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18 Apr 2012 5:43 PM #1Sencha User
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ExtJS does not handle LARGE numbers
ExtJS does not handle LARGE numbers
As JavaScript does not handle very large numbers very well...
I recommend that we add BigInteger into the framework.JavaScript only stores 53 significant bits, and then it uses some
more bits to tell how many zeroes comes after those.
That is why
Math.pow(2,52) != Math.pow(2,52)+1
but
Math.pow(2,53) == Math.pow(2,53)+1
It needs 54 bits to represent 2^53+1 precisely. Since there are only 53 bits
available, the least significant bit is lost.
(There are some extra details about how the bits are really used, but
I think they would only confuze matters here
From: https://github.com/silentmatt/javasc.../biginteger.js
PHP Code:/*
JavaScript BigInteger library version 0.9
http://silentmatt.com/biginteger/
Copyright (c) 2009 Matthew Crumley <email@matthewcrumley.com>
Copyright (c) 2010,2011 by John Tobey <John.Tobey@gmail.com>
Licensed under the MIT license.
Support for arbitrary internal representation base was added by
Vitaly Magerya.
*/
/*
File: biginteger.js
Exports:
<BigInteger>
*/
/*
Class: BigInteger
An arbitrarily-large integer.
<BigInteger> objects should be considered immutable. None of the "built-in"
methods modify *this* or their arguments. All properties should be
considered private.
All the methods of <BigInteger> instances can be called "statically". The
static versions are convenient if you don't already have a <BigInteger>
object.
As an example, these calls are equivalent.
> BigInteger(4).multiply(5); // returns BigInteger(20);
> BigInteger.multiply(4, 5); // returns BigInteger(20);
> var a = 42;
> var a = BigInteger.toJSValue("0b101010"); // Not completely useless...
*/
// IE doesn't support Array.prototype.map
if (!Array.prototype.map) {
Array.prototype.map = function (fun /*, thisp*/ ) {
var len = this.length >>> 0;
if (typeof fun !== "function") {
throw new TypeError();
}
var res = new Array(len);
var thisp = arguments[1];
for (var i = 0; i < len; i++) {
if (i in this) {
res[i] = fun.call(thisp, this[i], i, this);
}
}
return res;
};
}
/*
Constructor: BigInteger()
Convert a value to a <BigInteger>.
Although <BigInteger()> is the constructor for <BigInteger> objects, it is
best not to call it as a constructor. If *n* is a <BigInteger> object, it is
simply returned as-is. Otherwise, <BigInteger()> is equivalent to <parse>
without a radix argument.
> var n0 = BigInteger(); // Same as <BigInteger.ZERO>
> var n1 = BigInteger("123"); // Create a new <BigInteger> with value 123
> var n2 = BigInteger(123); // Create a new <BigInteger> with value 123
> var n3 = BigInteger(n2); // Return n2, unchanged
The constructor form only takes an array and a sign. *n* must be an
array of numbers in little-endian order, where each digit is between 0
and BigInteger.base. The second parameter sets the sign: -1 for
negative, +1 for positive, or 0 for zero. The array is *not copied and
may be modified*. If the array contains only zeros, the sign parameter
is ignored and is forced to zero.
> new BigInteger([5], -1): create a new BigInteger with value -5
Parameters:
n - Value to convert to a <BigInteger>.
Returns:
A <BigInteger> value.
See Also:
<parse>, <BigInteger>
*/
function BigInteger(n, s) {
if (!(this instanceof BigInteger)) {
if (n instanceof BigInteger) {
return n;
} else if (typeof n === "undefined") {
return BigInteger.ZERO;
}
return BigInteger.parse(n);
}
n = n || []; // Provide the nullary constructor for subclasses.
while (n.length && !n[n.length - 1]) {
--n.length;
}
this._d = n;
this._s = n.length ? (s || 1) : 0;
}
// Base-10 speedup hacks in parse, toString, exp10 and log functions
// require base to be a power of 10. 10^7 is the largest such power
// that won't cause a precision loss when digits are multiplied.
BigInteger.base = 10000000;
BigInteger.base_log10 = 7;
// Constant: ZERO
// <BigInteger> 0.
BigInteger.ZERO = new BigInteger([], 0);
// Constant: ONE
// <BigInteger> 1.
BigInteger.ONE = new BigInteger([1], 1);
// Constant: M_ONE
// <BigInteger> -1.
BigInteger.M_ONE = new BigInteger(BigInteger.ONE._d, -1);
// Constant: _0
// Shortcut for <ZERO>.
BigInteger._0 = BigInteger.ZERO;
// Constant: _1
// Shortcut for <ONE>.
BigInteger._1 = BigInteger.ONE;
/*
Constant: small
Array of <BigIntegers> from 0 to 36.
These are used internally for parsing, but useful when you need a "small"
<BigInteger>.
