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// 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 a Long class for representing a 64-bit two's-complement
* integer value, which faithfully simulates the behavior of a Java "long". This
* implementation is derived from LongLib in GWT.
*
*/
// goog.provide('goog.math.Long');
var goog = {}; goog.math = {};
/**
* Constructs a 64-bit two's-complement integer, given its low and high 32-bit
* values as *signed* integers. See the from* functions below for more
* convenient ways of constructing Longs.
*
* The internal representation of a long is the two given signed, 32-bit values.
* 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.
*
* In the algorithms below, we frequently reduce the negative case to the
* positive case by negating the input(s) and then post-processing the result.
* Note that we must ALWAYS check specially whether those values are MIN_VALUE
* (-2^63) because -MIN_VALUE == MIN_VALUE (since 2^63 cannot be represented as
* a positive number, it overflows back into a negative). Not handling this
* case would often result in infinite recursion.
*
* @param {number} low The low (signed) 32 bits of the long.
* @param {number} high The high (signed) 32 bits of the long.
* @constructor
* @final
*/
goog.math.Long = function(low, high) {
/**
* @type {number}
* @private
*/
this.low_ = low | 0; // force into 32 signed bits.
/**
* @type {number}
* @private
*/
this.high_ = high | 0; // force into 32 signed bits.
};
// NOTE: Common constant values ZERO, ONE, NEG_ONE, etc. are defined below the
// from* methods on which they depend.
/**
* A cache of the Long representations of small integer values.
* @type {!Object}
* @private
*/
goog.math.Long.IntCache_ = {};
/**
* Returns a Long representing the given (32-bit) integer value.
* @param {number} value The 32-bit integer in question.
* @return {!goog.math.Long} The corresponding Long value.
*/
goog.math.Long.fromInt = function(value) {
if (-128 <= value && value < 128) {
var cachedObj = goog.math.Long.IntCache_[value];
if (cachedObj) {
return cachedObj;
}
}
var obj = new goog.math.Long(value | 0, value < 0 ? -1 : 0);
if (-128 <= value && value < 128) {
goog.math.Long.IntCache_[value] = obj;
}
return obj;
};
/**
* Returns a Long representing the given value, provided that it is a finite
* number. Otherwise, zero is returned.
* @param {number} value The number in question.
* @return {!goog.math.Long} The corresponding Long value.
*/
goog.math.Long.fromNumber = function(value) {
if (isNaN(value) || !isFinite(value)) {
return goog.math.Long.ZERO;
} else if (value <= -goog.math.Long.TWO_PWR_63_DBL_) {
return goog.math.Long.MIN_VALUE;
} else if (value + 1 >= goog.math.Long.TWO_PWR_63_DBL_) {
return goog.math.Long.MAX_VALUE;
} else if (value < 0) {
return goog.math.Long.fromNumber(-value).negate();
} else {
return new goog.math.Long(
(value % goog.math.Long.TWO_PWR_32_DBL_) | 0,
(value / goog.math.Long.TWO_PWR_32_DBL_) | 0);
}
};
/**
* Returns a Long representing the 64-bit integer that comes by concatenating
* the given high and low bits. Each is assumed to use 32 bits.
* @param {number} lowBits The low 32-bits.
* @param {number} highBits The high 32-bits.
* @return {!goog.math.Long} The corresponding Long value.
*/
goog.math.Long.fromBits = function(lowBits, highBits) {
return new goog.math.Long(lowBits, highBits);
};
/**
* Returns a Long representation of the given string, written using the given
* radix.
* @param {string} str The textual representation of the Long.
* @param {number=} opt_radix The radix in which the text is written.
* @return {!goog.math.Long} The corresponding Long value.
*/
goog.math.Long.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.Long.fromString(str.substring(1), radix).negate();
} else if (str.indexOf('-') >= 0) {
throw Error('number format error: interior "-" character: ' + str);
}
// 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.Long.fromNumber(Math.pow(radix, 8));
var result = goog.math.Long.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.Long.fromNumber(Math.pow(radix, size));
result = result.multiply(power).add(goog.math.Long.fromNumber(value));
} else {
result = result.multiply(radixToPower);
result = result.add(goog.math.Long.fromNumber(value));
}
}
return result;
};
// NOTE: the compiler should inline these constant values below and then remove
// these variables, so there should be no runtime penalty for these.
