Package js.math

Source Code of js.math.MutableBigInteger

/*
* Copyright (C) 2014 Nameless Production Committee
*
* Licensed under the MIT License (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
*          http://opensource.org/licenses/mit-license.php
*/
package js.math;

import static js.math.APIConveter.*;
import static js.math.JSBigDecimal.*;
import static js.math.JSBigInteger.*;

import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.Arrays;

/**
* A class used to represent multiprecision integers that makes efficient use of allocated space by
* allowing a number to occupy only part of an array so that the arrays do not have to be
* reallocated as often. When performing an operation with many iterations the array used to hold a
* number is only reallocated when necessary and does not have to be the same size as the number it
* represents. A mutable number allows calculations to occur on the same number without having to
* create a new number for every step of the calculation as occurs with BigIntegers.
*
* @see BigInteger
* @author Michael McCloskey
* @author Timothy Buktu
* @since 1.3
*/

// @JavaAPIProvider(JDKEmulator.class)
class MutableBigInteger {

    /**
     * Holds the magnitude of this MutableBigInteger in big endian order. The magnitude may start at
     * an offset into the value array, and it may end before the length of the value array.
     */
    int[] value;

    /**
     * The number of ints of the value array that are currently used to hold the magnitude of this
     * MutableBigInteger. The magnitude starts at an offset and offset + intLen may be less than
     * value.length.
     */
    int intLen;

    /**
     * The offset into the value array where the magnitude of this MutableBigInteger begins.
     */
    int offset = 0;

    // Constants
    /**
     * MutableBigInteger with one element value array with the value 1. Used by BigDecimal
     * divideAndRound to increment the quotient. Use this constant only when the method is not going
     * to modify this object.
     */
    static final MutableBigInteger ONE = new MutableBigInteger(1);

    /**
     * The minimum {@code intLen} for cancelling powers of two before dividing. If the number of
     * ints is less than this threshold, {@code divideKnuth} does not eliminate common powers of two
     * from the dividend and divisor.
     */
    static final int KNUTH_POW2_THRESH_LEN = 6;

    /**
     * The minimum number of trailing zero ints for cancelling powers of two before dividing. If the
     * dividend and divisor don't share at least this many zero ints at the end, {@code divideKnuth}
     * does not eliminate common powers of two from the dividend and divisor.
     */
    static final int KNUTH_POW2_THRESH_ZEROS = 3;

    // Constructors

    /**
     * The default constructor. An empty MutableBigInteger is created with a one word capacity.
     */
    MutableBigInteger() {
        value = new int[1];
        intLen = 0;
    }

    /**
     * Construct a new MutableBigInteger with a magnitude specified by the int val.
     */
    MutableBigInteger(int val) {
        value = new int[1];
        intLen = 1;
        value[0] = val;
    }

    /**
     * Construct a new MutableBigInteger with the specified value array up to the length of the
     * array supplied.
     */
    MutableBigInteger(int[] val) {
        value = val;
        intLen = val.length;
    }

    /**
     * Construct a new MutableBigInteger with a magnitude equal to the specified BigInteger.
     */
    MutableBigInteger(BigInteger b) {
        intLen = $(b).mag.length;
        value = Arrays.copyOf($(b).mag, intLen);
    }

    /**
     * Construct a new MutableBigInteger with a magnitude equal to the specified MutableBigInteger.
     */
    MutableBigInteger(MutableBigInteger val) {
        intLen = val.intLen;
        value = Arrays.copyOfRange(val.value, val.offset, val.offset + intLen);
    }

    /**
     * Makes this number an {@code n}-int number all of whose bits are ones. Used by
     * Burnikel-Ziegler division.
     *
     * @param n number of ints in the {@code value} array
     * @return a number equal to {@code ((1<<(32*n)))-1}
     */
    private void ones(int n) {
        if (n > value.length) {
            value = new int[n];
        }

        Arrays.fill(value, -1);
        offset = 0;
        intLen = n;
    }

    /**
     * Internal helper method to return the magnitude array. The caller is not supposed to modify
     * the returned array.
     */
    private int[] getMagnitudeArray() {
        if (offset > 0 || value.length != intLen) {
            return Arrays.copyOfRange(value, offset, offset + intLen);
        }
        return value;
    }

    /**
     * Convert this MutableBigInteger to a long value. The caller has to make sure this
     * MutableBigInteger can be fit into long.
     */
    private long toLong() {
        if (intLen == 0) {
            return 0;
        }
        long d = value[offset] & LONG_MASK;
        return (intLen == 2) ? d << 32 | (value[offset + 1] & LONG_MASK) : d;
    }

    /**
     * Convert this MutableBigInteger to a BigInteger object.
     */
    BigInteger toBigInteger(int sign) {
        if (intLen == 0 || sign == 0) {
            return BigInteger.ZERO;
        }
        return $(new JSBigInteger(getMagnitudeArray(), sign));
    }

    /**
     * Converts this number to a nonnegative {@code BigInteger}.
     */
    BigInteger toBigInteger() {
        normalize();
        return toBigInteger(isZero() ? 0 : 1);
    }

    /**
     * Convert this MutableBigInteger to BigDecimal object with the specified sign and scale.
     */
    BigDecimal toBigDecimal(int sign, int scale) {
        if (intLen == 0 || sign == 0) {
            return JSBigDecimal.zeroValueOf(scale);
        }
        int[] mag = getMagnitudeArray();
        int len = mag.length;
        int d = mag[0];
        // If this MutableBigInteger can't be fit into long, we need to
        // make a BigInteger object for the resultant BigDecimal object.
        if (len > 2 || (d < 0 && len == 2)) {
            return $(new JSBigDecimal($(new JSBigInteger(mag, sign)), INFLATED, scale, 0));
        }

        long v = (len == 2) ? ((mag[1] & LONG_MASK) | (d & LONG_MASK) << 32) : d & LONG_MASK;
        return BigDecimal.valueOf(sign == -1 ? -v : v, scale);
    }

    /**
     * This is for internal use in converting from a MutableBigInteger object into a long value
     * given a specified sign. returns INFLATED if value is not fit into long
     */
    long toCompactValue(int sign) {
        if (intLen == 0 || sign == 0) {
            return 0L;
        }
        int[] mag = getMagnitudeArray();
        int len = mag.length;
        int d = mag[0];
        // If this MutableBigInteger can not be fitted into long, we need to
        // make a BigInteger object for the resultant BigDecimal object.
        if (len > 2 || (d < 0 && len == 2)) return INFLATED;
        long v = (len == 2) ? ((mag[1] & LONG_MASK) | (d & LONG_MASK) << 32) : d & LONG_MASK;
        return sign == -1 ? -v : v;
    }

    /**
     * Clear out a MutableBigInteger for reuse.
     */
    void clear() {
        offset = intLen = 0;
        for (int index = 0, n = value.length; index < n; index++)
            value[index] = 0;
    }

    /**
     * Set a MutableBigInteger to zero, removing its offset.
     */
    void reset() {
        offset = intLen = 0;
    }

    /**
     * Compare the magnitude of two MutableBigIntegers. Returns -1, 0 or 1 as this MutableBigInteger
     * is numerically less than, equal to, or greater than <tt>b</tt>.
     */
    final int compare(MutableBigInteger b) {
        int blen = b.intLen;
        if (intLen < blen) return -1;
        if (intLen > blen) return 1;

        // Add Integer.MIN_VALUE to make the comparison act as unsigned integer
        // comparison.
        int[] bval = b.value;
        for (int i = offset, j = b.offset; i < intLen + offset; i++, j++) {
            int b1 = value[i] + 0x80000000;
            int b2 = bval[j] + 0x80000000;
            if (b1 < b2) return -1;
            if (b1 > b2) return 1;
        }
        return 0;
    }

    /**
     * Returns a value equal to what {@code b.leftShift(32*ints); return compare(b);} would return,
     * but doesn't change the value of {@code b}.
     */
    private int compareShifted(MutableBigInteger b, int ints) {
        int blen = b.intLen;
        int alen = intLen - ints;
        if (alen < blen) return -1;
        if (alen > blen) return 1;

        // Add Integer.MIN_VALUE to make the comparison act as unsigned integer
        // comparison.
        int[] bval = b.value;
        for (int i = offset, j = b.offset; i < alen + offset; i++, j++) {
            int b1 = value[i] + 0x80000000;
            int b2 = bval[j] + 0x80000000;
            if (b1 < b2) return -1;
            if (b1 > b2) return 1;
        }
        return 0;
    }

