PK jL*:Ԕ README.mdnu W+A
# big.js #
A small, fast JavaScript library for arbitrary-precision decimal arithmetic.
The little sister to [bignumber.js](https://github.com/MikeMcl/bignumber.js/).
See also [decimal.js](https://github.com/MikeMcl/decimal.js/), and [here](https://github.com/MikeMcl/big.js/wiki) for the difference between them.
## Features
- Faster, smaller and easier-to-use than JavaScript versions of Java's BigDecimal
- Only 5.9 KB minified and 2.7 KB gzipped
- Simple API
- Replicates the `toExponential`, `toFixed` and `toPrecision` methods of JavaScript's Number type
- Includes a `sqrt` method
- Stores values in an accessible decimal floating point format
- No dependencies
- Comprehensive [documentation](http://mikemcl.github.io/big.js/) and test set
## Load
The library is the single JavaScript file *big.js* (or *big.min.js*, which is *big.js* minified).
It can be loaded via a script tag in an HTML document for the browser
or as a CommonJS, [Node.js](http://nodejs.org) or AMD module using `require`.
var Big = require('big.js');
For Node.js, the library is available from the npm registry:
$ npm install big.js
## Use
*In all examples below, `var`, semicolons and `toString` calls are not shown.
If a commented-out value is in quotes it means `toString` has been called on the preceding expression.*
The library exports a single function: Big, the constructor of Big number instances.
It accepts a value of type Number, String or Big number Object.
x = new Big(123.4567)
y = Big('123456.7e-3') // 'new' is optional
z = new Big(x)
x.eq(y) && x.eq(z) && y.eq(z) // true
A Big number is immutable in the sense that it is not changed by its methods.
0.3 - 0.1 // 0.19999999999999998
x = new Big(0.3)
x.minus(0.1) // "0.2"
x // "0.3"
The methods that return a Big number can be chained.
x.div(y).plus(z).times(9).minus('1.234567801234567e+8').plus(976.54321).div('2598.11772')
x.sqrt().div(y).pow(3).gt(y.mod(z)) // true
Like JavaScript's Number type, there are `toExponential`, `toFixed` and `toPrecision` methods.
x = new Big(255.5)
x.toExponential(5) // "2.55500e+2"
x.toFixed(5) // "255.50000"
x.toPrecision(5) // "255.50"
The maximum number of decimal places and the rounding mode used to round the results of the `div`, `sqrt` and `pow`
(with negative exponent) methods is determined by the value of the `DP` and `RM` properties of the `Big` number constructor.
The other methods always give the exact result.
(From *v3.0.0*, multiple Big number constructors can be created, see Change Log below.)
Big.DP = 10
Big.RM = 1
x = new Big(2);
y = new Big(3);
z = x.div(y) // "0.6666666667"
z.sqrt() // "0.8164965809"
z.pow(-3) // "3.3749999995"
z.times(z) // "0.44444444448888888889"
z.times(z).round(10) // "0.4444444445"
The value of a Big number is stored in a decimal floating point format in terms of a coefficient, exponent and sign.
x = new Big(-123.456);
x.c // [1,2,3,4,5,6] coefficient (i.e. significand)
x.e // 2 exponent
x.s // -1 sign
For further information see the [API](http://mikemcl.github.io/big.js/) reference from the *doc* folder.
## Test
The *test* directory contains the test scripts for each Big number method.
The tests can be run with Node or a browser.
To test a single method, from a command-line shell at the *test* directory, use e.g.
$ node toFixed
To test all the methods
$ node every-test
For the browser, see *single-test.html* and *every-test.html* in the *test/browser* directory.
*big-vs-number.html* enables some of the methods of big.js to be compared with those of JavaScript's Number type.
## Performance
The *perf* directory contains two applications and a *lib* directory containing the BigDecimal libraries used by both.
*big-vs-bigdecimal.html* tests the performance of big.js against the JavaScript translations of two versions of BigDecimal, its use should be more or less self-explanatory.
(The GWT version doesn't work in IE 6.)
* GWT: java.math.BigDecimal
* ICU4J: com.ibm.icu.math.BigDecimal
The BigDecimal in Node's npm registry is the GWT version. Despite its seeming popularity I have found it to have some serious bugs, see the Node script *perf/lib/bigdecimal_GWT/bugs.js* for examples of flaws in its *remainder*, *divide* and *compareTo* methods.
*bigtime.js* is a Node command-line application which tests the performance of big.js against the GWT version of
BigDecimal from the npm registry.
For example, to compare the time taken by the big.js `plus` method and the BigDecimal `add` method:
$ node bigtime plus 10000 40
This will time 10000 calls to each, using operands of up to 40 random digits and will check that the results match.
For help:
$ node bigtime -h
## Build
I.e. minify.
For Node, if uglify-js is installed globally ( `npm install uglify-js -g` ) then
uglifyjs -o ./big.min.js ./big.js
will create *big.min.js*.
## TypeScript
The [DefinitelyTyped](https://github.com/borisyankov/DefinitelyTyped) project has a TypeScript [definitions file](https://github.com/borisyankov/DefinitelyTyped/blob/master/big.js/big.js.d.ts) for big.js.
The definitions file can be added to your project via the [big.js.TypeScript.DefinitelyTyped](https://www.nuget.org/packages/big.js.TypeScript.DefinitelyTyped/0.0.1) NuGet package or via [tsd](http://definitelytyped.org/tsd/).
tsd query big.js --action install
Any questions about the TypeScript definitions file should be addressed to the DefinitelyTyped project.
## Feedback
Feedback is welcome.
Bugs/comments/questions?
Open an issue, or email
Michael
M8ch88l@gmail.com
## Licence
See LICENCE.
## Change Log
####5.0.0
* 13/10/17
* Return `-0` from `valueOf` for negative zero.
* Refactor the methods which return a string.
* Amend error messaging.
* Update API document and change its colour scheme.
* Add `Big.version`.
* Remove bitcoin address.
####4.0.2
* 28/09/17
* Add *big.mjs* for use with Node.js with `--experimental-modules` flag.
####4.0.0
* 27/09/17
* Rename `Big.E_POS` to `Big.PE`, `Big.E_NEG` to `Big.NE`.
* Refactor error messaging.
* Throw if `null` is passed to `toFixed` etc.
####3.2.0
* 14/09/17 Aid ES6 import.
####3.1.3
* Minor documentation updates.
####3.1.2
* README typo.
####3.1.1
* API documentation update, including FAQ additions.
####3.1.0
* Renamed and exposed `TO_EXP_NEG` and `TO_EXP_POS` as `Big.E_NEG` and `Big.E_POS`.
####3.0.2
* Remove *.npmignore*, use `files` field in *package.json* instead.
####3.0.1
* Added `sub`, `add` and `mul` aliases.
* Clean-up after lint.
