--- a/jdk/src/java.base/share/classes/sun/misc/FDBigInteger.java Thu Dec 24 10:33:21 2015 -0800
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,1508 +0,0 @@
-/*
- * Copyright (c) 2013, Oracle and/or its affiliates. All rights reserved.
- * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
- *
- * This code is free software; you can redistribute it and/or modify it
- * under the terms of the GNU General Public License version 2 only, as
- * published by the Free Software Foundation. Oracle designates this
- * particular file as subject to the "Classpath" exception as provided
- * by Oracle in the LICENSE file that accompanied this code.
- *
- * This code is distributed in the hope that it will be useful, but WITHOUT
- * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
- * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
- * version 2 for more details (a copy is included in the LICENSE file that
- * accompanied this code).
- *
- * You should have received a copy of the GNU General Public License version
- * 2 along with this work; if not, write to the Free Software Foundation,
- * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
- *
- * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
- * or visit www.oracle.com if you need additional information or have any
- * questions.
- */
-package sun.misc;
-
-import java.math.BigInteger;
-import java.util.Arrays;
-//@ model import org.jmlspecs.models.JMLMath;
-
-/**
- * A simple big integer package specifically for floating point base conversion.
- */
-public /*@ spec_bigint_math @*/ class FDBigInteger {
-
- //
- // This class contains many comments that start with "/*@" mark.
- // They are behavourial specification in
- // the Java Modelling Language (JML):
- // http://www.eecs.ucf.edu/~leavens/JML//index.shtml
- //
-
- /*@
- @ public pure model static \bigint UNSIGNED(int v) {
- @ return v >= 0 ? v : v + (((\bigint)1) << 32);
- @ }
- @
- @ public pure model static \bigint UNSIGNED(long v) {
- @ return v >= 0 ? v : v + (((\bigint)1) << 64);
- @ }
- @
- @ public pure model static \bigint AP(int[] data, int len) {
- @ return (\sum int i; 0 <= 0 && i < len; UNSIGNED(data[i]) << (i*32));
- @ }
- @
- @ public pure model static \bigint pow52(int p5, int p2) {
- @ ghost \bigint v = 1;
- @ for (int i = 0; i < p5; i++) v *= 5;
- @ return v << p2;
- @ }
- @
- @ public pure model static \bigint pow10(int p10) {
- @ return pow52(p10, p10);
- @ }
- @*/
-
- static final int[] SMALL_5_POW = {
- 1,
- 5,
- 5 * 5,
- 5 * 5 * 5,
- 5 * 5 * 5 * 5,
- 5 * 5 * 5 * 5 * 5,
- 5 * 5 * 5 * 5 * 5 * 5,
- 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5
- };
-
- static final long[] LONG_5_POW = {
- 1L,
- 5L,
- 5L * 5,
- 5L * 5 * 5,
- 5L * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- 5L * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
- };
-
- // Maximum size of cache of powers of 5 as FDBigIntegers.
- private static final int MAX_FIVE_POW = 340;
-
- // Cache of big powers of 5 as FDBigIntegers.
- private static final FDBigInteger POW_5_CACHE[];
-
- // Initialize FDBigInteger cache of powers of 5.
- static {
- POW_5_CACHE = new FDBigInteger[MAX_FIVE_POW];
- int i = 0;
- while (i < SMALL_5_POW.length) {
- FDBigInteger pow5 = new FDBigInteger(new int[]{SMALL_5_POW[i]}, 0);
- pow5.makeImmutable();
- POW_5_CACHE[i] = pow5;
- i++;
- }
- FDBigInteger prev = POW_5_CACHE[i - 1];
- while (i < MAX_FIVE_POW) {
- POW_5_CACHE[i] = prev = prev.mult(5);
- prev.makeImmutable();
- i++;
- }
- }
-
- // Zero as an FDBigInteger.
- public static final FDBigInteger ZERO = new FDBigInteger(new int[0], 0);
-
- // Ensure ZERO is immutable.
- static {
- ZERO.makeImmutable();
- }
-
- // Constant for casting an int to a long via bitwise AND.
- private static final long LONG_MASK = 0xffffffffL;
-
- //@ spec_public non_null;
- private int data[]; // value: data[0] is least significant
- //@ spec_public;
- private int offset; // number of least significant zero padding ints
- //@ spec_public;
- private int nWords; // data[nWords-1]!=0, all values above are zero
- // if nWords==0 -> this FDBigInteger is zero
- //@ spec_public;
- private boolean isImmutable = false;
-
- /*@
- @ public invariant 0 <= nWords && nWords <= data.length && offset >= 0;
- @ public invariant nWords == 0 ==> offset == 0;
- @ public invariant nWords > 0 ==> data[nWords - 1] != 0;
- @ public invariant (\forall int i; nWords <= i && i < data.length; data[i] == 0);
- @ public pure model \bigint value() {
- @ return AP(data, nWords) << (offset*32);
- @ }
- @*/
-
- /**
- * Constructs an <code>FDBigInteger</code> from data and padding. The
- * <code>data</code> parameter has the least significant <code>int</code> at
- * the zeroth index. The <code>offset</code> parameter gives the number of
- * zero <code>int</code>s to be inferred below the least significant element
- * of <code>data</code>.
- *
- * @param data An array containing all non-zero <code>int</code>s of the value.
- * @param offset An offset indicating the number of zero <code>int</code>s to pad
- * below the least significant element of <code>data</code>.
- */
- /*@
- @ requires data != null && offset >= 0;
- @ ensures this.value() == \old(AP(data, data.length) << (offset*32));
- @ ensures this.data == \old(data);
- @*/
- private FDBigInteger(int[] data, int offset) {
- this.data = data;
- this.offset = offset;
- this.nWords = data.length;
- trimLeadingZeros();
- }
-
- /**
- * Constructs an <code>FDBigInteger</code> from a starting value and some
- * decimal digits.
- *
- * @param lValue The starting value.
- * @param digits The decimal digits.
- * @param kDigits The initial index into <code>digits</code>.
- * @param nDigits The final index into <code>digits</code>.
- */
- /*@
- @ requires digits != null;
- @ requires 0 <= kDigits && kDigits <= nDigits && nDigits <= digits.length;
- @ requires (\forall int i; 0 <= i && i < nDigits; '0' <= digits[i] && digits[i] <= '9');
- @ ensures this.value() == \old(lValue * pow10(nDigits - kDigits) + (\sum int i; kDigits <= i && i < nDigits; (digits[i] - '0') * pow10(nDigits - i - 1)));
- @*/
- public FDBigInteger(long lValue, char[] digits, int kDigits, int nDigits) {
- int n = Math.max((nDigits + 8) / 9, 2); // estimate size needed.
