lkarch.org/tools/mathisfun/www.mathsisfun.com/numbers/images/decimal.js

;(function(globalScope){'use strict';var EXP_LIMIT=9e15,MAX_DIGITS=1e9,NUMERALS='0123456789abcdef',LN10='2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058',PI='3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789',DEFAULTS={precision:20,rounding:4,modulo:1,toExpNeg:-7,toExpPos:21,minE:-EXP_LIMIT,maxE:EXP_LIMIT,crypto:false},Decimal,inexact,noConflict,quadrant,external=true,decimalError='[DecimalError] ',invalidArgument=decimalError+'Invalid argument: ',precisionLimitExceeded=decimalError+'Precision limit exceeded',cryptoUnavailable=decimalError+'crypto unavailable',mathfloor=Math.floor,mathpow=Math.pow,isBinary=/^0b([01]+(\.[01]*)?|\.[01]+)(p[+-]?\d+)?$/i,isHex=/^0x([0-9a-f]+(\.[0-9a-f]*)?|\.[0-9a-f]+)(p[+-]?\d+)?$/i,isOctal=/^0o([0-7]+(\.[0-7]*)?|\.[0-7]+)(p[+-]?\d+)?$/i,isDecimal=/^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,BASE=1e7,LOG_BASE=7,MAX_SAFE_INTEGER=9007199254740991,LN10_PRECISION=LN10.length-1,PI_PRECISION=PI.length-1,P={name:'[object Decimal]'};P.absoluteValue=P.abs=function(){var x=new this.constructor(this);if(x.s<0)x.s=1;return finalise(x);};P.ceil=function(){return finalise(new this.constructor(this),this.e+1,2);};P.comparedTo=P.cmp=function(y){var i,j,xdL,ydL,x=this,xd=x.d,yd=(y=new x.constructor(y)).d,xs=x.s,ys=y.s;if(!xd||!yd){return!xs||!ys?NaN:xs!==ys?xs:xd===yd?0:!xd^xs<0?1:-1;}
if(!xd[0]||!yd[0])return xd[0]?xs:yd[0]?-ys:0;if(xs!==ys)return xs;if(x.e!==y.e)return x.e>y.e^xs<0?1:-1;xdL=xd.length;ydL=yd.length;for(i=0,j=xdL<ydL?xdL:ydL;i<j;++i){if(xd[i]!==yd[i])return xd[i]>yd[i]^xs<0?1:-1;}
return xdL===ydL?0:xdL>ydL^xs<0?1:-1;};P.cosine=P.cos=function(){var pr,rm,x=this,Ctor=x.constructor;if(!x.d)return new Ctor(NaN);if(!x.d[0])return new Ctor(1);pr=Ctor.precision;rm=Ctor.rounding;Ctor.precision=pr+Math.max(x.e,x.sd())+LOG_BASE;Ctor.rounding=1;x=cosine(Ctor,toLessThanHalfPi(Ctor,x));Ctor.precision=pr;Ctor.rounding=rm;return finalise(quadrant==2||quadrant==3?x.neg():x,pr,rm,true);};P.cubeRoot=P.cbrt=function(){var e,m,n,r,rep,s,sd,t,t3,t3plusx,x=this,Ctor=x.constructor;if(!x.isFinite()||x.isZero())return new Ctor(x);external=false;s=x.s*mathpow(x.s*x,1/3);if(!s||Math.abs(s)==1/0){n=digitsToString(x.d);e=x.e;if(s=(e-n.length+1)%3)n+=(s==1||s==-2?'0':'00');s=mathpow(n,1/3);e=mathfloor((e+1)/3)-(e%3==(e<0?-1:2));if(s==1/0){n='5e'+e;}else{n=s.toExponential();n=n.slice(0,n.indexOf('e')+1)+e;}
r=new Ctor(n);r.s=x.s;}else{r=new Ctor(s.toString());}
sd=(e=Ctor.precision)+3;for(;;){t=r;t3=t.times(t).times(t);t3plusx=t3.plus(x);r=divide(t3plusx.plus(x).times(t),t3plusx.plus(t3),sd+2,1);if(digitsToString(t.d).slice(0,sd)===(n=digitsToString(r.d)).slice(0,sd)){n=n.slice(sd-3,sd+1);if(n=='9999'||!rep&&n=='4999'){if(!rep){finalise(t,e+1,0);if(t.times(t).times(t).eq(x)){r=t;break;}}
sd+=4;rep=1;}else{if(!+n||!+n.slice(1)&&n.charAt(0)=='5'){finalise(r,e+1,1);m=!r.times(r).times(r).eq(x);}
break;}}}
external=true;return finalise(r,e,Ctor.rounding,m);};P.decimalPlaces=P.dp=function(){var w,d=this.d,n=NaN;if(d){w=d.length-1;n=(w-mathfloor(this.e/LOG_BASE))*LOG_BASE;w=d[w];if(w)for(;w%10==0;w/=10)n--;if(n<0)n=0;}
return n;};P.dividedBy=P.div=function(y){return divide(this,new this.constructor(y));};P.dividedToIntegerBy=P.divToInt=function(y){var x=this,Ctor=x.constructor;return finalise(divide(x,new Ctor(y),0,1,1),Ctor.precision,Ctor.rounding);};P.equals=P.eq=function(y){return this.cmp(y)===0;};P.floor=function(){return finalise(new this.constructor(this),this.e+1,3);};P.greaterThan=P.gt=function(y){return this.cmp(y)>0;};P.greaterThanOrEqualTo=P.gte=function(y){var k=this.cmp(y);return k==1||k===0;};P.hyperbolicCosine=P.cosh=function(){var k,n,pr,rm,len,x=this,Ctor=x.constructor,one=new Ctor(1);if(!x.isFinite())return new Ctor(x.s?1/0:NaN);if(x.isZero())return one;pr=Ctor.precision;rm=Ctor.rounding;Ctor.precision=pr+Math.max(x.e,x.sd())+4;Ctor.rounding=1;len=x.d.length;if(len<32){k=Math.ceil(len/3);n=(1/tinyPow(4,k)).toString();}else{k=16;n='2.3283064365386962890625e-10';}
x=taylorSeries(Ctor,1,x.times(n),new Ctor(1),true);var cosh2_x,i=k,d8=new Ctor(8);for(;i--;){cosh2_x=x.times(x);x=one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8))));}
return finalise(x,Ctor.precision=pr,Ctor.rounding=rm,true);};P.hyperbolicSine=P.sinh=function(){var k,pr,rm,len,x=this,Ctor=x.constructor;if(!x.isFinite()||x.isZero())return new Ctor(x);pr=Ctor.precision;rm=Ctor.rounding;Ctor.precision=pr+Math.max(x.e,x.sd())+4;Ctor.rounding=1;len=x.d.length;if(len<3){x=taylorSeries(Ctor,2,x,x,true);}else{k=1.4*Math.sqrt(len);k=k>16?16:k|0;x=x.times(1/tinyPow(5,k));x=taylorSeries(Ctor,2,x,x,true);var sinh2_x,d5=new Ctor(5),d16=new Ctor(16),d20=new Ctor(20);for(;k--;){sinh2_x=x.times(x);x=x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20))));}}