####3.0.0
* 10/12/14 Added [multiple constructor functionality](http://mikemcl.github.io/big.js/#faq).
* No breaking changes or other additions, but a major code reorganisation, so *v3* seemed appropiate.
####2.5.2
* 1/11/14 Added bower.json.
####2.5.1
* 8/06/14 Amend README requires.
####2.5.0
* 26/01/14 Added `toJSON` method so serialization uses `toString`.
####2.4.1
* 17/10/13 Conform signed zero to IEEEE 754 (2008).
####2.4.0
* 19/09/13 Throw instances of `Error`.
####2.3.0
* 16/09/13 Added `cmp` method.
####2.2.0
* 11/07/13 Added 'round up' mode.
####2.1.0
* 26/06/13 Allow e.g. `.1` and `2.`.
####2.0.0
* 12/05/13 Added `abs` method and replaced `cmp` with `eq`, `gt`, `gte`, `lt`, and `lte` methods.
####1.0.1
* Changed default value of MAX_DP to 1E6
####1.0.0
* 7/11/2012 Initial release
PK jLn(pX X LICENCEnu W+A The MIT Licence (Expat).
Copyright (c) 2017 Michael Mclaughlin
Permission is hereby granted, free of charge, to any person obtaining
a copy of this software and associated documentation files (the
'Software'), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:
The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
PK jLY Y big.jsnu W+A /*
* big.js v5.0.0
* A small, fast, easy-to-use library for arbitrary-precision decimal arithmetic.
* Copyright (c) 2017 Michael Mclaughlin
* https://github.com/MikeMcl/big.js/LICENCE
*/
;(function (GLOBAL) {
'use strict';
var Big,
/************************************** EDITABLE DEFAULTS *****************************************/
// The default values below must be integers within the stated ranges.
/*
* The maximum number of decimal places (DP) of the results of operations involving division:
* div and sqrt, and pow with negative exponents.
*/
DP = 20, // 0 to MAX_DP
/*
* The rounding mode (RM) used when rounding to the above decimal places.
*
* 0 Towards zero (i.e. truncate, no rounding). (ROUND_DOWN)
* 1 To nearest neighbour. If equidistant, round up. (ROUND_HALF_UP)
* 2 To nearest neighbour. If equidistant, to even. (ROUND_HALF_EVEN)
* 3 Away from zero. (ROUND_UP)
*/
RM = 1, // 0, 1, 2 or 3
// The maximum value of DP and Big.DP.
MAX_DP = 1E6, // 0 to 1000000
// The maximum magnitude of the exponent argument to the pow method.
MAX_POWER = 1E6, // 1 to 1000000
/*
* The negative exponent (NE) at and beneath which toString returns exponential notation.
* (JavaScript numbers: -7)
* -1000000 is the minimum recommended exponent value of a Big.
*/
NE = -7, // 0 to -1000000
/*
* The positive exponent (PE) at and above which toString returns exponential notation.
* (JavaScript numbers: 21)
* 1000000 is the maximum recommended exponent value of a Big.
* (This limit is not enforced or checked.)
*/
PE = 21, // 0 to 1000000
/**************************************************************************************************/
// Error messages.
NAME = '[big.js] ',
INVALID = NAME + 'Invalid ',
INVALID_DP = INVALID + 'decimal places',
DIV_BY_ZERO = NAME + 'Division by zero',
// The shared prototype object.
P = {},
UNDEFINED = void 0,
NUMERIC = /^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i;
/*
* Create and return a Big constructor.
*
*/
function factory() {
/*
* The Big constructor and exported function.
* Create and return a new instance of a Big number object.
*
* n {number|string|Big} A numeric value.
*/
function Big(n) {
var x = this;
// Enable constructor usage without new.
if (!(x instanceof Big)) return n === UNDEFINED ? factory() : new Big(n);
// Duplicate.
if (n instanceof Big) {
x.s = n.s;
x.e = n.e;
x.c = n.c.slice();
} else {
parse(x, n);
}
/*
* Retain a reference to this Big constructor, and shadow Big.prototype.constructor which
* points to Object.
*/
x.constructor = Big;
}
Big.prototype = P;
Big.DP = DP;
Big.RM = RM;
Big.NE = NE;
Big.PE = PE;
Big.version = '4.0.2';
return Big;
}
/*
* Parse the number or string value passed to a Big constructor.
*
* x {Big} A Big number instance.
* n {number|string} A numeric value.
*/
function parse(x, n) {
var e, i, nl;
// Minus zero?
if (n === 0 && 1 / n < 0) n = '-0';
else if (!NUMERIC.test(n += '')) throw Error(INVALID + 'number');
// Determine sign.
x.s = n.charAt(0) == '-' ? (n = n.slice(1), -1) : 1;
// Decimal point?
if ((e = n.indexOf('.')) > -1) n = n.replace('.', '');
// Exponential form?
if ((i = n.search(/e/i)) > 0) {
// Determine exponent.
if (e < 0) e = i;
e += +n.slice(i + 1);
n = n.substring(0, i);
} else if (e < 0) {
// Integer.
e = n.length;
}
nl = n.length;
// Determine leading zeros.
for (i = 0; i < nl && n.charAt(i) == '0';) ++i;
if (i == nl) {
// Zero.
x.c = [x.e = 0];
} else {
// Determine trailing zeros.
for (; nl > 0 && n.charAt(--nl) == '0';);
x.e = e - i - 1;
x.c = [];
// Convert string to array of digits without leading/trailing zeros.
for (e = 0; i <= nl;) x.c[e++] = +n.charAt(i++);
}
return x;
}
/*
* Round Big x to a maximum of dp decimal places using rounding mode rm.
* Called by stringify, P.div, P.round and P.sqrt.
*
* x {Big} The Big to round.
* dp {number} Integer, 0 to MAX_DP inclusive.
* rm {number} 0, 1, 2 or 3 (DOWN, HALF_UP, HALF_EVEN, UP)
* [more] {boolean} Whether the result of division was truncated.
*/
function round(x, dp, rm, more) {
var xc = x.c,
i = x.e + dp + 1;
if (rm === 1) {
// xc[i] is the digit after the digit that may be rounded up.
more = xc[i] >= 5;
} else if (rm === 2) {
more = xc[i] > 5 || xc[i] == 5 && (more || i < 0 || xc[i + 1] !== UNDEFINED || xc[i - 1] & 1);
} else if (rm === 3) {
more = more || xc[i] !== UNDEFINED || i < 0;
} else {
more = false;
if (rm !== 0) throw Error(INVALID + 'rounding mode');
}
if (i < 1 || !xc[0]) {
xc.length = 1;
if (more) {
// 1, 0.1, 0.01, 0.001, 0.0001 etc.
x.e = -dp;
xc[0] = 1;
} else {
// Zero.
xc[0] = x.e = 0;
}
} else {
// Remove any digits after the required decimal places.
xc.length = i--;
// Round up?
if (more) {
// Rounding up may mean the previous digit has to be rounded up.
for (; ++xc[i] > 9;) {
xc[i] = 0;
if (!i--) {
++x.e;
xc.unshift(1);
}
}
}
// Remove trailing zeros.
for (i = xc.length; !xc[--i];) xc.pop();
}
return x;
}
/*
* Return a string representing the value of Big x in normal or exponential notation.