See Also:
<ZERO>, <ONE>, <_0>, <_1>
*/
BigInteger.small = [
BigInteger.ZERO, BigInteger.ONE,
/* Assuming BigInteger.base > 36 */
new BigInteger([2], 1), new BigInteger([3], 1), new BigInteger([4], 1), new BigInteger([5], 1), new BigInteger([6], 1), new BigInteger([7], 1), new BigInteger([8], 1), new BigInteger([9], 1), new BigInteger([10], 1), new BigInteger([11], 1), new BigInteger([12], 1), new BigInteger([13], 1), new BigInteger([14], 1), new BigInteger([15], 1), new BigInteger([16], 1), new BigInteger([17], 1), new BigInteger([18], 1), new BigInteger([19], 1), new BigInteger([20], 1), new BigInteger([21], 1), new BigInteger([22], 1), new BigInteger([23], 1), new BigInteger([24], 1), new BigInteger([25], 1), new BigInteger([26], 1), new BigInteger([27], 1), new BigInteger([28], 1), new BigInteger([29], 1), new BigInteger([30], 1), new BigInteger([31], 1), new BigInteger([32], 1), new BigInteger([33], 1), new BigInteger([34], 1), new BigInteger([35], 1), new BigInteger([36], 1)];
// Used for parsing/radix conversion
BigInteger.digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ".split("");
/*
Method: toString
Convert a <BigInteger> to a string.
When *base* is greater than 10, letters are upper case.
Parameters:
base - Optional base to represent the number in (default is base 10).
Must be between 2 and 36 inclusive, or an Error will be thrown.
Returns:
The string representation of the <BigInteger>.
*/
BigInteger.prototype.toString = function (base) {
base = +base || 10;
if (base < 2 || base > 36) {
throw new Error("illegal radix " + base + ".");
}
if (this._s === 0) {
return "0";
}
if (base === 10) {
var str = this._s < 0 ? "-" : "";
str += this._d[this._d.length - 1].toString();
for (var i = this._d.length - 2; i >= 0; i--) {
var group = this._d[i].toString();
while (group.length < BigInteger.base_log10) group = '0' + group;
str += group;
}
return str;
} else {
var numerals = BigInteger.digits;
base = BigInteger.small[base];
var sign = this._s;
var n = this.abs();
var digits = [];
var digit;
while (n._s !== 0) {
var divmod = n.divRem(base);
n = divmod[0];
digit = divmod[1];
// TODO: This could be changed to unshift instead of reversing at the end.
// Benchmark both to compare speeds.
digits.push(numerals[digit.valueOf()]);
}
return (sign < 0 ? "-" : "") + digits.reverse().join("");
}
};
// Verify strings for parsing
BigInteger.radixRegex = [/^$/, /^$/, /^[01]*$/, /^[012]*$/, /^[0-3]*$/, /^[0-4]*$/, /^[0-5]*$/, /^[0-6]*$/, /^[0-7]*$/, /^[0-8]*$/, /^[0-9]*$/, /^[0-9aA]*$/, /^[0-9abAB]*$/, /^[0-9abcABC]*$/, /^[0-9a-dA-D]*$/, /^[0-9a-eA-E]*$/, /^[0-9a-fA-F]*$/, /^[0-9a-gA-G]*$/, /^[0-9a-hA-H]*$/, /^[0-9a-iA-I]*$/, /^[0-9a-jA-J]*$/, /^[0-9a-kA-K]*$/, /^[0-9a-lA-L]*$/, /^[0-9a-mA-M]*$/, /^[0-9a-nA-N]*$/, /^[0-9a-oA-O]*$/, /^[0-9a-pA-P]*$/, /^[0-9a-qA-Q]*$/, /^[0-9a-rA-R]*$/, /^[0-9a-sA-S]*$/, /^[0-9a-tA-T]*$/, /^[0-9a-uA-U]*$/, /^[0-9a-vA-V]*$/, /^[0-9a-wA-W]*$/, /^[0-9a-xA-X]*$/, /^[0-9a-yA-Y]*$/, /^[0-9a-zA-Z]*$/];
/*
Function: parse
Parse a string into a <BigInteger>.
*base* is optional but, if provided, must be from 2 to 36 inclusive. If
*base* is not provided, it will be guessed based on the leading characters
of *s* as follows:
- "0x" or "0X": *base* = 16
- "0c" or "0C": *base* = 8
- "0b" or "0B": *base* = 2
- else: *base* = 10
If no base is provided, or *base* is 10, the number can be in exponential
form. For example, these are all valid:
> BigInteger.parse("1e9"); // Same as "1000000000"
> BigInteger.parse("1.234*10^3"); // Same as 1234
> BigInteger.parse("56789 * 10 ** -2"); // Same as 567
If any characters fall outside the range defined by the radix, an exception
will be thrown.
Parameters:
s - The string to parse.
base - Optional radix (default is to guess based on *s*).
Returns:
a <BigInteger> instance.
