		@@ -0,1 +1,10 @@
		## 1.0.0 (November 05, 2022)

		- Add modular exponentiation - `powm()`
		- Do not expose `trimTrailingZeros()` anymore. Zero trimming is still available through the third parameter at toFixed(), toExponential() and toPrecision()
		- Radian angles handled more precisely. Trigonometric functions now provide exact results for expressions like `sin(PI/6)=0.5`
		- Not using BigInt literals anymore, because they are not compatible with some FE frameworks
		- Performance improvements by memoizing common BigInt values
		- Fixed bug with zeros not being trimmed corectly

		## 0.11.0 (October 29, 2022)
		@@ -2,0 +11,0 @@

dist/index.esm.min.js

		/*!
		* exactnumber v0.11.0 (https://www.npmjs.com/package/exactnumber)
		* exactnumber v1.0.0 (https://www.npmjs.com/package/exactnumber)
		* (c) Dani Biro
		@@ -7,2 +7,2 @@ * @license MIT

		var t,n;!function(t){t[t.NEAREST_TO_POSITIVE=201008]="NEAREST_TO_POSITIVE",t[t.NEAREST_TO_NEGATIVE=201009]="NEAREST_TO_NEGATIVE",t[t.NEAREST_TO_EVEN=201010]="NEAREST_TO_EVEN",t[t.NEAREST_TO_ZERO=201011]="NEAREST_TO_ZERO",t[t.NEAREST_AWAY_FROM_ZERO=201012]="NEAREST_AWAY_FROM_ZERO",t[t.TO_POSITIVE=201001]="TO_POSITIVE",t[t.TO_NEGATIVE=201002]="TO_NEGATIVE",t[t.TO_ZERO=201003]="TO_ZERO",t[t.AWAY_FROM_ZERO=201004]="AWAY_FROM_ZERO"}(t\|\|(t={})),function(t){t.TRUNCATED="T",t.FLOORED="F",t.EUCLIDEAN="E"}(n\|\|(n={}));const r=t=>{const n=t.indexOf(".");if(-1===n)return t;let r=t.length;for(;r>n&&"0"===t.charAt(r-1);)r--;const e=n===r-1?n:r;return 0===e?"0":t.slice(0,e)},e=(t,n,e,i)=>{let o=t.toString();if(0===n&&0===e)return o;const s=o.startsWith("-");if(s&&(o=o.slice(1)),n>=o.length&&(o="0".repeat(n-o.length+1)+o),n>0){const t=o.slice(0,-n),s=o.slice(-n),u=e<=n?s.slice(0,e):`${s}${"0".repeat(e-n)}`;0!==u.length?(o=`${t}.${u}`,i&&(o=r(o))):o=t}else e>0&&(o=`${o}.${"0".repeat(e)}`);return s?`-${o}`:o},i=(n,r)=>(n=n.normalize())instanceof o?n.round(r,t.NEAREST_AWAY_FROM_ZERO):n;class o{constructor(t,n=0){if(this.type="fixed","bigint"==typeof t)this.number=t,this.decimalPos=n;else{const n=this.parseConstructorParameter(t);this.number=n.number,this.decimalPos=n.decimalPos}}parseConstructorParameter(t){if(t instanceof o)return{number:t.number,decimalPos:t.decimalPos};if(t instanceof s){if(!t.isInteger())throw new Error("Cannot create FixedNumber from non-integer Fraction");return{number:t.trunc().number,decimalPos:0}}if("number"==typeof t){if(!Number.isSafeInteger(t))throw new Error("The specified number cannot be exactly represented as an integer. Please provide a string instead.");return{number:BigInt(t),decimalPos:0}}if("string"==typeof t){if(0===(t=t.trim()).length)throw new Error("Empty string is not allowed");const n=t.match(/^(-?[0-9])(?:\.([0-9]))?(?:[eE]([+-]?[0-9]+))?$/);if(!n)throw new Error(`Cannot parse number "${t}"`);let r=0,e=n[1]??"0";if(void 0!==n[2]&&(e+=n[2],r+=n[2].length),void 0!==n[3]){const t=Number(n[3]);t>0?e+="0".repeat(t):r-=t}return{number:BigInt(e),decimalPos:r}}throw new Error("Unsupported parameter!")}scaleNumber(t,n){const r=Math.max(this.decimalPos,n);return{a:r===this.decimalPos?this.number:this.number10nBigInt(r-this.decimalPos),b:r===n?t:t10n*BigInt(r-n),decimalPos:r}}add(t){const n=u(t);if(n instanceof s)return n.add(this);const r=n,{a:e,b:i,decimalPos:a}=this.scaleNumber(r.number,r.decimalPos);return new o(e+i,a)}sub(t){const n=u(t);return this.add(n.neg())}mul(t){const n=u(t);if(n instanceof s)return n.mul(this);const r=n,e=this.numberr.number;return new o(e,this.decimalPos+r.decimalPos)}pow(t){const n=u(t).toNumber();if(!Number.isSafeInteger(n))throw new Error("Unsupported parameter");const r=Math.abs(n),e=new o(this.number*BigInt(r),this.decimalPosr);return n<0?e.inv():e}div(t){return this.convertToFraction().div(t)}divToInt(t){const n=u(t);if(n instanceof s)return this.convertToFraction().divToInt(n);const r=n,{a:e,b:i}=this.scaleNumber(r.number,r.decimalPos);return new o(e/i)}mod(t,r=n.TRUNCATED){const e=u(t);if(e instanceof s)return this.convertToFraction().mod(e);const i=e,{a:a,b:c,decimalPos:m}=this.scaleNumber(i.number,i.decimalPos),h=a%c,l=new o(h,m);if(r===n.TRUNCATED)return l;if(r===n.FLOORED)return Number(a<0)^Number(c<0)?l.add(c):l;if(r===n.EUCLIDEAN)return h<0?l.add(c<0?-c:c):l;throw new Error("Invalid ModType")}abs(){return new o(this.number<0?-this.number:this.number,this.decimalPos)}neg(){return this.mul(-1n)}inv(){return this.convertToFraction().inv()}floor(n){return 0===this.decimalPos?this:this.round(n,t.TO_NEGATIVE)}ceil(n){return 0===this.decimalPos?this:this.round(n,t.TO_POSITIVE)}trunc(n){return 0===this.decimalPos?this:this.round(n,t.TO_ZERO)}isTieStr(t){if("5"!==t[0])return!1;for(let n=1;n<t.length;n++)if("0"!==t[n])return!1;return!0}_round(n,r){const e=this.decimalPos-n;if(e<=0)return this;const i=10n*BigInt(e),s=this.number/i;if(r===t.TO_ZERO)return new o(s,n);const u=this.number%i;if(0n===u)return new o(s,n);if(r===t.AWAY_FROM_ZERO){const t=this.number<0n?s-1n:s+1n;return new o(t,n)}if(r===t.TO_POSITIVE){const t=this.number<0n?s:s+1n;return new o(t,n)}if(r===t.TO_NEGATIVE){const t=this.number>=0n?s:s-1n;return new o(t,n)}if(![void 0,t.NEAREST_TO_ZERO,t.NEAREST_AWAY_FROM_ZERO,t.NEAREST_TO_POSITIVE,t.NEAREST_TO_NEGATIVE,t.NEAREST_TO_EVEN].includes(r))throw new Error("Invalid rounding mode. Use the predefined values from the RoundingMode enum.");let a=(u<0n?-u:u).toString();if(a.length<e&&(a="0"),this.isTieStr(a)){if(r===t.NEAREST_TO_ZERO)return new o(s,n);if(r===t.NEAREST_AWAY_FROM_ZERO){const t=this.number<0n?s-1n:s+1n;return new o(t,n)}if(void 0===r\|\|r===t.NEAREST_TO_POSITIVE){const t=this.number<0n?s:s+1n;return new o(t,n)}if(r===t.NEAREST_TO_NEGATIVE){const t=this.number>=0n?s:s-1n;return new o(t,n)}if(r===t.NEAREST_TO_EVEN){if(s%2n===0n)return new o(s,n);return new o(s<0n?s-1n:s+1n,n)}}if(Number(a[0])<5)return new o(s,n);const c=this.number<0?s-1n:s+1n;return new o(c,n)}round(t,n){if(t=void 0===t?0:t,!Number.isSafeInteger(t)\|\|t<0)throw new Error("Invalid value for decimals");return this._round(t,n).normalize()}_incExponent(t){if(0===t)return this;let n=this.number,r=this.decimalPos;if(t<0)r-=t;else{const e=Math.min(t,this.decimalPos);r-=e;const i=t-e;i>0&&(n=10nBigInt(i))}return new o(n,r)}countDigits(){if(0n===this.number)return 1;let t=0,n=this.number<0?-this.number:this.number;for(;n>0n;)n/=10n,t++;return t}toSubZeroNum(){const t=this.countDigits();return{subZeroNum:new o(this.number,t),exponentDiff:t-this.decimalPos}}roundToDigits(t,n){if(!Number.isSafeInteger(t)\|\|t<1)throw new Error("Invalid value for digits");const{subZeroNum:r,exponentDiff:e}=this.toSubZeroNum();let i=r.round(t,n);return i=i._incExponent(e),i}intPart(){return this.trunc()}fracPart(){return this.sub(this.trunc())}sign(){return this.number<0n?-1:1}bitwiseAnd(t){if(t=a(t),!this.isInteger()\|\|-1===this.sign()\|\|!t.isInteger()\|\|-1===t.sign())throw new Error("Only positive integers are supported");t instanceof s&&(t=t.trunc());const n=2n24n;let r=this.normalize().number,e=t.trunc().normalize().number,i=0n,u=1n;for(;r>0&&e>0;){const t=BigInt.asUintN(24,r),o=BigInt.asUintN(24,e);i+=BigInt(Number(t)&Number(o))u,u=n,r/=n,e/=n}return new o(i)}bitwiseOr(t){if(t=a(t),!this.isInteger()\|\|-1===this.sign()\|\|!t.isInteger()\|\|-1===t.sign())throw new Error("Only positive integers are supported");t instanceof s&&(t=t.trunc());const n=2n*24n;let r=this.normalize().number,e=t.trunc().normalize().number,i=0n,u=1n;for(;r>0\|\|e>0;){const t=BigInt.asUintN(24,r),o=BigInt.asUintN(24,e);i+=BigInt(Number(t)\|Number(o))u,u=n,r/=n,e/=n}return new o(i)}bitwiseXor(t){if(t=a(t),!this.isInteger()\|\|-1===this.sign()\|\|!t.isInteger()\|\|-1===t.sign())throw new Error("Only positive integers are supported");t instanceof s&&(t=t.trunc());const n=2n24n;let r=this.normalize().number,e=t.trunc().normalize().number,i=0n,u=1n;for(;r>0\|\|e>0;){const t=BigInt.asUintN(24,r),o=BigInt.asUintN(24,e);i+=BigInt(Number(t)^Number(o))u,u=n,r/=n,e/=n}return new o(i)}shiftLeft(t){if(!this.isInteger()\|\|-1===this.sign())throw new Error("Only positive integers are supported");if(!Number.isSafeInteger(t)\|\|t<0)throw new Error("Invalid value for bitCount");const n=2nBigInt(t);return this.mul(n)}shiftRight(t){if(!this.isInteger()\|\|-1===this.sign())throw new Error("Only positive integers are supported");if(!Number.isSafeInteger(t)\|\|t<0)throw new Error("Invalid value for bitCount");const n=2nBigInt(t);return new o(this.normalize().number/n)}cmp(t){const n=u(t);if(n instanceof s)return-n.cmp(this);const r=n,{a:e,b:i}=this.scaleNumber(r.number,r.decimalPos);return e===i?0:e>i?1:-1}eq(t){return 0===this.cmp(t)}lt(t){return-1===this.cmp(t)}lte(t){return this.cmp(t)<=0}gt(t){return 1===this.cmp(t)}gte(t){return this.cmp(t)>=0}clamp(t,n){const r=a(t),e=a(n);if(r.gt(e))throw new Error("Min parameter has to be smaller than max");return this.lt(r)?r:this.gt(e)?e:this}isZero(){return 0n===this.number}isOne(){if(0===this.decimalPos)return 1n===this.number;const t=10nBigInt(this.decimalPos),n=this.number/t;return 1n===n&&nt===this.number}isInteger(){return 0===this.decimalPos\|\|this.number%10nBigInt(this.decimalPos)===0n}serialize(){return[this.number,this.decimalPos]}getFractionParts(t=!0){return this.convertToFraction().getFractionParts(t)}normalize(){if(0===this.decimalPos)return this;let t=this.decimalPos,n=this.number;for(;t>0&&n%10n===0n;)t--,n/=10n;return new o(n,t)}convertToFraction(){if(0===this.decimalPos)return new s(this.number,1n);const t=10nBigInt(this.decimalPos);return new s(this.number,t)}toNumber(){return Number(this.toPrecision(20))}toFixed(n,r=t.TO_ZERO){if(!Number.isSafeInteger(n)\|\|n<0)throw new Error("Invalid parameter");const i=this._round(n,r);return e(i.number,i.decimalPos,n,!1)}toExponential(n,r=t.TO_ZERO){if(!Number.isSafeInteger(n)\|\|n<0)throw new Error("Invalid parameter");const e=this.roundToDigits(n+1,r).normalize(),i=-1===e.sign(),o=e.abs(),s=o.number.toString(),u=s.length<=n?`${s}${"0".repeat(n-s.length+1)}`:s.slice(0,n+1),a=u.length>1?`${u.slice(0,1)}.${u.slice(1)}`:u,c=o.decimalPos,m=s.length-1-c;return`${i?"-":""}${a}e${m>=0?"+":""}${m}`}toBase(t,n){if(!Number.isSafeInteger(t)\|\|t<2\|\|t>16)throw new Error("Invalid radix");if(void 0!==n&&(!Number.isSafeInteger(n)\|\|n<0))throw new Error("Invalid parameter");const r=this.normalize();if(0===r.decimalPos)return r.number.toString(t);const e=void 0===n?Number.MAX_SAFE_INTEGER:n;let i=r.intPart(),o=r.sub(i);const s=-1===r.sign();s&&(i=i.neg(),o=o.neg());const u=new Map;let a=[];for(;!o.isZero();){const n=o.mul(t),r=n.toString(),i=u.get(r);if(void 0!==i){a=[...a.slice(0,i-1),"(",...a.slice(i-1),")"];break}if(a.length===e)break;const s=Math.abs(n.intPart().toNumber());a.push(s.toString(t)),o=n.fracPart(),u.set(r,a.length)}return[s?"-":"",i.number.toString(t),a.length?".":"",...a].join("")}toFraction(){return this.convertToFraction().toFraction()}toString(t,n){if(void 0===t\|\|10===t){const t=void 0!==n?this.trunc(n):this;return e(t.number,t.decimalPos,t.decimalPos,!0)}return this.toBase(t,n)}toPrecision(n,r=t.TO_ZERO){if(!Number.isSafeInteger(n)\|\|n<1)throw new Error("Invalid parameter");const i=this.roundToDigits(n,r),{subZeroNum:o,exponentDiff:s}=i.toSubZeroNum(),u=-1===o.sign();let a=e(o.number,o.decimalPos,o.decimalPos,!1);a=a.slice(u?3:2),a=a.slice(0,Math.max(n,s));const c=a.slice(0,Math.max(0,s)),m=a.slice(Math.max(0,s)),h=Math.max(0,n-c.length-m.length),l="0".repeat(h),d="0".repeat(s<0?