スポンサーリンク

JavaScriptでbig-integerでできること

スポンサーリンク
JavaScript
スポンサーリンク

スポンサーリンク

概要

JavScriptのモジュールbig-integerを使ってできることのメモ

big-integer
An arbitrary length integer library for Javascript

定数

bigInt.one // bigInt(1)に相当
bigInt.zero // bigInt(0)に相当
bigInt.minusOne // bigInt(-1)に相当

メソッド

abs

絶対値

bigInt(-45).abs() // 45
bigInt(45).abs() // 45

add, plus

加算

bigInt(5).add(7) // 12
bigInt(5).plus(7) // 12

and

ビット単位のand演算を行う。

bigInt(6).and(3) // 2
bigInt(6).and(-3) // 4

bitLength

数値をバイナリで表すのに必要な桁数

bigInt(5).bitLength() // 3(5 101は3桁のバイナリであるため)

compare compareTo

数値の比較。compareToはcompareのエイリアス

bigInt(5).compare(5) // 5 == 5 => 0
bigInt(5).compare(4) // 5 > 4 => 1
bigInt(4).compare(5) // 4 < 5 => -1

compareAmb

絶対値としての比較

bigInt(5).compareAbs(-5) // 0
bigInt(5).compareAbs(4) // 1
bigInt(4).compareAbs(-5) // -1

divide, over

整数の除算

bigInt(59).divide(5) // 11
bigInt(59).over(5) // 11

divmod

除算を実行し、「除算の結果」と「あまり」を返す。

bigInt(59).divmod(5) // {quotient: bigInt(11), remainder: bigInt(4) }
bigInt(-5).divmod(2) // {quotient: bigInt(-2), 

equals, eq

2つの数値が等しいか。eqはequalsのエイリアス

bigInt(5).equals(5) // true
bigInt(4).equals(7) // false

greater, gt

最初の数値が2番目の数値より大きいかどうか計算。同じ値の場合はfalse。gtはエイリアス

bigInt(5).greater(6) // false
bigInt(5).greater(5) // false
bigInt(5).greater(4) // true

greaterOrEquals, geq

最初の数値が2番目の数値より大きいかどうか判定。同じ値の場合はtrue。geqはエイリアス

bigInt(5).greaterOrEquals(6) // false
bigInt(5).greaterOrEquals(5) // true
bigInt(5).greaterOrEquals(4) // true

isDivisibleBy

割り切れるかどうか

bigInt(999).isDivisibleBy(333) // true
bigInt(99).isDivisibleBy(5) // false

isEven

偶数判定

bigInt(6).isEven() // true
bigInt(3).isEven() // false

isNegative

負の数の場合trueを返す

bigInt(-23).isNegative() // true
bigInt(50).isNegative() // false

isOdd

奇数判定

bigInt(13).isOdd() // true
bigInt(40).isOdd() // false

isPositive

正の整数か

bigInt(54).isPositive() // true
bigInt(-1).isPositive() // false

isPrime

素数判定

bigInt(5).isPrime() // true
bigInt(6).isPrime() // false

isProbablePrime

数値が素数である可能性が高い時にtrueを返す。出なければfalse。ミラーラビンの素数判定によって計算される

bigInt(5).isProbablePrime() // true
bigInt(49).isProbablePrime() // false
bigInt(1729).isProbablePrime() // false
bigInt(1729).isProbablePrime(1, () => 0.1) // false
bigInt(1729).isProbablePrime(1, () => 0.2) // true

isUnit

数値が1 もしくは -1 のときにtrueを返す

bigInt.one.isUnit() // true
bigInt.minusOne.isUnit() // true
bigInt(5).isUnit() // false

isZero

数値が0のときにtrueを返す

bigInt.zero.isZero() // true
bigInt("-0").isZero() // true
bigInt(50).isZero() // false

lesser, lt

最初の数値が2番目の数値より小さいかどうか判定。ltはエイリアス

bigInt(5).lesser(6) // true
bigInt(5).lesser(5) // false
bigInt(5).lesser(4) // false

lesserOrEquals, leq

最初の数値が2番目の数値以下かどうか判定。leqはエイリアス

bigInt(5).lesserOrEquals(6) // true
bigInt(5).lesserOrEquals(5) // true
bigInt(5).lesserOrEquals(4) // false