Ctor.precision=pr;Ctor.rounding=rm;return finalise(x,pr,rm,true);};P.hyperbolicTangent=P.tanh=function(){var pr,rm,x=this,Ctor=x.constructor;if(!x.isFinite())return new Ctor(x.s);if(x.isZero())return new Ctor(x);pr=Ctor.precision;rm=Ctor.rounding;Ctor.precision=pr+7;Ctor.rounding=1;return divide(x.sinh(),x.cosh(),Ctor.precision=pr,Ctor.rounding=rm);};P.inverseCosine=P.acos=function(){var halfPi,x=this,Ctor=x.constructor,k=x.abs().cmp(1),pr=Ctor.precision,rm=Ctor.rounding;if(k!==-1){return k===0?x.isNeg()?getPi(Ctor,pr,rm):new Ctor(0):new Ctor(NaN);}
if(x.isZero())return getPi(Ctor,pr+4,rm).times(0.5);Ctor.precision=pr+6;Ctor.rounding=1;x=x.asin();halfPi=getPi(Ctor,pr+4,rm).times(0.5);Ctor.precision=pr;Ctor.rounding=rm;return halfPi.minus(x);};P.inverseHyperbolicCosine=P.acosh=function(){var pr,rm,x=this,Ctor=x.constructor;if(x.lte(1))return new Ctor(x.eq(1)?0:NaN);if(!x.isFinite())return new Ctor(x);pr=Ctor.precision;rm=Ctor.rounding;Ctor.precision=pr+Math.max(Math.abs(x.e),x.sd())+4;Ctor.rounding=1;external=false;x=x.times(x).minus(1).sqrt().plus(x);external=true;Ctor.precision=pr;Ctor.rounding=rm;return x.ln();};P.inverseHyperbolicSine=P.asinh=function(){var pr,rm,x=this,Ctor=x.constructor;if(!x.isFinite()||x.isZero())return new Ctor(x);pr=Ctor.precision;rm=Ctor.rounding;Ctor.precision=pr+2*Math.max(Math.abs(x.e),x.sd())+6;Ctor.rounding=1;external=false;x=x.times(x).plus(1).sqrt().plus(x);external=true;Ctor.precision=pr;Ctor.rounding=rm;return x.ln();};P.inverseHyperbolicTangent=P.atanh=function(){var pr,rm,wpr,xsd,x=this,Ctor=x.constructor;if(!x.isFinite())return new Ctor(NaN);if(x.e>=0)return new Ctor(x.abs().eq(1)?x.s/0:x.isZero()?x:NaN);pr=Ctor.precision;rm=Ctor.rounding;xsd=x.sd();if(Math.max(xsd,pr)<2*-x.e-1)return finalise(new Ctor(x),pr,rm,true);Ctor.precision=wpr=xsd-x.e;x=divide(x.plus(1),new Ctor(1).minus(x),wpr+pr,1);Ctor.precision=pr+4;Ctor.rounding=1;x=x.ln();Ctor.precision=pr;Ctor.rounding=rm;return x.times(0.5);};P.inverseSine=P.asin=function(){var halfPi,k,pr,rm,x=this,Ctor=x.constructor;if(x.isZero())return new Ctor(x);k=x.abs().cmp(1);pr=Ctor.precision;rm=Ctor.rounding;if(k!==-1){if(k===0){halfPi=getPi(Ctor,pr+4,rm).times(0.5);halfPi.s=x.s;return halfPi;}
return new Ctor(NaN);}
Ctor.precision=pr+6;Ctor.rounding=1;x=x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan();Ctor.precision=pr;Ctor.rounding=rm;return x.times(2);};P.inverseTangent=P.atan=function(){var i,j,k,n,px,t,r,wpr,x2,x=this,Ctor=x.constructor,pr=Ctor.precision,rm=Ctor.rounding;if(!x.isFinite()){if(!x.s)return new Ctor(NaN);if(pr+4<=PI_PRECISION){r=getPi(Ctor,pr+4,rm).times(0.5);r.s=x.s;return r;}}else if(x.isZero()){return new Ctor(x);}else if(x.abs().eq(1)&&pr+4<=PI_PRECISION){r=getPi(Ctor,pr+4,rm).times(0.25);r.s=x.s;return r;}
Ctor.precision=wpr=pr+10;Ctor.rounding=1;k=Math.min(28,wpr/LOG_BASE+2|0);for(i=k;i;--i)x=x.div(x.times(x).plus(1).sqrt().plus(1));external=false;j=Math.ceil(wpr/LOG_BASE);n=1;x2=x.times(x);r=new Ctor(x);px=x;for(;i!==-1;){px=px.times(x2);t=r.minus(px.div(n+=2));px=px.times(x2);r=t.plus(px.div(n+=2));if(r.d[j]!==void 0)for(i=j;r.d[i]===t.d[i]&&i--;);}
if(k)r=r.times(2<<(k-1));external=true;return finalise(r,Ctor.precision=pr,Ctor.rounding=rm,true);};P.isFinite=function(){return!!this.d;};P.isInteger=P.isInt=function(){return!!this.d&&mathfloor(this.e/LOG_BASE)>this.d.length-2;};P.isNaN=function(){return!this.s;};P.isNegative=P.isNeg=function(){return this.s<0;};P.isPositive=P.isPos=function(){return this.s>0;};P.isZero=function(){return!!this.d&&this.d[0]===0;};P.lessThan=P.lt=function(y){return this.cmp(y)<0;};P.lessThanOrEqualTo=P.lte=function(y){return this.cmp(y)<1;};P.logarithm=P.log=function(base){var isBase10,d,denominator,k,inf,num,sd,r,arg=this,Ctor=arg.constructor,pr=Ctor.precision,rm=Ctor.rounding,guard=5;if(base==null){base=new Ctor(10);isBase10=true;}else{base=new Ctor(base);d=base.d;if(base.s<0||!d||!d[0]||base.eq(1))return new Ctor(NaN);isBase10=base.eq(10);}
d=arg.d;if(arg.s<0||!d||!d[0]||arg.eq(1)){return new Ctor(d&&!d[0]?-1/0:arg.s!=1?NaN:d?0:1/0);}
if(isBase10){if(d.length>1){inf=true;}else{for(k=d[0];k%10===0;)k/=10;inf=k!==1;}}
external=false;sd=pr+guard;num=naturalLogarithm(arg,sd);denominator=isBase10?getLn10(Ctor,sd+10):naturalLogarithm(base,sd);r=divide(num,denominator,sd,1);if(checkRoundingDigits(r.d,k=pr,rm)){do{sd+=10;num=naturalLogarithm(arg,sd);denominator=isBase10?getLn10(Ctor,sd+10):naturalLogarithm(base,sd);r=divide(num,denominator,sd,1);if(!inf){if(+digitsToString(r.d).slice(k+1,k+15)+1==1e14){r=finalise(r,pr+1,0);}
break;}}while(checkRoundingDigits(r.d,k+=10,rm));}
external=true;return finalise(r,pr,rm);};P.minus=P.sub=function(y){var d,e,i,j,k,len,pr,rm,xd,xe,xLTy,yd,x=this,Ctor=x.constructor;y=new Ctor(y);if(!x.d||!y.d){if(!x.s||!y.s)y=new Ctor(NaN);else if(x.d)y.s=-y.s;else y=new Ctor(y.d||x.s!==y.s?x:NaN);return y;}
if(x.s!=y.s){y.s=-y.s;return x.plus(y);}
xd=x.d;yd=y.d;pr=Ctor.precision;rm=Ctor.rounding;if(!xd[0]||!yd[0]){if(yd[0])y.s=-y.s;else if(xd[0])y=new Ctor(x);else return new Ctor(rm===3?-0:0);return external?finalise(y,pr,rm):y;}
e=mathfloor(y.e/LOG_BASE);xe=mathfloor(x.e/LOG_BASE);xd=xd.slice();k=xe-e;if(k){xLTy=k<0;if(xLTy){d=xd;k=-k;len=yd.length;}else{d=yd;e=xe;len=xd.length;}
i=Math.max(Math.ceil(pr/LOG_BASE),len)+2;if(k>i){k=i;d.length=1;}
