// Copyright 2009 The Closure Library Authors. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS-IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
/**
* @fileoverview Defines an Integer class for representing (potentially)
* infinite length two's-complement integer values.
*
* For the specific case of 64-bit integers, use goog.math.Long, which is more
* efficient.
*
*/
goog.provide('goog.math.Integer');
/**
* Constructs a two's-complement integer an array containing bits of the
* integer in 32-bit (signed) pieces, given in little-endian order (i.e.,
* lowest-order bits in the first piece), and the sign of -1 or 0.
*
* See the from* functions below for other convenient ways of constructing
* Integers.
*
* The internal representation of an integer is an array of 32-bit signed
* pieces, along with a sign (0 or -1) that indicates the contents of all the
* other 32-bit pieces out to infinity. We use 32-bit pieces because these are
* the size of integers on which Javascript performs bit-operations. For
* operations like addition and multiplication, we split each number into 16-bit
* pieces, which can easily be multiplied within Javascript's floating-point
* representation without overflow or change in sign.
*
* @struct
* @constructor
* @param {Array<number>} bits Array containing the bits of the number.
* @param {number} sign The sign of the number: -1 for negative and 0 positive.
* @final
*/
goog.math.Integer = function(bits, sign) {
/**
* @type {!Array<number>}
* @private
*/
this.bits_ = [];
/**
* @type {number}
* @private
*/
this.sign_ = sign;
// Copy the 32-bit signed integer values passed in. We prune out those at the
// top that equal the sign since they are redundant.
var top = true;
for (var i = bits.length - 1; i >= 0; i--) {
var val = bits[i] | 0;
if (!top || val != sign) {
this.bits_[i] = val;
top = false;
}
}
};
// NOTE: Common constant values ZERO, ONE, NEG_ONE, etc. are defined below the
// from* methods on which they depend.
/**
* A cache of the Integer representations of small integer values.
* @type {!Object}
* @private
*/
goog.math.Integer.IntCache_ = {};
/**
* Returns an Integer representing the given (32-bit) integer value.
* @param {number} value A 32-bit integer value.
* @return {!goog.math.Integer} The corresponding Integer value.
*/
goog.math.Integer.fromInt = function(value) {
if (-128 <= value && value < 128) {
var cachedObj = goog.math.Integer.IntCache_[value];
if (cachedObj) {
return cachedObj;
}
}
var obj = new goog.math.Integer([value | 0], value < 0 ? -1 : 0);
if (-128 <= value && value < 128) {
goog.math.Integer.IntCache_[value] = obj;
}
return obj;
};
/**
* Returns an Integer representing the given value, provided that it is a finite
* number. Otherwise, zero is returned.
* @param {number} value The value in question.
* @return {!goog.math.Integer} The corresponding Integer value.
*/
goog.math.Integer.fromNumber = function(value) {
if (isNaN(value) || !isFinite(value)) {
return goog.math.Integer.ZERO;
} else if (value < 0) {
return goog.math.Integer.fromNumber(-value).negate();
} else {
var bits = [];
var pow = 1;
for (var i = 0; value >= pow; i++) {
bits[i] = (value / pow) | 0;
pow *= goog.math.Integer.TWO_PWR_32_DBL_;
}
return new goog.math.Integer(bits, 0);
}
};
/**
* Returns a Integer representing the value that comes by concatenating the
* given entries, each is assumed to be 32 signed bits, given in little-endian
* order (lowest order bits in the lowest index), and sign-extending the highest
* order 32-bit value.
* @param {Array<number>} bits The bits of the number, in 32-bit signed pieces,
* in little-endian order.
* @return {!goog.math.Integer} The corresponding Integer value.
*/
goog.math.Integer.fromBits = function(bits) {
var high = bits[bits.length - 1];
return new goog.math.Integer(bits, high & (1 << 31) ? -1 : 0);
};
/**
* Returns an Integer representation of the given string, written using the
* given radix.
* @param {string} str The textual representation of the Integer.
* @param {number=} opt_radix The radix in which the text is written.
* @return {!goog.math.Integer} The corresponding Integer value.