    /**
     * Compare this against half of a MutableBigInteger object (Needed for remainder tests). Assumes
     * no leading unnecessary zeros, which holds for results from divide().
     */
    final int compareHalf(MutableBigInteger b) {
        int blen = b.intLen;
        int len = intLen;
        if (len <= 0) return blen <= 0 ? 0 : -1;
        if (len > blen) return 1;
        if (len < blen - 1) return -1;
        int[] bval = b.value;
        int bstart = 0;
        int carry = 0;
        // Only 2 cases left:len == blen or len == blen - 1
        if (len != blen) { // len == blen - 1
            if (bval[bstart] == 1) {
                ++bstart;
                carry = 0x80000000;
            } else
                return -1;
        }
        // compare values with right-shifted values of b,
        // carrying shifted-out bits across words
        int[] val = value;
        for (int i = offset, j = bstart; i < len + offset;) {
            int bv = bval[j++];
            long hb = ((bv >>> 1) + carry) & LONG_MASK;
            long v = val[i++] & LONG_MASK;
            if (v != hb) return v < hb ? -1 : 1;
            carry = (bv & 1) << 31; // carray will be either 0x80000000 or 0
        }
        return carry == 0 ? 0 : -1;
    }

    /**
     * Return the index of the lowest set bit in this MutableBigInteger. If the magnitude of this
     * MutableBigInteger is zero, -1 is returned.
     */
    private final int getLowestSetBit() {
        if (intLen == 0) return -1;
        int j, b;
        for (j = intLen - 1; (j > 0) && (value[j + offset] == 0); j--);
        b = value[j + offset];
        if (b == 0) return -1;
        return ((intLen - 1 - j) << 5) + Integer.numberOfTrailingZeros(b);
    }

    /**
     * Return the int in use in this MutableBigInteger at the specified index. This method is not
     * used because it is not inlined on all platforms.
     */
    private final int getInt(int index) {
        return value[offset + index];
    }

    /**
     * Return a long which is equal to the unsigned value of the int in use in this
     * MutableBigInteger at the specified index. This method is not used because it is not inlined
     * on all platforms.
     */
    private final long getLong(int index) {
        return value[offset + index] & LONG_MASK;
    }

    /**
     * Ensure that the MutableBigInteger is in normal form, specifically making sure that there are
     * no leading zeros, and that if the magnitude is zero, then intLen is zero.
     */
    final void normalize() {
        if (intLen == 0) {
            offset = 0;
            return;
        }

        int index = offset;
        if (value[index] != 0) return;

        int indexBound = index + intLen;
        do {
            index++;
        } while (index < indexBound && value[index] == 0);

        int numZeros = index - offset;
        intLen -= numZeros;
        offset = (intLen == 0 ? 0 : offset + numZeros);
    }

    /**
     * If this MutableBigInteger cannot hold len words, increase the size of the value array to len
     * words.
     */
    private final void ensureCapacity(int len) {
        if (value.length < len) {
            value = new int[len];
            offset = 0;
            intLen = len;
        }
    }

    /**
     * Convert this MutableBigInteger into an int array with no leading zeros, of a length that is
     * equal to this MutableBigInteger's intLen.
     */
    int[] toIntArray() {
        int[] result = new int[intLen];
        for (int i = 0; i < intLen; i++)
            result[i] = value[offset + i];
        return result;
    }

    /**
     * Sets the int at index+offset in this MutableBigInteger to val. This does not get inlined on
     * all platforms so it is not used as often as originally intended.
     */
    void setInt(int index, int val) {
        value[offset + index] = val;
    }

    /**
     * Sets this MutableBigInteger's value array to the specified array. The intLen is set to the
     * specified length.
     */
    void setValue(int[] val, int length) {
        value = val;
        intLen = length;
        offset = 0;
    }

    /**
     * Sets this MutableBigInteger's value array to a copy of the specified array. The intLen is set
     * to the length of the new array.
     */
    void copyValue(MutableBigInteger src) {
        int len = src.intLen;
        if (value.length < len) {
            value = new int[len];
        }
        System.arraycopy(src.value, src.offset, value, 0, len);
        intLen = len;
        offset = 0;
    }

    /**
     * Sets this MutableBigInteger's value array to a copy of the specified array. The intLen is set
     * to the length of the specified array.
     */
    void copyValue(int[] val) {
        int len = val.length;
        if (value.length < len) {
            value = new int[len];
        }
        System.arraycopy(val, 0, value, 0, len);
        intLen = len;
        offset = 0;
    }

    /**
     * Returns true iff this MutableBigInteger has a value of one.
     */
    boolean isOne() {
        return (intLen == 1) && (value[offset] == 1);
    }

    /**
     * Returns true iff this MutableBigInteger has a value of zero.
     */
    boolean isZero() {
        return (intLen == 0);
    }

    /**
     * Returns true iff this MutableBigInteger is even.
     */
    boolean isEven() {
        return (intLen == 0) || ((value[offset + intLen - 1] & 1) == 0);
    }

    /**
     * Returns true iff this MutableBigInteger is odd.
     */
    boolean isOdd() {
        return isZero() ? false : ((value[offset + intLen - 1] & 1) == 1);
    }

    /**
     * Returns true iff this MutableBigInteger is in normal form. A MutableBigInteger is in normal
     * form if it has no leading zeros after the offset, and intLen + offset <= value.length.
     */
    boolean isNormal() {
        if (intLen + offset > value.length) return false;
        if (intLen == 0) return true;
        return (value[offset] != 0);
    }

    /**
     * Returns a String representation of this MutableBigInteger in radix 10.
     */
    @Override
    public String toString() {
        BigInteger b = toBigInteger(1);
        return b.toString();
    }

    /**
     * Like {@link #rightShift(int)} but {@code n} can be greater than the length of the number.
     */
    void safeRightShift(int n) {
        if (n / 32 >= intLen) {
            reset();
        } else {
            rightShift(n);
        }
    }

    /**
     * Right shift this MutableBigInteger n bits. The MutableBigInteger is left in normal form.
     */
    void rightShift(int n) {
        if (intLen == 0) return;
        int nInts = n >>> 5;
        int nBits = n & 0x1F;
        this.intLen -= nInts;
        if (nBits == 0) return;
        int bitsInHighWord = JSBigInteger.bitLengthForInt(value[offset]);
        if (nBits >= bitsInHighWord) {
            this.primitiveLeftShift(32 - nBits);
            this.intLen--;
        } else {
            primitiveRightShift(nBits);
        }
    }

    /**
     * Like {@link #leftShift(int)} but {@code n} can be zero.
     */
    void safeLeftShift(int n) {
        if (n > 0) {
            leftShift(n);
        }
    }

    /**
     * Left shift this MutableBigInteger n bits.
     */
    void leftShift(int n) {
        /*
         * If there is enough storage space in this MutableBigInteger already the available space
         * will be used. Space to the right of the used ints in the value array is faster to
         * utilize, so the extra space will be taken from the right if possible.
         */
        if (intLen == 0) return;
        int nInts = n >>> 5;
        int nBits = n & 0x1F;
        int bitsInHighWord = JSBigInteger.bitLengthForInt(value[offset]);

        // If shift can be done without moving words, do so
        if (n <= (32 - bitsInHighWord)) {
            primitiveLeftShift(nBits);
            return;
        }

        int newLen = intLen + nInts + 1;
        if (nBits <= (32 - bitsInHighWord)) newLen--;
        if (value.length < newLen) {
            // The array must grow
            int[] result = new int[newLen];
            for (int i = 0; i < intLen; i++)
                result[i] = value[offset + i];
            setValue(result, newLen);
        } else if (value.length - offset >= newLen) {
            // Use space on right
            for (int i = 0; i < newLen - intLen; i++)
                value[offset + intLen + i] = 0;
        } else {
            // Must use space on left
            for (int i = 0; i < intLen; i++)
                value[i] = value[offset + i];
            for (int i = intLen; i < newLen; i++)
                value[i] = 0;
            offset = 0;
        }
        intLen = newLen;
        if (nBits == 0) return;
        if (nBits <= (32 - bitsInHighWord))
            primitiveLeftShift(nBits);
        else
            primitiveRightShift(32 - nBits);
    }

    /**
     * A primitive used for division. This method adds in one multiple of the divisor a back to the
     * dividend result at a specified offset. It is used when qhat was estimated too large, and must
     * be adjusted.
     */
    private int divadd(int[] a, int[] result, int offset) {
        long carry = 0;

        for (int j = a.length - 1; j >= 0; j--) {
            long sum = (a[j] & LONG_MASK) + (result[j + offset] & LONG_MASK) + carry;
            result[j + offset] = (int) sum;
            carry = sum >>> 32;
        }
        return (int) carry;
    }