d.reverse();for(i=k;i--;)d.push(0);d.reverse();}else{i=xd.length;len=yd.length;xLTy=i<len;if(xLTy)len=i;for(i=0;i<len;i++){if(xd[i]!=yd[i]){xLTy=xd[i]<yd[i];break;}}
k=0;}
if(xLTy){d=xd;xd=yd;yd=d;y.s=-y.s;}
len=xd.length;for(i=yd.length-len;i>0;--i)xd[len++]=0;for(i=yd.length;i>k;){if(xd[--i]<yd[i]){for(j=i;j&&xd[--j]===0;)xd[j]=BASE-1;--xd[j];xd[i]+=BASE;}
xd[i]-=yd[i];}
for(;xd[--len]===0;)xd.pop();for(;xd[0]===0;xd.shift())--e;if(!xd[0])return new Ctor(rm===3?-0:0);y.d=xd;y.e=getBase10Exponent(xd,e);return external?finalise(y,pr,rm):y;};P.modulo=P.mod=function(y){var q,x=this,Ctor=x.constructor;y=new Ctor(y);if(!x.d||!y.s||y.d&&!y.d[0])return new Ctor(NaN);if(!y.d||x.d&&!x.d[0]){return finalise(new Ctor(x),Ctor.precision,Ctor.rounding);}
external=false;if(Ctor.modulo==9){q=divide(x,y.abs(),0,3,1);q.s*=y.s;}else{q=divide(x,y,0,Ctor.modulo,1);}
q=q.times(y);external=true;return x.minus(q);};P.naturalExponential=P.exp=function(){return naturalExponential(this);};P.naturalLogarithm=P.ln=function(){return naturalLogarithm(this);};P.negated=P.neg=function(){var x=new this.constructor(this);x.s=-x.s;return finalise(x);};P.plus=P.add=function(y){var carry,d,e,i,k,len,pr,rm,xd,yd,x=this,Ctor=x.constructor;y=new Ctor(y);if(!x.d||!y.d){if(!x.s||!y.s)y=new Ctor(NaN);else if(!x.d)y=new Ctor(y.d||x.s===y.s?x:NaN);return y;}
if(x.s!=y.s){y.s=-y.s;return x.minus(y);}
xd=x.d;yd=y.d;pr=Ctor.precision;rm=Ctor.rounding;if(!xd[0]||!yd[0]){if(!yd[0])y=new Ctor(x);return external?finalise(y,pr,rm):y;}
k=mathfloor(x.e/LOG_BASE);e=mathfloor(y.e/LOG_BASE);xd=xd.slice();i=k-e;if(i){if(i<0){d=xd;i=-i;len=yd.length;}else{d=yd;e=k;len=xd.length;}
k=Math.ceil(pr/LOG_BASE);len=k>len?k+1:len+1;if(i>len){i=len;d.length=1;}
d.reverse();for(;i--;)d.push(0);d.reverse();}
len=xd.length;i=yd.length;if(len-i<0){i=len;d=yd;yd=xd;xd=d;}
for(carry=0;i;){carry=(xd[--i]=xd[i]+yd[i]+carry)/BASE|0;xd[i]%=BASE;}
if(carry){xd.unshift(carry);++e;}
for(len=xd.length;xd[--len]==0;)xd.pop();y.d=xd;y.e=getBase10Exponent(xd,e);return external?finalise(y,pr,rm):y;};P.precision=P.sd=function(z){var k,x=this;if(z!==void 0&&z!==!!z&&z!==1&&z!==0)throw Error(invalidArgument+z);if(x.d){k=getPrecision(x.d);if(z&&x.e+1>k)k=x.e+1;}else{k=NaN;}
return k;};P.round=function(){var x=this,Ctor=x.constructor;return finalise(new Ctor(x),x.e+1,Ctor.rounding);};P.sine=P.sin=function(){var pr,rm,x=this,Ctor=x.constructor;if(!x.isFinite())return new Ctor(NaN);if(x.isZero())return new Ctor(x);pr=Ctor.precision;rm=Ctor.rounding;Ctor.precision=pr+Math.max(x.e,x.sd())+LOG_BASE;Ctor.rounding=1;x=sine(Ctor,toLessThanHalfPi(Ctor,x));Ctor.precision=pr;Ctor.rounding=rm;return finalise(quadrant>2?x.neg():x,pr,rm,true);};P.squareRoot=P.sqrt=function(){var m,n,sd,r,rep,t,x=this,d=x.d,e=x.e,s=x.s,Ctor=x.constructor;if(s!==1||!d||!d[0]){return new Ctor(!s||s<0&&(!d||d[0])?NaN:d?x:1/0);}
external=false;s=Math.sqrt(+x);if(s==0||s==1/0){n=digitsToString(d);if((n.length+e)%2==0)n+='0';s=Math.sqrt(n);e=mathfloor((e+1)/2)-(e<0||e%2);if(s==1/0){n='5e'+e;}else{n=s.toExponential();n=n.slice(0,n.indexOf('e')+1)+e;}
r=new Ctor(n);}else{r=new Ctor(s.toString());}
sd=(e=Ctor.precision)+3;for(;;){t=r;r=t.plus(divide(x,t,sd+2,1)).times(0.5);if(digitsToString(t.d).slice(0,sd)===(n=digitsToString(r.d)).slice(0,sd)){n=n.slice(sd-3,sd+1);if(n=='9999'||!rep&&n=='4999'){if(!rep){finalise(t,e+1,0);if(t.times(t).eq(x)){r=t;break;}}
sd+=4;rep=1;}else{if(!+n||!+n.slice(1)&&n.charAt(0)=='5'){finalise(r,e+1,1);m=!r.times(r).eq(x);}
break;}}}
external=true;return finalise(r,e,Ctor.rounding,m);};P.tangent=P.tan=function(){var pr,rm,x=this,Ctor=x.constructor;if(!x.isFinite())return new Ctor(NaN);if(x.isZero())return new Ctor(x);pr=Ctor.precision;rm=Ctor.rounding;Ctor.precision=pr+10;Ctor.rounding=1;x=x.sin();x.s=1;x=divide(x,new Ctor(1).minus(x.times(x)).sqrt(),pr+10,0);Ctor.precision=pr;Ctor.rounding=rm;return finalise(quadrant==2||quadrant==4?x.neg():x,pr,rm,true);};P.times=P.mul=function(y){var carry,e,i,k,r,rL,t,xdL,ydL,x=this,Ctor=x.constructor,xd=x.d,yd=(y=new Ctor(y)).d;y.s*=x.s;if(!xd||!xd[0]||!yd||!yd[0]){return new Ctor(!y.s||xd&&!xd[0]&&!yd||yd&&!yd[0]&&!xd?NaN:!xd||!yd?y.s/0:y.s*0);}
e=mathfloor(x.e/LOG_BASE)+mathfloor(y.e/LOG_BASE);xdL=xd.length;ydL=yd.length;if(xdL<ydL){r=xd;xd=yd;yd=r;rL=xdL;xdL=ydL;ydL=rL;}
r=[];rL=xdL+ydL;for(i=rL;i--;)r.push(0);for(i=ydL;--i>=0;){carry=0;for(k=xdL+i;k>i;){t=r[k]+yd[i]*xd[k-i-1]+carry;r[k--]=t%BASE|0;carry=t/BASE|0;}
r[k]=(r[k]+carry)%BASE|0;}
for(;!r[--rL];)r.pop();if(carry)++e;else r.shift();y.d=r;y.e=getBase10Exponent(r,e);return external?finalise(y,Ctor.precision,Ctor.rounding):y;};P.toBinary=function(sd,rm){return toStringBinary(this,2,sd,rm);};P.toDecimalPlaces=P.toDP=function(dp,rm){var x=this,Ctor=x.constructor;x=new Ctor(x);if(dp===void 0)return x;checkInt32(dp,0,MAX_DIGITS);if(rm===void 0)rm=Ctor.rounding;else checkInt32(rm,0,8);return finalise(x,dp+x.e+1,rm);};P.toExponential=function(dp,rm){var str,x=this,Ctor=x.constructor;if(dp===void 0){str=finiteToString(x,true);}else{checkInt32(dp,0,MAX_DIGITS);if(rm===void 0)rm=Ctor.rounding;else checkInt32(rm,0,8);x=finalise(new Ctor(x),dp+1,rm);str=finiteToString(x,true,dp+1);}