minus, subtract

減算をする

bigInt(3).minus(5) // -2
bigInt(3).subtract(5) // -2

mod, remaider

除算を実行し、商を無視して剰余​​を返します。remaiderはmodのエイリアス。

bigInt(59).mod(5) // 4
bigInt(-5).mod(2) // -1

modInv

モジュラ逆数(乗法)を求める

bigInt(3).modInv(11) // 4
bigInt(42).modInv(2017) // 1969

modPow

冪剰余を求める

bigInt(10).modPow(3, 30) // 10

multiply, times

乗算

bigInt(111).multiply(111) // 12321
bigInt(111).times(111) // 12321

next

1つ加算する

bigInt(6).next() // 7

not

ビット単位のnot演算を実行する

bigInt(10).not() // -11
bigInt(0).not() // -1

notEquals, neq

2つの数値が等しくないかどうかを判定。neqはエイリアス

bigInt(5).notEquals(5) // false
bigInt(4).notEquals(7) // true

or

ビット単位のOR演算を実行します

bigInt(13).or(10) // 15
bigInt(13).or(-8) // -3

pow

べき乗を実行します。指数が0より小さい場合、0を返します。

bigInt(16).pow(16) // 18446744073709551616

prev

数値から1を引く

bigInt(6).prev() // 5

shiftLeft

左シフト

bigInt(8).shiftLeft(2) // 32
bigInt(8).shiftLeft(-2) // 2

shiftRight

右シフト

bigInt(8).shiftRight(2) // 2
bigInt(8).shiftRight(-2) // 32

square

2乗する

bigInt(3).square() // 9

toArray

プロパティ「value」および「isNegative」を持つbigIntオブジェクトに変換します。「value」は、指定された基数を法とする整数の配列です。「isNegative」は、結果の符号を表すbool値です。

bigInt("1e9").toArray(10) // { value: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], isNegative: false }
bigInt("1e9").toArray(16) // { value: [3, 11, 9, 10, 12, 10, 0, 0], isNegative: false }
bigInt(567890).toArray(100) // { value: [56, 78, 90], isNegative: false }
bigInt(12345).toArray(-10) // { value: [2, 8, 4, 6, 5], isNegative: false }
bigInt(-15).toArray(1) // { value: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], isNegative: true }
bigInt(-15).toArray(-1) // { value: [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0], isNegative: false }
bigInt(0).toArray(0) // { value: [0], isNegative: false }
bigInt(1).toArray(0) // Error: Cannot convert nonzero numbers to base 0.

toJsNumber

bigIntオブジェクトをJSの数値型に変換します。ただし、〜-9007199254740992、9007199254740992〜は精度を失います。

bigInt("18446744073709551616").toJSNumber() // 18446744073709552000

xor

ビット単位のxorを計算します。

bigInt(12).xor(5) // 9
bigInt(12).xor(-5) // -9

静的メソッド

fromArray

配列からbigIntオブジェクトを生成する。第二引数で基数を指定できる。第三引数で正負を選択する。

bigInt.fromArray([1, 2, 3, 4, 5], 10) // 12345
bigInt.fromArray([1, 0, 0], 2, true) // -4

