--- /dev/null 2013-06-07 13:08:34.000000000 -0700
+++ new/src/share/classes/sun/misc/FDBigInteger.java 2013-06-07 13:08:34.000000000 -0700
@@ -0,0 +1,1508 @@
+/*
+ * 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 final static 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 FDBigInteger from data and padding. The
+ * data parameter has the least significant int at
+ * the zeroth index. The offset parameter gives the number of
+ * zero ints to be inferred below the least significant element
+ * of data.
+ *
+ * @param data An array containing all non-zero ints of the value.
+ * @param offset An offset indicating the number of zero ints to pad
+ * below the least significant element of data.
+ */
+ /*@
+ @ 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 FDBigInteger from a starting value and some
+ * decimal digits.
+ *
+ * @param lValue The starting value.
+ * @param digits The decimal digits.
+ * @param kDigits The initial index into digits.
+ * @param nDigits The final index into digits.
+ */
+ /*@
+ @ 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 FDBigInteger with the numerical value
+ * 5p5 * 2p2.
+ *
+ * @param p5 The exponent of the power-of-five factor.
+ * @param p2 The exponent of the power-of-two factor.
+ * @return 5p5 * 2p2
+ */
+ /*@
+ @ 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 FDBigInteger with the numerical value
+ * value * 5p5 * 2p2.
+ *
+ * @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 value * 5p5 * 2p2
+ */
+ /*@
+ @ 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 FDBigInteger with the numerical value
+ * 2p2.
+ *
+ * @param p2 The exponent of 2.
+ * @return 2p2
+ */
+ /*@
+ @ 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 FDBigInteger 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 FDBigIntger. 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:
+ * (highestWord & 0xf0000000) == 0, but the next bit should be 1
+ * (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., 32-bitcount.
+ * @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 FDBigInteger to the left. The shift is performed
+ * in-place unless the FDBigInteger is immutable in which case
+ * a new instance of FDBigInteger is returned.
+ *
+ * @param shift The number of bits to shift left.
+ * @return The shifted FDBigInteger.
+ */
+ /*@
+ @ 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 ints this FDBigInteger represents.
+ *
+ * @return Number of ints required to represent this FDBigInteger.
+ */
+ /*@
+ @ 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
+ *
+ * q = (int)( this / S )
+ * this = 10 * ( this mod S )
+ * Return q.
+ *
+ * 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, 0 <= q < 10.
+ *
+ * @param The divisor of this FDBigInteger.
+ * @return q = (int)(this / S).
+ */
+ /*@
+ @ 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 FDBigInteger by 10. The operation will be
+ * performed in place unless the FDBigInteger is immutable in
+ * which case a new FDBigInteger will be returned.
+ *
+ * @return The FDBigInteger 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 FDBigInteger by
+ * 5p5 * 2p2. The operation will be
+ * performed in place if possible, otherwise a new FDBigInteger
+ * will be returned.
+ *
+ * @param p5 The exponent of the power-of-five factor.
+ * @param p2 The exponent of the power-of-two factor.
+ * @return
+ */
+ /*@
+ @ 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 s1 to use.
+ * @param s2 The second array factor.
+ * @param s2Len The number of elements of s2 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 FDBigInteger subtrahend from this
+ * FDBigInteger. Assert that the result is positive.
+ * If the subtrahend is immutable, store the result in this(minuend).
+ * If this(minuend) is immutable a new FDBigInteger is created.
+ *
+ * @param subtrahend The FDBigInteger to be subtracted.
+ * @return This FDBigInteger 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, 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 FDBigInteger subtrahend from this
+ * FDBigInteger. Assert that the result is positive.
+ * If the this(minuend) is immutable, store the result in subtrahend.
+ * If subtrahend is immutable a new FDBigInteger is created.
+ *
+ * @param subtrahend The FDBigInteger to be subtracted.
+ * @return This FDBigInteger 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, 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 FDBigInteger. Returns an
+ * integer accordingly as:
+ *
+ * >0: this > other
+ * 0: this == other
+ * <0: this < other
+ *
+ *
+ * @param other The FDBigInteger 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 FDBigInteger with
+ * 5p5 * 2p2.
+ * Returns an integer accordingly as:
+ *
+ * >0: this > other
+ * 0: this == other
+ * <0: this < other
+ *
+ * @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 FDBigInteger with x + y. Returns a
+ * value according to the comparison as:
+ *
+ * -1: this < x + y
+ * 0: this == x + y
+ * 1: this > x + y
+ *
+ * @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 FDBigInteger immutable.
+ */
+ /*@
+ @ assignable this.isImmutable;
+ @ ensures this.isImmutable;
+ @*/
+ public void makeImmutable() {
+ this.isImmutable = true;
+ }
+
+ /**
+ * Multiplies this FDBigInteger by an integer.
+ *
+ * @param i The factor by which to multiply this FDBigInteger.
+ * @return This FDBigInteger 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 FDBigInteger by another FDBigInteger.
+ *
+ * @param other The FDBigInteger factor by which to multiply.
+ * @return The product of this and the parameter FDBigIntegers.
+ */
+ /*@
+ @ 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 FDBigInteger to this FDBigInteger.
+ *
+ * @param other The FDBigInteger to add.
+ * @return The sum of the FDBigIntegers.
+ */
+ /*@
+ @ 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 FDBigInteger by an int and adds another int. The
+ * result is computed in place. This method is intended only to be invoked
+ * from
+ *
+ * FDBigInteger(long lValue, char[] digits, int kDigits, int nDigits)
+ * .
+ *
+ * @param iv The factor by which to multiply this FDBigInteger.
+ * @param addend The value to add to the product of this
+ * FDBigInteger and iv.
+ */
+ /*@
+ @ 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
+ * FDBigInteger.
+ *
+ * @param q The integer parameter.
+ * @param S The FDBigInteger parameter.
+ * @return this - q*S.
+ */
+ /*@
+ @ 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 src 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 int.
+ *
+ * @param src The array representation of the big integer.
+ * @param srcLen The number of elements of src 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 ints.
+ *
+ * @param src The array representation of the big integer.
+ * @param srcLen The number of elements of src 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 5 raised to a given power.
+ *
+ * @param p The exponent of 5.
+ * @return 5p.
+ */
+ 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 5 raised to a given power.
+ *
+ * @param p The exponent of 5.
+ * @return 5p.
+ */
+ 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 FDBigInteger 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 FDBigInteger to a BigInteger.
+ *
+ * @return The BigInteger 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 FDBigInteger to a string.
+ *
+ * @return The string representation.
+ */
+ @Override
+ public String toString(){
+ return toBigInteger().toString();
+ }
+}