* Handles P.toExponential, P.toFixed, P.toJSON, P.toPrecision, P.toString and P.valueOf.
*
* x {Big}
* id? {number} Caller id.
* 1 toExponential
* 2 toFixed
* 3 toPrecision
* 4 valueOf
* n? {number|undefined} Caller's argument.
* k? {number|undefined}
*/
function stringify(x, id, n, k) {
var e, s,
Big = x.constructor,
z = !x.c[0];
if (n !== UNDEFINED) {
if (n !== ~~n || n < (id == 3) || n > MAX_DP) {
throw Error(id == 3 ? INVALID + 'precision' : INVALID_DP);
}
x = new Big(x);
// The index of the digit that may be rounded up.
n = k - x.e;
// Round?
if (x.c.length > ++k) round(x, n, Big.RM);
// toFixed: recalculate k as x.e may have changed if value rounded up.
if (id == 2) k = x.e + n + 1;
// Append zeros?
for (; x.c.length < k;) x.c.push(0);
}
e = x.e;
s = x.c.join('');
n = s.length;
// Exponential notation?
if (id != 2 && (id == 1 || id == 3 && k <= e || e <= Big.NE || e >= Big.PE)) {
s = s.charAt(0) + (n > 1 ? '.' + s.slice(1) : '') + (e < 0 ? 'e' : 'e+') + e;
// Normal notation.
} else if (e < 0) {
for (; ++e;) s = '0' + s;
s = '0.' + s;
} else if (e > 0) {
if (++e > n) for (e -= n; e--;) s += '0';
else if (e < n) s = s.slice(0, e) + '.' + s.slice(e);
} else if (n > 1) {
s = s.charAt(0) + '.' + s.slice(1);
}
return x.s < 0 && (!z || id == 4) ? '-' + s : s;
}
// Prototype/instance methods
/*
* Return a new Big whose value is the absolute value of this Big.
*/
P.abs = function () {
var x = new this.constructor(this);
x.s = 1;
return x;
};
/*
* Return 1 if the value of this Big is greater than the value of Big y,
* -1 if the value of this Big is less than the value of Big y, or
* 0 if they have the same value.
*/
P.cmp = function (y) {
var isneg,
x = this,
xc = x.c,
yc = (y = new x.constructor(y)).c,
i = x.s,
j = y.s,
k = x.e,
l = y.e;
// Either zero?
if (!xc[0] || !yc[0]) return !xc[0] ? !yc[0] ? 0 : -j : i;
// Signs differ?
if (i != j) return i;
isneg = i < 0;
// Compare exponents.
if (k != l) return k > l ^ isneg ? 1 : -1;
j = (k = xc.length) < (l = yc.length) ? k : l;
// Compare digit by digit.
for (i = -1; ++i < j;) {
if (xc[i] != yc[i]) return xc[i] > yc[i] ^ isneg ? 1 : -1;
}
// Compare lengths.
return k == l ? 0 : k > l ^ isneg ? 1 : -1;
};
/*
* Return a new Big whose value is the value of this Big divided by the value of Big y, rounded,
* if necessary, to a maximum of Big.DP decimal places using rounding mode Big.RM.
*/
P.div = function (y) {
var x = this,
Big = x.constructor,
a = x.c, // dividend
b = (y = new Big(y)).c, // divisor
k = x.s == y.s ? 1 : -1,
dp = Big.DP;
if (dp !== ~~dp || dp < 0 || dp > MAX_DP) throw Error(INVALID_DP);
// Divisor is zero?
if (!b[0]) throw Error(DIV_BY_ZERO);
// Dividend is 0? Return +-0.
if (!a[0]) return new Big(k * 0);
var bl, bt, n, cmp, ri,
bz = b.slice(),
ai = bl = b.length,
al = a.length,
r = a.slice(0, bl), // remainder
rl = r.length,
q = y, // quotient
qc = q.c = [],
qi = 0,
d = dp + (q.e = x.e - y.e) + 1; // number of digits of the result
q.s = k;
k = d < 0 ? 0 : d;
// Create version of divisor with leading zero.
bz.unshift(0);
// Add zeros to make remainder as long as divisor.
for (; rl++ < bl;) r.push(0);
do {
// n is how many times the divisor goes into current remainder.
for (n = 0; n < 10; n++) {
// Compare divisor and remainder.
if (bl != (rl = r.length)) {
cmp = bl > rl ? 1 : -1;
} else {
for (ri = -1, cmp = 0; ++ri < bl;) {
if (b[ri] != r[ri]) {
cmp = b[ri] > r[ri] ? 1 : -1;
break;
}
}
}
// If divisor < remainder, subtract divisor from remainder.
if (cmp < 0) {
// Remainder can't be more than 1 digit longer than divisor.
// Equalise lengths using divisor with extra leading zero?
for (bt = rl == bl ? b : bz; rl;) {
if (r[--rl] < bt[rl]) {
ri = rl;
for (; ri && !r[--ri];) r[ri] = 9;
--r[ri];
r[rl] += 10;
}
r[rl] -= bt[rl];
}
for (; !r[0];) r.shift();
} else {
break;
}
}
// Add the digit n to the result array.
qc[qi++] = cmp ? n : ++n;
// Update the remainder.
if (r[0] && cmp) r[rl] = a[ai] || 0;
else r = [a[ai]];
} while ((ai++ < al || r[0] !== UNDEFINED) && k--);
// Leading zero? Do not remove if result is simply zero (qi == 1).
if (!qc[0] && qi != 1) {
// There can't be more than one zero.
qc.shift();
q.e--;
}
// Round?
if (qi > d) round(q, dp, Big.RM, r[0] !== UNDEFINED);
return q;
};
/*
* Return true if the value of this Big is equal to the value of Big y, otherwise return false.
*/
P.eq = function (y) {
return !this.cmp(y);
};
/*
* Return true if the value of this Big is greater than the value of Big y, otherwise return
* false.
*/
P.gt = function (y) {
return this.cmp(y) > 0;
};
/*
* Return true if the value of this Big is greater than or equal to the value of Big y, otherwise
* return false.
*/
P.gte = function (y) {
return this.cmp(y) > -1;
};
/*
* Return true if the value of this Big is less than the value of Big y, otherwise return false.
*/
P.lt = function (y) {
return this.cmp(y) < 0;
};
/*
* Return true if the value of this Big is less than or equal to the value of Big y, otherwise
* return false.