-s:0);let f=c\|\|"0";return m.length+d.length+h>0&&(f+=`.${d}${m}${l}`),u?`-${f}`:f}valueOf(){throw new Error("Unsafe conversion to Number type! Use toNumber() instead.")}}class s{constructor(t,n){if(this.type="fraction","bigint"==typeof t&&"bigint"==typeof n)this.numerator=t,this.denominator=n;else{const r=this.parseParameter(t),e=this.parseParameter(n),i=r.div(e),s=i instanceof o?i.convertToFraction():i;this.numerator=s.numerator,this.denominator=s.denominator}if(0n===this.denominator)throw new Error("Division by zero")}parseRepeatingDecimal(t){if(!t.includes("("))return new o(t).convertToFraction();const n=(t=t.trim()).match(/^(-?[0-9])\.([0-9]+)?$([0-9]+)$(?:[eE]([+-]?[0-9]+))?$/);if(!n)throw new Error(`Cannot parse string "${t}"`);const r="-"===n[1]?"-0":n[1],e=n[2]??"",i=n[3],u=n[4],a=BigInt(r+e+i)-BigInt(r+e),c=BigInt("9".repeat(i.length)+"0".repeat(e.length)),m=new s(a,c);if(void 0!==u){const t=u.startsWith("-"),n=10nBigInt(t?u.slice(1):u);return t?m.div(n).normalize():m.mul(n).normalize()}return m.simplify()}parseParameter(t){if(t instanceof s)return t;if(t instanceof o)return t.convertToFraction();if("number"==typeof t){if(!Number.isSafeInteger(t))throw new Error("Floating point values as numbers are unsafe. Please provide them as a string.");return new s(BigInt(t),1n)}if("bigint"==typeof t)return new s(t,1n);if("string"==typeof t){const n=t.split("/");if(n.length>2)throw new Error(`Cannot parse string '${t}'`);const r=this.parseRepeatingDecimal(n[0]),e=n[1]?this.parseRepeatingDecimal(n[1]):new s(1n,1n);return r.div(e).convertToFraction()}throw new Error("Unsupported parameter!")}add(t){const{numerator:n,denominator:r}=this.parseParameter(t);return this.denominator===r?new s(this.numerator+n,this.denominator):new s(this.numeratorr+nthis.denominator,rthis.denominator)}sub(t){const{numerator:n,denominator:r}=this.parseParameter(t);return this.add(new s(-n,r))}mul(t){const{numerator:n,denominator:r}=this.parseParameter(t);return new s(this.numeratorn,this.denominatorr)}div(t){const{numerator:n,denominator:r}=this.parseParameter(t);return this.mul(new s(r,n))}divToInt(t){return this.div(t).trunc()}mod(t,r=n.TRUNCATED){const e=this.parseParameter(t),i=e.denominatorthis.numerator%(e.numeratorthis.denominator),o=this.denominatore.denominator,u=new s(i,o);if(r===n.TRUNCATED)return u;if(r===n.FLOORED)return Number(-1===this.sign())^Number(-1===e.sign())?u.add(e):u;if(r===n.EUCLIDEAN)return u.sign()<0?u.add(e.sign()<0?e.neg():e):u;throw new Error("Invalid ModType")}pow(t){const n=this.parseParameter(t);if(!n.isInteger())throw new Error("Unsupported parameter");const r=n.numerator/n.denominator,e=r<0?-r:r,i=new s(this.numeratore,this.denominatore);return r<0?i.inv():i}inv(){return new s(this.denominator,this.numerator)}floor(n){return 1n===this.denominator?new o(this.numerator):this.round(n,t.TO_NEGATIVE)}ceil(n){return 1n===this.denominator?new o(this.numerator):this.round(n,t.TO_POSITIVE)}trunc(n){return 1n===this.denominator?new o(this.numerator):this.round(n,t.TO_ZERO)}round(t,n){if(t=void 0===t?0:t,!Number.isSafeInteger(t)\|\|t<0)throw new Error("Invalid value for decimals");const r=this.toFixedNumber(t+1);if(this.sub(r).isZero())return r.round(t,n);return new o(`${r.toFixed(t+1)}1`).round(t,n)}roundToDigits(t,n){if(!Number.isSafeInteger(t)\|\|t<1)throw new Error("Invalid value for digits");if(this.isZero())return new o(0n);let r=this.abs(),e=0;for(;r.gte(1n);)r=r.div(10n),e++;const i=new s(1n,10n);for(;r.lt(i);)r=r.mul(10n),e--;let u=r.round(t,n);return u=u._incExponent(e),-1===this.sign()?u.neg():u}gcd(t,n){let r=t<0?-t:t,e=n<0?-n:n;if(e>r){const t=r;r=e,e=t}for(;;){if(0n===e)return r;if(r%=e,0n===r)return e;e%=r}}simplify(){let{numerator:t,denominator:n}=this;const r=this.gcd(t,n);return r>1n&&(t/=r,n/=r),n<0n&&(t=-t,n=-n),new s(t,n)}normalize(){const{numerator:n,denominator:r}=this.simplify();if(1n===r)return new o(n,0);const e=new s(n,r),{cycleLen:i,cycleStart:u}=e.getDecimalFormat(0);return 0!==i?e:e.round(u,t.TO_ZERO)}getFractionParts(t=!0){const n=t?this.simplify():this;return{numerator:new o(n.numerator),denominator:new o(n.denominator)}}sign(){return(this.numerator<0n?-1:1)(this.denominator<0n?-1:1)}abs(){return new s(this.numerator<0n?-this.numerator:this.numerator,this.denominator<0n?-this.denominator:this.denominator)}neg(){return this.mul(-1n)}intPart(){return this.trunc()}fracPart(){return this.sub(this.trunc())}cmp(t){const n=this.parseParameter(t),r=this.denominator===n.denominator,e=r?this.numerator:this.numeratorn.denominator,i=r?n.numerator:n.numeratorthis.denominator;return e===i?0:e>i?1:-1}eq(t){return 0===this.cmp(t)}lt(t){return-1===this.cmp(t)}lte(t){return this.cmp(t)<=0}gt(t){return 1===this.cmp(t)}gte(t){return this.cmp(t)>=0}clamp(t,n){const r=a(t),e=a(n);if(r.gt(e))throw new Error("Min parameter has to be smaller than max");return this.lt(r)?r:this.gt(e)?e:this}isZero(){return 0n===this.numerator}isOne(){return this.numerator===this.denominator}isInteger(){return this.numerator%this.denominator===0n}serialize(){return[this.numerator,this.denominator]}toNumber(){return Number(this.toPrecision(20))}convertToFraction(){return this}getNumberForBitwiseOp(){if(!this.isInteger()\|\|-1===this.sign())throw new Error("Only positive integers are supported");return this.intPart()}bitwiseAnd(t){return this.getNumberForBitwiseOp().bitwiseAnd(t)}bitwiseOr(t){return this.getNumberForBitwiseOp().bitwiseOr(t)}bitwiseXor(t){return this.getNumberForBitwiseOp().bitwiseXor(t)}shiftLeft(t){return this.getNumberForBitwiseOp().shiftLeft(t)}shiftRight(t){return this.getNumberForBitwiseOp().shiftRight(t)}getDecimalFormat(t){t=void 0===t?Number.MAX_SAFE_INTEGER:t;let n=this.denominator<0?-this.denominator:this.denominator,r=0;for(;n%2n===0n;)n/=2n,r++;let e=0;for(;n%5n===0n;)n/=5n,e++;const i=Math.max(r,e);if(1n===n)return{cycleLen:0,cycleStart:i};const o=Math.max(1,t-i);let s=10n%n,u=1;for(;1n!==s;){if(u===o)return{cycleLen:null,cycleStart:i};s=10ns%n,u++}return{cycleLen:u,cycleStart:i}}toFixed(n,r=t.TO_ZERO){if(!Number.isSafeInteger(n)\|\|n<0)throw new Error("Invalid parameter");return this.round(n,r).toFixed(n)}toRepeatingParts(t){if(this.isZero())return["0","",""];const{cycleLen:n,cycleStart:e}=this.simplify().getDecimalFormat(t);if(null===n\|\|0===n){const n=t??e,i=this.toFixed(n),o=r(i).split(".");return[o[0],o[1]??"",""]}const i=e+n,o=this.toFixed(i).split(".");return[o[0],o[1].slice(0,e),o[1].slice(e)]}toRepeatingDigits(t){const n=this.toRepeatingParts(t);let r=n[0];return(n[1]\|\|n[2])&&(r+=`.${n[1]}`),n[2]&&(r+=`(${n[2]})`),r}toExponential(n,r=t.TO_ZERO){if(!Number.isSafeInteger(n)\|\|n<0)throw new Error("Invalid parameters");return this.toFixedNumber(n).toExponential(n,r)}toFraction(){const{numerator:t,denominator:n}=this.getFractionParts(!0);return`${t.toString()}/${n.toString()}`}toFixedNumber(t){const n=this.numerator10n*BigInt(t);return new o(n/this.denominator,t)}toBase(t,n){if(!Number.isSafeInteger(t)\|\|t<2\|\|t>16)throw new Error("Invalid radix");if(void 0!==n&&(!Number.isSafeInteger(n)\|\|n<0))throw new Error("Invalid parameter");if(10===t)return void 0===n?this.toRepeatingDigits(n):r(this.toFixed(n));const e=this.normalize(),i=void 0===n?Number.MAX_SAFE_INTEGER:n+1;let o=e.intPart(),s=e.sub(o);const u=-1===e.sign();u&&(o=o.neg(),s=s.neg());const a=new Map;let c=[];for(;!s.isZero()&&c.length!==i;){const n=s.mul(t),r=n.normalize().toFraction(),e=a.get(r);if(void 0!==e){c=[...c.slice(0,e-1),"(",...c.slice(e-1),")"];break}const i=Math.abs(n.intPart().toNumber());c.push(i.toString(t)),s=n.fracPart(),a.set(r,c.length)}return c.length===i&&c.pop(),[u?"-":"",o.toString(t),c.length?".":"",...c].join("")}toString(t,n){return void 0===t\|\|10===t?this.toRepeatingDigits(n):this.toBase(t,n)}toPrecision(n,r=t.TO_ZERO){if(!Number.isSafeInteger(n)\|\|n<1)throw new Error("Invalid parameter");return this.roundToDigits(n,r).toPrecision(n)}valueOf(){throw new Error("Unsafe conversion to Number type! Use toNumber() instead.")}}function u(t){if(t instanceof o\|\|t instanceof s)return t;if("bigint"==typeof t)return new o(t);if("number"==typeof t){if(!Number.isSafeInteger(t))throw new Error("Floating point values as numbers are unsafe. Please provide them as a string.");return new o(t)}if("string"==typeof t)return t.includes("/")\|\|t.includes("(")?new s(t,1n):new o(t);throw new Error("Unsupported parameter type")}const a=(t,n)=>{if(void 0===t)throw new Error("First parameter cannot be undefined");const r=u(t);if(void 0===n)return r;const e=u(n);return new s(r,1n).div(new s(e,1n))};a.min=(...t)=>{if(0===t.length)throw new Error("Got empty array");let n=a(t[0]);for(let r=1;r<t.length;r++){const e=a(t[r]);e.lt(n)&&(n=e)}return n},a.max=(...t)=>{if(0===t.length)throw new Error("Got empty array");let n=a(t[0]);for(let r=1;r<t.length;r++){const e=a(t[r]);e.gt(n)&&(n=e)}return n};const c=(t,n)=>{let r=0n;for(let e=0;e<t.length;e++){const i=t.charAt(e),o=parseInt(i,n);if(Number.isNaN(o))throw new Error(`Invalid digit "${i}"`);r=BigInt(n),r+=BigInt(o)}return r};a.fromBase=(t,n)=>{if("string"!=typeof t)throw new Error("First parameter must be string");if(!Number.isSafeInteger(n)\|\|n<2\|\|n>16)throw new Error("Invalid radix");if(10===n)return a(t);if(0===(t=t.trim()).length)throw new Error("Empty string is not allowed");const r=t.startsWith("-");r&&(t=t.slice(1));const e=t.match(/^([0-9a-f])(?:\.([0-9a-f])(?:$([0-9a-f]+)$)?)?$/i);if(!e)throw new Error(`Cannot parse number "${t}"`);const i=e[1]??"",o=e[2]??"",u=e[3]??"";if(u.length>0){const t=c([i,o,u].join(""),n)-c([i,o].join(""),n),e=c((n-1).toString(n).repeat(u.length)+"0".repeat(o.length),n),a=new s(t,e).normalize();return r?a.neg():a}const m=c(i,n),h=c(o,n),l=new s(h,BigInt(n)*BigInt(o.length)),d=new s(m,1n).add(l).normalize();return r?d.neg():d},a.range=function(t,n,r){const e=a(n),i=a(r??1);let o=a(t);for(;o.lt(e);)yield o,o=o.add(i)},a.gcd=(t,n)=>{const r=a(t).abs(),e=a(n).abs();let i=e.gt(r)?e:r,o=i.eq(r)?e:r;for(;;){if(o.isZero())return i;if(i=i.mod(o),i.isZero())return o;o=o.mod(i)}},a.lcm=(t,n)=>{const r=a(t).abs(),e=a(n).abs(),i=r.mul(e);if(i.isZero())throw new Error("LCM of zero is undefined");const o=a.gcd(r,e);return i.div(o)};const m=(t,n,r)=>{const e=((t,n)=>{let r=n.toNumber();if(Number.isFinite(r)){const n=r<0;n&&(r=-r);let e=r*(1/t);return n&&(e=-e),e.toString()}const e=n.abs().toFixed(0).length,i=Math.ceil(e/t);return`${1===n.sign()?"":"-"}5e${i}`})(t,n);let i=new o("0"!==e?e:"1");const u=new s(t-1,t),a=new s(n,t),c=BigInt(t-1);let m=i.trunc(r+5);for(;i=u.mul(i).add(a.mul(i.pow(c).inv())),i=i.trunc(r+5),!i.isZero()&&!m.eq(i);)m=i;return i.trunc(r)},h=(t,n,r)=>{if(!Number.isSafeInteger(t))throw new Error("Integer is expected for N");if(t<0)throw new Error("Negative N is not supported");if(0===t)throw new Error("N cannot be zero");const e=i(a(n),r);if(1===t)return e.trunc(r);if(t%2==0&&-1===e.sign())throw new Error("Complex numbers are not supported");if(e.isZero())return new o(0n).trunc(r);if(e.isOne())return new o(1n).trunc(r);return m(t,e,r)},l=(t,n)=>h(2,t,n),d=(t,n)=>h(3,t,n);class f{constructor(t,n){this.cachedDecimals=0,this.fn=t,this.max=n}get(t){if(t<=this.cachedDecimals)return this.cache.trunc(t);const n=new o(this.fn(t)),r=Math.min(this.max,t);return this.cachedDecimals!