return x.isNeg()&&!x.isZero()?'-'+str:str;};P.toFixed=function(dp,rm){var str,y,x=this,Ctor=x.constructor;if(dp===void 0){str=finiteToString(x);}else{checkInt32(dp,0,MAX_DIGITS);if(rm===void 0)rm=Ctor.rounding;else checkInt32(rm,0,8);y=finalise(new Ctor(x),dp+x.e+1,rm);str=finiteToString(y,false,dp+y.e+1);}
return x.isNeg()&&!x.isZero()?'-'+str:str;};P.toFraction=function(maxD){var d,d0,d1,d2,e,k,n,n0,n1,pr,q,r,x=this,xd=x.d,Ctor=x.constructor;if(!xd)return new Ctor(x);n1=d0=new Ctor(1);d1=n0=new Ctor(0);d=new Ctor(d1);e=d.e=getPrecision(xd)-x.e-1;k=e%LOG_BASE;d.d[0]=mathpow(10,k<0?LOG_BASE+k:k);if(maxD==null){maxD=e>0?d:n1;}else{n=new Ctor(maxD);if(!n.isInt()||n.lt(n1))throw Error(invalidArgument+n);maxD=n.gt(d)?(e>0?d:n1):n;}
external=false;n=new Ctor(digitsToString(xd));pr=Ctor.precision;Ctor.precision=e=xd.length*LOG_BASE*2;for(;;){q=divide(n,d,0,1,1);d2=d0.plus(q.times(d1));if(d2.cmp(maxD)==1)break;d0=d1;d1=d2;d2=n1;n1=n0.plus(q.times(d2));n0=d2;d2=d;d=n.minus(q.times(d2));n=d2;}
d2=divide(maxD.minus(d0),d1,0,1,1);n0=n0.plus(d2.times(n1));d0=d0.plus(d2.times(d1));n0.s=n1.s=x.s;r=divide(n1,d1,e,1).minus(x).abs().cmp(divide(n0,d0,e,1).minus(x).abs())<1?[n1,d1]:[n0,d0];Ctor.precision=pr;external=true;return r;};P.toHexadecimal=P.toHex=function(sd,rm){return toStringBinary(this,16,sd,rm);};P.toNearest=function(y,rm){var x=this,Ctor=x.constructor;x=new Ctor(x);if(y==null){if(!x.d)return x;y=new Ctor(1);rm=Ctor.rounding;}else{y=new Ctor(y);if(rm===void 0){rm=Ctor.rounding;}else{checkInt32(rm,0,8);}
if(!x.d)return y.s?x:y;if(!y.d){if(y.s)y.s=x.s;return y;}}
if(y.d[0]){external=false;x=divide(x,y,0,rm,1).times(y);external=true;finalise(x);}else{y.s=x.s;x=y;}
return x;};P.toNumber=function(){return+this;};P.toOctal=function(sd,rm){return toStringBinary(this,8,sd,rm);};P.toPower=P.pow=function(y){var e,k,pr,r,rm,s,x=this,Ctor=x.constructor,yn=+(y=new Ctor(y));if(!x.d||!y.d||!x.d[0]||!y.d[0])return new Ctor(mathpow(+x,yn));x=new Ctor(x);if(x.eq(1))return x;pr=Ctor.precision;rm=Ctor.rounding;if(y.eq(1))return finalise(x,pr,rm);e=mathfloor(y.e/LOG_BASE);if(e>=y.d.length-1&&(k=yn<0?-yn:yn)<=MAX_SAFE_INTEGER){r=intPow(Ctor,x,k,pr);return y.s<0?new Ctor(1).div(r):finalise(r,pr,rm);}
s=x.s;if(s<0){if(e<y.d.length-1)return new Ctor(NaN);if((y.d[e]&1)==0)s=1;if(x.e==0&&x.d[0]==1&&x.d.length==1){x.s=s;return x;}}
k=mathpow(+x,yn);e=k==0||!isFinite(k)?mathfloor(yn*(Math.log('0.'+digitsToString(x.d))/Math.LN10+x.e+1)):new Ctor(k+'').e;if(e>Ctor.maxE+1||e<Ctor.minE-1)return new Ctor(e>0?s/0:0);external=false;Ctor.rounding=x.s=1;k=Math.min(12,(e+'').length);r=naturalExponential(y.times(naturalLogarithm(x,pr+k)),pr);if(r.d){r=finalise(r,pr+5,1);if(checkRoundingDigits(r.d,pr,rm)){e=pr+10;r=finalise(naturalExponential(y.times(naturalLogarithm(x,e+k)),e),e+5,1);if(+digitsToString(r.d).slice(pr+1,pr+15)+1==1e14){r=finalise(r,pr+1,0);}}}
r.s=s;external=true;Ctor.rounding=rm;return finalise(r,pr,rm);};P.toPrecision=function(sd,rm){var str,x=this,Ctor=x.constructor;if(sd===void 0){str=finiteToString(x,x.e<=Ctor.toExpNeg||x.e>=Ctor.toExpPos);}else{checkInt32(sd,1,MAX_DIGITS);if(rm===void 0)rm=Ctor.rounding;else checkInt32(rm,0,8);x=finalise(new Ctor(x),sd,rm);str=finiteToString(x,sd<=x.e||x.e<=Ctor.toExpNeg,sd);}
return x.isNeg()&&!x.isZero()?'-'+str:str;};P.toSignificantDigits=P.toSD=function(sd,rm){var x=this,Ctor=x.constructor;if(sd===void 0){sd=Ctor.precision;rm=Ctor.rounding;}else{checkInt32(sd,1,MAX_DIGITS);if(rm===void 0)rm=Ctor.rounding;else checkInt32(rm,0,8);}
return finalise(new Ctor(x),sd,rm);};P.toString=function(){var x=this,Ctor=x.constructor,str=finiteToString(x,x.e<=Ctor.toExpNeg||x.e>=Ctor.toExpPos);return x.isNeg()&&!x.isZero()?'-'+str:str;};P.truncated=P.trunc=function(){return finalise(new this.constructor(this),this.e+1,1);};P.valueOf=P.toJSON=function(){var x=this,Ctor=x.constructor,str=finiteToString(x,x.e<=Ctor.toExpNeg||x.e>=Ctor.toExpPos);return x.isNeg()?'-'+str:str;};function digitsToString(d){var i,k,ws,indexOfLastWord=d.length-1,str='',w=d[0];if(indexOfLastWord>0){str+=w;for(i=1;i<indexOfLastWord;i++){ws=d[i]+'';k=LOG_BASE-ws.length;if(k)str+=getZeroString(k);str+=ws;}
w=d[i];ws=w+'';k=LOG_BASE-ws.length;if(k)str+=getZeroString(k);}else if(w===0){return '0';}
for(;w%10===0;)w/=10;return str+w;}
function checkInt32(i,min,max){if(i!==~~i||i<min||i>max){throw Error(invalidArgument+i);}}
function checkRoundingDigits(d,i,rm,repeating){var di,k,r,rd;for(k=d[0];k>=10;k/=10)--i;if(--i<0){i+=LOG_BASE;di=0;}else{di=Math.ceil((i+1)/LOG_BASE);i%=LOG_BASE;}
k=mathpow(10,LOG_BASE-i);rd=d[di]%k|0;if(repeating==null){if(i<3){if(i==0)rd=rd/100|0;else if(i==1)rd=rd/10|0;r=rm<4&&rd==99999||rm>3&&rd==49999||rd==50000||rd==0;}else{r=(rm<4&&rd+1==k||rm>3&&rd+1==k/2)&&(d[di+1]/k/100|0)==mathpow(10,i-2)-1||(rd==k/2||rd==0)&&(d[di+1]/k/100|0)==0;}}else{if(i<4){if(i==0)rd=rd/1000|0;else if(i==1)rd=rd/100|0;else if(i==2)rd=rd/10|0;r=(repeating||rm<4)&&rd==9999||!repeating&&rm>3&&rd==4999;}else{r=((repeating||rm<4)&&rd+1==k||(!repeating&&rm>3)&&rd+1==k/2)&&(d[di+1]/k/1000|0)==mathpow(10,i-3)-1;}}