*/
goog.math.Integer.fromString = function(str, opt_radix) {
if (str.length == 0) {
throw Error('number format error: empty string');
}
var radix = opt_radix || 10;
if (radix < 2 || 36 < radix) {
throw Error('radix out of range: ' + radix);
}
if (str.charAt(0) == '-') {
return goog.math.Integer.fromString(str.substring(1), radix).negate();
} else if (str.indexOf('-') >= 0) {
throw Error('number format error: interior "-" character');
}
// Do several (8) digits each time through the loop, so as to
// minimize the calls to the very expensive emulated div.
var radixToPower = goog.math.Integer.fromNumber(Math.pow(radix, 8));
var result = goog.math.Integer.ZERO;
for (var i = 0; i < str.length; i += 8) {
var size = Math.min(8, str.length - i);
var value = parseInt(str.substring(i, i + size), radix);
if (size < 8) {
var power = goog.math.Integer.fromNumber(Math.pow(radix, size));
result = result.multiply(power).add(goog.math.Integer.fromNumber(value));
} else {
result = result.multiply(radixToPower);
result = result.add(goog.math.Integer.fromNumber(value));
}
}
return result;
};
/**
* A number used repeatedly in calculations. This must appear before the first
* call to the from* functions below.
* @type {number}
* @private
*/
goog.math.Integer.TWO_PWR_32_DBL_ = (1 << 16) * (1 << 16);
/** @type {!goog.math.Integer} */
goog.math.Integer.ZERO = goog.math.Integer.fromInt(0);
/** @type {!goog.math.Integer} */
goog.math.Integer.ONE = goog.math.Integer.fromInt(1);
/**
* @type {!goog.math.Integer}
* @private
*/
goog.math.Integer.TWO_PWR_24_ = goog.math.Integer.fromInt(1 << 24);
/**
* Returns the value, assuming it is a 32-bit integer.
* @return {number} The corresponding int value.
*/
goog.math.Integer.prototype.toInt = function() {
return this.bits_.length > 0 ? this.bits_[0] : this.sign_;
};
/** @return {number} The closest floating-point representation to this value. */
goog.math.Integer.prototype.toNumber = function() {
if (this.isNegative()) {
return -this.negate().toNumber();
} else {
var val = 0;
var pow = 1;
for (var i = 0; i < this.bits_.length; i++) {
val += this.getBitsUnsigned(i) * pow;
pow *= goog.math.Integer.TWO_PWR_32_DBL_;
}
return val;
}
};
/**
* @param {number=} opt_radix The radix in which the text should be written.
* @return {string} The textual representation of this value.
* @override
*/
goog.math.Integer.prototype.toString = function(opt_radix) {
var radix = opt_radix || 10;
if (radix < 2 || 36 < radix) {
throw Error('radix out of range: ' + radix);
}
if (this.isZero()) {
return '0';
} else if (this.isNegative()) {
return '-' + this.negate().toString(radix);
}
// Do several (6) digits each time through the loop, so as to
// minimize the calls to the very expensive emulated div.
var radixToPower = goog.math.Integer.fromNumber(Math.pow(radix, 6));
var rem = this;
var result = '';
while (true) {
var remDiv = rem.divide(radixToPower);
// The right shifting fixes negative values in the case when
// intval >= 2^31; for more details see
// https://github.com/google/closure-library/pull/498
var intval = rem.subtract(remDiv.multiply(radixToPower)).toInt() >>> 0;
var digits = intval.toString(radix);
rem = remDiv;
if (rem.isZero()) {
return digits + result;
} else {
while (digits.length < 6) {
digits = '0' + digits;
}
result = '' + digits + result;
}
}
};
/**
* Returns the index-th 32-bit (signed) piece of the Integer according to
* little-endian order (i.e., index 0 contains the smallest bits).
* @param {number} index The index in question.
* @return {number} The requested 32-bits as a signed number.
*/
goog.math.Integer.prototype.getBits = function(index) {
if (index < 0) {
return 0; // Allowing this simplifies bit shifting operations below...