==r&&(this.cache=n.trunc(r),this.cachedDecimals=r),n}}const g=(t,n)=>{let r=i(a(t),n);if(r.isOne())return new o(0).trunc(n);if(r.lte(0n))throw new Error("Invalid parameter");let e=0;const s=a("0.1");for(;r.sub(1n).abs().gt(s);)r=new o(l(r,n+10)),e++;const u=function(t,n){const r=t.pow(2n).normalize();let e=t,i=1n,o=a(t);for(;;){e=e.mul(r),i+=2n;const t=e.div(i).trunc(n+10);o=o.add(t),yield{term:t,sum:o}}}(r.sub(1n).div(r.add(1n)),n);for(const{term:t,sum:r}of u)if(t.isZero()){return r.mul(2n*BigInt(e+1)).trunc(n)}return a(0)},w=(t,n,r)=>{if(!Number.isSafeInteger(t)\|\|t<2)throw new Error("Invalid parameter for N");const e=g(n,r+10),i=g(t,r+10);return new o(e).div(i).trunc(r)},b=new f((t=>g(2n,t)),200),E=(t,n)=>new o(g(t,n+10)).div(b.get(n+10)).trunc(n),p=new f((t=>g(10n,t)),200),N=(t,n)=>new o(g(t,n+10)).div(p.get(n+10)).trunc(n);const I=(t,n)=>{const r=i(a(t),n),e=a(`1e-${n+5}`),o=function(t,n){let r=t.add(1n),e=6n,i=4n;const o=t.pow(2n);let s=o;for(;;){const u=s.mul(t.add(i-1n)).div(e);e=i(i+1n),i+=2n,s=s.mul(o),r=r.add(u).trunc(n+5),yield{term:u,sum:r}}}(r,n);for(const{term:t,sum:r}of o)if(t.abs().lt(e))return r.trunc(n);return a(0)},v=(t,n,r)=>{const e=i(a(t),r),o=i(a(n),r);if(o.isInteger()&&Number.isSafeInteger(o.toNumber()))return e.pow(o).trunc(r);if(-1===e.sign()&&!o.isInteger())throw new Error("Complex numbers are not supported");const s=g(e,r+5),u=o.mul(s);return I(u,r+5).trunc(r)},O=new f((t=>{if(0===t)return a(3n);let n=1n,r=3n10nBigInt(t+20),e=r;for(;0n!==r;)r=rn/(4n(n+1n)),n+=2n,e+=r/n;return a(`3.${e.toString().slice(1,t+1)}`)}),1e3),T=t=>0===t?a(3):O.get(t).trunc(t),P=(n,r)=>{const e=new o(T(r+5)),i=e.mul(2n);let s=n.round(r+5,t.NEAREST_AWAY_FROM_ZERO).div(i).fracPart();s.lt(0n)&&(s=s.add(1n)),s=s.round(r+5);const u=s.div("0.25").floor().toNumber()+1;let c=i.mul(s),m=s.mul(360n);return 4===u?(c=i.sub(c),m=a(360).sub(m)):3===u?(c=c.sub(e),m=m.sub(180)):2===u&&(c=e.sub(c),m=a(180).sub(m)),{quadrantDegrees:m.round(r),quadrant:u,subHalfPiAngle:c}};const _=(t,n,r)=>{let e=a(t);return n&&(e=e.neg()),e.trunc(r)},S=(n,r)=>{const e=r+10,o=i(a(n),r+5),{quadrantDegrees:s,subHalfPiAngle:u,quadrant:c}=P(o,r),m=2===c\|\|3===c;if(s.isZero())return _("1",m,r);if(s.eq(30n))return _(a(l(3n,r+5)).div(2n),m,r);if(s.eq(45n))return _(a(l(2n,r+5)).div(2n),m,r);if(s.eq(60n))return _("0.5",m,r);if(s.eq(90n))return _("0",m,r);const h=a(`1e-${e}`),d=function(n,r){const e=n.round(r+10,t.NEAREST_AWAY_FROM_ZERO).pow(2n);let i=e,o=2n,s=a(1n).sub(i.div(o).trunc(r+10)),u=3n;for(;;){o=u(u+1n),u+=2n;const t=u(u+1n);u+=2n,i=i.mul(e),o=t;let n=i.mul(t);i=i.mul(e),n=n.sub(i);const a=n.div(o).trunc(r+10);s=s.add(a),yield{term:a,sum:s}}}(u,r);for(const{term:t,sum:n}of d)if(t.lt(h))return _(n,m,r);return a(0)},R=(t,n)=>{const r=new o(T(n+10)),e=i(a(t),n+5);return S(r.div(2n).sub(e),n+5).trunc(n)},A=(t,n)=>{const r=i(a(t),n+5),{quadrantDegrees:e,quadrant:o,subHalfPiAngle:s}=P(r,n+5),u=1===o\|\|3===o;if(e.isZero())return _("0",u,n);if(e.eq(30n))return _(a(1n).div(l(3n,n+5)),u,n);if(e.eq(45n))return _("1",u,n);if(e.eq(60n))return _(l(3n,n+5),u,n);if(e.eq(90n))throw new Error("Out of range");const c=a(S(s.mul(2n),n+5)),m=a(1n).sub(c).div(a(1n).add(c)).round(n+5),h=l(m,n+5).trunc(n);return u?h:h.neg()};const F=(t,n)=>{let r=i(a(t),n);if(r.isZero())return a(0);if(r.abs().isOne())return a(T(n)).div(4r.sign()).trunc(n);let e=0;const o=a("0.42");for(;r.abs().gt(o);){const t=a(l(r.pow(2n).add(1n),n+10));r=r.div(t.add(1n)),e++}const s=a(`1e-${n+10}`),u=function(t,n){const r=t.pow(2n).normalize(),e=r.pow(2n).normalize();let i=3n,o=t.sub(t.mul(r).div(i)),s=t.mul(e);for(;;){i+=2n;const t=i+2n,u=s.mul(r.mul(-i).add(t)).div(it);i=t,s=s.mul(e),o=o.add(u).trunc(n+10),yield{term:u,sum:o}}}(r,n);for(const{term:t,sum:r}of u)if(t.abs().lt(s)){return r.mul(2nBigInt(e)).trunc(n)}return a(0)},y=(t,n)=>{const r=i(a(t),n);if(r.isZero())return a(0);if(r.abs().isOne())return a(T(n)).mul(r.sign()).div(2n).trunc(n);if(r.abs().eq("1/2"))return a(T(n)).mul(r.sign()).div(6n).trunc(n);if(r.gt(1n)\|\|r.lt(-1n))throw new Error("Out of range");const e=a(l(r.pow(2n).neg().add(1),n+10));return a(F(r.div(e.add(1n)),n+10)).mul(2).trunc(n)},Z=(t,n)=>{const r=i(a(t),n);if(r.isZero())return a(T(n)).div(2n).trunc(n);if(r.isOne())return a(0);if(r.abs().isOne())return T(n);if(r.abs().eq("1/2")){const t=a(T(n)).div(3n);return-1===r.sign()?t.mul(2n).trunc(n):t.trunc(n)}if(r.gt(1n)\|\|r.lt(-1n))throw new Error("Out of range");return a(T(n+10)).div(2n).sub(y(r,n+10)).trunc(n)};const B=(t,n)=>{const r=i(a(t),n),e=new o(`1e-${n+5}`),s=function(t,n){let r=t,e=1n;const i=t.pow(2n).normalize();let o=t.trunc(n+5),s=2n;for(;;){r=r.mul(i),e=s(s+1n),s+=2n;const t=r.div(e);o=o.add(t).trunc(n+5),yield{term:t,sum:o}}}(r,n);for(const{term:t,sum:r}of s)if(t.abs().lt(e))return r.trunc(n);return a(0)};const x=(t,n)=>{const r=i(a(t),n),e=new o(`1e-${n+5}`),s=function(t,n){const r=t.pow(2n).normalize();let e=r,i=2n,o=e.div(i).add(1n).trunc(n+5),s=3n;for(;;){e=e.mul(r),i=s*(s+1n),s+=2n;const t=e.div(i);o=o.add(t).trunc(n+5),yield{term:t,sum:o}}}(r,n);for(const{term:t,sum:r}of s)if(t.abs().lt(e))return r.trunc(n);return a(0)},$=(t,n)=>{const r=i(a(t),n);if(r.isZero())return a(0);const e=x(r,n+10).abs();return l(e.pow(2).sub(1),n+10).div(e).mul(r.sign()).trunc(n)},D=(t,n)=>{const r=i(a(t),n);if(r.isZero())return a(0);const e=l(r.pow(2).add(1n),n+5);return g(r.add(e),n+5).trunc(n)},M=(t,n)=>{const r=i(a(t),n);if(r.isOne())return a(0);if(r.lt(1n))throw new Error("Out of range");const e=l(r.pow(2).sub(1n),n+5);return g(r.add(e),n+5).trunc(n)},z=(t,n)=>{const r=i(a(t),n);if(r.abs().gte(1n))throw new Error("Out of range");if(r.isZero())return a(0);const e=g(r.add(1n).div(r.neg().add(1n)),n+5);return a(e).div(2n).trunc(n)};export{a as ExactNumber,n as ModType,T as PI,t as RoundingMode,Z as acos,M as acosh,y as asin,D as asinh,F as atan,z as atanh,d as cbrt,S as cos,x as cosh,I as exp,g as log,N as log10,E as log2,w as logn,h as nthroot,v as pow,R as sin,B as sinh,l as sqrt,A as tan,$ as tanh,r as trimTrailingZeros};
		var t,r;!function(t){t[t.NEAREST_TO_POSITIVE=201008]="NEAREST_TO_POSITIVE",t[t.NEAREST_TO_NEGATIVE=201009]="NEAREST_TO_NEGATIVE",t[t.NEAREST_TO_EVEN=201010]="NEAREST_TO_EVEN",t[t.NEAREST_TO_ZERO=201011]="NEAREST_TO_ZERO",t[t.NEAREST_AWAY_FROM_ZERO=201012]="NEAREST_AWAY_FROM_ZERO",t[t.TO_POSITIVE=201001]="TO_POSITIVE",t[t.TO_NEGATIVE=201002]="TO_NEGATIVE",t[t.TO_ZERO=201003]="TO_ZERO",t[t.AWAY_FROM_ZERO=201004]="AWAY_FROM_ZERO"}(t\|\|(t={})),function(t){t.TRUNCATED="T",t.FLOORED="F",t.EUCLIDEAN="E"}(r\|\|(r={}));const e=t=>{const r=t.indexOf(".");if(-1===r)return t;let e=t.length;for(;e>r&&"0"===t.charAt(e-1);)e--;const n=r===e-1?r:e;return 0===n?"0":t.slice(0,n)},n=(t,r,n,i)=>{let o=t.toString();if(0===r&&0===n)return o;const s=o.startsWith("-");if(s&&(o=o.slice(1)),r>=o.length&&(o="0".repeat(r-o.length+1)+o),r>0){const t=o.slice(0,-r),s=o.slice(-r),u=n<=r?s.slice(0,n):`${s}${"0".repeat(n-r)}`;0!==u.length?(o=`${t}.${u}`,i&&(o=e(o))):o=t}else n>0&&!i&&(o=`${o}.${"0".repeat(n)}`);return s?`-${o}`:o},i=(r,e)=>(r=r.normalize())instanceof d?r.round(e,t.NEAREST_AWAY_FROM_ZERO):r,o=BigInt(0),s=BigInt(1),u=BigInt(2),a=BigInt(3),c=BigInt(4),m=BigInt(5),h=BigInt(10),l=BigInt(24);class d{constructor(t,r=0){if(this.type="fixed","bigint"==typeof t)this.number=t,this.decimalPos=r;else{const r=this.parseConstructorParameter(t);this.number=r.number,this.decimalPos=r.decimalPos}}parseConstructorParameter(t){if(t instanceof d)return{number:t.number,decimalPos:t.decimalPos};if(t instanceof f){if(!t.isInteger())throw new Error("Cannot create FixedNumber from non-integer Fraction");return{number:t.trunc().number,decimalPos:0}}if("number"==typeof t){if(!Number.isSafeInteger(t))throw new Error("The specified number cannot be exactly represented as an integer. Please provide a string instead.");return{number:BigInt(t),decimalPos:0}}if("string"==typeof t){if(0===(t=t.trim()).length)throw new Error("Empty string is not allowed");const r=t.match(/^(-?[0-9])(?:\.([0-9]))?(?:[eE]([+-]?[0-9]+))?$/);if(!r)throw new Error(`Cannot parse number "${t}"`);let e=0,n=r[1]??"0";if(void 0!==r[2]&&(n+=r[2],e+=r[2].length),void 0!==r[3]){const t=Number(r[3]);t>0?n+="0".repeat(t):e-=t}return{number:BigInt(n),decimalPos:e}}throw new Error("Unsupported parameter!")}scaleNumber(t,r){const e=Math.max(this.decimalPos,r);return{a:e===this.decimalPos?this.number:this.numberhBigInt(e-this.decimalPos),b:e===r?t:th*BigInt(e-r),decimalPos:e}}add(t){const r=g(t);if(r instanceof f)return r.add(this);const e=r,{a:n,b:i,decimalPos:o}=this.scaleNumber(e.number,e.decimalPos);return new d(n+i,o)}sub(t){const r=g(t);return this.add(r.neg())}mul(t){const r=g(t);if(r instanceof f)return r.mul(this);const e=r,n=this.numbere.number;return new d(n,this.decimalPos+e.decimalPos)}pow(t){const r=g(t).toNumber();if(!Number.isSafeInteger(r))throw new Error("Unsupported parameter");const e=Math.abs(r),n=new d(this.number*BigInt(e),this.decimalPose);return r<0?n.inv():n}powm(t,r,e){let n=g(t).toNumber();if(!Number.isSafeInteger(n))throw new Error("Unsupported parameter");const i=g(r);let o=this,a=new d(s);for(;0!==n;)n%2!=0&&(a=a.mul(o).mod(i,e)),o=o.pow(u).mod(i,e),n=Math.floor(n/2);return a}div(t){return this.convertToFraction().div(t)}divToInt(t){const r=g(t);if(r instanceof f)return this.convertToFraction().divToInt(r);const e=r,{a:n,b:i}=this.scaleNumber(e.number,e.decimalPos);return new d(n/i)}mod(t,e=r.TRUNCATED){const n=g(t);if(n instanceof f)return this.convertToFraction().mod(n);const i=n,{a:s,b:u,decimalPos:a}=this.scaleNumber(i.number,i.decimalPos),c=s%u,m=new d(c,a);if(e===r.TRUNCATED)return m;if(e===r.FLOORED)return Number(s<o)^Number(u<o)?m.add(u):m;if(e===r.EUCLIDEAN)return c<o?m.add(u<o?-u:u):m;throw new Error("Invalid ModType")}abs(){return new d(this.number<o?-this.number:this.number,this.decimalPos)}neg(){return this.mul(-s)}inv(){return this.convertToFraction().inv()}floor(r){return 0===this.decimalPos?this:this.round(r,t.TO_NEGATIVE)}ceil(r){return 0===this.decimalPos?this:this.round(r,t.TO_POSITIVE)}trunc(r){return 0===this.decimalPos?this:this.round(r,t.TO_ZERO)}isTieStr(t){if("5"!==t[0])return!1;for(let r=1;r<t.length;r++)if("0"!==t[r])return!1;return!0}_round(r,e){const n=this.decimalPos-r;if(n<=0)return this;const i=h*BigInt(n),a=this.number/i;if(e===t.TO_ZERO)return new d(a,r);const c=this.number%i;if(c===o)return new d(a,r);if(e===t.AWAY_FROM_ZERO){const t=this.number<o?a-s:a+s;return new d(t,r)}if(e===t.TO_POSITIVE){const t=this.number<o?a:a+s;return new d(t,r)}if(e===t.TO_NEGATIVE){const t=this.number>=o?a:a-s;return new d(t,r)}if(![void 0,t.NEAREST_TO_ZERO,t.NEAREST_AWAY_FROM_ZERO,t.NEAREST_TO_POSITIVE,t.NEAREST_TO_NEGATIVE,t.NEAREST_TO_EVEN].includes(e))throw new Error("Invalid rounding mode. Use the predefined values from the RoundingMode enum.");let m=(c<o?-c:c).toString();if(m.length<n&&(m="0"),this.isTieStr(m)){if(e===t.NEAREST_TO_ZERO)return new d(a,r);if(e===t.NEAREST_AWAY_FROM_ZERO){const t=this.number<o?a-s:a+s;return new d(t,r)}if(void 0===e\|\|e===t.NEAREST_TO_POSITIVE){const t=this.number<o?a:a+s;return new d(t,r)}if(e===t.NEAREST_TO_NEGATIVE){const t=this.number>=o?a:a-s;return new d(t,r)}if(e===t.NEAREST_TO_EVEN){if(a%u===o)return new d(a,r);return new d(a<o?a-s:a+s,r)}}if(Number(m[0])<5)return new d(a,r);const l=this.number<o?a-s:a+s;return new d(l,r)}round(t,r){if(t=void 0===t?0:t,!Number.isSafeInteger(t)\|\|t<0)throw new Error("Invalid value for decimals");return this._round(t,r).normalize()}_incExponent(t){if(0===t)return this;let r=this.number,e=this.decimalPos;if(t<0)e-=t;else{const n=Math.min(t,this.decimalPos);e-=n;const i=t-n;i>0&&(r=hBigInt(i))}return new d(r,e)}countDigits(){if(this.number===o)return 1;let t=0,r=this.number<o?