*/
P.lte = function (y) {
return this.cmp(y) < 1;
};
/*
* Return a new Big whose value is the value of this Big minus the value of Big y.
*/
P.minus = P.sub = function (y) {
var i, j, t, xlty,
x = this,
Big = x.constructor,
a = x.s,
b = (y = new Big(y)).s;
// Signs differ?
if (a != b) {
y.s = -b;
return x.plus(y);
}
var xc = x.c.slice(),
xe = x.e,
yc = y.c,
ye = y.e;
// Either zero?
if (!xc[0] || !yc[0]) {
// y is non-zero? x is non-zero? Or both are zero.
return yc[0] ? (y.s = -b, y) : new Big(xc[0] ? x : 0);
}
// Determine which is the bigger number. Prepend zeros to equalise exponents.
if (a = xe - ye) {
if (xlty = a < 0) {
a = -a;
t = xc;
} else {
ye = xe;
t = yc;
}
t.reverse();
for (b = a; b--;) t.push(0);
t.reverse();
} else {
// Exponents equal. Check digit by digit.
j = ((xlty = xc.length < yc.length) ? xc : yc).length;
for (a = b = 0; b < j; b++) {
if (xc[b] != yc[b]) {
xlty = xc[b] < yc[b];
break;
}
}
}
// x < y? Point xc to the array of the bigger number.
if (xlty) {
t = xc;
xc = yc;
yc = t;
y.s = -y.s;
}
/*
* Append zeros to xc if shorter. No need to add zeros to yc if shorter as subtraction only
* needs to start at yc.length.
*/
if ((b = (j = yc.length) - (i = xc.length)) > 0) for (; b--;) xc[i++] = 0;
// Subtract yc from xc.
for (b = i; j > a;) {
if (xc[--j] < yc[j]) {
for (i = j; i && !xc[--i];) xc[i] = 9;
--xc[i];
xc[j] += 10;
}
xc[j] -= yc[j];
}
// Remove trailing zeros.
for (; xc[--b] === 0;) xc.pop();
// Remove leading zeros and adjust exponent accordingly.
for (; xc[0] === 0;) {
xc.shift();
--ye;
}
if (!xc[0]) {
// n - n = +0
y.s = 1;
// Result must be zero.
xc = [ye = 0];
}
y.c = xc;
y.e = ye;
return y;
};
/*
* Return a new Big whose value is the value of this Big modulo the value of Big y.
*/
P.mod = function (y) {
var ygtx,
x = this,
Big = x.constructor,
a = x.s,
b = (y = new Big(y)).s;
if (!y.c[0]) throw Error(DIV_BY_ZERO);
x.s = y.s = 1;
ygtx = y.cmp(x) == 1;
x.s = a;
y.s = b;
if (ygtx) return new Big(x);
a = Big.DP;
b = Big.RM;
Big.DP = Big.RM = 0;
x = x.div(y);
Big.DP = a;
Big.RM = b;
return this.minus(x.times(y));
};
/*
* Return a new Big whose value is the value of this Big plus the value of Big y.
*/
P.plus = P.add = function (y) {
var t,
x = this,
Big = x.constructor,
a = x.s,
b = (y = new Big(y)).s;
// Signs differ?
if (a != b) {
y.s = -b;
return x.minus(y);
}
var xe = x.e,
xc = x.c,
ye = y.e,
yc = y.c;
// Either zero? y is non-zero? x is non-zero? Or both are zero.
if (!xc[0] || !yc[0]) return yc[0] ? y : new Big(xc[0] ? x : a * 0);
xc = xc.slice();
// Prepend zeros to equalise exponents.
// Note: Faster to use reverse then do unshifts.
if (a = xe - ye) {
if (a > 0) {
ye = xe;
t = yc;
} else {
a = -a;
t = xc;
}
t.reverse();
for (; a--;) t.push(0);
t.reverse();
}
// Point xc to the longer array.
if (xc.length - yc.length < 0) {
t = yc;
yc = xc;
xc = t;
}
a = yc.length;
// Only start adding at yc.length - 1 as the further digits of xc can be left as they are.
for (b = 0; a; xc[a] %= 10) b = (xc[--a] = xc[a] + yc[a] + b) / 10 | 0;
// No need to check for zero, as +x + +y != 0 && -x + -y != 0
if (b) {
xc.unshift(b);
++ye;
}
// Remove trailing zeros.
for (a = xc.length; xc[--a] === 0;) xc.pop();
y.c = xc;
y.e = ye;
return y;
};
/*
* Return a Big whose value is the value of this Big raised to the power n.
* If n is negative, round to a maximum of Big.DP decimal places using rounding
* mode Big.RM.
*
* n {number} Integer, -MAX_POWER to MAX_POWER inclusive.
*/
P.pow = function (n) {
var x = this,
one = new x.constructor(1),
y = one,
isneg = n < 0;
if (n !== ~~n || n < -MAX_POWER || n > MAX_POWER) throw Error(INVALID + 'exponent');
if (isneg) n = -n;
for (;;) {
if (n & 1) y = y.times(x);
n >>= 1;
if (!n) break;
x = x.times(x);
}
return isneg ? one.div(y) : y;
};
/*
* Return a new Big whose value is the value of this Big rounded to a maximum of dp decimal
* places using rounding mode rm.
* If dp is not specified, round to 0 decimal places.
* If rm is not specified, use Big.RM.
*
* dp? {number} Integer, 0 to MAX_DP inclusive.
* rm? 0, 1, 2 or 3 (ROUND_DOWN, ROUND_HALF_UP, ROUND_HALF_EVEN, ROUND_UP)
*/
P.round = function (dp, rm) {
var Big = this.constructor;
if (dp === UNDEFINED) dp = 0;
else if (dp !== ~~dp || dp < 0 || dp > MAX_DP) throw Error(INVALID_DP);
return round(new Big(this), dp, rm === UNDEFINED ? Big.RM : rm);
};
/*
* Return a new Big whose value is the square root of the value of this Big, rounded, if
* necessary, to a maximum of Big.DP decimal places using rounding mode Big.RM.
*/
P.sqrt = function () {
var r, c, t,
x = this,
Big = x.constructor,
s = x.s,
e = x.e,
half = new Big(0.5);
// Zero?
if (!x.c[0]) return new Big(x);
// Negative?
if (s < 0) throw Error(NAME + 'No square root');
// Estimate.
s = Math.sqrt(x.toString());
// Math.sqrt underflow/overflow?
// Re-estimate: pass x to Math.sqrt as integer, then adjust the result exponent.
if (s === 0 || s === 1 / 0) {
c = x.c.join('');
if (!(c.length + e & 1)) c += '0';
r = new Big(Math.sqrt(c).toString());
r.e = ((e + 1) / 2 | 0) - (e < 0 || e & 1);
} else {
r = new Big(s.toString());
}
e = r.e + (Big.DP += 4);
// Newton-Raphson iteration.
do {
t = r;
r = half.times(t.plus(x.div(t)));
} while (t.c.slice(0, e).join('') !== r.c.slice(0, e).join(''));
return round(r, Big.DP -= 4, Big.RM);
};
/*
* Return a new Big whose value is the value of this Big times the value of Big y.