    /**
     * This method is used for division. It multiplies an n word input a by one word input x, and
     * subtracts the n word product from q. This is needed when subtracting qhat*divisor from
     * dividend.
     */
    private int mulsub(int[] q, int[] a, int x, int len, int offset) {
        long xLong = x & LONG_MASK;
        long carry = 0;
        offset += len;

        for (int j = len - 1; j >= 0; j--) {
            long product = (a[j] & LONG_MASK) * xLong + carry;
            long difference = q[offset] - product;
            q[offset--] = (int) difference;
            carry = (product >>> 32) + (((difference & LONG_MASK) > (((~(int) product) & LONG_MASK))) ? 1 : 0);
        }
        return (int) carry;
    }

    /**
     * The method is the same as mulsun, except the fact that q array is not updated, the only
     * result of the method is borrow flag.
     */
    private int mulsubBorrow(int[] q, int[] a, int x, int len, int offset) {
        long xLong = x & LONG_MASK;
        long carry = 0;
        offset += len;
        for (int j = len - 1; j >= 0; j--) {
            long product = (a[j] & LONG_MASK) * xLong + carry;
            long difference = q[offset--] - product;
            carry = (product >>> 32) + (((difference & LONG_MASK) > (((~(int) product) & LONG_MASK))) ? 1 : 0);
        }
        return (int) carry;
    }

    /**
     * Right shift this MutableBigInteger n bits, where n is less than 32. Assumes that intLen > 0,
     * n > 0 for speed
     */
    private final void primitiveRightShift(int n) {
        int[] val = value;
        int n2 = 32 - n;
        for (int i = offset + intLen - 1, c = val[i]; i > offset; i--) {
            int b = c;
            c = val[i - 1];
            val[i] = (c << n2) | (b >>> n);
        }
        val[offset] >>>= n;
    }

    /**
     * Left shift this MutableBigInteger n bits, where n is less than 32. Assumes that intLen > 0, n
     * > 0 for speed
     */
    private final void primitiveLeftShift(int n) {
        int[] val = value;
        int n2 = 32 - n;
        for (int i = offset, c = val[i], m = i + intLen - 1; i < m; i++) {
            int b = c;
            c = val[i + 1];
            val[i] = (b << n) | (c >>> n2);
        }
        val[offset + intLen - 1] <<= n;
    }

    /**
     * Returns a {@code BigInteger} equal to the {@code n} low ints of this number.
     */
    private BigInteger getLower(int n) {
        if (isZero()) {
            return BigInteger.ZERO;
        } else if (intLen < n) {
            return toBigInteger(1);
        } else {
            // strip zeros
            int len = n;
            while (len > 0 && value[offset + intLen - len] == 0) {
                len--;
            }
            int sign = len > 0 ? 1 : 0;
            return $(new JSBigInteger(Arrays.copyOfRange(value, offset + intLen - len, offset + intLen), sign));
        }
    }

    /**
     * Discards all ints whose index is greater than {@code n}.
     */
    private void keepLower(int n) {
        if (intLen >= n) {
            offset += intLen - n;
            intLen = n;
        }
    }

    /**
     * Adds the contents of two MutableBigInteger objects.The result is placed within this
     * MutableBigInteger. The contents of the addend are not changed.
     */
    void add(MutableBigInteger addend) {
        int x = intLen;
        int y = addend.intLen;
        int resultLen = (intLen > addend.intLen ? intLen : addend.intLen);
        int[] result = (value.length < resultLen ? new int[resultLen] : value);

        int rstart = result.length - 1;
        long sum;
        long carry = 0;

        // Add common parts of both numbers
        while (x > 0 && y > 0) {
            x--;
            y--;
            sum = (value[x + offset] & LONG_MASK) + (addend.value[y + addend.offset] & LONG_MASK) + carry;
            result[rstart--] = (int) sum;
            carry = sum >>> 32;
        }

        // Add remainder of the longer number
        while (x > 0) {
            x--;
            if (carry == 0 && result == value && rstart == (x + offset)) return;
            sum = (value[x + offset] & LONG_MASK) + carry;
            result[rstart--] = (int) sum;
            carry = sum >>> 32;
        }
        while (y > 0) {
            y--;
            sum = (addend.value[y + addend.offset] & LONG_MASK) + carry;
            result[rstart--] = (int) sum;
            carry = sum >>> 32;
        }

        if (carry > 0) { // Result must grow in length
            resultLen++;
            if (result.length < resultLen) {
                int temp[] = new int[resultLen];
                // Result one word longer from carry-out; copy low-order
                // bits into new result.
                System.arraycopy(result, 0, temp, 1, result.length);
                temp[0] = 1;
                result = temp;
            } else {
                result[rstart--] = 1;
            }
        }

        value = result;
        intLen = resultLen;
        offset = result.length - resultLen;
    }

    /**
     * Adds the value of {@code addend} shifted {@code n} ints to the left. Has the same effect as
     * {@code addend.leftShift(32*ints); add(addend);} but doesn't change the value of
     * {@code addend}.
     */
    void addShifted(MutableBigInteger addend, int n) {
        if (addend.isZero()) {
            return;
        }

        int x = intLen;
        int y = addend.intLen + n;
        int resultLen = (intLen > y ? intLen : y);
        int[] result = (value.length < resultLen ? new int[resultLen] : value);

        int rstart = result.length - 1;
        long sum;
        long carry = 0;

        // Add common parts of both numbers
        while (x > 0 && y > 0) {
            x--;
            y--;
            int bval = y + addend.offset < addend.value.length ? addend.value[y + addend.offset] : 0;
            sum = (value[x + offset] & LONG_MASK) + (bval & LONG_MASK) + carry;
            result[rstart--] = (int) sum;
            carry = sum >>> 32;
        }

        // Add remainder of the longer number
        while (x > 0) {
            x--;
            if (carry == 0 && result == value && rstart == (x + offset)) {
                return;
            }
            sum = (value[x + offset] & LONG_MASK) + carry;
            result[rstart--] = (int) sum;
            carry = sum >>> 32;
        }
        while (y > 0) {
            y--;
            int bval = y + addend.offset < addend.value.length ? addend.value[y + addend.offset] : 0;
            sum = (bval & LONG_MASK) + carry;
            result[rstart--] = (int) sum;
            carry = sum >>> 32;
        }

        if (carry > 0) { // Result must grow in length
            resultLen++;
            if (result.length < resultLen) {
                int temp[] = new int[resultLen];
                // Result one word longer from carry-out; copy low-order
                // bits into new result.
                System.arraycopy(result, 0, temp, 1, result.length);
                temp[0] = 1;
                result = temp;
            } else {
                result[rstart--] = 1;
            }
        }

        value = result;
        intLen = resultLen;
        offset = result.length - resultLen;
    }

    /**
     * Like {@link #addShifted(MutableBigInteger, int)} but {@code this.intLen} must not be greater
     * than {@code n}. In other words, concatenates {@code this} and {@code addend}.
     */
    void addDisjoint(MutableBigInteger addend, int n) {
        if (addend.isZero()) return;

        int x = intLen;
        int y = addend.intLen + n;
        int resultLen = (intLen > y ? intLen : y);
        int[] result;
        if (value.length < resultLen)
            result = new int[resultLen];
        else {
            result = value;
            Arrays.fill(value, offset + intLen, value.length, 0);
        }

        int rstart = result.length - 1;

        // copy from this if needed
        System.arraycopy(value, offset, result, rstart + 1 - x, x);
        y -= x;
        rstart -= x;

        int len = Math.min(y, addend.value.length - addend.offset);
        System.arraycopy(addend.value, addend.offset, result, rstart + 1 - y, len);

        // zero the gap
        for (int i = rstart + 1 - y + len; i < rstart + 1; i++)
            result[i] = 0;

        value = result;
        intLen = resultLen;
        offset = result.length - resultLen;
    }

    /**
     * Adds the low {@code n} ints of {@code addend}.
     */
    void addLower(MutableBigInteger addend, int n) {
        MutableBigInteger a = new MutableBigInteger(addend);
        if (a.offset + a.intLen >= n) {
            a.offset = a.offset + a.intLen - n;
            a.intLen = n;
        }
        a.normalize();
        add(a);
    }

    /**
     * Subtracts the smaller of this and b from the larger and places the result into this
     * MutableBigInteger.
     */
    int subtract(MutableBigInteger b) {
        MutableBigInteger a = this;

        int[] result = value;
        int sign = a.compare(b);

        if (sign == 0) {
            reset();
            return 0;
        }
        if (sign < 0) {
            MutableBigInteger tmp = a;
            a = b;
            b = tmp;
        }

        int resultLen = a.intLen;
        if (result.length < resultLen) result = new int[resultLen];

        long diff = 0;
        int x = a.intLen;
        int y = b.intLen;
        int rstart = result.length - 1;

