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/* big.js v3.1.3 https://github.com/MikeMcl/big.js/LICENCE */
;(function (global) {
'use strict';
/*
big.js v3.1.3
A small, fast, easy-to-use library for arbitrary-precision decimal arithmetic.
https://github.com/MikeMcl/big.js/
Copyright (c) 2014 Michael Mclaughlin <[email protected]>
MIT Expat Licence
*/
/***************************** EDITABLE DEFAULTS ******************************/
// The default values below must be integers within the stated ranges.
/*
* The maximum number of decimal places of the results of operations
* involving division: div and sqrt, and pow with negative exponents.
*/
var DP = 20, // 0 to MAX_DP
/*
* The rounding mode 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 exponent value at and beneath which toString returns exponential
* notation.
* JavaScript's Number type: -7
* -1000000 is the minimum recommended exponent value of a Big.
*/
E_NEG = -7, // 0 to -1000000
/*
* The exponent value at and above which toString returns exponential
* notation.
* JavaScript's Number type: 21
* 1000000 is the maximum recommended exponent value of a Big.
* (This limit is not enforced or checked.)
*/
E_POS = 21, // 0 to 1000000
/******************************************************************************/
// The shared prototype object.
P = {},
isValid = /^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,
Big;
/*
* Create and return a Big constructor.
*
*/
function bigFactory() {
/*
* 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 === void 0 ? bigFactory() : 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.E_NEG = E_NEG;
Big.E_POS = E_POS;
return Big;
}
// Private functions
/*
* Return a string representing the value of Big x in normal or exponential
* notation to dp fixed decimal places or significant digits.
*
* x {Big} The Big to format.
* dp {number} Integer, 0 to MAX_DP inclusive.
* toE {number} 1 (toExponential), 2 (toPrecision) or undefined (toFixed).
*/
function format(x, dp, toE) {
var Big = x.constructor,
// The index (normal notation) of the digit that may be rounded up.
i = dp - (x = new Big(x)).e,
c = x.c;
// Round?
if (c.length > ++dp) {
rnd(x, i, Big.RM);
}
if (!c[0]) {
++i;
} else if (toE) {
i = dp;
// toFixed
} else {
c = x.c;
// Recalculate i as x.e may have changed if value rounded up.
i = x.e + i + 1;
}
// Append zeros?
for (; c.length < i; c.push(0)) {
}
i = x.e;
/*
* toPrecision returns exponential notation if the number of
* significant digits specified is less than the number of digits
* necessary to represent the integer part of the value in normal
* notation.
*/
return toE === 1 || toE && (dp <= i || i <= Big.E_NEG) ?
// Exponential notation.
(x.s < 0 && c[0] ? '-' : '') +
(c.length > 1 ? c[0] + '.' + c.join('').slice(1) : c[0]) +
(i < 0 ? 'e' : 'e+') + i
// Normal notation.
: x.toString();
}
/*
* 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';
// Ensure n is string and check validity.
} else if (!isValid.test(n += '')) {
throwErr(NaN);
}
// 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;
}
// Determine leading zeros.
for (i = 0; n.charAt(i) == '0'; i++) {
}
if (i == (nL = n.length)) {
// Zero.
x.c = [ x.e = 0 ];
} else {
// Determine trailing zeros.
for (; 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 div, sqrt and round.
*
* 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 rnd(x, dp, rm, more) {
var u,
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] !== u || xc[i - 1] & 1);
} else if (rm === 3) {
more = more || xc[i] !== u || i < 0;
} else {
more = false;
if (rm !== 0) {
throwErr('!Big.RM!');
}
}
if (i < 1 || !xc[0]) {
if (more) {
// 1, 0.1, 0.01, 0.001, 0.0001 etc.
x.e = -dp;
x.c = [1];
} else {
// Zero.
x.c = [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;
}
/*
* Throw a BigError.
*
* message {string} The error message.
