of the int arrays x and y. This method allocates
|
||
|
|
* a new int array to hold the answer and returns a reference to that
|
||
|
|
* array.
|
||
|
|
*/
|
||
|
|
private static int[] add(int[] x, int[] y) {
|
||
|
|
// If x is shorter, swap the two arrays
|
||
|
|
if (x.length < y.length) {
|
||
|
|
int[] tmp = x;
|
||
|
|
x = y;
|
||
|
|
y = tmp;
|
||
|
|
}
|
||
|
|
|
||
|
|
int xIndex = x.length;
|
||
|
|
int yIndex = y.length;
|
||
|
|
int result[] = new int[xIndex];
|
||
|
|
long sum = 0;
|
||
|
|
if (yIndex == 1) {
|
||
|
|
sum = (x[--xIndex] & LONG_MASK) + (y[0] & LONG_MASK) ;
|
||
|
|
result[xIndex] = (int)sum;
|
||
|
|
} else {
|
||
|
|
// Add common parts of both numbers
|
||
|
|
while (yIndex > 0) {
|
||
|
|
sum = (x[--xIndex] & LONG_MASK) +
|
||
|
|
(y[--yIndex] & LONG_MASK) + (sum >>> 32);
|
||
|
|
result[xIndex] = (int)sum;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// Copy remainder of longer number while carry propagation is required
|
||
|
|
boolean carry = (sum >>> 32 != 0);
|
||
|
|
while (xIndex > 0 && carry)
|
||
|
|
carry = ((result[--xIndex] = x[xIndex] + 1) == 0);
|
||
|
|
|
||
|
|
// Copy remainder of longer number
|
||
|
|
while (xIndex > 0)
|
||
|
|
result[--xIndex] = x[xIndex];
|
||
|
|
|
||
|
|
// Grow result if necessary
|
||
|
|
if (carry) {
|
||
|
|
int bigger[] = new int[result.length + 1];
|
||
|
|
System.arraycopy(result, 0, bigger, 1, result.length);
|
||
|
|
bigger[0] = 0x01;
|
||
|
|
return bigger;
|
||
|
|
}
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
private static int[] subtract(long val, int[] little) {
|
||
|
|
int highWord = (int)(val >>> 32);
|
||
|
|
if (highWord == 0) {
|
||
|
|
int result[] = new int[1];
|
||
|
|
result[0] = (int)(val - (little[0] & LONG_MASK));
|
||
|
|
return result;
|
||
|
|
} else {
|
||
|
|
int result[] = new int[2];
|
||
|
|
if (little.length == 1) {
|
||
|
|
long difference = ((int)val & LONG_MASK) - (little[0] & LONG_MASK);
|
||
|
|
result[1] = (int)difference;
|
||
|
|
// Subtract remainder of longer number while borrow propagates
|
||
|
|
boolean borrow = (difference >> 32 != 0);
|
||
|
|
if (borrow) {
|
||
|
|
result[0] = highWord - 1;
|
||
|
|
} else { // Copy remainder of longer number
|
||
|
|
result[0] = highWord;
|
||
|
|
}
|
||
|
|
return result;
|
||
|
|
} else { // little.length == 2
|
||
|
|
long difference = ((int)val & LONG_MASK) - (little[1] & LONG_MASK);
|
||
|
|
result[1] = (int)difference;
|
||
|
|
difference = (highWord & LONG_MASK) - (little[0] & LONG_MASK) + (difference >> 32);
|
||
|
|
result[0] = (int)difference;
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Subtracts the contents of the second argument (val) from the
|
||
|
|
* first (big). The first int array (big) must represent a larger number
|
||
|
|
* than the second. This method allocates the space necessary to hold the
|
||
|
|
* answer.
|
||
|
|
* assumes val >= 0
|
||
|
|
*/
|
||
|
|
private static int[] subtract(int[] big, long val) {
|
||
|
|
int highWord = (int)(val >>> 32);
|
||
|
|
int bigIndex = big.length;
|
||
|
|
int result[] = new int[bigIndex];
|
||
|
|
long difference = 0;
|
||
|
|
|
||
|
|
if (highWord == 0) {
|
||
|
|
difference = (big[--bigIndex] & LONG_MASK) - val;
|
||
|
|
result[bigIndex] = (int)difference;
|
||
|
|
} else {
|
||
|
|
difference = (big[--bigIndex] & LONG_MASK) - (val & LONG_MASK);
|
||
|
|
result[bigIndex] = (int)difference;
|
||
|
|
difference = (big[--bigIndex] & LONG_MASK) - (highWord & LONG_MASK) + (difference >> 32);
|
||
|
|
result[bigIndex] = (int)difference;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Subtract remainder of longer number while borrow propagates
|
||
|
|
boolean borrow = (difference >> 32 != 0);
|
||
|
|
while (bigIndex > 0 && borrow)
|
||
|
|
borrow = ((result[--bigIndex] = big[bigIndex] - 1) == -1);
|
||
|
|
|
||
|
|
// Copy remainder of longer number
|
||
|
|
while (bigIndex > 0)
|
||
|
|
result[--bigIndex] = big[bigIndex];
|
||
|
|
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this - val)}.
|
||
|
|
*
|
||
|
|
* @param val value to be subtracted from this BigInteger.
|
||
|
|
* @return {@code this - val}
|
||
|
|
*/
|
||
|
|
public BigInteger subtract(BigInteger val) {
|
||
|
|
if (val.signum == 0)
|
||
|
|
return this;
|
||
|
|
if (signum == 0)
|
||
|
|
return val.negate();
|
||
|
|
if (val.signum != signum)
|
||
|
|
return new BigInteger(add(mag, val.mag), signum);
|
||
|
|
|
||
|
|
int cmp = compareMagnitude(val);
|
||
|
|
if (cmp == 0)
|
||
|
|
return ZERO;
|
||
|
|
int[] resultMag = (cmp > 0 ? subtract(mag, val.mag)
|
||
|
|
: subtract(val.mag, mag));
|
||
|
|
resultMag = trustedStripLeadingZeroInts(resultMag);
|
||
|
|
return new BigInteger(resultMag, cmp == signum ? 1 : -1);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Subtracts the contents of the second int arrays (little) from the
|
||
|
|
* first (big). The first int array (big) must represent a larger number
|
||
|
|
* than the second. This method allocates the space necessary to hold the
|
||
|
|
* answer.
|
||
|
|
*/
|
||
|
|
private static int[] subtract(int[] big, int[] little) {
|
||
|
|
int bigIndex = big.length;
|
||
|
|
int result[] = new int[bigIndex];
|
||
|
|
int littleIndex = little.length;
|
||
|
|
long difference = 0;
|
||
|
|
|
||
|
|
// Subtract common parts of both numbers
|
||
|
|
while (littleIndex > 0) {
|
||
|
|
difference = (big[--bigIndex] & LONG_MASK) -
|
||
|
|
(little[--littleIndex] & LONG_MASK) +
|
||
|
|
(difference >> 32);
|
||
|
|
result[bigIndex] = (int)difference;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Subtract remainder of longer number while borrow propagates
|
||
|
|
boolean borrow = (difference >> 32 != 0);
|
||
|
|
while (bigIndex > 0 && borrow)
|
||
|
|
borrow = ((result[--bigIndex] = big[bigIndex] - 1) == -1);
|
||
|
|
|
||
|
|
// Copy remainder of longer number
|
||
|
|
while (bigIndex > 0)
|
||
|
|
result[--bigIndex] = big[bigIndex];
|
||
|
|
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this * val)}.
|
||
|
|
*
|
||
|
|
* @implNote An implementation may offer better algorithmic
|
||
|
|
* performance when {@code val == this}.
|
||
|
|
*
|
||
|
|
* @param val value to be multiplied by this BigInteger.
|
||
|
|
* @return {@code this * val}
|
||
|
|
*/
|
||
|
|
public BigInteger multiply(BigInteger val) {
|
||
|
|
return multiply(val, false);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this * val)}. If
|
||
|
|
* the invocation is recursive certain overflow checks are skipped.
|
||
|
|
*
|
||
|
|
* @param val value to be multiplied by this BigInteger.
|
||
|
|
* @param isRecursion whether this is a recursive invocation
|
||
|
|
* @return {@code this * val}
|
||
|
|
*/
|
||
|
|
private BigInteger multiply(BigInteger val, boolean isRecursion) {
|
||
|
|
if (val.signum == 0 || signum == 0)
|
||
|
|
return ZERO;
|
||
|
|
|
||
|
|
int xlen = mag.length;
|
||
|
|
|
||
|
|
// BEGIN Android-changed: Fall back to the boringssl implementation for
|
||
|
|
// large arguments.
|
||
|
|
final int BORINGSSL_MUL_THRESHOLD = 50;
|
||
|
|
|
||
|
|
if (val == this && xlen > MULTIPLY_SQUARE_THRESHOLD
|
||
|
|
&& xlen < BORINGSSL_MUL_THRESHOLD) {
|
||
|
|
return square();
|
||
|
|
}
|
||
|
|
|
||
|
|
int ylen = val.mag.length;
|
||
|
|
|
||
|
|
int resultSign = signum == val.signum ? 1 : -1;
|
||
|
|
if ((xlen < BORINGSSL_MUL_THRESHOLD) || (ylen < BORINGSSL_MUL_THRESHOLD)) {
|
||
|
|
if (val.mag.length == 1) {
|
||
|
|
return multiplyByInt(mag,val.mag[0], resultSign);
|
||
|
|
}
|
||
|
|
if (mag.length == 1) {
|
||
|
|
return multiplyByInt(val.mag,mag[0], resultSign);
|
||
|
|
}
|
||
|
|
int[] result = multiplyToLen(mag, xlen,
|
||
|
|
val.mag, ylen, null);
|
||
|
|
result = trustedStripLeadingZeroInts(result);
|
||
|
|
return new BigInteger(result, resultSign);
|
||
|
|
} else {
|
||
|
|
long xBN = 0, yBN = 0, resultBN = 0;
|
||
|
|
try {
|
||
|
|
xBN = bigEndInts2NewBN(mag, /* neg= */false);
|
||
|
|
yBN = bigEndInts2NewBN(val.mag, /* neg= */false);
|
||
|
|
resultBN = NativeBN.BN_new();
|
||
|
|
NativeBN.BN_mul(resultBN, xBN, yBN);
|
||
|
|
return new BigInteger(resultSign, bn2BigEndInts(resultBN));
|
||
|
|
} finally {
|
||
|
|
NativeBN.BN_free(xBN);
|
||
|
|
NativeBN.BN_free(yBN);
|
||
|
|
NativeBN.BN_free(resultBN);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
if ((xlen < TOOM_COOK_THRESHOLD) && (ylen < TOOM_COOK_THRESHOLD)) {
|
||
|
|
return multiplyKaratsuba(this, val);
|
||
|
|
} else {
|
||
|
|
//
|
||
|
|
// In "Hacker's Delight" section 2-13, p.33, it is explained
|
||
|
|
// that if x and y are unsigned 32-bit quantities and m and n
|
||
|
|
// are their respective numbers of leading zeros within 32 bits,
|
||
|
|
// then the number of leading zeros within their product as a
|
||
|
|
// 64-bit unsigned quantity is either m + n or m + n + 1. If
|
||
|
|
// their product is not to overflow, it cannot exceed 32 bits,
|
||
|
|
// and so the number of leading zeros of the product within 64
|
||
|
|
// bits must be at least 32, i.e., the leftmost set bit is at
|
||
|
|
// zero-relative position 31 or less.
|
||
|
|
//
|
||
|
|
// From the above there are three cases:
|
||
|
|
//
|
||
|
|
// m + n leftmost set bit condition
|
||
|
|
// ----- ---------------- ---------
|
||
|
|
// >= 32 x <= 64 - 32 = 32 no overflow
|
||
|
|
// == 31 x >= 64 - 32 = 32 possible overflow
|
||
|
|
// <= 30 x >= 64 - 31 = 33 definite overflow
|
||
|
|
//
|
||
|
|
// The "possible overflow" condition cannot be detected by
|
||
|
|
// examning data lengths alone and requires further calculation.
|
||
|
|
//
|
||
|
|
// By analogy, if 'this' and 'val' have m and n as their
|
||
|
|
// respective numbers of leading zeros within 32*MAX_MAG_LENGTH
|
||
|
|
// bits, then:
|
||
|
|
//
|
||
|
|
// m + n >= 32*MAX_MAG_LENGTH no overflow
|
||
|
|
// m + n == 32*MAX_MAG_LENGTH - 1 possible overflow
|
||
|
|
// m + n <= 32*MAX_MAG_LENGTH - 2 definite overflow
|
||
|
|
//
|
||
|
|
// Note however that if the number of ints in the result
|
||
|
|
// were to be MAX_MAG_LENGTH and mag[0] < 0, then there would
|
||
|
|
// be overflow. As a result the leftmost bit (of mag[0]) cannot
|
||
|
|
// be used and the constraints must be adjusted by one bit to:
|
||
|
|
//
|
||
|
|
// m + n > 32*MAX_MAG_LENGTH no overflow
|
||
|
|
// m + n == 32*MAX_MAG_LENGTH possible overflow
|
||
|
|
// m + n < 32*MAX_MAG_LENGTH definite overflow
|
||
|
|
//
|
||
|
|
// The foregoing leading zero-based discussion is for clarity
|
||
|
|
// only. The actual calculations use the estimated bit length
|
||
|
|
// of the product as this is more natural to the internal
|
||
|
|
// array representation of the magnitude which has no leading
|
||
|
|
// zero elements.
|
||
|
|
//
|
||
|
|
if (!isRecursion) {
|
||
|
|
// The bitLength() instance method is not used here as we
|
||
|
|
// are only considering the magnitudes as non-negative. The
|
||
|
|
// Toom-Cook multiplication algorithm determines the sign
|
||
|
|
// at its end from the two signum values.
|
||
|
|
if ((long)bitLength(mag, mag.length) +
|
||
|
|
(long)bitLength(val.mag, val.mag.length) >
|
||
|
|
32L*MAX_MAG_LENGTH) {
|
||
|
|
reportOverflow();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return multiplyToomCook3(this, val);
|
||
|
|
}
|
||
|
|
*/
|
||
|
|
// END Android-changed: Fall back to the boringssl implementation for
|
||
|
|
// large arguments.
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
private static BigInteger multiplyByInt(int[] x, int y, int sign) {
|
||
|
|
if (Integer.bitCount(y) == 1) {
|
||
|
|
return new BigInteger(shiftLeft(x,Integer.numberOfTrailingZeros(y)), sign);
|
||
|
|
}
|
||
|
|
int xlen = x.length;
|
||
|
|
// BEGIN Android-changed: Try to predict result length to avoid copy. http://b/140780742
|
||
|
|
/*
|
||
|
|
int[] rmag = new int[xlen + 1];
|
||
|
|
long carry = 0;
|
||
|
|
long yl = y & LONG_MASK;
|
||
|
|
int rstart = rmag.length - 1;
|
||
|
|
for (int i = xlen - 1; i >= 0; i--) {
|
||
|
|
long product = (x[i] & LONG_MASK) * yl + carry;
|
||
|
|
rmag[rstart--] = (int)product;
|
||
|
|
carry = product >>> 32;
|
||
|
|
}
|
||
|
|
if (carry == 0L) {
|
||
|
|
rmag = java.util.Arrays.copyOfRange(rmag, 1, rmag.length);
|
||
|
|
} else {
|
||
|
|
rmag[rstart] = (int)carry;
|
||
|
|
}
|
||
|
|
*/
|
||
|
|
long carry = 0;
|
||
|
|
long yl = y & LONG_MASK;
|
||
|
|
// Bound the 2 most significant product (int-sized) "digits". Less-significant ints in x's
|
||
|
|
// magnitude cannot contribute more than 1 in the uppermost int.
|
||
|
|
long highDigitsBound = ((x[0] & LONG_MASK) + 1) * yl; // Cannot overflow as unsigned long.
|
||
|
|
int rlen = ((highDigitsBound >>> 32) == 0) ? xlen : xlen + 1;
|
||
|
|
int[] rmag = new int[rlen];
|
||
|
|
int rindex = rlen - 1;
|
||
|
|
for (int i = xlen - 1; i >= 0; i--) {
|
||
|
|
long product = (x[i] & LONG_MASK) * yl + carry;
|
||
|
|
rmag[rindex--] = (int)product;
|
||
|
|
carry = product >>> 32;
|
||
|
|
}
|
||
|
|
if (rindex == -1) {
|
||
|
|
assert(carry == 0);
|
||
|
|
} else {
|
||
|
|
assert(rindex == 0);
|
||
|
|
if (carry == 0) {
|
||
|
|
// We mis-estimated the length. Very rare.
|
||
|
|
rmag = java.util.Arrays.copyOfRange(rmag, 1, rmag.length);
|
||
|
|
} else {
|
||
|
|
rmag[0] = (int)carry;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// END Android-changed: Try to predict result length to avoid copy.
|
||
|
|
return new BigInteger(rmag, sign);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Package private methods used by BigDecimal code to multiply a BigInteger
|
||
|
|
* with a long. Assumes v is not equal to INFLATED.
|
||
|
|
*/
|
||
|
|
BigInteger multiply(long v) {
|
||
|
|
if (v == 0 || signum == 0)
|
||
|
|
return ZERO;
|
||
|
|
if (v == BigDecimal.INFLATED)
|
||
|
|
return multiply(BigInteger.valueOf(v));
|
||
|
|
int rsign = (v > 0 ? signum : -signum);
|
||
|
|
if (v < 0)
|
||
|
|
v = -v;
|
||
|
|
long dh = v >>> 32; // higher order bits
|
||
|
|
long dl = v & LONG_MASK; // lower order bits
|
||
|
|
|
||
|
|
int xlen = mag.length;
|
||
|
|
int[] value = mag;
|
||
|
|
int[] rmag = (dh == 0L) ? (new int[xlen + 1]) : (new int[xlen + 2]);
|
||
|
|
long carry = 0;
|
||
|
|
int rstart = rmag.length - 1;
|
||
|
|
for (int i = xlen - 1; i >= 0; i--) {
|
||
|
|
long product = (value[i] & LONG_MASK) * dl + carry;
|
||
|
|
rmag[rstart--] = (int)product;
|
||
|
|
carry = product >>> 32;
|
||
|
|
}
|
||
|
|
rmag[rstart] = (int)carry;
|
||
|
|
if (dh != 0L) {
|
||
|
|
carry = 0;
|
||
|
|
rstart = rmag.length - 2;
|
||
|
|
for (int i = xlen - 1; i >= 0; i--) {
|
||
|
|
long product = (value[i] & LONG_MASK) * dh +
|
||
|
|
(rmag[rstart] & LONG_MASK) + carry;
|
||
|
|
rmag[rstart--] = (int)product;
|
||
|
|
carry = product >>> 32;
|
||
|
|
}
|
||
|
|
rmag[0] = (int)carry;
|
||
|
|
}
|
||
|
|
if (carry == 0L)
|
||
|
|
rmag = java.util.Arrays.copyOfRange(rmag, 1, rmag.length);
|
||
|
|
return new BigInteger(rmag, rsign);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Multiplies int arrays x and y to the specified lengths and places
|
||
|
|
* the result into z. There will be no leading zeros in the resultant array.
|
||
|
|
*/
|
||
|
|
private static int[] multiplyToLen(int[] x, int xlen, int[] y, int ylen, int[] z) {
|
||
|
|
multiplyToLenCheck(x, xlen);
|
||
|
|
multiplyToLenCheck(y, ylen);
|
||
|
|
return implMultiplyToLen(x, xlen, y, ylen, z);
|
||
|
|
}
|
||
|
|
|
||
|
|
@IntrinsicCandidate
|
||
|
|
private static int[] implMultiplyToLen(int[] x, int xlen, int[] y, int ylen, int[] z) {
|
||
|
|
int xstart = xlen - 1;
|
||
|
|
int ystart = ylen - 1;
|
||
|
|
|
||
|
|
if (z == null || z.length < (xlen+ ylen))
|
||
|
|
z = new int[xlen+ylen];
|
||
|
|
|
||
|
|
long carry = 0;
|
||
|
|
for (int j=ystart, k=ystart+1+xstart; j >= 0; j--, k--) {
|
||
|
|
long product = (y[j] & LONG_MASK) *
|
||
|
|
(x[xstart] & LONG_MASK) + carry;
|
||
|
|
z[k] = (int)product;
|
||
|
|
carry = product >>> 32;
|
||
|
|
}
|
||
|
|
z[xstart] = (int)carry;
|
||
|
|
|
||
|
|
for (int i = xstart-1; i >= 0; i--) {
|
||
|
|
carry = 0;
|
||
|
|
for (int j=ystart, k=ystart+1+i; j >= 0; j--, k--) {
|
||
|
|
long product = (y[j] & LONG_MASK) *
|
||
|
|
(x[i] & LONG_MASK) +
|
||
|
|
(z[k] & LONG_MASK) + carry;
|
||
|
|
z[k] = (int)product;
|
||
|
|
carry = product >>> 32;
|
||
|
|
}
|
||
|
|
z[i] = (int)carry;
|
||
|
|
}
|
||
|
|
return z;
|
||
|
|
}
|
||
|
|
|
||
|
|
private static void multiplyToLenCheck(int[] array, int length) {
|
||
|
|
if (length <= 0) {
|
||
|
|
return; // not an error because multiplyToLen won't execute if len <= 0
|
||
|
|
}
|
||
|
|
|
||
|
|
Objects.requireNonNull(array);
|
||
|
|
|
||
|
|
if (length > array.length) {
|
||
|
|
throw new ArrayIndexOutOfBoundsException(length - 1);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// BEGIN Android-removed: Fall back to boringssl for large problems.