*/
P.times = P.mul = function (y) {
var c,
x = this,
Big = x.constructor,
xc = x.c,
yc = (y = new Big(y)).c,
a = xc.length,
b = yc.length,
i = x.e,
j = y.e;
// Determine sign of result.
y.s = x.s == y.s ? 1 : -1;
// Return signed 0 if either 0.
if (!xc[0] || !yc[0]) return new Big(y.s * 0);
// Initialise exponent of result as x.e + y.e.
y.e = i + j;
// If array xc has fewer digits than yc, swap xc and yc, and lengths.
if (a < b) {
c = xc;
xc = yc;
yc = c;
j = a;
a = b;
b = j;
}
// Initialise coefficient array of result with zeros.
for (c = new Array(j = a + b); j--;) c[j] = 0;
// Multiply.
// i is initially xc.length.
for (i = b; i--;) {
b = 0;
// a is yc.length.
for (j = a + i; j > i;) {
// Current sum of products at this digit position, plus carry.
b = c[j] + yc[i] * xc[j - i - 1] + b;
c[j--] = b % 10;
// carry
b = b / 10 | 0;
}
c[j] = (c[j] + b) % 10;
}
// Increment result exponent if there is a final carry, otherwise remove leading zero.
if (b) ++y.e;
else c.shift();
// Remove trailing zeros.
for (i = c.length; !c[--i];) c.pop();
y.c = c;
return y;
};
/*
* Return a string representing the value of this Big in exponential notation to dp fixed decimal
* places and rounded using Big.RM.
*
* dp? {number} Integer, 0 to MAX_DP inclusive.
*/
P.toExponential = function (dp) {
return stringify(this, 1, dp, dp);
};
/*
* Return a string representing the value of this Big in normal notation to dp fixed decimal
* places and rounded using Big.RM.
*
* dp? {number} Integer, 0 to MAX_DP inclusive.
*
* (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'.
* (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.
*/
P.toFixed = function (dp) {
return stringify(this, 2, dp, this.e + dp);
};
/*
* Return a string representing the value of this Big rounded to sd significant digits using
* Big.RM. Use exponential notation if sd is less than the number of digits necessary to represent
* the integer part of the value in normal notation.
*
* sd {number} Integer, 1 to MAX_DP inclusive.
*/
P.toPrecision = function (sd) {
return stringify(this, 3, sd, sd - 1);
};
/*
* Return a string representing the value of this Big.
* Return exponential notation if this Big has a positive exponent equal to or greater than
* Big.PE, or a negative exponent equal to or less than Big.NE.
* Omit the sign for negative zero.
*/
P.toString = function () {
return stringify(this);
};
/*
* Return a string representing the value of this Big.
* Return exponential notation if this Big has a positive exponent equal to or greater than
* Big.PE, or a negative exponent equal to or less than Big.NE.
* Include the sign for negative zero.
*/
P.valueOf = P.toJSON = function () {
return stringify(this, 4);
};
// Export
Big = factory();
Big['default'] = Big.Big = Big;
//AMD.
if (typeof define === 'function' && define.amd) {
define(function () { return Big; });
// Node and other CommonJS-like environments that support module.exports.
} else if (typeof module !== 'undefined' && module.exports) {
module.exports = Big;
//Browser.
} else {
GLOBAL.Big = Big;
}
})(this);
PK jL$
R R big.mjsnu W+A /*
* big.js v5.0.0
* A small, fast, easy-to-use library for arbitrary-precision decimal arithmetic.
* Copyright (c) 2017 Michael Mclaughlin
* https://github.com/MikeMcl/big.js/LICENCE
*/
var Big,
/************************************** EDITABLE DEFAULTS *****************************************/
// The default values below must be integers within the stated ranges.
/*
* The maximum number of decimal places (DP) of the results of operations involving division:
* div and sqrt, and pow with negative exponents.
*/
DP = 20, // 0 to MAX_DP
/*
* The rounding mode (RM) used when rounding to the above decimal places.
*
* 0 Towards zero (i.e. truncate, no rounding). (ROUND_DOWN)
* 1 To nearest neighbour. If equidistant, round up. (ROUND_HALF_UP)
* 2 To nearest neighbour. If equidistant, to even. (ROUND_HALF_EVEN)
* 3 Away from zero. (ROUND_UP)
*/
RM = 1, // 0, 1, 2 or 3
// The maximum value of DP and Big.DP.
MAX_DP = 1E6, // 0 to 1000000
// The maximum magnitude of the exponent argument to the pow method.
MAX_POWER = 1E6, // 1 to 1000000
/*
* The negative exponent (NE) at and beneath which toString returns exponential notation.
* (JavaScript numbers: -7)
* -1000000 is the minimum recommended exponent value of a Big.
*/
NE = -7, // 0 to -1000000
/*
* The positive exponent (PE) at and above which toString returns exponential notation.
* (JavaScript numbers: 21)
* 1000000 is the maximum recommended exponent value of a Big.
* (This limit is not enforced or checked.)
*/
PE = 21, // 0 to 1000000
/**************************************************************************************************/
// Error messages.
NAME = '[big.js] ',
INVALID = NAME + 'Invalid ',
INVALID_DP = INVALID + 'decimal places',
DIV_BY_ZERO = NAME + 'Division by zero',
// The shared prototype object.
P = {},
UNDEFINED = void 0,
NUMERIC = /^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i;
/*
* Create and return a Big constructor.
*
*/
function factory() {
/*
* The Big constructor and exported function.
* Create and return a new instance of a Big number object.
*
* n {number|string|Big} A numeric value.
*/
function Big(n) {
var x = this;
// Enable constructor usage without new.
if (!(x instanceof Big)) return n === UNDEFINED ? factory() : new Big(n);
// Duplicate.
if (n instanceof Big) {
x.s = n.s;
x.e = n.e;
x.c = n.c.slice();
} else {
parse(x, n);
}
/*
* Retain a reference to this Big constructor, and shadow Big.prototype.constructor which
* points to Object.
*/
x.constructor = Big;
}
Big.prototype = P;
Big.DP = DP;
Big.RM = RM;
Big.NE = NE;
Big.PE = PE;
Big.version = '4.0.2';
return Big;
}
/*
* Parse the number or string value passed to a Big constructor.
*
* x {Big} A Big number instance.
* n {number|string} A numeric value.