- data = new int[n]; // allocate enough space
- data[0] = (int) lValue; // starting value
- data[1] = (int) (lValue >>> 32);
- offset = 0;
- nWords = 2;
- int i = kDigits;
- int limit = nDigits - 5; // slurp digits 5 at a time.
- int v;
- while (i < limit) {
- int ilim = i + 5;
- v = (int) digits[i++] - (int) '0';
- while (i < ilim) {
- v = 10 * v + (int) digits[i++] - (int) '0';
- }
- multAddMe(100000, v); // ... where 100000 is 10^5.
- }
- int factor = 1;
- v = 0;
- while (i < nDigits) {
- v = 10 * v + (int) digits[i++] - (int) '0';
- factor *= 10;
- }
- if (factor != 1) {
- multAddMe(factor, v);
- }
- trimLeadingZeros();
- }
-
- /**
- * Returns an <code>FDBigInteger</code> with the numerical value
- * <code>5<sup>p5</sup> * 2<sup>p2</sup></code>.
- *
- * @param p5 The exponent of the power-of-five factor.
- * @param p2 The exponent of the power-of-two factor.
- * @return <code>5<sup>p5</sup> * 2<sup>p2</sup></code>
- */
- /*@
- @ requires p5 >= 0 && p2 >= 0;
- @ assignable \nothing;
- @ ensures \result.value() == \old(pow52(p5, p2));
- @*/
- public static FDBigInteger valueOfPow52(int p5, int p2) {
- if (p5 != 0) {
- if (p2 == 0) {
- return big5pow(p5);
- } else if (p5 < SMALL_5_POW.length) {
- int pow5 = SMALL_5_POW[p5];
- int wordcount = p2 >> 5;
- int bitcount = p2 & 0x1f;
- if (bitcount == 0) {
- return new FDBigInteger(new int[]{pow5}, wordcount);
- } else {
- return new FDBigInteger(new int[]{
- pow5 << bitcount,
- pow5 >>> (32 - bitcount)
- }, wordcount);
- }
- } else {
- return big5pow(p5).leftShift(p2);
- }
- } else {
- return valueOfPow2(p2);
- }
- }
-
- /**
- * Returns an <code>FDBigInteger</code> with the numerical value
- * <code>value * 5<sup>p5</sup> * 2<sup>p2</sup></code>.
- *
- * @param value The constant factor.
- * @param p5 The exponent of the power-of-five factor.
- * @param p2 The exponent of the power-of-two factor.
- * @return <code>value * 5<sup>p5</sup> * 2<sup>p2</sup></code>
- */
- /*@
- @ requires p5 >= 0 && p2 >= 0;
- @ assignable \nothing;
- @ ensures \result.value() == \old(UNSIGNED(value) * pow52(p5, p2));
- @*/
- public static FDBigInteger valueOfMulPow52(long value, int p5, int p2) {
- assert p5 >= 0 : p5;
- assert p2 >= 0 : p2;
- int v0 = (int) value;
- int v1 = (int) (value >>> 32);
- int wordcount = p2 >> 5;
- int bitcount = p2 & 0x1f;
- if (p5 != 0) {
- if (p5 < SMALL_5_POW.length) {
- long pow5 = SMALL_5_POW[p5] & LONG_MASK;
- long carry = (v0 & LONG_MASK) * pow5;
- v0 = (int) carry;
- carry >>>= 32;
- carry = (v1 & LONG_MASK) * pow5 + carry;
- v1 = (int) carry;
- int v2 = (int) (carry >>> 32);
- if (bitcount == 0) {
- return new FDBigInteger(new int[]{v0, v1, v2}, wordcount);
- } else {
- return new FDBigInteger(new int[]{
- v0 << bitcount,
- (v1 << bitcount) | (v0 >>> (32 - bitcount)),
- (v2 << bitcount) | (v1 >>> (32 - bitcount)),
- v2 >>> (32 - bitcount)
- }, wordcount);
- }
- } else {
- FDBigInteger pow5 = big5pow(p5);
- int[] r;
- if (v1 == 0) {
- r = new int[pow5.nWords + 1 + ((p2 != 0) ? 1 : 0)];
- mult(pow5.data, pow5.nWords, v0, r);
- } else {
- r = new int[pow5.nWords + 2 + ((p2 != 0) ? 1 : 0)];
- mult(pow5.data, pow5.nWords, v0, v1, r);
- }
- return (new FDBigInteger(r, pow5.offset)).leftShift(p2);
- }
- } else if (p2 != 0) {
- if (bitcount == 0) {
- return new FDBigInteger(new int[]{v0, v1}, wordcount);
- } else {
- return new FDBigInteger(new int[]{
- v0 << bitcount,
- (v1 << bitcount) | (v0 >>> (32 - bitcount)),
- v1 >>> (32 - bitcount)
- }, wordcount);
- }
- }
- return new FDBigInteger(new int[]{v0, v1}, 0);
- }
-
- /**
- * Returns an <code>FDBigInteger</code> with the numerical value
- * <code>2<sup>p2</sup></code>.
- *
- * @param p2 The exponent of 2.
- * @return <code>2<sup>p2</sup></code>
- */
- /*@
- @ requires p2 >= 0;
- @ assignable \nothing;
- @ ensures \result.value() == pow52(0, p2);
- @*/
- private static FDBigInteger valueOfPow2(int p2) {
- int wordcount = p2 >> 5;
- int bitcount = p2 & 0x1f;
- return new FDBigInteger(new int[]{1 << bitcount}, wordcount);
- }
-
- /**
- * Removes all leading zeros from this <code>FDBigInteger</code> adjusting
- * the offset and number of non-zero leading words accordingly.
- */
- /*@
- @ requires data != null;
- @ requires 0 <= nWords && nWords <= data.length && offset >= 0;
- @ requires nWords == 0 ==> offset == 0;
- @ ensures nWords == 0 ==> offset == 0;
- @ ensures nWords > 0 ==> data[nWords - 1] != 0;
- @*/
- private /*@ helper @*/ void trimLeadingZeros() {
- int i = nWords;
- if (i > 0 && (data[--i] == 0)) {
- //for (; i > 0 && data[i - 1] == 0; i--) ;
- while(i > 0 && data[i - 1] == 0) {
- i--;
- }
- this.nWords = i;
- if (i == 0) { // all words are zero
- this.offset = 0;
- }
- }
- }
-
- /**
- * Retrieves the normalization bias of the <code>FDBigIntger</code>. The
- * normalization bias is a left shift such that after it the highest word
- * of the value will have the 4 highest bits equal to zero:
- * {@code (highestWord & 0xf0000000) == 0}, but the next bit should be 1
- * {@code (highestWord & 0x08000000) != 0}.