|
||
|
|
/**
|
||
|
|
* Multiplies two BigIntegers using the Karatsuba multiplication
|
||
|
|
* algorithm. This is a recursive divide-and-conquer algorithm which is
|
||
|
|
* more efficient for large numbers than what is commonly called the
|
||
|
|
* "grade-school" algorithm used in multiplyToLen. If the numbers to be
|
||
|
|
* multiplied have length n, the "grade-school" algorithm has an
|
||
|
|
* asymptotic complexity of O(n^2). In contrast, the Karatsuba algorithm
|
||
|
|
* has complexity of O(n^(log2(3))), or O(n^1.585). It achieves this
|
||
|
|
* increased performance by doing 3 multiplies instead of 4 when
|
||
|
|
* evaluating the product. As it has some overhead, should be used when
|
||
|
|
* both numbers are larger than a certain threshold (found
|
||
|
|
* experimentally).
|
||
|
|
*
|
||
|
|
* See: http://en.wikipedia.org/wiki/Karatsuba_algorithm
|
||
|
|
*/
|
||
|
|
/*
|
||
|
|
private static BigInteger multiplyKaratsuba(BigInteger x, BigInteger y) {
|
||
|
|
int xlen = x.mag.length;
|
||
|
|
int ylen = y.mag.length;
|
||
|
|
|
||
|
|
// The number of ints in each half of the number.
|
||
|
|
int half = (Math.max(xlen, ylen)+1) / 2;
|
||
|
|
|
||
|
|
// xl and yl are the lower halves of x and y respectively,
|
||
|
|
// xh and yh are the upper halves.
|
||
|
|
BigInteger xl = x.getLower(half);
|
||
|
|
BigInteger xh = x.getUpper(half);
|
||
|
|
BigInteger yl = y.getLower(half);
|
||
|
|
BigInteger yh = y.getUpper(half);
|
||
|
|
|
||
|
|
BigInteger p1 = xh.multiply(yh); // p1 = xh*yh
|
||
|
|
BigInteger p2 = xl.multiply(yl); // p2 = xl*yl
|
||
|
|
|
||
|
|
// p3=(xh+xl)*(yh+yl)
|
||
|
|
BigInteger p3 = xh.add(xl).multiply(yh.add(yl));
|
||
|
|
|
||
|
|
// result = p1 * 2^(32*2*half) + (p3 - p1 - p2) * 2^(32*half) + p2
|
||
|
|
BigInteger result = p1.shiftLeft(32*half).add(p3.subtract(p1).subtract(p2)).shiftLeft(32*half).add(p2);
|
||
|
|
|
||
|
|
if (x.signum != y.signum) {
|
||
|
|
return result.negate();
|
||
|
|
} else {
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
*/
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Multiplies two BigIntegers using a 3-way Toom-Cook multiplication
|
||
|
|
* algorithm. This is a recursive divide-and-conquer algorithm which is
|
||
|
|
* more efficient for large numbers than what is commonly called the
|
||
|
|
* "grade-school" algorithm used in multiplyToLen. If the numbers to be
|
||
|
|
* multiplied have length n, the "grade-school" algorithm has an
|
||
|
|
* asymptotic complexity of O(n^2). In contrast, 3-way Toom-Cook has a
|
||
|
|
* complexity of about O(n^1.465). It achieves this increased asymptotic
|
||
|
|
* performance by breaking each number into three parts and by doing 5
|
||
|
|
* multiplies instead of 9 when evaluating the product. Due to overhead
|
||
|
|
* (additions, shifts, and one division) in the Toom-Cook algorithm, it
|
||
|
|
* should only be used when both numbers are larger than a certain
|
||
|
|
* threshold (found experimentally). This threshold is generally larger
|
||
|
|
* than that for Karatsuba multiplication, so this algorithm is generally
|
||
|
|
* only used when numbers become significantly larger.
|
||
|
|
*
|
||
|
|
* The algorithm used is the "optimal" 3-way Toom-Cook algorithm outlined
|
||
|
|
* by Marco Bodrato.
|
||
|
|
*
|
||
|
|
* See: http://bodrato.it/toom-cook/
|
||
|
|
* http://bodrato.it/papers/#WAIFI2007
|
||
|
|
*
|
||
|
|
* "Towards Optimal Toom-Cook Multiplication for Univariate and
|
||
|
|
* Multivariate Polynomials in Characteristic 2 and 0." by Marco BODRATO;
|
||
|
|
* In C.Carlet and B.Sunar, Eds., "WAIFI'07 proceedings", p. 116-133,
|
||
|
|
* LNCS #4547. Springer, Madrid, Spain, June 21-22, 2007.
|
||
|
|
*
|
||
|
|
*/
|
||
|
|
/*
|
||
|
|
private static BigInteger multiplyToomCook3(BigInteger a, BigInteger b) {
|
||
|
|
int alen = a.mag.length;
|
||
|
|
int blen = b.mag.length;
|
||
|
|
|
||
|
|
int largest = Math.max(alen, blen);
|
||
|
|
|
||
|
|
// k is the size (in ints) of the lower-order slices.
|
||
|
|
int k = (largest+2)/3; // Equal to ceil(largest/3)
|
||
|
|
|
||
|
|
// r is the size (in ints) of the highest-order slice.
|
||
|
|
int r = largest - 2*k;
|
||
|
|
|
||
|
|
// Obtain slices of the numbers. a2 and b2 are the most significant
|
||
|
|
// bits of the numbers a and b, and a0 and b0 the least significant.
|
||
|
|
BigInteger a0, a1, a2, b0, b1, b2;
|
||
|
|
a2 = a.getToomSlice(k, r, 0, largest);
|
||
|
|
a1 = a.getToomSlice(k, r, 1, largest);
|
||
|
|
a0 = a.getToomSlice(k, r, 2, largest);
|
||
|
|
b2 = b.getToomSlice(k, r, 0, largest);
|
||
|
|
b1 = b.getToomSlice(k, r, 1, largest);
|
||
|
|
b0 = b.getToomSlice(k, r, 2, largest);
|
||
|
|
|
||
|
|
BigInteger v0, v1, v2, vm1, vinf, t1, t2, tm1, da1, db1;
|
||
|
|
|
||
|
|
v0 = a0.multiply(b0, true);
|
||
|
|
da1 = a2.add(a0);
|
||
|
|
db1 = b2.add(b0);
|
||
|
|
vm1 = da1.subtract(a1).multiply(db1.subtract(b1), true);
|
||
|
|
da1 = da1.add(a1);
|
||
|
|
db1 = db1.add(b1);
|
||
|
|
v1 = da1.multiply(db1, true);
|
||
|
|
v2 = da1.add(a2).shiftLeft(1).subtract(a0).multiply(
|
||
|
|
db1.add(b2).shiftLeft(1).subtract(b0), true);
|
||
|
|
vinf = a2.multiply(b2, true);
|
||
|
|
|
||
|
|
// The algorithm requires two divisions by 2 and one by 3.
|
||
|
|
// All divisions are known to be exact, that is, they do not produce
|
||
|
|
// remainders, and all results are positive. The divisions by 2 are
|
||
|
|
// implemented as right shifts which are relatively efficient, leaving
|
||
|
|
// only an exact division by 3, which is done by a specialized
|
||
|
|
// linear-time algorithm.
|
||
|
|
t2 = v2.subtract(vm1).exactDivideBy3();
|
||
|
|
tm1 = v1.subtract(vm1).shiftRight(1);
|
||
|
|
t1 = v1.subtract(v0);
|
||
|
|
t2 = t2.subtract(t1).shiftRight(1);
|
||
|
|
t1 = t1.subtract(tm1).subtract(vinf);
|
||
|
|
t2 = t2.subtract(vinf.shiftLeft(1));
|
||
|
|
tm1 = tm1.subtract(t2);
|
||
|
|
|
||
|
|
// Number of bits to shift left.
|
||
|
|
int ss = k*32;
|
||
|
|
|
||
|
|
BigInteger result = vinf.shiftLeft(ss).add(t2).shiftLeft(ss).add(t1).shiftLeft(ss).add(tm1).shiftLeft(ss).add(v0);
|
||
|
|
|
||
|
|
if (a.signum != b.signum) {
|
||
|
|
return result.negate();
|
||
|
|
} else {
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
*/
|
||
|
|
// END Android-removed: Fall back to boringssl for large problems.
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a slice of a BigInteger for use in Toom-Cook multiplication.
|
||
|
|
*
|
||
|
|
* @param lowerSize The size of the lower-order bit slices.
|
||
|
|
* @param upperSize The size of the higher-order bit slices.
|
||
|
|
* @param slice The index of which slice is requested, which must be a
|
||
|
|
* number from 0 to size-1. Slice 0 is the highest-order bits, and slice
|
||
|
|
* size-1 are the lowest-order bits. Slice 0 may be of different size than
|
||
|
|
* the other slices.
|
||
|
|
* @param fullsize The size of the larger integer array, used to align
|
||
|
|
* slices to the appropriate position when multiplying different-sized
|
||
|
|
* numbers.
|
||
|
|
*/
|
||
|
|
private BigInteger getToomSlice(int lowerSize, int upperSize, int slice,
|
||
|
|
int fullsize) {
|
||
|
|
int start, end, sliceSize, len, offset;
|
||
|
|
|
||
|
|
len = mag.length;
|
||
|
|
offset = fullsize - len;
|
||
|
|
|
||
|
|
if (slice == 0) {
|
||
|
|
start = 0 - offset;
|
||
|
|
end = upperSize - 1 - offset;
|
||
|
|
} else {
|
||
|
|
start = upperSize + (slice-1)*lowerSize - offset;
|
||
|
|
end = start + lowerSize - 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (start < 0) {
|
||
|
|
start = 0;
|
||
|
|
}
|
||
|
|
if (end < 0) {
|
||
|
|
return ZERO;
|
||
|
|
}
|
||
|
|
|
||
|
|
sliceSize = (end-start) + 1;
|
||
|
|
|
||
|
|
if (sliceSize <= 0) {
|
||
|
|
return ZERO;
|
||
|
|
}
|
||
|
|
|
||
|
|
// While performing Toom-Cook, all slices are positive and
|
||
|
|
// the sign is adjusted when the final number is composed.
|
||
|
|
if (start == 0 && sliceSize >= len) {
|
||
|
|
return this.abs();
|
||
|
|
}
|
||
|
|
|
||
|
|
int intSlice[] = new int[sliceSize];
|
||
|
|
System.arraycopy(mag, start, intSlice, 0, sliceSize);
|
||
|
|
|
||
|
|
return new BigInteger(trustedStripLeadingZeroInts(intSlice), 1);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Does an exact division (that is, the remainder is known to be zero)
|
||
|
|
* of the specified number by 3. This is used in Toom-Cook
|
||
|
|
* multiplication. This is an efficient algorithm that runs in linear
|
||
|
|
* time. If the argument is not exactly divisible by 3, results are
|
||
|
|
* undefined. Note that this is expected to be called with positive
|
||
|
|
* arguments only.
|
||
|
|
*/
|
||
|
|
private BigInteger exactDivideBy3() {
|
||
|
|
int len = mag.length;
|
||
|
|
int[] result = new int[len];
|
||
|
|
long x, w, q, borrow;
|
||
|
|
borrow = 0L;
|
||
|
|
for (int i=len-1; i >= 0; i--) {
|
||
|
|
x = (mag[i] & LONG_MASK);
|
||
|
|
w = x - borrow;
|
||
|
|
if (borrow > x) { // Did we make the number go negative?
|
||
|
|
borrow = 1L;
|
||
|
|
} else {
|
||
|
|
borrow = 0L;
|
||
|
|
}
|
||
|
|
|
||
|
|
// 0xAAAAAAAB is the modular inverse of 3 (mod 2^32). Thus,
|
||
|
|
// the effect of this is to divide by 3 (mod 2^32).
|
||
|
|
// This is much faster than division on most architectures.
|
||
|
|
q = (w * 0xAAAAAAABL) & LONG_MASK;
|
||
|
|
result[i] = (int) q;
|
||
|
|
|
||
|
|
// Now check the borrow. The second check can of course be
|
||
|
|
// eliminated if the first fails.
|
||
|
|
if (q >= 0x55555556L) {
|
||
|
|
borrow++;
|
||
|
|
if (q >= 0xAAAAAAABL)
|
||
|
|
borrow++;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
result = trustedStripLeadingZeroInts(result);
|
||
|
|
return new BigInteger(result, signum);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a new BigInteger representing n lower ints of the number.
|
||
|
|
* This is used by Karatsuba multiplication and Karatsuba squaring.
|
||
|
|
*/
|
||
|
|
private BigInteger getLower(int n) {
|
||
|
|
int len = mag.length;
|
||
|
|
|
||
|
|
if (len <= n) {
|
||
|
|
return abs();
|
||
|
|
}
|
||
|
|
|
||
|
|
int lowerInts[] = new int[n];
|
||
|
|
System.arraycopy(mag, len-n, lowerInts, 0, n);
|
||
|
|
|
||
|
|
return new BigInteger(trustedStripLeadingZeroInts(lowerInts), 1);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a new BigInteger representing mag.length-n upper
|
||
|
|
* ints of the number. This is used by Karatsuba multiplication and
|
||
|
|
* Karatsuba squaring.
|
||
|
|
*/
|
||
|
|
private BigInteger getUpper(int n) {
|
||
|
|
int len = mag.length;
|
||
|
|
|
||
|
|
if (len <= n) {
|
||
|
|
return ZERO;
|
||
|
|
}
|
||
|
|
|
||
|
|
int upperLen = len - n;
|
||
|
|
int upperInts[] = new int[upperLen];
|
||
|
|
System.arraycopy(mag, 0, upperInts, 0, upperLen);
|
||
|
|
|
||
|
|
return new BigInteger(trustedStripLeadingZeroInts(upperInts), 1);
|
||
|
|
}
|
||
|
|
|
||
|
|
// Squaring
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this<sup>2</sup>)}.
|
||
|
|
*
|
||
|
|
* @return {@code this<sup>2</sup>}
|
||
|
|
*/
|
||
|
|
private BigInteger square() {
|
||
|
|
return square(false);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this<sup>2</sup>)}. If
|
||
|
|
* the invocation is recursive certain overflow checks are skipped.
|
||
|
|
*
|
||
|
|
* @param isRecursion whether this is a recursive invocation
|
||
|
|
* @return {@code this<sup>2</sup>}
|
||
|
|
*/
|
||
|
|
private BigInteger square(boolean isRecursion) {
|
||
|
|
if (signum == 0) {
|
||
|
|
return ZERO;
|
||
|
|
}
|
||
|
|
int len = mag.length;
|
||
|
|
|
||
|
|
if (len < KARATSUBA_SQUARE_THRESHOLD) {
|
||
|
|
int[] z = squareToLen(mag, len, null);
|
||
|
|
return new BigInteger(trustedStripLeadingZeroInts(z), 1);
|
||
|
|
} else {
|
||
|
|
if (len < TOOM_COOK_SQUARE_THRESHOLD) {
|
||
|
|
return squareKaratsuba();
|
||
|
|
} else {
|
||
|
|
//
|
||
|
|
// For a discussion of overflow detection see multiply()
|
||
|
|
//
|
||
|
|
if (!isRecursion) {
|
||
|
|
if (bitLength(mag, mag.length) > 16L*MAX_MAG_LENGTH) {
|
||
|
|
reportOverflow();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return squareToomCook3();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Squares the contents of the int array x. The result is placed into the
|
||
|
|
* int array z. The contents of x are not changed.
|
||
|
|
*/
|
||
|
|
private static final int[] squareToLen(int[] x, int len, int[] z) {
|
||
|
|
int zlen = len << 1;
|
||
|
|
if (z == null || z.length < zlen)
|
||
|
|
z = new int[zlen];
|
||
|
|
|
||
|
|
// Execute checks before calling intrinsified method.
|
||
|
|
implSquareToLenChecks(x, len, z, zlen);
|
||
|
|
return implSquareToLen(x, len, z, zlen);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Parameters validation.
|
||
|
|
*/
|
||
|
|
private static void implSquareToLenChecks(int[] x, int len, int[] z, int zlen) throws RuntimeException {
|
||
|
|
if (len < 1) {
|
||
|
|
throw new IllegalArgumentException("invalid input length: " + len);
|
||
|
|
}
|
||
|
|
if (len > x.length) {
|
||
|
|
throw new IllegalArgumentException("input length out of bound: " +
|
||
|
|
len + " > " + x.length);
|
||
|
|
}
|
||
|
|
if (len * 2 > z.length) {
|
||
|
|
throw new IllegalArgumentException("input length out of bound: " +
|
||
|
|
(len * 2) + " > " + z.length);
|
||
|
|
}
|
||
|
|
if (zlen < 1) {
|
||
|
|
throw new IllegalArgumentException("invalid input length: " + zlen);
|
||
|
|
}
|
||
|
|
if (zlen > z.length) {
|
||
|
|
throw new IllegalArgumentException("input length out of bound: " +
|
||
|
|
len + " > " + z.length);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Java Runtime may use intrinsic for this method.
|
||
|
|
*/
|
||
|
|
@IntrinsicCandidate
|
||
|
|
private static final int[] implSquareToLen(int[] x, int len, int[] z, int zlen) {
|
||
|
|
/*
|
||
|
|
* The algorithm used here is adapted from Colin Plumb's C library.
|
||
|
|
* Technique: Consider the partial products in the multiplication
|
||
|
|
* of "abcde" by itself:
|
||
|
|
*
|
||
|
|
* a b c d e
|
||
|
|
* * a b c d e
|
||
|
|
* ==================
|
||
|
|
* ae be ce de ee
|
||
|
|
* ad bd cd dd de
|
||
|
|
* ac bc cc cd ce
|
||
|
|
* ab bb bc bd be
|
||
|
|
* aa ab ac ad ae
|
||
|
|
*
|
||
|
|
* Note that everything above the main diagonal:
|
||
|
|
* ae be ce de = (abcd) * e
|
||
|
|
* ad bd cd = (abc) * d
|
||
|
|
* ac bc = (ab) * c
|
||
|
|
* ab = (a) * b
|
||
|
|
*
|
||
|
|
* is a copy of everything below the main diagonal:
|
||
|
|
* de
|
||
|
|
* cd ce
|
||
|
|
* bc bd be
|
||
|
|
* ab ac ad ae
|
||
|
|
*
|
||
|
|
* Thus, the sum is 2 * (off the diagonal) + diagonal.
|
||
|
|
*
|
||
|
|
* This is accumulated beginning with the diagonal (which
|
||
|
|
* consist of the squares of the digits of the input), which is then
|
||
|
|
* divided by two, the off-diagonal added, and multiplied by two
|
||
|
|
* again. The low bit is simply a copy of the low bit of the
|
||
|
|
* input, so it doesn't need special care.
|
||
|
|
*/
|
||
|
|
|
||
|
|
// Store the squares, right shifted one bit (i.e., divided by 2)
|
||
|
|
int lastProductLowWord = 0;
|
||
|
|
for (int j=0, i=0; j < len; j++) {
|
||
|
|
long piece = (x[j] & LONG_MASK);
|
||
|
|
long product = piece * piece;
|
||
|
|
z[i++] = (lastProductLowWord << 31) | (int)(product >>> 33);
|
||
|
|
z[i++] = (int)(product >>> 1);
|
||
|
|
lastProductLowWord = (int)product;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Add in off-diagonal sums
|
||
|
|
for (int i=len, offset=1; i > 0; i--, offset+=2) {
|
||
|
|
int t = x[i-1];
|
||
|
|
t = mulAdd(z, x, offset, i-1, t);
|
||
|
|
addOne(z, offset-1, i, t);
|
||
|
|
}
|
||
|
|
|
||
|
|
// Shift back up and set low bit
|
||
|
|
primitiveLeftShift(z, zlen, 1);
|
||
|
|
z[zlen-1] |= x[len-1] & 1;
|
||
|
|
|
||
|
|
return z;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Squares a BigInteger using the Karatsuba squaring algorithm. It should
|
||
|
|
* be used when both numbers are larger than a certain threshold (found
|
||
|
|
* experimentally). It is a recursive divide-and-conquer algorithm that
|
||
|
|
* has better asymptotic performance than the algorithm used in
|
||
|
|
* squareToLen.
|
||
|
|
*/
|
||
|
|
private BigInteger squareKaratsuba() {
|
||
|
|
int half = (mag.length+1) / 2;
|
||
|
|
|
||
|
|
BigInteger xl = getLower(half);
|
||
|
|
BigInteger xh = getUpper(half);
|
||
|
|
|
||
|
|
BigInteger xhs = xh.square(); // xhs = xh^2
|
||
|
|
BigInteger xls = xl.square(); // xls = xl^2
|
||
|
|
|
||
|
|
// xh^2 << 64 + (((xl+xh)^2 - (xh^2 + xl^2)) << 32) + xl^2
|
||
|
|
return xhs.shiftLeft(half*32).add(xl.add(xh).square().subtract(xhs.add(xls))).shiftLeft(half*32).add(xls);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Squares a BigInteger using the 3-way Toom-Cook squaring algorithm. It
|
||
|
|
* should be used when both numbers are larger than a certain threshold
|
||
|
|
* (found experimentally). It is a recursive divide-and-conquer algorithm
|
||
|
|
* that has better asymptotic performance than the algorithm used in
|
||
|
|
* squareToLen or squareKaratsuba.
|
||
|
|
*/
|
||
|
|
private BigInteger squareToomCook3() {
|
||
|
|
int len = mag.length;
|
||
|
|
|
||
|
|
// k is the size (in ints) of the lower-order slices.
|
||
|
|
int k = (len+2)/3; // Equal to ceil(largest/3)
|
||
|
|
|
||
|
|
// r is the size (in ints) of the highest-order slice.
|
||
|
|
int r = len - 2*k;
|
||
|
|
|
||
|
|
// Obtain slices of the numbers. a2 is the most significant
|
||
|
|
// bits of the number, and a0 the least significant.