/**
* Number used repeated below in calculations. This must appear before the
* first call to any from* function below.
* @type {number}
* @private
*/
goog.math.Long.TWO_PWR_16_DBL_ = 1 << 16;
/**
* @type {number}
* @private
*/
goog.math.Long.TWO_PWR_24_DBL_ = 1 << 24;
/**
* @type {number}
* @private
*/
goog.math.Long.TWO_PWR_32_DBL_ =
goog.math.Long.TWO_PWR_16_DBL_ * goog.math.Long.TWO_PWR_16_DBL_;
/**
* @type {number}
* @private
*/
goog.math.Long.TWO_PWR_31_DBL_ =
goog.math.Long.TWO_PWR_32_DBL_ / 2;
/**
* @type {number}
* @private
*/
goog.math.Long.TWO_PWR_48_DBL_ =
goog.math.Long.TWO_PWR_32_DBL_ * goog.math.Long.TWO_PWR_16_DBL_;
/**
* @type {number}
* @private
*/
goog.math.Long.TWO_PWR_64_DBL_ =
goog.math.Long.TWO_PWR_32_DBL_ * goog.math.Long.TWO_PWR_32_DBL_;
/**
* @type {number}
* @private
*/
goog.math.Long.TWO_PWR_63_DBL_ =
goog.math.Long.TWO_PWR_64_DBL_ / 2;
/** @type {!goog.math.Long} */
goog.math.Long.ZERO = goog.math.Long.fromInt(0);
/** @type {!goog.math.Long} */
goog.math.Long.ONE = goog.math.Long.fromInt(1);
/** @type {!goog.math.Long} */
goog.math.Long.NEG_ONE = goog.math.Long.fromInt(-1);
/** @type {!goog.math.Long} */
goog.math.Long.MAX_VALUE =
goog.math.Long.fromBits(0xFFFFFFFF | 0, 0x7FFFFFFF | 0);
/** @type {!goog.math.Long} */
goog.math.Long.MIN_VALUE = goog.math.Long.fromBits(0, 0x80000000 | 0);
/**
* @type {!goog.math.Long}
* @private
*/
goog.math.Long.TWO_PWR_24_ = goog.math.Long.fromInt(1 << 24);
/** @return {number} The value, assuming it is a 32-bit integer. */
goog.math.Long.prototype.toInt = function() {
return this.low_;
};
/** @return {number} The closest floating-point representation to this value. */
goog.math.Long.prototype.toNumber = function() {
return this.high_ * goog.math.Long.TWO_PWR_32_DBL_ +
this.getLowBitsUnsigned();
};
/**
* @param {number=} opt_radix The radix in which the text should be written.
* @return {string} The textual representation of this value.
* @override
*/
goog.math.Long.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';
}
if (this.isNegative()) {
if (this.equals(goog.math.Long.MIN_VALUE)) {
// We need to change the Long value before it can be negated, so we remove
// the bottom-most digit in this base and then recurse to do the rest.
var radixLong = goog.math.Long.fromNumber(radix);
var div = this.div(radixLong);
var rem = div.multiply(radixLong).subtract(this);
return div.toString(radix) + rem.toInt().toString(radix);
} else {
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.Long.fromNumber(Math.pow(radix, 6));
var rem = this;
var result = '';
while (true) {
var remDiv = rem.div(radixToPower);
var intval = rem.subtract(remDiv.multiply(radixToPower)).toInt() >>> 0; // wraps around for base 36 (dcode)
console.log(intval);
var digits = intval.toString(radix);
rem = remDiv;
if (rem.isZero()) {
return digits + result;
} else {
while (digits.length < 6) {
digits = '0' + digits;
}
result = '' + digits + result;
}
}
};
/** @return {number} The high 32-bits as a signed value. */
goog.math.Long.prototype.getHighBits = function() {
return this.high_;
};
/** @return {number} The low 32-bits as a signed value. */
goog.math.Long.prototype.getLowBits = function() {
return this.low_;
};
/** @return {number} The low 32-bits as an unsigned value. */
goog.math.Long.prototype.getLowBitsUnsigned = function() {
return (this.low_ >= 0) ?
this.low_ : goog.math.Long.TWO_PWR_32_DBL_ + this.low_;
};
/**
* @return {number} Returns the number of bits needed to represent the absolute
* value of this Long.