} else if (index < this.bits_.length) {
return this.bits_[index];
} else {
return this.sign_;
}
};
/**
* Returns the index-th 32-bit piece as an unsigned number.
* @param {number} index The index in question.
* @return {number} The requested 32-bits as an unsigned number.
*/
goog.math.Integer.prototype.getBitsUnsigned = function(index) {
var val = this.getBits(index);
return val >= 0 ? val : goog.math.Integer.TWO_PWR_32_DBL_ + val;
};
/** @return {number} The sign bit of this number, -1 or 0. */
goog.math.Integer.prototype.getSign = function() {
return this.sign_;
};
/** @return {boolean} Whether this value is zero. */
goog.math.Integer.prototype.isZero = function() {
if (this.sign_ != 0) {
return false;
}
for (var i = 0; i < this.bits_.length; i++) {
if (this.bits_[i] != 0) {
return false;
}
}
return true;
};
/** @return {boolean} Whether this value is negative. */
goog.math.Integer.prototype.isNegative = function() {
return this.sign_ == -1;
};
/** @return {boolean} Whether this value is odd. */
goog.math.Integer.prototype.isOdd = function() {
return (this.bits_.length == 0) && (this.sign_ == -1) ||
(this.bits_.length > 0) && ((this.bits_[0] & 1) != 0);
};
/**
* @param {goog.math.Integer} other Integer to compare against.
* @return {boolean} Whether this Integer equals the other.
*/
goog.math.Integer.prototype.equals = function(other) {
if (this.sign_ != other.sign_) {
return false;
}
var len = Math.max(this.bits_.length, other.bits_.length);
for (var i = 0; i < len; i++) {
if (this.getBits(i) != other.getBits(i)) {
return false;
}
}
return true;
};
/**
* @param {goog.math.Integer} other Integer to compare against.
* @return {boolean} Whether this Integer does not equal the other.
*/
goog.math.Integer.prototype.notEquals = function(other) {
return !this.equals(other);
};
/**
* @param {goog.math.Integer} other Integer to compare against.
* @return {boolean} Whether this Integer is greater than the other.
*/
goog.math.Integer.prototype.greaterThan = function(other) {
return this.compare(other) > 0;
};
/**
* @param {goog.math.Integer} other Integer to compare against.
* @return {boolean} Whether this Integer is greater than or equal to the other.
*/
goog.math.Integer.prototype.greaterThanOrEqual = function(other) {
return this.compare(other) >= 0;
};
/**
* @param {goog.math.Integer} other Integer to compare against.
* @return {boolean} Whether this Integer is less than the other.
*/
goog.math.Integer.prototype.lessThan = function(other) {
return this.compare(other) < 0;
};
/**
* @param {goog.math.Integer} other Integer to compare against.
* @return {boolean} Whether this Integer is less than or equal to the other.
*/
goog.math.Integer.prototype.lessThanOrEqual = function(other) {
return this.compare(other) <= 0;
};
/**
* Compares this Integer with the given one.
* @param {goog.math.Integer} other Integer to compare against.
* @return {number} 0 if they are the same, 1 if the this is greater, and -1
* if the given one is greater.
*/
goog.math.Integer.prototype.compare = function(other) {
var diff = this.subtract(other);
if (diff.isNegative()) {
return -1;
} else if (diff.isZero()) {
return 0;
} else {
return +1;
}
};
/**
* Returns an integer with only the first numBits bits of this value, sign
* extended from the final bit.
* @param {number} numBits The number of bits by which to shift.
* @return {!goog.math.Integer} The shorted integer value.
*/
goog.math.Integer.prototype.shorten = function(numBits) {
var arr_index = (numBits - 1) >> 5;
var bit_index = (numBits - 1) % 32;
var bits = [];
for (var i = 0; i < arr_index; i++) {
bits[i] = this.getBits(i);
}
var sigBits = bit_index == 31 ? 0xFFFFFFFF : (1 << (bit_index + 1)) - 1;
var val = this.getBits(arr_index) & sigBits;
if (val & (1 << bit_index)) {
val |= 0xFFFFFFFF - sigBits;
bits[arr_index] = val;
return new goog.math.Integer(bits, -1);
} else {
bits[arr_index] = val;
return new goog.math.Integer(bits, 0);
}
};
/** @return {!goog.math.Integer} The negation of this value. */
goog.math.Integer.prototype.negate = function() {
return this.not().add(goog.math.Integer.ONE);
};
/**
* Returns the sum of this and the given Integer.