gcd

最大公約数の計算

bigInt.gcd(42,56) // 14

isInstance

bigIntmオブジェクトかの判定

bigInt.isInstance(bigInt(14)) // true
bigInt.isInstance(14) // false

lcm

最小公倍数の計算

bigInt.lcm(21, 6) // 42

max

最大値の計算

bigInt.max(77, 432) // 432

min

最小値の計算

bigInt.min(77, 432) // 77

randBetween

乱数の生成

モジュールの利用

タグ

npm

npm install big-integer

ワンライナー

var bigInt=function(undefined){"use strict";var BASE=1e7,LOG_BASE=7,MAX_INT=9007199254740992,MAX_INT_ARR=smallToArray(MAX_INT),LOG_MAX_INT=Math.log(MAX_INT);function Integer(v,radix){if(typeof v==="undefined")return Integer[0];if(typeof radix!=="undefined")return+radix===10?parseValue(v):parseBase(v,radix);return parseValue(v)}function BigInteger(value,sign){this.value=value;this.sign=sign;this.isSmall=false}BigInteger.prototype=Object.create(Integer.prototype);function SmallInteger(value){this.value=value;this.sign=value<0;this.isSmall=true}SmallInteger.prototype=Object.create(Integer.prototype);function isPrecise(n){return-MAX_INT0)return Math.floor(n);return Math.ceil(n)}function add(a,b){var l_a=a.length,l_b=b.length,r=new Array(l_a),carry=0,base=BASE,sum,i;for(i=0;i=base?1:0;r[i]=sum-carry*base}while(i0)r.push(carry);return r}function addAny(a,b){if(a.length>=b.length)return add(a,b);return add(b,a)}function addSmall(a,carry){var l=a.length,r=new Array(l),base=BASE,sum,i;for(i=0;i0){r[i++]=carry%base;carry=Math.floor(carry/base)}return r}BigInteger.prototype.add=function(v){var n=parseValue(v);if(this.sign!==n.sign){return this.subtract(n.negate())}var a=this.value,b=n.value;if(n.isSmall){return new BigInteger(addSmall(a,Math.abs(b)),this.sign)}return new BigInteger(addAny(a,b),this.sign)};BigInteger.prototype.plus=BigInteger.prototype.add;SmallInteger.prototype.add=function(v){var n=parseValue(v);var a=this.value;if(a<0!==n.sign){return this.subtract(n.negate())}var b=n.value;if(n.isSmall){if(isPrecise(a+b))return new SmallInteger(a+b);b=smallToArray(Math.abs(b))}return new BigInteger(addSmall(b,Math.abs(a)),a<0)};SmallInteger.prototype.plus=SmallInteger.prototype.add;function subtract(a,b){var a_l=a.length,b_l=b.length,r=new Array(a_l),borrow=0,base=BASE,i,difference;for(i=0;i=0){value=subtract(a,b)}else{value=subtract(b,a);sign=!sign}value=arrayToSmall(value);if(typeof value==="number"){if(sign)value=-value;return new SmallInteger(value)}return new BigInteger(value,sign)}function subtractSmall(a,b,sign){var l=a.length,r=new Array(l),carry=-b,base=BASE,i,difference;for(i=0;i=0)};SmallInteger.prototype.minus=SmallInteger.prototype.subtract;BigInteger.prototype.negate=function(){return new BigInteger(this.value,!this.sign)};SmallInteger.prototype.negate=function(){var sign=this.sign;var small=new SmallInteger(-this.value);small.sign=!sign;return small};BigInteger.prototype.abs=function(){return new BigInteger(this.value,false)};SmallInteger.prototype.abs=function(){return new SmallInteger(Math.abs(this.value))};function multiplyLong(a,b){var a_l=a.length,b_l=b.length,l=a_l+b_l,r=createArray(l),base=BASE,product,carry,i,a_i,b_j;for(i=0;i0){r[i++]=carry%base;carry=Math.floor(carry/base)}return r}function shiftLeft(x,n){var r=[];while(n-- >0)r.push(0);return r.concat(x)}function multiplyKaratsuba(x,y){var n=Math.max(x.length,y.length);if(n<=30)return multiplyLong(x,y);n=Math.ceil(n/2);var b=x.slice(n),a=x.slice(0,n),d=y.slice(n),c=y.slice(0,n);var ac=multiplyKaratsuba(a,c),bd=multiplyKaratsuba(b,d),abcd=multiplyKaratsuba(addAny(a,b),addAny(c,d));var product=addAny(addAny(ac,shiftLeft(subtract(subtract(abcd,ac),bd),n)),shiftLeft(bd,2*n));trim(product);return product}function useKaratsuba(l1,l2){return-.012*l1-.012*l2+15e-6*l1*l2>0}BigInteger.prototype.multiply=function(v){var n=parseValue(v),a=this.value,b=n.value,sign=this.sign!