*/
BigInteger.parse = function (s, base) {
// Expands a number in exponential form to decimal form.
// expandExponential("-13.441*10^5") === "1344100";
// expandExponential("1.12300e-1") === "0.112300";
// expandExponential(1000000000000000000000000000000) === "1000000000000000000000000000000";
function expandExponential(str) {
str = str.replace(/\s*[*xX]\s*10\s*(\^|\*\*)\s*/, "e");
return str.replace(/^([+\-])?(\d+)\.?(\d*)[eE]([+\-]?\d+)$/, function (x, s, n, f, c) {
c = +c;
var l = c < 0;
var i = n.length + c;
x = (l ? n : f).length;
c = ((c = Math.abs(c)) >= x ? c - x + l : 0);
var z = (new Array(c + 1)).join("0");
var r = n + f;
return (s || "") + (l ? r = z + r : r += z).substr(0, i += l ? z.length : 0) + (i < r.length ? "." + r.substr(i) : "");
});
}
s = s.toString();
if (typeof base === "undefined" || +base === 10) {
s = expandExponential(s);
}
var parts = /^([+\-]?)(0[xXcCbB])?([0-9A-Za-z]*)(?:\.\d*)?$/.exec(s);
if (parts) {
var sign = parts[1] || "+";
var baseSection = parts[2] || "";
var digits = parts[3] || "";
if (typeof base === "undefined") {
// Guess base
if (baseSection === "0x" || baseSection === "0X") { // Hex
base = 16;
} else if (baseSection === "0c" || baseSection === "0C") { // Octal
base = 8;
} else if (baseSection === "0b" || baseSection === "0B") { // Binary
base = 2;
} else {
base = 10;
}
} else if (base < 2 || base > 36) {
throw new Error("Illegal radix " + base + ".");
}
base = +base;
// Check for digits outside the range
if (!(BigInteger.radixRegex[base].test(digits))) {
throw new Error("Bad digit for radix " + base);
}
// Strip leading zeros, and convert to array
digits = digits.replace(/^0+/, "").split("");
if (digits.length === 0) {
return BigInteger.ZERO;
}
// Get the sign (we know it's not zero)
sign = (sign === "-") ? -1 : 1;
// Optimize 10
if (base == 10) {
var d = [];
while (digits.length >= BigInteger.base_log10) {
d.push(parseInt(digits.splice(-BigInteger.base_log10).join(''), 10));
}
d.push(parseInt(digits.join(''), 10));
return new BigInteger(d, sign);
}
// Optimize base
if (base === BigInteger.base) {
return new BigInteger(digits.map(Number).reverse(), sign);
}
// Do the conversion
var d = BigInteger.ZERO;
base = BigInteger.small[base];
var small = BigInteger.small;
for (var i = 0; i < digits.length; i++) {
d = d.multiply(base).add(small[parseInt(digits[i], 36)]);
}
return new BigInteger(d._d, sign);
} else {
throw new Error("Invalid BigInteger format: " + s);
}
};
/*
Function: add
Add two <BigIntegers>.
Parameters:
n - The number to add to *this*. Will be converted to a <BigInteger>.
Returns:
The numbers added together.
See Also:
<subtract>, <multiply>, <quotient>, <next>
*/
BigInteger.prototype.add = function (n) {
if (this._s === 0) {
return BigInteger(n);
}
n = BigInteger(n);
if (n._s === 0) {
return this;
}
if (this._s !== n._s) {
n = n.negate();
return this.subtract(n);
}
var a = this._d;
var b = n._d;
var al = a.length;
var bl = b.length;
var sum = new Array(Math.max(al, bl) + 1);
var size = Math.min(al, bl);
var carry = 0;
var digit;
for (var i = 0; i < size; i++) {
digit = a[i] + b[i] + carry;
sum[i] = digit % BigInteger.base;
carry = (digit / BigInteger.base) | 0;
}
if (bl > al) {
a = b;
al = bl;
}
for (i = size; carry && i < al; i++) {
digit = a[i] + carry;
sum[i] = digit % BigInteger.base;
carry = (digit / BigInteger.base) | 0;
}
if (carry) {
sum[i] = carry;
}
for (; i < al; i++) {
sum[i] = a[i];
}
return new BigInteger(sum, this._s);
};
/*
Function: negate
Get the additive inverse of a <BigInteger>.
Returns:
A <BigInteger> with the same magnatude, but with the opposite sign.
See Also:
<abs>
*/
BigInteger.prototype.negate = function () {
return new BigInteger(this._d, -this._s);
};
/*
Function: abs
Get the absolute value of a <BigInteger>.
Returns:
A <BigInteger> with the same magnatude, but always positive (or zero).
See Also:
<negate>
*/
BigInteger.prototype.abs = function () {
return (this._s < 0) ? this.negate() : this;
};
/*
Function: subtract
Subtract two <BigIntegers>.
Parameters:
n - The number to subtract from *this*. Will be converted to a <BigInteger>.