*/
function parse(x, n) {
var e, i, nl;
// Minus zero?
if (n === 0 && 1 / n < 0) n = '-0';
else if (!NUMERIC.test(n += '')) throw Error(INVALID + 'number');
// Determine sign.
x.s = n.charAt(0) == '-' ? (n = n.slice(1), -1) : 1;
// Decimal point?
if ((e = n.indexOf('.')) > -1) n = n.replace('.', '');
// Exponential form?
if ((i = n.search(/e/i)) > 0) {
// Determine exponent.
if (e < 0) e = i;
e += +n.slice(i + 1);
n = n.substring(0, i);
} else if (e < 0) {
// Integer.
e = n.length;
}
nl = n.length;
// Determine leading zeros.
for (i = 0; i < nl && n.charAt(i) == '0';) ++i;
if (i == nl) {
// Zero.
x.c = [x.e = 0];
} else {
// Determine trailing zeros.
for (; nl > 0 && n.charAt(--nl) == '0';);
x.e = e - i - 1;
x.c = [];
// Convert string to array of digits without leading/trailing zeros.
for (e = 0; i <= nl;) x.c[e++] = +n.charAt(i++);
}
return x;
}
/*
* Round Big x to a maximum of dp decimal places using rounding mode rm.
* Called by stringify, P.div, P.round and P.sqrt.
*
* x {Big} The Big to round.
* dp {number} Integer, 0 to MAX_DP inclusive.
* rm {number} 0, 1, 2 or 3 (DOWN, HALF_UP, HALF_EVEN, UP)
* [more] {boolean} Whether the result of division was truncated.
*/
function round(x, dp, rm, more) {
var xc = x.c,
i = x.e + dp + 1;
if (rm === 1) {
// xc[i] is the digit after the digit that may be rounded up.
more = xc[i] >= 5;
} else if (rm === 2) {
more = xc[i] > 5 || xc[i] == 5 && (more || i < 0 || xc[i + 1] !== UNDEFINED || xc[i - 1] & 1);
} else if (rm === 3) {
more = more || xc[i] !== UNDEFINED || i < 0;
} else {
more = false;
if (rm !== 0) throw Error(INVALID + 'rounding mode');
}
if (i < 1 || !xc[0]) {
xc.length = 1;
if (more) {
// 1, 0.1, 0.01, 0.001, 0.0001 etc.
x.e = -dp;
xc[0] = 1;
} else {
// Zero.
xc[0] = x.e = 0;
}
} else {
// Remove any digits after the required decimal places.
xc.length = i--;
// Round up?
if (more) {
// Rounding up may mean the previous digit has to be rounded up.
for (; ++xc[i] > 9;) {
xc[i] = 0;
if (!i--) {
++x.e;
xc.unshift(1);
}
}
}
// Remove trailing zeros.
for (i = xc.length; !xc[--i];) xc.pop();
}
return x;
}
/*
* Return a string representing the value of Big x in normal or exponential notation.
* Handles P.toExponential, P.toFixed, P.toJSON, P.toPrecision, P.toString and P.valueOf.
*
* x {Big}
* id? {number} Caller id.
* 1 toExponential
* 2 toFixed
* 3 toPrecision
* 4 valueOf
* n? {number|undefined} Caller's argument.
* k? {number|undefined}
*/
function stringify(x, id, n, k) {
var e, s,
Big = x.constructor,
z = !x.c[0];
if (n !== UNDEFINED) {
if (n !== ~~n || n < (id == 3) || n > MAX_DP) {
throw Error(id == 3 ? INVALID + 'precision' : INVALID_DP);
}
x = new Big(x);
// The index of the digit that may be rounded up.
n = k - x.e;
// Round?
if (x.c.length > ++k) round(x, n, Big.RM);
// toFixed: recalculate k as x.e may have changed if value rounded up.
if (id == 2) k = x.e + n + 1;
// Append zeros?
for (; x.c.length < k;) x.c.push(0);
}
e = x.e;
s = x.c.join('');
n = s.length;
// Exponential notation?
if (id != 2 && (id == 1 || id == 3 && k <= e || e <= Big.NE || e >= Big.PE)) {
s = s.charAt(0) + (n > 1 ? '.' + s.slice(1) : '') + (e < 0 ? 'e' : 'e+') + e;
// Normal notation.
} else if (e < 0) {
for (; ++e;) s = '0' + s;
s = '0.' + s;
} else if (e > 0) {
if (++e > n) for (e -= n; e--;) s += '0';
else if (e < n) s = s.slice(0, e) + '.' + s.slice(e);
} else if (n > 1) {
s = s.charAt(0) + '.' + s.slice(1);
}
return x.s < 0 && (!z || id == 4) ? '-' + s : s;
}
// Prototype/instance methods
/*
* Return a new Big whose value is the absolute value of this Big.
*/
P.abs = function () {
var x = new this.constructor(this);
x.s = 1;
return x;
};
/*
* Return 1 if the value of this Big is greater than the value of Big y,
* -1 if the value of this Big is less than the value of Big y, or
* 0 if they have the same value.
*/
P.cmp = function (y) {
var isneg,
x = this,
xc = x.c,
yc = (y = new x.constructor(y)).c,
i = x.s,
j = y.s,
k = x.e,
l = y.e;
// Either zero?
if (!xc[0] || !yc[0]) return !xc[0] ? !yc[0] ? 0 : -j : i;
// Signs differ?
if (i != j) return i;
isneg = i < 0;
// Compare exponents.
if (k != l) return k > l ^ isneg ? 1 : -1;
j = (k = xc.length) < (l = yc.length) ? k : l;
// Compare digit by digit.
for (i = -1; ++i < j;) {
if (xc[i] != yc[i]) return xc[i] > yc[i] ^ isneg ? 1 : -1;
}
// Compare lengths.
return k == l ? 0 : k > l ^ isneg ? 1 : -1;
};
/*
* Return a new Big whose value is the value of this Big divided by the value of Big y, rounded,
* if necessary, to a maximum of Big.DP decimal places using rounding mode Big.RM.
*/
P.div = function (y) {
var x = this,
Big = x.constructor,
a = x.c, // dividend
b = (y = new Big(y)).c, // divisor
k = x.s == y.s ? 1 : -1,
dp = Big.DP;
if (dp !== ~~dp || dp < 0 || dp > MAX_DP) throw Error(INVALID_DP);
// Divisor is zero?
if (!b[0]) throw Error(DIV_BY_ZERO);
// Dividend is 0? Return +-0.
if (!a[0]) return new Big(k * 0);
var bl, bt, n, cmp, ri,
bz = b.slice(),
ai = bl = b.length,
al = a.length,
r = a.slice(0, bl), // remainder
rl = r.length,
q = y, // quotient
qc = q.c = [],
qi = 0,
d = dp + (q.e = x.e - y.e) + 1; // number of digits of the result
q.s = k;
k = d < 0 ? 0 : d;
// Create version of divisor with leading zero.
bz.unshift(0);
// Add zeros to make remainder as long as divisor.
for (; rl++ < bl;) r.push(0);
do {
// n is how many times the divisor goes into current remainder.
for (n = 0; n < 10; n++) {
// Compare divisor and remainder.
if (bl != (rl = r.length)) {
cmp = bl > rl ? 1 : -1;
} else {
for (ri = -1, cmp = 0; ++ri < bl;) {
if (b[ri] != r[ri]) {
cmp = b[ri] > r[ri] ? 1 : -1;
break;
}
}
}
// If divisor < remainder, subtract divisor from remainder.
if (cmp < 0) {
// Remainder can't be more than 1 digit longer than divisor.
