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Merge
This commit is contained in:
Jesper Wilhelmsson
commit
a8c5f1e59a
64 changed files with 1781 additions and 378 deletions
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@ -1,5 +1,5 @@
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/*
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* Copyright (c) 1996, 2017, Oracle and/or its affiliates. All rights reserved.
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* Copyright (c) 1996, 2018, 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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@ -31,6 +31,7 @@ package java.math;
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import static java.math.BigInteger.LONG_MASK;
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import java.util.Arrays;
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import java.util.Objects;
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/**
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* Immutable, arbitrary-precision signed decimal numbers. A
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@ -424,9 +425,14 @@ public class BigDecimal extends Number implements Comparable<BigDecimal> {
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* @since 1.5
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*/
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public BigDecimal(char[] in, int offset, int len, MathContext mc) {
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// protect against huge length.
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if (offset + len > in.length || offset < 0)
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throw new NumberFormatException("Bad offset or len arguments for char[] input.");
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// protect against huge length, negative values, and integer overflow
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try {
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Objects.checkFromIndexSize(offset, len, in.length);
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} catch (IndexOutOfBoundsException e) {
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throw new NumberFormatException
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("Bad offset or len arguments for char[] input.");
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}
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// This is the primary string to BigDecimal constructor; all
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// incoming strings end up here; it uses explicit (inline)
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// parsing for speed and generates at most one intermediate
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@ -307,10 +307,8 @@ public class BigInteger extends Number implements Comparable<BigInteger> {
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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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} else if ((off < 0) || (off >= val.length) || (len < 0) ||
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(len > val.length - off)) { // 0 <= off < val.length
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throw new IndexOutOfBoundsException();
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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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@ -395,12 +393,8 @@ public class BigInteger extends Number implements Comparable<BigInteger> {
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public BigInteger(int signum, byte[] magnitude, int off, int len) {
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if (signum < -1 || signum > 1) {
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throw(new NumberFormatException("Invalid signum value"));
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} else if ((off < 0) || (len < 0) ||
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(len > 0 &&
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((off >= magnitude.length) ||
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(len > magnitude.length - off)))) { // 0 <= off < magnitude.length
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throw new IndexOutOfBoundsException();
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}
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Objects.checkFromIndexSize(off, len, magnitude.length);
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// stripLeadingZeroBytes() returns a zero length array if len == 0
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this.mag = stripLeadingZeroBytes(magnitude, off, len);
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@ -1239,6 +1233,14 @@ public class BigInteger extends Number implements Comparable<BigInteger> {
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private static final double LOG_TWO = Math.log(2.0);
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static {
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assert 0 < KARATSUBA_THRESHOLD
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&& KARATSUBA_THRESHOLD < TOOM_COOK_THRESHOLD
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&& TOOM_COOK_THRESHOLD < Integer.MAX_VALUE
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&& 0 < KARATSUBA_SQUARE_THRESHOLD
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&& KARATSUBA_SQUARE_THRESHOLD < TOOM_COOK_SQUARE_THRESHOLD
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&& TOOM_COOK_SQUARE_THRESHOLD < Integer.MAX_VALUE :
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"Algorithm thresholds are inconsistent";
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for (int i = 1; i <= MAX_CONSTANT; i++) {
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int[] magnitude = new int[1];
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magnitude[0] = i;
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@ -1562,6 +1564,18 @@ public class BigInteger extends Number implements Comparable<BigInteger> {
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* @return {@code this * val}
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*/
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public BigInteger multiply(BigInteger val) {
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return multiply(val, false);
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}
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/**
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* Returns a BigInteger whose value is {@code (this * val)}. If
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* the invocation is recursive certain overflow checks are skipped.
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*
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* @param val value to be multiplied by this BigInteger.
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* @param isRecursion whether this is a recursive invocation
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* @return {@code this * val}
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*/
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private BigInteger multiply(BigInteger val, boolean isRecursion) {
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if (val.signum == 0 || signum == 0)
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return ZERO;
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@ -1589,6 +1603,63 @@ public class BigInteger extends Number implements Comparable<BigInteger> {
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if ((xlen < TOOM_COOK_THRESHOLD) && (ylen < TOOM_COOK_THRESHOLD)) {
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return multiplyKaratsuba(this, val);
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} else {
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//
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// In "Hacker's Delight" section 2-13, p.33, it is explained
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// that if x and y are unsigned 32-bit quantities and m and n
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// are their respective numbers of leading zeros within 32 bits,
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// then the number of leading zeros within their product as a
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// 64-bit unsigned quantity is either m + n or m + n + 1. If
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// their product is not to overflow, it cannot exceed 32 bits,
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// and so the number of leading zeros of the product within 64
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// bits must be at least 32, i.e., the leftmost set bit is at
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// zero-relative position 31 or less.