* @param {goog.math.Integer} other The Integer to add to this.
* @return {!goog.math.Integer} The Integer result.
*/
goog.math.Integer.prototype.add = function(other) {
var len = Math.max(this.bits_.length, other.bits_.length);
var arr = [];
var carry = 0;
for (var i = 0; i <= len; i++) {
var a1 = this.getBits(i) >>> 16;
var a0 = this.getBits(i) & 0xFFFF;
var b1 = other.getBits(i) >>> 16;
var b0 = other.getBits(i) & 0xFFFF;
var c0 = carry + a0 + b0;
var c1 = (c0 >>> 16) + a1 + b1;
carry = c1 >>> 16;
c0 &= 0xFFFF;
c1 &= 0xFFFF;
arr[i] = (c1 << 16) | c0;
}
return goog.math.Integer.fromBits(arr);
};
/**
* Returns the difference of this and the given Integer.
* @param {goog.math.Integer} other The Integer to subtract from this.
* @return {!goog.math.Integer} The Integer result.
*/
goog.math.Integer.prototype.subtract = function(other) {
return this.add(other.negate());
};
/**
* Returns the product of this and the given Integer.
* @param {goog.math.Integer} other The Integer to multiply against this.
* @return {!goog.math.Integer} The product of this and the other.
*/
goog.math.Integer.prototype.multiply = function(other) {
if (this.isZero()) {
return goog.math.Integer.ZERO;
} else if (other.isZero()) {
return goog.math.Integer.ZERO;
}
if (this.isNegative()) {
if (other.isNegative()) {
return this.negate().multiply(other.negate());
} else {
return this.negate().multiply(other).negate();
}
} else if (other.isNegative()) {
return this.multiply(other.negate()).negate();
}
// If both numbers are small, use float multiplication
if (this.lessThan(goog.math.Integer.TWO_PWR_24_) &&
other.lessThan(goog.math.Integer.TWO_PWR_24_)) {
return goog.math.Integer.fromNumber(this.toNumber() * other.toNumber());
}
// Fill in an array of 16-bit products.
var len = this.bits_.length + other.bits_.length;
var arr = [];
for (var i = 0; i < 2 * len; i++) {
arr[i] = 0;
}
for (var i = 0; i < this.bits_.length; i++) {
for (var j = 0; j < other.bits_.length; j++) {
var a1 = this.getBits(i) >>> 16;
var a0 = this.getBits(i) & 0xFFFF;
var b1 = other.getBits(j) >>> 16;
var b0 = other.getBits(j) & 0xFFFF;
arr[2 * i + 2 * j] += a0 * b0;
goog.math.Integer.carry16_(arr, 2 * i + 2 * j);
arr[2 * i + 2 * j + 1] += a1 * b0;
goog.math.Integer.carry16_(arr, 2 * i + 2 * j + 1);
arr[2 * i + 2 * j + 1] += a0 * b1;
goog.math.Integer.carry16_(arr, 2 * i + 2 * j + 1);
arr[2 * i + 2 * j + 2] += a1 * b1;
goog.math.Integer.carry16_(arr, 2 * i + 2 * j + 2);
}
}
// Combine the 16-bit values into 32-bit values.
for (var i = 0; i < len; i++) {
arr[i] = (arr[2 * i + 1] << 16) | arr[2 * i];
}
for (var i = len; i < 2 * len; i++) {
arr[i] = 0;
}
return new goog.math.Integer(arr, 0);
};
/**
* Carries any overflow from the given index into later entries.
* @param {Array<number>} bits Array of 16-bit values in little-endian order.
* @param {number} index The index in question.