// Equalise lengths using divisor with extra leading zero?
for (bt = rl == bl ? b : bz; rl;) {
if (r[--rl] < bt[rl]) {
ri = rl;
for (; ri && !r[--ri];) r[ri] = 9;
--r[ri];
r[rl] += 10;
}
r[rl] -= bt[rl];
}
for (; !r[0];) r.shift();
} else {
break;
}
}
// Add the digit n to the result array.
qc[qi++] = cmp ? n : ++n;
// Update the remainder.
if (r[0] && cmp) r[rl] = a[ai] || 0;
else r = [a[ai]];
} while ((ai++ < al || r[0] !== UNDEFINED) && k--);
// Leading zero? Do not remove if result is simply zero (qi == 1).
if (!qc[0] && qi != 1) {
// There can't be more than one zero.
qc.shift();
q.e--;
}
// Round?
if (qi > d) round(q, dp, Big.RM, r[0] !== UNDEFINED);
return q;
};
/*
* Return true if the value of this Big is equal to the value of Big y, otherwise return false.
*/
P.eq = function (y) {
return !this.cmp(y);
};
/*
* Return true if the value of this Big is greater than the value of Big y, otherwise return
* false.
*/
P.gt = function (y) {
return this.cmp(y) > 0;
};
/*
* Return true if the value of this Big is greater than or equal to the value of Big y, otherwise
* return false.
*/
P.gte = function (y) {
return this.cmp(y) > -1;
};
/*
* Return true if the value of this Big is less than the value of Big y, otherwise return false.
*/
P.lt = function (y) {
return this.cmp(y) < 0;
};
/*
* Return true if the value of this Big is less than or equal to the value of Big y, otherwise
* return false.
*/
P.lte = function (y) {
return this.cmp(y) < 1;
};
/*
* Return a new Big whose value is the value of this Big minus the value of Big y.
*/
P.minus = P.sub = function (y) {
var i, j, t, xlty,
x = this,
Big = x.constructor,
a = x.s,
b = (y = new Big(y)).s;
// Signs differ?
if (a != b) {
y.s = -b;
return x.plus(y);
}
var xc = x.c.slice(),
xe = x.e,
yc = y.c,
ye = y.e;
// Either zero?
if (!xc[0] || !yc[0]) {
// y is non-zero? x is non-zero? Or both are zero.
return yc[0] ? (y.s = -b, y) : new Big(xc[0] ? x : 0);
}
// Determine which is the bigger number. Prepend zeros to equalise exponents.
if (a = xe - ye) {
if (xlty = a < 0) {
a = -a;
t = xc;
} else {
ye = xe;
t = yc;
}
t.reverse();
for (b = a; b--;) t.push(0);
t.reverse();
} else {
// Exponents equal. Check digit by digit.
j = ((xlty = xc.length < yc.length) ? xc : yc).length;
for (a = b = 0; b < j; b++) {
if (xc[b] != yc[b]) {
xlty = xc[b] < yc[b];
break;
}
}
}
// x < y? Point xc to the array of the bigger number.
if (xlty) {
t = xc;
xc = yc;
yc = t;
y.s = -y.s;
}
/*
* Append zeros to xc if shorter. No need to add zeros to yc if shorter as subtraction only
* needs to start at yc.length.
*/
if ((b = (j = yc.length) - (i = xc.length)) > 0) for (; b--;) xc[i++] = 0;
// Subtract yc from xc.
for (b = i; j > a;) {
if (xc[--j] < yc[j]) {
for (i = j; i && !xc[--i];) xc[i] = 9;
--xc[i];
xc[j] += 10;
}
xc[j] -= yc[j];
}
// Remove trailing zeros.
for (; xc[--b] === 0;) xc.pop();
// Remove leading zeros and adjust exponent accordingly.
for (; xc[0] === 0;) {
xc.shift();
--ye;
}
if (!xc[0]) {
// n - n = +0
y.s = 1;
// Result must be zero.
xc = [ye = 0];
}
y.c = xc;
y.e = ye;
return y;
};
/*
* Return a new Big whose value is the value of this Big modulo the value of Big y.
*/
P.mod = function (y) {
var ygtx,
x = this,
Big = x.constructor,
a = x.s,
b = (y = new Big(y)).s;
if (!y.c[0]) throw Error(DIV_BY_ZERO);
x.s = y.s = 1;
ygtx = y.cmp(x) == 1;
x.s = a;
y.s = b;
if (ygtx) return new Big(x);
a = Big.DP;
b = Big.RM;
Big.DP = Big.RM = 0;
x = x.div(y);
Big.DP = a;
Big.RM = b;
return this.minus(x.times(y));
};
/*
* Return a new Big whose value is the value of this Big plus the value of Big y.
*/
P.plus = P.add = function (y) {
var t,
x = this,
Big = x.constructor,
a = x.s,
b = (y = new Big(y)).s;
// Signs differ?
if (a != b) {
y.s = -b;
return x.minus(y);
}
var xe = x.e,
xc = x.c,
ye = y.e,
yc = y.c;
// Either zero? y is non-zero? x is non-zero? Or both are zero.
if (!xc[0] || !yc[0]) return yc[0] ? y : new Big(xc[0] ? x : a * 0);
xc = xc.slice();
// Prepend zeros to equalise exponents.
// Note: Faster to use reverse then do unshifts.
if (a = xe - ye) {
if (a > 0) {
ye = xe;
t = yc;
} else {
a = -a;
t = xc;
}
t.reverse();
for (; a--;) t.push(0);
t.reverse();
}
// Point xc to the longer array.
if (xc.length - yc.length < 0) {
t = yc;
yc = xc;
xc = t;
}
a = yc.length;
// Only start adding at yc.length - 1 as the further digits of xc can be left as they are.
for (b = 0; a; xc[a] %= 10) b = (xc[--a] = xc[a] + yc[a] + b) / 10 | 0;
// No need to check for zero, as +x + +y != 0 && -x + -y != 0
if (b) {
xc.unshift(b);
++ye;
}
// Remove trailing zeros.
for (a = xc.length; xc[--a] === 0;) xc.pop();
y.c = xc;
y.e = ye;
return y;
};
/*
* Return a Big whose value is the value of this Big raised to the power n.
* If n is negative, round to a maximum of Big.DP decimal places using rounding
* mode Big.RM.
*
* n {number} Integer, -MAX_POWER to MAX_POWER inclusive.