|
||
|
|
BigInteger a0, a1, a2;
|
||
|
|
a2 = getToomSlice(k, r, 0, len);
|
||
|
|
a1 = getToomSlice(k, r, 1, len);
|
||
|
|
a0 = getToomSlice(k, r, 2, len);
|
||
|
|
BigInteger v0, v1, v2, vm1, vinf, t1, t2, tm1, da1;
|
||
|
|
|
||
|
|
v0 = a0.square(true);
|
||
|
|
da1 = a2.add(a0);
|
||
|
|
vm1 = da1.subtract(a1).square(true);
|
||
|
|
da1 = da1.add(a1);
|
||
|
|
v1 = da1.square(true);
|
||
|
|
vinf = a2.square(true);
|
||
|
|
v2 = da1.add(a2).shiftLeft(1).subtract(a0).square(true);
|
||
|
|
|
||
|
|
// The algorithm requires two divisions by 2 and one by 3.
|
||
|
|
// All divisions are known to be exact, that is, they do not produce
|
||
|
|
// remainders, and all results are positive. The divisions by 2 are
|
||
|
|
// implemented as right shifts which are relatively efficient, leaving
|
||
|
|
// only a division by 3.
|
||
|
|
// The division by 3 is done by an optimized algorithm for this case.
|
||
|
|
t2 = v2.subtract(vm1).exactDivideBy3();
|
||
|
|
tm1 = v1.subtract(vm1).shiftRight(1);
|
||
|
|
t1 = v1.subtract(v0);
|
||
|
|
t2 = t2.subtract(t1).shiftRight(1);
|
||
|
|
t1 = t1.subtract(tm1).subtract(vinf);
|
||
|
|
t2 = t2.subtract(vinf.shiftLeft(1));
|
||
|
|
tm1 = tm1.subtract(t2);
|
||
|
|
|
||
|
|
// Number of bits to shift left.
|
||
|
|
int ss = k*32;
|
||
|
|
|
||
|
|
return vinf.shiftLeft(ss).add(t2).shiftLeft(ss).add(t1).shiftLeft(ss).add(tm1).shiftLeft(ss).add(v0);
|
||
|
|
}
|
||
|
|
|
||
|
|
// Division
|
||
|
|
|
||
|
|
|
||
|
|
// BEGIN Android-changed: Fall back to boringssl for large problems.
|
||
|
|
private static final int BORINGSSL_DIV_THRESHOLD = 40;
|
||
|
|
private static final int BORINGSSL_DIV_OFFSET = 20;
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this / val)}.
|
||
|
|
*
|
||
|
|
* @param val value by which this BigInteger is to be divided.
|
||
|
|
* @return {@code this / val}
|
||
|
|
* @throws ArithmeticException if {@code val} is zero.
|
||
|
|
*/
|
||
|
|
public BigInteger divide(BigInteger val) {
|
||
|
|
/*
|
||
|
|
if (val.mag.length < BURNIKEL_ZIEGLER_THRESHOLD ||
|
||
|
|
mag.length - val.mag.length < BURNIKEL_ZIEGLER_OFFSET) {
|
||
|
|
*/
|
||
|
|
if (mag.length < BORINGSSL_DIV_THRESHOLD ||
|
||
|
|
mag.length - val.mag.length < BORINGSSL_DIV_OFFSET) {
|
||
|
|
return divideKnuth(val);
|
||
|
|
} else {
|
||
|
|
/*
|
||
|
|
return divideBurnikelZiegler(val);
|
||
|
|
*/
|
||
|
|
return divideAndRemainder(val)[0];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// END Android-changed: Fall back to boringssl for large problems.
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this / val)} using an O(n^2) algorithm from Knuth.
|
||
|
|
*
|
||
|
|
* @param val value by which this BigInteger is to be divided.
|
||
|
|
* @return {@code this / val}
|
||
|
|
* @throws ArithmeticException if {@code val} is zero.
|
||
|
|
* @see MutableBigInteger#divideKnuth(MutableBigInteger, MutableBigInteger, boolean)
|
||
|
|
*/
|
||
|
|
private BigInteger divideKnuth(BigInteger val) {
|
||
|
|
MutableBigInteger q = new MutableBigInteger(),
|
||
|
|
a = new MutableBigInteger(this.mag),
|
||
|
|
b = new MutableBigInteger(val.mag);
|
||
|
|
|
||
|
|
a.divideKnuth(b, q, false);
|
||
|
|
return q.toBigInteger(this.signum * val.signum);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns an array of two BigIntegers containing {@code (this / val)}
|
||
|
|
* followed by {@code (this % val)}.
|
||
|
|
*
|
||
|
|
* @param val value by which this BigInteger is to be divided, and the
|
||
|
|
* remainder computed.
|
||
|
|
* @return an array of two BigIntegers: the quotient {@code (this / val)}
|
||
|
|
* is the initial element, and the remainder {@code (this % val)}
|
||
|
|
* is the final element.
|
||
|
|
* @throws ArithmeticException if {@code val} is zero.
|
||
|
|
*/
|
||
|
|
public BigInteger[] divideAndRemainder(BigInteger val) {
|
||
|
|
// BEGIN Android-changed: Fall back to boringssl for large problems.
|
||
|
|
/*
|
||
|
|
if (val.mag.length < BURNIKEL_ZIEGLER_THRESHOLD ||
|
||
|
|
mag.length - val.mag.length < BURNIKEL_ZIEGLER_OFFSET) {
|
||
|
|
*/
|
||
|
|
if (val.mag.length < BORINGSSL_DIV_THRESHOLD ||
|
||
|
|
mag.length < BORINGSSL_DIV_OFFSET ||
|
||
|
|
mag.length - val.mag.length < BORINGSSL_DIV_OFFSET) {
|
||
|
|
return divideAndRemainderKnuth(val);
|
||
|
|
} else {
|
||
|
|
/*
|
||
|
|
return divideAndRemainderBurnikelZiegler(val);
|
||
|
|
*/
|
||
|
|
int quotSign = signum == val.signum ? 1 : -1; // 0 divided doesn't get here.
|
||
|
|
long xBN = 0, yBN = 0, quotBN = 0, remBN = 0;
|
||
|
|
try {
|
||
|
|
xBN = bigEndInts2NewBN(mag, /* neg= */false);
|
||
|
|
yBN = bigEndInts2NewBN(val.mag, /* neg= */false);
|
||
|
|
quotBN = NativeBN.BN_new();
|
||
|
|
remBN = NativeBN.BN_new();
|
||
|
|
NativeBN.BN_div(quotBN, remBN, xBN, yBN);
|
||
|
|
BigInteger quotient = new BigInteger(quotSign, bn2BigEndInts(quotBN));
|
||
|
|
// The sign of a zero quotient is fixed by the constructor.
|
||
|
|
BigInteger remainder = new BigInteger(signum, bn2BigEndInts(remBN));
|
||
|
|
BigInteger[] result = {quotient, remainder};
|
||
|
|
return result;
|
||
|
|
} finally {
|
||
|
|
NativeBN.BN_free(xBN);
|
||
|
|
NativeBN.BN_free(yBN);
|
||
|
|
NativeBN.BN_free(quotBN);
|
||
|
|
NativeBN.BN_free(remBN);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// END Android-changed: Fall back to boringssl for large problems.
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Long division */
|
||
|
|
private BigInteger[] divideAndRemainderKnuth(BigInteger val) {
|
||
|
|
BigInteger[] result = new BigInteger[2];
|
||
|
|
MutableBigInteger q = new MutableBigInteger(),
|
||
|
|
a = new MutableBigInteger(this.mag),
|
||
|
|
b = new MutableBigInteger(val.mag);
|
||
|
|
MutableBigInteger r = a.divideKnuth(b, q);
|
||
|
|
result[0] = q.toBigInteger(this.signum == val.signum ? 1 : -1);
|
||
|
|
result[1] = r.toBigInteger(this.signum);
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this % val)}.
|
||
|
|
*
|
||
|
|
* @param val value by which this BigInteger is to be divided, and the
|
||
|
|
* remainder computed.
|
||
|
|
* @return {@code this % val}
|
||
|
|
* @throws ArithmeticException if {@code val} is zero.
|
||
|
|
*/
|
||
|
|
public BigInteger remainder(BigInteger val) {
|
||
|
|
// BEGIN Android-changed: Fall back to boringssl for large problems.
|
||
|
|
/*
|
||
|
|
if (val.mag.length < BURNIKEL_ZIEGLER_THRESHOLD ||
|
||
|
|
mag.length - val.mag.length < BURNIKEL_ZIEGLER_OFFSET) {
|
||
|
|
*/
|
||
|
|
if (val.mag.length < BORINGSSL_DIV_THRESHOLD ||
|
||
|
|
mag.length - val.mag.length < BORINGSSL_DIV_THRESHOLD) {
|
||
|
|
return remainderKnuth(val);
|
||
|
|
} else {
|
||
|
|
/*
|
||
|
|
return remainderBurnikelZiegler(val);
|
||
|
|
*/
|
||
|
|
return divideAndRemainder(val)[1];
|
||
|
|
}
|
||
|
|
// END Android-changed: Fall back to boringssl for large problems.
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Long division */
|
||
|
|
private BigInteger remainderKnuth(BigInteger val) {
|
||
|
|
MutableBigInteger q = new MutableBigInteger(),
|
||
|
|
a = new MutableBigInteger(this.mag),
|
||
|
|
b = new MutableBigInteger(val.mag);
|
||
|
|
|
||
|
|
return a.divideKnuth(b, q).toBigInteger(this.signum);
|
||
|
|
}
|
||
|
|
|
||
|
|
// BEGIN Android-removed: Fall back to boringssl for large problems.
|
||
|
|
/**
|
||
|
|
* Calculates {@code this / val} using the Burnikel-Ziegler algorithm.
|
||
|
|
* @param val the divisor
|
||
|
|
* @return {@code this / val}
|
||
|
|
*/
|
||
|
|
/*
|
||
|
|
private BigInteger divideBurnikelZiegler(BigInteger val) {
|
||
|
|
return divideAndRemainderBurnikelZiegler(val)[0];
|
||
|
|
}
|
||
|
|
*/
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Calculates {@code this % val} using the Burnikel-Ziegler algorithm.
|
||
|
|
* @param val the divisor
|
||
|
|
* @return {@code this % val}
|
||
|
|
*/
|
||
|
|
/*
|
||
|
|
private BigInteger remainderBurnikelZiegler(BigInteger val) {
|
||
|
|
return divideAndRemainderBurnikelZiegler(val)[1];
|
||
|
|
}
|
||
|
|
*/
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Computes {@code this / val} and {@code this % val} using the
|
||
|
|
* Burnikel-Ziegler algorithm.
|
||
|
|
* @param val the divisor
|
||
|
|
* @return an array containing the quotient and remainder
|
||
|
|
*/
|
||
|
|
/*
|
||
|
|
private BigInteger[] divideAndRemainderBurnikelZiegler(BigInteger val) {
|
||
|
|
MutableBigInteger q = new MutableBigInteger();
|
||
|
|
MutableBigInteger r = new MutableBigInteger(this).divideAndRemainderBurnikelZiegler(new MutableBigInteger(val), q);
|
||
|
|
BigInteger qBigInt = q.isZero() ? ZERO : q.toBigInteger(signum*val.signum);
|
||
|
|
BigInteger rBigInt = r.isZero() ? ZERO : r.toBigInteger(signum);
|
||
|
|
return new BigInteger[] {qBigInt, rBigInt};
|
||
|
|
}
|
||
|
|
*/
|
||
|
|
// END Android-removed: Fall back to boringssl for large problems.
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is <code>(this<sup>exponent</sup>)</code>.
|
||
|
|
* Note that {@code exponent} is an integer rather than a BigInteger.
|
||
|
|
*
|
||
|
|
* @param exponent exponent to which this BigInteger is to be raised.
|
||
|
|
* @return <code>this<sup>exponent</sup></code>
|
||
|
|
* @throws ArithmeticException {@code exponent} is negative. (This would
|
||
|
|
* cause the operation to yield a non-integer value.)
|
||
|
|
*/
|
||
|
|
public BigInteger pow(int exponent) {
|
||
|
|
if (exponent < 0) {
|
||
|
|
throw new ArithmeticException("Negative exponent");
|
||
|
|
}
|
||
|
|
if (signum == 0) {
|
||
|
|
return (exponent == 0 ? ONE : this);
|
||
|
|
}
|
||
|
|
|
||
|
|
BigInteger partToSquare = this.abs();
|
||
|
|
|
||
|
|
// Factor out powers of two from the base, as the exponentiation of
|
||
|
|
// these can be done by left shifts only.
|
||
|
|
// The remaining part can then be exponentiated faster. The
|
||
|
|
// powers of two will be multiplied back at the end.
|
||
|
|
int powersOfTwo = partToSquare.getLowestSetBit();
|
||
|
|
long bitsToShiftLong = (long)powersOfTwo * exponent;
|
||
|
|
if (bitsToShiftLong > Integer.MAX_VALUE) {
|
||
|
|
reportOverflow();
|
||
|
|
}
|
||
|
|
int bitsToShift = (int)bitsToShiftLong;
|
||
|
|
|
||
|
|
int remainingBits;
|
||
|
|
|
||
|
|
// Factor the powers of two out quickly by shifting right, if needed.
|
||
|
|
if (powersOfTwo > 0) {
|
||
|
|
partToSquare = partToSquare.shiftRight(powersOfTwo);
|
||
|
|
remainingBits = partToSquare.bitLength();
|
||
|
|
if (remainingBits == 1) { // Nothing left but +/- 1?
|
||
|
|
if (signum < 0 && (exponent&1) == 1) {
|
||
|
|
return NEGATIVE_ONE.shiftLeft(bitsToShift);
|
||
|
|
} else {
|
||
|
|
return ONE.shiftLeft(bitsToShift);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
remainingBits = partToSquare.bitLength();
|
||
|
|
if (remainingBits == 1) { // Nothing left but +/- 1?
|
||
|
|
if (signum < 0 && (exponent&1) == 1) {
|
||
|
|
return NEGATIVE_ONE;
|
||
|
|
} else {
|
||
|
|
return ONE;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// This is a quick way to approximate the size of the result,
|
||
|
|
// similar to doing log2[n] * exponent. This will give an upper bound
|
||
|
|
// of how big the result can be, and which algorithm to use.
|
||
|
|
long scaleFactor = (long)remainingBits * exponent;
|
||
|
|
|
||
|
|
// Use slightly different algorithms for small and large operands.
|
||
|
|
// See if the result will safely fit into a long. (Largest 2^63-1)
|
||
|
|
if (partToSquare.mag.length == 1 && scaleFactor <= 62) {
|
||
|
|
// Small number algorithm. Everything fits into a long.
|
||
|
|
int newSign = (signum <0 && (exponent&1) == 1 ? -1 : 1);
|
||
|
|
long result = 1;
|
||
|
|
long baseToPow2 = partToSquare.mag[0] & LONG_MASK;
|
||
|
|
|
||
|
|
int workingExponent = exponent;
|
||
|
|
|
||
|
|
// Perform exponentiation using repeated squaring trick
|
||
|
|
while (workingExponent != 0) {
|
||
|
|
if ((workingExponent & 1) == 1) {
|
||
|
|
result = result * baseToPow2;
|
||
|
|
}
|
||
|
|
|
||
|
|
if ((workingExponent >>>= 1) != 0) {
|
||
|
|
baseToPow2 = baseToPow2 * baseToPow2;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// Multiply back the powers of two (quickly, by shifting left)
|
||
|
|
if (powersOfTwo > 0) {
|
||
|
|
if (bitsToShift + scaleFactor <= 62) { // Fits in long?
|
||
|
|
return valueOf((result << bitsToShift) * newSign);
|
||
|
|
} else {
|
||
|
|
return valueOf(result*newSign).shiftLeft(bitsToShift);
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
return valueOf(result*newSign);
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
if ((long)bitLength() * exponent / Integer.SIZE > MAX_MAG_LENGTH) {
|
||
|
|
reportOverflow();
|
||
|
|
}
|
||
|
|
|
||
|
|
// Large number algorithm. This is basically identical to
|
||
|
|
// the algorithm above, but calls multiply() and square()
|
||
|
|
// which may use more efficient algorithms for large numbers.
|
||
|
|
BigInteger answer = ONE;
|
||
|
|
|
||
|
|
int workingExponent = exponent;
|
||
|
|
// Perform exponentiation using repeated squaring trick
|
||
|
|
while (workingExponent != 0) {
|
||
|
|
if ((workingExponent & 1) == 1) {
|
||
|
|
answer = answer.multiply(partToSquare);
|
||
|
|
}
|
||
|
|
|
||
|
|
if ((workingExponent >>>= 1) != 0) {
|
||
|
|
partToSquare = partToSquare.square();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// Multiply back the (exponentiated) powers of two (quickly,
|
||
|
|
// by shifting left)
|
||
|
|
if (powersOfTwo > 0) {
|
||
|
|
answer = answer.shiftLeft(bitsToShift);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (signum < 0 && (exponent&1) == 1) {
|
||
|
|
return answer.negate();
|
||
|
|
} else {
|
||
|
|
return answer;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the integer square root of this BigInteger. The integer square
|
||
|
|
* root of the corresponding mathematical integer {@code n} is the largest
|
||
|
|
* mathematical integer {@code s} such that {@code s*s <= n}. It is equal
|
||
|
|
* to the value of {@code floor(sqrt(n))}, where {@code sqrt(n)} denotes the
|
||
|
|
* real square root of {@code n} treated as a real. Note that the integer
|
||
|
|
* square root will be less than the real square root if the latter is not
|
||
|
|
* representable as an integral value.
|
||
|
|
*
|
||
|
|
* @return the integer square root of {@code this}
|
||
|
|
* @throws ArithmeticException if {@code this} is negative. (The square
|
||
|
|
* root of a negative integer {@code val} is
|
||
|
|
* {@code (i * sqrt(-val))} where <i>i</i> is the
|
||
|
|
* <i>imaginary unit</i> and is equal to
|
||
|
|
* {@code sqrt(-1)}.)
|
||
|
|
* @since 9
|
||
|
|
*/
|
||
|
|
public BigInteger sqrt() {
|
||
|
|
if (this.signum < 0) {
|
||
|
|
throw new ArithmeticException("Negative BigInteger");
|
||
|
|
}
|
||
|
|
|
||
|
|
return new MutableBigInteger(this.mag).sqrt().toBigInteger();
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns an array of two BigIntegers containing the integer square root
|
||
|
|
* {@code s} of {@code this} and its remainder {@code this - s*s},
|
||
|
|
* respectively.
|
||
|
|
*
|
||
|
|
* @return an array of two BigIntegers with the integer square root at
|
||
|
|
* offset 0 and the remainder at offset 1
|
||
|
|
* @throws ArithmeticException if {@code this} is negative. (The square
|
||
|
|
* root of a negative integer {@code val} is
|
||
|
|
* {@code (i * sqrt(-val))} where <i>i</i> is the
|
||
|
|
* <i>imaginary unit</i> and is equal to
|
||
|
|
* {@code sqrt(-1)}.)
|
||
|
|
* @see #sqrt()
|
||
|
|
* @since 9
|
||
|
|
*/
|
||
|
|
public BigInteger[] sqrtAndRemainder() {
|
||
|
|
BigInteger s = sqrt();
|
||
|
|
BigInteger r = this.subtract(s.square());
|
||
|
|
assert r.compareTo(BigInteger.ZERO) >= 0;
|
||
|
|
return new BigInteger[] {s, r};
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is the greatest common divisor of
|
||
|
|
* {@code abs(this)} and {@code abs(val)}. Returns 0 if
|
||
|
|
* {@code this == 0 && val == 0}.
|
||
|
|
*
|
||
|
|
* @param val value with which the GCD is to be computed.
|
||
|
|
* @return {@code GCD(abs(this), abs(val))}
|
||
|
|
*/
|
||
|
|
public BigInteger gcd(BigInteger val) {
|
||
|
|
if (val.signum == 0)
|
||
|
|
return this.abs();
|
||
|
|
else if (this.signum == 0)
|
||
|
|
return val.abs();
|
||
|
|
|
||
|
|
MutableBigInteger a = new MutableBigInteger(this);
|
||
|
|
MutableBigInteger b = new MutableBigInteger(val);
|
||
|
|
|
||
|
|
MutableBigInteger result = a.hybridGCD(b);
|
||
|
|
|
||
|
|
return result.toBigInteger(1);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Package private method to return bit length for an integer.
|
||
|
|
*/
|
||
|
|
static int bitLengthForInt(int n) {
|
||
|
|
return 32 - Integer.numberOfLeadingZeros(n);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Left shift int array a up to len by n bits. Returns the array that
|
||
|
|
* results from the shift since space may have to be reallocated.
|
||
|
|
*/
|
||
|
|
private static int[] leftShift(int[] a, int len, int n) {
|
||
|
|
int nInts = n >>> 5;
|
||
|
|
int nBits = n&0x1F;
|
||
|
|
int bitsInHighWord = bitLengthForInt(a[0]);
|
||
|
|
|
||
|
|
// If shift can be done without recopy, do so
|
||
|
|
if (n <= (32-bitsInHighWord)) {
|
||
|
|
primitiveLeftShift(a, len, nBits);
|
||
|
|
return a;
|
||
|
|
} else { // Array must be resized
|
||
|
|
if (nBits <= (32-bitsInHighWord)) {
|
||
|
|
int result[] = new int[nInts+len];
|
||
|
|
System.arraycopy(a, 0, result, 0, len);
|
||
|
|
primitiveLeftShift(result, result.length, nBits);
|
||
|
|
return result;
|
||
|
|
} else {
|
||
|
|
int result[] = new int[nInts+len+1];
|
||
|
|
System.arraycopy(a, 0, result, 0, len);
|
||
|
|
primitiveRightShift(result, result.length, 32 - nBits);
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// shifts a up to len right n bits assumes no leading zeros, 0<n<32
|
||
|
|
static void primitiveRightShift(int[] a, int len, int n) {
|
||
|
|
Objects.checkFromToIndex(0, len, a.length);
|
||
|
|
shiftRightImplWorker(a, a, 1, n, len-1);
|
||
|
|
a[0] >>>= n;
|
||
|
|
}
|
||
|
|
|
||
|
|
// shifts a up to len left n bits assumes no leading zeros, 0<=n<32
|
||
|
|
static void primitiveLeftShift(int[] a, int len, int n) {
|
||
|
|
if (len == 0 || n == 0)
|
||
|
|
return;
|
||
|
|
Objects.checkFromToIndex(0, len, a.length);
|
||
|
|
shiftLeftImplWorker(a, a, 0, n, len-1);
|
||
|
|
a[len-1] <<= n;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Calculate bitlength of contents of the first len elements an int array,
|
||
|
|
* assuming there are no leading zero ints.