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//
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// From the above there are three cases:
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//
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// m + n leftmost set bit condition
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// ----- ---------------- ---------
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// >= 32 x <= 64 - 32 = 32 no overflow
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// == 31 x >= 64 - 32 = 32 possible overflow
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// <= 30 x >= 64 - 31 = 33 definite overflow
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//
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// The "possible overflow" condition cannot be detected by
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// examning data lengths alone and requires further calculation.
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//
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// By analogy, if 'this' and 'val' have m and n as their
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// respective numbers of leading zeros within 32*MAX_MAG_LENGTH
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// bits, then:
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//
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// m + n >= 32*MAX_MAG_LENGTH no overflow
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// m + n == 32*MAX_MAG_LENGTH - 1 possible overflow
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// m + n <= 32*MAX_MAG_LENGTH - 2 definite overflow
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//
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// Note however that if the number of ints in the result
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// were to be MAX_MAG_LENGTH and mag[0] < 0, then there would
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// be overflow. As a result the leftmost bit (of mag[0]) cannot
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// be used and the constraints must be adjusted by one bit to:
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//
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// m + n > 32*MAX_MAG_LENGTH no overflow
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// m + n == 32*MAX_MAG_LENGTH possible overflow
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// m + n < 32*MAX_MAG_LENGTH definite overflow
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//
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// The foregoing leading zero-based discussion is for clarity
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// only. The actual calculations use the estimated bit length
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// of the product as this is more natural to the internal
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// array representation of the magnitude which has no leading
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// zero elements.
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//
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if (!isRecursion) {
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// The bitLength() instance method is not used here as we
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// are only considering the magnitudes as non-negative. The
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// Toom-Cook multiplication algorithm determines the sign
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// at its end from the two signum values.
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if (bitLength(mag, mag.length) +
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bitLength(val.mag, val.mag.length) >
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32L*MAX_MAG_LENGTH) {
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reportOverflow();
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}
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}
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return multiplyToomCook3(this, val);
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}
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}
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@ -1674,7 +1745,7 @@ public class BigInteger extends Number implements Comparable<BigInteger> {
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int ystart = ylen - 1;
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if (z == null || z.length < (xlen+ ylen))
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z = new int[xlen+ylen];
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z = new int[xlen+ylen];
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long carry = 0;
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for (int j=ystart, k=ystart+1+xstart; j >= 0; j--, k--) {
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@ -1808,16 +1879,16 @@ public class BigInteger extends Number implements Comparable<BigInteger> {
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BigInteger v0, v1, v2, vm1, vinf, t1, t2, tm1, da1, db1;
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v0 = a0.multiply(b0);
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v0 = a0.multiply(b0, true);
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da1 = a2.add(a0);
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db1 = b2.add(b0);
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vm1 = da1.subtract(a1).multiply(db1.subtract(b1));
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vm1 = da1.subtract(a1).multiply(db1.subtract(b1), true);
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da1 = da1.add(a1);
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db1 = db1.add(b1);
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v1 = da1.multiply(db1);
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v1 = da1.multiply(db1, true);
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v2 = da1.add(a2).shiftLeft(1).subtract(a0).multiply(
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db1.add(b2).shiftLeft(1).subtract(b0));
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vinf = a2.multiply(b2);
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db1.add(b2).shiftLeft(1).subtract(b0), true);
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vinf = a2.multiply(b2, true);
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// The algorithm requires two divisions by 2 and one by 3.
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// All divisions are known to be exact, that is, they do not produce
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@ -1983,6 +2054,17 @@ public class BigInteger extends Number implements Comparable<BigInteger> {
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* @return {@code this<sup>2</sup>}
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*/
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private BigInteger square() {
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return square(false);
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}
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/**
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* Returns a BigInteger whose value is {@code (this<sup>2</sup>)}. If
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* the invocation is recursive certain overflow checks are skipped.