*/
function throwErr(message) {
var err = new Error(message);
err.name = 'BigError';
throw err;
}
// 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 xNeg,
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;
}
xNeg = i < 0;
// Compare exponents.
if (k != l) {
return k > l ^ xNeg ? 1 : -1;
}
i = -1;
j = (k = xc.length) < (l = yc.length) ? k : l;
// Compare digit by digit.
for (; ++i < j;) {
if (xc[i] != yc[i]) {
return xc[i] > yc[i] ^ xNeg ? 1 : -1;
}
}
// Compare lengths.
return k == l ? 0 : k > l ^ xNeg ? 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,
// dividend
dvd = x.c,
//divisor
dvs = (y = new Big(y)).c,
s = x.s == y.s ? 1 : -1,
dp = Big.DP;
if (dp !== ~~dp || dp < 0 || dp > MAX_DP) {
throwErr('!Big.DP!');
}
// Either 0?
if (!dvd[0] || !dvs[0]) {
// If both are 0, throw NaN
if (dvd[0] == dvs[0]) {
throwErr(NaN);
}
// If dvs is 0, throw +-Infinity.
if (!dvs[0]) {
throwErr(s / 0);
}
// dvd is 0, return +-0.
return new Big(s * 0);
}
var dvsL, dvsT, next, cmp, remI, u,
dvsZ = dvs.slice(),
dvdI = dvsL = dvs.length,
dvdL = dvd.length,
// remainder
rem = dvd.slice(0, dvsL),
remL = rem.length,
// quotient
q = y,
qc = q.c = [],
qi = 0,
digits = dp + (q.e = x.e - y.e) + 1;
q.s = s;
s = digits < 0 ? 0 : digits;
// Create version of divisor with leading zero.
dvsZ.unshift(0);
// Add zeros to make remainder as long as divisor.
for (; remL++ < dvsL; rem.push(0)) {
}
do {
// 'next' is how many times the divisor goes into current remainder.
for (next = 0; next < 10; next++) {
// Compare divisor and remainder.
if (dvsL != (remL = rem.length)) {
cmp = dvsL > remL ? 1 : -1;
} else {
for (remI = -1, cmp = 0; ++remI < dvsL;) {
if (dvs[remI] != rem[remI]) {
cmp = dvs[remI] > rem[remI] ? 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 (dvsT = remL == dvsL ? dvs : dvsZ; remL;) {
if (rem[--remL] < dvsT[remL]) {
remI = remL;
for (; remI && !rem[--remI]; rem[remI] = 9) {
}
--rem[remI];
rem[remL] += 10;
}
rem[remL] -= dvsT[remL];
}
for (; !rem[0]; rem.shift()) {
}
} else {
break;
}
}
// Add the 'next' digit to the result array.
qc[qi++] = cmp ? next : ++next;
// Update the remainder.
if (rem[0] && cmp) {
rem[remL] = dvd[dvdI] || 0;
} else {
rem = [ dvd[dvdI] ];
}
} while ((dvdI++ < dvdL || rem[0] !== u) && s--);
// 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 > digits) {
rnd(q, dp, Big.RM, rem[0] !== u);
}
return q;
};
/*
* Return true if the value of this Big is equal to the value of Big y,
* otherwise returns 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 returns 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 returns 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 returns 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 returns 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.sub = P.minus = 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]) {
throwErr(NaN);
}
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.add = P.plus = 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?
if (!xc[0] || !yc[0]) {
// y is non-zero? x is non-zero? Or both are zero.
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;) {
b = (xc[--a] = xc[a] + yc[a] + b) / 10 | 0;
xc[a] %= 10;
}
// 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, if necessary, 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) {
throwErr('!pow!');
}
n = 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 x = this,
Big = x.constructor;
if (dp == null) {
dp = 0;
} else if (dp !== ~~dp || dp < 0 || dp > MAX_DP) {
throwErr('!round!');
}
rnd(x = new Big(x), dp, rm == null ? Big.RM : rm);
return x;
};
/*
* 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 estimate, r, approx,
x = this,
Big = x.constructor,
xc = x.c,
i = x.s,
e = x.e,
half = new Big('0.5');
// Zero?
if (!xc[0]) {
return new Big(x);
}
// If negative, throw NaN.
if (i < 0) {
throwErr(NaN);
}
// Estimate.
i = Math.sqrt(x.toString());
// Math.sqrt underflow/overflow?