Returns:
The *n* subtracted from *this*.
See Also:
<add>, <multiply>, <quotient>, <prev>
*/
BigInteger.prototype.subtract = function (n) {
if (this._s === 0) {
return BigInteger(n).negate();
}
n = BigInteger(n);
if (n._s === 0) {
return this;
}
if (this._s !== n._s) {
n = n.negate();
return this.add(n);
}
var m = this;
var t;
// negative - negative => -|a| - -|b| => -|a| + |b| => |b| - |a|
if (this._s < 0) {
t = m;
m = new BigInteger(n._d, 1);
n = new BigInteger(t._d, 1);
}
// Both are positive => a - b
var sign = m.compareAbs(n);
if (sign === 0) {
return BigInteger.ZERO;
} else if (sign < 0) {
// swap m and n
t = n;
n = m;
m = t;
}
// a > b
var a = m._d;
var b = n._d;
var al = a.length;
var bl = b.length;
var diff = new Array(al); // al >= bl since a > b
var borrow = 0;
var i;
var digit;
for (i = 0; i < bl; i++) {
digit = a[i] - borrow - b[i];
if (digit < 0) {
digit += BigInteger.base;
borrow = 1;
} else {
borrow = 0;
}
diff[i] = digit;
}
for (i = bl; i < al; i++) {
digit = a[i] - borrow;
if (digit < 0) {
digit += BigInteger.base;
} else {
diff[i++] = digit;
break;
}
diff[i] = digit;
}
for (; i < al; i++) {
diff[i] = a[i];
}
return new BigInteger(diff, sign);
};
(function () {
function addOne(n, sign) {
var a = n._d;
var sum = a.slice();
var carry = true;
var i = 0;
while (true) {
var digit = (a[i] || 0) + 1;
sum[i] = digit % BigInteger.base;
if (digit <= BigInteger.base - 1) {
break;
}++i;
}
return new BigInteger(sum, sign);
}
function subtractOne(n, sign) {
var a = n._d;
var sum = a.slice();
var borrow = true;
var i = 0;
while (true) {
var digit = (a[i] || 0) - 1;
if (digit < 0) {
sum[i] = digit + BigInteger.base;
} else {
sum[i] = digit;
break;
}++i;
}
return new BigInteger(sum, sign);
}
/*
Function: next
Get the next <BigInteger> (add one).
Returns:
*this* + 1.
See Also:
<add>, <prev>
*/
BigInteger.prototype.next = function () {
switch (this._s) {
case 0:
return BigInteger.ONE;
case -1:
return subtractOne(this, -1);
// case 1:
default:
return addOne(this, 1);
}
};
/*
Function: prev
Get the previous <BigInteger> (subtract one).
Returns:
*this* - 1.
See Also:
<next>, <subtract>
*/
BigInteger.prototype.prev = function () {
switch (this._s) {
case 0:
return BigInteger.M_ONE;
case -1:
return addOne(this, -1);
// case 1:
default:
return subtractOne(this, 1);
}
};
})();
/*
Function: compareAbs
Compare the absolute value of two <BigIntegers>.
Calling <compareAbs> is faster than calling <abs> twice, then <compare>.
Parameters:
n - The number to compare to *this*. Will be converted to a <BigInteger>.
Returns:
-1, 0, or +1 if *|this|* is less than, equal to, or greater than *|n|*.
See Also:
<compare>, <abs>
*/
BigInteger.prototype.compareAbs = function (n) {
if (this === n) {
return 0;
}
if (!(n instanceof BigInteger)) {
if (!isFinite(n)) {
return (isNaN(n) ? n : -1);
}
n = BigInteger(n);
}
if (this._s === 0) {
return (n._s !== 0) ? -1 : 0;
}
if (n._s === 0) {
return 1;
}
var l = this._d.length;
var nl = n._d.length;
if (l < nl) {
return -1;
} else if (l > nl) {
return 1;
}
var a = this._d;
var b = n._d;
for (var i = l - 1; i >= 0; i--) {
if (a[i] !== b[i]) {
return a[i] < b[i] ? -1 : 1;
}
}
return 0;
};
/*
Function: compare
Compare two <BigIntegers>.
Parameters:
n - The number to compare to *this*. Will be converted to a <BigInteger>.
Returns:
-1, 0, or +1 if *this* is less than, equal to, or greater than *n*.
See Also:
<compareAbs>, <isPositive>, <isNegative>, <isUnit>
*/
BigInteger.prototype.compare = function (n) {
if (this === n) {
return 0;
}
n = BigInteger(n);
if (this._s === 0) {
return -n._s;
}
if (this._s === n._s) { // both positive or both negative
var cmp = this.compareAbs(n);
return cmp * this._s;
} else {
return this._s;
}
};
/*
Function: isUnit
Return true iff *this* is either 1 or -1.
Returns:
true if *this* compares equal to <BigInteger.ONE> or <BigInteger.M_ONE>.