return r;}
function convertBase(str,baseIn,baseOut){var j,arr=[0],arrL,i=0,strL=str.length;for(;i<strL;){for(arrL=arr.length;arrL--;)arr[arrL]*=baseIn;arr[0]+=NUMERALS.indexOf(str.charAt(i++));for(j=0;j<arr.length;j++){if(arr[j]>baseOut-1){if(arr[j+1]===void 0)arr[j+1]=0;arr[j+1]+=arr[j]/baseOut|0;arr[j]%=baseOut;}}}
return arr.reverse();}
function cosine(Ctor,x){var k,y,len=x.d.length;if(len<32){k=Math.ceil(len/3);y=(1/tinyPow(4,k)).toString();}else{k=16;y='2.3283064365386962890625e-10';}
Ctor.precision+=k;x=taylorSeries(Ctor,1,x.times(y),new Ctor(1));for(var i=k;i--;){var cos2x=x.times(x);x=cos2x.times(cos2x).minus(cos2x).times(8).plus(1);}
Ctor.precision-=k;return x;}
var divide=(function(){function multiplyInteger(x,k,base){var temp,carry=0,i=x.length;for(x=x.slice();i--;){temp=x[i]*k+carry;x[i]=temp%base|0;carry=temp/base|0;}
if(carry)x.unshift(carry);return x;}
function compare(a,b,aL,bL){var i,r;if(aL!=bL){r=aL>bL?1:-1;}else{for(i=r=0;i<aL;i++){if(a[i]!=b[i]){r=a[i]>b[i]?1:-1;break;}}}
return r;}
function subtract(a,b,aL,base){var i=0;for(;aL--;){a[aL]-=i;i=a[aL]<b[aL]?1:0;a[aL]=i*base+a[aL]-b[aL];}
for(;!a[0]&&a.length>1;)a.shift();}
return function(x,y,pr,rm,dp,base){var cmp,e,i,k,logBase,more,prod,prodL,q,qd,rem,remL,rem0,sd,t,xi,xL,yd0,yL,yz,Ctor=x.constructor,sign=x.s==y.s?1:-1,xd=x.d,yd=y.d;if(!xd||!xd[0]||!yd||!yd[0]){return new Ctor(!x.s||!y.s||(xd?yd&&xd[0]==yd[0]:!yd)?NaN:xd&&xd[0]==0||!yd?sign*0:sign/0);}
if(base){logBase=1;e=x.e-y.e;}else{base=BASE;logBase=LOG_BASE;e=mathfloor(x.e/logBase)-mathfloor(y.e/logBase);}
yL=yd.length;xL=xd.length;q=new Ctor(sign);qd=q.d=[];for(i=0;yd[i]==(xd[i]||0);i++);if(yd[i]>(xd[i]||0))e--;if(pr==null){sd=pr=Ctor.precision;rm=Ctor.rounding;}else if(dp){sd=pr+(x.e-y.e)+1;}else{sd=pr;}
if(sd<0){qd.push(1);more=true;}else{sd=sd/logBase+2|0;i=0;if(yL==1){k=0;yd=yd[0];sd++;for(;(i<xL||k)&&sd--;i++){t=k*base+(xd[i]||0);qd[i]=t/yd|0;k=t%yd|0;}
more=k||i<xL;}else{k=base/(yd[0]+1)|0;if(k>1){yd=multiplyInteger(yd,k,base);xd=multiplyInteger(xd,k,base);yL=yd.length;xL=xd.length;}
xi=yL;rem=xd.slice(0,yL);remL=rem.length;for(;remL<yL;)rem[remL++]=0;yz=yd.slice();yz.unshift(0);yd0=yd[0];if(yd[1]>=base/2)++yd0;do{k=0;cmp=compare(yd,rem,yL,remL);if(cmp<0){rem0=rem[0];if(yL!=remL)rem0=rem0*base+(rem[1]||0);k=rem0/yd0|0;if(k>1){if(k>=base)k=base-1;prod=multiplyInteger(yd,k,base);prodL=prod.length;remL=rem.length;cmp=compare(prod,rem,prodL,remL);if(cmp==1){k--;subtract(prod,yL<prodL?yz:yd,prodL,base);}}else{if(k==0)cmp=k=1;prod=yd.slice();}
prodL=prod.length;if(prodL<remL)prod.unshift(0);subtract(rem,prod,remL,base);if(cmp==-1){remL=rem.length;cmp=compare(yd,rem,yL,remL);if(cmp<1){k++;subtract(rem,yL<remL?yz:yd,remL,base);}}
remL=rem.length;}else if(cmp===0){k++;rem=[0];}
qd[i++]=k;if(cmp&&rem[0]){rem[remL++]=xd[xi]||0;}else{rem=[xd[xi]];remL=1;}}while((xi++<xL||rem[0]!==void 0)&&sd--);more=rem[0]!==void 0;}
if(!qd[0])qd.shift();}
if(logBase==1){q.e=e;inexact=more;}else{for(i=1,k=qd[0];k>=10;k/=10)i++;q.e=i+e*logBase-1;finalise(q,dp?pr+q.e+1:pr,rm,more);}
return q;};})();function finalise(x,sd,rm,isTruncated){var digits,i,j,k,rd,roundUp,w,xd,xdi,Ctor=x.constructor;out:if(sd!=null){xd=x.d;if(!xd)return x;for(digits=1,k=xd[0];k>=10;k/=10)digits++;i=sd-digits;if(i<0){i+=LOG_BASE;j=sd;w=xd[xdi=0];rd=w/mathpow(10,digits-j-1)%10|0;}else{xdi=Math.ceil((i+1)/LOG_BASE);k=xd.length;if(xdi>=k){if(isTruncated){for(;k++<=xdi;)xd.push(0);w=rd=0;digits=1;i%=LOG_BASE;j=i-LOG_BASE+1;}else{break out;}}else{w=k=xd[xdi];for(digits=1;k>=10;k/=10)digits++;i%=LOG_BASE;j=i-LOG_BASE+digits;rd=j<0?0:w/mathpow(10,digits-j-1)%10|0;}}
isTruncated=isTruncated||sd<0||xd[xdi+1]!==void 0||(j<0?w:w%mathpow(10,digits-j-1));roundUp=rm<4?(rd||isTruncated)&&(rm==0||rm==(x.s<0?3:2)):rd>5||rd==5&&(rm==4||isTruncated||rm==6&&((i>0?j>0?w/mathpow(10,digits-j):0:xd[xdi-1])%10)&1||rm==(x.s<0?8:7));if(sd<1||!xd[0]){xd.length=0;if(roundUp){sd-=x.e+1;xd[0]=mathpow(10,(LOG_BASE-sd%LOG_BASE)%LOG_BASE);x.e=-sd||0;}else{xd[0]=x.e=0;}
return x;}
if(i==0){xd.length=xdi;k=1;xdi--;}else{xd.length=xdi+1;k=mathpow(10,LOG_BASE-i);xd[xdi]=j>0?(w/mathpow(10,digits-j)%mathpow(10,j)|0)*k:0;}
if(roundUp){for(;;){if(xdi==0){for(i=1,j=xd[0];j>=10;j/=10)i++;j=xd[0]+=k;for(k=1;j>=10;j/=10)k++;if(i!=k){x.e++;if(xd[0]==BASE)xd[0]=1;}
break;}else{xd[xdi]+=k;if(xd[xdi]!=BASE)break;xd[xdi--]=0;k=1;}}}
for(i=xd.length;xd[--i]===0;)xd.pop();}
if(external){if(x.e>Ctor.maxE){x.d=null;x.e=NaN;}else if(x.e<Ctor.minE){x.e=0;x.d=[0];}}
return x;}
function finiteToString(x,isExp,sd){if(!x.isFinite())return nonFiniteToString(x);var k,e=x.e,str=digitsToString(x.d),len=str.length;if(isExp){if(sd&&(k=sd-len)>0){str=str.charAt(0)+'.'+str.slice(1)+getZeroString(k);}else if(len>1){str=str.charAt(0)+'.'+str.slice(1);}
str=str+(x.e<0?'e':'e+')+x.e;}else if(e<0){str='0.'+getZeroString(-e-1)+str;if(sd&&(k=sd-len)>0)str+=getZeroString(k);}else if(e>=len){str+=getZeroString(e+1-len);if(sd&&(k=sd-e-1)>0)str=str+'.'+getZeroString(k);}else{if((k=e+1)<len)str=str.slice(0,k)+'.'+str.slice(k);if(sd&&(k=sd-len)>0){if(e+1===len)str+='.';str+=getZeroString(k);}}