|
||
|
|
*/
|
||
|
|
private static int bitLength(int[] val, int len) {
|
||
|
|
if (len == 0)
|
||
|
|
return 0;
|
||
|
|
return ((len - 1) << 5) + bitLengthForInt(val[0]);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is the absolute value of this
|
||
|
|
* BigInteger.
|
||
|
|
*
|
||
|
|
* @return {@code abs(this)}
|
||
|
|
*/
|
||
|
|
public BigInteger abs() {
|
||
|
|
return (signum >= 0 ? this : this.negate());
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (-this)}.
|
||
|
|
*
|
||
|
|
* @return {@code -this}
|
||
|
|
*/
|
||
|
|
public BigInteger negate() {
|
||
|
|
return new BigInteger(this.mag, -this.signum);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the signum function of this BigInteger.
|
||
|
|
*
|
||
|
|
* @return -1, 0 or 1 as the value of this BigInteger is negative, zero or
|
||
|
|
* positive.
|
||
|
|
*/
|
||
|
|
public int signum() {
|
||
|
|
return this.signum;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Modular Arithmetic Operations
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this mod m}). This method
|
||
|
|
* differs from {@code remainder} in that it always returns a
|
||
|
|
* <i>non-negative</i> BigInteger.
|
||
|
|
*
|
||
|
|
* @param m the modulus.
|
||
|
|
* @return {@code this mod m}
|
||
|
|
* @throws ArithmeticException {@code m} ≤ 0
|
||
|
|
* @see #remainder
|
||
|
|
*/
|
||
|
|
public BigInteger mod(BigInteger m) {
|
||
|
|
if (m.signum <= 0)
|
||
|
|
throw new ArithmeticException("BigInteger: modulus not positive");
|
||
|
|
|
||
|
|
BigInteger result = this.remainder(m);
|
||
|
|
return (result.signum >= 0 ? result : result.add(m));
|
||
|
|
}
|
||
|
|
|
||
|
|
// BEGIN Android-added: Support fallback to boringssl where it makes sense.
|
||
|
|
// The conversion itself takes linear time, so this only makes sense for largish superlinear
|
||
|
|
// operations.
|
||
|
|
|
||
|
|
private static int[] reverse(int[] arg) {
|
||
|
|
int len = arg.length;
|
||
|
|
int[] result = new int[len];
|
||
|
|
for (int i = 0; i < len; ++i) {
|
||
|
|
result[i] = arg[len - i - 1];
|
||
|
|
}
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
private static long /* BN */ bigEndInts2NewBN(int[] beArray, boolean neg) {
|
||
|
|
// The input is an array of ints arranged in big-endian order, i.e. most significant int
|
||
|
|
// first. BN deals with big-endian or little-endian byte arrays, so we need to reverse order.
|
||
|
|
int[] leArray = reverse(beArray);
|
||
|
|
long resultBN = NativeBN.BN_new();
|
||
|
|
NativeBN.litEndInts2bn(leArray, leArray.length, neg, resultBN);
|
||
|
|
return resultBN;
|
||
|
|
}
|
||
|
|
|
||
|
|
private int[] bn2BigEndInts(long bn) {
|
||
|
|
return reverse(NativeBN.bn2litEndInts(bn));
|
||
|
|
}
|
||
|
|
|
||
|
|
// END Android-added: Support fallback to boringssl.
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is
|
||
|
|
* <code>(this<sup>exponent</sup> mod m)</code>. (Unlike {@code pow}, this
|
||
|
|
* method permits negative exponents.)
|
||
|
|
*
|
||
|
|
* @param exponent the exponent.
|
||
|
|
* @param m the modulus.
|
||
|
|
* @return <code>this<sup>exponent</sup> mod m</code>
|
||
|
|
* @throws ArithmeticException {@code m} ≤ 0 or the exponent is
|
||
|
|
* negative and this BigInteger is not <i>relatively
|
||
|
|
* prime</i> to {@code m}.
|
||
|
|
* @see #modInverse
|
||
|
|
*/
|
||
|
|
public BigInteger modPow(BigInteger exponent, BigInteger m) {
|
||
|
|
if (m.signum <= 0)
|
||
|
|
throw new ArithmeticException("BigInteger: modulus not positive");
|
||
|
|
|
||
|
|
// Trivial cases
|
||
|
|
if (exponent.signum == 0)
|
||
|
|
return (m.equals(ONE) ? ZERO : ONE);
|
||
|
|
|
||
|
|
if (this.equals(ONE))
|
||
|
|
return (m.equals(ONE) ? ZERO : ONE);
|
||
|
|
|
||
|
|
if (this.equals(ZERO) && exponent.signum >= 0)
|
||
|
|
return ZERO;
|
||
|
|
|
||
|
|
if (this.equals(negConst[1]) && (!exponent.testBit(0)))
|
||
|
|
return (m.equals(ONE) ? ZERO : ONE);
|
||
|
|
|
||
|
|
boolean invertResult;
|
||
|
|
if ((invertResult = (exponent.signum < 0)))
|
||
|
|
exponent = exponent.negate();
|
||
|
|
|
||
|
|
BigInteger base = (this.signum < 0 || this.compareTo(m) >= 0
|
||
|
|
? this.mod(m) : this);
|
||
|
|
BigInteger result;
|
||
|
|
// BEGIN Android-added: Fall back to the boringssl implementation, which
|
||
|
|
// is usually faster.
|
||
|
|
final int BORINGSSL_MOD_EXP_THRESHOLD = 3;
|
||
|
|
if (m.mag.length >= BORINGSSL_MOD_EXP_THRESHOLD) {
|
||
|
|
long baseBN = 0, expBN = 0, modBN = 0, resultBN = 0;
|
||
|
|
try {
|
||
|
|
baseBN = bigEndInts2NewBN(base.mag, /* neg= */false);
|
||
|
|
expBN = bigEndInts2NewBN(exponent.mag, /* neg= */false);
|
||
|
|
modBN = bigEndInts2NewBN(m.mag, /* neg= */false);
|
||
|
|
resultBN = NativeBN.BN_new();
|
||
|
|
NativeBN.BN_mod_exp(resultBN, baseBN, expBN, modBN);
|
||
|
|
result = new BigInteger(1, bn2BigEndInts(resultBN));
|
||
|
|
// The sign of a zero result is fixed by the constructor.
|
||
|
|
return (invertResult ? result.modInverse(m) : result);
|
||
|
|
} finally {
|
||
|
|
NativeBN.BN_free(baseBN);
|
||
|
|
NativeBN.BN_free(expBN);
|
||
|
|
NativeBN.BN_free(modBN);
|
||
|
|
NativeBN.BN_free(resultBN);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// END Android-added: Fall back to the boringssl implementation.
|
||
|
|
if (m.testBit(0)) { // odd modulus
|
||
|
|
result = base.oddModPow(exponent, m);
|
||
|
|
} else {
|
||
|
|
/*
|
||
|
|
* Even modulus. Tear it into an "odd part" (m1) and power of two
|
||
|
|
* (m2), exponentiate mod m1, manually exponentiate mod m2, and
|
||
|
|
* use Chinese Remainder Theorem to combine results.
|
||
|
|
*/
|
||
|
|
|
||
|
|
// Tear m apart into odd part (m1) and power of 2 (m2)
|
||
|
|
int p = m.getLowestSetBit(); // Max pow of 2 that divides m
|
||
|
|
|
||
|
|
BigInteger m1 = m.shiftRight(p); // m/2**p
|
||
|
|
BigInteger m2 = ONE.shiftLeft(p); // 2**p
|
||
|
|
|
||
|
|
// Calculate new base from m1
|
||
|
|
BigInteger base2 = (this.signum < 0 || this.compareTo(m1) >= 0
|
||
|
|
? this.mod(m1) : this);
|
||
|
|
|
||
|
|
// Calculate (base ** exponent) mod m1.
|
||
|
|
BigInteger a1 = (m1.equals(ONE) ? ZERO :
|
||
|
|
base2.oddModPow(exponent, m1));
|
||
|
|
|
||
|
|
// Calculate (this ** exponent) mod m2
|
||
|
|
BigInteger a2 = base.modPow2(exponent, p);
|
||
|
|
|
||
|
|
// Combine results using Chinese Remainder Theorem
|
||
|
|
BigInteger y1 = m2.modInverse(m1);
|
||
|
|
BigInteger y2 = m1.modInverse(m2);
|
||
|
|
|
||
|
|
if (m.mag.length < MAX_MAG_LENGTH / 2) {
|
||
|
|
result = a1.multiply(m2).multiply(y1).add(a2.multiply(m1).multiply(y2)).mod(m);
|
||
|
|
} else {
|
||
|
|
MutableBigInteger t1 = new MutableBigInteger();
|
||
|
|
new MutableBigInteger(a1.multiply(m2)).multiply(new MutableBigInteger(y1), t1);
|
||
|
|
MutableBigInteger t2 = new MutableBigInteger();
|
||
|
|
new MutableBigInteger(a2.multiply(m1)).multiply(new MutableBigInteger(y2), t2);
|
||
|
|
t1.add(t2);
|
||
|
|
MutableBigInteger q = new MutableBigInteger();
|
||
|
|
result = t1.divide(new MutableBigInteger(m), q).toBigInteger();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return (invertResult ? result.modInverse(m) : result);
|
||
|
|
}
|
||
|
|
|
||
|
|
// Montgomery multiplication. These are wrappers for
|
||
|
|
// implMontgomeryXX routines which are expected to be replaced by
|
||
|
|
// virtual machine intrinsics. We don't use the intrinsics for
|
||
|
|
// very large operands: MONTGOMERY_INTRINSIC_THRESHOLD should be
|
||
|
|
// larger than any reasonable crypto key.
|
||
|
|
private static int[] montgomeryMultiply(int[] a, int[] b, int[] n, int len, long inv,
|
||
|
|
int[] product) {
|
||
|
|
implMontgomeryMultiplyChecks(a, b, n, len, product);
|
||
|
|
if (len > MONTGOMERY_INTRINSIC_THRESHOLD) {
|
||
|
|
// Very long argument: do not use an intrinsic
|
||
|
|
product = multiplyToLen(a, len, b, len, product);
|
||
|
|
return montReduce(product, n, len, (int)inv);
|
||
|
|
} else {
|
||
|
|
return implMontgomeryMultiply(a, b, n, len, inv, materialize(product, len));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
private static int[] montgomerySquare(int[] a, int[] n, int len, long inv,
|
||
|
|
int[] product) {
|
||
|
|
implMontgomeryMultiplyChecks(a, a, n, len, product);
|
||
|
|
if (len > MONTGOMERY_INTRINSIC_THRESHOLD) {
|
||
|
|
// Very long argument: do not use an intrinsic
|
||
|
|
product = squareToLen(a, len, product);
|
||
|
|
return montReduce(product, n, len, (int)inv);
|
||
|
|
} else {
|
||
|
|
return implMontgomerySquare(a, n, len, inv, materialize(product, len));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// Range-check everything.
|
||
|
|
private static void implMontgomeryMultiplyChecks
|
||
|
|
(int[] a, int[] b, int[] n, int len, int[] product) throws RuntimeException {
|
||
|
|
if (len % 2 != 0) {
|
||
|
|
throw new IllegalArgumentException("input array length must be even: " + len);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (len < 1) {
|
||
|
|
throw new IllegalArgumentException("invalid input length: " + len);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (len > a.length ||
|
||
|
|
len > b.length ||
|
||
|
|
len > n.length ||
|
||
|
|
(product != null && len > product.length)) {
|
||
|
|
throw new IllegalArgumentException("input array length out of bound: " + len);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// Make sure that the int array z (which is expected to contain
|
||
|
|
// the result of a Montgomery multiplication) is present and
|
||
|
|
// sufficiently large.
|
||
|
|
private static int[] materialize(int[] z, int len) {
|
||
|
|
if (z == null || z.length < len)
|
||
|
|
z = new int[len];
|
||
|
|
return z;
|
||
|
|
}
|
||
|
|
|
||
|
|
// These methods are intended to be replaced by virtual machine
|
||
|
|
// intrinsics.
|
||
|
|
@IntrinsicCandidate
|
||
|
|
private static int[] implMontgomeryMultiply(int[] a, int[] b, int[] n, int len,
|
||
|
|
long inv, int[] product) {
|
||
|
|
product = multiplyToLen(a, len, b, len, product);
|
||
|
|
return montReduce(product, n, len, (int)inv);
|
||
|
|
}
|
||
|
|
@IntrinsicCandidate
|
||
|
|
private static int[] implMontgomerySquare(int[] a, int[] n, int len,
|
||
|
|
long inv, int[] product) {
|
||
|
|
product = squareToLen(a, len, product);
|
||
|
|
return montReduce(product, n, len, (int)inv);
|
||
|
|
}
|
||
|
|
|
||
|
|
static int[] bnExpModThreshTable = {7, 25, 81, 241, 673, 1793,
|
||
|
|
Integer.MAX_VALUE}; // Sentinel
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is x to the power of y mod z.
|
||
|
|
* Assumes: z is odd && x < z.
|
||
|
|
*/
|
||
|
|
private BigInteger oddModPow(BigInteger y, BigInteger z) {
|
||
|
|
/*
|
||
|
|
* The algorithm is adapted from Colin Plumb's C library.
|
||
|
|
*
|
||
|
|
* The window algorithm:
|
||
|
|
* The idea is to keep a running product of b1 = n^(high-order bits of exp)
|
||
|
|
* and then keep appending exponent bits to it. The following patterns
|
||
|
|
* apply to a 3-bit window (k = 3):
|
||
|
|
* To append 0: square
|
||
|
|
* To append 1: square, multiply by n^1
|
||
|
|
* To append 10: square, multiply by n^1, square
|
||
|
|
* To append 11: square, square, multiply by n^3
|
||
|
|
* To append 100: square, multiply by n^1, square, square
|
||
|
|
* To append 101: square, square, square, multiply by n^5
|
||
|
|
* To append 110: square, square, multiply by n^3, square
|
||
|
|
* To append 111: square, square, square, multiply by n^7
|
||
|
|
*
|
||
|
|
* Since each pattern involves only one multiply, the longer the pattern
|
||
|
|
* the better, except that a 0 (no multiplies) can be appended directly.
|
||
|
|
* We precompute a table of odd powers of n, up to 2^k, and can then
|
||
|
|
* multiply k bits of exponent at a time. Actually, assuming random
|
||
|
|
* exponents, there is on average one zero bit between needs to
|
||
|
|
* multiply (1/2 of the time there's none, 1/4 of the time there's 1,
|
||
|
|
* 1/8 of the time, there's 2, 1/32 of the time, there's 3, etc.), so
|
||
|
|
* you have to do one multiply per k+1 bits of exponent.
|
||
|
|
*
|
||
|
|
* The loop walks down the exponent, squaring the result buffer as
|
||
|
|
* it goes. There is a wbits+1 bit lookahead buffer, buf, that is
|
||
|
|
* filled with the upcoming exponent bits. (What is read after the
|
||
|
|
* end of the exponent is unimportant, but it is filled with zero here.)
|
||
|
|
* When the most-significant bit of this buffer becomes set, i.e.
|
||
|
|
* (buf & tblmask) != 0, we have to decide what pattern to multiply
|
||
|
|
* by, and when to do it. We decide, remember to do it in future
|
||
|
|
* after a suitable number of squarings have passed (e.g. a pattern
|
||
|
|
* of "100" in the buffer requires that we multiply by n^1 immediately;
|
||
|
|
* a pattern of "110" calls for multiplying by n^3 after one more
|
||
|
|
* squaring), clear the buffer, and continue.
|
||
|
|
*
|
||
|
|
* When we start, there is one more optimization: the result buffer
|
||
|
|
* is implcitly one, so squaring it or multiplying by it can be
|
||
|
|
* optimized away. Further, if we start with a pattern like "100"
|
||
|
|
* in the lookahead window, rather than placing n into the buffer
|
||
|
|
* and then starting to square it, we have already computed n^2
|
||
|
|
* to compute the odd-powers table, so we can place that into
|
||
|
|
* the buffer and save a squaring.
|
||
|
|
*
|
||
|
|
* This means that if you have a k-bit window, to compute n^z,
|
||
|
|
* where z is the high k bits of the exponent, 1/2 of the time
|
||
|
|
* it requires no squarings. 1/4 of the time, it requires 1
|
||
|
|
* squaring, ... 1/2^(k-1) of the time, it requires k-2 squarings.
|
||
|
|
* And the remaining 1/2^(k-1) of the time, the top k bits are a
|
||
|
|
* 1 followed by k-1 0 bits, so it again only requires k-2
|
||
|
|
* squarings, not k-1. The average of these is 1. Add that
|
||
|
|
* to the one squaring we have to do to compute the table,
|
||
|
|
* and you'll see that a k-bit window saves k-2 squarings
|
||
|
|
* as well as reducing the multiplies. (It actually doesn't
|
||
|
|
* hurt in the case k = 1, either.)
|
||
|
|
*/
|
||
|
|
// Special case for exponent of one
|
||
|
|
if (y.equals(ONE))
|
||
|
|
return this;
|
||
|
|
|
||
|
|
// Special case for base of zero
|
||
|
|
if (signum == 0)
|
||
|
|
return ZERO;
|
||
|
|
|
||
|
|
int[] base = mag.clone();
|
||
|
|
int[] exp = y.mag;
|
||
|
|
int[] mod = z.mag;
|
||
|
|
int modLen = mod.length;
|
||
|
|
|
||
|
|
// Make modLen even. It is conventional to use a cryptographic
|
||
|
|
// modulus that is 512, 768, 1024, or 2048 bits, so this code
|
||
|
|
// will not normally be executed. However, it is necessary for
|
||
|
|
// the correct functioning of the HotSpot intrinsics.
|
||
|
|
if ((modLen & 1) != 0) {
|
||
|
|
int[] x = new int[modLen + 1];
|
||
|
|
System.arraycopy(mod, 0, x, 1, modLen);
|
||
|
|
mod = x;
|
||
|
|
modLen++;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Select an appropriate window size
|
||
|
|
int wbits = 0;
|
||
|
|
int ebits = bitLength(exp, exp.length);
|
||
|
|
// if exponent is 65537 (0x10001), use minimum window size
|
||
|
|
if ((ebits != 17) || (exp[0] != 65537)) {
|
||
|
|
while (ebits > bnExpModThreshTable[wbits]) {
|
||
|
|
wbits++;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// Calculate appropriate table size
|
||
|
|
int tblmask = 1 << wbits;
|
||
|
|
|
||
|
|
// Allocate table for precomputed odd powers of base in Montgomery form
|
||
|
|
int[][] table = new int[tblmask][];
|
||
|
|
for (int i=0; i < tblmask; i++)
|
||
|
|
table[i] = new int[modLen];
|
||
|
|
|
||
|
|
// Compute the modular inverse of the least significant 64-bit
|
||
|
|
// digit of the modulus
|
||
|
|
long n0 = (mod[modLen-1] & LONG_MASK) + ((mod[modLen-2] & LONG_MASK) << 32);
|
||
|
|
long inv = -MutableBigInteger.inverseMod64(n0);
|
||
|
|
|
||
|
|
// Convert base to Montgomery form
|
||
|
|
int[] a = leftShift(base, base.length, modLen << 5);
|
||
|
|
|
||
|
|
MutableBigInteger q = new MutableBigInteger(),
|
||
|
|
a2 = new MutableBigInteger(a),
|
||
|
|
b2 = new MutableBigInteger(mod);
|
||
|
|
b2.normalize(); // MutableBigInteger.divide() assumes that its
|
||
|
|
// divisor is in normal form.