        // Subtract common parts of both numbers
        while (y > 0) {
            x--;
            y--;
            diff = (a.value[x + a.offset] & LONG_MASK) - (b.value[y + b.offset] & LONG_MASK) - ((int) -(diff >> 32));
            result[rstart--] = (int) diff;
        }
        // Subtract remainder of longer number
        while (x > 0) {
            x--;
            diff = (a.value[x + a.offset] & LONG_MASK) - ((int) -(diff >> 32));
            result[rstart--] = (int) diff;
        }

        value = result;
        intLen = resultLen;
        offset = value.length - resultLen;
        normalize();
        return sign;
    }

    /**
     * Subtracts the smaller of a and b from the larger and places the result into the larger.
     * Returns 1 if the answer is in a, -1 if in b, 0 if no operation was performed.
     */
    private int difference(MutableBigInteger b) {
        MutableBigInteger a = this;
        int sign = a.compare(b);
        if (sign == 0) return 0;
        if (sign < 0) {
            MutableBigInteger tmp = a;
            a = b;
            b = tmp;
        }

        long diff = 0;
        int x = a.intLen;
        int y = b.intLen;

        // Subtract common parts of both numbers
        while (y > 0) {
            x--;
            y--;
            diff = (a.value[a.offset + x] & LONG_MASK) - (b.value[b.offset + y] & LONG_MASK) - ((int) -(diff >> 32));
            a.value[a.offset + x] = (int) diff;
        }
        // Subtract remainder of longer number
        while (x > 0) {
            x--;
            diff = (a.value[a.offset + x] & LONG_MASK) - ((int) -(diff >> 32));
            a.value[a.offset + x] = (int) diff;
        }

        a.normalize();
        return sign;
    }

    /**
     * Multiply the contents of two MutableBigInteger objects. The result is placed into
     * MutableBigInteger z. The contents of y are not changed.
     */
    void multiply(MutableBigInteger y, MutableBigInteger z) {
        int xLen = intLen;
        int yLen = y.intLen;
        int newLen = xLen + yLen;

        // Put z into an appropriate state to receive product
        if (z.value.length < newLen) z.value = new int[newLen];
        z.offset = 0;
        z.intLen = newLen;

        // The first iteration is hoisted out of the loop to avoid extra add
        long carry = 0;
        for (int j = yLen - 1, k = yLen + xLen - 1; j >= 0; j--, k--) {
            long product = (y.value[j + y.offset] & LONG_MASK) * (value[xLen - 1 + offset] & LONG_MASK) + carry;
            z.value[k] = (int) product;
            carry = product >>> 32;
        }
        z.value[xLen - 1] = (int) carry;

        // Perform the multiplication word by word
        for (int i = xLen - 2; i >= 0; i--) {
            carry = 0;
            for (int j = yLen - 1, k = yLen + i; j >= 0; j--, k--) {
                long product = (y.value[j + y.offset] & LONG_MASK) * (value[i + offset] & LONG_MASK) + (z.value[k] & LONG_MASK) + carry;
                z.value[k] = (int) product;
                carry = product >>> 32;
            }
            z.value[i] = (int) carry;
        }

        // Remove leading zeros from product
        z.normalize();
    }

    /**
     * Multiply the contents of this MutableBigInteger by the word y. The result is placed into z.
     */
    void mul(int y, MutableBigInteger z) {
        if (y == 1) {
            z.copyValue(this);
            return;
        }

        if (y == 0) {
            z.clear();
            return;
        }

        // Perform the multiplication word by word
        long ylong = y & LONG_MASK;
        int[] zval = (z.value.length < intLen + 1 ? new int[intLen + 1] : z.value);
        long carry = 0;
        for (int i = intLen - 1; i >= 0; i--) {
            long product = ylong * (value[i + offset] & LONG_MASK) + carry;
            zval[i + 1] = (int) product;
            carry = product >>> 32;
        }

        if (carry == 0) {
            z.offset = 1;
            z.intLen = intLen;
        } else {
            z.offset = 0;
            z.intLen = intLen + 1;
            zval[0] = (int) carry;
        }
        z.value = zval;
    }

    /**
     * This method is used for division of an n word dividend by a one word divisor. The quotient is
     * placed into quotient. The one word divisor is specified by divisor.
     *
     * @return the remainder of the division is returned.
     */
    int divideOneWord(int divisor, MutableBigInteger quotient) {
        long divisorLong = divisor & LONG_MASK;

        // Special case of one word dividend
        if (intLen == 1) {
            long dividendValue = value[offset] & LONG_MASK;
            int q = (int) (dividendValue / divisorLong);
            int r = (int) (dividendValue - q * divisorLong);
            quotient.value[0] = q;
            quotient.intLen = (q == 0) ? 0 : 1;
            quotient.offset = 0;
            return r;
        }

        if (quotient.value.length < intLen) quotient.value = new int[intLen];
        quotient.offset = 0;
        quotient.intLen = intLen;

        // Normalize the divisor
        int shift = Integer.numberOfLeadingZeros(divisor);

        int rem = value[offset];
        long remLong = rem & LONG_MASK;
        if (remLong < divisorLong) {
            quotient.value[0] = 0;
        } else {
            quotient.value[0] = (int) (remLong / divisorLong);
            rem = (int) (remLong - (quotient.value[0] * divisorLong));
            remLong = rem & LONG_MASK;
        }
        int xlen = intLen;
        while (--xlen > 0) {
            long dividendEstimate = (remLong << 32) | (value[offset + intLen - xlen] & LONG_MASK);
            int q;
            if (dividendEstimate >= 0) {
                q = (int) (dividendEstimate / divisorLong);
                rem = (int) (dividendEstimate - q * divisorLong);
            } else {
                long tmp = divWord(dividendEstimate, divisor);
                q = (int) (tmp & LONG_MASK);
                rem = (int) (tmp >>> 32);
            }
            quotient.value[intLen - xlen] = q;
            remLong = rem & LONG_MASK;
        }

        quotient.normalize();
        // Unnormalize
        if (shift > 0)
            return rem % divisor;
        else
            return rem;
    }

    /**
     * Calculates the quotient of this div b and places the quotient in the provided
     * MutableBigInteger objects and the remainder object is returned.
     */
    MutableBigInteger divide(MutableBigInteger b, MutableBigInteger quotient) {
        return divide(b, quotient, true);
    }

    MutableBigInteger divide(MutableBigInteger b, MutableBigInteger quotient, boolean needRemainder) {
        if (b.intLen < JSBigInteger.BURNIKEL_ZIEGLER_THRESHOLD || intLen - b.intLen < JSBigInteger.BURNIKEL_ZIEGLER_OFFSET) {
            return divideKnuth(b, quotient, needRemainder);
        } else {
            return divideAndRemainderBurnikelZiegler(b, quotient);
        }
    }

    /**
     * @see #divideKnuth(MutableBigInteger, MutableBigInteger, boolean)
     */
    MutableBigInteger divideKnuth(MutableBigInteger b, MutableBigInteger quotient) {
        return divideKnuth(b, quotient, true);
    }

    /**
     * Calculates the quotient of this div b and places the quotient in the provided
     * MutableBigInteger objects and the remainder object is returned. Uses Algorithm D in Knuth
     * section 4.3.1. Many optimizations to that algorithm have been adapted from the Colin Plumb C
     * library. It special cases one word divisors for speed. The content of b is not changed.
     */
    MutableBigInteger divideKnuth(MutableBigInteger b, MutableBigInteger quotient, boolean needRemainder) {
        if (b.intLen == 0) throw new ArithmeticException("BigInteger divide by zero");

        // Dividend is zero
        if (intLen == 0) {
            quotient.intLen = quotient.offset = 0;
            return needRemainder ? new MutableBigInteger() : null;
        }

        int cmp = compare(b);
        // Dividend less than divisor
        if (cmp < 0) {
            quotient.intLen = quotient.offset = 0;
            return needRemainder ? new MutableBigInteger(this) : null;
        }
        // Dividend equal to divisor
        if (cmp == 0) {
            quotient.value[0] = quotient.intLen = 1;
            quotient.offset = 0;
            return needRemainder ? new MutableBigInteger() : null;
        }

        quotient.clear();
        // Special case one word divisor
        if (b.intLen == 1) {
            int r = divideOneWord(b.value[b.offset], quotient);
            if (needRemainder) {
                if (r == 0) return new MutableBigInteger();
                return new MutableBigInteger(r);
            } else {
                return null;
            }
        }