==n.sign,abs;if(n.isSmall){if(b===0)return Integer[0];if(b===1)return this;if(b===-1)return this.negate();abs=Math.abs(b);if(abs=0;shift--){quotientDigit=base-1;if(remainder[shift+b_l]!==divisorMostSignificantDigit){quotientDigit=Math.floor((remainder[shift+b_l]*base+remainder[shift+b_l-1])/divisorMostSignificantDigit)}carry=0;borrow=0;l=divisor.length;for(i=0;ib_l){highx=(highx+1)*base}guess=Math.ceil(highx/highy);do{check=multiplySmall(b,guess);if(compareAbs(check,part)<=0)break;guess--}while(guess);result.push(guess);part=subtract(part,check)}result.reverse();return[arrayToSmall(result),arrayToSmall(part)]}function divModSmall(value,lambda){var length=value.length,quotient=createArray(length),base=BASE,i,q,remainder,divisor;remainder=0;for(i=length-1;i>=0;--i){divisor=remainder*base+value[i];q=truncate(divisor/lambda);remainder=divisor-q*lambda;quotient[i]=q|0}return[quotient,remainder|0]}function divModAny(self,v){var value,n=parseValue(v);var a=self.value,b=n.value;var quotient;if(b===0)throw new Error("Cannot divide by zero");if(self.isSmall){if(n.isSmall){return[new SmallInteger(truncate(a/b)),new SmallInteger(a%b)]}return[Integer[0],self]}if(n.isSmall){if(b===1)return[self,Integer[0]];if(b==-1)return[self.negate(),Integer[0]];var abs=Math.abs(b);if(absb.length?1:-1}for(var i=a.length-1;i>=0;i--){if(a[i]!==b[i])return a[i]>b[i]?1:-1}return 0}BigInteger.prototype.compareAbs=function(v){var n=parseValue(v),a=this.value,b=n.value;if(n.isSmall)return 1;return compareAbs(a,b)};SmallInteger.prototype.compareAbs=function(v){var n=parseValue(v),a=Math.abs(this.value),b=n.value;if(n.isSmall){b=Math.abs(b);return a===b?0:a>b?1:-1}return-1};BigInteger.prototype.compare=function(v){if(v===Infinity){return-1}if(v===-Infinity){return 1}var n=parseValue(v),a=this.value,b=n.value;if(this.sign!==n.sign){return n.sign?1:-1}if(n.isSmall){return this.sign?-1:1}return compareAbs(a,b)*(this.sign?-1:1)};BigInteger.prototype.compareTo=BigInteger.prototype.compare;SmallInteger.prototype.compare=function(v){if(v===Infinity){return-1}if(v===-Infinity){return 1}var n=parseValue(v),a=this.value,b=n.value;if(n.isSmall){return a==b?0:a>b?1:-1}if(a<0!==n.sign){return a<0?-1:1}return a<0?1:-1};SmallInteger.prototype.compareTo=SmallInteger.prototype.compare;BigInteger.prototype.equals=function(v){return this.compare(v)===0};SmallInteger.prototype.eq=SmallInteger.prototype.equals=BigInteger.prototype.eq=BigInteger.prototype.equals;BigInteger.prototype.notEquals=function(v){return this.compare(v)!==0};SmallInteger.prototype.neq=SmallInteger.prototype.notEquals=BigInteger.prototype.neq=BigInteger.prototype.notEquals;BigInteger.prototype.greater=function(v){return this.compare(v)>0};SmallInteger.prototype.gt=SmallInteger.prototype.greater=BigInteger.prototype.gt=BigInteger.prototype.greater;BigInteger.prototype.lesser=function(v){return this.compare(v)<0};SmallInteger.prototype.lt=SmallInteger.prototype.lesser=BigInteger.prototype.lt=BigInteger.prototype.lesser;BigInteger.prototype.greaterOrEquals=function(v){return this.compare(v)>=0};SmallInteger.prototype.geq=SmallInteger.prototype.greaterOrEquals=BigInteger.prototype.geq=BigInteger.prototype.greaterOrEquals;BigInteger.prototype.lesserOrEquals=function(v){return