See Also:
<isZero>, <isNegative>, <isPositive>, <compareAbs>, <compare>,
<BigInteger.ONE>, <BigInteger.M_ONE>
*/
BigInteger.prototype.isUnit = function () {
return this === BigInteger.ONE || this === BigInteger.M_ONE || (this._d.length === 1 && this._d[0] === 1);
};
/*
Function: multiply
Multiply two <BigIntegers>.
Parameters:
n - The number to multiply *this* by. Will be converted to a
<BigInteger>.
Returns:
The numbers multiplied together.
See Also:
<add>, <subtract>, <quotient>, <square>
*/
BigInteger.prototype.multiply = function (n) {
// TODO: Consider adding Karatsuba multiplication for large numbers
if (this._s === 0) {
return BigInteger.ZERO;
}
n = BigInteger(n);
if (n._s === 0) {
return BigInteger.ZERO;
}
if (this.isUnit()) {
if (this._s < 0) {
return n.negate();
}
return n;
}
if (n.isUnit()) {
if (n._s < 0) {
return this.negate();
}
return this;
}
if (this === n) {
return this.square();
}
var r = (this._d.length >= n._d.length);
var a = (r ? this : n)._d; // a will be longer than b
var b = (r ? n : this)._d;
var al = a.length;
var bl = b.length;
var pl = al + bl;
var partial = new Array(pl);
var i;
for (i = 0; i < pl; i++) {
partial[i] = 0;
}
for (i = 0; i < bl; i++) {
var carry = 0;
var bi = b[i];
var jlimit = al + i;
var digit;
for (var j = i; j < jlimit; j++) {
digit = partial[j] + bi * a[j - i] + carry;
carry = (digit / BigInteger.base) | 0;
partial[j] = (digit % BigInteger.base) | 0;
}
if (carry) {
digit = partial[j] + carry;
carry = (digit / BigInteger.base) | 0;
partial[j] = digit % BigInteger.base;
}
}
return new BigInteger(partial, this._s * n._s);
};
// Multiply a BigInteger by a single-digit native number
// Assumes that this and n are >= 0
// This is not really intended to be used outside the library itself
BigInteger.prototype.multiplySingleDigit = function (n) {
if (n === 0 || this._s === 0) {
return BigInteger.ZERO;
}
if (n === 1) {
return this;
}
var digit;
if (this._d.length === 1) {
digit = this._d[0] * n;
if (digit >= BigInteger.base) {
return new BigInteger([(digit % BigInteger.base) | 0, (digit / BigInteger.base) | 0], 1);
}
return new BigInteger([digit], 1);
}
if (n === 2) {
return this.add(this);
}
if (this.isUnit()) {
return new BigInteger([n], 1);
}
var a = this._d;
var al = a.length;
var pl = al + 1;
var partial = new Array(pl);
for (var i = 0; i < pl; i++) {
partial[i] = 0;
}
var carry = 0;
for (var j = 0; j < al; j++) {
digit = n * a[j] + carry;
carry = (digit / BigInteger.base) | 0;
partial[j] = (digit % BigInteger.base) | 0;
}
if (carry) {
digit = carry;
carry = (digit / BigInteger.base) | 0;
partial[j] = digit % BigInteger.base;
}
return new BigInteger(partial, 1);
};
/*
Function: square
Multiply a <BigInteger> by itself.
This is slightly faster than regular multiplication, since it removes the
duplicated multiplcations.
Returns:
> this.multiply(this)
See Also:
<multiply>
*/
BigInteger.prototype.square = function () {
// Normally, squaring a 10-digit number would take 100 multiplications.
// Of these 10 are unique diagonals, of the remaining 90 (100-10), 45 are repeated.
// This procedure saves (N*(N-1))/2 multiplications, (e.g., 45 of 100 multiplies).
// Based on code by Gary Darby, Intellitech Systems Inc., www.DelphiForFun.org
if (this._s === 0) {
return BigInteger.ZERO;
}
if (this.isUnit()) {
return BigInteger.ONE;
}
var digits = this._d;
var length = digits.length;
var imult1 = new Array(length + length + 1);
var product, carry, k;
var i;
// Calculate diagonal
for (i = 0; i < length; i++) {
k = i * 2;
product = digits[i] * digits[i];
carry = (product / BigInteger.base) | 0;
imult1[k] = product % BigInteger.base;
imult1[k + 1] = carry;
}
// Calculate repeating part
for (i = 0; i < length; i++) {
carry = 0;
k = i * 2 + 1;
for (var j = i + 1; j < length; j++, k++) {
product = digits[j] * digits[i] * 2 + imult1[k] + carry;
carry = (product / BigInteger.base) | 0;
imult1[k] = product % BigInteger.base;
}
k = length + i;
var digit = carry + imult1[k];
carry = (digit / BigInteger.base) | 0;
imult1[k] = digit % BigInteger.base;
imult1[k + 1] += carry;
}
return new BigInteger(imult1, 1);
};
/*
Function: quotient
Divide two <BigIntegers> and truncate towards zero.