        // Cancel common powers of two if we're above the KNUTH_POW2_* thresholds
        if (intLen >= KNUTH_POW2_THRESH_LEN) {
            int trailingZeroBits = Math.min(getLowestSetBit(), b.getLowestSetBit());
            if (trailingZeroBits >= KNUTH_POW2_THRESH_ZEROS * 32) {
                MutableBigInteger a = new MutableBigInteger(this);
                b = new MutableBigInteger(b);
                a.rightShift(trailingZeroBits);
                b.rightShift(trailingZeroBits);
                MutableBigInteger r = a.divideKnuth(b, quotient);
                r.leftShift(trailingZeroBits);
                return r;
            }
        }

        return divideMagnitude(b, quotient, needRemainder);
    }

    /**
     * Computes {@code this/b} and {@code this%b} using the <a
     * href="http://cr.yp.to/bib/1998/burnikel.ps"> Burnikel-Ziegler algorithm</a>. This method
     * implements algorithm 3 from pg. 9 of the Burnikel-Ziegler paper. The parameter beta was
     * chosen to b 2<sup>32</sup> so almost all shifts are multiples of 32 bits.<br/>
     * {@code this} and {@code b} must be nonnegative.
     *
     * @param b the divisor
     * @param quotient output parameter for {@code this/b}
     * @return the remainder
     */
    MutableBigInteger divideAndRemainderBurnikelZiegler(MutableBigInteger b, MutableBigInteger quotient) {
        int r = intLen;
        int s = b.intLen;

        // Clear the quotient
        quotient.offset = quotient.intLen = 0;

        if (r < s) {
            return this;
        } else {
            // Unlike Knuth division, we don't check for common powers of two here because
            // BZ already runs faster if both numbers contain powers of two and cancelling them has
            // no
            // additional benefit.

            // step 1: let m = min{2^k | (2^k)*BURNIKEL_ZIEGLER_THRESHOLD > s}
            int m = 1 << (32 - Integer.numberOfLeadingZeros(s / JSBigInteger.BURNIKEL_ZIEGLER_THRESHOLD));

            int j = (s + m - 1) / m; // step 2a: j = ceil(s/m)
            int n = j * m; // step 2b: block length in 32-bit units
            long n32 = 32L * n; // block length in bits
            int sigma = (int) Math.max(0, n32 - b.bitLength()); // step 3: sigma = max{T | (2^T)*B <
                                                                // beta^n}
            MutableBigInteger bShifted = new MutableBigInteger(b);
            bShifted.safeLeftShift(sigma); // step 4a: shift b so its length is a multiple of n
            safeLeftShift(sigma); // step 4b: shift this by the same amount

            // step 5: t is the number of blocks needed to accommodate this plus one additional bit
            int t = (int) ((bitLength() + n32) / n32);
            if (t < 2) {
                t = 2;
            }

            // step 6: conceptually split this into blocks a[t-1], ..., a[0]
            MutableBigInteger a1 = getBlock(t - 1, t, n); // the most significant block of this

            // step 7: z[t-2] = [a[t-1], a[t-2]]
            MutableBigInteger z = getBlock(t - 2, t, n); // the second to most significant block
            z.addDisjoint(a1, n); // z[t-2]

            // do schoolbook division on blocks, dividing 2-block numbers by 1-block numbers
            MutableBigInteger qi = new MutableBigInteger();
            MutableBigInteger ri;
            for (int i = t - 2; i > 0; i--) {
                // step 8a: compute (qi,ri) such that z=b*qi+ri
                ri = z.divide2n1n(bShifted, qi);

                // step 8b: z = [ri, a[i-1]]
                z = getBlock(i - 1, t, n); // a[i-1]
                z.addDisjoint(ri, n);
                quotient.addShifted(qi, i * n); // update q (part of step 9)
            }
            // final iteration of step 8: do the loop one more time for i=0 but leave z unchanged
            ri = z.divide2n1n(bShifted, qi);
            quotient.add(qi);

            ri.rightShift(sigma); // step 9: this and b were shifted, so shift back
            return ri;
        }
    }

    /**
     * This method implements algorithm 1 from pg. 4 of the Burnikel-Ziegler paper. It divides a
     * 2n-digit number by a n-digit number.<br/>
     * The parameter beta is 2<sup>32</sup> so all shifts are multiples of 32 bits. <br/>
     * {@code this} must be a nonnegative number such that
     * {@code this.bitLength() <= 2*b.bitLength()}
     *
     * @param b a positive number such that {@code b.bitLength()} is even
     * @param quotient output parameter for {@code this/b}
     * @return {@code this%b}
     */
    private MutableBigInteger divide2n1n(MutableBigInteger b, MutableBigInteger quotient) {
        int n = b.intLen;

        // step 1: base case
        if (n % 2 != 0 || n < JSBigInteger.BURNIKEL_ZIEGLER_THRESHOLD) {
            return divideKnuth(b, quotient);
        }

        // step 2: view this as [a1,a2,a3,a4] where each ai is n/2 ints or less
        MutableBigInteger aUpper = new MutableBigInteger(this);
        aUpper.safeRightShift(32 * (n / 2)); // aUpper = [a1,a2,a3]
        keepLower(n / 2); // this = a4

        // step 3: q1=aUpper/b, r1=aUpper%b
        MutableBigInteger q1 = new MutableBigInteger();
        MutableBigInteger r1 = aUpper.divide3n2n(b, q1);

        // step 4: quotient=[r1,this]/b, r2=[r1,this]%b
        addDisjoint(r1, n / 2); // this = [r1,this]
        MutableBigInteger r2 = divide3n2n(b, quotient);

        // step 5: let quotient=[q1,quotient] and return r2
        quotient.addDisjoint(q1, n / 2);
        return r2;
    }

    /**
     * This method implements algorithm 2 from pg. 5 of the Burnikel-Ziegler paper. It divides a
     * 3n-digit number by a 2n-digit number.<br/>
     * The parameter beta is 2<sup>32</sup> so all shifts are multiples of 32 bits.<br/>
     * <br/>
     * {@code this} must be a nonnegative number such that
     * {@code 2*this.bitLength() <= 3*b.bitLength()}
     *
     * @param quotient output parameter for {@code this/b}
     * @return {@code this%b}
     */
    private MutableBigInteger divide3n2n(MutableBigInteger b, MutableBigInteger quotient) {
        int n = b.intLen / 2; // half the length of b in ints

        // step 1: view this as [a1,a2,a3] where each ai is n ints or less; let a12=[a1,a2]
        MutableBigInteger a12 = new MutableBigInteger(this);
        a12.safeRightShift(32 * n);

        // step 2: view b as [b1,b2] where each bi is n ints or less
        MutableBigInteger b1 = new MutableBigInteger(b);
        b1.safeRightShift(n * 32);
        BigInteger b2 = b.getLower(n);

        MutableBigInteger r;
        MutableBigInteger d;
        if (compareShifted(b, n) < 0) {
            // step 3a: if a1<b1, let quotient=a12/b1 and r=a12%b1
            r = a12.divide2n1n(b1, quotient);

            // step 4: d=quotient*b2
            d = new MutableBigInteger(quotient.toBigInteger().multiply(b2));
        } else {
            // step 3b: if a1>=b1, let quotient=beta^n-1 and r=a12-b1*2^n+b1
            quotient.ones(n);
            a12.add(b1);
            b1.leftShift(32 * n);
            a12.subtract(b1);
            r = a12;

            // step 4: d=quotient*b2=(b2 << 32*n) - b2
            d = new MutableBigInteger(b2);
            d.leftShift(32 * n);
            d.subtract(new MutableBigInteger(b2));
        }

        // step 5: r = r*beta^n + a3 - d (paper says a4)
        // However, don't subtract d until after the while loop so r doesn't become negative
        r.leftShift(32 * n);
        r.addLower(this, n);

        // step 6: add b until r>=d
        while (r.compare(d) < 0) {
            r.add(b);
            quotient.subtract(MutableBigInteger.ONE);
        }
        r.subtract(d);

        return r;
    }

    /**
     * Returns a {@code MutableBigInteger} containing {@code blockLength} ints from {@code this}
     * number, starting at {@code index*blockLength}.<br/>
     * Used by Burnikel-Ziegler division.
     *
     * @param index the block index
     * @param numBlocks the total number of blocks in {@code this} number
     * @param blockLength length of one block in units of 32 bits
     * @return
     */
    private MutableBigInteger getBlock(int index, int numBlocks, int blockLength) {
        int blockStart = index * blockLength;
        if (blockStart >= intLen) {
            return new MutableBigInteger();
        }

        int blockEnd;
        if (index == numBlocks - 1) {
            blockEnd = intLen;
        } else {
            blockEnd = (index + 1) * blockLength;
        }
        if (blockEnd > intLen) {
            return new MutableBigInteger();
        }

        int[] newVal = Arrays.copyOfRange(value, offset + intLen - blockEnd, offset + intLen - blockStart);
        return new MutableBigInteger(newVal);
    }