- *
- * @return The normalization bias.
- */
- /*@
- @ requires this.value() > 0;
- @*/
- public /*@ pure @*/ int getNormalizationBias() {
- if (nWords == 0) {
- throw new IllegalArgumentException("Zero value cannot be normalized");
- }
- int zeros = Integer.numberOfLeadingZeros(data[nWords - 1]);
- return (zeros < 4) ? 28 + zeros : zeros - 4;
- }
-
- // TODO: Why is anticount param needed if it is always 32 - bitcount?
- /**
- * Left shifts the contents of one int array into another.
- *
- * @param src The source array.
- * @param idx The initial index of the source array.
- * @param result The destination array.
- * @param bitcount The left shift.
- * @param anticount The left anti-shift, e.g., <code>32-bitcount</code>.
- * @param prev The prior source value.
- */
- /*@
- @ requires 0 < bitcount && bitcount < 32 && anticount == 32 - bitcount;
- @ requires src.length >= idx && result.length > idx;
- @ assignable result[*];
- @ ensures AP(result, \old(idx + 1)) == \old((AP(src, idx) + UNSIGNED(prev) << (idx*32)) << bitcount);
- @*/
- private static void leftShift(int[] src, int idx, int result[], int bitcount, int anticount, int prev){
- for (; idx > 0; idx--) {
- int v = (prev << bitcount);
- prev = src[idx - 1];
- v |= (prev >>> anticount);
- result[idx] = v;
- }
- int v = prev << bitcount;
- result[0] = v;
- }
-
- /**
- * Shifts this <code>FDBigInteger</code> to the left. The shift is performed
- * in-place unless the <code>FDBigInteger</code> is immutable in which case
- * a new instance of <code>FDBigInteger</code> is returned.
- *
- * @param shift The number of bits to shift left.
- * @return The shifted <code>FDBigInteger</code>.
- */
- /*@
- @ requires this.value() == 0 || shift == 0;
- @ assignable \nothing;
- @ ensures \result == this;
- @
- @ also
- @
- @ requires this.value() > 0 && shift > 0 && this.isImmutable;
- @ assignable \nothing;
- @ ensures \result.value() == \old(this.value() << shift);
- @
- @ also
- @
- @ requires this.value() > 0 && shift > 0 && this.isImmutable;
- @ assignable \nothing;
- @ ensures \result == this;
- @ ensures \result.value() == \old(this.value() << shift);
- @*/
- public FDBigInteger leftShift(int shift) {
- if (shift == 0 || nWords == 0) {
- return this;
- }
- int wordcount = shift >> 5;
- int bitcount = shift & 0x1f;
- if (this.isImmutable) {
- if (bitcount == 0) {
- return new FDBigInteger(Arrays.copyOf(data, nWords), offset + wordcount);
- } else {
- int anticount = 32 - bitcount;
- int idx = nWords - 1;
- int prev = data[idx];
- int hi = prev >>> anticount;
- int[] result;
- if (hi != 0) {
- result = new int[nWords + 1];
- result[nWords] = hi;
- } else {
- result = new int[nWords];
- }
- leftShift(data,idx,result,bitcount,anticount,prev);
- return new FDBigInteger(result, offset + wordcount);
- }
- } else {
- if (bitcount != 0) {
- int anticount = 32 - bitcount;
- if ((data[0] << bitcount) == 0) {
- int idx = 0;
- int prev = data[idx];
- for (; idx < nWords - 1; idx++) {
- int v = (prev >>> anticount);
- prev = data[idx + 1];
- v |= (prev << bitcount);
- data[idx] = v;
- }
- int v = prev >>> anticount;
- data[idx] = v;
- if(v==0) {
- nWords--;
- }
- offset++;
- } else {
- int idx = nWords - 1;
- int prev = data[idx];
- int hi = prev >>> anticount;
- int[] result = data;
- int[] src = data;
- if (hi != 0) {
- if(nWords == data.length) {
- data = result = new int[nWords + 1];
- }
- result[nWords++] = hi;
- }
- leftShift(src,idx,result,bitcount,anticount,prev);
- }
- }
- offset += wordcount;
- return this;
- }
- }
-
- /**
- * Returns the number of <code>int</code>s this <code>FDBigInteger</code> represents.
- *
- * @return Number of <code>int</code>s required to represent this <code>FDBigInteger</code>.
- */
- /*@
- @ requires this.value() == 0;
- @ ensures \result == 0;
- @
- @ also
- @
- @ requires this.value() > 0;
- @ ensures ((\bigint)1) << (\result - 1) <= this.value() && this.value() <= ((\bigint)1) << \result;
- @*/
- private /*@ pure @*/ int size() {
- return nWords + offset;
- }
-
-
- /**
- * Computes
- * <pre>
- * q = (int)( this / S )
- * this = 10 * ( this mod S )
- * Return q.
- * </pre>
- * This is the iteration step of digit development for output.
- * We assume that S has been normalized, as above, and that
- * "this" has been left-shifted accordingly.
- * Also assumed, of course, is that the result, q, can be expressed
- * as an integer, {@code 0 <= q < 10}.
- *
- * @param S The divisor of this <code>FDBigInteger</code>.
- * @return <code>q = (int)(this / S)</code>.
- */
- /*@
- @ requires !this.isImmutable;
- @ requires this.size() <= S.size();
- @ requires this.data.length + this.offset >= S.size();
- @ requires S.value() >= ((\bigint)1) << (S.size()*32 - 4);
- @ assignable this.nWords, this.offset, this.data, this.data[*];
- @ ensures \result == \old(this.value() / S.value());
- @ ensures this.value() == \old(10 * (this.value() % S.value()));
- @*/
- public int quoRemIteration(FDBigInteger S) throws IllegalArgumentException {
- assert !this.isImmutable : "cannot modify immutable value";
- // ensure that this and S have the same number of
- // digits. If S is properly normalized and q < 10 then
- // this must be so.
- int thSize = this.size();
- int sSize = S.size();
- if (thSize < sSize) {
- // this value is significantly less than S, result of division is zero.
- // just mult this by 10.
- int p = multAndCarryBy10(this.data, this.nWords, this.data);
- if(p!=0) {
- this.data[nWords++] = p;
- } else {
- trimLeadingZeros();
- }
- return 0;
- } else if (thSize > sSize) {
- throw new IllegalArgumentException("disparate values");
- }
- // estimate q the obvious way. We will usually be
- // right. If not, then we're only off by a little and
- // will re-add.