-this.number:this.number;for(;r>o;)r/=h,t++;return t}toSubZeroNum(){const t=this.countDigits();return{subZeroNum:new d(this.number,t),exponentDiff:t-this.decimalPos}}roundToDigits(t,r){if(!Number.isSafeInteger(t)\|\|t<1)throw new Error("Invalid value for digits");const{subZeroNum:e,exponentDiff:n}=this.toSubZeroNum();let i=e.round(t,r);return i=i._incExponent(n),i}intPart(){return this.trunc()}fracPart(){return this.sub(this.trunc())}sign(){return this.number<o?-1:1}bitwiseAnd(t){if(t=w(t),!this.isInteger()\|\|-1===this.sign()\|\|!t.isInteger()\|\|-1===t.sign())throw new Error("Only positive integers are supported");t instanceof f&&(t=t.trunc());const r=ul;let e=this.normalize().number,n=t.trunc().normalize().number,i=o,a=s;for(;e>o&&n>o;){const t=BigInt.asUintN(24,e),o=BigInt.asUintN(24,n);i+=BigInt(Number(t)&Number(o))a,a=r,e/=r,n/=r}return new d(i)}bitwiseOr(t){if(t=w(t),!this.isInteger()\|\|-1===this.sign()\|\|!t.isInteger()\|\|-1===t.sign())throw new Error("Only positive integers are supported");t instanceof f&&(t=t.trunc());const r=u*l;let e=this.normalize().number,n=t.trunc().normalize().number,i=o,a=s;for(;e>o\|\|n>o;){const t=BigInt.asUintN(24,e),o=BigInt.asUintN(24,n);i+=BigInt(Number(t)\|Number(o))a,a=r,e/=r,n/=r}return new d(i)}bitwiseXor(t){if(t=w(t),!this.isInteger()\|\|-1===this.sign()\|\|!t.isInteger()\|\|-1===t.sign())throw new Error("Only positive integers are supported");t instanceof f&&(t=t.trunc());const r=ul;let e=this.normalize().number,n=t.trunc().normalize().number,i=o,a=s;for(;e>o\|\|n>o;){const t=BigInt.asUintN(24,e),o=BigInt.asUintN(24,n);i+=BigInt(Number(t)^Number(o))a,a=r,e/=r,n/=r}return new d(i)}shiftLeft(t){if(!this.isInteger()\|\|-1===this.sign())throw new Error("Only positive integers are supported");if(!Number.isSafeInteger(t)\|\|t<0)throw new Error("Invalid value for bitCount");const r=uBigInt(t);return this.mul(r)}shiftRight(t){if(!this.isInteger()\|\|-1===this.sign())throw new Error("Only positive integers are supported");if(!Number.isSafeInteger(t)\|\|t<0)throw new Error("Invalid value for bitCount");const r=uBigInt(t);return new d(this.normalize().number/r)}cmp(t){const r=g(t);if(r instanceof f)return-r.cmp(this);const e=r,{a:n,b:i}=this.scaleNumber(e.number,e.decimalPos);return n===i?0:n>i?1:-1}eq(t){return 0===this.cmp(t)}lt(t){return-1===this.cmp(t)}lte(t){return this.cmp(t)<=0}gt(t){return 1===this.cmp(t)}gte(t){return this.cmp(t)>=0}clamp(t,r){const e=w(t),n=w(r);if(e.gt(n))throw new Error("Min parameter has to be smaller than max");return this.lt(e)?e:this.gt(n)?n:this}isZero(){return this.number===o}isOne(){if(0===this.decimalPos)return this.number===s;const t=hBigInt(this.decimalPos),r=this.number/t;return r===s&&rt===this.number}isInteger(){return 0===this.decimalPos\|\|this.number%hBigInt(this.decimalPos)===o}serialize(){return[this.number,this.decimalPos]}getFractionParts(t=!0){return this.convertToFraction().getFractionParts(t)}normalize(){if(0===this.decimalPos)return this;let t=this.decimalPos,r=this.number;for(;t>0&&r%h===o;)t--,r/=h;return new d(r,t)}convertToFraction(){if(0===this.decimalPos)return new f(this.number,s);const t=hBigInt(this.decimalPos);return new f(this.number,t)}toNumber(){return Number(this.toPrecision(20))}toFixed(r,e=t.TO_ZERO,i=!1){if(!Number.isSafeInteger(r)\|\|r<0)throw new Error("Invalid parameter");const o=this._round(r,e);return n(o.number,o.decimalPos,r,i)}toExponential(r,n=t.TO_ZERO,i=!1){if(!Number.isSafeInteger(r)\|\|r<0)throw new Error("Invalid parameter");const o=this.roundToDigits(r+1,n).normalize(),s=-1===o.sign(),u=o.abs(),a=u.number.toString(),c=a.length<=r?`${a}${"0".repeat(r-a.length+1)}`:a.slice(0,r+1);let m=c;c.length>1&&(m=`${c.slice(0,1)}.${c.slice(1)}`,i&&(m=e(m)));const h=u.decimalPos,l=a.length-1-h;return`${s?"-":""}${m}e${l>=0?"+":""}${l}`}toBase(t,r){if(!Number.isSafeInteger(t)\|\|t<2\|\|t>16)throw new Error("Invalid radix");if(void 0!==r&&(!Number.isSafeInteger(r)\|\|r<0))throw new Error("Invalid parameter");const e=this.normalize();if(0===e.decimalPos)return e.number.toString(t);const n=void 0===r?Number.MAX_SAFE_INTEGER:r;let i=e.intPart(),o=e.sub(i);const s=-1===e.sign();s&&(i=i.neg(),o=o.neg());const u=new Map;let a=[];for(;!o.isZero();){const r=o.mul(t),e=r.toString(),i=u.get(e);if(void 0!==i){a=[...a.slice(0,i-1),"(",...a.slice(i-1),")"];break}if(a.length===n)break;const s=Math.abs(r.intPart().toNumber());a.push(s.toString(t)),o=r.fracPart(),u.set(e,a.length)}const c=a.join("");return`${s?"-":""}${i.number.toString(t)}${a.length?".":""}${c}`}toFraction(){return this.convertToFraction().toFraction()}toString(t,r){if(void 0===t\|\|10===t){const t=void 0!==r?this.trunc(r):this;return n(t.number,t.decimalPos,t.decimalPos,!0)}return this.toBase(t,r)}toPrecision(r,i=t.TO_ZERO,o=!1){if(!Number.isSafeInteger(r)\|\|r<1)throw new Error("Invalid parameter");const s=this.roundToDigits(r,i),{subZeroNum:u,exponentDiff:a}=s.toSubZeroNum(),c=-1===u.sign();let m=n(u.number,u.decimalPos,u.decimalPos,!1);m=m.slice(c?3:2),m=m.slice(0,Math.max(r,a));const h=m.slice(0,Math.max(0,a)),l=m.slice(Math.max(0,a)),d=Math.max(0,r-h.length-l.length),f="0".repeat(a<0?-a:0);let g=h\|\|"0";if(l.length+f.length+d>0){g+=`.${f}${l}${"0".repeat(d)}`,o&&(g=e(g))}return c?`-${g}`:g}valueOf(){throw new Error("Unsafe conversion to Number type! Use toNumber() instead.")}}class f{constructor(t,r){if(this.type="fraction","bigint"==typeof t&&"bigint"==typeof r)this.numerator=t,this.denominator=r;else{const e=this.parseParameter(t),n=this.parseParameter(r),i=e.div(n),o=i instanceof d?i.convertToFraction():i;this.numerator=o.numerator,this.denominator=o.denominator}if(this.denominator===o)throw new Error("Division by zero")}parseRepeatingDecimal(t){if(!t.includes("("))return new d(t).convertToFraction();const r=(t=t.trim()).match(/^(-?[0-9])\.([0-9]+)?$([0-9]+)$(?:[eE]([+-]?[0-9]+))?$/);if(!r)throw new Error(`Cannot parse string "${t}"`);const e="-"===r[1]?"-0":r[1],n=r[2]??"",i=r[3],o=r[4],s=BigInt(e+n+i)-BigInt(e+n),u=BigInt("9".repeat(i.length)+"0".repeat(n.length)),a=new f(s,u);if(void 0!==o){const t=o.startsWith("-"),r=hBigInt(t?o.slice(1):o);return t?a.div(r).normalize():a.mul(r).normalize()}return a.simplify()}parseParameter(t){if(t instanceof f)return t;if(t instanceof d)return t.convertToFraction();if("number"==typeof t){if(!Number.isSafeInteger(t))throw new Error("Floating point values as numbers are unsafe. Please provide them as a string.");return new f(BigInt(t),s)}if("bigint"==typeof t)return new f(t,s);if("string"==typeof t){const r=t.split("/");if(r.length>2)throw new Error(`Cannot parse string '${t}'`);const e=this.parseRepeatingDecimal(r[0]),n=r[1]?this.parseRepeatingDecimal(r[1]):new f(s,s);return e.div(n).convertToFraction()}throw new Error("Unsupported parameter!")}add(t){const{numerator:r,denominator:e}=this.parseParameter(t);return this.denominator===e?new f(this.numerator+r,this.denominator):new f(this.numeratore+rthis.denominator,ethis.denominator)}sub(t){const{numerator:r,denominator:e}=this.parseParameter(t);return this.add(new f(-r,e))}mul(t){const{numerator:r,denominator:e}=this.parseParameter(t);return new f(this.numeratorr,this.denominatore)}div(t){const{numerator:r,denominator:e}=this.parseParameter(t);return this.mul(new f(e,r))}divToInt(t){return this.div(t).trunc()}mod(t,e=r.TRUNCATED){const n=this.parseParameter(t),i=n.denominatorthis.numerator%(n.numeratorthis.denominator),o=this.denominatorn.denominator,s=new f(i,o);if(e===r.TRUNCATED)return s;if(e===r.FLOORED)return Number(-1===this.sign())^Number(-1===n.sign())?s.add(n):s;if(e===r.EUCLIDEAN)return-1===s.sign()?s.add(-1===n.sign()?n.neg():n):s;throw new Error("Invalid ModType")}pow(t){const r=this.parseParameter(t);if(!r.isInteger())throw new Error("Unsupported parameter");const e=r.numerator/r.denominator,n=e<o?-e:e,i=new f(this.numeratorn,this.denominatorn);return e<o?i.inv():i}powm(t,r,e){const n=this.parseParameter(t);if(!n.isInteger())throw new Error("Unsupported parameter");let i=n.toNumber();const o=this.parseParameter(r);let a=this,c=new f(s,s);for(;0!==i;)i%2!=0&&(c=c.mul(a).mod(o,e)),a=a.pow(u).mod(o,e),i=Math.floor(i/2);return c}inv(){return new f(this.denominator,this.numerator)}floor(r){return this.denominator===s?new d(this.numerator):this.round(r,t.TO_NEGATIVE)}ceil(r){return this.denominator===s?new d(this.numerator):this.round(r,t.TO_POSITIVE)}trunc(r){return this.denominator===s?new d(this.numerator):this.round(r,t.TO_ZERO)}round(t,r){if(t=void 0===t?0:t,!Number.isSafeInteger(t)\|\|t<0)throw new Error("Invalid value for decimals");const e=this.toFixedNumber(t+1);if(this.sub(e).isZero())return e.round(t,r);return new d(`${e.toFixed(t+1)}1`).round(t,r)}roundToDigits(t,r){if(!Number.isSafeInteger(t)\|\|t<1)throw new Error("Invalid value for digits");if(this.isZero())return new d(o);let e=this.abs(),n=0;for(;e.gte(s);)e=e.div(h),n++;const i=new f(s,h);for(;e.lt(i);)e=e.mul(h),n--;let u=e.round(t,r);return u=u._incExponent(n),-1===this.sign()?u.neg():u}gcd(t,r){let e=t<o?-t:t,n=r<o?-r:r;if(n>e){const t=e;e=n,n=t}for(;;){if(n===o)return e;if(e%=n,e===o)return n;n%=e}}simplify(){let{numerator:t,denominator:r}=this;const e=this.gcd(t,r);return e>s&&(t/=e,r/=e),r<o&&(t=-t,r=-r),new f(t,r)}normalize(){const{numerator:r,denominator:e}=this.simplify();if(e===s)return new d(r,0);const n=new f(r,e),{cycleLen:i,cycleStart:o}=n.getDecimalFormat(0);return 0!==i?n:n.round(o,t.TO_ZERO)}getFractionParts(t=!0){const r=t?this.simplify():this;return{numerator:new d(r.numerator),denominator:new d(r.denominator)}}sign(){return(this.numerator<o?-1:1)(this.denominator<o?-1:1)}abs(){return new f(this.numerator<o?-this.numerator:this.numerator,this.denominator<o?-this.denominator:this.denominator)}neg(){return this.mul(-s)}intPart(){return this.trunc()}fracPart(){return this.sub(this.trunc())}cmp(t){const r=this.parseParameter(t),e=this.denominator===r.denominator,n=e?this.numerator:this.numeratorr.denominator,i=e?r.numerator:r.numeratorthis.denominator;return n===i?0:n>i?1:-1}eq(t){return 0===this.cmp(t)}lt(t){return-1===this.cmp(t)}lte(t){return this.cmp(t)<=0}gt(t){return 1===this.cmp(t)}gte(t){return this.cmp(t)>=0}clamp(t,r){const e=w(t),n=w(r);if(e.gt(n))throw new Error("Min parameter has to be smaller than max");return this.lt(e)?e:this.gt(n)?n:this}isZero(){return this.numerator===o}isOne(){return this.numerator===this.denominator}isInteger(){return this.numerator%this.denominator===o}serialize(){return[this.numerator,this.denominator]}toNumber(){return Number(this.toPrecision(20))}convertToFraction(){return this}getNumberForBitwiseOp(){if(!this.isInteger()\|\|-1===this.sign())throw new Error("Only positive integers are supported");return this.intPart()}bitwiseAnd(t){return this.getNumberForBitwiseOp().bitwiseAnd(t)}bitwiseOr(t){return this.getNumberForBitwiseOp().bitwiseOr(t)}bitwiseXor(t){return this.getNumberForBitwiseOp().bitwiseXor(t)}shiftLeft(t){return this.getNumberForBitwiseOp().shiftLeft(t)}shiftRight(t){return this.getNumberForBitwiseOp().shiftRight(t)}getDecimalFormat(t){t=void 0===t?Number.MAX_SAFE_INTEGER:t;let r=this.denominator<o?