    /** @see BigInteger#bitLength() */
    long bitLength() {
        if (intLen == 0) return 0;
        return intLen * 32L - Integer.numberOfLeadingZeros(value[offset]);
    }

    /**
     * Internally used to calculate the quotient of this div v and places the quotient in the
     * provided MutableBigInteger object and the remainder is returned.
     *
     * @return the remainder of the division will be returned.
     */
    long divide(long v, MutableBigInteger quotient) {
        if (v == 0) throw new ArithmeticException("BigInteger divide by zero");

        // Dividend is zero
        if (intLen == 0) {
            quotient.intLen = quotient.offset = 0;
            return 0;
        }
        if (v < 0) v = -v;

        int d = (int) (v >>> 32);
        quotient.clear();
        // Special case on word divisor
        if (d == 0)
            return divideOneWord((int) v, quotient) & LONG_MASK;
        else {
            return divideLongMagnitude(v, quotient).toLong();
        }
    }

    private static void copyAndShift(int[] src, int srcFrom, int srcLen, int[] dst, int dstFrom, int shift) {
        int n2 = 32 - shift;
        int c = src[srcFrom];
        for (int i = 0; i < srcLen - 1; i++) {
            int b = c;
            c = src[++srcFrom];
            dst[dstFrom + i] = (b << shift) | (c >>> n2);
        }
        dst[dstFrom + srcLen - 1] = c << shift;
    }

    /**
     * Divide this MutableBigInteger by the divisor. The quotient will be placed into the provided
     * quotient object & the remainder object is returned.
     */
    private MutableBigInteger divideMagnitude(MutableBigInteger div, MutableBigInteger quotient, boolean needRemainder) {
        // assert div.intLen > 1
        // D1 normalize the divisor
        int shift = Integer.numberOfLeadingZeros(div.value[div.offset]);
        // Copy divisor value to protect divisor
        final int dlen = div.intLen;
        int[] divisor;
        MutableBigInteger rem; // Remainder starts as dividend with space for a leading zero
        if (shift > 0) {
            divisor = new int[dlen];
            copyAndShift(div.value, div.offset, dlen, divisor, 0, shift);
            if (Integer.numberOfLeadingZeros(value[offset]) >= shift) {
                int[] remarr = new int[intLen + 1];
                rem = new MutableBigInteger(remarr);
                rem.intLen = intLen;
                rem.offset = 1;
                copyAndShift(value, offset, intLen, remarr, 1, shift);
            } else {
                int[] remarr = new int[intLen + 2];
                rem = new MutableBigInteger(remarr);
                rem.intLen = intLen + 1;
                rem.offset = 1;
                int rFrom = offset;
                int c = 0;
                int n2 = 32 - shift;
                for (int i = 1; i < intLen + 1; i++, rFrom++) {
                    int b = c;
                    c = value[rFrom];
                    remarr[i] = (b << shift) | (c >>> n2);
                }
                remarr[intLen + 1] = c << shift;
            }
        } else {
            divisor = Arrays.copyOfRange(div.value, div.offset, div.offset + div.intLen);
            rem = new MutableBigInteger(new int[intLen + 1]);
            System.arraycopy(value, offset, rem.value, 1, intLen);
            rem.intLen = intLen;
            rem.offset = 1;
        }

        int nlen = rem.intLen;

        // Set the quotient size
        final int limit = nlen - dlen + 1;
        if (quotient.value.length < limit) {
            quotient.value = new int[limit];
            quotient.offset = 0;
        }
        quotient.intLen = limit;
        int[] q = quotient.value;

        // Must insert leading 0 in rem if its length did not change
        if (rem.intLen == nlen) {
            rem.offset = 0;
            rem.value[0] = 0;
            rem.intLen++;
        }

        int dh = divisor[0];
        long dhLong = dh & LONG_MASK;
        int dl = divisor[1];

        // D2 Initialize j
        for (int j = 0; j < limit - 1; j++) {
            // D3 Calculate qhat
            // estimate qhat
            int qhat = 0;
            int qrem = 0;
            boolean skipCorrection = false;
            int nh = rem.value[j + rem.offset];
            int nh2 = nh + 0x80000000;
            int nm = rem.value[j + 1 + rem.offset];

            if (nh == dh) {
                qhat = ~0;
                qrem = nh + nm;
                skipCorrection = qrem + 0x80000000 < nh2;
            } else {
                long nChunk = (((long) nh) << 32) | (nm & LONG_MASK);
                if (nChunk >= 0) {
                    qhat = (int) (nChunk / dhLong);
                    qrem = (int) (nChunk - (qhat * dhLong));
                } else {
                    long tmp = divWord(nChunk, dh);
                    qhat = (int) (tmp & LONG_MASK);
                    qrem = (int) (tmp >>> 32);
                }
            }

            if (qhat == 0) continue;

            if (!skipCorrection) { // Correct qhat
                long nl = rem.value[j + 2 + rem.offset] & LONG_MASK;
                long rs = ((qrem & LONG_MASK) << 32) | nl;
                long estProduct = (dl & LONG_MASK) * (qhat & LONG_MASK);

                if (unsignedLongCompare(estProduct, rs)) {
                    qhat--;
                    qrem = (int) ((qrem & LONG_MASK) + dhLong);
                    if ((qrem & LONG_MASK) >= dhLong) {
                        estProduct -= (dl & LONG_MASK);
                        rs = ((qrem & LONG_MASK) << 32) | nl;
                        if (unsignedLongCompare(estProduct, rs)) qhat--;
                    }
                }
            }

            // D4 Multiply and subtract
            rem.value[j + rem.offset] = 0;
            int borrow = mulsub(rem.value, divisor, qhat, dlen, j + rem.offset);

            // D5 Test remainder
            if (borrow + 0x80000000 > nh2) {
                // D6 Add back
                divadd(divisor, rem.value, j + 1 + rem.offset);
                qhat--;
            }

            // Store the quotient digit
            q[j] = qhat;
        } // D7 loop on j
          // D3 Calculate qhat
          // estimate qhat
        int qhat = 0;
        int qrem = 0;
        boolean skipCorrection = false;
        int nh = rem.value[limit - 1 + rem.offset];
        int nh2 = nh + 0x80000000;
        int nm = rem.value[limit + rem.offset];

        if (nh == dh) {
            qhat = ~0;
            qrem = nh + nm;
            skipCorrection = qrem + 0x80000000 < nh2;
        } else {
            long nChunk = (((long) nh) << 32) | (nm & LONG_MASK);
            if (nChunk >= 0) {
                qhat = (int) (nChunk / dhLong);
                qrem = (int) (nChunk - (qhat * dhLong));
            } else {
                long tmp = divWord(nChunk, dh);
                qhat = (int) (tmp & LONG_MASK);
                qrem = (int) (tmp >>> 32);
            }
        }
        if (qhat != 0) {
            if (!skipCorrection) { // Correct qhat
                long nl = rem.value[limit + 1 + rem.offset] & LONG_MASK;
                long rs = ((qrem & LONG_MASK) << 32) | nl;
                long estProduct = (dl & LONG_MASK) * (qhat & LONG_MASK);

                if (unsignedLongCompare(estProduct, rs)) {
                    qhat--;
                    qrem = (int) ((qrem & LONG_MASK) + dhLong);
                    if ((qrem & LONG_MASK) >= dhLong) {
                        estProduct -= (dl & LONG_MASK);
                        rs = ((qrem & LONG_MASK) << 32) | nl;
                        if (unsignedLongCompare(estProduct, rs)) qhat--;
                    }
                }
            }

            // D4 Multiply and subtract
            int borrow;
            rem.value[limit - 1 + rem.offset] = 0;
            if (needRemainder)
                borrow = mulsub(rem.value, divisor, qhat, dlen, limit - 1 + rem.offset);
            else
                borrow = mulsubBorrow(rem.value, divisor, qhat, dlen, limit - 1 + rem.offset);

            // D5 Test remainder
            if (borrow + 0x80000000 > nh2) {
                // D6 Add back
                if (needRemainder) divadd(divisor, rem.value, limit - 1 + 1 + rem.offset);
                qhat--;
            }

            // Store the quotient digit
            q[(limit - 1)] = qhat;
        }

        if (needRemainder) {
            // D8 Unnormalize
            if (shift > 0) rem.rightShift(shift);
            rem.normalize();
        }
        quotient.normalize();
        return needRemainder ? rem : null;
    }