* @private
*/
goog.math.Integer.carry16_ = function(bits, index) {
while ((bits[index] & 0xFFFF) != bits[index]) {
bits[index + 1] += bits[index] >>> 16;
bits[index] &= 0xFFFF;
}
};
/**
* Returns "this" Integer divided by the given one. Both "this" and the given
* Integer MUST be positive.
*
* This method is only needed for very large numbers (>10^308),
* for which the original division algorithm gets into an infinite
* loop (see https://github.com/google/closure-library/issues/500).
*
* The algorithm has some possible performance enhancements (or
* could be rewritten entirely), it's just an initial solution for
* the issue linked above.
*
* @param {!goog.math.Integer} other The Integer to divide "this" by.
* @return {!goog.math.Integer} "this" value divided by the given one.
* @private
*/
goog.math.Integer.prototype.slowDivide_ = function(other) {
if (this.isNegative() || other.isNegative()) {
throw Error('slowDivide_ only works with positive integers.');
}
var twoPower = goog.math.Integer.ONE;
var multiple = other;
// First we have to figure out what the highest bit of the result
// is, so we increase "twoPower" and "multiple" until "multiple"
// exceeds "this".
while (multiple.lessThanOrEqual(this)) {
twoPower = twoPower.shiftLeft(1);
multiple = multiple.shiftLeft(1);
}
// Rewind by one power of two, giving us the highest bit of the
// result.
var res = twoPower.shiftRight(1);
var total = multiple.shiftRight(1);
// Now we starting decreasing "multiple" and "twoPower" to find the
// rest of the bits of the result.
var total2;
multiple = multiple.shiftRight(2);
twoPower = twoPower.shiftRight(2);
while (!multiple.isZero()) {
// whenever we can add "multiple" to the total and not exceed
// "this", that means we've found a 1 bit. Else we've found a 0
// and don't need to add to the result.
total2 = total.add(multiple);
if (total2.lessThanOrEqual(this)) {
res = res.add(twoPower);
total = total2;
}
multiple = multiple.shiftRight(1);
twoPower = twoPower.shiftRight(1);
}
return res;
};
/**
* Returns this Integer divided by the given one.
* @param {!goog.math.Integer} other The Integer to divide this by.
* @return {!goog.math.Integer} This value divided by the given one.
*/
goog.math.Integer.prototype.divide = function(other) {
if (other.isZero()) {
throw Error('division by zero');
} else if (this.isZero()) {
return goog.math.Integer.ZERO;
}
if (this.isNegative()) {
if (other.isNegative()) {
return this.negate().divide(other.negate());
} else {
return this.negate().divide(other).negate();
}
} else if (other.isNegative()) {
return this.divide(other.negate()).negate();
}
// Have to degrade to slowDivide for Very Large Numbers, because
// they're out of range for the floating-point approximation
// technique used below.
if (this.bits_.length > 30) {
return this.slowDivide_(other);
}
// Repeat the following until the remainder is less than other: find a
// floating-point that approximates remainder / other *from below*, add this
// into the result, and subtract it from the remainder. It is critical that
// the approximate value is less than or equal to the real value so that the
// remainder never becomes negative.
var res = goog.math.Integer.ZERO;
var rem = this;
while (rem.greaterThanOrEqual(other)) {
// Approximate the result of division. This may be a little greater or
// smaller than the actual value.
var approx = Math.max(1, Math.floor(rem.toNumber() / other.toNumber()));
// We will tweak the approximate result by changing it in the 48-th digit or
// the smallest non-fractional digit, whichever is larger.
var log2 = Math.ceil(Math.log(approx) / Math.LN2);
var delta = (log2 <= 48) ? 1 : Math.pow(2, log2 - 48);
// Decrease the approximation until it is smaller than the remainder. Note
// that if it is too large, the product overflows and is negative.
var approxRes = goog.math.Integer.fromNumber(approx);
var approxRem = approxRes.multiply(other);
while (approxRem.isNegative() || approxRem.greaterThan(rem)) {
approx -= delta;
approxRes = goog.math.Integer.fromNumber(approx);
approxRem = approxRes.multiply(other);
}
// We know the answer can't be zero... and actually, zero would cause
// infinite recursion since we would make no progress.
if (approxRes.isZero()) {
approxRes = goog.math.Integer.ONE;
}
res = res.add(approxRes);
rem = rem.subtract(approxRem);
}
return res;
};
/**
* Returns this Integer modulo the given one.