<quotient> throws an exception if *n* is zero.
Parameters:
n - The number to divide *this* by. Will be converted to a <BigInteger>.
Returns:
The *this* / *n*, truncated to an integer.
See Also:
<add>, <subtract>, <multiply>, <divRem>, <remainder>
*/
BigInteger.prototype.quotient = function (n) {
return this.divRem(n)[0];
};
/*
Function: divide
Deprecated synonym for <quotient>.
*/
BigInteger.prototype.divide = BigInteger.prototype.quotient;
/*
Function: remainder
Calculate the remainder of two <BigIntegers>.
<remainder> throws an exception if *n* is zero.
Parameters:
n - The remainder after *this* is divided *this* by *n*. Will be
converted to a <BigInteger>.
Returns:
*this* % *n*.
See Also:
<divRem>, <quotient>
*/
BigInteger.prototype.remainder = function (n) {
return this.divRem(n)[1];
};
/*
Function: divRem
Calculate the integer quotient and remainder of two <BigIntegers>.
<divRem> throws an exception if *n* is zero.
Parameters:
n - The number to divide *this* by. Will be converted to a <BigInteger>.
Returns:
A two-element array containing the quotient and the remainder.
> a.divRem(b)
is exactly equivalent to
> [a.quotient(b), a.remainder(b)]
except it is faster, because they are calculated at the same time.
See Also:
<quotient>, <remainder>
*/
BigInteger.prototype.divRem = function (n) {
n = BigInteger(n);
if (n._s === 0) {
throw new Error("Divide by zero");
}
if (this._s === 0) {
return [BigInteger.ZERO, BigInteger.ZERO];
}
if (n._d.length === 1) {
return this.divRemSmall(n._s * n._d[0]);
}
// Test for easy cases -- |n1| <= |n2|
switch (this.compareAbs(n)) {
case 0:
// n1 == n2
return [this._s === n._s ? BigInteger.ONE : BigInteger.M_ONE, BigInteger.ZERO];
case -1:
// |n1| < |n2|
return [BigInteger.ZERO, this];
}
var sign = this._s * n._s;
var a = n.abs();
var b_digits = this._d.slice();
var digits = n._d.length;
var max = b_digits.length;
var quot = [];
var guess;
var part = new BigInteger([], 1);
part._s = 1;
while (b_digits.length) {
part._d.unshift(b_digits.pop());
part = new BigInteger(part._d, 1);
if (part.compareAbs(n) < 0) {
quot.push(0);
continue;
}
if (part._s === 0) {
guess = 0;
} else {
var xlen = part._d.length,
ylen = a._d.length;
var highx = part._d[xlen - 1] * BigInteger.base + part._d[xlen - 2];
var highy = a._d[ylen - 1] * BigInteger.base + a._d[ylen - 2];
if (part._d.length > a._d.length) {
// The length of part._d can either match a._d length,
// or exceed it by one.
highx = (highx + 1) * BigInteger.base;
}
guess = Math.ceil(highx / highy);
}
do {
var check = a.multiplySingleDigit(guess);
if (check.compareAbs(part) <= 0) {
break;
}
guess--;
} while (guess);
quot.push(guess);
if (!guess) {
continue;
}
var diff = part.subtract(check);
part._d = diff._d.slice();
}
return [new BigInteger(quot.reverse(), sign), new BigInteger(part._d, this._s)];
};
// Throws an exception if n is outside of (-BigInteger.base, -1] or
// [1, BigInteger.base). It's not necessary to call this, since the
// other division functions will call it if they are able to.
BigInteger.prototype.divRemSmall = function (n) {
var r;
n = +n;
if (n === 0) {
throw new Error("Divide by zero");
}
var n_s = n < 0 ? -1 : 1;
var sign = this._s * n_s;
n = Math.abs(n);
if (n < 1 || n >= BigInteger.base) {
throw new Error("Argument out of range");
}
if (this._s === 0) {
return [BigInteger.ZERO, BigInteger.ZERO];
}
if (n === 1 || n === -1) {
return [(sign === 1) ? this.abs() : new BigInteger(this._d, sign), BigInteger.ZERO];
}
// 2 <= n < BigInteger.base
// divide a single digit by a single digit
if (this._d.length === 1) {
var q = new BigInteger([(this._d[0] / n) | 0], 1);
r = new BigInteger([(this._d[0] % n) | 0], 1);
if (sign < 0) {
q = q.negate();
}
if (this._s < 0) {
r = r.negate();
}
return [q, r];
}
var digits = this._d.slice();
var quot = new Array(digits.length);
var part = 0;
var diff = 0;
var i = 0;
var guess;
while (digits.length) {
part = part * BigInteger.base + digits[digits.length - 1];
if (part < n) {
quot[i++] = 0;
digits.pop();
diff = BigInteger.base * diff + part;
continue;
}
if (part === 0) {
guess = 0;
} else {
guess = (part / n) | 0;
}
var check = n * guess;
diff = part - check;
quot[i++] = guess;
if (!guess) {
digits.pop();
continue;
}
digits.pop();
part = diff;
}
r = new BigInteger([diff], 1);
if (this._s < 0) {
r = r.negate();
}
return [new BigInteger(quot.reverse(), sign), r];
};
/*
Function: isEven
Return true iff *this* is divisible by two.