return str;}
function getBase10Exponent(digits,e){var w=digits[0];for(e*=LOG_BASE;w>=10;w/=10)e++;return e;}
function getLn10(Ctor,sd,pr){if(sd>LN10_PRECISION){external=true;if(pr)Ctor.precision=pr;throw Error(precisionLimitExceeded);}
return finalise(new Ctor(LN10),sd,1,true);}
function getPi(Ctor,sd,rm){if(sd>PI_PRECISION)throw Error(precisionLimitExceeded);return finalise(new Ctor(PI),sd,rm,true);}
function getPrecision(digits){var w=digits.length-1,len=w*LOG_BASE+1;w=digits[w];if(w){for(;w%10==0;w/=10)len--;for(w=digits[0];w>=10;w/=10)len++;}
return len;}
function getZeroString(k){var zs='';for(;k--;)zs+='0';return zs;}
function intPow(Ctor,x,n,pr){var isTruncated,r=new Ctor(1),k=Math.ceil(pr/LOG_BASE+4);external=false;for(;;){if(n%2){r=r.times(x);if(truncate(r.d,k))isTruncated=true;}
n=mathfloor(n/2);if(n===0){n=r.d.length-1;if(isTruncated&&r.d[n]===0)++r.d[n];break;}
x=x.times(x);truncate(x.d,k);}
external=true;return r;}
function isOdd(n){return n.d[n.d.length-1]&1;}
function maxOrMin(Ctor,args,ltgt){var y,x=new Ctor(args[0]),i=0;for(;++i<args.length;){y=new Ctor(args[i]);if(!y.s){x=y;break;}else if(x[ltgt](y)){x=y;}}
return x;}
function naturalExponential(x,sd){var denominator,guard,j,pow,sum,t,wpr,rep=0,i=0,k=0,Ctor=x.constructor,rm=Ctor.rounding,pr=Ctor.precision;if(!x.d||!x.d[0]||x.e>17){return new Ctor(x.d?!x.d[0]?1:x.s<0?0:1/0:x.s?x.s<0?0:x:0/0);}
if(sd==null){external=false;wpr=pr;}else{wpr=sd;}
t=new Ctor(0.03125);while(x.e>-2){x=x.times(t);k+=5;}
guard=Math.log(mathpow(2,k))/Math.LN10*2+5|0;wpr+=guard;denominator=pow=sum=new Ctor(1);Ctor.precision=wpr;for(;;){pow=finalise(pow.times(x),wpr,1);denominator=denominator.times(++i);t=sum.plus(divide(pow,denominator,wpr,1));if(digitsToString(t.d).slice(0,wpr)===digitsToString(sum.d).slice(0,wpr)){j=k;while(j--)sum=finalise(sum.times(sum),wpr,1);if(sd==null){if(rep<3&&checkRoundingDigits(sum.d,wpr-guard,rm,rep)){Ctor.precision=wpr+=10;denominator=pow=t=new Ctor(1);i=0;rep++;}else{return finalise(sum,Ctor.precision=pr,rm,external=true);}}else{Ctor.precision=pr;return sum;}}
sum=t;}}
function naturalLogarithm(y,sd){var c,c0,denominator,e,numerator,rep,sum,t,wpr,x1,x2,n=1,guard=10,x=y,xd=x.d,Ctor=x.constructor,rm=Ctor.rounding,pr=Ctor.precision;if(x.s<0||!xd||!xd[0]||!x.e&&xd[0]==1&&xd.length==1){return new Ctor(xd&&!xd[0]?-1/0:x.s!=1?NaN:xd?0:x);}
if(sd==null){external=false;wpr=pr;}else{wpr=sd;}
Ctor.precision=wpr+=guard;c=digitsToString(xd);c0=c.charAt(0);if(Math.abs(e=x.e)<1.5e15){while(c0<7&&c0!=1||c0==1&&c.charAt(1)>3){x=x.times(y);c=digitsToString(x.d);c0=c.charAt(0);n++;}
e=x.e;if(c0>1){x=new Ctor('0.'+c);e++;}else{x=new Ctor(c0+'.'+c.slice(1));}}else{t=getLn10(Ctor,wpr+2,pr).times(e+'');x=naturalLogarithm(new Ctor(c0+'.'+c.slice(1)),wpr-guard).plus(t);Ctor.precision=pr;return sd==null?finalise(x,pr,rm,external=true):x;}
x1=x;sum=numerator=x=divide(x.minus(1),x.plus(1),wpr,1);x2=finalise(x.times(x),wpr,1);denominator=3;for(;;){numerator=finalise(numerator.times(x2),wpr,1);t=sum.plus(divide(numerator,new Ctor(denominator),wpr,1));if(digitsToString(t.d).slice(0,wpr)===digitsToString(sum.d).slice(0,wpr)){sum=sum.times(2);if(e!==0)sum=sum.plus(getLn10(Ctor,wpr+2,pr).times(e+''));sum=divide(sum,new Ctor(n),wpr,1);if(sd==null){if(checkRoundingDigits(sum.d,wpr-guard,rm,rep)){Ctor.precision=wpr+=guard;t=numerator=x=divide(x1.minus(1),x1.plus(1),wpr,1);x2=finalise(x.times(x),wpr,1);denominator=rep=1;}else{return finalise(sum,Ctor.precision=pr,rm,external=true);}}else{Ctor.precision=pr;return sum;}}
sum=t;denominator+=2;}}
function nonFiniteToString(x){return String(x.s*x.s/0);}
function parseDecimal(x,str){var e,i,len;if((e=str.indexOf('.'))>-1)str=str.replace('.','');if((i=str.search(/e/i))>0){if(e<0)e=i;e+=+str.slice(i+1);str=str.substring(0,i);}else if(e<0){e=str.length;}
for(i=0;str.charCodeAt(i)===48;i++);for(len=str.length;str.charCodeAt(len-1)===48;--len);str=str.slice(i,len);if(str){len-=i;x.e=e=e-i-1;x.d=[];i=(e+1)%LOG_BASE;if(e<0)i+=LOG_BASE;if(i<len){if(i)x.d.push(+str.slice(0,i));for(len-=LOG_BASE;i<len;)x.d.push(+str.slice(i,i+=LOG_BASE));str=str.slice(i);i=LOG_BASE-str.length;}else{i-=len;}
for(;i--;)str+='0';x.d.push(+str);if(external){if(x.e>x.constructor.maxE){x.d=null;x.e=NaN;}else if(x.e<x.constructor.minE){x.e=0;x.d=[0];}}}else{x.e=0;x.d=[0];}
return x;}
function parseOther(x,str){var base,Ctor,divisor,i,isFloat,len,p,xd,xe;if(str==='Infinity'||str==='NaN'){if(!+str)x.s=NaN;x.e=NaN;x.d=null;return x;}
if(isHex.test(str)){base=16;str=str.toLowerCase();}else if(isBinary.test(str)){base=2;}else if(isOctal.test(str)){base=8;}else{throw Error(invalidArgument+str);}
i=str.search(/p/i);if(i>0){p=+str.slice(i+1);str=str.substring(2,i);}else{str=str.slice(2);}
i=str.indexOf('.');isFloat=i>=0;Ctor=x.constructor;if(isFloat){str=str.replace('.','');len=str.length;i=len-i;divisor=intPow(Ctor,new Ctor(base),i,i*2);}