|
||
|
|
|
||
|
|
MutableBigInteger r= a2.divide(b2, q);
|
||
|
|
table[0] = r.toIntArray();
|
||
|
|
|
||
|
|
// Pad table[0] with leading zeros so its length is at least modLen
|
||
|
|
if (table[0].length < modLen) {
|
||
|
|
int offset = modLen - table[0].length;
|
||
|
|
int[] t2 = new int[modLen];
|
||
|
|
System.arraycopy(table[0], 0, t2, offset, table[0].length);
|
||
|
|
table[0] = t2;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Set b to the square of the base
|
||
|
|
int[] b = montgomerySquare(table[0], mod, modLen, inv, null);
|
||
|
|
|
||
|
|
// Set t to high half of b
|
||
|
|
int[] t = Arrays.copyOf(b, modLen);
|
||
|
|
|
||
|
|
// Fill in the table with odd powers of the base
|
||
|
|
for (int i=1; i < tblmask; i++) {
|
||
|
|
table[i] = montgomeryMultiply(t, table[i-1], mod, modLen, inv, null);
|
||
|
|
}
|
||
|
|
|
||
|
|
// Pre load the window that slides over the exponent
|
||
|
|
int bitpos = 1 << ((ebits-1) & (32-1));
|
||
|
|
|
||
|
|
int buf = 0;
|
||
|
|
int elen = exp.length;
|
||
|
|
int eIndex = 0;
|
||
|
|
for (int i = 0; i <= wbits; i++) {
|
||
|
|
buf = (buf << 1) | (((exp[eIndex] & bitpos) != 0)?1:0);
|
||
|
|
bitpos >>>= 1;
|
||
|
|
if (bitpos == 0) {
|
||
|
|
eIndex++;
|
||
|
|
bitpos = 1 << (32-1);
|
||
|
|
elen--;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
int multpos = ebits;
|
||
|
|
|
||
|
|
// The first iteration, which is hoisted out of the main loop
|
||
|
|
ebits--;
|
||
|
|
boolean isone = true;
|
||
|
|
|
||
|
|
multpos = ebits - wbits;
|
||
|
|
while ((buf & 1) == 0) {
|
||
|
|
buf >>>= 1;
|
||
|
|
multpos++;
|
||
|
|
}
|
||
|
|
|
||
|
|
int[] mult = table[buf >>> 1];
|
||
|
|
|
||
|
|
buf = 0;
|
||
|
|
if (multpos == ebits)
|
||
|
|
isone = false;
|
||
|
|
|
||
|
|
// The main loop
|
||
|
|
while (true) {
|
||
|
|
ebits--;
|
||
|
|
// Advance the window
|
||
|
|
buf <<= 1;
|
||
|
|
|
||
|
|
if (elen != 0) {
|
||
|
|
buf |= ((exp[eIndex] & bitpos) != 0) ? 1 : 0;
|
||
|
|
bitpos >>>= 1;
|
||
|
|
if (bitpos == 0) {
|
||
|
|
eIndex++;
|
||
|
|
bitpos = 1 << (32-1);
|
||
|
|
elen--;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// Examine the window for pending multiplies
|
||
|
|
if ((buf & tblmask) != 0) {
|
||
|
|
multpos = ebits - wbits;
|
||
|
|
while ((buf & 1) == 0) {
|
||
|
|
buf >>>= 1;
|
||
|
|
multpos++;
|
||
|
|
}
|
||
|
|
mult = table[buf >>> 1];
|
||
|
|
buf = 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Perform multiply
|
||
|
|
if (ebits == multpos) {
|
||
|
|
if (isone) {
|
||
|
|
b = mult.clone();
|
||
|
|
isone = false;
|
||
|
|
} else {
|
||
|
|
t = b;
|
||
|
|
a = montgomeryMultiply(t, mult, mod, modLen, inv, a);
|
||
|
|
t = a; a = b; b = t;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// Check if done
|
||
|
|
if (ebits == 0)
|
||
|
|
break;
|
||
|
|
|
||
|
|
// Square the input
|
||
|
|
if (!isone) {
|
||
|
|
t = b;
|
||
|
|
a = montgomerySquare(t, mod, modLen, inv, a);
|
||
|
|
t = a; a = b; b = t;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// Convert result out of Montgomery form and return
|
||
|
|
int[] t2 = new int[2*modLen];
|
||
|
|
System.arraycopy(b, 0, t2, modLen, modLen);
|
||
|
|
|
||
|
|
b = montReduce(t2, mod, modLen, (int)inv);
|
||
|
|
|
||
|
|
t2 = Arrays.copyOf(b, modLen);
|
||
|
|
|
||
|
|
return new BigInteger(1, t2);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Montgomery reduce n, modulo mod. This reduces modulo mod and divides
|
||
|
|
* by 2^(32*mlen). Adapted from Colin Plumb's C library.
|
||
|
|
*/
|
||
|
|
private static int[] montReduce(int[] n, int[] mod, int mlen, int inv) {
|
||
|
|
int c=0;
|
||
|
|
int len = mlen;
|
||
|
|
int offset=0;
|
||
|
|
|
||
|
|
do {
|
||
|
|
int nEnd = n[n.length-1-offset];
|
||
|
|
int carry = mulAdd(n, mod, offset, mlen, inv * nEnd);
|
||
|
|
c += addOne(n, offset, mlen, carry);
|
||
|
|
offset++;
|
||
|
|
} while (--len > 0);
|
||
|
|
|
||
|
|
while (c > 0)
|
||
|
|
c += subN(n, mod, mlen);
|
||
|
|
|
||
|
|
while (intArrayCmpToLen(n, mod, mlen) >= 0)
|
||
|
|
subN(n, mod, mlen);
|
||
|
|
|
||
|
|
return n;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
* Returns -1, 0 or +1 as big-endian unsigned int array arg1 is less than,
|
||
|
|
* equal to, or greater than arg2 up to length len.
|
||
|
|
*/
|
||
|
|
private static int intArrayCmpToLen(int[] arg1, int[] arg2, int len) {
|
||
|
|
for (int i=0; i < len; i++) {
|
||
|
|
long b1 = arg1[i] & LONG_MASK;
|
||
|
|
long b2 = arg2[i] & LONG_MASK;
|
||
|
|
if (b1 < b2)
|
||
|
|
return -1;
|
||
|
|
if (b1 > b2)
|
||
|
|
return 1;
|
||
|
|
}
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Subtracts two numbers of same length, returning borrow.
|
||
|
|
*/
|
||
|
|
private static int subN(int[] a, int[] b, int len) {
|
||
|
|
long sum = 0;
|
||
|
|
|
||
|
|
while (--len >= 0) {
|
||
|
|
sum = (a[len] & LONG_MASK) -
|
||
|
|
(b[len] & LONG_MASK) + (sum >> 32);
|
||
|
|
a[len] = (int)sum;
|
||
|
|
}
|
||
|
|
|
||
|
|
return (int)(sum >> 32);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Multiply an array by one word k and add to result, return the carry
|
||
|
|
*/
|
||
|
|
static int mulAdd(int[] out, int[] in, int offset, int len, int k) {
|
||
|
|
implMulAddCheck(out, in, offset, len, k);
|
||
|
|
return implMulAdd(out, in, offset, len, k);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Parameters validation.
|
||
|
|
*/
|
||
|
|
private static void implMulAddCheck(int[] out, int[] in, int offset, int len, int k) {
|
||
|
|
if (len > in.length) {
|
||
|
|
throw new IllegalArgumentException("input length is out of bound: " + len + " > " + in.length);
|
||
|
|
}
|
||
|
|
if (offset < 0) {
|
||
|
|
throw new IllegalArgumentException("input offset is invalid: " + offset);
|
||
|
|
}
|
||
|
|
if (offset > (out.length - 1)) {
|
||
|
|
throw new IllegalArgumentException("input offset is out of bound: " + offset + " > " + (out.length - 1));
|
||
|
|
}
|
||
|
|
if (len > (out.length - offset)) {
|
||
|
|
throw new IllegalArgumentException("input len is out of bound: " + len + " > " + (out.length - offset));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Java Runtime may use intrinsic for this method.
|
||
|
|
*/
|
||
|
|
@IntrinsicCandidate
|
||
|
|
private static int implMulAdd(int[] out, int[] in, int offset, int len, int k) {
|
||
|
|
long kLong = k & LONG_MASK;
|
||
|
|
long carry = 0;
|
||
|
|
|
||
|
|
offset = out.length-offset - 1;
|
||
|
|
for (int j=len-1; j >= 0; j--) {
|
||
|
|
long product = (in[j] & LONG_MASK) * kLong +
|
||
|
|
(out[offset] & LONG_MASK) + carry;
|
||
|
|
out[offset--] = (int)product;
|
||
|
|
carry = product >>> 32;
|
||
|
|
}
|
||
|
|
return (int)carry;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Add one word to the number a mlen words into a. Return the resulting
|
||
|
|
* carry.
|
||
|
|
*/
|
||
|
|
static int addOne(int[] a, int offset, int mlen, int carry) {
|
||
|
|
offset = a.length-1-mlen-offset;
|
||
|
|
long t = (a[offset] & LONG_MASK) + (carry & LONG_MASK);
|
||
|
|
|
||
|
|
a[offset] = (int)t;
|
||
|
|
if ((t >>> 32) == 0)
|
||
|
|
return 0;
|
||
|
|
while (--mlen >= 0) {
|
||
|
|
if (--offset < 0) { // Carry out of number
|
||
|
|
return 1;
|
||
|
|
} else {
|
||
|
|
a[offset]++;
|
||
|
|
if (a[offset] != 0)
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is (this ** exponent) mod (2**p)
|
||
|
|
*/
|
||
|
|
private BigInteger modPow2(BigInteger exponent, int p) {
|
||
|
|
/*
|
||
|
|
* Perform exponentiation using repeated squaring trick, chopping off
|
||
|
|
* high order bits as indicated by modulus.
|
||
|
|
*/
|
||
|
|
BigInteger result = ONE;
|
||
|
|
BigInteger baseToPow2 = this.mod2(p);
|
||
|
|
int expOffset = 0;
|
||
|
|
|
||
|
|
int limit = exponent.bitLength();
|
||
|
|
|
||
|
|
if (this.testBit(0))
|
||
|
|
limit = (p-1) < limit ? (p-1) : limit;
|
||
|
|
|
||
|
|
while (expOffset < limit) {
|
||
|
|
if (exponent.testBit(expOffset))
|
||
|
|
result = result.multiply(baseToPow2).mod2(p);
|
||
|
|
expOffset++;
|
||
|
|
if (expOffset < limit)
|
||
|
|
baseToPow2 = baseToPow2.square().mod2(p);
|
||
|
|
}
|
||
|
|
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is this mod(2**p).
|
||
|
|
* Assumes that this {@code BigInteger >= 0} and {@code p > 0}.
|
||
|
|
*/
|
||
|
|
private BigInteger mod2(int p) {
|
||
|
|
if (bitLength() <= p)
|
||
|
|
return this;
|
||
|
|
|
||
|
|
// Copy remaining ints of mag
|
||
|
|
int numInts = (p + 31) >>> 5;
|
||
|
|
int[] mag = new int[numInts];
|
||
|
|
System.arraycopy(this.mag, (this.mag.length - numInts), mag, 0, numInts);
|
||
|
|
|
||
|
|
// Mask out any excess bits
|
||
|
|
int excessBits = (numInts << 5) - p;
|
||
|
|
mag[0] &= (1L << (32-excessBits)) - 1;
|
||
|
|
|
||
|
|
return (mag[0] == 0 ? new BigInteger(1, mag) : new BigInteger(mag, 1));
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this}<sup>-1</sup> {@code mod m)}.
|
||
|
|
*
|
||
|
|
* @param m the modulus.
|
||
|
|
* @return {@code this}<sup>-1</sup> {@code mod m}.
|
||
|
|
* @throws ArithmeticException {@code m} ≤ 0, or this BigInteger
|
||
|
|
* has no multiplicative inverse mod m (that is, this BigInteger
|
||
|
|
* is not <i>relatively prime</i> to m).
|
||
|
|
*/
|
||
|
|
public BigInteger modInverse(BigInteger m) {
|
||
|
|
if (m.signum != 1)
|
||
|
|
throw new ArithmeticException("BigInteger: modulus not positive");
|
||
|
|
|
||
|
|
if (m.equals(ONE))
|
||
|
|
return ZERO;
|
||
|
|
|
||
|
|
// Calculate (this mod m)
|
||
|
|
BigInteger modVal = this;
|
||
|
|
if (signum < 0 || (this.compareMagnitude(m) >= 0))
|
||
|
|
modVal = this.mod(m);
|
||
|
|
|
||
|
|
if (modVal.equals(ONE))
|
||
|
|
return ONE;
|
||
|
|
|
||
|
|
MutableBigInteger a = new MutableBigInteger(modVal);
|
||
|
|
MutableBigInteger b = new MutableBigInteger(m);
|
||
|
|
|
||
|
|
MutableBigInteger result = a.mutableModInverse(b);
|
||
|
|
return result.toBigInteger(1);
|
||
|
|
}
|
||
|
|
|
||
|
|
// Shift Operations
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this << n)}.
|
||
|
|
* The shift distance, {@code n}, may be negative, in which case
|
||
|
|
* this method performs a right shift.
|
||
|
|
* (Computes <code>floor(this * 2<sup>n</sup>)</code>.)
|
||
|
|
*
|
||
|
|
* @param n shift distance, in bits.
|
||
|
|
* @return {@code this << n}
|
||
|
|
* @see #shiftRight
|
||
|
|
*/
|
||
|
|
public BigInteger shiftLeft(int n) {
|
||
|
|
if (signum == 0)
|
||
|
|
return ZERO;
|
||
|
|
if (n > 0) {
|
||
|
|
return new BigInteger(shiftLeft(mag, n), signum);
|
||
|
|
} else if (n == 0) {
|
||
|
|
return this;
|
||
|
|
} else {
|
||
|
|
// Possible int overflow in (-n) is not a trouble,
|
||
|
|
// because shiftRightImpl considers its argument unsigned
|
||
|
|
return shiftRightImpl(-n);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a magnitude array whose value is {@code (mag << n)}.
|
||
|
|
* The shift distance, {@code n}, is considered unnsigned.
|
||
|
|
* (Computes <code>this * 2<sup>n</sup></code>.)
|
||
|
|
*
|
||
|
|
* @param mag magnitude, the most-significant int ({@code mag[0]}) must be non-zero.
|
||
|
|
* @param n unsigned shift distance, in bits.
|
||
|
|
* @return {@code mag << n}
|
||
|
|
*/
|
||
|
|
private static int[] shiftLeft(int[] mag, int n) {
|
||
|
|
int nInts = n >>> 5;
|
||
|
|
int nBits = n & 0x1f;
|
||
|
|
int magLen = mag.length;
|
||
|
|
int newMag[] = null;
|
||
|
|
|
||
|
|
if (nBits == 0) {
|
||
|
|
newMag = new int[magLen + nInts];
|
||
|
|
System.arraycopy(mag, 0, newMag, 0, magLen);
|
||
|
|
} else {
|
||
|
|
int i = 0;
|
||
|
|
int nBits2 = 32 - nBits;
|
||
|
|
int highBits = mag[0] >>> nBits2;
|
||
|
|
if (highBits != 0) {
|
||
|
|
newMag = new int[magLen + nInts + 1];
|
||
|
|
newMag[i++] = highBits;
|
||
|
|
} else {
|
||
|
|
newMag = new int[magLen + nInts];
|
||
|
|
}
|
||
|
|
int numIter = magLen - 1;
|
||
|
|
Objects.checkFromToIndex(0, numIter + 1, mag.length);
|
||
|
|
Objects.checkFromToIndex(i, numIter + i + 1, newMag.length);
|
||
|
|
shiftLeftImplWorker(newMag, mag, i, nBits, numIter);
|
||
|
|
newMag[numIter + i] = mag[numIter] << nBits;
|
||
|
|
}
|
||
|
|
return newMag;
|
||
|
|
}
|
||
|
|
|
||
|
|
private static void shiftLeftImplWorker(int[] newArr, int[] oldArr, int newIdx, int shiftCount, int numIter) {
|
||
|
|
int shiftCountRight = 32 - shiftCount;
|
||
|
|
int oldIdx = 0;
|
||
|
|
while (oldIdx < numIter) {
|
||
|
|
newArr[newIdx++] = (oldArr[oldIdx++] << shiftCount) | (oldArr[oldIdx] >>> shiftCountRight);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this >> n)}. Sign
|
||
|
|
* extension is performed. The shift distance, {@code n}, may be
|
||
|
|
* negative, in which case this method performs a left shift.
|
||
|
|
* (Computes <code>floor(this / 2<sup>n</sup>)</code>.)
|
||
|
|
*
|
||
|
|
* @param n shift distance, in bits.
|
||
|
|
* @return {@code this >> n}
|
||
|
|
* @see #shiftLeft
|
||
|
|
*/
|
||
|
|
public BigInteger shiftRight(int n) {
|
||
|
|
if (signum == 0)
|
||
|
|
return ZERO;
|
||
|
|
if (n > 0) {
|
||
|
|
return shiftRightImpl(n);
|
||
|
|
} else if (n == 0) {
|
||
|
|
return this;
|
||
|
|
} else {
|
||
|
|
// Possible int overflow in {@code -n} is not a trouble,
|
||
|
|
// because shiftLeft considers its argument unsigned
|
||
|
|
return new BigInteger(shiftLeft(mag, -n), signum);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this >> n)}. The shift
|
||
|
|
* distance, {@code n}, is considered unsigned.
|
||
|
|
* (Computes <code>floor(this * 2<sup>-n</sup>)</code>.)
|
||
|
|
*
|
||
|
|
* @param n unsigned shift distance, in bits.
|
||
|
|
* @return {@code this >> n}
|
||
|
|
*/
|
||
|
|
private BigInteger shiftRightImpl(int n) {
|
||
|
|
int nInts = n >>> 5;
|
||
|
|
int nBits = n & 0x1f;
|
||
|
|
int magLen = mag.length;
|
||
|
|
int newMag[] = null;
|
||
|
|
|
||
|
|
// Special case: entire contents shifted off the end
|
||
|
|
if (nInts >= magLen)
|
||
|
|
return (signum >= 0 ? ZERO : negConst[1]);
|
||
|
|
|
||
|
|
if (nBits == 0) {
|
||
|
|
int newMagLen = magLen - nInts;
|
||
|
|
newMag = Arrays.copyOf(mag, newMagLen);
|
||
|
|
} else {
|
||
|
|
int i = 0;
|
||
|
|
int highBits = mag[0] >>> nBits;
|
||
|
|
if (highBits != 0) {
|
||
|
|
newMag = new int[magLen - nInts];
|
||
|
|
newMag[i++] = highBits;
|
||
|
|
} else {
|
||
|
|
newMag = new int[magLen - nInts -1];
|
||
|
|
}
|
||
|
|
int numIter = magLen - nInts - 1;
|
||
|
|
Objects.checkFromToIndex(0, numIter + 1, mag.length);
|
||
|
|
Objects.checkFromToIndex(i, numIter + i, newMag.length);
|
||
|
|
shiftRightImplWorker(newMag, mag, i, nBits, numIter);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (signum < 0) {
|
||
|
|
// Find out whether any one-bits were shifted off the end.
|
||
|
|
boolean onesLost = false;
|
||
|
|
for (int i=magLen-1, j=magLen-nInts; i >= j && !onesLost; i--)
|
||
|
|
onesLost = (mag[i] != 0);
|
||
|
|
if (!onesLost && nBits != 0)
|
||
|
|
onesLost = (mag[magLen - nInts - 1] << (32 - nBits) != 0);
|
||
|
|
|
||
|
|
if (onesLost)
|
||
|
|
newMag = javaIncrement(newMag);
|
||
|
|
}
|
||
|
|
|
||
|
|
return new BigInteger(newMag, signum);
|
||
|
|
}
|
||
|
|
|
||
|
|
private static void shiftRightImplWorker(int[] newArr, int[] oldArr, int newIdx, int shiftCount, int numIter) {
|
||
|
|
int shiftCountLeft = 32 - shiftCount;
|
||
|
|
int idx = numIter;
|
||
|
|
int nidx = (newIdx == 0) ? numIter - 1 : numIter;
|
||
|
|
while (nidx >= newIdx) {
|
||
|
|
newArr[nidx--] = (oldArr[idx--] >>> shiftCount) | (oldArr[idx] << shiftCountLeft);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
int[] javaIncrement(int[] val) {
|
||
|
|
int lastSum = 0;
|
||
|
|
for (int i=val.length-1; i >= 0 && lastSum == 0; i--)
|
||
|
|
lastSum = (val[i] += 1);
|
||
|
|
if (lastSum == 0) {
|
||
|
|
val = new int[val.length+1];
|
||
|
|
val[0] = 1;
|
||
|
|
}
|
||
|
|
return val;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Bitwise Operations
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this & val)}. (This
|
||
|
|
* method returns a negative BigInteger if and only if this and val are
|
||
|
|
* both negative.)
|
||
|
|
*
|
||
|
|
* @param val value to be AND'ed with this BigInteger.
|
||
|
|
* @return {@code this & val}
|
||
|
|
*/
|
||
|
|
public BigInteger and(BigInteger val) {
|
||
|
|
int[] result = new int[Math.max(intLength(), val.intLength())];
|
||
|
|
for (int i=0; i < result.length; i++)
|
||
|
|
result[i] = (getInt(result.length-i-1)
|
||
|
|
& val.getInt(result.length-i-1));
|
||
|
|
|
||
|
|
return valueOf(result);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this | val)}. (This method
|
||
|
|
* returns a negative BigInteger if and only if either this or val is
|
||
|
|
* negative.)
|
||
|
|
*
|
||
|
|
* @param val value to be OR'ed with this BigInteger.
|
||
|
|
* @return {@code this | val}
|
||
|
|
*/
|
||
|
|
public BigInteger or(BigInteger val) {
|
||
|
|
int[] result = new int[Math.max(intLength(), val.intLength())];
|
||
|
|
for (int i=0; i < result.length; i++)
|
||
|
|
result[i] = (getInt(result.length-i-1)
|
||
|
|
| val.getInt(result.length-i-1));
|
||
|
|
|
||
|
|
return valueOf(result);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this ^ val)}. (This method
|
||
|
|
* returns a negative BigInteger if and only if exactly one of this and
|
||
|
|
* val are negative.)
|
||
|
|
*
|
||
|
|
* @param val value to be XOR'ed with this BigInteger.
|
||
|
|
* @return {@code this ^ val}
|
||
|
|
*/
|
||
|
|
public BigInteger xor(BigInteger val) {
|
||
|
|
int[] result = new int[Math.max(intLength(), val.intLength())];
|
||
|
|
for (int i=0; i < result.length; i++)
|
||
|
|
result[i] = (getInt(result.length-i-1)
|
||
|
|
^ val.getInt(result.length-i-1));
|
||
|
|
|
||
|
|
return valueOf(result);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (~this)}. (This method
|
||
|
|
* returns a negative value if and only if this BigInteger is
|
||
|
|
* non-negative.)
|
||
|
|
*
|
||
|
|
* @return {@code ~this}
|
||
|
|
*/
|
||
|
|
public BigInteger not() {
|
||
|
|
int[] result = new int[intLength()];
|
||
|
|
for (int i=0; i < result.length; i++)
|
||
|
|
result[i] = ~getInt(result.length-i-1);
|
||
|
|
|
||
|
|
return valueOf(result);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is {@code (this & ~val)}. This
|
||
|
|
* method, which is equivalent to {@code and(val.not())}, is provided as
|
||
|
|
* a convenience for masking operations. (This method returns a negative
|
||
|
|
* BigInteger if and only if {@code this} is negative and {@code val} is
|
||
|
|
* positive.)