    /**
     * Divide this MutableBigInteger by the divisor represented by positive long value. The quotient
     * will be placed into the provided quotient object & the remainder object is returned.
     */
    private MutableBigInteger divideLongMagnitude(long ldivisor, MutableBigInteger quotient) {
        // Remainder starts as dividend with space for a leading zero
        MutableBigInteger rem = new MutableBigInteger(new int[intLen + 1]);
        System.arraycopy(value, offset, rem.value, 1, intLen);
        rem.intLen = intLen;
        rem.offset = 1;

        int nlen = rem.intLen;

        int limit = nlen - 2 + 1;
        if (quotient.value.length < limit) {
            quotient.value = new int[limit];
            quotient.offset = 0;
        }
        quotient.intLen = limit;
        int[] q = quotient.value;

        // D1 normalize the divisor
        int shift = Long.numberOfLeadingZeros(ldivisor);
        if (shift > 0) {
            ldivisor <<= shift;
            rem.leftShift(shift);
        }

        // Must insert leading 0 in rem if its length did not change
        if (rem.intLen == nlen) {
            rem.offset = 0;
            rem.value[0] = 0;
            rem.intLen++;
        }

        int dh = (int) (ldivisor >>> 32);
        long dhLong = dh & LONG_MASK;
        int dl = (int) (ldivisor & LONG_MASK);

        // D2 Initialize j
        for (int j = 0; j < limit; j++) {
            // D3 Calculate qhat
            // estimate qhat
            int qhat = 0;
            int qrem = 0;
            boolean skipCorrection = false;
            int nh = rem.value[j + rem.offset];
            int nh2 = nh + 0x80000000;
            int nm = rem.value[j + 1 + rem.offset];

            if (nh == dh) {
                qhat = ~0;
                qrem = nh + nm;
                skipCorrection = qrem + 0x80000000 < nh2;
            } else {
                long nChunk = (((long) nh) << 32) | (nm & LONG_MASK);
                if (nChunk >= 0) {
                    qhat = (int) (nChunk / dhLong);
                    qrem = (int) (nChunk - (qhat * dhLong));
                } else {
                    long tmp = divWord(nChunk, dh);
                    qhat = (int) (tmp & LONG_MASK);
                    qrem = (int) (tmp >>> 32);
                }
            }

            if (qhat == 0) continue;

            if (!skipCorrection) { // Correct qhat
                long nl = rem.value[j + 2 + rem.offset] & LONG_MASK;
                long rs = ((qrem & LONG_MASK) << 32) | nl;
                long estProduct = (dl & LONG_MASK) * (qhat & LONG_MASK);

                if (unsignedLongCompare(estProduct, rs)) {
                    qhat--;
                    qrem = (int) ((qrem & LONG_MASK) + dhLong);
                    if ((qrem & LONG_MASK) >= dhLong) {
                        estProduct -= (dl & LONG_MASK);
                        rs = ((qrem & LONG_MASK) << 32) | nl;
                        if (unsignedLongCompare(estProduct, rs)) qhat--;
                    }
                }
            }

            // D4 Multiply and subtract
            rem.value[j + rem.offset] = 0;
            int borrow = mulsubLong(rem.value, dh, dl, qhat, j + rem.offset);

            // D5 Test remainder
            if (borrow + 0x80000000 > nh2) {
                // D6 Add back
                divaddLong(dh, dl, rem.value, j + 1 + rem.offset);
                qhat--;
            }

            // Store the quotient digit
            q[j] = qhat;
        } // D7 loop on j

        // D8 Unnormalize
        if (shift > 0) rem.rightShift(shift);

        quotient.normalize();
        rem.normalize();
        return rem;
    }

    /**
     * A primitive used for division by long. Specialized version of the method divadd. dh is a high
     * part of the divisor, dl is a low part
     */
    private int divaddLong(int dh, int dl, int[] result, int offset) {
        long carry = 0;

        long sum = (dl & LONG_MASK) + (result[1 + offset] & LONG_MASK);
        result[1 + offset] = (int) sum;

        sum = (dh & LONG_MASK) + (result[offset] & LONG_MASK) + carry;
        result[offset] = (int) sum;
        carry = sum >>> 32;
        return (int) carry;
    }

    /**
     * This method is used for division by long. Specialized version of the method sulsub. dh is a
     * high part of the divisor, dl is a low part
     */
    private int mulsubLong(int[] q, int dh, int dl, int x, int offset) {
        long xLong = x & LONG_MASK;
        offset += 2;
        long product = (dl & LONG_MASK) * xLong;
        long difference = q[offset] - product;
        q[offset--] = (int) difference;
        long carry = (product >>> 32) + (((difference & LONG_MASK) > (((~(int) product) & LONG_MASK))) ? 1 : 0);
        product = (dh & LONG_MASK) * xLong + carry;
        difference = q[offset] - product;
        q[offset--] = (int) difference;
        carry = (product >>> 32) + (((difference & LONG_MASK) > (((~(int) product) & LONG_MASK))) ? 1 : 0);
        return (int) carry;
    }

    /**
     * Compare two longs as if they were unsigned. Returns true iff one is bigger than two.
     */
    private boolean unsignedLongCompare(long one, long two) {
        return (one + Long.MIN_VALUE) > (two + Long.MIN_VALUE);
    }

    /**
     * This method divides a long quantity by an int to estimate qhat for two multi precision
     * numbers. It is used when the signed value of n is less than zero. Returns long value where
     * high 32 bits contain remainder value and low 32 bits contain quotient value.
     */
    static long divWord(long n, int d) {
        long dLong = d & LONG_MASK;
        long r;
        long q;
        if (dLong == 1) {
            q = (int) n;
            r = 0;
            return (r << 32) | (q & LONG_MASK);
        }

        // Approximate the quotient and remainder
        q = (n >>> 1) / (dLong >>> 1);
        r = n - q * dLong;

        // Correct the approximation
        while (r < 0) {
            r += dLong;
            q--;
        }
        while (r >= dLong) {
            r -= dLong;
            q++;
        }
        // n - q*dlong == r && 0 <= r <dLong, hence we're done.
        return (r << 32) | (q & LONG_MASK);
    }

    /**
     * Calculate GCD of this and b. This and b are changed by the computation.
     */
    MutableBigInteger hybridGCD(MutableBigInteger b) {
        // Use Euclid's algorithm until the numbers are approximately the
        // same length, then use the binary GCD algorithm to find the GCD.
        MutableBigInteger a = this;
        MutableBigInteger q = new MutableBigInteger();

        while (b.intLen != 0) {
            if (Math.abs(a.intLen - b.intLen) < 2) return a.binaryGCD(b);

            MutableBigInteger r = a.divide(b, q);
            a = b;
            b = r;
        }
        return a;
    }

    /**
     * Calculate GCD of this and v. Assumes that this and v are not zero.
     */
    private MutableBigInteger binaryGCD(MutableBigInteger v) {
        // Algorithm B from Knuth section 4.5.2
        MutableBigInteger u = this;
        MutableBigInteger r = new MutableBigInteger();

        // step B1
        int s1 = u.getLowestSetBit();
        int s2 = v.getLowestSetBit();
        int k = (s1 < s2) ? s1 : s2;
        if (k != 0) {
            u.rightShift(k);
            v.rightShift(k);
        }

        // step B2
        boolean uOdd = (k == s1);
        MutableBigInteger t = uOdd ? v : u;
        int tsign = uOdd ? -1 : 1;

        int lb;
        while ((lb = t.getLowestSetBit()) >= 0) {
            // steps B3 and B4
            t.rightShift(lb);
            // step B5
            if (tsign > 0)
                u = t;
            else
                v = t;

            // Special case one word numbers
            if (u.intLen < 2 && v.intLen < 2) {
                int x = u.value[u.offset];
                int y = v.value[v.offset];
                x = binaryGcd(x, y);
                r.value[0] = x;
                r.intLen = 1;
                r.offset = 0;
                if (k > 0) r.leftShift(k);
                return r;
            }

            // step B6
            if ((tsign = u.difference(v)) == 0) break;
            t = (tsign >= 0) ? u : v;
        }

        if (k > 0) u.leftShift(k);
        return u;
    }

    /**
     * Calculate GCD of a and b interpreted as unsigned integers.
     */
    static int binaryGcd(int a, int b) {
        if (b == 0) return a;
        if (a == 0) return b;

        // Right shift a & b till their last bits equal to 1.
        int aZeros = Integer.numberOfTrailingZeros(a);
        int bZeros = Integer.numberOfTrailingZeros(b);
        a >>>= aZeros;
        b >>>= bZeros;

        int t = (aZeros < bZeros ? aZeros : bZeros);

        while (a != b) {
            if ((a + 0x80000000) > (b + 0x80000000)) { // a > b as unsigned
                a -= b;
                a >>>= Integer.numberOfTrailingZeros(a);
            } else {
                b -= a;
                b >>>= Integer.numberOfTrailingZeros(b);
            }
        }
        return a << t;
    }