xd=convertBase(str,base,BASE);xe=xd.length-1;for(i=xe;xd[i]===0;--i)xd.pop();if(i<0)return new Ctor(x.s*0);x.e=getBase10Exponent(xd,xe);x.d=xd;external=false;if(isFloat)x=divide(x,divisor,len*4);if(p)x=x.times(Math.abs(p)<54?mathpow(2,p):Decimal.pow(2,p));external=true;return x;}
function sine(Ctor,x){var k,len=x.d.length;if(len<3)return taylorSeries(Ctor,2,x,x);k=1.4*Math.sqrt(len);k=k>16?16:k|0;x=x.times(1/tinyPow(5,k));x=taylorSeries(Ctor,2,x,x);var sin2_x,d5=new Ctor(5),d16=new Ctor(16),d20=new Ctor(20);for(;k--;){sin2_x=x.times(x);x=x.times(d5.plus(sin2_x.times(d16.times(sin2_x).minus(d20))));}
return x;}
function taylorSeries(Ctor,n,x,y,isHyperbolic){var j,t,u,x2,i=1,pr=Ctor.precision,k=Math.ceil(pr/LOG_BASE);external=false;x2=x.times(x);u=new Ctor(y);for(;;){t=divide(u.times(x2),new Ctor(n++*n++),pr,1);u=isHyperbolic?y.plus(t):y.minus(t);y=divide(t.times(x2),new Ctor(n++*n++),pr,1);t=u.plus(y);if(t.d[k]!==void 0){for(j=k;t.d[j]===u.d[j]&&j--;);if(j==-1)break;}
j=u;u=y;y=t;t=j;i++;}
external=true;t.d.length=k+1;return t;}
function tinyPow(b,e){var n=b;while(--e)n*=b;return n;}
function toLessThanHalfPi(Ctor,x){var t,isNeg=x.s<0,pi=getPi(Ctor,Ctor.precision,1),halfPi=pi.times(0.5);x=x.abs();if(x.lte(halfPi)){quadrant=isNeg?4:1;return x;}
t=x.divToInt(pi);if(t.isZero()){quadrant=isNeg?3:2;}else{x=x.minus(t.times(pi));if(x.lte(halfPi)){quadrant=isOdd(t)?(isNeg?2:3):(isNeg?4:1);return x;}
quadrant=isOdd(t)?(isNeg?1:4):(isNeg?3:2);}
return x.minus(pi).abs();}
function toStringBinary(x,baseOut,sd,rm){var base,e,i,k,len,roundUp,str,xd,y,Ctor=x.constructor,isExp=sd!==void 0;if(isExp){checkInt32(sd,1,MAX_DIGITS);if(rm===void 0)rm=Ctor.rounding;else checkInt32(rm,0,8);}else{sd=Ctor.precision;rm=Ctor.rounding;}
if(!x.isFinite()){str=nonFiniteToString(x);}else{str=finiteToString(x);i=str.indexOf('.');if(isExp){base=2;if(baseOut==16){sd=sd*4-3;}else if(baseOut==8){sd=sd*3-2;}}else{base=baseOut;}
if(i>=0){str=str.replace('.','');y=new Ctor(1);y.e=str.length-i;y.d=convertBase(finiteToString(y),10,base);y.e=y.d.length;}
xd=convertBase(str,10,base);e=len=xd.length;for(;xd[--len]==0;)xd.pop();if(!xd[0]){str=isExp?'0p+0':'0';}else{if(i<0){e--;}else{x=new Ctor(x);x.d=xd;x.e=e;x=divide(x,y,sd,rm,0,base);xd=x.d;e=x.e;roundUp=inexact;}
i=xd[sd];k=base/2;roundUp=roundUp||xd[sd+1]!==void 0;roundUp=rm<4?(i!==void 0||roundUp)&&(rm===0||rm===(x.s<0?3:2)):i>k||i===k&&(rm===4||roundUp||rm===6&&xd[sd-1]&1||rm===(x.s<0?8:7));xd.length=sd;if(roundUp){for(;++xd[--sd]>base-1;){xd[sd]=0;if(!sd){++e;xd.unshift(1);}}}
for(len=xd.length;!xd[len-1];--len);for(i=0,str='';i<len;i++)str+=NUMERALS.charAt(xd[i]);if(isExp){if(len>1){if(baseOut==16||baseOut==8){i=baseOut==16?4:3;for(--len;len%i;len++)str+='0';xd=convertBase(str,base,baseOut);for(len=xd.length;!xd[len-1];--len);for(i=1,str='1.';i<len;i++)str+=NUMERALS.charAt(xd[i]);}else{str=str.charAt(0)+'.'+str.slice(1);}}
str=str+(e<0?'p':'p+')+e;}else if(e<0){for(;++e;)str='0'+str;str='0.'+str;}else{if(++e>len)for(e-=len;e--;)str+='0';else if(e<len)str=str.slice(0,e)+'.'+str.slice(e);}}
str=(baseOut==16?'0x':baseOut==2?'0b':baseOut==8?'0o':'')+str;}
return x.s<0?'-'+str:str;}
function truncate(arr,len){if(arr.length>len){arr.length=len;return true;}}
function abs(x){return new this(x).abs();}
function acos(x){return new this(x).acos();}
function acosh(x){return new this(x).acosh();}
function add(x,y){return new this(x).plus(y);}
function asin(x){return new this(x).asin();}
function asinh(x){return new this(x).asinh();}
function atan(x){return new this(x).atan();}
function atanh(x){return new this(x).atanh();}
function atan2(y,x){y=new this(y);x=new this(x);var r,pr=this.precision,rm=this.rounding,wpr=pr+4;if(!y.s||!x.s){r=new this(NaN);}else if(!y.d&&!x.d){r=getPi(this,wpr,1).times(x.s>0?0.25:0.75);r.s=y.s;}else if(!x.d||y.isZero()){r=x.s<0?getPi(this,pr,rm):new this(0);r.s=y.s;}else if(!y.d||x.isZero()){r=getPi(this,wpr,1).times(0.5);r.s=y.s;}else if(x.s<0){this.precision=wpr;this.rounding=1;r=this.atan(divide(y,x,wpr,1));x=getPi(this,wpr,1);this.precision=pr;this.rounding=rm;r=y.s<0?r.minus(x):r.plus(x);}else{r=this.atan(divide(y,x,wpr,1));}
return r;}
function cbrt(x){return new this(x).cbrt();}
function ceil(x){return finalise(x=new this(x),x.e+1,2);}
function config(obj){if(!obj||typeof obj!=='object')throw Error(decimalError+'Object expected');var i,p,v,useDefaults=obj.defaults===true,ps=['precision',1,MAX_DIGITS,'rounding',0,8,'toExpNeg',-EXP_LIMIT,0,'toExpPos',0,EXP_LIMIT,'maxE',0,EXP_LIMIT,'minE',-EXP_LIMIT,0,'modulo',0,9];for(i=0;i<ps.length;i+=3){if(p=ps[i],useDefaults)this[p]=DEFAULTS[p];if((v=obj[p])!==void 0){if(mathfloor(v)===v&&v>=ps[i+1]&&v<=ps[i+2])this[p]=v;else throw Error(invalidArgument+p+': '+v);}}
if(p='crypto',useDefaults)this[p]=DEFAULTS[p];if((v=obj[p])!==void 0){if(v===true||v===false||v===0||v===1){if(v){if(typeof crypto!='undefined'&&crypto&&(crypto.getRandomValues||crypto.randomBytes)){this[p]=true;}else{throw Error(cryptoUnavailable);}}else{this[p]=false;}}else{throw Error(invalidArgument+p+': '+v);}}
return this;}
function cos(x){return new this(x).cos();}
function cosh(x){return new this(x).cosh();}