|
||
|
|
*
|
||
|
|
* @param val value to be complemented and AND'ed with this BigInteger.
|
||
|
|
* @return {@code this & ~val}
|
||
|
|
*/
|
||
|
|
public BigInteger andNot(BigInteger val) {
|
||
|
|
int[] result = new int[Math.max(intLength(), val.intLength())];
|
||
|
|
for (int i=0; i < result.length; i++)
|
||
|
|
result[i] = (getInt(result.length-i-1)
|
||
|
|
& ~val.getInt(result.length-i-1));
|
||
|
|
|
||
|
|
return valueOf(result);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// Single Bit Operations
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns {@code true} if and only if the designated bit is set.
|
||
|
|
* (Computes {@code ((this & (1<<n)) != 0)}.)
|
||
|
|
*
|
||
|
|
* @param n index of bit to test.
|
||
|
|
* @return {@code true} if and only if the designated bit is set.
|
||
|
|
* @throws ArithmeticException {@code n} is negative.
|
||
|
|
*/
|
||
|
|
public boolean testBit(int n) {
|
||
|
|
if (n < 0)
|
||
|
|
throw new ArithmeticException("Negative bit address");
|
||
|
|
|
||
|
|
return (getInt(n >>> 5) & (1 << (n & 31))) != 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is equivalent to this BigInteger
|
||
|
|
* with the designated bit set. (Computes {@code (this | (1<<n))}.)
|
||
|
|
*
|
||
|
|
* @param n index of bit to set.
|
||
|
|
* @return {@code this | (1<<n)}
|
||
|
|
* @throws ArithmeticException {@code n} is negative.
|
||
|
|
*/
|
||
|
|
public BigInteger setBit(int n) {
|
||
|
|
if (n < 0)
|
||
|
|
throw new ArithmeticException("Negative bit address");
|
||
|
|
|
||
|
|
int intNum = n >>> 5;
|
||
|
|
int[] result = new int[Math.max(intLength(), intNum+2)];
|
||
|
|
|
||
|
|
for (int i=0; i < result.length; i++)
|
||
|
|
result[result.length-i-1] = getInt(i);
|
||
|
|
|
||
|
|
result[result.length-intNum-1] |= (1 << (n & 31));
|
||
|
|
|
||
|
|
return valueOf(result);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is equivalent to this BigInteger
|
||
|
|
* with the designated bit cleared.
|
||
|
|
* (Computes {@code (this & ~(1<<n))}.)
|
||
|
|
*
|
||
|
|
* @param n index of bit to clear.
|
||
|
|
* @return {@code this & ~(1<<n)}
|
||
|
|
* @throws ArithmeticException {@code n} is negative.
|
||
|
|
*/
|
||
|
|
public BigInteger clearBit(int n) {
|
||
|
|
if (n < 0)
|
||
|
|
throw new ArithmeticException("Negative bit address");
|
||
|
|
|
||
|
|
int intNum = n >>> 5;
|
||
|
|
int[] result = new int[Math.max(intLength(), ((n + 1) >>> 5) + 1)];
|
||
|
|
|
||
|
|
for (int i=0; i < result.length; i++)
|
||
|
|
result[result.length-i-1] = getInt(i);
|
||
|
|
|
||
|
|
result[result.length-intNum-1] &= ~(1 << (n & 31));
|
||
|
|
|
||
|
|
return valueOf(result);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a BigInteger whose value is equivalent to this BigInteger
|
||
|
|
* with the designated bit flipped.
|
||
|
|
* (Computes {@code (this ^ (1<<n))}.)
|
||
|
|
*
|
||
|
|
* @param n index of bit to flip.
|
||
|
|
* @return {@code this ^ (1<<n)}
|
||
|
|
* @throws ArithmeticException {@code n} is negative.
|
||
|
|
*/
|
||
|
|
public BigInteger flipBit(int n) {
|
||
|
|
if (n < 0)
|
||
|
|
throw new ArithmeticException("Negative bit address");
|
||
|
|
|
||
|
|
int intNum = n >>> 5;
|
||
|
|
int[] result = new int[Math.max(intLength(), intNum+2)];
|
||
|
|
|
||
|
|
for (int i=0; i < result.length; i++)
|
||
|
|
result[result.length-i-1] = getInt(i);
|
||
|
|
|
||
|
|
result[result.length-intNum-1] ^= (1 << (n & 31));
|
||
|
|
|
||
|
|
return valueOf(result);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the index of the rightmost (lowest-order) one bit in this
|
||
|
|
* BigInteger (the number of zero bits to the right of the rightmost
|
||
|
|
* one bit). Returns -1 if this BigInteger contains no one bits.
|
||
|
|
* (Computes {@code (this == 0? -1 : log2(this & -this))}.)
|
||
|
|
*
|
||
|
|
* @return index of the rightmost one bit in this BigInteger.
|
||
|
|
*/
|
||
|
|
public int getLowestSetBit() {
|
||
|
|
int lsb = lowestSetBitPlusTwo - 2;
|
||
|
|
if (lsb == -2) { // lowestSetBit not initialized yet
|
||
|
|
lsb = 0;
|
||
|
|
if (signum == 0) {
|
||
|
|
lsb -= 1;
|
||
|
|
} else {
|
||
|
|
// Search for lowest order nonzero int
|
||
|
|
int i,b;
|
||
|
|
for (i=0; (b = getInt(i)) == 0; i++)
|
||
|
|
;
|
||
|
|
lsb += (i << 5) + Integer.numberOfTrailingZeros(b);
|
||
|
|
}
|
||
|
|
lowestSetBitPlusTwo = lsb + 2;
|
||
|
|
}
|
||
|
|
return lsb;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// Miscellaneous Bit Operations
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the number of bits in the minimal two's-complement
|
||
|
|
* representation of this BigInteger, <em>excluding</em> a sign bit.
|
||
|
|
* For positive BigIntegers, this is equivalent to the number of bits in
|
||
|
|
* the ordinary binary representation. For zero this method returns
|
||
|
|
* {@code 0}. (Computes {@code (ceil(log2(this < 0 ? -this : this+1)))}.)
|
||
|
|
*
|
||
|
|
* @return number of bits in the minimal two's-complement
|
||
|
|
* representation of this BigInteger, <em>excluding</em> a sign bit.
|
||
|
|
*/
|
||
|
|
public int bitLength() {
|
||
|
|
int n = bitLengthPlusOne - 1;
|
||
|
|
if (n == -1) { // bitLength not initialized yet
|
||
|
|
int[] m = mag;
|
||
|
|
int len = m.length;
|
||
|
|
if (len == 0) {
|
||
|
|
n = 0; // offset by one to initialize
|
||
|
|
} else {
|
||
|
|
// Calculate the bit length of the magnitude
|
||
|
|
int magBitLength = ((len - 1) << 5) + bitLengthForInt(mag[0]);
|
||
|
|
if (signum < 0) {
|
||
|
|
// Check if magnitude is a power of two
|
||
|
|
boolean pow2 = (Integer.bitCount(mag[0]) == 1);
|
||
|
|
for (int i=1; i< len && pow2; i++)
|
||
|
|
pow2 = (mag[i] == 0);
|
||
|
|
|
||
|
|
n = (pow2 ? magBitLength - 1 : magBitLength);
|
||
|
|
} else {
|
||
|
|
n = magBitLength;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
bitLengthPlusOne = n + 1;
|
||
|
|
}
|
||
|
|
return n;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the number of bits in the two's complement representation
|
||
|
|
* of this BigInteger that differ from its sign bit. This method is
|
||
|
|
* useful when implementing bit-vector style sets atop BigIntegers.
|
||
|
|
*
|
||
|
|
* @return number of bits in the two's complement representation
|
||
|
|
* of this BigInteger that differ from its sign bit.
|
||
|
|
*/
|
||
|
|
public int bitCount() {
|
||
|
|
int bc = bitCountPlusOne - 1;
|
||
|
|
if (bc == -1) { // bitCount not initialized yet
|
||
|
|
bc = 0; // offset by one to initialize
|
||
|
|
// Count the bits in the magnitude
|
||
|
|
for (int i=0; i < mag.length; i++)
|
||
|
|
bc += Integer.bitCount(mag[i]);
|
||
|
|
if (signum < 0) {
|
||
|
|
// Count the trailing zeros in the magnitude
|
||
|
|
int magTrailingZeroCount = 0, j;
|
||
|
|
for (j=mag.length-1; mag[j] == 0; j--)
|
||
|
|
magTrailingZeroCount += 32;
|
||
|
|
magTrailingZeroCount += Integer.numberOfTrailingZeros(mag[j]);
|
||
|
|
bc += magTrailingZeroCount - 1;
|
||
|
|
}
|
||
|
|
bitCountPlusOne = bc + 1;
|
||
|
|
}
|
||
|
|
return bc;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Primality Testing
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns {@code true} if this BigInteger is probably prime,
|
||
|
|
* {@code false} if it's definitely composite. If
|
||
|
|
* {@code certainty} is ≤ 0, {@code true} is
|
||
|
|
* returned.
|
||
|
|
*
|
||
|
|
* @param certainty a measure of the uncertainty that the caller is
|
||
|
|
* willing to tolerate: if the call returns {@code true}
|
||
|
|
* the probability that this BigInteger is prime exceeds
|
||
|
|
* (1 - 1/2<sup>{@code certainty}</sup>). The execution time of
|
||
|
|
* this method is proportional to the value of this parameter.
|
||
|
|
* @return {@code true} if this BigInteger is probably prime,
|
||
|
|
* {@code false} if it's definitely composite.
|
||
|
|
*/
|
||
|
|
public boolean isProbablePrime(int certainty) {
|
||
|
|
if (certainty <= 0)
|
||
|
|
return true;
|
||
|
|
BigInteger w = this.abs();
|
||
|
|
if (w.equals(TWO))
|
||
|
|
return true;
|
||
|
|
if (!w.testBit(0) || w.equals(ONE))
|
||
|
|
return false;
|
||
|
|
|
||
|
|
return w.primeToCertainty(certainty, null);
|
||
|
|
}
|
||
|
|
|
||
|
|
// Comparison Operations
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Compares this BigInteger with the specified BigInteger. This
|
||
|
|
* method is provided in preference to individual methods for each
|
||
|
|
* of the six boolean comparison operators ({@literal <}, ==,
|
||
|
|
* {@literal >}, {@literal >=}, !=, {@literal <=}). The suggested
|
||
|
|
* idiom for performing these comparisons is: {@code
|
||
|
|
* (x.compareTo(y)} <<i>op</i>> {@code 0)}, where
|
||
|
|
* <<i>op</i>> is one of the six comparison operators.
|
||
|
|
*
|
||
|
|
* @param val BigInteger to which this BigInteger is to be compared.
|
||
|
|
* @return -1, 0 or 1 as this BigInteger is numerically less than, equal
|
||
|
|
* to, or greater than {@code val}.
|
||
|
|
*/
|
||
|
|
public int compareTo(BigInteger val) {
|
||
|
|
if (signum == val.signum) {
|
||
|
|
return switch (signum) {
|
||
|
|
case 1 -> compareMagnitude(val);
|
||
|
|
case -1 -> val.compareMagnitude(this);
|
||
|
|
default -> 0;
|
||
|
|
};
|
||
|
|
}
|
||
|
|
return signum > val.signum ? 1 : -1;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Compares the magnitude array of this BigInteger with the specified
|
||
|
|
* BigInteger's. This is the version of compareTo ignoring sign.
|
||
|
|
*
|
||
|
|
* @param val BigInteger whose magnitude array to be compared.
|
||
|
|
* @return -1, 0 or 1 as this magnitude array is less than, equal to or
|
||
|
|
* greater than the magnitude aray for the specified BigInteger's.
|
||
|
|
*/
|
||
|
|
final int compareMagnitude(BigInteger val) {
|
||
|
|
int[] m1 = mag;
|
||
|
|
int len1 = m1.length;
|
||
|
|
int[] m2 = val.mag;
|
||
|
|
int len2 = m2.length;
|
||
|
|
if (len1 < len2)
|
||
|
|
return -1;
|
||
|
|
if (len1 > len2)
|
||
|
|
return 1;
|
||
|
|
for (int i = 0; i < len1; i++) {
|
||
|
|
int a = m1[i];
|
||
|
|
int b = m2[i];
|
||
|
|
if (a != b)
|
||
|
|
return ((a & LONG_MASK) < (b & LONG_MASK)) ? -1 : 1;
|
||
|
|
}
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Version of compareMagnitude that compares magnitude with long value.
|
||
|
|
* val can't be Long.MIN_VALUE.
|
||
|
|
*/
|
||
|
|
final int compareMagnitude(long val) {
|
||
|
|
assert val != Long.MIN_VALUE;
|
||
|
|
int[] m1 = mag;
|
||
|
|
int len = m1.length;
|
||
|
|
if (len > 2) {
|
||
|
|
return 1;
|
||
|
|
}
|
||
|
|
if (val < 0) {
|
||
|
|
val = -val;
|
||
|
|
}
|
||
|
|
int highWord = (int)(val >>> 32);
|
||
|
|
if (highWord == 0) {
|
||
|
|
if (len < 1)
|
||
|
|
return -1;
|
||
|
|
if (len > 1)
|
||
|
|
return 1;
|
||
|
|
int a = m1[0];
|
||
|
|
int b = (int)val;
|
||
|
|
if (a != b) {
|
||
|
|
return ((a & LONG_MASK) < (b & LONG_MASK))? -1 : 1;
|
||
|
|
}
|
||
|
|
return 0;
|
||
|
|
} else {
|
||
|
|
if (len < 2)
|
||
|
|
return -1;
|
||
|
|
int a = m1[0];
|
||
|
|
int b = highWord;
|
||
|
|
if (a != b) {
|
||
|
|
return ((a & LONG_MASK) < (b & LONG_MASK))? -1 : 1;
|
||
|
|
}
|
||
|
|
a = m1[1];
|
||
|
|
b = (int)val;
|
||
|
|
if (a != b) {
|
||
|
|
return ((a & LONG_MASK) < (b & LONG_MASK))? -1 : 1;
|
||
|
|
}
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Compares this BigInteger with the specified Object for equality.
|
||
|
|
*
|
||
|
|
* @param x Object to which this BigInteger is to be compared.
|
||
|
|
* @return {@code true} if and only if the specified Object is a
|
||
|
|
* BigInteger whose value is numerically equal to this BigInteger.
|
||
|
|
*/
|
||
|
|
public boolean equals(Object x) {
|
||
|
|
// This test is just an optimization, which may or may not help
|
||
|
|
if (x == this)
|
||
|
|
return true;
|
||
|
|
|
||
|
|
if (!(x instanceof BigInteger xInt))
|
||
|
|
return false;
|
||
|
|
|
||
|
|
if (xInt.signum != signum)
|
||
|
|
return false;
|
||
|
|
|
||
|
|
int[] m = mag;
|
||
|
|
int len = m.length;
|
||
|
|
int[] xm = xInt.mag;
|
||
|
|
if (len != xm.length)
|
||
|
|
return false;
|
||
|
|
|
||
|
|
for (int i = 0; i < len; i++)
|
||
|
|
if (xm[i] != m[i])
|
||
|
|
return false;
|
||
|
|
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the minimum of this BigInteger and {@code val}.
|
||
|
|
*
|
||
|
|
* @param val value with which the minimum is to be computed.
|
||
|
|
* @return the BigInteger whose value is the lesser of this BigInteger and
|
||
|
|
* {@code val}. If they are equal, either may be returned.
|
||
|
|
*/
|
||
|
|
public BigInteger min(BigInteger val) {
|
||
|
|
return (compareTo(val) < 0 ? this : val);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the maximum of this BigInteger and {@code val}.
|
||
|
|
*
|
||
|
|
* @param val value with which the maximum is to be computed.
|
||
|
|
* @return the BigInteger whose value is the greater of this and
|
||
|
|
* {@code val}. If they are equal, either may be returned.
|
||
|
|
*/
|
||
|
|
public BigInteger max(BigInteger val) {
|
||
|
|
return (compareTo(val) > 0 ? this : val);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// Hash Function
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the hash code for this BigInteger.
|
||
|
|
*
|
||
|
|
* @return hash code for this BigInteger.
|
||
|
|
*/
|
||
|
|
public int hashCode() {
|
||
|
|
int hashCode = 0;
|
||
|
|
|
||
|
|
for (int i=0; i < mag.length; i++)
|
||
|
|
hashCode = (int)(31*hashCode + (mag[i] & LONG_MASK));
|
||
|
|
|
||
|
|
return hashCode * signum;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the String representation of this BigInteger in the
|
||
|
|
* given radix. If the radix is outside the range from {@link
|
||
|
|
* Character#MIN_RADIX} to {@link Character#MAX_RADIX} inclusive,
|
||
|
|
* it will default to 10 (as is the case for
|
||
|
|
* {@code Integer.toString}). The digit-to-character mapping
|
||
|
|
* provided by {@code Character.forDigit} is used, and a minus
|
||
|
|
* sign is prepended if appropriate. (This representation is
|
||
|
|
* compatible with the {@link #BigInteger(String, int) (String,
|
||
|
|
* int)} constructor.)
|
||
|
|
*
|
||
|
|
* @param radix radix of the String representation.
|
||
|
|
* @return String representation of this BigInteger in the given radix.
|
||
|
|
* @see Integer#toString
|
||
|
|
* @see Character#forDigit
|
||
|
|
* @see #BigInteger(java.lang.String, int)
|
||
|
|
*/
|
||
|
|
public String toString(int radix) {
|
||
|
|
if (signum == 0)
|
||
|
|
return "0";
|
||
|
|
if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
|
||
|
|
radix = 10;
|
||
|
|
|
||
|
|
BigInteger abs = this.abs();
|
||
|
|
|
||
|
|
// Ensure buffer capacity sufficient to contain string representation
|
||
|
|
// floor(bitLength*log(2)/log(radix)) + 1
|
||
|
|
// plus an additional character for the sign if negative.
|
||
|
|
int b = abs.bitLength();
|
||
|
|
int numChars = (int)(Math.floor(b*LOG_TWO/logCache[radix]) + 1) +
|
||
|
|
(signum < 0 ? 1 : 0);
|
||
|
|
StringBuilder sb = new StringBuilder(numChars);
|
||
|
|
|
||
|
|
if (signum < 0) {
|
||
|
|
sb.append('-');
|
||
|
|
}
|
||
|
|
|
||
|
|
// Use recursive toString.
|
||
|
|
toString(abs, sb, radix, 0);
|
||
|
|
|
||
|
|
return sb.toString();
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* If {@code numZeros > 0}, appends that many zeros to the
|
||
|
|
* specified StringBuilder; otherwise, does nothing.
|
||
|
|
*
|
||
|
|
* @param buf The StringBuilder that will be appended to.
|
||
|
|
* @param numZeros The number of zeros to append.
|
||
|
|
*/
|
||
|
|
private static void padWithZeros(StringBuilder buf, int numZeros) {
|
||
|
|
while (numZeros >= NUM_ZEROS) {
|
||
|
|
buf.append(ZEROS);
|
||
|
|
numZeros -= NUM_ZEROS;
|
||
|
|
}
|
||
|
|
if (numZeros > 0) {
|
||
|
|
buf.append(ZEROS, 0, numZeros);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* This method is used to perform toString when arguments are small.
|
||
|
|
* The value must be non-negative. If {@code digits <= 0} no padding
|
||
|
|
* (pre-pending with zeros) will be effected.
|
||
|
|
*
|
||
|
|
* @param radix The base to convert to.
|
||
|
|
* @param buf The StringBuilder that will be appended to in place.
|
||
|
|
* @param digits The minimum number of digits to pad to.
|
||
|
|
*/
|
||
|
|
private void smallToString(int radix, StringBuilder buf, int digits) {
|
||
|
|
assert signum >= 0;
|
||
|
|
|
||
|
|
if (signum == 0) {
|
||
|
|
padWithZeros(buf, digits);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Compute upper bound on number of digit groups and allocate space
|
||
|
|
int maxNumDigitGroups = (4*mag.length + 6)/7;
|
||
|
|
long[] digitGroups = new long[maxNumDigitGroups];
|
||
|
|
|
||
|
|
// Translate number to string, a digit group at a time
|
||
|
|
BigInteger tmp = this;
|
||
|
|
int numGroups = 0;
|
||
|
|
while (tmp.signum != 0) {
|
||
|
|
BigInteger d = longRadix[radix];
|
||
|
|
|
||
|
|
MutableBigInteger q = new MutableBigInteger(),
|
||
|
|
a = new MutableBigInteger(tmp.mag),
|
||
|
|
b = new MutableBigInteger(d.mag);
|
||
|
|
MutableBigInteger r = a.divide(b, q);
|
||
|
|
BigInteger q2 = q.toBigInteger(tmp.signum * d.signum);
|
||
|
|
BigInteger r2 = r.toBigInteger(tmp.signum * d.signum);
|
||
|
|
|
||
|
|
digitGroups[numGroups++] = r2.longValue();
|
||
|
|
tmp = q2;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Get string version of first digit group
|
||
|
|
String s = Long.toString(digitGroups[numGroups-1], radix);
|
||
|
|
|
||
|
|
// Pad with internal zeros if necessary.