    /**
     * Returns the modInverse of this mod p. This and p are not affected by the operation.
     */
    MutableBigInteger mutableModInverse(MutableBigInteger p) {
        // Modulus is odd, use Schroeppel's algorithm
        if (p.isOdd()) return modInverse(p);

        // Base and modulus are even, throw exception
        if (isEven()) throw new ArithmeticException("BigInteger not invertible.");

        // Get even part of modulus expressed as a power of 2
        int powersOf2 = p.getLowestSetBit();

        // Construct odd part of modulus
        MutableBigInteger oddMod = new MutableBigInteger(p);
        oddMod.rightShift(powersOf2);

        if (oddMod.isOne()) return modInverseMP2(powersOf2);

        // Calculate 1/a mod oddMod
        MutableBigInteger oddPart = modInverse(oddMod);

        // Calculate 1/a mod evenMod
        MutableBigInteger evenPart = modInverseMP2(powersOf2);

        // Combine the results using Chinese Remainder Theorem
        MutableBigInteger y1 = modInverseBP2(oddMod, powersOf2);
        MutableBigInteger y2 = oddMod.modInverseMP2(powersOf2);

        MutableBigInteger temp1 = new MutableBigInteger();
        MutableBigInteger temp2 = new MutableBigInteger();
        MutableBigInteger result = new MutableBigInteger();

        oddPart.leftShift(powersOf2);
        oddPart.multiply(y1, result);

        evenPart.multiply(oddMod, temp1);
        temp1.multiply(y2, temp2);

        result.add(temp2);
        return result.divide(p, temp1);
    }

    /*
     * Calculate the multiplicative inverse of this mod 2^k.
     */
    MutableBigInteger modInverseMP2(int k) {
        if (isEven()) throw new ArithmeticException("Non-invertible. (GCD != 1)");

        if (k > 64) return euclidModInverse(k);

        int t = inverseMod32(value[offset + intLen - 1]);

        if (k < 33) {
            t = (k == 32 ? t : t & ((1 << k) - 1));
            return new MutableBigInteger(t);
        }

        long pLong = (value[offset + intLen - 1] & LONG_MASK);
        if (intLen > 1) pLong |= ((long) value[offset + intLen - 2] << 32);
        long tLong = t & LONG_MASK;
        tLong = tLong * (2 - pLong * tLong); // 1 more Newton iter step
        tLong = (k == 64 ? tLong : tLong & ((1L << k) - 1));

        MutableBigInteger result = new MutableBigInteger(new int[2]);
        result.value[0] = (int) (tLong >>> 32);
        result.value[1] = (int) tLong;
        result.intLen = 2;
        result.normalize();
        return result;
    }

    /**
     * Returns the multiplicative inverse of val mod 2^32. Assumes val is odd.
     */
    static int inverseMod32(int val) {
        // Newton's iteration!
        int t = val;
        t *= 2 - val * t;
        t *= 2 - val * t;
        t *= 2 - val * t;
        t *= 2 - val * t;
        return t;
    }

    /**
     * Calculate the multiplicative inverse of 2^k mod mod, where mod is odd.
     */
    static MutableBigInteger modInverseBP2(MutableBigInteger mod, int k) {
        // Copy the mod to protect original
        return fixup(new MutableBigInteger(1), new MutableBigInteger(mod), k);
    }

    /**
     * Calculate the multiplicative inverse of this mod mod, where mod is odd. This and mod are not
     * changed by the calculation. This method implements an algorithm due to Richard Schroeppel,
     * that uses the same intermediate representation as Montgomery Reduction ("Montgomery Form").
     * The algorithm is described in an unpublished manuscript entitled "Fast Modular Reciprocals."
     */
    private MutableBigInteger modInverse(MutableBigInteger mod) {
        MutableBigInteger p = new MutableBigInteger(mod);
        MutableBigInteger f = new MutableBigInteger(this);
        MutableBigInteger g = new MutableBigInteger(p);
        SignedMutableBigInteger c = new SignedMutableBigInteger(1);
        SignedMutableBigInteger d = new SignedMutableBigInteger();
        MutableBigInteger temp = null;
        SignedMutableBigInteger sTemp = null;

        int k = 0;
        // Right shift f k times until odd, left shift d k times
        if (f.isEven()) {
            int trailingZeros = f.getLowestSetBit();
            f.rightShift(trailingZeros);
            d.leftShift(trailingZeros);
            k = trailingZeros;
        }

        // The Almost Inverse Algorithm
        while (!f.isOne()) {
            // If gcd(f, g) != 1, number is not invertible modulo mod
            if (f.isZero()) throw new ArithmeticException("BigInteger not invertible.");

            // If f < g exchange f, g and c, d
            if (f.compare(g) < 0) {
                temp = f;
                f = g;
                g = temp;
                sTemp = d;
                d = c;
                c = sTemp;
            }

            // If f == g (mod 4)
            if (((f.value[f.offset + f.intLen - 1] ^ g.value[g.offset + g.intLen - 1]) & 3) == 0) {
                f.subtract(g);
                c.signedSubtract(d);
            } else { // If f != g (mod 4)
                f.add(g);
                c.signedAdd(d);
            }

            // Right shift f k times until odd, left shift d k times
            int trailingZeros = f.getLowestSetBit();
            f.rightShift(trailingZeros);
            d.leftShift(trailingZeros);
            k += trailingZeros;
        }

        while (c.sign < 0) {
            c.signedAdd(p);
        }

        return fixup(c, p, k);
    }

    /**
     * The Fixup Algorithm Calculates X such that X = C * 2^(-k) (mod P) Assumes C
     * <P
     * and P is odd.
     */
    static MutableBigInteger fixup(MutableBigInteger c, MutableBigInteger p, int k) {
        MutableBigInteger temp = new MutableBigInteger();
        // Set r to the multiplicative inverse of p mod 2^32
        int r = -inverseMod32(p.value[p.offset + p.intLen - 1]);

        for (int i = 0, numWords = k >> 5; i < numWords; i++) {
            // V = R * c (mod 2^j)
            int v = r * c.value[c.offset + c.intLen - 1];
            // c = c + (v * p)
            p.mul(v, temp);
            c.add(temp);
            // c = c / 2^j
            c.intLen--;
        }
        int numBits = k & 0x1f;
        if (numBits != 0) {
            // V = R * c (mod 2^j)
            int v = r * c.value[c.offset + c.intLen - 1];
            v &= ((1 << numBits) - 1);
            // c = c + (v * p)
            p.mul(v, temp);
            c.add(temp);
            // c = c / 2^j
            c.rightShift(numBits);
        }

        // In theory, c may be greater than p at this point (Very rare!)
        while (c.compare(p) >= 0) {
            c.subtract(p);
        }

        return c;
    }

    /**
     * Uses the extended Euclidean algorithm to compute the modInverse of base mod a modulus that is
     * a power of 2. The modulus is 2^k.
     */
    MutableBigInteger euclidModInverse(int k) {
        MutableBigInteger b = new MutableBigInteger(1);
        b.leftShift(k);
        MutableBigInteger mod = new MutableBigInteger(b);

        MutableBigInteger a = new MutableBigInteger(this);
        MutableBigInteger q = new MutableBigInteger();
        MutableBigInteger r = b.divide(a, q);

        MutableBigInteger swapper = b;
        // swap b & r
        b = r;
        r = swapper;

        MutableBigInteger t1 = new MutableBigInteger(q);
        MutableBigInteger t0 = new MutableBigInteger(1);
        MutableBigInteger temp = new MutableBigInteger();

        while (!b.isOne()) {
            r = a.divide(b, q);

            if (r.intLen == 0) {
                throw new ArithmeticException("BigInteger not invertible.");
            }

            swapper = r;
            a = swapper;

            if (q.intLen == 1) {
                t1.mul(q.value[q.offset], temp);
            } else {
                q.multiply(t1, temp);
            }
            swapper = q;
            q = temp;
            temp = swapper;
            t0.add(q);

            if (a.isOne()) return t0;

            r = b.divide(a, q);

            if (r.intLen == 0) {
                throw new ArithmeticException("BigInteger not invertible.");
            }

            swapper = b;
            b = r;

            if (q.intLen == 1) {
                t0.mul(q.value[q.offset], temp);
            } else {
                q.multiply(t0, temp);
            }
            swapper = q;
            q = temp;
            temp = swapper;

            t1.add(q);
        }
        mod.subtract(t1);
        return mod;
    }
}
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Related Classes of js.math.MutableBigInteger

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