- long q = (this.data[this.nWords - 1] & LONG_MASK) / (S.data[S.nWords - 1] & LONG_MASK);
- long diff = multDiffMe(q, S);
- if (diff != 0L) {
- //@ assert q != 0;
- //@ assert this.offset == \old(Math.min(this.offset, S.offset));
- //@ assert this.offset <= S.offset;
-
- // q is too big.
- // add S back in until this turns +. This should
- // not be very many times!
- long sum = 0L;
- int tStart = S.offset - this.offset;
- //@ assert tStart >= 0;
- int[] sd = S.data;
- int[] td = this.data;
- while (sum == 0L) {
- for (int sIndex = 0, tIndex = tStart; tIndex < this.nWords; sIndex++, tIndex++) {
- sum += (td[tIndex] & LONG_MASK) + (sd[sIndex] & LONG_MASK);
- td[tIndex] = (int) sum;
- sum >>>= 32; // Signed or unsigned, answer is 0 or 1
- }
- //
- // Originally the following line read
- // "if ( sum !=0 && sum != -1 )"
- // but that would be wrong, because of the
- // treatment of the two values as entirely unsigned,
- // it would be impossible for a carry-out to be interpreted
- // as -1 -- it would have to be a single-bit carry-out, or +1.
- //
- assert sum == 0 || sum == 1 : sum; // carry out of division correction
- q -= 1;
- }
- }
- // finally, we can multiply this by 10.
- // it cannot overflow, right, as the high-order word has
- // at least 4 high-order zeros!
- int p = multAndCarryBy10(this.data, this.nWords, this.data);
- assert p == 0 : p; // Carry out of *10
- trimLeadingZeros();
- return (int) q;
- }
-
- /**
- * Multiplies this <code>FDBigInteger</code> by 10. The operation will be
- * performed in place unless the <code>FDBigInteger</code> is immutable in
- * which case a new <code>FDBigInteger</code> will be returned.
- *
- * @return The <code>FDBigInteger</code> multiplied by 10.
- */
- /*@
- @ requires this.value() == 0;
- @ assignable \nothing;
- @ ensures \result == this;
- @
- @ also
- @
- @ requires this.value() > 0 && this.isImmutable;
- @ assignable \nothing;
- @ ensures \result.value() == \old(this.value() * 10);
- @
- @ also
- @
- @ requires this.value() > 0 && !this.isImmutable;
- @ assignable this.nWords, this.data, this.data[*];
- @ ensures \result == this;
- @ ensures \result.value() == \old(this.value() * 10);
- @*/
- public FDBigInteger multBy10() {
- if (nWords == 0) {
- return this;
- }
- if (isImmutable) {
- int[] res = new int[nWords + 1];
- res[nWords] = multAndCarryBy10(data, nWords, res);
- return new FDBigInteger(res, offset);
- } else {
- int p = multAndCarryBy10(this.data, this.nWords, this.data);
- if (p != 0) {
- if (nWords == data.length) {
- if (data[0] == 0) {
- System.arraycopy(data, 1, data, 0, --nWords);
- offset++;
- } else {
- data = Arrays.copyOf(data, data.length + 1);
- }
- }
- data[nWords++] = p;
- } else {
- trimLeadingZeros();
- }
- return this;
- }
- }
-
- /**
- * Multiplies this <code>FDBigInteger</code> by
- * <code>5<sup>p5</sup> * 2<sup>p2</sup></code>. The operation will be
- * performed in place if possible, otherwise a new <code>FDBigInteger</code>
- * will be returned.
- *
- * @param p5 The exponent of the power-of-five factor.
- * @param p2 The exponent of the power-of-two factor.
- * @return The multiplication result.
- */
- /*@
- @ requires this.value() == 0 || p5 == 0 && p2 == 0;
- @ assignable \nothing;
- @ ensures \result == this;
- @
- @ also
- @
- @ requires this.value() > 0 && (p5 > 0 && p2 >= 0 || p5 == 0 && p2 > 0 && this.isImmutable);
- @ assignable \nothing;
- @ ensures \result.value() == \old(this.value() * pow52(p5, p2));
- @
- @ also
- @
- @ requires this.value() > 0 && p5 == 0 && p2 > 0 && !this.isImmutable;
- @ assignable this.nWords, this.data, this.data[*];
- @ ensures \result == this;
- @ ensures \result.value() == \old(this.value() * pow52(p5, p2));
- @*/
- public FDBigInteger multByPow52(int p5, int p2) {
- if (this.nWords == 0) {
- return this;
- }
- FDBigInteger res = this;
- if (p5 != 0) {
- int[] r;
- int extraSize = (p2 != 0) ? 1 : 0;
- if (p5 < SMALL_5_POW.length) {
- r = new int[this.nWords + 1 + extraSize];
- mult(this.data, this.nWords, SMALL_5_POW[p5], r);
- res = new FDBigInteger(r, this.offset);
- } else {
- FDBigInteger pow5 = big5pow(p5);
- r = new int[this.nWords + pow5.size() + extraSize];
- mult(this.data, this.nWords, pow5.data, pow5.nWords, r);
- res = new FDBigInteger(r, this.offset + pow5.offset);
- }
- }
- return res.leftShift(p2);
- }
-
- /**
- * Multiplies two big integers represented as int arrays.
- *
- * @param s1 The first array factor.
- * @param s1Len The number of elements of <code>s1</code> to use.
- * @param s2 The second array factor.
- * @param s2Len The number of elements of <code>s2</code> to use.
- * @param dst The product array.
- */
- /*@
- @ requires s1 != dst && s2 != dst;
- @ requires s1.length >= s1Len && s2.length >= s2Len && dst.length >= s1Len + s2Len;
- @ assignable dst[0 .. s1Len + s2Len - 1];
- @ ensures AP(dst, s1Len + s2Len) == \old(AP(s1, s1Len) * AP(s2, s2Len));
- @*/
- private static void mult(int[] s1, int s1Len, int[] s2, int s2Len, int[] dst) {
- for (int i = 0; i < s1Len; i++) {
- long v = s1[i] & LONG_MASK;
- long p = 0L;
- for (int j = 0; j < s2Len; j++) {
- p += (dst[i + j] & LONG_MASK) + v * (s2[j] & LONG_MASK);
- dst[i + j] = (int) p;
- p >>>= 32;
- }
- dst[i + s2Len] = (int) p;
- }
- }
-
- /**
- * Subtracts the supplied <code>FDBigInteger</code> subtrahend from this
- * <code>FDBigInteger</code>. Assert that the result is positive.
- * If the subtrahend is immutable, store the result in this(minuend).