|
||
|
|
padWithZeros(buf, digits - (s.length() +
|
||
|
|
(numGroups - 1)*digitsPerLong[radix]));
|
||
|
|
|
||
|
|
// Put first digit group into result buffer
|
||
|
|
buf.append(s);
|
||
|
|
|
||
|
|
// Append remaining digit groups each padded with leading zeros
|
||
|
|
for (int i=numGroups-2; i >= 0; i--) {
|
||
|
|
// Prepend (any) leading zeros for this digit group
|
||
|
|
s = Long.toString(digitGroups[i], radix);
|
||
|
|
int numLeadingZeros = digitsPerLong[radix] - s.length();
|
||
|
|
if (numLeadingZeros != 0) {
|
||
|
|
buf.append(ZEROS, 0, numLeadingZeros);
|
||
|
|
}
|
||
|
|
buf.append(s);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Converts the specified BigInteger to a string and appends to
|
||
|
|
* {@code sb}. This implements the recursive Schoenhage algorithm
|
||
|
|
* for base conversions. This method can only be called for non-negative
|
||
|
|
* numbers.
|
||
|
|
* <p>
|
||
|
|
* See Knuth, Donald, _The Art of Computer Programming_, Vol. 2,
|
||
|
|
* Answers to Exercises (4.4) Question 14.
|
||
|
|
*
|
||
|
|
* @param u The number to convert to a string.
|
||
|
|
* @param sb The StringBuilder that will be appended to in place.
|
||
|
|
* @param radix The base to convert to.
|
||
|
|
* @param digits The minimum number of digits to pad to.
|
||
|
|
*/
|
||
|
|
private static void toString(BigInteger u, StringBuilder sb,
|
||
|
|
int radix, int digits) {
|
||
|
|
assert u.signum() >= 0;
|
||
|
|
|
||
|
|
// If we're smaller than a certain threshold, use the smallToString
|
||
|
|
// method, padding with leading zeroes when necessary unless we're
|
||
|
|
// at the beginning of the string or digits <= 0. As u.signum() >= 0,
|
||
|
|
// smallToString() will not prepend a negative sign.
|
||
|
|
if (u.mag.length <= SCHOENHAGE_BASE_CONVERSION_THRESHOLD) {
|
||
|
|
u.smallToString(radix, sb, digits);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Calculate a value for n in the equation radix^(2^n) = u
|
||
|
|
// and subtract 1 from that value. This is used to find the
|
||
|
|
// cache index that contains the best value to divide u.
|
||
|
|
int b = u.bitLength();
|
||
|
|
int n = (int) Math.round(Math.log(b * LOG_TWO / logCache[radix]) /
|
||
|
|
LOG_TWO - 1.0);
|
||
|
|
|
||
|
|
BigInteger v = getRadixConversionCache(radix, n);
|
||
|
|
BigInteger[] results;
|
||
|
|
results = u.divideAndRemainder(v);
|
||
|
|
|
||
|
|
int expectedDigits = 1 << n;
|
||
|
|
|
||
|
|
// Now recursively build the two halves of each number.
|
||
|
|
toString(results[0], sb, radix, digits - expectedDigits);
|
||
|
|
toString(results[1], sb, radix, expectedDigits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the value radix^(2^exponent) from the cache.
|
||
|
|
* If this value doesn't already exist in the cache, it is added.
|
||
|
|
* <p>
|
||
|
|
* This could be changed to a more complicated caching method using
|
||
|
|
* {@code Future}.
|
||
|
|
*/
|
||
|
|
private static BigInteger getRadixConversionCache(int radix, int exponent) {
|
||
|
|
BigInteger[] cacheLine = powerCache[radix]; // volatile read
|
||
|
|
if (exponent < cacheLine.length) {
|
||
|
|
return cacheLine[exponent];
|
||
|
|
}
|
||
|
|
|
||
|
|
int oldLength = cacheLine.length;
|
||
|
|
cacheLine = Arrays.copyOf(cacheLine, exponent + 1);
|
||
|
|
for (int i = oldLength; i <= exponent; i++) {
|
||
|
|
cacheLine[i] = cacheLine[i - 1].pow(2);
|
||
|
|
}
|
||
|
|
|
||
|
|
BigInteger[][] pc = powerCache; // volatile read again
|
||
|
|
if (exponent >= pc[radix].length) {
|
||
|
|
pc = pc.clone();
|
||
|
|
pc[radix] = cacheLine;
|
||
|
|
powerCache = pc; // volatile write, publish
|
||
|
|
}
|
||
|
|
return cacheLine[exponent];
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Size of ZEROS string. */
|
||
|
|
private static int NUM_ZEROS = 63;
|
||
|
|
|
||
|
|
/* ZEROS is a string of NUM_ZEROS consecutive zeros. */
|
||
|
|
private static final String ZEROS = "0".repeat(NUM_ZEROS);
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the decimal String representation of this BigInteger.
|
||
|
|
* The digit-to-character mapping provided by
|
||
|
|
* {@code Character.forDigit} is used, and a minus sign is
|
||
|
|
* prepended if appropriate. (This representation is compatible
|
||
|
|
* with the {@link #BigInteger(String) (String)} constructor, and
|
||
|
|
* allows for String concatenation with Java's + operator.)
|
||
|
|
*
|
||
|
|
* @return decimal String representation of this BigInteger.
|
||
|
|
* @see Character#forDigit
|
||
|
|
* @see #BigInteger(java.lang.String)
|
||
|
|
*/
|
||
|
|
public String toString() {
|
||
|
|
return toString(10);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a byte array containing the two's-complement
|
||
|
|
* representation of this BigInteger. The byte array will be in
|
||
|
|
* <i>big-endian</i> byte-order: the most significant byte is in
|
||
|
|
* the zeroth element. The array will contain the minimum number
|
||
|
|
* of bytes required to represent this BigInteger, including at
|
||
|
|
* least one sign bit, which is {@code (ceil((this.bitLength() +
|
||
|
|
* 1)/8))}. (This representation is compatible with the
|
||
|
|
* {@link #BigInteger(byte[]) (byte[])} constructor.)
|
||
|
|
*
|
||
|
|
* @return a byte array containing the two's-complement representation of
|
||
|
|
* this BigInteger.
|
||
|
|
* @see #BigInteger(byte[])
|
||
|
|
*/
|
||
|
|
public byte[] toByteArray() {
|
||
|
|
int byteLen = bitLength()/8 + 1;
|
||
|
|
byte[] byteArray = new byte[byteLen];
|
||
|
|
|
||
|
|
for (int i=byteLen-1, bytesCopied=4, nextInt=0, intIndex=0; i >= 0; i--) {
|
||
|
|
if (bytesCopied == 4) {
|
||
|
|
nextInt = getInt(intIndex++);
|
||
|
|
bytesCopied = 1;
|
||
|
|
} else {
|
||
|
|
nextInt >>>= 8;
|
||
|
|
bytesCopied++;
|
||
|
|
}
|
||
|
|
byteArray[i] = (byte)nextInt;
|
||
|
|
}
|
||
|
|
return byteArray;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Converts this BigInteger to an {@code int}. This
|
||
|
|
* conversion is analogous to a
|
||
|
|
* <i>narrowing primitive conversion</i> from {@code long} to
|
||
|
|
* {@code int} as defined in
|
||
|
|
* <cite>The Java Language Specification</cite>:
|
||
|
|
* if this BigInteger is too big to fit in an
|
||
|
|
* {@code int}, only the low-order 32 bits are returned.
|
||
|
|
* Note that this conversion can lose information about the
|
||
|
|
* overall magnitude of the BigInteger value as well as return a
|
||
|
|
* result with the opposite sign.
|
||
|
|
*
|
||
|
|
* @return this BigInteger converted to an {@code int}.
|
||
|
|
* @see #intValueExact()
|
||
|
|
* @jls 5.1.3 Narrowing Primitive Conversion
|
||
|
|
*/
|
||
|
|
public int intValue() {
|
||
|
|
int result = 0;
|
||
|
|
result = getInt(0);
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Converts this BigInteger to a {@code long}. This
|
||
|
|
* conversion is analogous to a
|
||
|
|
* <i>narrowing primitive conversion</i> from {@code long} to
|
||
|
|
* {@code int} as defined in
|
||
|
|
* <cite>The Java Language Specification</cite>:
|
||
|
|
* if this BigInteger is too big to fit in a
|
||
|
|
* {@code long}, only the low-order 64 bits are returned.
|
||
|
|
* Note that this conversion can lose information about the
|
||
|
|
* overall magnitude of the BigInteger value as well as return a
|
||
|
|
* result with the opposite sign.
|
||
|
|
*
|
||
|
|
* @return this BigInteger converted to a {@code long}.
|
||
|
|
* @see #longValueExact()
|
||
|
|
* @jls 5.1.3 Narrowing Primitive Conversion
|
||
|
|
*/
|
||
|
|
public long longValue() {
|
||
|
|
long result = 0;
|
||
|
|
|
||
|
|
for (int i=1; i >= 0; i--)
|
||
|
|
result = (result << 32) + (getInt(i) & LONG_MASK);
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Converts this BigInteger to a {@code float}. This
|
||
|
|
* conversion is similar to the
|
||
|
|
* <i>narrowing primitive conversion</i> from {@code double} to
|
||
|
|
* {@code float} as defined in
|
||
|
|
* <cite>The Java Language Specification</cite>:
|
||
|
|
* if this BigInteger has too great a magnitude
|
||
|
|
* to represent as a {@code float}, it will be converted to
|
||
|
|
* {@link Float#NEGATIVE_INFINITY} or {@link
|
||
|
|
* Float#POSITIVE_INFINITY} as appropriate. Note that even when
|
||
|
|
* the return value is finite, this conversion can lose
|
||
|
|
* information about the precision of the BigInteger value.
|
||
|
|
*
|
||
|
|
* @return this BigInteger converted to a {@code float}.
|
||
|
|
* @jls 5.1.3 Narrowing Primitive Conversion
|
||
|
|
*/
|
||
|
|
public float floatValue() {
|
||
|
|
if (signum == 0) {
|
||
|
|
return 0.0f;
|
||
|
|
}
|
||
|
|
|
||
|
|
int exponent = ((mag.length - 1) << 5) + bitLengthForInt(mag[0]) - 1;
|
||
|
|
|
||
|
|
// exponent == floor(log2(abs(this)))
|
||
|
|
if (exponent < Long.SIZE - 1) {
|
||
|
|
return longValue();
|
||
|
|
} else if (exponent > Float.MAX_EXPONENT) {
|
||
|
|
return signum > 0 ? Float.POSITIVE_INFINITY : Float.NEGATIVE_INFINITY;
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
* We need the top SIGNIFICAND_WIDTH bits, including the "implicit"
|
||
|
|
* one bit. To make rounding easier, we pick out the top
|
||
|
|
* SIGNIFICAND_WIDTH + 1 bits, so we have one to help us round up or
|
||
|
|
* down. twiceSignifFloor will contain the top SIGNIFICAND_WIDTH + 1
|
||
|
|
* bits, and signifFloor the top SIGNIFICAND_WIDTH.
|
||
|
|
*
|
||
|
|
* It helps to consider the real number signif = abs(this) *
|
||
|
|
* 2^(SIGNIFICAND_WIDTH - 1 - exponent).
|
||
|
|
*/
|
||
|
|
int shift = exponent - FloatConsts.SIGNIFICAND_WIDTH;
|
||
|
|
|
||
|
|
int twiceSignifFloor;
|
||
|
|
// twiceSignifFloor will be == abs().shiftRight(shift).intValue()
|
||
|
|
// We do the shift into an int directly to improve performance.
|
||
|
|
|
||
|
|
int nBits = shift & 0x1f;
|
||
|
|
int nBits2 = 32 - nBits;
|
||
|
|
|
||
|
|
if (nBits == 0) {
|
||
|
|
twiceSignifFloor = mag[0];
|
||
|
|
} else {
|
||
|
|
twiceSignifFloor = mag[0] >>> nBits;
|
||
|
|
if (twiceSignifFloor == 0) {
|
||
|
|
twiceSignifFloor = (mag[0] << nBits2) | (mag[1] >>> nBits);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
int signifFloor = twiceSignifFloor >> 1;
|
||
|
|
signifFloor &= FloatConsts.SIGNIF_BIT_MASK; // remove the implied bit
|
||
|
|
|
||
|
|
/*
|
||
|
|
* We round up if either the fractional part of signif is strictly
|
||
|
|
* greater than 0.5 (which is true if the 0.5 bit is set and any lower
|
||
|
|
* bit is set), or if the fractional part of signif is >= 0.5 and
|
||
|
|
* signifFloor is odd (which is true if both the 0.5 bit and the 1 bit
|
||
|
|
* are set). This is equivalent to the desired HALF_EVEN rounding.
|
||
|
|
*/
|
||
|
|
boolean increment = (twiceSignifFloor & 1) != 0
|
||
|
|
&& ((signifFloor & 1) != 0 || abs().getLowestSetBit() < shift);
|
||
|
|
int signifRounded = increment ? signifFloor + 1 : signifFloor;
|
||
|
|
int bits = ((exponent + FloatConsts.EXP_BIAS))
|
||
|
|
<< (FloatConsts.SIGNIFICAND_WIDTH - 1);
|
||
|
|
bits += signifRounded;
|
||
|
|
/*
|
||
|
|
* If signifRounded == 2^24, we'd need to set all of the significand
|
||
|
|
* bits to zero and add 1 to the exponent. This is exactly the behavior
|
||
|
|
* we get from just adding signifRounded to bits directly. If the
|
||
|
|
* exponent is Float.MAX_EXPONENT, we round up (correctly) to
|
||
|
|
* Float.POSITIVE_INFINITY.
|
||
|
|
*/
|
||
|
|
bits |= signum & FloatConsts.SIGN_BIT_MASK;
|
||
|
|
return Float.intBitsToFloat(bits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Converts this BigInteger to a {@code double}. This
|
||
|
|
* conversion is similar to the
|
||
|
|
* <i>narrowing primitive conversion</i> from {@code double} to
|
||
|
|
* {@code float} as defined in
|
||
|
|
* <cite>The Java Language Specification</cite>:
|
||
|
|
* if this BigInteger has too great a magnitude
|
||
|
|
* to represent as a {@code double}, it will be converted to
|
||
|
|
* {@link Double#NEGATIVE_INFINITY} or {@link
|
||
|
|
* Double#POSITIVE_INFINITY} as appropriate. Note that even when
|
||
|
|
* the return value is finite, this conversion can lose
|
||
|
|
* information about the precision of the BigInteger value.
|
||
|
|
*
|
||
|
|
* @return this BigInteger converted to a {@code double}.
|
||
|
|
* @jls 5.1.3 Narrowing Primitive Conversion
|
||
|
|
*/
|
||
|
|
public double doubleValue() {
|
||
|
|
if (signum == 0) {
|
||
|
|
return 0.0;
|
||
|
|
}
|
||
|
|
|
||
|
|
int exponent = ((mag.length - 1) << 5) + bitLengthForInt(mag[0]) - 1;
|
||
|
|
|
||
|
|
// exponent == floor(log2(abs(this))Double)
|
||
|
|
if (exponent < Long.SIZE - 1) {
|
||
|
|
return longValue();
|
||
|
|
} else if (exponent > Double.MAX_EXPONENT) {
|
||
|
|
return signum > 0 ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY;
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
* We need the top SIGNIFICAND_WIDTH bits, including the "implicit"
|
||
|
|
* one bit. To make rounding easier, we pick out the top
|
||
|
|
* SIGNIFICAND_WIDTH + 1 bits, so we have one to help us round up or
|
||
|
|
* down. twiceSignifFloor will contain the top SIGNIFICAND_WIDTH + 1
|
||
|
|
* bits, and signifFloor the top SIGNIFICAND_WIDTH.
|
||
|
|
*
|
||
|
|
* It helps to consider the real number signif = abs(this) *
|
||
|
|
* 2^(SIGNIFICAND_WIDTH - 1 - exponent).
|
||
|
|
*/
|
||
|
|
int shift = exponent - DoubleConsts.SIGNIFICAND_WIDTH;
|
||
|
|
|
||
|
|
long twiceSignifFloor;
|
||
|
|
// twiceSignifFloor will be == abs().shiftRight(shift).longValue()
|
||
|
|
// We do the shift into a long directly to improve performance.
|
||
|
|
|
||
|
|
int nBits = shift & 0x1f;
|
||
|
|
int nBits2 = 32 - nBits;
|
||
|
|
|
||
|
|
int highBits;
|
||
|
|
int lowBits;
|
||
|
|
if (nBits == 0) {
|
||
|
|
highBits = mag[0];
|
||
|
|
lowBits = mag[1];
|
||
|
|
} else {
|
||
|
|
highBits = mag[0] >>> nBits;
|
||
|
|
lowBits = (mag[0] << nBits2) | (mag[1] >>> nBits);
|
||
|
|
if (highBits == 0) {
|
||
|
|
highBits = lowBits;
|
||
|
|
lowBits = (mag[1] << nBits2) | (mag[2] >>> nBits);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
twiceSignifFloor = ((highBits & LONG_MASK) << 32)
|
||
|
|
| (lowBits & LONG_MASK);
|
||
|
|
|
||
|
|
long signifFloor = twiceSignifFloor >> 1;
|
||
|
|
signifFloor &= DoubleConsts.SIGNIF_BIT_MASK; // remove the implied bit
|
||
|
|
|
||
|
|
/*
|
||
|
|
* We round up if either the fractional part of signif is strictly
|
||
|
|
* greater than 0.5 (which is true if the 0.5 bit is set and any lower
|
||
|
|
* bit is set), or if the fractional part of signif is >= 0.5 and
|
||
|
|
* signifFloor is odd (which is true if both the 0.5 bit and the 1 bit
|
||
|
|
* are set). This is equivalent to the desired HALF_EVEN rounding.
|
||
|
|
*/
|
||
|
|
boolean increment = (twiceSignifFloor & 1) != 0
|
||
|
|
&& ((signifFloor & 1) != 0 || abs().getLowestSetBit() < shift);
|
||
|
|
long signifRounded = increment ? signifFloor + 1 : signifFloor;
|
||
|
|
long bits = (long) ((exponent + DoubleConsts.EXP_BIAS))
|
||
|
|
<< (DoubleConsts.SIGNIFICAND_WIDTH - 1);
|
||
|
|
bits += signifRounded;
|
||
|
|
/*
|
||
|
|
* If signifRounded == 2^53, we'd need to set all of the significand
|
||
|
|
* bits to zero and add 1 to the exponent. This is exactly the behavior
|
||
|
|
* we get from just adding signifRounded to bits directly. If the
|
||
|
|
* exponent is Double.MAX_EXPONENT, we round up (correctly) to
|
||
|
|
* Double.POSITIVE_INFINITY.
|
||
|
|
*/
|
||
|
|
bits |= signum & DoubleConsts.SIGN_BIT_MASK;
|
||
|
|
return Double.longBitsToDouble(bits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a copy of the input array stripped of any leading zero bytes.
|
||
|
|
*/
|
||
|
|
private static int[] stripLeadingZeroInts(int val[]) {
|
||
|
|
int vlen = val.length;
|
||
|
|
int keep;
|
||
|
|
|
||
|
|
// Find first nonzero byte
|
||
|
|
for (keep = 0; keep < vlen && val[keep] == 0; keep++)
|
||
|
|
;
|
||
|
|
return java.util.Arrays.copyOfRange(val, keep, vlen);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the input array stripped of any leading zero bytes.
|
||
|
|
* Since the source is trusted the copying may be skipped.
|
||
|
|
*/
|
||
|
|
private static int[] trustedStripLeadingZeroInts(int val[]) {
|
||
|
|
int vlen = val.length;
|
||
|
|
int keep;
|
||
|
|
|
||
|
|
// Find first nonzero byte
|
||
|
|
for (keep = 0; keep < vlen && val[keep] == 0; keep++)
|
||
|
|
;
|
||
|
|
return keep == 0 ? val : java.util.Arrays.copyOfRange(val, keep, vlen);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns a copy of the input array stripped of any leading zero bytes.
|
||
|
|
*/
|
||
|
|
private static int[] stripLeadingZeroBytes(byte a[], int off, int len) {
|
||
|
|
int indexBound = off + len;
|
||
|
|
int keep;
|
||
|
|
|
||
|
|
// Find first nonzero byte
|
||
|
|
for (keep = off; keep < indexBound && a[keep] == 0; keep++)
|
||
|
|
;
|
||
|
|
|
||
|
|
// Allocate new array and copy relevant part of input array
|
||
|
|
int intLength = ((indexBound - keep) + 3) >>> 2;
|
||
|
|
int[] result = new int[intLength];
|
||
|
|
int b = indexBound - 1;
|
||
|
|
for (int i = intLength-1; i >= 0; i--) {
|
||
|
|
result[i] = a[b--] & 0xff;
|
||
|
|
int bytesRemaining = b - keep + 1;
|
||
|
|
int bytesToTransfer = Math.min(3, bytesRemaining);
|
||
|
|
for (int j=8; j <= (bytesToTransfer << 3); j += 8)
|
||
|
|
result[i] |= ((a[b--] & 0xff) << j);
|
||
|
|
}
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Takes an array a representing a negative 2's-complement number and
|
||
|
|
* returns the minimal (no leading zero bytes) unsigned whose value is -a.