// Pass x to Math.sqrt as integer, then adjust the result exponent.
if (i === 0 || i === 1 / 0) {
estimate = xc.join('');
if (!(estimate.length + e & 1)) {
estimate += '0';
}
r = new Big( Math.sqrt(estimate).toString() );
r.e = ((e + 1) / 2 | 0) - (e < 0 || e & 1);
} else {
r = new Big(i.toString());
}
i = r.e + (Big.DP += 4);
// Newton-Raphson iteration.
do {
approx = r;
r = half.times( approx.plus( x.div(approx) ) );
} while ( approx.c.slice(0, i).join('') !==
r.c.slice(0, i).join('') );
rnd(r, Big.DP -= 4, Big.RM);
return r;
};
/*
* Return a new Big whose value is the value of this Big times the value of
* Big y.
*/
P.mul = P.times = 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.
if (b) {
++y.e;
}
// Remove any leading zero.
if (!c[0]) {
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.
* Return exponential notation if this Big has a positive exponent equal to
* or greater than Big.E_POS, or a negative exponent equal to or less than
* Big.E_NEG.
*/
P.toString = P.valueOf = P.toJSON = function () {
var x = this,
Big = x.constructor,
e = x.e,
str = x.c.join(''),
strL = str.length;
// Exponential notation?
if (e <= Big.E_NEG || e >= Big.E_POS) {
str = str.charAt(0) + (strL > 1 ? '.' + str.slice(1) : '') +
(e < 0 ? 'e' : 'e+') + e;
// Negative exponent?
} else if (e < 0) {
// Prepend zeros.
for (; ++e; str = '0' + str) {
}
str = '0.' + str;
// Positive exponent?
} else if (e > 0) {
if (++e > strL) {
// Append zeros.
for (e -= strL; e-- ; str += '0') {
}
} else if (e < strL) {
str = str.slice(0, e) + '.' + str.slice(e);
}
// Exponent zero.
} else if (strL > 1) {
str = str.charAt(0) + '.' + str.slice(1);
}
// Avoid '-0'
return x.s < 0 && x.c[0] ? '-' + str : str;
};
/*
***************************************************************************
* If toExponential, toFixed, toPrecision and format are not required they
* can safely be commented-out or deleted. No redundant code will be left.
* format is used only by toExponential, toFixed and toPrecision.
***************************************************************************
*/
/*
* Return a string representing the value of this Big in exponential
* notation to dp fixed decimal places and rounded, if necessary, using
* Big.RM.
*
* [dp] {number} Integer, 0 to MAX_DP inclusive.
*/
P.toExponential = function (dp) {
if (dp == null) {
dp = this.c.length - 1;
} else if (dp !== ~~dp || dp < 0 || dp > MAX_DP) {
throwErr('!toExp!');
}
return format(this, dp, 1);
};
/*
* Return a string representing the value of this Big in normal notation
* to dp fixed decimal places and rounded, if necessary, using Big.RM.
*
* [dp] {number} Integer, 0 to MAX_DP inclusive.
*/
P.toFixed = function (dp) {
var str,
x = this,
Big = x.constructor,
neg = Big.E_NEG,
pos = Big.E_POS;
// Prevent the possibility of exponential notation.
Big.E_NEG = -(Big.E_POS = 1 / 0);
if (dp == null) {
str = x.toString();
} else if (dp === ~~dp && dp >= 0 && dp <= MAX_DP) {
str = format(x, x.e + dp);
// (-0).toFixed() is '0', but (-0.1).toFixed() is '-0'.
// (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.
if (x.s < 0 && x.c[0] && str.indexOf('-') < 0) {
//E.g. -0.5 if rounded to -0 will cause toString to omit the minus sign.
str = '-' + str;
}
}
Big.E_NEG = neg;
Big.E_POS = pos;
if (!str) {
throwErr('!toFix!');
}
return str;
};
/*
* 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) {
if (sd == null) {
return this.toString();
} else if (sd !== ~~sd || sd < 1 || sd > MAX_DP) {
throwErr('!toPre!');
}
return format(this, sd - 1, 2);
};
// Export
Big = bigFactory();
//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);