-this.denominator:this.denominator,e=0;for(;r%u===o;)r/=u,e++;let n=0;for(;r%m===o;)r/=m,n++;const i=Math.max(e,n);if(r===s)return{cycleLen:0,cycleStart:i};const a=Math.max(1,t-i);let c=h%r,l=1;for(;c!==s;){if(l===a)return{cycleLen:null,cycleStart:i};c=ch%r,l++}return{cycleLen:l,cycleStart:i}}toFixed(r,e=t.TO_ZERO,n=!1){if(!Number.isSafeInteger(r)\|\|r<0)throw new Error("Invalid parameter");return this.round(r,e).toFixed(r,t.TO_ZERO,n)}toRepeatingParts(t){if(this.isZero())return["0","",""];const{cycleLen:r,cycleStart:n}=this.simplify().getDecimalFormat(t);if(null===r\|\|0===r){const r=t??n,i=this.toFixed(r),o=e(i).split(".");return[o[0],o[1]??"",""]}const i=n+r,o=this.toFixed(i).split(".");return[o[0],o[1].slice(0,n),o[1].slice(n)]}toRepeatingDigits(t){const r=this.toRepeatingParts(t);let e=r[0];return(r[1]\|\|r[2])&&(e+=`.${r[1]}`),r[2]&&(e+=`(${r[2]})`),e}toExponential(r,e=t.TO_ZERO,n=!1){if(!Number.isSafeInteger(r)\|\|r<0)throw new Error("Invalid parameters");return this.toFixedNumber(r).toExponential(r,e,n)}toFraction(){const{numerator:t,denominator:r}=this.getFractionParts(!0);return`${t.toString()}/${r.toString()}`}toFixedNumber(t){const 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r=new d(this.fn(t)),e=Math.min(this.max,t);return this.cachedDecimals!==e&&(this.cache=r.trunc(e),this.cachedDecimals=e),r}}const O=(t,r)=>{let e=i(w(t),r);if(e.isOne())return new d(0).trunc(r);if(e.lte(0))throw new Error("Invalid parameter");let n=0;const a=w("0.1");for(;e.sub(s).abs().gt(a);)e=new d(I(e,r+10)),n++;const c=function(t,r){const e=t.pow(u).normalize();let n=t,i=s,o=w(t);for(;;){n=n.mul(e),i+=u;const t=n.div(i).trunc(r+10);o=o.add(t),yield{term:t,sum:o}}}(e.sub(s).div(e.add(s)),r);for(const{term:t,sum:e}of c)if(t.isZero()){return e.mul(u*BigInt(n+1)).trunc(r)}return w(o)},T=(t,r,e)=>{if(!Number.isSafeInteger(t)\|\|t<2)throw new Error("Invalid parameter for N");const n=O(r,e+10),i=O(t,e+10);return new d(n).div(i).trunc(e)},P=new v((t=>O(u,t)),200),_=(t,r)=>new d(O(t,r+10)).div(P.get(r+10)).trunc(r),S=new v((t=>O(h,t)),200),R=(t,r)=>new d(O(t,r+10)).div(S.get(r+10)).trunc(r);const A=(t,r)=>{const e=i(w(t),r),n=w(`1e-${r+5}`),a=function(t,r){let 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a=r.div(o).trunc(e+10);c=c.add(a),yield{term:a,sum:c}}}(h,e);for(const{term:t,sum:r}of g)if(t.lt(f))return $(r,d,e);return w(0)},D=(t,r)=>{const e=new d(B(r+10)),n=i(w(t),r+5);return x(e.div(u).sub(n),r+5).trunc(r)},M=(t,r)=>{const e=i(w(t),r+5),{specialCaseDeg:n,quadrant:o,subHalfPiAngle:c}=Z(e,r),m=1===o\|\|3===o;if(null!==n){if(0===n)return $("0",m,r);if(30===n)return $(w(s).div(I(a,r+5)),m,r);if(4===n)return $("1",m,r);if(60===n)return $(I(a,r+5),m,r);if(90===n)throw new Error("Out of range");throw new Error}const h=w(x(c.mul(u),r+5)),l=w(s).sub(h).div(w(s).add(h)).round(r+5),d=I(l,r+5).trunc(r);return m?d:d.neg()};const z=(t,r)=>{let e=i(w(t),r);if(e.isZero())return w(0);if(e.abs().isOne())return w(B(r)).div(4e.sign()).trunc(r);let n=0;const o=w("0.42");for(;e.abs().gt(o);){const t=w(I(e.pow(u).add(s),r+10));e=e.div(t.add(s)),n++}const c=w(`1e-${r+10}`),m=function(t,r){const e=t.pow(u).normalize(),n=e.pow(u).normalize();let i=a,o=t.sub(t.mul(e).div(i)),s=t.mul(n);for(;;){i+=u;const t=i+u,a=s.mul(e.mul(-i).add(t)).div(it);i=t,s=s.mul(n),o=o.add(a).trunc(r+10),yield{term:a,sum:o}}}(e,r);for(const{term:t,sum:e}of m)if(t.abs().lt(c)){return e.mul(u*BigInt(n)).trunc(r)}return w(0)},U=(t,r)=>{const e=i(w(t),r);if(e.isZero())return w(o);if(e.abs().isOne())return w(B(r)).mul(e.sign()).div(u).trunc(r);if(e.abs().eq("1/2"))return w(B(r)).mul(e.sign()).div(6).trunc(r);if(e.gt(s)\|\|e.lt(-s))throw new Error("Out of range");const n=w(I(e.pow(u).neg().add(s),r+10));return w(z(e.div(n.add(s)),r+10)).mul(u).trunc(r)},C=(t,r)=>{const e=i(w(t),r);if(e.isZero())return w(B(r)).div(u).trunc(r);if(e.isOne())return w(o);if(e.abs().isOne())return B(r);if(e.abs().eq("1/2")){const t=w(B(r)).div(a);return-1===e.sign()?t.mul(u).trunc(r):t.trunc(r)}if(e.gt(s)\|\|e.lt(-s))throw new Error("Out of range");return w(B(r+10)).div(u).sub(U(e,r+10)).trunc(r)};const V=(t,r)=>{const e=i(w(t),r),n=new d(`1e-${r+5}`),a=function(t,r){let e=t,n=s;const i=t.pow(u).normalize();let o=t.trunc(r+5),a=u;for(;;){e=e.mul(i),n=a(a+s),a+=u;const t=e.div(n);o=o.add(t).trunc(r+5),yield{term:t,sum:o}}}(e,r);for(const{term:t,sum:e}of a)if(t.abs().lt(n))return e.trunc(r);return w(o)};const L=(t,r)=>{const e=i(w(t),r),n=new d(`1e-${r+5}`),c=function(t,r){const e=t.pow(u).normalize();let n=e,i=u,o=n.div(i).add(s).trunc(r+5),c=a;for(;;){n=n.mul(e),i=c*(c+s),c+=u;const t=n.div(i);o=o.add(t).trunc(r+5),yield{term:t,sum:o}}}(e,r);for(const{term:t,sum:e}of c)if(t.abs().lt(n))return e.trunc(r);return w(o)},G=(t,r)=>{const e=i(w(t),r);if(e.isZero())return w(o);const n=L(e,r+10).abs();return I(n.pow(u).sub(s),r+10).div(n).mul(e.sign()).trunc(r)},W=(t,r)=>{const e=i(w(t),r);if(e.isZero())return w(o);const n=I(e.pow(u).add(s),r+5);return O(e.add(n),r+5).trunc(r)},q=(t,r)=>{const e=i(w(t),r);if(e.isOne())return w(o);if(e.lt(s))throw new Error("Out of range");const n=I(e.pow(u).sub(s),r+5);return O(e.add(n),r+5).trunc(r)},Y=(t,r)=>{const e=i(w(t),r);if(e.abs().gte(s))throw new Error("Out of range");if(e.isZero())return w(o);const n=O(e.add(s).div(e.neg().add(s)),r+5);return w(n).div(u).trunc(r)};export{w as ExactNumber,r as ModType,B as PI,t as RoundingMode,C as acos,q as acosh,U as asin,W as asinh,z as atan,Y as atanh,N as cbrt,x as cos,L as cosh,A as exp,O as log,R as log10,_ as log2,T as logn,p as nthroot,F as pow,D as sin,V as sinh,I as sqrt,M as tan,G as tanh};

dist/index.umd.min.js

		/*!
		* exactnumber v0.11.0 (https://www.npmjs.com/package/exactnumber)
		* exactnumber v1.0.0 (https://www.npmjs.com/package/exactnumber)
		* (c) Dani Biro
		@@ -7,2 +7,2 @@ * @license MIT

		!function(n,t){"object"==typeof exports&&"undefined"!=typeof module?t(exports):"function"==typeof define&&define.amd?define(["exports"],t):t((n="undefined"!=typeof globalThis?globalThis:n\|\|self).exactnumber={})}(this,(function(n){"use strict";var t,r;n.RoundingMode=void 0,(t=n.RoundingMode\|\|(n.RoundingMode={}))[t.NEAREST_TO_POSITIVE=201008]="NEAREST_TO_POSITIVE",t[t.NEAREST_TO_NEGATIVE=201009]="NEAREST_TO_NEGATIVE",t[t.NEAREST_TO_EVEN=201010]="NEAREST_TO_EVEN",t[t.NEAREST_TO_ZERO=201011]="NEAREST_TO_ZERO",t[t.NEAREST_AWAY_FROM_ZERO=201012]="NEAREST_AWAY_FROM_ZERO",t[t.TO_POSITIVE=201001]="TO_POSITIVE",t[t.TO_NEGATIVE=201002]="TO_NEGATIVE",t[t.TO_ZERO=201003]="TO_ZERO",t[t.AWAY_FROM_ZERO=201004]="AWAY_FROM_ZERO",n.ModType=void 0,(r=n.ModType\|\|(n.ModType={})).TRUNCATED="T",r.FLOORED="F",r.EUCLIDEAN="E";const e=n=>{const t=n.indexOf(".");if(-1===t)return n;let r=n.length;for(;r>t&&"0"===n.charAt(r-1);)r--;const e=t===r-1?t:r;return 0===e?"0":n.slice(0,e)},i=(n,t,r,i)=>{let o=n.toString();if(0===t&&0===r)return o;const s=o.startsWith("-");if(s&&(o=o.slice(1)),t>=o.length&&(o="0".repeat(t-o.length+1)+o),t>0){const n=o.slice(0,-t),s=o.slice(-t),u=r<=t?s.slice(0,r):`${s}${"0".repeat(r-t)}`;0!==u.length?(o=`${n}.${u}`,i&&(o=e(o))):o=n}else r>0&&(o=`${o}.${"0".repeat(r)}`);return s?`-${o}`:o},o=(t,r)=>(t=t.normalize())instanceof s?t.round(r,n.RoundingMode.NEAREST_AWAY_FROM_ZERO):t;class s{constructor(n,t=0){if(this.type="fixed","bigint"==typeof n)this.number=n,this.decimalPos=t;else{const t=this.parseConstructorParameter(n);this.number=t.number,this.decimalPos=t.decimalPos}}parseConstructorParameter(n){if(n instanceof s)return{number:n.number,decimalPos:n.decimalPos};if(n instanceof u){if(!n.isInteger())throw new Error("Cannot create FixedNumber from non-integer Fraction");return{number:n.trunc().number,decimalPos:0}}if("number"==typeof n){if(!Number.isSafeInteger(n))throw new Error("The specified number cannot be exactly represented as an integer. Please provide a string instead.");return{number:BigInt(n),decimalPos:0}}if("string"==typeof n){if(0===(n=n.trim()).length)throw new Error("Empty string is not allowed");const t=n.match(/^(-?[0-9])(?:\.([0-9]))?(?:[eE]([+-]?[0-9]+))?$/);if(!t)throw new Error(`Cannot parse number "${n}"`);let r=0,e=t[1]??"0";if(void 0!==t[2]&&(e+=t[2],r+=t[2].length),void 0!==t[3]){const n=Number(t[3]);n>0?e+="0".repeat(n):r-=n}return{number:BigInt(e),decimalPos:r}}throw new Error("Unsupported parameter!")}scaleNumber(n,t){const r=Math.max(this.decimalPos,t);return{a:r===this.decimalPos?this.number:this.number10nBigInt(r-this.decimalPos),b:r===t?n:n10n*BigInt(r-t),decimalPos:r}}add(n){const t=a(n);if(t instanceof u)return t.add(this);const r=t,{a:e,b:i,decimalPos:o}=this.scaleNumber(r.number,r.decimalPos);return new s(e+i,o)}sub(n){const t=a(n);return this.add(t.neg())}mul(n){const t=a(n);if(t instanceof u)return t.mul(this);const r=t,e=this.numberr.number;return new s(e,this.decimalPos+r.decimalPos)}pow(n){const t=a(n).toNumber();if(!Number.isSafeInteger(t))throw new Error("Unsupported parameter");const r=Math.abs(t),e=new s(this.number*BigInt(r),this.decimalPosr);return t<0?e.inv():e}div(n){return this.convertToFraction().div(n)}divToInt(n){const t=a(n);if(t instanceof u)return this.convertToFraction().divToInt(t);const r=t,{a:e,b:i}=this.scaleNumber(r.number,r.decimalPos);return new s(e/i)}mod(t,r=n.ModType.TRUNCATED){const e=a(t);if(e instanceof u)return this.convertToFraction().mod(e);const i=e,{a:o,b:c,decimalPos:m}=this.scaleNumber(i.number,i.decimalPos),d=o%c,h=new s(d,m);if(r===n.ModType.TRUNCATED)return h;if(r===n.ModType.FLOORED)return Number(o<0)^Number(c<0)?h.add(c):h;if(r===n.ModType.EUCLIDEAN)return d<0?h.add(c<0?-c:c):h;throw new Error("Invalid ModType")}abs(){return new s(this.number<0?-this.number:this.number,this.decimalPos)}neg(){return this.mul(-1n)}inv(){return this.convertToFraction().inv()}floor(t){return 0===this.decimalPos?this:this.round(t,n.RoundingMode.TO_NEGATIVE)}ceil(t){return 0===this.decimalPos?this:this.round(t,n.RoundingMode.TO_POSITIVE)}trunc(t){return 0===this.decimalPos?this:this.round(t,n.RoundingMode.TO_ZERO)}isTieStr(n){if("5"!==n[0])return!1;for(let t=1;t<n.length;t++)if("0"!==n[t])return!1;return!0}_round(t,r){const e=this.decimalPos-t;if(e<=0)return this;const i=10n*BigInt(e),o=this.number/i;if(r===n.RoundingMode.TO_ZERO)return new s(o,t);const u=this.number%i;if(0n===u)return new s(o,t);if(r===n.RoundingMode.AWAY_FROM_ZERO){const n=this.number<0n?o-1n:o+1n;return new s(n,t)}if(r===n.RoundingMode.TO_POSITIVE){const n=this.number<0n?o:o+1n;return new s(n,t)}if(r===n.RoundingMode.TO_NEGATIVE){const n=this.number>=0n?o:o-1n;return new s(n,t)}if(![void 0,n.RoundingMode.NEAREST_TO_ZERO,n.RoundingMode.NEAREST_AWAY_FROM_ZERO,n.RoundingMode.NEAREST_TO_POSITIVE,n.RoundingMode.NEAREST_TO_NEGATIVE,n.RoundingMode.NEAREST_TO_EVEN].includes(r))throw new Error("Invalid rounding mode. Use the predefined values from the RoundingMode enum.");let a=(u<0n?