- * If this(minuend) is immutable a new <code>FDBigInteger</code> is created.
- *
- * @param subtrahend The <code>FDBigInteger</code> to be subtracted.
- * @return This <code>FDBigInteger</code> less the subtrahend.
- */
- /*@
- @ requires this.isImmutable;
- @ requires this.value() >= subtrahend.value();
- @ assignable \nothing;
- @ ensures \result.value() == \old(this.value() - subtrahend.value());
- @
- @ also
- @
- @ requires !subtrahend.isImmutable;
- @ requires this.value() >= subtrahend.value();
- @ assignable this.nWords, this.offset, this.data, this.data[*];
- @ ensures \result == this;
- @ ensures \result.value() == \old(this.value() - subtrahend.value());
- @*/
- public FDBigInteger leftInplaceSub(FDBigInteger subtrahend) {
- assert this.size() >= subtrahend.size() : "result should be positive";
- FDBigInteger minuend;
- if (this.isImmutable) {
- minuend = new FDBigInteger(this.data.clone(), this.offset);
- } else {
- minuend = this;
- }
- int offsetDiff = subtrahend.offset - minuend.offset;
- int[] sData = subtrahend.data;
- int[] mData = minuend.data;
- int subLen = subtrahend.nWords;
- int minLen = minuend.nWords;
- if (offsetDiff < 0) {
- // need to expand minuend
- int rLen = minLen - offsetDiff;
- if (rLen < mData.length) {
- System.arraycopy(mData, 0, mData, -offsetDiff, minLen);
- Arrays.fill(mData, 0, -offsetDiff, 0);
- } else {
- int[] r = new int[rLen];
- System.arraycopy(mData, 0, r, -offsetDiff, minLen);
- minuend.data = mData = r;
- }
- minuend.offset = subtrahend.offset;
- minuend.nWords = minLen = rLen;
- offsetDiff = 0;
- }
- long borrow = 0L;
- int mIndex = offsetDiff;
- for (int sIndex = 0; sIndex < subLen && mIndex < minLen; sIndex++, mIndex++) {
- long diff = (mData[mIndex] & LONG_MASK) - (sData[sIndex] & LONG_MASK) + borrow;
- mData[mIndex] = (int) diff;
- borrow = diff >> 32; // signed shift
- }
- for (; borrow != 0 && mIndex < minLen; mIndex++) {
- long diff = (mData[mIndex] & LONG_MASK) + borrow;
- mData[mIndex] = (int) diff;
- borrow = diff >> 32; // signed shift
- }
- assert borrow == 0L : borrow; // borrow out of subtract,
- // result should be positive
- minuend.trimLeadingZeros();
- return minuend;
- }
-
- /**
- * Subtracts the supplied <code>FDBigInteger</code> subtrahend from this
- * <code>FDBigInteger</code>. Assert that the result is positive.
- * If the this(minuend) is immutable, store the result in subtrahend.
- * If subtrahend is immutable a new <code>FDBigInteger</code> is created.
- *
- * @param subtrahend The <code>FDBigInteger</code> to be subtracted.
- * @return This <code>FDBigInteger</code> less the subtrahend.
- */
- /*@
- @ requires subtrahend.isImmutable;
- @ requires this.value() >= subtrahend.value();
- @ assignable \nothing;
- @ ensures \result.value() == \old(this.value() - subtrahend.value());
- @
- @ also
- @
- @ requires !subtrahend.isImmutable;
- @ requires this.value() >= subtrahend.value();
- @ assignable subtrahend.nWords, subtrahend.offset, subtrahend.data, subtrahend.data[*];
- @ ensures \result == subtrahend;
- @ ensures \result.value() == \old(this.value() - subtrahend.value());
- @*/
- public FDBigInteger rightInplaceSub(FDBigInteger subtrahend) {
- assert this.size() >= subtrahend.size() : "result should be positive";
- FDBigInteger minuend = this;
- if (subtrahend.isImmutable) {
- subtrahend = new FDBigInteger(subtrahend.data.clone(), subtrahend.offset);
- }
- int offsetDiff = minuend.offset - subtrahend.offset;
- int[] sData = subtrahend.data;
- int[] mData = minuend.data;
- int subLen = subtrahend.nWords;
- int minLen = minuend.nWords;
- if (offsetDiff < 0) {
- int rLen = minLen;
- if (rLen < sData.length) {
- System.arraycopy(sData, 0, sData, -offsetDiff, subLen);
- Arrays.fill(sData, 0, -offsetDiff, 0);
- } else {
- int[] r = new int[rLen];
- System.arraycopy(sData, 0, r, -offsetDiff, subLen);
- subtrahend.data = sData = r;
- }
- subtrahend.offset = minuend.offset;
- subLen -= offsetDiff;
- offsetDiff = 0;
- } else {
- int rLen = minLen + offsetDiff;
- if (rLen >= sData.length) {
- subtrahend.data = sData = Arrays.copyOf(sData, rLen);
- }
- }
- //@ assert minuend == this && minuend.value() == \old(this.value());
- //@ assert mData == minuend.data && minLen == minuend.nWords;
- //@ assert subtrahend.offset + subtrahend.data.length >= minuend.size();
- //@ assert sData == subtrahend.data;
- //@ assert AP(subtrahend.data, subtrahend.data.length) << subtrahend.offset == \old(subtrahend.value());
- //@ assert subtrahend.offset == Math.min(\old(this.offset), minuend.offset);
- //@ assert offsetDiff == minuend.offset - subtrahend.offset;
- //@ assert 0 <= offsetDiff && offsetDiff + minLen <= sData.length;
- int sIndex = 0;
- long borrow = 0L;
- for (; sIndex < offsetDiff; sIndex++) {
- long diff = 0L - (sData[sIndex] & LONG_MASK) + borrow;
- sData[sIndex] = (int) diff;
- borrow = diff >> 32; // signed shift
- }
- //@ assert sIndex == offsetDiff;
- for (int mIndex = 0; mIndex < minLen; sIndex++, mIndex++) {
- //@ assert sIndex == offsetDiff + mIndex;
- long diff = (mData[mIndex] & LONG_MASK) - (sData[sIndex] & LONG_MASK) + borrow;
- sData[sIndex] = (int) diff;
- borrow = diff >> 32; // signed shift
- }
- assert borrow == 0L : borrow; // borrow out of subtract,
- // result should be positive
- subtrahend.nWords = sIndex;
- subtrahend.trimLeadingZeros();
- return subtrahend;
-
- }
-
- /**
- * Determines whether all elements of an array are zero for all indices less
- * than a given index.
- *
- * @param a The array to be examined.