*/
goog.math.Long.prototype.getNumBitsAbs = function() {
if (this.isNegative()) {
if (this.equals(goog.math.Long.MIN_VALUE)) {
return 64;
} else {
return this.negate().getNumBitsAbs();
}
} else {
var val = this.high_ != 0 ? this.high_ : this.low_;
for (var bit = 31; bit > 0; bit--) {
if ((val & (1 << bit)) != 0) {
break;
}
}
return this.high_ != 0 ? bit + 33 : bit + 1;
}
};
/** @return {boolean} Whether this value is zero. */
goog.math.Long.prototype.isZero = function() {
return this.high_ == 0 && this.low_ == 0;
};
/** @return {boolean} Whether this value is negative. */
goog.math.Long.prototype.isNegative = function() {
return this.high_ < 0;
};
/** @return {boolean} Whether this value is odd. */
goog.math.Long.prototype.isOdd = function() {
return (this.low_ & 1) == 1;
};
/**
* @param {goog.math.Long} other Long to compare against.
* @return {boolean} Whether this Long equals the other.
*/
goog.math.Long.prototype.equals = function(other) {
return (this.high_ == other.high_) && (this.low_ == other.low_);
};
/**
* @param {goog.math.Long} other Long to compare against.
* @return {boolean} Whether this Long does not equal the other.
*/
goog.math.Long.prototype.notEquals = function(other) {
return (this.high_ != other.high_) || (this.low_ != other.low_);
};
/**
* @param {goog.math.Long} other Long to compare against.
* @return {boolean} Whether this Long is less than the other.
*/
goog.math.Long.prototype.lessThan = function(other) {
return this.compare(other) < 0;
};
/**
* @param {goog.math.Long} other Long to compare against.
* @return {boolean} Whether this Long is less than or equal to the other.
*/
goog.math.Long.prototype.lessThanOrEqual = function(other) {
return this.compare(other) <= 0;
};
/**
* @param {goog.math.Long} other Long to compare against.
* @return {boolean} Whether this Long is greater than the other.
*/
goog.math.Long.prototype.greaterThan = function(other) {
return this.compare(other) > 0;
};
/**
* @param {goog.math.Long} other Long to compare against.
* @return {boolean} Whether this Long is greater than or equal to the other.
*/
goog.math.Long.prototype.greaterThanOrEqual = function(other) {
return this.compare(other) >= 0;
};
/**
* Compares this Long with the given one.
* @param {goog.math.Long} other Long 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.Long.prototype.compare = function(other) {
if (this.equals(other)) {
return 0;
}
var thisNeg = this.isNegative();
var otherNeg = other.isNegative();
if (thisNeg && !otherNeg) {
return -1;
}
if (!thisNeg && otherNeg) {
return 1;
}
// at this point, the signs are the same, so subtraction will not overflow
if (this.subtract(other).isNegative()) {
return -1;
} else {
return 1;
}
};
/** @return {!goog.math.Long} The negation of this value. */
goog.math.Long.prototype.negate = function() {
if (this.equals(goog.math.Long.MIN_VALUE)) {
return goog.math.Long.MIN_VALUE;
} else {
return this.not().add(goog.math.Long.ONE);
}
};
/**
* Returns the sum of this and the given Long.
* @param {goog.math.Long} other Long to add to this one.
* @return {!goog.math.Long} The sum of this and the given Long.
*/
goog.math.Long.prototype.add = function(other) {
// Divide each number into 4 chunks of 16 bits, and then sum the chunks.
var a48 = this.high_ >>> 16;
var a32 = this.high_ & 0xFFFF;
var a16 = this.low_ >>> 16;
var a00 = this.low_ & 0xFFFF;
var b48 = other.high_ >>> 16;
var b32 = other.high_ & 0xFFFF;
var b16 = other.low_ >>> 16;
var b00 = other.low_ & 0xFFFF;
var c48 = 0, c32 = 0, c16 = 0, c00 = 0;
c00 += a00 + b00;
c16 += c00 >>> 16;
c00 &= 0xFFFF;
c16 += a16 + b16;
c32 += c16 >>> 16;
c16 &= 0xFFFF;
c32 += a32 + b32;
c48 += c32 >>> 16;
c32 &= 0xFFFF;
c48 += a48 + b48;
c48 &= 0xFFFF;
return goog.math.Long.fromBits((c16 << 16) | c00, (c48 << 16) | c32);
};
/**
* Returns the difference of this and the given Long.