-u:u).toString();if(a.length<e&&(a="0"),this.isTieStr(a)){if(r===n.RoundingMode.NEAREST_TO_ZERO)return new s(o,t);if(r===n.RoundingMode.NEAREST_AWAY_FROM_ZERO){const n=this.number<0n?o-1n:o+1n;return new s(n,t)}if(void 0===r\|\|r===n.RoundingMode.NEAREST_TO_POSITIVE){const n=this.number<0n?o:o+1n;return new s(n,t)}if(r===n.RoundingMode.NEAREST_TO_NEGATIVE){const n=this.number>=0n?o:o-1n;return new s(n,t)}if(r===n.RoundingMode.NEAREST_TO_EVEN){if(o%2n===0n)return new s(o,t);return new s(o<0n?o-1n:o+1n,t)}}if(Number(a[0])<5)return new s(o,t);const c=this.number<0?o-1n:o+1n;return new s(c,t)}round(n,t){if(n=void 0===n?0:n,!Number.isSafeInteger(n)\|\|n<0)throw new Error("Invalid value for decimals");return this._round(n,t).normalize()}_incExponent(n){if(0===n)return this;let t=this.number,r=this.decimalPos;if(n<0)r-=n;else{const e=Math.min(n,this.decimalPos);r-=e;const i=n-e;i>0&&(t=10nBigInt(i))}return new s(t,r)}countDigits(){if(0n===this.number)return 1;let n=0,t=this.number<0?-this.number:this.number;for(;t>0n;)t/=10n,n++;return n}toSubZeroNum(){const n=this.countDigits();return{subZeroNum:new s(this.number,n),exponentDiff:n-this.decimalPos}}roundToDigits(n,t){if(!Number.isSafeInteger(n)\|\|n<1)throw new Error("Invalid value for digits");const{subZeroNum:r,exponentDiff:e}=this.toSubZeroNum();let i=r.round(n,t);return i=i._incExponent(e),i}intPart(){return this.trunc()}fracPart(){return this.sub(this.trunc())}sign(){return this.number<0n?-1:1}bitwiseAnd(n){if(n=c(n),!this.isInteger()\|\|-1===this.sign()\|\|!n.isInteger()\|\|-1===n.sign())throw new Error("Only positive integers are supported");n instanceof u&&(n=n.trunc());const t=2n24n;let r=this.normalize().number,e=n.trunc().normalize().number,i=0n,o=1n;for(;r>0&&e>0;){const n=BigInt.asUintN(24,r),s=BigInt.asUintN(24,e);i+=BigInt(Number(n)&Number(s))o,o=t,r/=t,e/=t}return new s(i)}bitwiseOr(n){if(n=c(n),!this.isInteger()\|\|-1===this.sign()\|\|!n.isInteger()\|\|-1===n.sign())throw new Error("Only positive integers are supported");n instanceof u&&(n=n.trunc());const t=2n*24n;let r=this.normalize().number,e=n.trunc().normalize().number,i=0n,o=1n;for(;r>0\|\|e>0;){const n=BigInt.asUintN(24,r),s=BigInt.asUintN(24,e);i+=BigInt(Number(n)\|Number(s))o,o=t,r/=t,e/=t}return new s(i)}bitwiseXor(n){if(n=c(n),!this.isInteger()\|\|-1===this.sign()\|\|!n.isInteger()\|\|-1===n.sign())throw new Error("Only positive integers are supported");n instanceof u&&(n=n.trunc());const t=2n24n;let r=this.normalize().number,e=n.trunc().normalize().number,i=0n,o=1n;for(;r>0\|\|e>0;){const n=BigInt.asUintN(24,r),s=BigInt.asUintN(24,e);i+=BigInt(Number(n)^Number(s))o,o=t,r/=t,e/=t}return new s(i)}shiftLeft(n){if(!this.isInteger()\|\|-1===this.sign())throw new Error("Only positive integers are supported");if(!Number.isSafeInteger(n)\|\|n<0)throw new Error("Invalid value for bitCount");const t=2nBigInt(n);return this.mul(t)}shiftRight(n){if(!this.isInteger()\|\|-1===this.sign())throw new Error("Only positive integers are supported");if(!Number.isSafeInteger(n)\|\|n<0)throw new Error("Invalid value for bitCount");const t=2nBigInt(n);return new s(this.normalize().number/t)}cmp(n){const t=a(n);if(t instanceof u)return-t.cmp(this);const r=t,{a:e,b:i}=this.scaleNumber(r.number,r.decimalPos);return e===i?0:e>i?1:-1}eq(n){return 0===this.cmp(n)}lt(n){return-1===this.cmp(n)}lte(n){return this.cmp(n)<=0}gt(n){return 1===this.cmp(n)}gte(n){return this.cmp(n)>=0}clamp(n,t){const r=c(n),e=c(t);if(r.gt(e))throw new Error("Min parameter has to be smaller than max");return this.lt(r)?r:this.gt(e)?e:this}isZero(){return 0n===this.number}isOne(){if(0===this.decimalPos)return 1n===this.number;const n=10nBigInt(this.decimalPos),t=this.number/n;return 1n===t&&tn===this.number}isInteger(){return 0===this.decimalPos\|\|this.number%10nBigInt(this.decimalPos)===0n}serialize(){return[this.number,this.decimalPos]}getFractionParts(n=!0){return this.convertToFraction().getFractionParts(n)}normalize(){if(0===this.decimalPos)return this;let n=this.decimalPos,t=this.number;for(;n>0&&t%10n===0n;)n--,t/=10n;return new s(t,n)}convertToFraction(){if(0===this.decimalPos)return new u(this.number,1n);const n=10nBigInt(this.decimalPos);return new u(this.number,n)}toNumber(){return Number(this.toPrecision(20))}toFixed(t,r=n.RoundingMode.TO_ZERO){if(!Number.isSafeInteger(t)\|\|t<0)throw new Error("Invalid parameter");const e=this._round(t,r);return i(e.number,e.decimalPos,t,!1)}toExponential(t,r=n.RoundingMode.TO_ZERO){if(!Number.isSafeInteger(t)\|\|t<0)throw new Error("Invalid parameter");const e=this.roundToDigits(t+1,r).normalize(),i=-1===e.sign(),o=e.abs(),s=o.number.toString(),u=s.length<=t?`${s}${"0".repeat(t-s.length+1)}`:s.slice(0,t+1),a=u.length>1?`${u.slice(0,1)}.${u.slice(1)}`:u,c=o.decimalPos,m=s.length-1-c;return`${i?"-":""}${a}e${m>=0?"+":""}${m}`}toBase(n,t){if(!Number.isSafeInteger(n)\|\|n<2\|\|n>16)throw new Error("Invalid radix");if(void 0!==t&&(!Number.isSafeInteger(t)\|\|t<0))throw new Error("Invalid parameter");const r=this.normalize();if(0===r.decimalPos)return r.number.toString(n);const e=void 0===t?Number.MAX_SAFE_INTEGER:t;let i=r.intPart(),o=r.sub(i);const s=-1===r.sign();s&&(i=i.neg(),o=o.neg());const u=new Map;let a=[];for(;!o.isZero();){const t=o.mul(n),r=t.toString(),i=u.get(r);if(void 0!==i){a=[...a.slice(0,i-1),"(",...a.slice(i-1),")"];break}if(a.length===e)break;const s=Math.abs(t.intPart().toNumber());a.push(s.toString(n)),o=t.fracPart(),u.set(r,a.length)}return[s?"-":"",i.number.toString(n),a.length?".":"",...a].join("")}toFraction(){return this.convertToFraction().toFraction()}toString(n,t){if(void 0===n\|\|10===n){const n=void 0!==t?this.trunc(t):this;return i(n.number,n.decimalPos,n.decimalPos,!0)}return this.toBase(n,t)}toPrecision(t,r=n.RoundingMode.TO_ZERO){if(!Number.isSafeInteger(t)\|\|t<1)throw new Error("Invalid parameter");const e=this.roundToDigits(t,r),{subZeroNum:o,exponentDiff:s}=e.toSubZeroNum(),u=-1===o.sign();let a=i(o.number,o.decimalPos,o.decimalPos,!1);a=a.slice(u?3:2),a=a.slice(0,Math.max(t,s));const c=a.slice(0,Math.max(0,s)),m=a.slice(Math.max(0,s)),d=Math.max(0,t-c.length-m.length),h="0".repeat(d),l="0".repeat(s<0?-s:0);let f=c\|\|"0";return m.length+l.length+d>0&&(f+=`.${l}${m}${h}`),u?`-${f}`:f}valueOf(){throw new Error("Unsafe conversion to Number type! Use toNumber() instead.")}}class u{constructor(n,t){if(this.type="fraction","bigint"==typeof n&&"bigint"==typeof t)this.numerator=n,this.denominator=t;else{const r=this.parseParameter(n),e=this.parseParameter(t),i=r.div(e),o=i instanceof s?i.convertToFraction():i;this.numerator=o.numerator,this.denominator=o.denominator}if(0n===this.denominator)throw new Error("Division by zero")}parseRepeatingDecimal(n){if(!n.includes("("))return new s(n).convertToFraction();const t=(n=n.trim()).match(/^(-?[0-9])\.([0-9]+)?$([0-9]+)$(?:[eE]([+-]?[0-9]+))?$/);if(!t)throw new Error(`Cannot parse string "${n}"`);const r="-"===t[1]?"-0":t[1],e=t[2]??"",i=t[3],o=t[4],a=BigInt(r+e+i)-BigInt(r+e),c=BigInt("9".repeat(i.length)+"0".repeat(e.length)),m=new u(a,c);if(void 0!==o){const n=o.startsWith("-"),t=10nBigInt(n?o.slice(1):o);return n?m.div(t).normalize():m.mul(t).normalize()}return m.simplify()}parseParameter(n){if(n instanceof u)return n;if(n instanceof s)return n.convertToFraction();if("number"==typeof n){if(!Number.isSafeInteger(n))throw new Error("Floating point values as numbers are unsafe. Please provide them as a string.");return new u(BigInt(n),1n)}if("bigint"==typeof n)return new u(n,1n);if("string"==typeof n){const t=n.split("/");if(t.length>2)throw new Error(`Cannot parse string '${n}'`);const r=this.parseRepeatingDecimal(t[0]),e=t[1]?this.parseRepeatingDecimal(t[1]):new u(1n,1n);return r.div(e).convertToFraction()}throw new Error("Unsupported parameter!")}add(n){const{numerator:t,denominator:r}=this.parseParameter(n);return this.denominator===r?new u(this.numerator+t,this.denominator):new u(this.numeratorr+tthis.denominator,rthis.denominator)}sub(n){const{numerator:t,denominator:r}=this.parseParameter(n);return this.add(new u(-t,r))}mul(n){const{numerator:t,denominator:r}=this.parseParameter(n);return new u(this.numeratort,this.denominatorr)}div(n){const{numerator:t,denominator:r}=this.parseParameter(n);return this.mul(new u(r,t))}divToInt(n){return this.div(n).trunc()}mod(t,r=n.ModType.TRUNCATED){const e=this.parseParameter(t),i=e.denominatorthis.numerator%(e.numeratorthis.denominator),o=this.denominatore.denominator,s=new u(i,o);if(r===n.ModType.TRUNCATED)return s;if(r===n.ModType.FLOORED)return Number(-1===this.sign())^Number(-1===e.sign())?s.add(e):s;if(r===n.ModType.EUCLIDEAN)return s.sign()<0?s.add(e.sign()<0?e.neg():e):s;throw new Error("Invalid ModType")}pow(n){const t=this.parseParameter(n);if(!t.isInteger())throw new Error("Unsupported parameter");const r=t.numerator/t.denominator,e=r<0?-r:r,i=new u(this.numeratore,this.denominatore);return r<0?i.inv():i}inv(){return new u(this.denominator,this.numerator)}floor(t){return 1n===this.denominator?new s(this.numerator):this.round(t,n.RoundingMode.TO_NEGATIVE)}ceil(t){return 1n===this.denominator?new s(this.numerator):this.round(t,n.RoundingMode.TO_POSITIVE)}trunc(t){return 1n===this.denominator?new s(this.numerator):this.round(t,n.RoundingMode.TO_ZERO)}round(n,t){if(n=void 0===n?0:n,!Number.isSafeInteger(n)\|\|n<0)throw new Error("Invalid value for decimals");const r=this.toFixedNumber(n+1);if(this.sub(r).isZero())return r.round(n,t);return new s(`${r.toFixed(n+1)}1`).round(n,t)}roundToDigits(n,t){if(!Number.isSafeInteger(n)\|\|n<1)throw new Error("Invalid value for digits");if(this.isZero())return new s(0n);let r=this.abs(),e=0;for(;r.gte(1n);)r=r.div(10n),e++;const i=new u(1n,10n);for(;r.lt(i);)r=r.mul(10n),e--;let o=r.round(n,t);return o=o._incExponent(e),-1===this.sign()?o.neg():o}gcd(n,t){let r=n<0?-n:n,e=t<0?-t:t;if(e>r){const n=r;r=e,e=n}for(;;){if(0n===e)return r;if(r%=e,0n===r)return e;e%=r}}simplify(){let{numerator:n,denominator:t}=this;const r=this.gcd(n,t);return r>1n&&(n/=r,t/=r),t<0n&&(n=-n,t=-t),new u(n,t)}normalize(){const{numerator:t,denominator:r}=this.simplify();if(1n===r)return new s(t,0);const e=new u(t,r),{cycleLen:i,cycleStart:o}=e.getDecimalFormat(0);return 0!==i?e:e.round(o,n.RoundingMode.TO_ZERO)}getFractionParts(n=!0){const t=n?this.simplify():this;return{numerator:new s(t.numerator),denominator:new s(t.denominator)}}sign(){return(this.numerator<0n?-1:1)(this.denominator<0n?-1:1)}abs(){return new u(this.numerator<0n?-this.numerator:this.numerator,this.denominator<0n?-this.denominator:this.denominator)}neg(){return this.mul(-1n)}intPart(){return this.trunc()}fracPart(){return this.sub(this.trunc())}cmp(n){const t=this.parseParameter(n),r=this.denominator===t.denominator,e=r?this.numerator:this.numeratort.denominator,i=r?t.numerator:t.numeratorthis.denominator;return e===i?0:e>i?1:-1}eq(n){return 0===this.cmp(n)}lt(n){return-1===this.cmp(n)}lte(n){return this.cmp(n)<=0}gt(n){return 1===this.cmp(n)}gte(n){return this.cmp(n)>=0}clamp(n,t){const r=c(n),e=c(t);if(r.gt(e))throw new Error("Min parameter has to be smaller than max");return this.lt(r)?r:this.gt(e)?e:this}isZero(){return 0n===this.numerator}isOne(){return this.numerator===this.denominator}isInteger(){return this.numerator%this.denominator===0n}serialize(){return[this.numerator,this.denominator]}toNumber(){return Number(this.toPrecision(20))}convertToFraction(){return this}getNumberForBitwiseOp(){if(!this.isInteger()\|\|-1===this.sign())throw new Error("Only positive integers are supported");return this.intPart()}bitwiseAnd(n){return this.getNumberForBitwiseOp().bitwiseAnd(n)}bitwiseOr(n){return this.getNumberForBitwiseOp().bitwiseOr(n)}bitwiseXor(n){return this.getNumberForBitwiseOp().bitwiseXor(n)}shiftLeft(n){return this.getNumberForBitwiseOp().shiftLeft(n)}shiftRight(n){return this.getNumberForBitwiseOp().shiftRight(n)}getDecimalFormat(n){n=void 0===n?Number.MAX_SAFE_INTEGER:n;let t=this.denominator<0?