- * @param from The index strictly below which elements are to be examined.
- * @return Zero if all elements in range are zero, 1 otherwise.
- */
- /*@
- @ requires 0 <= from && from <= a.length;
- @ ensures \result == (AP(a, from) == 0 ? 0 : 1);
- @*/
- private /*@ pure @*/ static int checkZeroTail(int[] a, int from) {
- while (from > 0) {
- if (a[--from] != 0) {
- return 1;
- }
- }
- return 0;
- }
-
- /**
- * Compares the parameter with this <code>FDBigInteger</code>. Returns an
- * integer accordingly as:
- * <pre>{@code
- * > 0: this > other
- * 0: this == other
- * < 0: this < other
- * }</pre>
- *
- * @param other The <code>FDBigInteger</code> to compare.
- * @return A negative value, zero, or a positive value according to the
- * result of the comparison.
- */
- /*@
- @ ensures \result == (this.value() < other.value() ? -1 : this.value() > other.value() ? +1 : 0);
- @*/
- public /*@ pure @*/ int cmp(FDBigInteger other) {
- int aSize = nWords + offset;
- int bSize = other.nWords + other.offset;
- if (aSize > bSize) {
- return 1;
- } else if (aSize < bSize) {
- return -1;
- }
- int aLen = nWords;
- int bLen = other.nWords;
- while (aLen > 0 && bLen > 0) {
- int a = data[--aLen];
- int b = other.data[--bLen];
- if (a != b) {
- return ((a & LONG_MASK) < (b & LONG_MASK)) ? -1 : 1;
- }
- }
- if (aLen > 0) {
- return checkZeroTail(data, aLen);
- }
- if (bLen > 0) {
- return -checkZeroTail(other.data, bLen);
- }
- return 0;
- }
-
- /**
- * Compares this <code>FDBigInteger</code> with
- * <code>5<sup>p5</sup> * 2<sup>p2</sup></code>.
- * Returns an integer accordingly as:
- * <pre>{@code
- * > 0: this > other
- * 0: this == other
- * < 0: this < other
- * }</pre>
- * @param p5 The exponent of the power-of-five factor.
- * @param p2 The exponent of the power-of-two factor.
- * @return A negative value, zero, or a positive value according to the
- * result of the comparison.
- */
- /*@
- @ requires p5 >= 0 && p2 >= 0;
- @ ensures \result == (this.value() < pow52(p5, p2) ? -1 : this.value() > pow52(p5, p2) ? +1 : 0);
- @*/
- public /*@ pure @*/ int cmpPow52(int p5, int p2) {
- if (p5 == 0) {
- int wordcount = p2 >> 5;
- int bitcount = p2 & 0x1f;
- int size = this.nWords + this.offset;
- if (size > wordcount + 1) {
- return 1;
- } else if (size < wordcount + 1) {
- return -1;
- }
- int a = this.data[this.nWords -1];
- int b = 1 << bitcount;
- if (a != b) {
- return ( (a & LONG_MASK) < (b & LONG_MASK)) ? -1 : 1;
- }
- return checkZeroTail(this.data, this.nWords - 1);
- }
- return this.cmp(big5pow(p5).leftShift(p2));
- }
-
- /**
- * Compares this <code>FDBigInteger</code> with <code>x + y</code>. Returns a
- * value according to the comparison as:
- * <pre>{@code
- * -1: this < x + y
- * 0: this == x + y
- * 1: this > x + y
- * }</pre>
- * @param x The first addend of the sum to compare.
- * @param y The second addend of the sum to compare.
- * @return -1, 0, or 1 according to the result of the comparison.
- */
- /*@
- @ ensures \result == (this.value() < x.value() + y.value() ? -1 : this.value() > x.value() + y.value() ? +1 : 0);
- @*/
- public /*@ pure @*/ int addAndCmp(FDBigInteger x, FDBigInteger y) {
- FDBigInteger big;
- FDBigInteger small;
- int xSize = x.size();
- int ySize = y.size();
- int bSize;
- int sSize;
- if (xSize >= ySize) {
- big = x;
- small = y;
- bSize = xSize;
- sSize = ySize;
- } else {
- big = y;
- small = x;
- bSize = ySize;
- sSize = xSize;
- }
- int thSize = this.size();
- if (bSize == 0) {
- return thSize == 0 ? 0 : 1;
- }
- if (sSize == 0) {
- return this.cmp(big);
- }
- if (bSize > thSize) {
- return -1;
- }
- if (bSize + 1 < thSize) {
- return 1;
- }
- long top = (big.data[big.nWords - 1] & LONG_MASK);
- if (sSize == bSize) {
- top += (small.data[small.nWords - 1] & LONG_MASK);
- }
- if ((top >>> 32) == 0) {
- if (((top + 1) >>> 32) == 0) {
- // good case - no carry extension
- if (bSize < thSize) {
- return 1;
- }
- // here sum.nWords == this.nWords
- long v = (this.data[this.nWords - 1] & LONG_MASK);
- if (v < top) {
- return -1;
- }
- if (v > top + 1) {
- return 1;
- }
- }
- } else { // (top>>>32)!=0 guaranteed carry extension
- if (bSize + 1 > thSize) {
- return -1;
- }
- // here sum.nWords == this.nWords
- top >>>= 32;
- long v = (this.data[this.nWords - 1] & LONG_MASK);
- if (v < top) {
- return -1;
- }
- if (v > top + 1) {
- return 1;
- }
- }
- return this.cmp(big.add(small));
- }
-
- /**
- * Makes this <code>FDBigInteger</code> immutable.
- */
- /*@
- @ assignable this.isImmutable;
- @ ensures this.isImmutable;
- @*/
- public void makeImmutable() {
- this.isImmutable = true;
- }
-
- /**
- * Multiplies this <code>FDBigInteger</code> by an integer.
- *
- * @param i The factor by which to multiply this <code>FDBigInteger</code>.
- * @return This <code>FDBigInteger</code> multiplied by an integer.
- */
- /*@
- @ requires this.value() == 0;
- @ assignable \nothing;
- @ ensures \result == this;
- @
- @ also
- @
- @ requires this.value() != 0;
- @ assignable \nothing;
- @ ensures \result.value() == \old(this.value() * UNSIGNED(i));
- @*/
- private FDBigInteger mult(int i) {
- if (this.nWords == 0) {
- return this;
- }
- int[] r = new int[nWords + 1];
- mult(data, nWords, i, r);
- return new FDBigInteger(r, offset);
- }
-
- /**
- * Multiplies this <code>FDBigInteger</code> by another <code>FDBigInteger</code>.
- *
- * @param other The <code>FDBigInteger</code> factor by which to multiply.