this.compare(v)<=0};SmallInteger.prototype.leq=SmallInteger.prototype.lesserOrEquals=BigInteger.prototype.leq=BigInteger.prototype.lesserOrEquals;BigInteger.prototype.isEven=function(){return(this.value[0]&1)===0};SmallInteger.prototype.isEven=function(){return(this.value&1)===0};BigInteger.prototype.isOdd=function(){return(this.value[0]&1)===1};SmallInteger.prototype.isOdd=function(){return(this.value&1)===1};BigInteger.prototype.isPositive=function(){return!this.sign};SmallInteger.prototype.isPositive=function(){return this.value>0};BigInteger.prototype.isNegative=function(){return this.sign};SmallInteger.prototype.isNegative=function(){return this.value<0};BigInteger.prototype.isUnit=function(){return false};SmallInteger.prototype.isUnit=function(){return Math.abs(this.value)===1};BigInteger.prototype.isZero=function(){return false};SmallInteger.prototype.isZero=function(){return this.value===0};BigInteger.prototype.isDivisibleBy=function(v){var n=parseValue(v);var value=n.value;if(value===0)return false;if(value===1)return true;if(value===2)return this.isEven();return this.mod(n).equals(Integer[0])};SmallInteger.prototype.isDivisibleBy=BigInteger.prototype.isDivisibleBy;function isBasicPrime(v){var n=v.abs();if(n.isUnit())return false;if(n.equals(2)||n.equals(3)||n.equals(5))return true;if(n.isEven()||n.isDivisibleBy(3)||n.isDivisibleBy(5))return false;if(n.lesser(25))return true}BigInteger.prototype.isPrime=function(){var isPrime=isBasicPrime(this);if(isPrime!==undefined)return isPrime;var n=this.abs(),nPrev=n.prev();var a=[2,3,5,7,11,13,17,19],b=nPrev,d,t,i,x;while(b.isEven())b=b.divide(2);for(i=0;i-MAX_INT)return new SmallInteger(value-1);return new BigInteger(MAX_INT_ARR,true)};var powersOfTwo=[1];while(2*powersOfTwo[powersOfTwo.length-1]<=BASE)powersOfTwo.push(2*powersOfTwo[powersOfTwo.length-1]);var powers2Length=powersOfTwo.length,highestPower2=powersOfTwo[powers2Length-1];function shift_isSmall(n){return(typeof n==="number"||typeof n==="string")&&+Math.abs(n)<=BASE||n instanceof BigInteger&&n.value.length<=1}BigInteger.prototype.shiftLeft=function(n){if(!shift_isSmall(n)){throw new Error(String(n)+" is too large for shifting.")}n=+n;if(n<0)return this.shiftRight(-n);var result=this;if(result.isZero())return result;while(n>=powers2Length){result=result.multiply(highestPower2);n-=powers2Length-1}return result.multiply(powersOfTwo[n])};SmallInteger.prototype.shiftLeft=BigInteger.prototype.shiftLeft;BigInteger.prototype.shiftRight=function(n){var remQuo;if(!shift_isSmall(n)){throw new Error(String(n)+" is too large for shifting.")}n=+n;if(n<0)return this.shiftLeft(-n);var result=this;while(n>=powers2Length){if(result.isZero()||result.isNegative()&&result.isUnit())return result;remQuo=divModAny(result,highestPower2);result=remQuo[1].isNegative()?remQuo[0].prev():remQuo[0];n-=powers2Length-1}remQuo=divModAny(result,powersOfTwo[n]);return remQuo[1].isNegative()?remQuo[0].prev():remQuo[0]};SmallInteger.prototype.shiftRight=BigInteger.prototype.shiftRight;function bitwise(x,y,fn){y=parseValue(y);var xSign=x.isNegative(),ySign=y.isNegative();var xRem=xSign?x.not():x,yRem=ySign?y.not():y;var xDigit=0,yDigit=0;var xDivMod=null,yDivMod=null;var result=[];while(!xRem.isZero()||!yRem.isZero()){xDivMod=divModAny(xRem,highestPower2);xDigit=xDivMod[1].toJSNumber();if(xSign){xDigit=highestPower2-1-xDigit}yDivMod=divModAny(yRem,highestPower2);yDigit=yDivMod[1].toJSNumber();if(ySign){yDigit=highestPower2-1-yDigit}xRem=xDivMod[0];yRem=yDivMod[0];result.push(fn(xDigit,yDigit))}var sum=fn(xSign?1:0,ySign?1:0)!