|
||
|
|
*/
|
||
|
|
private static int[] makePositive(byte a[], int off, int len) {
|
||
|
|
int keep, k;
|
||
|
|
int indexBound = off + len;
|
||
|
|
|
||
|
|
// Find first non-sign (0xff) byte of input
|
||
|
|
for (keep=off; keep < indexBound && a[keep] == -1; keep++)
|
||
|
|
;
|
||
|
|
|
||
|
|
|
||
|
|
/* Allocate output array. If all non-sign bytes are 0x00, we must
|
||
|
|
* allocate space for one extra output byte. */
|
||
|
|
for (k=keep; k < indexBound && a[k] == 0; k++)
|
||
|
|
;
|
||
|
|
|
||
|
|
int extraByte = (k == indexBound) ? 1 : 0;
|
||
|
|
int intLength = ((indexBound - keep + extraByte) + 3) >>> 2;
|
||
|
|
int result[] = new int[intLength];
|
||
|
|
|
||
|
|
/* Copy one's complement of input into output, leaving extra
|
||
|
|
* byte (if it exists) == 0x00 */
|
||
|
|
int b = indexBound - 1;
|
||
|
|
for (int i = intLength-1; i >= 0; i--) {
|
||
|
|
result[i] = a[b--] & 0xff;
|
||
|
|
int numBytesToTransfer = Math.min(3, b-keep+1);
|
||
|
|
if (numBytesToTransfer < 0)
|
||
|
|
numBytesToTransfer = 0;
|
||
|
|
for (int j=8; j <= 8*numBytesToTransfer; j += 8)
|
||
|
|
result[i] |= ((a[b--] & 0xff) << j);
|
||
|
|
|
||
|
|
// Mask indicates which bits must be complemented
|
||
|
|
int mask = -1 >>> (8*(3-numBytesToTransfer));
|
||
|
|
result[i] = ~result[i] & mask;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Add one to one's complement to generate two's complement
|
||
|
|
for (int i=result.length-1; i >= 0; i--) {
|
||
|
|
result[i] = (int)((result[i] & LONG_MASK) + 1);
|
||
|
|
if (result[i] != 0)
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Takes an array a representing a negative 2's-complement number and
|
||
|
|
* returns the minimal (no leading zero ints) unsigned whose value is -a.
|
||
|
|
*/
|
||
|
|
private static int[] makePositive(int a[]) {
|
||
|
|
int keep, j;
|
||
|
|
|
||
|
|
// Find first non-sign (0xffffffff) int of input
|
||
|
|
for (keep=0; keep < a.length && a[keep] == -1; keep++)
|
||
|
|
;
|
||
|
|
|
||
|
|
/* Allocate output array. If all non-sign ints are 0x00, we must
|
||
|
|
* allocate space for one extra output int. */
|
||
|
|
for (j=keep; j < a.length && a[j] == 0; j++)
|
||
|
|
;
|
||
|
|
int extraInt = (j == a.length ? 1 : 0);
|
||
|
|
int result[] = new int[a.length - keep + extraInt];
|
||
|
|
|
||
|
|
/* Copy one's complement of input into output, leaving extra
|
||
|
|
* int (if it exists) == 0x00 */
|
||
|
|
for (int i = keep; i < a.length; i++)
|
||
|
|
result[i - keep + extraInt] = ~a[i];
|
||
|
|
|
||
|
|
// Add one to one's complement to generate two's complement
|
||
|
|
for (int i=result.length-1; ++result[i] == 0; i--)
|
||
|
|
;
|
||
|
|
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
* The following two arrays are used for fast String conversions. Both
|
||
|
|
* are indexed by radix. The first is the number of digits of the given
|
||
|
|
* radix that can fit in a Java long without "going negative", i.e., the
|
||
|
|
* highest integer n such that radix**n < 2**63. The second is the
|
||
|
|
* "long radix" that tears each number into "long digits", each of which
|
||
|
|
* consists of the number of digits in the corresponding element in
|
||
|
|
* digitsPerLong (longRadix[i] = i**digitPerLong[i]). Both arrays have
|
||
|
|
* nonsense values in their 0 and 1 elements, as radixes 0 and 1 are not
|
||
|
|
* used.
|
||
|
|
*/
|
||
|
|
private static int digitsPerLong[] = {0, 0,
|
||
|
|
62, 39, 31, 27, 24, 22, 20, 19, 18, 18, 17, 17, 16, 16, 15, 15, 15, 14,
|
||
|
|
14, 14, 14, 13, 13, 13, 13, 13, 13, 12, 12, 12, 12, 12, 12, 12, 12};
|
||
|
|
|
||
|
|
private static BigInteger longRadix[] = {null, null,
|
||
|
|
valueOf(0x4000000000000000L), valueOf(0x383d9170b85ff80bL),
|
||
|
|
valueOf(0x4000000000000000L), valueOf(0x6765c793fa10079dL),
|
||
|
|
valueOf(0x41c21cb8e1000000L), valueOf(0x3642798750226111L),
|
||
|
|
valueOf(0x1000000000000000L), valueOf(0x12bf307ae81ffd59L),
|
||
|
|
valueOf( 0xde0b6b3a7640000L), valueOf(0x4d28cb56c33fa539L),
|
||
|
|
valueOf(0x1eca170c00000000L), valueOf(0x780c7372621bd74dL),
|
||
|
|
valueOf(0x1e39a5057d810000L), valueOf(0x5b27ac993df97701L),
|
||
|
|
valueOf(0x1000000000000000L), valueOf(0x27b95e997e21d9f1L),
|
||
|
|
valueOf(0x5da0e1e53c5c8000L), valueOf( 0xb16a458ef403f19L),
|
||
|
|
valueOf(0x16bcc41e90000000L), valueOf(0x2d04b7fdd9c0ef49L),
|
||
|
|
valueOf(0x5658597bcaa24000L), valueOf( 0x6feb266931a75b7L),
|
||
|
|
valueOf( 0xc29e98000000000L), valueOf(0x14adf4b7320334b9L),
|
||
|
|
valueOf(0x226ed36478bfa000L), valueOf(0x383d9170b85ff80bL),
|
||
|
|
valueOf(0x5a3c23e39c000000L), valueOf( 0x4e900abb53e6b71L),
|
||
|
|
valueOf( 0x7600ec618141000L), valueOf( 0xaee5720ee830681L),
|
||
|
|
valueOf(0x1000000000000000L), valueOf(0x172588ad4f5f0981L),
|
||
|
|
valueOf(0x211e44f7d02c1000L), valueOf(0x2ee56725f06e5c71L),
|
||
|
|
valueOf(0x41c21cb8e1000000L)};
|
||
|
|
|
||
|
|
/*
|
||
|
|
* These two arrays are the integer analogue of above.
|
||
|
|
*/
|
||
|
|
private static int digitsPerInt[] = {0, 0, 30, 19, 15, 13, 11,
|
||
|
|
11, 10, 9, 9, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6,
|
||
|
|
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5};
|
||
|
|
|
||
|
|
private static int intRadix[] = {0, 0,
|
||
|
|
0x40000000, 0x4546b3db, 0x40000000, 0x48c27395, 0x159fd800,
|
||
|
|
0x75db9c97, 0x40000000, 0x17179149, 0x3b9aca00, 0xcc6db61,
|
||
|
|
0x19a10000, 0x309f1021, 0x57f6c100, 0xa2f1b6f, 0x10000000,
|
||
|
|
0x18754571, 0x247dbc80, 0x3547667b, 0x4c4b4000, 0x6b5a6e1d,
|
||
|
|
0x6c20a40, 0x8d2d931, 0xb640000, 0xe8d4a51, 0x1269ae40,
|
||
|
|
0x17179149, 0x1cb91000, 0x23744899, 0x2b73a840, 0x34e63b41,
|
||
|
|
0x40000000, 0x4cfa3cc1, 0x5c13d840, 0x6d91b519, 0x39aa400
|
||
|
|
};
|
||
|
|
|
||
|
|
/**
|
||
|
|
* These routines provide access to the two's complement representation
|
||
|
|
* of BigIntegers.
|
||
|
|
*/
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the length of the two's complement representation in ints,
|
||
|
|
* including space for at least one sign bit.
|
||
|
|
*/
|
||
|
|
private int intLength() {
|
||
|
|
return (bitLength() >>> 5) + 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Returns sign bit */
|
||
|
|
private int signBit() {
|
||
|
|
return signum < 0 ? 1 : 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Returns an int of sign bits */
|
||
|
|
private int signInt() {
|
||
|
|
return signum < 0 ? -1 : 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the specified int of the little-endian two's complement
|
||
|
|
* representation (int 0 is the least significant). The int number can
|
||
|
|
* be arbitrarily high (values are logically preceded by infinitely many
|
||
|
|
* sign ints).
|
||
|
|
*/
|
||
|
|
private int getInt(int n) {
|
||
|
|
if (n < 0)
|
||
|
|
return 0;
|
||
|
|
if (n >= mag.length)
|
||
|
|
return signInt();
|
||
|
|
|
||
|
|
int magInt = mag[mag.length-n-1];
|
||
|
|
|
||
|
|
return (signum >= 0 ? magInt :
|
||
|
|
(n <= firstNonzeroIntNum() ? -magInt : ~magInt));
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the index of the int that contains the first nonzero int in the
|
||
|
|
* little-endian binary representation of the magnitude (int 0 is the
|
||
|
|
* least significant). If the magnitude is zero, return value is undefined.
|
||
|
|
*
|
||
|
|
* <p>Note: never used for a BigInteger with a magnitude of zero.
|
||
|
|
* @see #getInt
|
||
|
|
*/
|
||
|
|
private int firstNonzeroIntNum() {
|
||
|
|
int fn = firstNonzeroIntNumPlusTwo - 2;
|
||
|
|
if (fn == -2) { // firstNonzeroIntNum not initialized yet
|
||
|
|
// Search for the first nonzero int
|
||
|
|
int i;
|
||
|
|
int mlen = mag.length;
|
||
|
|
for (i = mlen - 1; i >= 0 && mag[i] == 0; i--)
|
||
|
|
;
|
||
|
|
fn = mlen - i - 1;
|
||
|
|
firstNonzeroIntNumPlusTwo = fn + 2; // offset by two to initialize
|
||
|
|
}
|
||
|
|
return fn;
|
||
|
|
}
|
||
|
|
|
||
|
|
/** use serialVersionUID from JDK 1.1. for interoperability */
|
||
|
|
@java.io.Serial
|
||
|
|
private static final long serialVersionUID = -8287574255936472291L;
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Serializable fields for BigInteger.
|
||
|
|
*
|
||
|
|
* @serialField signum int
|
||
|
|
* signum of this BigInteger
|
||
|
|
* @serialField magnitude byte[]
|
||
|
|
* magnitude array of this BigInteger
|
||
|
|
* @serialField bitCount int
|
||
|
|
* appears in the serialized form for backward compatibility
|
||
|
|
* @serialField bitLength int
|
||
|
|
* appears in the serialized form for backward compatibility
|
||
|
|
* @serialField firstNonzeroByteNum int
|
||
|
|
* appears in the serialized form for backward compatibility
|
||
|
|
* @serialField lowestSetBit int
|
||
|
|
* appears in the serialized form for backward compatibility
|
||
|
|
*/
|
||
|
|
@java.io.Serial
|
||
|
|
private static final ObjectStreamField[] serialPersistentFields = {
|
||
|
|
new ObjectStreamField("signum", Integer.TYPE),
|
||
|
|
new ObjectStreamField("magnitude", byte[].class),
|
||
|
|
new ObjectStreamField("bitCount", Integer.TYPE),
|
||
|
|
new ObjectStreamField("bitLength", Integer.TYPE),
|
||
|
|
new ObjectStreamField("firstNonzeroByteNum", Integer.TYPE),
|
||
|
|
new ObjectStreamField("lowestSetBit", Integer.TYPE)
|
||
|
|
};
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Reconstitute the {@code BigInteger} instance from a stream (that is,
|
||
|
|
* deserialize it). The magnitude is read in as an array of bytes
|
||
|
|
* for historical reasons, but it is converted to an array of ints
|
||
|
|
* and the byte array is discarded.
|
||
|
|
* Note:
|
||
|
|
* The current convention is to initialize the cache fields, bitCountPlusOne,
|
||
|
|
* bitLengthPlusOne and lowestSetBitPlusTwo, to 0 rather than some other
|
||
|
|
* marker value. Therefore, no explicit action to set these fields needs to
|
||
|
|
* be taken in readObject because those fields already have a 0 value by
|
||
|
|
* default since defaultReadObject is not being used.
|
||
|
|
*
|
||
|
|
* @param s the stream being read.
|
||
|
|
* @throws IOException if an I/O error occurs
|
||
|
|
* @throws ClassNotFoundException if a serialized class cannot be loaded
|
||
|
|
*/
|
||
|
|
@java.io.Serial
|
||
|
|
private void readObject(java.io.ObjectInputStream s)
|
||
|
|
throws java.io.IOException, ClassNotFoundException {
|
||
|
|
// prepare to read the alternate persistent fields
|
||
|
|
ObjectInputStream.GetField fields = s.readFields();
|
||
|
|
|
||
|
|
// Read and validate the alternate persistent fields that we
|
||
|
|
// care about, signum and magnitude
|
||
|
|
|
||
|
|
// Read and validate signum
|
||
|
|
int sign = fields.get("signum", -2);
|
||
|
|
if (sign < -1 || sign > 1) {
|
||
|
|
String message = "BigInteger: Invalid signum value";
|
||
|
|
if (fields.defaulted("signum"))
|
||
|
|
message = "BigInteger: Signum not present in stream";
|
||
|
|
throw new java.io.StreamCorruptedException(message);
|
||
|
|
}
|
||
|
|
|
||
|
|
// Read and validate magnitude
|
||
|
|
byte[] magnitude = (byte[])fields.get("magnitude", null);
|
||
|
|
magnitude = magnitude.clone(); // defensive copy
|
||
|
|
int[] mag = stripLeadingZeroBytes(magnitude, 0, magnitude.length);
|
||
|
|
if ((mag.length == 0) != (sign == 0)) {
|
||
|
|
String message = "BigInteger: signum-magnitude mismatch";
|
||
|
|
if (fields.defaulted("magnitude"))
|
||
|
|
message = "BigInteger: Magnitude not present in stream";
|
||
|
|
throw new java.io.StreamCorruptedException(message);
|
||
|
|
}
|
||
|
|
|
||
|
|
// Equivalent to checkRange() on mag local without assigning
|
||
|
|
// this.mag field
|
||
|
|
if (mag.length > MAX_MAG_LENGTH ||
|
||
|
|
(mag.length == MAX_MAG_LENGTH && mag[0] < 0)) {
|
||
|
|
throw new java.io.StreamCorruptedException("BigInteger: Out of the supported range");
|
||
|
|
}
|
||
|
|
|
||
|
|
// Commit final fields via Unsafe
|
||
|
|
UnsafeHolder.putSignAndMag(this, sign, mag);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Serialization without data not supported for this class.
|
||
|
|
*/
|
||
|
|
@java.io.Serial
|
||
|
|
private void readObjectNoData()
|
||
|
|
throws ObjectStreamException {
|
||
|
|
throw new InvalidObjectException("Deserialized BigInteger objects need data");
|
||
|
|
}
|
||
|
|
|
||
|
|
// Support for resetting final fields while deserializing
|
||
|
|
private static class UnsafeHolder {
|
||
|
|
private static final sun.misc.Unsafe unsafe;
|
||
|
|
private static final long signumOffset;
|
||
|
|
private static final long magOffset;
|
||
|
|
static {
|
||
|
|
try {
|
||
|
|
unsafe = sun.misc.Unsafe.getUnsafe();
|
||
|
|
signumOffset = unsafe.objectFieldOffset
|
||
|
|
(BigInteger.class.getDeclaredField("signum"));
|
||
|
|
magOffset = unsafe.objectFieldOffset
|
||
|
|
(BigInteger.class.getDeclaredField("mag"));
|
||
|
|
} catch (Exception ex) {
|
||
|
|
throw new ExceptionInInitializerError(ex);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
static void putSignAndMag(BigInteger bi, int sign, int[] magnitude) {
|
||
|
|
unsafe.putIntVolatile(bi, signumOffset, sign);
|
||
|
|
unsafe.putObjectVolatile(bi, magOffset, magnitude);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Save the {@code BigInteger} instance to a stream. The magnitude of a
|
||
|
|
* {@code BigInteger} is serialized as a byte array for historical reasons.
|
||
|
|
* To maintain compatibility with older implementations, the integers
|
||
|
|
* -1, -1, -2, and -2 are written as the values of the obsolete fields
|
||
|
|
* {@code bitCount}, {@code bitLength}, {@code lowestSetBit}, and
|
||
|
|
* {@code firstNonzeroByteNum}, respectively. These values are compatible
|
||
|
|
* with older implementations, but will be ignored by current
|
||
|
|
* implementations.
|
||
|
|
*
|
||
|
|
* @param s the stream to serialize to.
|
||
|
|
* @throws IOException if an I/O error occurs
|
||
|
|
*/
|
||
|
|
@java.io.Serial
|
||
|
|
private void writeObject(ObjectOutputStream s) throws IOException {
|
||
|
|
// set the values of the Serializable fields
|
||
|
|
ObjectOutputStream.PutField fields = s.putFields();
|
||
|
|
fields.put("signum", signum);
|
||
|
|
fields.put("magnitude", magSerializedForm());
|
||
|
|
// The values written for cached fields are compatible with older
|
||
|
|
// versions, but are ignored in readObject so don't otherwise matter.
|
||
|
|
// BEGIN Android-changed: Don't include the following fields.
|
||
|
|
/*
|
||
|
|
fields.put("bitCount", -1);
|
||
|
|
fields.put("bitLength", -1);
|
||
|
|
fields.put("lowestSetBit", -2);
|
||
|
|
fields.put("firstNonzeroByteNum", -2);
|
||
|
|
*/
|
||
|
|
// END Android-changed: Don't include the following fields.
|
||
|
|
|
||
|
|
// save them
|
||
|
|
s.writeFields();
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Returns the mag array as an array of bytes.
|
||
|
|
*/
|
||
|
|
private byte[] magSerializedForm() {
|
||
|
|
int len = mag.length;
|
||
|
|
|
||
|
|
int bitLen = (len == 0 ? 0 : ((len - 1) << 5) + bitLengthForInt(mag[0]));
|
||
|
|
int byteLen = (bitLen + 7) >>> 3;
|
||
|
|
byte[] result = new byte[byteLen];
|
||
|
|
|
||
|
|
for (int i = byteLen - 1, bytesCopied = 4, intIndex = len - 1, nextInt = 0;
|
||
|
|
i >= 0; i--) {
|
||
|
|
if (bytesCopied == 4) {
|
||
|
|
nextInt = mag[intIndex--];
|
||
|
|
bytesCopied = 1;
|
||
|
|
} else {
|
||
|
|
nextInt >>>= 8;
|
||
|
|
bytesCopied++;
|
||
|
|
}
|
||
|
|
result[i] = (byte)nextInt;
|
||
|
|
}
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Converts this {@code BigInteger} to a {@code long}, checking
|
||
|
|
* for lost information. If the value of this {@code BigInteger}
|
||
|
|
* is out of the range of the {@code long} type, then an
|
||
|
|
* {@code ArithmeticException} is thrown.
|
||
|
|
*
|
||
|
|
* @return this {@code BigInteger} converted to a {@code long}.
|
||
|
|
* @throws ArithmeticException if the value of {@code this} will
|
||
|
|
* not exactly fit in a {@code long}.
|
||
|
|
* @see BigInteger#longValue
|
||
|
|
* @since 1.8
|
||
|
|
*/
|
||
|
|
public long longValueExact() {
|
||
|
|
if (mag.length <= 2 && bitLength() <= 63)
|
||
|
|
return longValue();
|
||
|
|
else
|
||
|
|
throw new ArithmeticException("BigInteger out of long range");
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Converts this {@code BigInteger} to an {@code int}, checking
|
||
|
|
* for lost information. If the value of this {@code BigInteger}
|
||
|
|
* is out of the range of the {@code int} type, then an
|
||
|
|
* {@code ArithmeticException} is thrown.
|
||
|
|
*
|
||
|
|
* @return this {@code BigInteger} converted to an {@code int}.
|
||
|
|
* @throws ArithmeticException if the value of {@code this} will
|
||
|
|
* not exactly fit in an {@code int}.
|
||
|
|
* @see BigInteger#intValue
|
||
|
|
* @since 1.8
|
||
|
|
*/
|
||
|
|
public int intValueExact() {
|
||
|
|
if (mag.length <= 1 && bitLength() <= 31)
|
||
|
|
return intValue();
|
||
|
|
else
|
||
|
|
throw new ArithmeticException("BigInteger out of int range");
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Converts this {@code BigInteger} to a {@code short}, checking
|
||
|
|
* for lost information. If the value of this {@code BigInteger}
|
||
|
|
* is out of the range of the {@code short} type, then an
|
||
|
|
* {@code ArithmeticException} is thrown.
|
||
|
|
*
|
||
|
|
* @return this {@code BigInteger} converted to a {@code short}.
|
||
|
|
* @throws ArithmeticException if the value of {@code this} will
|
||
|
|
* not exactly fit in a {@code short}.
|
||
|
|
* @see BigInteger#shortValue
|
||
|
|
* @since 1.8
|
||
|
|
*/
|
||
|
|
public short shortValueExact() {
|
||
|
|
if (mag.length <= 1 && bitLength() <= 31) {
|
||
|
|
int value = intValue();
|
||
|
|
if (value >= Short.MIN_VALUE && value <= Short.MAX_VALUE)
|
||
|
|
return shortValue();
|
||
|
|
}
|
||
|
|
throw new ArithmeticException("BigInteger out of short range");
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Converts this {@code BigInteger} to a {@code byte}, checking
|
||
|
|
* for lost information. If the value of this {@code BigInteger}
|
||
|
|
* is out of the range of the {@code byte} type, then an
|
||
|
|
* {@code ArithmeticException} is thrown.
|
||
|
|
*
|
||
|
|
* @return this {@code BigInteger} converted to a {@code byte}.
|
||
|
|
* @throws ArithmeticException if the value of {@code this} will
|
||
|
|
* not exactly fit in a {@code byte}.
|
||
|
|
* @see BigInteger#byteValue
|
||
|
|
* @since 1.8
|
||
|
|
*/
|
||
|
|
public byte byteValueExact() {
|
||
|
|
if (mag.length <= 1 && bitLength() <= 31) {
|
||
|
|
int value = intValue();
|
||
|
|
if (value >= Byte.MIN_VALUE && value <= Byte.MAX_VALUE)
|
||
|
|
return byteValue();
|
||
|
|
}
|
||
|
|
throw new ArithmeticException("BigInteger out of byte range");
|
||
|
|
}
|
||
|
|
}
|