- * @return The product of this and the parameter <code>FDBigInteger</code>s.
- */
- /*@
- @ requires this.value() == 0;
- @ assignable \nothing;
- @ ensures \result == this;
- @
- @ also
- @
- @ requires this.value() != 0 && other.value() == 0;
- @ assignable \nothing;
- @ ensures \result == other;
- @
- @ also
- @
- @ requires this.value() != 0 && other.value() != 0;
- @ assignable \nothing;
- @ ensures \result.value() == \old(this.value() * other.value());
- @*/
- private FDBigInteger mult(FDBigInteger other) {
- if (this.nWords == 0) {
- return this;
- }
- if (this.size() == 1) {
- return other.mult(data[0]);
- }
- if (other.nWords == 0) {
- return other;
- }
- if (other.size() == 1) {
- return this.mult(other.data[0]);
- }
- int[] r = new int[nWords + other.nWords];
- mult(this.data, this.nWords, other.data, other.nWords, r);
- return new FDBigInteger(r, this.offset + other.offset);
- }
-
- /**
- * Adds another <code>FDBigInteger</code> to this <code>FDBigInteger</code>.
- *
- * @param other The <code>FDBigInteger</code> to add.
- * @return The sum of the <code>FDBigInteger</code>s.
- */
- /*@
- @ assignable \nothing;
- @ ensures \result.value() == \old(this.value() + other.value());
- @*/
- private FDBigInteger add(FDBigInteger other) {
- FDBigInteger big, small;
- int bigLen, smallLen;
- int tSize = this.size();
- int oSize = other.size();
- if (tSize >= oSize) {
- big = this;
- bigLen = tSize;
- small = other;
- smallLen = oSize;
- } else {
- big = other;
- bigLen = oSize;
- small = this;
- smallLen = tSize;
- }
- int[] r = new int[bigLen + 1];
- int i = 0;
- long carry = 0L;
- for (; i < smallLen; i++) {
- carry += (i < big.offset ? 0L : (big.data[i - big.offset] & LONG_MASK) )
- + ((i < small.offset ? 0L : (small.data[i - small.offset] & LONG_MASK)));
- r[i] = (int) carry;
- carry >>= 32; // signed shift.
- }
- for (; i < bigLen; i++) {
- carry += (i < big.offset ? 0L : (big.data[i - big.offset] & LONG_MASK) );
- r[i] = (int) carry;
- carry >>= 32; // signed shift.
- }
- r[bigLen] = (int) carry;
- return new FDBigInteger(r, 0);
- }
-
-
- /**
- * Multiplies a <code>FDBigInteger</code> by an int and adds another int. The
- * result is computed in place. This method is intended only to be invoked
- * from
- * <code>
- * FDBigInteger(long lValue, char[] digits, int kDigits, int nDigits)
- * </code>.
- *
- * @param iv The factor by which to multiply this <code>FDBigInteger</code>.
- * @param addend The value to add to the product of this
- * <code>FDBigInteger</code> and <code>iv</code>.
- */
- /*@
- @ requires this.value()*UNSIGNED(iv) + UNSIGNED(addend) < ((\bigint)1) << ((this.data.length + this.offset)*32);
- @ assignable this.data[*];
- @ ensures this.value() == \old(this.value()*UNSIGNED(iv) + UNSIGNED(addend));
- @*/
- private /*@ helper @*/ void multAddMe(int iv, int addend) {
- long v = iv & LONG_MASK;
- // unroll 0th iteration, doing addition.
- long p = v * (data[0] & LONG_MASK) + (addend & LONG_MASK);
- data[0] = (int) p;
- p >>>= 32;
- for (int i = 1; i < nWords; i++) {
- p += v * (data[i] & LONG_MASK);
- data[i] = (int) p;
- p >>>= 32;
- }
- if (p != 0L) {
- data[nWords++] = (int) p; // will fail noisily if illegal!
- }
- }
-
- //
- // original doc:
- //
- // do this -=q*S
- // returns borrow
- //
- /**
- * Multiplies the parameters and subtracts them from this
- * <code>FDBigInteger</code>.
- *
- * @param q The integer parameter.
- * @param S The <code>FDBigInteger</code> parameter.
- * @return <code>this - q*S</code>.
- */
- /*@
- @ ensures nWords == 0 ==> offset == 0;
- @ ensures nWords > 0 ==> data[nWords - 1] != 0;
- @*/
- /*@
- @ requires 0 < q && q <= (1L << 31);
- @ requires data != null;
- @ requires 0 <= nWords && nWords <= data.length && offset >= 0;
- @ requires !this.isImmutable;
- @ requires this.size() == S.size();
- @ requires this != S;
- @ assignable this.nWords, this.offset, this.data, this.data[*];
- @ ensures -q <= \result && \result <= 0;
- @ ensures this.size() == \old(this.size());
- @ ensures this.value() + (\result << (this.size()*32)) == \old(this.value() - q*S.value());
- @ ensures this.offset == \old(Math.min(this.offset, S.offset));
- @ ensures \old(this.offset <= S.offset) ==> this.nWords == \old(this.nWords);
- @ ensures \old(this.offset <= S.offset) ==> this.offset == \old(this.offset);
- @ ensures \old(this.offset <= S.offset) ==> this.data == \old(this.data);
- @
- @ also
- @
- @ requires q == 0;
- @ assignable \nothing;
- @ ensures \result == 0;
- @*/
- private /*@ helper @*/ long multDiffMe(long q, FDBigInteger S) {
- long diff = 0L;
- if (q != 0) {
- int deltaSize = S.offset - this.offset;
- if (deltaSize >= 0) {
- int[] sd = S.data;
- int[] td = this.data;
- for (int sIndex = 0, tIndex = deltaSize; sIndex < S.nWords; sIndex++, tIndex++) {
- diff += (td[tIndex] & LONG_MASK) - q * (sd[sIndex] & LONG_MASK);
- td[tIndex] = (int) diff;
- diff >>= 32; // N.B. SIGNED shift.
- }
- } else {
- deltaSize = -deltaSize;
- int[] rd = new int[nWords + deltaSize];
- int sIndex = 0;
- int rIndex = 0;
- int[] sd = S.data;
- for (; rIndex < deltaSize && sIndex < S.nWords; sIndex++, rIndex++) {
- diff -= q * (sd[sIndex] & LONG_MASK);
- rd[rIndex] = (int) diff;
- diff >>= 32; // N.B. SIGNED shift.