==0?bigInt(-1):bigInt(0);for(var i=result.length-1;i>=0;i-=1){sum=sum.multiply(highestPower2).add(bigInt(result[i]))}return sum}BigInteger.prototype.not=function(){return this.negate().prev()};SmallInteger.prototype.not=BigInteger.prototype.not;BigInteger.prototype.and=function(n){return bitwise(this,n,function(a,b){return a&b})};SmallInteger.prototype.and=BigInteger.prototype.and;BigInteger.prototype.or=function(n){return bitwise(this,n,function(a,b){return a|b})};SmallInteger.prototype.or=BigInteger.prototype.or;BigInteger.prototype.xor=function(n){return bitwise(this,n,function(a,b){return a^b})};SmallInteger.prototype.xor=BigInteger.prototype.xor;var LOBMASK_I=1<<30,LOBMASK_BI=(BASE&-BASE)*(BASE&-BASE)|LOBMASK_I;function roughLOB(n){var v=n.value,x=typeof v==="number"?v|LOBMASK_I:v[0]+v[1]*BASE|LOBMASK_BI;return x&-x}function integerLogarithm(value,base){if(base.compareTo(value)<=0){var tmp=integerLogarithm(value,base.square(base));var p=tmp.p;var e=tmp.e;var t=p.multiply(base);return t.compareTo(value)<=0?{p:t,e:e*2+1}:{p:p,e:e*2}}return{p:bigInt(1),e:0}}BigInteger.prototype.bitLength=function(){var n=this;if(n.compareTo(bigInt(0))<0){n=n.negate().subtract(bigInt(1))}if(n.compareTo(bigInt(0))===0){return bigInt(0)}return bigInt(integerLogarithm(n,bigInt(2)).e).add(bigInt(1))};SmallInteger.prototype.bitLength=BigInteger.prototype.bitLength;function max(a,b){a=parseValue(a);b=parseValue(b);return a.greater(b)?a:b}function min(a,b){a=parseValue(a);b=parseValue(b);return a.lesser(b)?a:b}function gcd(a,b){a=parseValue(a).abs();b=parseValue(b).abs();if(a.equals(b))return a;if(a.isZero())return b;if(b.isZero())return a;var c=Integer[1],d,t;while(a.isEven()&&b.isEven()){d=Math.min(roughLOB(a),roughLOB(b));a=a.divide(d);b=b.divide(d);c=c.multiply(d)}while(a.isEven()){a=a.divide(roughLOB(a))}do{while(b.isEven()){b=b.divide(roughLOB(b))}if(a.greater(b)){t=b;b=a;a=t}b=b.subtract(a)}while(!b.isZero());return c.isUnit()?a:a.multiply(c)}function lcm(a,b){a=parseValue(a).abs();b=parseValue(b).abs();return a.divide(gcd(a,b)).multiply(b)}function randBetween(a,b){a=parseValue(a);b=parseValue(b);var low=min(a,b),high=max(a,b);var range=high.subtract(low).add(1);if(range.isSmall)return low.add(Math.floor(Math.random()*range));var length=range.value.length-1;var result=[],restricted=true;for(var i=length;i>=0;i--){var top=restricted?range.value[i]:BASE;var digit=truncate(Math.random()*top);result.unshift(digit);if(digit=absBase){if(c==="1"&&absBase===1)continue;throw new Error(c+" is not a valid digit in base "+base+".")}else if(c.charCodeAt(0)-87>=absBase){throw new Error(c+" is not a valid digit in base "+base+".")}}}if(2<=base&&base<=36){if(length<=LOG_MAX_INT/Math.log(base)){var result=parseInt(text,base);if(isNaN(result)){throw new Error(c+" is not a valid digit in base "+base+".")}return new SmallInteger(parseInt(text,base))}}base=parseValue(base);var digits=[];var isNegative=text[0]==="-";for(i=isNegative?1:0;i");digits.push(parseValue(text.slice(start+1,i)))}else throw new Error(c+" is not a valid character")}return parseBaseFromArray(digits,base,isNegative)};function parseBaseFromArray(digits,base,isNegative){var val=Integer[0],pow=Integer[1],i;for(i=digits.length-1;i>=0;i--){val=val.add(digits[i].times(pow));pow=pow.times(base)}return isNegative?val.negate():val}function stringify(digit){if(digit<=35){return"0123456789abcdefghijklmnopqrstuvwxyz".charAt(digit)}return"<"+digit+">"}function toBase(n,base){base=bigInt(base);if(base.isZero()){if(n.isZero())return{value:[0],isNegative:false};throw new Error("Cannot convert nonzero numbers to base 0.")