* @param {goog.math.Long} other Long to subtract from this.
* @return {!goog.math.Long} The difference of this and the given Long.
*/
goog.math.Long.prototype.subtract = function(other) {
return this.add(other.negate());
};
/**
* Returns the product of this and the given long.
* @param {goog.math.Long} other Long to multiply with this.
* @return {!goog.math.Long} The product of this and the other.
*/
goog.math.Long.prototype.multiply = function(other) {
if (this.isZero()) {
return goog.math.Long.ZERO;
} else if (other.isZero()) {
return goog.math.Long.ZERO;
}
if (this.equals(goog.math.Long.MIN_VALUE)) {
return other.isOdd() ? goog.math.Long.MIN_VALUE : goog.math.Long.ZERO;
} else if (other.equals(goog.math.Long.MIN_VALUE)) {
return this.isOdd() ? goog.math.Long.MIN_VALUE : goog.math.Long.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 longs are small, use float multiplication
if (this.lessThan(goog.math.Long.TWO_PWR_24_) &&
other.lessThan(goog.math.Long.TWO_PWR_24_)) {
return goog.math.Long.fromNumber(this.toNumber() * other.toNumber());
}
// Divide each long into 4 chunks of 16 bits, and then add up 4x4 products.
// We can skip products that would overflow.
var a48 = this.high_ >>> 16;
var a32 = this.high_ & 0xFFFF;
var a16 = this.low_ >>> 16;
var a00 = this.low_ & 0xFFFF;
var b48 = other.high_ >>> 16;
var b32 = other.high_ & 0xFFFF;
var b16 = other.low_ >>> 16;
var b00 = other.low_ & 0xFFFF;
var c48 = 0, c32 = 0, c16 = 0, c00 = 0;
c00 += a00 * b00;
c16 += c00 >>> 16;
c00 &= 0xFFFF;
c16 += a16 * b00;
c32 += c16 >>> 16;
c16 &= 0xFFFF;
c16 += a00 * b16;
c32 += c16 >>> 16;
c16 &= 0xFFFF;
c32 += a32 * b00;
c48 += c32 >>> 16;
c32 &= 0xFFFF;
c32 += a16 * b16;
c48 += c32 >>> 16;
c32 &= 0xFFFF;
c32 += a00 * b32;
c48 += c32 >>> 16;
c32 &= 0xFFFF;
c48 += a48 * b00 + a32 * b16 + a16 * b32 + a00 * b48;
c48 &= 0xFFFF;
return goog.math.Long.fromBits((c16 << 16) | c00, (c48 << 16) | c32);
};
/**
* Returns this Long divided by the given one.
* @param {goog.math.Long} other Long by which to divide.
* @return {!goog.math.Long} This Long divided by the given one.
*/
goog.math.Long.prototype.div = function(other) {
if (other.isZero()) {
throw Error('division by zero');
} else if (this.isZero()) {
return goog.math.Long.ZERO;
}
if (this.equals(goog.math.Long.MIN_VALUE)) {
if (other.equals(goog.math.Long.ONE) ||
other.equals(goog.math.Long.NEG_ONE)) {
return goog.math.Long.MIN_VALUE; // recall that -MIN_VALUE == MIN_VALUE
} else if (other.equals(goog.math.Long.MIN_VALUE)) {
return goog.math.Long.ONE;
} else {
// At this point, we have |other| >= 2, so |this/other| < |MIN_VALUE|.