- }
- int tIndex = 0;
- int[] td = this.data;
- for (; sIndex < S.nWords; sIndex++, tIndex++, rIndex++) {
- diff += (td[tIndex] & LONG_MASK) - q * (sd[sIndex] & LONG_MASK);
- rd[rIndex] = (int) diff;
- diff >>= 32; // N.B. SIGNED shift.
- }
- this.nWords += deltaSize;
- this.offset -= deltaSize;
- this.data = rd;
- }
- }
- return diff;
- }
-
-
- /**
- * Multiplies by 10 a big integer represented as an array. The final carry
- * is returned.
- *
- * @param src The array representation of the big integer.
- * @param srcLen The number of elements of <code>src</code> to use.
- * @param dst The product array.
- * @return The final carry of the multiplication.
- */
- /*@
- @ requires src.length >= srcLen && dst.length >= srcLen;
- @ assignable dst[0 .. srcLen - 1];
- @ ensures 0 <= \result && \result < 10;
- @ ensures AP(dst, srcLen) + (\result << (srcLen*32)) == \old(AP(src, srcLen) * 10);
- @*/
- private static int multAndCarryBy10(int[] src, int srcLen, int[] dst) {
- long carry = 0;
- for (int i = 0; i < srcLen; i++) {
- long product = (src[i] & LONG_MASK) * 10L + carry;
- dst[i] = (int) product;
- carry = product >>> 32;
- }
- return (int) carry;
- }
-
- /**
- * Multiplies by a constant value a big integer represented as an array.
- * The constant factor is an <code>int</code>.
- *
- * @param src The array representation of the big integer.
- * @param srcLen The number of elements of <code>src</code> to use.
- * @param value The constant factor by which to multiply.
- * @param dst The product array.
- */
- /*@
- @ requires src.length >= srcLen && dst.length >= srcLen + 1;
- @ assignable dst[0 .. srcLen];
- @ ensures AP(dst, srcLen + 1) == \old(AP(src, srcLen) * UNSIGNED(value));
- @*/
- private static void mult(int[] src, int srcLen, int value, int[] dst) {
- long val = value & LONG_MASK;
- long carry = 0;
- for (int i = 0; i < srcLen; i++) {
- long product = (src[i] & LONG_MASK) * val + carry;
- dst[i] = (int) product;
- carry = product >>> 32;
- }
- dst[srcLen] = (int) carry;
- }
-
- /**
- * Multiplies by a constant value a big integer represented as an array.
- * The constant factor is a long represent as two <code>int</code>s.
- *
- * @param src The array representation of the big integer.
- * @param srcLen The number of elements of <code>src</code> to use.
- * @param v0 The lower 32 bits of the long factor.
- * @param v1 The upper 32 bits of the long factor.
- * @param dst The product array.
- */
- /*@
- @ requires src != dst;
- @ requires src.length >= srcLen && dst.length >= srcLen + 2;
- @ assignable dst[0 .. srcLen + 1];
- @ ensures AP(dst, srcLen + 2) == \old(AP(src, srcLen) * (UNSIGNED(v0) + (UNSIGNED(v1) << 32)));
- @*/
- private static void mult(int[] src, int srcLen, int v0, int v1, int[] dst) {
- long v = v0 & LONG_MASK;
- long carry = 0;
- for (int j = 0; j < srcLen; j++) {
- long product = v * (src[j] & LONG_MASK) + carry;
- dst[j] = (int) product;
- carry = product >>> 32;
- }
- dst[srcLen] = (int) carry;
- v = v1 & LONG_MASK;
- carry = 0;
- for (int j = 0; j < srcLen; j++) {
- long product = (dst[j + 1] & LONG_MASK) + v * (src[j] & LONG_MASK) + carry;
- dst[j + 1] = (int) product;
- carry = product >>> 32;
- }
- dst[srcLen + 1] = (int) carry;
- }
-
- // Fails assertion for negative exponent.
- /**
- * Computes <code>5</code> raised to a given power.
- *
- * @param p The exponent of 5.
- * @return <code>5<sup>p</sup></code>.
- */
- private static FDBigInteger big5pow(int p) {
- assert p >= 0 : p; // negative power of 5
- if (p < MAX_FIVE_POW) {
- return POW_5_CACHE[p];
- }
- return big5powRec(p);
- }
-
- // slow path
- /**
- * Computes <code>5</code> raised to a given power.
- *
- * @param p The exponent of 5.
- * @return <code>5<sup>p</sup></code>.
- */
- private static FDBigInteger big5powRec(int p) {
- if (p < MAX_FIVE_POW) {
- return POW_5_CACHE[p];
- }
- // construct the value.
- // recursively.
- int q, r;
- // in order to compute 5^p,
- // compute its square root, 5^(p/2) and square.
- // or, let q = p / 2, r = p -q, then
- // 5^p = 5^(q+r) = 5^q * 5^r
- q = p >> 1;
- r = p - q;
- FDBigInteger bigq = big5powRec(q);
- if (r < SMALL_5_POW.length) {
- return bigq.mult(SMALL_5_POW[r]);
- } else {
- return bigq.mult(big5powRec(r));
- }
- }
-
- // for debugging ...
- /**
- * Converts this <code>FDBigInteger</code> to a hexadecimal string.
- *
- * @return The hexadecimal string representation.
- */
- public String toHexString(){
- if(nWords ==0) {
- return "0";
- }
- StringBuilder sb = new StringBuilder((nWords +offset)*8);
- for(int i= nWords -1; i>=0; i--) {
- String subStr = Integer.toHexString(data[i]);
- for(int j = subStr.length(); j<8; j++) {
- sb.append('0');
- }
- sb.append(subStr);
- }
- for(int i=offset; i>0; i--) {
- sb.append("00000000");
- }
- return sb.toString();
- }
-
- // for debugging ...
- /**
- * Converts this <code>FDBigInteger</code> to a <code>BigInteger</code>.
- *
- * @return The <code>BigInteger</code> representation.
- */
- public BigInteger toBigInteger() {
- byte[] magnitude = new byte[nWords * 4 + 1];
- for (int i = 0; i < nWords; i++) {
- int w = data[i];
- magnitude[magnitude.length - 4 * i - 1] = (byte) w;
- magnitude[magnitude.length - 4 * i - 2] = (byte) (w >> 8);
- magnitude[magnitude.length - 4 * i - 3] = (byte) (w >> 16);
- magnitude[magnitude.length - 4 * i - 4] = (byte) (w >> 24);
- }
- return new BigInteger(magnitude).shiftLeft(offset * 32);
- }
-
- // for debugging ...
- /**
- * Converts this <code>FDBigInteger</code> to a string.
- *
- * @return The string representation.
- */
- @Override
- public String toString(){
- return toBigInteger().toString();
- }
-}