-this.denominator:this.denominator,r=0;for(;t%2n===0n;)t/=2n,r++;let e=0;for(;t%5n===0n;)t/=5n,e++;const i=Math.max(r,e);if(1n===t)return{cycleLen:0,cycleStart:i};const o=Math.max(1,n-i);let s=10n%t,u=1;for(;1n!==s;){if(u===o)return{cycleLen:null,cycleStart:i};s=10ns%t,u++}return{cycleLen:u,cycleStart:i}}toFixed(t,r=n.RoundingMode.TO_ZERO){if(!Number.isSafeInteger(t)\|\|t<0)throw new Error("Invalid parameter");return this.round(t,r).toFixed(t)}toRepeatingParts(n){if(this.isZero())return["0","",""];const{cycleLen:t,cycleStart:r}=this.simplify().getDecimalFormat(n);if(null===t\|\|0===t){const t=n??r,i=this.toFixed(t),o=e(i).split(".");return[o[0],o[1]??"",""]}const i=r+t,o=this.toFixed(i).split(".");return[o[0],o[1].slice(0,r),o[1].slice(r)]}toRepeatingDigits(n){const t=this.toRepeatingParts(n);let r=t[0];return(t[1]\|\|t[2])&&(r+=`.${t[1]}`),t[2]&&(r+=`(${t[2]})`),r}toExponential(t,r=n.RoundingMode.TO_ZERO){if(!Number.isSafeInteger(t)\|\|t<0)throw new Error("Invalid parameters");return this.toFixedNumber(t).toExponential(t,r)}toFraction(){const{numerator:n,denominator:t}=this.getFractionParts(!0);return`${n.toString()}/${t.toString()}`}toFixedNumber(n){const 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		!function(t,r){"object"==typeof exports&&"undefined"!=typeof module?r(exports):"function"==typeof define&&define.amd?define(["exports"],r):r((t="undefined"!=typeof globalThis?globalThis:t\|\|self).exactnumber={})}(this,(function(t){"use strict";var r,e;t.RoundingMode=void 0,(r=t.RoundingMode\|\|(t.RoundingMode={}))[r.NEAREST_TO_POSITIVE=201008]="NEAREST_TO_POSITIVE",r[r.NEAREST_TO_NEGATIVE=201009]="NEAREST_TO_NEGATIVE",r[r.NEAREST_TO_EVEN=201010]="NEAREST_TO_EVEN",r[r.NEAREST_TO_ZERO=201011]="NEAREST_TO_ZERO",r[r.NEAREST_AWAY_FROM_ZERO=201012]="NEAREST_AWAY_FROM_ZERO",r[r.TO_POSITIVE=201001]="TO_POSITIVE",r[r.TO_NEGATIVE=201002]="TO_NEGATIVE",r[r.TO_ZERO=201003]="TO_ZERO",r[r.AWAY_FROM_ZERO=201004]="AWAY_FROM_ZERO",t.ModType=void 0,(e=t.ModType\|\|(t.ModType={})).TRUNCATED="T",e.FLOORED="F",e.EUCLIDEAN="E";const n=t=>{const r=t.indexOf(".");if(-1===r)return t;let e=t.length;for(;e>r&&"0"===t.charAt(e-1);)e--;const n=r===e-1?r:e;return 0===n?"0":t.slice(0,n)},i=(t,r,e,i)=>{let o=t.toString();if(0===r&&0===e)return o;const s=o.startsWith("-");if(s&&(o=o.slice(1)),r>=o.length&&(o="0".repeat(r-o.length+1)+o),r>0){const t=o.slice(0,-r),s=o.slice(-r),u=e<=r?s.slice(0,e):`${s}${"0".repeat(e-r)}`;0!==u.length?(o=`${t}.${u}`,i&&(o=n(o))):o=t}else e>0&&!i&&(o=`${o}.${"0".repeat(e)}`);return s?`-${o}`:o},o=(r,e)=>(r=r.normalize())instanceof f?r.round(e,t.RoundingMode.NEAREST_AWAY_FROM_ZERO):r,s=BigInt(0),u=BigInt(1),a=BigInt(2),c=BigInt(3),m=BigInt(4),d=BigInt(5),h=BigInt(10),l=BigInt(24);class f{constructor(t,r=0){if(this.type="fixed","bigint"==typeof t)this.number=t,this.decimalPos=r;else{const r=this.parseConstructorParameter(t);this.number=r.number,this.decimalPos=r.decimalPos}}parseConstructorParameter(t){if(t instanceof f)return{number:t.number,decimalPos:t.decimalPos};if(t instanceof g){if(!t.isInteger())throw new Error("Cannot create FixedNumber from non-integer Fraction");return{number:t.trunc().number,decimalPos:0}}if("number"==typeof t){if(!Number.isSafeInteger(t))throw new Error("The specified number cannot be exactly represented as an integer. Please provide a string instead.");return{number:BigInt(t),decimalPos:0}}if("string"==typeof t){if(0===(t=t.trim()).length)throw new Error("Empty string is not allowed");const r=t.match(/^(-?[0-9])(?:\.([0-9]))?(?:[eE]([+-]?[0-9]+))?$/);if(!r)throw new Error(`Cannot parse number "${t}"`);let e=0,n=r[1]??"0";if(void 0!==r[2]&&(n+=r[2],e+=r[2].length),void 0!==r[3]){const t=Number(r[3]);t>0?n+="0".repeat(t):e-=t}return{number:BigInt(n),decimalPos:e}}throw new Error("Unsupported parameter!")}scaleNumber(t,r){const e=Math.max(this.decimalPos,r);return{a:e===this.decimalPos?this.number:this.numberhBigInt(e-this.decimalPos),b:e===r?t:th*BigInt(e-r),decimalPos:e}}add(t){const r=w(t);if(r instanceof g)return r.add(this);const e=r,{a:n,b:i,decimalPos:o}=this.scaleNumber(e.number,e.decimalPos);return new f(n+i,o)}sub(t){const r=w(t);return this.add(r.neg())}mul(t){const r=w(t);if(r instanceof g)return r.mul(this);const e=r,n=this.numbere.number;return new f(n,this.decimalPos+e.decimalPos)}pow(t){const r=w(t).toNumber();if(!Number.isSafeInteger(r))throw new Error("Unsupported parameter");const e=Math.abs(r),n=new f(this.number*BigInt(e),this.decimalPose);return r<0?n.inv():n}powm(t,r,e){let n=w(t).toNumber();if(!Number.isSafeInteger(n))throw new Error("Unsupported parameter");const i=w(r);let o=this,s=new f(u);for(;0!==n;)n%2!=0&&(s=s.mul(o).mod(i,e)),o=o.pow(a).mod(i,e),n=Math.floor(n/2);return s}div(t){return this.convertToFraction().div(t)}divToInt(t){const r=w(t);if(r instanceof g)return this.convertToFraction().divToInt(r);const e=r,{a:n,b:i}=this.scaleNumber(e.number,e.decimalPos);return new f(n/i)}mod(r,e=t.ModType.TRUNCATED){const n=w(r);if(n instanceof g)return this.convertToFraction().mod(n);const i=n,{a:o,b:u,decimalPos:a}=this.scaleNumber(i.number,i.decimalPos),c=o%u,m=new f(c,a);if(e===t.ModType.TRUNCATED)return m;if(e===t.ModType.FLOORED)return Number(o<s)^Number(u<s)?m.add(u):m;if(e===t.ModType.EUCLIDEAN)return c<s?m.add(u<s?-u:u):m;throw new Error("Invalid ModType")}abs(){return new f(this.number<s?-this.number:this.number,this.decimalPos)}neg(){return this.mul(-u)}inv(){return this.convertToFraction().inv()}floor(r){return 0===this.decimalPos?this:this.round(r,t.RoundingMode.TO_NEGATIVE)}ceil(r){return 0===this.decimalPos?this:this.round(r,t.RoundingMode.TO_POSITIVE)}trunc(r){return 0===this.decimalPos?this:this.round(r,t.RoundingMode.TO_ZERO)}isTieStr(t){if("5"!==t[0])return!1;for(let r=1;r<t.length;r++)if("0"!==t[r])return!1;return!0}_round(r,e){const n=this.decimalPos-r;if(n<=0)return this;const i=h*BigInt(n),o=this.number/i;if(e===t.RoundingMode.TO_ZERO)return new f(o,r);const c=this.number%i;if(c===s)return new f(o,r);if(e===t.RoundingMode.AWAY_FROM_ZERO){const t=this.number<s?o-u:o+u;return new f(t,r)}if(e===t.RoundingMode.TO_POSITIVE){const t=this.number<s?o:o+u;return new f(t,r)}if(e===t.RoundingMode.TO_NEGATIVE){const t=this.number>=s?o:o-u;return new f(t,r)}if(![void 0,t.RoundingMode.NEAREST_TO_ZERO,t.RoundingMode.NEAREST_AWAY_FROM_ZERO,t.RoundingMode.NEAREST_TO_POSITIVE,t.RoundingMode.NEAREST_TO_NEGATIVE,t.RoundingMode.NEAREST_TO_EVEN].includes(e))throw new Error("Invalid rounding mode. Use the predefined values from the RoundingMode enum.");let m=(c<s?-c:c).toString();if(m.length<n&&(m="0"),this.isTieStr(m)){if(e===t.RoundingMode.NEAREST_TO_ZERO)return new f(o,r);if(e===t.RoundingMode.NEAREST_AWAY_FROM_ZERO){const t=this.number<s?o-u:o+u;return new f(t,r)}if(void 0===e\|\|e===t.RoundingMode.NEAREST_TO_POSITIVE){const t=this.number<s?o:o+u;return new f(t,r)}if(e===t.RoundingMode.NEAREST_TO_NEGATIVE){const t=this.number>=s?o:o-u;return new f(t,r)}if(e===t.RoundingMode.NEAREST_TO_EVEN){if(o%a===s)return new f(o,r);return new f(o<s?o-u:o+u,r)}}if(Number(m[0])<5)return new f(o,r);const d=this.number<s?o-u:o+u;return new f(d,r)}round(t,r){if(t=void 0===t?0:t,!Number.isSafeInteger(t)\|\|t<0)throw new Error("Invalid value for decimals");return this._round(t,r).normalize()}_incExponent(t){if(0===t)return this;let r=this.number,e=this.decimalPos;if(t<0)e-=t;else{const n=Math.min(t,this.decimalPos);e-=n;const i=t-n;i>0&&(r=hBigInt(i))}return new f(r,e)}countDigits(){if(this.number===s)return 1;let t=0,r=this.number<s?-this.number:this.number;for(;r>s;)r/=h,t++;return t}toSubZeroNum(){const t=this.countDigits();return{subZeroNum:new f(this.number,t),exponentDiff:t-this.decimalPos}}roundToDigits(t,r){if(!Number.isSafeInteger(t)\|\|t<1)throw new Error("Invalid value for digits");const{subZeroNum:e,exponentDiff:n}=this.toSubZeroNum();let i=e.round(t,r);return i=i._incExponent(n),i}intPart(){return this.trunc()}fracPart(){return this.sub(this.trunc())}sign(){return this.number<s?-1:1}bitwiseAnd(t){if(t=b(t),!this.isInteger()\|\|-1===this.sign()\|\|!t.isInteger()\|\|-1===t.sign())throw new Error("Only positive integers are supported");t instanceof g&&(t=t.trunc());const r=al;let e=this.normalize().number,n=t.trunc().normalize().number,i=s,o=u;for(;e>s&&n>s;){const t=BigInt.asUintN(24,e),s=BigInt.asUintN(24,n);i+=BigInt(Number(t)&Number(s))o,o=r,e/=r,n/=r}return new f(i)}bitwiseOr(t){if(t=b(t),!this.isInteger()\|\|-1===this.sign()\|\|!t.isInteger()\|\|-1===t.sign())throw new Error("Only positive integers are supported");t instanceof g&&(t=t.trunc());const r=a*l;let e=this.normalize().number,n=t.trunc().normalize().number,i=s,o=u;for(;e>s\|\|n>s;){const t=BigInt.asUintN(24,e),s=BigInt.asUintN(24,n);i+=BigInt(Number(t)\|Number(s))o,o=r,e/=r,n/=r}return new f(i)}bitwiseXor(t){if(t=b(t),!this.isInteger()\|\|-1===this.sign()\|\|!t.isInteger()\|\|-1===t.sign())throw new Error("Only positive integers are supported");t instanceof g&&(t=t.trunc());const r=al;let e=this.normalize().number,n=t.trunc().normalize().number,i=s,o=u;for(;e>s\|\|n>s;){const t=BigInt.asUintN(24,e),s=BigInt.asUintN(24,n);i+=BigInt(Number(t)^Number(s))o,o=r,e/=r,n/=r}return new f(i)}shiftLeft(t){if(!this.isInteger()\|\|-1===this.sign())throw new Error("Only positive integers are supported");if(!Number.isSafeInteger(t)\|\|t<0)throw new Error("Invalid value for bitCount");const r=aBigInt(t);return this.mul(r)}shiftRight(t){if(!this.isInteger()\|\|-1===this.sign())throw new Error("Only positive integers are supported");if(!Number.isSafeInteger(t)\|\|t<0)throw new Error("Invalid value for bitCount");const r=aBigInt(t);return new f(this.normalize().number/r)}cmp(t){const r=w(t);if(r instanceof g)return-r.cmp(this);const e=r,{a:n,b:i}=this.scaleNumber(e.number,e.decimalPos);return n===i?0:n>i?1:-1}eq(t){return 0===this.cmp(t)}lt(t){return-1===this.cmp(t)}lte(t){return this.cmp(t)<=0}gt(t){return 1===this.cmp(t)}gte(t){return this.cmp(t)>=0}clamp(t,r){const e=b(t),n=b(r);if(e.gt(n))throw new Error("Min parameter has to be smaller than max");return this.lt(e)?e:this.gt(n)?n:this}isZero(){return this.number===s}isOne(){if(0===this.decimalPos)return this.number===u;const t=hBigInt(this.decimalPos),r=this.number/t;return r===u&&rt===this.number}isInteger(){return 0===this.decimalPos\|\|this.number%hBigInt(this.decimalPos)===s}serialize(){return[this.number,this.decimalPos]}getFractionParts(t=!0){return this.convertToFraction().getFractionParts(t)}normalize(){if(0===this.decimalPos)return this;let t=this.decimalPos,r=this.number;for(;t>0&&r%h===s;)t--,r/=h;return new f(r,t)}convertToFraction(){if(0===this.decimalPos)return new g(this.number,u);const t=hBigInt(this.decimalPos);return new g(this.number,t)}toNumber(){return Number(this.toPrecision(20))}toFixed(r,e=t.RoundingMode.TO_ZERO,n=!1){if(!Number.isSafeInteger(r)\|\|r<0)throw new Error("Invalid parameter");const o=this._round(r,e);return i(o.number,o.decimalPos,r,n)}toExponential(r,e=t.RoundingMode.TO_ZERO,i=!1){if(!Number.isSafeInteger(r)\|\|r<0)throw new Error("Invalid parameter");const o=this.roundToDigits(r+1,e).normalize(),s=-1===o.sign(),u=o.abs(),a=u.number.toString(),c=a.length<=r?