/*
* Copyright (c) 1999, 2007, 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 java.math;
/**
* 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
* @since 1.3
*/
import java.util.Arrays;
import static java.math.BigInteger.LONG_MASK;
import static java.math.BigDecimal.INFLATED;
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);
// 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);
}
/**
* 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() {
assert (intLen <= 2) : "this MutableBigInteger exceeds the range of long";
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 BigInteger(getMagnitudeArray(), sign);
}
/**
* Convert this MutableBigInteger to BigDecimal object with the specified sign
* and scale.
*/
BigDecimal toBigDecimal(int sign, int scale) {
if (intLen == 0 || sign == 0)
return BigDecimal.valueOf(0, 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 BigDecimal(new BigInteger(mag, sign), INFLATED, scale, 0);
long v = (len == 2) ?
((mag[1] & LONG_MASK) | (d & LONG_MASK) << 32) :
d & LONG_MASK;
return new BigDecimal(null, sign == -1 ? -v : v, scale, 0);
}
/**
* 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;
}
/**
* 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.
*/
public String toString() {
BigInteger b = toBigInteger(1);
return b.toString();
}
/**
* 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 = BigInteger.bitLengthForInt(value[offset]);
if (nBits >= bitsInHighWord) {
this.primitiveLeftShift(32 - nBits);
this.intLen--;
} else {
primitiveRightShift(nBits);
}
}
/**
* 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 = BigInteger.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;
}
/**
* 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;
}
/**
* 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;
}
/**
* 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;
int[] qWord = new int[2];
while (--xlen > 0) {
long dividendEstimate = (remLong<<32) |
(value[offset + intLen - xlen] & LONG_MASK);
if (dividendEstimate >= 0) {
qWord[0] = (int) (dividendEstimate / divisorLong);
qWord[1] = (int) (dividendEstimate - qWord[0] * divisorLong);
} else {
divWord(qWord, dividendEstimate, divisor);
}
quotient.value[intLen - xlen] = qWord[0];
rem = qWord[1];
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.
*
* 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 divide(MutableBigInteger b, MutableBigInteger quotient) {
if (b.intLen == 0)
throw new ArithmeticException("BigInteger divide by zero");
// Dividend is zero
if (intLen == 0) {
quotient.intLen = quotient.offset;
return new MutableBigInteger();
}
int cmp = compare(b);
// Dividend less than divisor
if (cmp < 0) {
quotient.intLen = quotient.offset = 0;
return new MutableBigInteger(this);
}
// Dividend equal to divisor
if (cmp == 0) {
quotient.value[0] = quotient.intLen = 1;
quotient.offset = 0;
return new MutableBigInteger();
}
quotient.clear();
// Special case one word divisor
if (b.intLen == 1) {
int r = divideOneWord(b.value[b.offset], quotient);
if (r == 0)
return new MutableBigInteger();
return new MutableBigInteger(r);
}
// Copy divisor value to protect divisor
int[] div = Arrays.copyOfRange(b.value, b.offset, b.offset + b.intLen);
return divideMagnitude(div, quotient);
}
/**
* 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 {
int[] div = new int[]{ d, (int)(v & LONG_MASK) };
return divideMagnitude(div, quotient).toLong();
}
}
/**
* Divide this MutableBigInteger by the divisor represented by its magnitude
* array. The quotient will be placed into the provided quotient object &
* the remainder object is returned.
*/
private MutableBigInteger divideMagnitude(int[] divisor,
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;
// Set the quotient size
int dlen = divisor.length;
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;
// D1 normalize the divisor
int shift = Integer.numberOfLeadingZeros(divisor[0]);
if (shift > 0) {
// First shift will not grow array
BigInteger.primitiveLeftShift(divisor, dlen, shift);
// But this one might
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 = divisor[0];
long dhLong = dh & LONG_MASK;
int dl = divisor[1];
int[] qWord = new int[2];
// 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 {
divWord(qWord, nChunk, dh);
qhat = qWord[0];
qrem = qWord[1];
}
}
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
// D8 Unnormalize
if (shift > 0)
rem.rightShift(shift);
quotient.normalize();
rem.normalize();
return rem;
}
/**
* 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.
*/
private void divWord(int[] result, long n, int d) {
long dLong = d & LONG_MASK;
if (dLong == 1) {
result[0] = (int)n;
result[1] = 0;
return;
}
// Approximate the quotient and remainder
long q = (n >>> 1) / (dLong >>> 1);
long 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.
result[0] = (int)q;
result[1] = (int)r;
}
/**
* 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;
}
}