Note that <BigInteger.ZERO> is even.
Returns:
true if *this* is even, false otherwise.
See Also:
<isOdd>
*/
BigInteger.prototype.isEven = function () {
var digits = this._d;
return this._s === 0 || digits.length === 0 || (digits[0] % 2) === 0;
};
/*
Function: isOdd
Return true iff *this* is not divisible by two.
Returns:
true if *this* is odd, false otherwise.
See Also:
<isEven>
*/
BigInteger.prototype.isOdd = function () {
return !this.isEven();
};
/*
Function: sign
Get the sign of a <BigInteger>.
Returns:
* -1 if *this* < 0
* 0 if *this* == 0
* +1 if *this* > 0
See Also:
<isZero>, <isPositive>, <isNegative>, <compare>, <BigInteger.ZERO>
*/
BigInteger.prototype.sign = function () {
return this._s;
};
/*
Function: isPositive
Return true iff *this* > 0.
Returns:
true if *this*.compare(<BigInteger.ZERO>) == 1.
See Also:
<sign>, <isZero>, <isNegative>, <isUnit>, <compare>, <BigInteger.ZERO>
*/
BigInteger.prototype.isPositive = function () {
return this._s > 0;
};
/*
Function: isNegative
Return true iff *this* < 0.
Returns:
true if *this*.compare(<BigInteger.ZERO>) == -1.
See Also:
<sign>, <isPositive>, <isZero>, <isUnit>, <compare>, <BigInteger.ZERO>
*/
BigInteger.prototype.isNegative = function () {
return this._s < 0;
};
/*
Function: isZero
Return true iff *this* == 0.
Returns:
true if *this*.compare(<BigInteger.ZERO>) == 0.
See Also:
<sign>, <isPositive>, <isNegative>, <isUnit>, <BigInteger.ZERO>
*/
BigInteger.prototype.isZero = function () {
return this._s === 0;
};
/*
Function: exp10
Multiply a <BigInteger> by a power of 10.
This is equivalent to, but faster than
> if (n >= 0) {
> return this.multiply(BigInteger("1e" + n));
> }
> else { // n <= 0
> return this.quotient(BigInteger("1e" + -n));
> }
Parameters:
n - The power of 10 to multiply *this* by. *n* is converted to a
javascipt number and must be no greater than <BigInteger.MAX_EXP>
(0x7FFFFFFF), or an exception will be thrown.
Returns:
*this* * (10 ** *n*), truncated to an integer if necessary.
See Also:
<pow>, <multiply>
*/
BigInteger.prototype.exp10 = function (n) {
n = +n;
if (n === 0) {
return this;
}
if (Math.abs(n) > Number(BigInteger.MAX_EXP)) {
throw new Error("exponent too large in BigInteger.exp10");
}
if (n > 0) {
var k = new BigInteger(this._d.slice(), this._s);
for (; n >= BigInteger.base_log10; n -= BigInteger.base_log10) {
k._d.unshift(0);
}
if (n == 0) return k;
k._s = 1;
k = k.multiplySingleDigit(Math.pow(10, n));
return (this._s < 0 ? k.negate() : k);
} else if (-n >= this._d.length * BigInteger.base_log10) {
return BigInteger.ZERO;
} else {
var k = new BigInteger(this._d.slice(), this._s);
for (n = -n; n >= BigInteger.base_log10; n -= BigInteger.base_log10) {
k._d.shift();
}
return (n == 0) ? k : k.divRemSmall(Math.pow(10, n))[0];
}
};
/*
Function: pow
Raise a <BigInteger> to a power.
In this implementation, 0**0 is 1.
Parameters:
n - The exponent to raise *this* by. *n* must be no greater than
<BigInteger.MAX_EXP> (0x7FFFFFFF), or an exception will be thrown.
Returns:
*this* raised to the *nth* power.
See Also:
<modPow>
*/
BigInteger.prototype.pow = function (n) {
if (this.isUnit()) {
if (this._s > 0) {
return this;
} else {
return BigInteger(n).isOdd() ? this : this.negate();
}
}
n = BigInteger(n);
if (n._s === 0) {
return BigInteger.ONE;
} else if (n._s < 0) {
if (this._s === 0) {
throw new Error("Divide by zero");
} else {
return BigInteger.ZERO;
}
}
if (this._s === 0) {
return BigInteger.ZERO;
}
if (n.isUnit()) {
return this;
}
if (n.compareAbs(BigInteger.MAX_EXP) > 0) {
throw new Error("exponent too large in BigInteger.pow");
}
var x = this;
var aux = BigInteger.ONE;
var two = BigInteger.small[2];
while (n.isPositive()) {
if (n.isOdd()) {
aux = aux.multiply(x);
if (n.isUnit()) {
return aux;
}
}
x = x.square();
n = n.quotient(two);
}
return aux;
};
/*
Function: modPow
Raise a <BigInteger> to a power (mod m).