}if(base.equals(-1)){if(n.isZero())return{value:[0],isNegative:false};if(n.isNegative())return{value:[].concat.apply([],Array.apply(null,Array(-n)).map(Array.prototype.valueOf,[1,0])),isNegative:false};var arr=Array.apply(null,Array(+n-1)).map(Array.prototype.valueOf,[0,1]);arr.unshift([1]);return{value:[].concat.apply([],arr),isNegative:false}}var neg=false;if(n.isNegative()&&base.isPositive()){neg=true;n=n.abs()}if(base.equals(1)){if(n.isZero())return{value:[0],isNegative:false};return{value:Array.apply(null,Array(+n)).map(Number.prototype.valueOf,1),isNegative:neg}}var out=[];var left=n,divmod;while(left.isNegative()||left.compareAbs(base)>=0){divmod=left.divmod(base);left=divmod.quotient;var digit=divmod.remainder;if(digit.isNegative()){digit=base.minus(digit).abs();left=left.next()}out.push(digit.toJSNumber())}out.push(left.toJSNumber());return{value:out.reverse(),isNegative:neg}}function toBaseString(n,base){var arr=toBase(n,base);return(arr.isNegative?"-":"")+arr.value.map(stringify).join("")}BigInteger.prototype.toArray=function(radix){return toBase(this,radix)};SmallInteger.prototype.toArray=function(radix){return toBase(this,radix)};BigInteger.prototype.toString=function(radix){if(radix===undefined)radix=10;if(radix!==10)return toBaseString(this,radix);var v=this.value,l=v.length,str=String(v[--l]),zeros="0000000",digit;while(--l>=0){digit=String(v[l]);str+=zeros.slice(digit.length)+digit}var sign=this.sign?"-":"";return sign+str};SmallInteger.prototype.toString=function(radix){if(radix===undefined)radix=10;if(radix!=10)return toBaseString(this,radix);return String(this.value)};BigInteger.prototype.toJSON=SmallInteger.prototype.toJSON=function(){return this.toString()};BigInteger.prototype.valueOf=function(){return parseInt(this.toString(),10)};BigInteger.prototype.toJSNumber=BigInteger.prototype.valueOf;SmallInteger.prototype.valueOf=function(){return this.value};SmallInteger.prototype.toJSNumber=SmallInteger.prototype.valueOf;function parseStringValue(v){if(isPrecise(+v)){var x=+v;if(x===truncate(x))return new SmallInteger(x);throw new Error("Invalid integer: "+v)}var sign=v[0]==="-";if(sign)v=v.slice(1);var split=v.split(/e/i);if(split.length>2)throw new Error("Invalid integer: "+split.join("e"));if(split.length===2){var exp=split[1];if(exp[0]==="+")exp=exp.slice(1);exp=+exp;if(exp!==truncate(exp)||!isPrecise(exp))throw new Error("Invalid integer: "+exp+" is not a valid exponent.");var text=split[0];var decimalPlace=text.indexOf(".");if(decimalPlace>=0){exp-=text.length-decimalPlace-1;text=text.slice(0,decimalPlace)+text.slice(decimalPlace+1)}if(exp<0)throw new Error("Cannot include negative exponent part for integers");text+=new Array(exp+1).join("0");v=text}var isValid=/^([0-9][0-9]*)$/.test(v);if(!isValid)throw new Error("Invalid integer: "+v);var r=[],max=v.length,l=LOG_BASE,min=max-l;while(max>0){r.push(+v.slice(min,max));min-=l;if(min<0)min=0;max-=l}trim(r);return new BigInteger(r,sign)}function parseNumberValue(v){if(isPrecise(v)){if(v!==truncate(v))throw new Error(v+" is not an integer.");return new SmallInteger(v)}return parseStringValue(v.toString())}function parseValue(v){if(typeof v==="number"){return parseNumberValue(v)}if(typeof v==="string"){return parseStringValue(v)}return v}for(var i=0;i<1e3;i++){Integer[i]=new SmallInteger(i);if(i>0)Integer[-i]=new SmallInteger(-i)}Integer.one=Integer[1];Integer.zero=Integer[0];Integer.minusOne=Integer[-1];Integer.max=max;Integer.min=min;Integer.gcd=gcd;Integer.lcm=lcm;Integer.isInstance=function(x){return x instanceof BigInteger||x instanceof SmallInteger};Integer.randBetween=randBetween;Integer.fromArray=function(digits,base,isNegative){return parseBaseFromArray(digits.map(parseValue),parseValue(base||10),isNegative)};return Integer}();
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