*/
P.pow = function (n) {
var x = this,
one = new x.constructor(1),
y = one,
isneg = n < 0;
if (n !== ~~n || n < -MAX_POWER || n > MAX_POWER) throw Error(INVALID + 'exponent');
if (isneg) n = -n;
for (;;) {
if (n & 1) y = y.times(x);
n >>= 1;
if (!n) break;
x = x.times(x);
}
return isneg ? one.div(y) : y;
};
/*
* Return a new Big whose value is the value of this Big rounded to a maximum of dp decimal
* places using rounding mode rm.
* If dp is not specified, round to 0 decimal places.
* If rm is not specified, use Big.RM.
*
* dp? {number} Integer, 0 to MAX_DP inclusive.
* rm? 0, 1, 2 or 3 (ROUND_DOWN, ROUND_HALF_UP, ROUND_HALF_EVEN, ROUND_UP)
*/
P.round = function (dp, rm) {
var Big = this.constructor;
if (dp === UNDEFINED) dp = 0;
else if (dp !== ~~dp || dp < 0 || dp > MAX_DP) throw Error(INVALID_DP);
return round(new Big(this), dp, rm === UNDEFINED ? Big.RM : rm);
};
/*
* Return a new Big whose value is the square root of the value of this Big, rounded, if
* necessary, to a maximum of Big.DP decimal places using rounding mode Big.RM.
*/
P.sqrt = function () {
var r, c, t,
x = this,
Big = x.constructor,
s = x.s,
e = x.e,
half = new Big(0.5);
// Zero?
if (!x.c[0]) return new Big(x);
// Negative?
if (s < 0) throw Error(NAME + 'No square root');
// Estimate.
s = Math.sqrt(x.toString());
// Math.sqrt underflow/overflow?
// Re-estimate: pass x to Math.sqrt as integer, then adjust the result exponent.
if (s === 0 || s === 1 / 0) {
c = x.c.join('');
if (!(c.length + e & 1)) c += '0';
r = new Big(Math.sqrt(c).toString());
r.e = ((e + 1) / 2 | 0) - (e < 0 || e & 1);
} else {
r = new Big(s.toString());
}
e = r.e + (Big.DP += 4);
// Newton-Raphson iteration.
do {
t = r;
r = half.times(t.plus(x.div(t)));
} while (t.c.slice(0, e).join('') !== r.c.slice(0, e).join(''));
return round(r, Big.DP -= 4, Big.RM);
};
/*
* Return a new Big whose value is the value of this Big times the value of Big y.
*/
P.times = P.mul = function (y) {
var c,
x = this,
Big = x.constructor,
xc = x.c,
yc = (y = new Big(y)).c,
a = xc.length,
b = yc.length,
i = x.e,
j = y.e;
// Determine sign of result.
y.s = x.s == y.s ? 1 : -1;
// Return signed 0 if either 0.
if (!xc[0] || !yc[0]) return new Big(y.s * 0);
// Initialise exponent of result as x.e + y.e.
y.e = i + j;
// If array xc has fewer digits than yc, swap xc and yc, and lengths.
if (a < b) {
c = xc;
xc = yc;
yc = c;
j = a;
a = b;
b = j;
}
// Initialise coefficient array of result with zeros.
for (c = new Array(j = a + b); j--;) c[j] = 0;
// Multiply.
// i is initially xc.length.
for (i = b; i--;) {
b = 0;
// a is yc.length.
for (j = a + i; j > i;) {
// Current sum of products at this digit position, plus carry.
b = c[j] + yc[i] * xc[j - i - 1] + b;
c[j--] = b % 10;
// carry
b = b / 10 | 0;
}
c[j] = (c[j] + b) % 10;
}
// Increment result exponent if there is a final carry, otherwise remove leading zero.
if (b) ++y.e;
else c.shift();
// Remove trailing zeros.
for (i = c.length; !c[--i];) c.pop();
y.c = c;
return y;
};
/*
* Return a string representing the value of this Big in exponential notation to dp fixed decimal
* places and rounded using Big.RM.
*
* dp? {number} Integer, 0 to MAX_DP inclusive.
*/
P.toExponential = function (dp) {
return stringify(this, 1, dp, dp);
};
/*
* Return a string representing the value of this Big in normal notation to dp fixed decimal
* places and rounded using Big.RM.
*
* dp? {number} Integer, 0 to MAX_DP inclusive.
*
* (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'.
* (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.
*/
P.toFixed = function (dp) {
return stringify(this, 2, dp, this.e + dp);
};
/*
* Return a string representing the value of this Big rounded to sd significant digits using
* Big.RM. Use exponential notation if sd is less than the number of digits necessary to represent
* the integer part of the value in normal notation.
*
* sd {number} Integer, 1 to MAX_DP inclusive.
*/
P.toPrecision = function (sd) {
return stringify(this, 3, sd, sd - 1);
};
/*
* Return a string representing the value of this Big.
* Return exponential notation if this Big has a positive exponent equal to or greater than
* Big.PE, or a negative exponent equal to or less than Big.NE.
* Omit the sign for negative zero.
*/
P.toString = function () {
return stringify(this);
};
/*
* Return a string representing the value of this Big.
* Return exponential notation if this Big has a positive exponent equal to or greater than
* Big.PE, or a negative exponent equal to or less than Big.NE.
* Include the sign for negative zero.
*/
P.valueOf = P.toJSON = function () {
return stringify(this, 4);
};
// Export
Big = factory();
Big.Big = Big;
export default Big;
PK jLF package.jsonnu W+A {
"name": "big.js",
"description": "A small, fast, easy-to-use library for arbitrary-precision decimal arithmetic",
"version": "5.0.0",
"keywords": [
"arbitrary",
"precision",
"arithmetic",
"big",
"number",
"decimal",
"float",
"biginteger",
"bigdecimal",
"bignumber",
"bigint",
"bignum"
],
"repository" : {
"type": "git",
"url": "https://github.com/MikeMcl/big.js.git"
},
"main": "big.js",
"author": {
"name": "Michael Mclaughlin",
"email": "M8ch88l@gmail.com"
},
"bugs": {
"url": "https://github.com/MikeMcl/big.js/issues"
},
"engines": {
"node": "*"
},
"license": "MIT",
"scripts": {
"test": "node ./test/every-test.js",
"build": "uglifyjs big.js --source-map doc/big.js.map -c -m -o big.min.js --preamble \"/* big.js v5.0.0 https://github.com/MikeMcl/big.js/LICENCE */\""
},
"files": [
"big.js",
"big.mjs",
"big.min.js"
]
}
PK jL2Yښ
big.min.jsnu W+A /* big.js v5.0.0 https://github.com/MikeMcl/big.js/LICENCE */
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R R big.mjsnu W+A PK jLF package.jsonnu W+A PK jL2Yښ
big.min.jsnu W+A PK