Because it is reduced by a modulus, <modPow> is not limited by
<BigInteger.MAX_EXP> like <pow>.
Parameters:
exponent - The exponent to raise *this* by. Must be positive.
modulus - The modulus.
Returns:
*this* ^ *exponent* (mod *modulus*).
See Also:
<pow>, <mod>
*/
BigInteger.prototype.modPow = function (exponent, modulus) {
var result = BigInteger.ONE;
var base = this;
while (exponent.isPositive()) {
if (exponent.isOdd()) {
result = result.multiply(base).remainder(modulus);
}
exponent = exponent.quotient(BigInteger.small[2]);
if (exponent.isPositive()) {
base = base.square().remainder(modulus);
}
}
return result;
};
/*
Function: log
Get the natural logarithm of a <BigInteger> as a native JavaScript number.
This is equivalent to
> Math.log(this.toJSValue())
but handles values outside of the native number range.
Returns:
log( *this* )
See Also:
<toJSValue>
*/
BigInteger.prototype.log = function () {
switch (this._s) {
case 0:
return -Infinity;
case -1:
return NaN;
default:
// Fall through.
}
var l = this._d.length;
if (l * BigInteger.base_log10 < 30) {
return Math.log(this.valueOf());
}
var N = Math.ceil(30 / BigInteger.base_log10);
var firstNdigits = this._d.slice(l - N);
return Math.log((new BigInteger(firstNdigits, 1)).valueOf()) + (l - N) * Math.log(BigInteger.base);
};
/*
Function: valueOf
Convert a <BigInteger> to a native JavaScript integer.
This is called automatically by JavaScipt to convert a <BigInteger> to a
native value.
Returns:
> parseInt(this.toString(), 10)
See Also:
<toString>, <toJSValue>
*/
BigInteger.prototype.valueOf = function () {
return parseInt(this.toString(), 10);
};
/*
Function: toJSValue
Convert a <BigInteger> to a native JavaScript integer.
This is the same as valueOf, but more explicitly named.
Returns:
> parseInt(this.toString(), 10)
See Also:
<toString>, <valueOf>
*/
BigInteger.prototype.toJSValue = function () {
return parseInt(this.toString(), 10);
};
// Constant: MAX_EXP
// The largest exponent allowed in <pow> and <exp10> (0x7FFFFFFF or 2147483647).
BigInteger.MAX_EXP = BigInteger(0x7FFFFFFF);
(function () {
function makeUnary(fn) {
return function (a) {
return fn.call(BigInteger(a));
};
}
function makeBinary(fn) {
return function (a, b) {
return fn.call(BigInteger(a), BigInteger(b));
};
}
function makeTrinary(fn) {
return function (a, b, c) {
return fn.call(BigInteger(a), BigInteger(b), BigInteger(c));
};
}
(function () {
var i, fn;
var unary = "toJSValue,isEven,isOdd,sign,isZero,isNegative,abs,isUnit,square,negate,isPositive,toString,next,prev,log".split(",");
var binary = "compare,remainder,divRem,subtract,add,quotient,divide,multiply,pow,compareAbs".split(",");
var trinary = ["modPow"];
for (i = 0; i < unary.length; i++) {
fn = unary[i];
BigInteger[fn] = makeUnary(BigInteger.prototype[fn]);
}
for (i = 0; i < binary.length; i++) {
fn = binary[i];
BigInteger[fn] = makeBinary(BigInteger.prototype[fn]);
}
for (i = 0; i < trinary.length; i++) {
fn = trinary[i];
BigInteger[fn] = makeTrinary(BigInteger.prototype[fn]);
}
BigInteger.exp10 = function (x, n) {
return BigInteger(x).exp10(n);
};
})();
})();
if (typeof exports !== 'undefined') {
exports.BigInteger = BigInteger;
}
Perfection as a goal is a nice idea that can point one in a specific direction. However, since "perfection" is an ever changing (evolving?) and moving target, one must admit that perfection can never be obtained...
When in doubt, check the d4mn source code!
-
20 Apr 2012 8:32 AM #2Sencha - Support Team
- Join Date
- Jul 2010
- Location
- Houston, Tx
- Posts
- 7,185
- Vote Rating
- 194
I have provided the suggestion to development. Since this is specialty item, I am not sure it will pass .. but you never know
Regards,
Scott.
Thank you for reporting this bug. We will make it our priority to review this report.
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