function clone(obj){var i,p,ps;function Decimal(v){var e,i,t,x=this;if(!(x instanceof Decimal))return new Decimal(v);x.constructor=Decimal;if(v instanceof Decimal){x.s=v.s;if(external){if(!v.d||v.e>Decimal.maxE){x.e=NaN;x.d=null;}else if(v.e<Decimal.minE){x.e=0;x.d=[0];}else{x.e=v.e;x.d=v.d.slice();}}else{x.e=v.e;x.d=v.d?v.d.slice():v.d;}
return;}
t=typeof v;if(t==='number'){if(v===0){x.s=1/v<0?-1:1;x.e=0;x.d=[0];return;}
if(v<0){v=-v;x.s=-1;}else{x.s=1;}
if(v===~~v&&v<1e7){for(e=0,i=v;i>=10;i/=10)e++;if(external){if(e>Decimal.maxE){x.e=NaN;x.d=null;}else if(e<Decimal.minE){x.e=0;x.d=[0];}else{x.e=e;x.d=[v];}}else{x.e=e;x.d=[v];}
return;}else if(v*0!==0){if(!v)x.s=NaN;x.e=NaN;x.d=null;return;}
return parseDecimal(x,v.toString());}else if(t!=='string'){throw Error(invalidArgument+v);}
if((i=v.charCodeAt(0))===45){v=v.slice(1);x.s=-1;}else{if(i===43)v=v.slice(1);x.s=1;}
return isDecimal.test(v)?parseDecimal(x,v):parseOther(x,v);}
Decimal.prototype=P;Decimal.ROUND_UP=0;Decimal.ROUND_DOWN=1;Decimal.ROUND_CEIL=2;Decimal.ROUND_FLOOR=3;Decimal.ROUND_HALF_UP=4;Decimal.ROUND_HALF_DOWN=5;Decimal.ROUND_HALF_EVEN=6;Decimal.ROUND_HALF_CEIL=7;Decimal.ROUND_HALF_FLOOR=8;Decimal.EUCLID=9;Decimal.config=Decimal.set=config;Decimal.clone=clone;Decimal.isDecimal=isDecimalInstance;Decimal.abs=abs;Decimal.acos=acos;Decimal.acosh=acosh;Decimal.add=add;Decimal.asin=asin;Decimal.asinh=asinh;Decimal.atan=atan;Decimal.atanh=atanh;Decimal.atan2=atan2;Decimal.cbrt=cbrt;Decimal.ceil=ceil;Decimal.cos=cos;Decimal.cosh=cosh;Decimal.div=div;Decimal.exp=exp;Decimal.floor=floor;Decimal.hypot=hypot;Decimal.ln=ln;Decimal.log=log;Decimal.log10=log10;Decimal.log2=log2;Decimal.max=max;Decimal.min=min;Decimal.mod=mod;Decimal.mul=mul;Decimal.pow=pow;Decimal.random=random;Decimal.round=round;Decimal.sign=sign;Decimal.sin=sin;Decimal.sinh=sinh;Decimal.sqrt=sqrt;Decimal.sub=sub;Decimal.tan=tan;Decimal.tanh=tanh;Decimal.trunc=trunc;if(obj===void 0)obj={};if(obj){if(obj.defaults!==true){ps=['precision','rounding','toExpNeg','toExpPos','maxE','minE','modulo','crypto'];for(i=0;i<ps.length;)if(!obj.hasOwnProperty(p=ps[i++]))obj[p]=this[p];}}
Decimal.config(obj);return Decimal;}
function div(x,y){return new this(x).div(y);}
function exp(x){return new this(x).exp();}
function floor(x){return finalise(x=new this(x),x.e+1,3);}
function hypot(){var i,n,t=new this(0);external=false;for(i=0;i<arguments.length;){n=new this(arguments[i++]);if(!n.d){if(n.s){external=true;return new this(1/0);}
t=n;}else if(t.d){t=t.plus(n.times(n));}}
external=true;return t.sqrt();}
function isDecimalInstance(obj){return obj instanceof Decimal||obj&&obj.name==='[object Decimal]'||false;}
function ln(x){return new this(x).ln();}
function log(x,y){return new this(x).log(y);}
function log2(x){return new this(x).log(2);}
function log10(x){return new this(x).log(10);}
function max(){return maxOrMin(this,arguments,'lt');}
function min(){return maxOrMin(this,arguments,'gt');}
function mod(x,y){return new this(x).mod(y);}
function mul(x,y){return new this(x).mul(y);}
function pow(x,y){return new this(x).pow(y);}
function random(sd){var d,e,k,n,i=0,r=new this(1),rd=[];if(sd===void 0)sd=this.precision;else checkInt32(sd,1,MAX_DIGITS);k=Math.ceil(sd/LOG_BASE);if(!this.crypto){for(;i<k;)rd[i++]=Math.random()*1e7|0;}else if(crypto.getRandomValues){d=crypto.getRandomValues(new Uint32Array(k));for(;i<k;){n=d[i];if(n>=4.29e9){d[i]=crypto.getRandomValues(new Uint32Array(1))[0];}else{rd[i++]=n%1e7;}}}else if(crypto.randomBytes){d=crypto.randomBytes(k*=4);for(;i<k;){n=d[i]+(d[i+1]<<8)+(d[i+2]<<16)+((d[i+3]&0x7f)<<24);if(n>=2.14e9){crypto.randomBytes(4).copy(d,i);}else{rd.push(n%1e7);i+=4;}}
i=k/4;}else{throw Error(cryptoUnavailable);}
k=rd[--i];sd%=LOG_BASE;if(k&&sd){n=mathpow(10,LOG_BASE-sd);rd[i]=(k/n|0)*n;}
for(;rd[i]===0;i--)rd.pop();if(i<0){e=0;rd=[0];}else{e=-1;for(;rd[0]===0;e-=LOG_BASE)rd.shift();for(k=1,n=rd[0];n>=10;n/=10)k++;if(k<LOG_BASE)e-=LOG_BASE-k;}
r.e=e;r.d=rd;return r;}
function round(x){return finalise(x=new this(x),x.e+1,this.rounding);}
function sign(x){x=new this(x);return x.d?(x.d[0]?x.s:0*x.s):x.s||NaN;}
function sin(x){return new this(x).sin();}
function sinh(x){return new this(x).sinh();}
function sqrt(x){return new this(x).sqrt();}
function sub(x,y){return new this(x).sub(y);}
function tan(x){return new this(x).tan();}
function tanh(x){return new this(x).tanh();}
function trunc(x){return finalise(x=new this(x),x.e+1,1);}
Decimal=clone(DEFAULTS);Decimal['default']=Decimal.Decimal=Decimal;LN10=new Decimal(LN10);PI=new Decimal(PI);if(typeof define=='function'&&define.amd){define(function(){return Decimal;});}else if(typeof module!='undefined'&&module.exports){if(typeof Symbol=='function'&&typeof Symbol.iterator=='symbol'){P[Symbol.for('nodejs.util.inspect.custom')]=P.toString;P[Symbol.toStringTag]='Decimal';}
module.exports=Decimal;}else{if(!globalScope){globalScope=typeof self!='undefined'&&self&&self.self==self?self:window;}
noConflict=globalScope.Decimal;Decimal.noConflict=function(){globalScope.Decimal=noConflict;return Decimal;};globalScope.Decimal=Decimal;}})(this);