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*
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* @param isRecursion whether this is a recursive invocation
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* @return {@code this<sup>2</sup>}
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*/
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private BigInteger square(boolean isRecursion) {
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if (signum == 0) {
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return ZERO;
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}
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@ -1995,6 +2077,15 @@ public class BigInteger extends Number implements Comparable<BigInteger> {
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if (len < TOOM_COOK_SQUARE_THRESHOLD) {
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return squareKaratsuba();
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} else {
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//
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// For a discussion of overflow detection see multiply()
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//
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if (!isRecursion) {
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if (bitLength(mag, mag.length) > 16L*MAX_MAG_LENGTH) {
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reportOverflow();
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}
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}
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return squareToomCook3();
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}
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}
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@ -2146,13 +2237,13 @@ public class BigInteger extends Number implements Comparable<BigInteger> {
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a0 = getToomSlice(k, r, 2, len);
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BigInteger v0, v1, v2, vm1, vinf, t1, t2, tm1, da1;
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v0 = a0.square();
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v0 = a0.square(true);
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da1 = a2.add(a0);
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vm1 = da1.subtract(a1).square();
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vm1 = da1.subtract(a1).square(true);
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da1 = da1.add(a1);
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v1 = da1.square();
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vinf = a2.square();
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v2 = da1.add(a2).shiftLeft(1).subtract(a0).square();
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v1 = da1.square(true);
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vinf = a2.square(true);
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v2 = da1.add(a2).shiftLeft(1).subtract(a0).square(true);
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// The algorithm requires two divisions by 2 and one by 3.
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// All divisions are known to be exact, that is, they do not produce
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@ -2323,10 +2414,11 @@ public class BigInteger extends Number implements Comparable<BigInteger> {
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// The remaining part can then be exponentiated faster. The
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// powers of two will be multiplied back at the end.
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int powersOfTwo = partToSquare.getLowestSetBit();
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long bitsToShift = (long)powersOfTwo * exponent;
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if (bitsToShift > Integer.MAX_VALUE) {
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long bitsToShiftLong = (long)powersOfTwo * exponent;
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if (bitsToShiftLong > Integer.MAX_VALUE) {
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reportOverflow();
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}
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int bitsToShift = (int)bitsToShiftLong;
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int remainingBits;
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@ -2336,9 +2428,9 @@ public class BigInteger extends Number implements Comparable<BigInteger> {
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remainingBits = partToSquare.bitLength();
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if (remainingBits == 1) { // Nothing left but +/- 1?
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if (signum < 0 && (exponent&1) == 1) {
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return NEGATIVE_ONE.shiftLeft(powersOfTwo*exponent);
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return NEGATIVE_ONE.shiftLeft(bitsToShift);
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} else {
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return ONE.shiftLeft(powersOfTwo*exponent);
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return ONE.shiftLeft(bitsToShift);
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}
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}
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} else {
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@ -2383,13 +2475,16 @@ public class BigInteger extends Number implements Comparable<BigInteger> {
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if (bitsToShift + scaleFactor <= 62) { // Fits in long?
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return valueOf((result << bitsToShift) * newSign);
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} else {
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return valueOf(result*newSign).shiftLeft((int) bitsToShift);
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return valueOf(result*newSign).shiftLeft(bitsToShift);
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}
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}
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else {
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} else {
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return valueOf(result*newSign);
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}
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} else {
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if ((long)bitLength() * exponent / Integer.SIZE > MAX_MAG_LENGTH) {
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reportOverflow();
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}
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// Large number algorithm. This is basically identical to
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// the algorithm above, but calls multiply() and square()
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// which may use more efficient algorithms for large numbers.
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@ -2409,7 +2504,7 @@ public class BigInteger extends Number implements Comparable<BigInteger> {
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// Multiply back the (exponentiated) powers of two (quickly,
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// by shifting left)
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if (powersOfTwo > 0) {
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answer = answer.shiftLeft(powersOfTwo*exponent);
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answer = answer.shiftLeft(bitsToShift);
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}
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if (signum < 0 && (exponent&1) == 1) {
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@ -3584,7 +3679,7 @@ public class BigInteger extends Number implements Comparable<BigInteger> {
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for (int i=1; i< len && pow2; i++)
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pow2 = (mag[i] == 0);
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n = (pow2 ? magBitLength -1 : magBitLength);
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n = (pow2 ? magBitLength - 1 : magBitLength);
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} else {
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n = magBitLength;
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}
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