* @param {!goog.math.Integer} other The Integer by which to mod.
* @return {!goog.math.Integer} This value modulo the given one.
*/
goog.math.Integer.prototype.modulo = function(other) {
return this.subtract(this.divide(other).multiply(other));
};
/** @return {!goog.math.Integer} The bitwise-NOT of this value. */
goog.math.Integer.prototype.not = function() {
var len = this.bits_.length;
var arr = [];
for (var i = 0; i < len; i++) {
arr[i] = ~this.bits_[i];
}
return new goog.math.Integer(arr, ~this.sign_);
};
/**
* Returns the bitwise-AND of this Integer and the given one.
* @param {goog.math.Integer} other The Integer to AND with this.
* @return {!goog.math.Integer} The bitwise-AND of this and the other.
*/
goog.math.Integer.prototype.and = function(other) {
var len = Math.max(this.bits_.length, other.bits_.length);
var arr = [];
for (var i = 0; i < len; i++) {
arr[i] = this.getBits(i) & other.getBits(i);
}
return new goog.math.Integer(arr, this.sign_ & other.sign_);
};
/**
* Returns the bitwise-OR of this Integer and the given one.
* @param {goog.math.Integer} other The Integer to OR with this.
* @return {!goog.math.Integer} The bitwise-OR of this and the other.
*/
goog.math.Integer.prototype.or = function(other) {
var len = Math.max(this.bits_.length, other.bits_.length);
var arr = [];
for (var i = 0; i < len; i++) {
arr[i] = this.getBits(i) | other.getBits(i);
}
return new goog.math.Integer(arr, this.sign_ | other.sign_);
};
/**
* Returns the bitwise-XOR of this Integer and the given one.
* @param {goog.math.Integer} other The Integer to XOR with this.
* @return {!goog.math.Integer} The bitwise-XOR of this and the other.
*/
goog.math.Integer.prototype.xor = function(other) {
var len = Math.max(this.bits_.length, other.bits_.length);
var arr = [];
for (var i = 0; i < len; i++) {
arr[i] = this.getBits(i) ^ other.getBits(i);
}
return new goog.math.Integer(arr, this.sign_ ^ other.sign_);
};
/**
* Returns this value with bits shifted to the left by the given amount.
* @param {number} numBits The number of bits by which to shift.
* @return {!goog.math.Integer} This shifted to the left by the given amount.
*/
goog.math.Integer.prototype.shiftLeft = function(numBits) {
var arr_delta = numBits >> 5;
var bit_delta = numBits % 32;
var len = this.bits_.length + arr_delta + (bit_delta > 0 ? 1 : 0);
var arr = [];
for (var i = 0; i < len; i++) {
if (bit_delta > 0) {
arr[i] = (this.getBits(i - arr_delta) << bit_delta) |
(this.getBits(i - arr_delta - 1) >>> (32 - bit_delta));
} else {
arr[i] = this.getBits(i - arr_delta);
}
}
return new goog.math.Integer(arr, this.sign_);
};
/**
* Returns this value with bits shifted to the right by the given amount.
* @param {number} numBits The number of bits by which to shift.
* @return {!goog.math.Integer} This shifted to the right by the given amount.
*/
goog.math.Integer.prototype.shiftRight = function(numBits) {
var arr_delta = numBits >> 5;
var bit_delta = numBits % 32;
var len = this.bits_.length - arr_delta;
var arr = [];
for (var i = 0; i < len; i++) {
if (bit_delta > 0) {
arr[i] = (this.getBits(i + arr_delta) >>> bit_delta) |
(this.getBits(i + arr_delta + 1) << (32 - bit_delta));
} else {
arr[i] = this.getBits(i + arr_delta);
}
}
return new goog.math.Integer(arr, this.sign_);
};