var halfThis = this.shiftRight(1);
var approx = halfThis.div(other).shiftLeft(1);
if (approx.equals(goog.math.Long.ZERO)) {
return other.isNegative() ? goog.math.Long.ONE : goog.math.Long.NEG_ONE;
} else {
var rem = this.subtract(other.multiply(approx));
var result = approx.add(rem.div(other));
return result;
}
}
} else if (other.equals(goog.math.Long.MIN_VALUE)) {
return goog.math.Long.ZERO;
}
if (this.isNegative()) {
if (other.isNegative()) {
return this.negate().div(other.negate());
} else {
return this.negate().div(other).negate();
}
} else if (other.isNegative()) {
return this.div(other.negate()).negate();
}
// 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.Long.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.Long.fromNumber(approx);
var approxRem = approxRes.multiply(other);
while (approxRem.isNegative() || approxRem.greaterThan(rem)) {
approx -= delta;
approxRes = goog.math.Long.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.Long.ONE;
}
res = res.add(approxRes);
rem = rem.subtract(approxRem);
}
return res;
};
/**
* Returns this Long modulo the given one.
* @param {goog.math.Long} other Long by which to mod.
* @return {!goog.math.Long} This Long modulo the given one.
*/
goog.math.Long.prototype.modulo = function(other) {
return this.subtract(this.div(other).multiply(other));
};
/** @return {!goog.math.Long} The bitwise-NOT of this value. */
goog.math.Long.prototype.not = function() {
return goog.math.Long.fromBits(~this.low_, ~this.high_);
};
/**
* Returns the bitwise-AND of this Long and the given one.
* @param {goog.math.Long} other The Long with which to AND.
* @return {!goog.math.Long} The bitwise-AND of this and the other.
*/
goog.math.Long.prototype.and = function(other) {
return goog.math.Long.fromBits(this.low_ & other.low_,
this.high_ & other.high_);
};
/**
* Returns the bitwise-OR of this Long and the given one.
* @param {goog.math.Long} other The Long with which to OR.
* @return {!goog.math.Long} The bitwise-OR of this and the other.
*/
goog.math.Long.prototype.or = function(other) {
return goog.math.Long.fromBits(this.low_ | other.low_,
this.high_ | other.high_);
};
/**
* Returns the bitwise-XOR of this Long and the given one.
* @param {goog.math.Long} other The Long with which to XOR.
* @return {!goog.math.Long} The bitwise-XOR of this and the other.
*/
goog.math.Long.prototype.xor = function(other) {
return goog.math.Long.fromBits(this.low_ ^ other.low_,
this.high_ ^ other.high_);
};
/**
* Returns this Long with bits shifted to the left by the given amount.
* @param {number} numBits The number of bits by which to shift.
* @return {!goog.math.Long} This shifted to the left by the given amount.
*/
goog.math.Long.prototype.shiftLeft = function(numBits) {
numBits &= 63;
if (numBits == 0) {
return this;
} else {
var low = this.low_;
if (numBits < 32) {
var high = this.high_;
return goog.math.Long.fromBits(
low << numBits,
(high << numBits) | (low >>> (32 - numBits)));
} else {
return goog.math.Long.fromBits(0, low << (numBits - 32));
}
}
};
/**
* Returns this Long with bits shifted to the right by the given amount.
* @param {number} numBits The number of bits by which to shift.
* @return {!goog.math.Long} This shifted to the right by the given amount.
*/
goog.math.Long.prototype.shiftRight = function(numBits) {
numBits &= 63;
if (numBits == 0) {
return this;
} else {
var high = this.high_;
if (numBits < 32) {
var low = this.low_;
return goog.math.Long.fromBits(
(low >>> numBits) | (high << (32 - numBits)),
high >> numBits);
} else {
return goog.math.Long.fromBits(
high >> (numBits - 32),
high >= 0 ? 0 : -1);
}
}
};
/**
* Returns this Long with bits shifted to the right by the given amount, with
* zeros placed into the new leading bits.
* @param {number} numBits The number of bits by which to shift.
* @return {!goog.math.Long} This shifted to the right by the given amount, with
* zeros placed into the new leading bits.
*/
goog.math.Long.prototype.shiftRightUnsigned = function(numBits) {
numBits &= 63;
if (numBits == 0) {
return this;
} else {
var high = this.high_;
if (numBits < 32) {
var low = this.low_;
return goog.math.Long.fromBits(
(low >>> numBits) | (high << (32 - numBits)),
high >>> numBits);
} else if (numBits == 32) {
return goog.math.Long.fromBits(high, 0);
} else {
return goog.math.Long.fromBits(high >>> (numBits - 32), 0);
}
}
};
module.exports = goog.math.Long;
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