`${a}${"0".repeat(r-a.length+1)}`:a.slice(0,r+1);let m=c;c.length>1&&(m=`${c.slice(0,1)}.${c.slice(1)}`,i&&(m=n(m)));const d=u.decimalPos,h=a.length-1-d;return`${s?"-":""}${m}e${h>=0?"+":""}${h}`}toBase(t,r){if(!Number.isSafeInteger(t)\|\|t<2\|\|t>16)throw new Error("Invalid radix");if(void 0!==r&&(!Number.isSafeInteger(r)\|\|r<0))throw new Error("Invalid parameter");const e=this.normalize();if(0===e.decimalPos)return e.number.toString(t);const n=void 0===r?Number.MAX_SAFE_INTEGER:r;let i=e.intPart(),o=e.sub(i);const s=-1===e.sign();s&&(i=i.neg(),o=o.neg());const u=new Map;let a=[];for(;!o.isZero();){const r=o.mul(t),e=r.toString(),i=u.get(e);if(void 0!==i){a=[...a.slice(0,i-1),"(",...a.slice(i-1),")"];break}if(a.length===n)break;const s=Math.abs(r.intPart().toNumber());a.push(s.toString(t)),o=r.fracPart(),u.set(e,a.length)}const c=a.join("");return`${s?"-":""}${i.number.toString(t)}${a.length?".":""}${c}`}toFraction(){return this.convertToFraction().toFraction()}toString(t,r){if(void 0===t\|\|10===t){const t=void 0!==r?this.trunc(r):this;return i(t.number,t.decimalPos,t.decimalPos,!0)}return this.toBase(t,r)}toPrecision(r,e=t.RoundingMode.TO_ZERO,o=!1){if(!Number.isSafeInteger(r)\|\|r<1)throw new Error("Invalid parameter");const s=this.roundToDigits(r,e),{subZeroNum:u,exponentDiff:a}=s.toSubZeroNum(),c=-1===u.sign();let m=i(u.number,u.decimalPos,u.decimalPos,!1);m=m.slice(c?3:2),m=m.slice(0,Math.max(r,a));const d=m.slice(0,Math.max(0,a)),h=m.slice(Math.max(0,a)),l=Math.max(0,r-d.length-h.length),f="0".repeat(a<0?-a:0);let g=d\|\|"0";if(h.length+f.length+l>0){g+=`.${f}${h}${"0".repeat(l)}`,o&&(g=n(g))}return c?`-${g}`:g}valueOf(){throw new Error("Unsafe conversion to Number type! Use toNumber() instead.")}}class g{constructor(t,r){if(this.type="fraction","bigint"==typeof t&&"bigint"==typeof r)this.numerator=t,this.denominator=r;else{const e=this.parseParameter(t),n=this.parseParameter(r),i=e.div(n),o=i instanceof f?i.convertToFraction():i;this.numerator=o.numerator,this.denominator=o.denominator}if(this.denominator===s)throw new Error("Division by zero")}parseRepeatingDecimal(t){if(!t.includes("("))return new f(t).convertToFraction();const r=(t=t.trim()).match(/^(-?[0-9])\.([0-9]+)?$([0-9]+)$(?:[eE]([+-]?[0-9]+))?$/);if(!r)throw new Error(`Cannot parse string "${t}"`);const e="-"===r[1]?"-0":r[1],n=r[2]??"",i=r[3],o=r[4],s=BigInt(e+n+i)-BigInt(e+n),u=BigInt("9".repeat(i.length)+"0".repeat(n.length)),a=new g(s,u);if(void 0!==o){const t=o.startsWith("-"),r=hBigInt(t?o.slice(1):o);return t?a.div(r).normalize():a.mul(r).normalize()}return a.simplify()}parseParameter(t){if(t instanceof g)return t;if(t instanceof f)return t.convertToFraction();if("number"==typeof t){if(!Number.isSafeInteger(t))throw new Error("Floating point values as numbers are unsafe. Please provide them as a string.");return new g(BigInt(t),u)}if("bigint"==typeof t)return new g(t,u);if("string"==typeof t){const r=t.split("/");if(r.length>2)throw new Error(`Cannot parse string '${t}'`);const e=this.parseRepeatingDecimal(r[0]),n=r[1]?this.parseRepeatingDecimal(r[1]):new g(u,u);return e.div(n).convertToFraction()}throw new Error("Unsupported parameter!")}add(t){const{numerator:r,denominator:e}=this.parseParameter(t);return this.denominator===e?new g(this.numerator+r,this.denominator):new g(this.numeratore+rthis.denominator,ethis.denominator)}sub(t){const{numerator:r,denominator:e}=this.parseParameter(t);return this.add(new g(-r,e))}mul(t){const{numerator:r,denominator:e}=this.parseParameter(t);return new g(this.numeratorr,this.denominatore)}div(t){const{numerator:r,denominator:e}=this.parseParameter(t);return this.mul(new g(e,r))}divToInt(t){return this.div(t).trunc()}mod(r,e=t.ModType.TRUNCATED){const n=this.parseParameter(r),i=n.denominatorthis.numerator%(n.numeratorthis.denominator),o=this.denominatorn.denominator,s=new g(i,o);if(e===t.ModType.TRUNCATED)return s;if(e===t.ModType.FLOORED)return Number(-1===this.sign())^Number(-1===n.sign())?s.add(n):s;if(e===t.ModType.EUCLIDEAN)return-1===s.sign()?s.add(-1===n.sign()?n.neg():n):s;throw new Error("Invalid ModType")}pow(t){const r=this.parseParameter(t);if(!r.isInteger())throw new Error("Unsupported parameter");const e=r.numerator/r.denominator,n=e<s?-e:e,i=new g(this.numeratorn,this.denominatorn);return e<s?i.inv():i}powm(t,r,e){const n=this.parseParameter(t);if(!n.isInteger())throw new Error("Unsupported parameter");let i=n.toNumber();const o=this.parseParameter(r);let s=this,c=new g(u,u);for(;0!==i;)i%2!=0&&(c=c.mul(s).mod(o,e)),s=s.pow(a).mod(o,e),i=Math.floor(i/2);return c}inv(){return new g(this.denominator,this.numerator)}floor(r){return this.denominator===u?new f(this.numerator):this.round(r,t.RoundingMode.TO_NEGATIVE)}ceil(r){return this.denominator===u?new f(this.numerator):this.round(r,t.RoundingMode.TO_POSITIVE)}trunc(r){return this.denominator===u?new f(this.numerator):this.round(r,t.RoundingMode.TO_ZERO)}round(t,r){if(t=void 0===t?0:t,!Number.isSafeInteger(t)\|\|t<0)throw new Error("Invalid value for decimals");const e=this.toFixedNumber(t+1);if(this.sub(e).isZero())return e.round(t,r);return new f(`${e.toFixed(t+1)}1`).round(t,r)}roundToDigits(t,r){if(!Number.isSafeInteger(t)\|\|t<1)throw new Error("Invalid value for digits");if(this.isZero())return new f(s);let e=this.abs(),n=0;for(;e.gte(u);)e=e.div(h),n++;const i=new g(u,h);for(;e.lt(i);)e=e.mul(h),n--;let o=e.round(t,r);return o=o._incExponent(n),-1===this.sign()?o.neg():o}gcd(t,r){let e=t<s?-t:t,n=r<s?-r:r;if(n>e){const t=e;e=n,n=t}for(;;){if(n===s)return e;if(e%=n,e===s)return n;n%=e}}simplify(){let{numerator:t,denominator:r}=this;const e=this.gcd(t,r);return e>u&&(t/=e,r/=e),r<s&&(t=-t,r=-r),new g(t,r)}normalize(){const{numerator:r,denominator:e}=this.simplify();if(e===u)return new f(r,0);const n=new g(r,e),{cycleLen:i,cycleStart:o}=n.getDecimalFormat(0);return 0!==i?n:n.round(o,t.RoundingMode.TO_ZERO)}getFractionParts(t=!0){const r=t?this.simplify():this;return{numerator:new f(r.numerator),denominator:new f(r.denominator)}}sign(){return(this.numerator<s?-1:1)(this.denominator<s?-1:1)}abs(){return new g(this.numerator<s?-this.numerator:this.numerator,this.denominator<s?-this.denominator:this.denominator)}neg(){return this.mul(-u)}intPart(){return this.trunc()}fracPart(){return this.sub(this.trunc())}cmp(t){const r=this.parseParameter(t),e=this.denominator===r.denominator,n=e?this.numerator:this.numeratorr.denominator,i=e?r.numerator:r.numeratorthis.denominator;return n===i?0:n>i?1:-1}eq(t){return 0===this.cmp(t)}lt(t){return-1===this.cmp(t)}lte(t){return this.cmp(t)<=0}gt(t){return 1===this.cmp(t)}gte(t){return this.cmp(t)>=0}clamp(t,r){const e=b(t),n=b(r);if(e.gt(n))throw new Error("Min parameter has to be smaller than max");return this.lt(e)?e:this.gt(n)?n:this}isZero(){return this.numerator===s}isOne(){return this.numerator===this.denominator}isInteger(){return this.numerator%this.denominator===s}serialize(){return[this.numerator,this.denominator]}toNumber(){return Number(this.toPrecision(20))}convertToFraction(){return this}getNumberForBitwiseOp(){if(!this.isInteger()\|\|-1===this.sign())throw new Error("Only positive integers are supported");return this.intPart()}bitwiseAnd(t){return this.getNumberForBitwiseOp().bitwiseAnd(t)}bitwiseOr(t){return this.getNumberForBitwiseOp().bitwiseOr(t)}bitwiseXor(t){return this.getNumberForBitwiseOp().bitwiseXor(t)}shiftLeft(t){return this.getNumberForBitwiseOp().shiftLeft(t)}shiftRight(t){return this.getNumberForBitwiseOp().shiftRight(t)}getDecimalFormat(t){t=void 0===t?Number.MAX_SAFE_INTEGER:t;let r=this.denominator<s?-this.denominator:this.denominator,e=0;for(;r%a===s;)r/=a,e++;let n=0;for(;r%d===s;)r/=d,n++;const i=Math.max(e,n);if(r===u)return{cycleLen:0,cycleStart:i};const o=Math.max(1,t-i);let c=h%r,m=1;for(;c!==u;){if(m===o)return{cycleLen:null,cycleStart:i};c=ch%r,m++}return{cycleLen:m,cycleStart:i}}toFixed(r,e=t.RoundingMode.TO_ZERO,n=!1){if(!Number.isSafeInteger(r)\|\|r<0)throw new Error("Invalid parameter");return this.round(r,e).toFixed(r,t.RoundingMode.TO_ZERO,n)}toRepeatingParts(t){if(this.isZero())return["0","",""];const{cycleLen:r,cycleStart:e}=this.simplify().getDecimalFormat(t);if(null===r\|\|0===r){const r=t??e,i=this.toFixed(r),o=n(i).split(".");return[o[0],o[1]??"",""]}const i=e+r,o=this.toFixed(i).split(".");return[o[0],o[1].slice(0,e),o[1].slice(e)]}toRepeatingDigits(t){const r=this.toRepeatingParts(t);let e=r[0];return(r[1]\|\|r[2])&&(e+=`.${r[1]}`),r[2]&&(e+=`(${r[2]})`),e}toExponential(r,e=t.RoundingMode.TO_ZERO,n=!1){if(!Number.isSafeInteger(r)\|\|r<0)throw new Error("Invalid parameters");return this.toFixedNumber(r).toExponential(r,e,n)}toFraction(){const{numerator:t,denominator:r}=this.getFractionParts(!0);return`${t.toString()}/${r.toString()}`}toFixedNumber(t){const r=this.numeratorh*BigInt(t);return new f(r/this.denominator,t)}toBase(t,r){if(!Number.isSafeInteger(t)\|\|t<2\|\|t>16)throw new Error("Invalid radix");if(void 0!==r&&(!Number.isSafeInteger(r)\|\|r<0))throw new Error("Invalid parameter");if(10===t)return void 0===r?this.toRepeatingDigits(r):n(this.toFixed(r));const e=this.normalize(),i=void 0===r?Number.MAX_SAFE_INTEGER:r+1;let o=e.intPart(),s=e.sub(o);const u=-1===e.sign();u&&(o=o.neg(),s=s.neg());const a=new Map;let c=[];for(;!s.isZero()&&c.length!==i;){const r=s.mul(t),e=r.normalize().toFraction(),n=a.get(e);if(void 0!==n){c=[...c.slice(0,n-1),"(",...c.slice(n-1),")"];break}const i=Math.abs(r.intPart().toNumber());c.push(i.toString(t)),s=r.fracPart(),a.set(e,c.length)}c.length===i&&c.pop();const m=c.join("");return`${u?"-":""}${o.toString(t)}${c.length?".":""}${m}`}toString(t,r){return void 0===t\|\|10===t?this.toRepeatingDigits(r):this.toBase(t,r)}toPrecision(r,e=t.RoundingMode.TO_ZERO,n=!1){if(!Number.isSafeInteger(r)\|\|r<1)throw new Error("Invalid parameter");return this.roundToDigits(r,e).toPrecision(r,t.RoundingMode.TO_ZERO,n)}valueOf(){throw new Error("Unsafe conversion to Number type! Use toNumber() instead.")}}function w(t){if(t instanceof f\|\|t instanceof g)return t;if("bigint"==typeof t)return new f(t);if("number"==typeof t){if(!Number.isSafeInteger(t))throw new Error("Floating point values as numbers are unsafe. Please provide them as a string.");return new f(t)}if("string"==typeof t)return t.includes("/")\|\|t.includes("(")?new g(t,u):new f(t);throw new Error("Unsupported parameter type")}const b=(t,r)=>{if(void 0===t)throw new Error("First parameter cannot be undefined");const e=w(t);if(void 0===r)return e;const n=w(r);return new g(e,u).div(new g(n,u))};b.min=(...t)=>{if(0===t.length)throw new Error("Got empty array");let r=b(t[0]);for(let e=1;e<t.length;e++){const n=b(t[e]);n.lt(r)&&(r=n)}return r},b.max=(...t)=>{if(0===t.length)throw new Error("Got empty array");let r=b(t[0]);for(let e=1;e<t.length;e++){const n=b(t[e]);n.gt(r)&&(r=n)}return r};const p=(t,r)=>{let e=s;for(let n=0;n<t.length;n++){const i=t.charAt(n),o=parseInt(i,r);if(Number.isNaN(o))throw new Error(`Invalid digit "${i}"`);e=BigInt(r),e+=BigInt(o)}return e};b.fromBase=(t,r)=>{if("string"!=typeof t)throw new Error("First parameter must be string");if(!Number.isSafeInteger(r)\|\|r<2\|\|r>16)throw new Error("Invalid radix");if(10===r)return b(t);if(0===(t=t.trim()).length)throw new Error("Empty string is not allowed");const e=t.startsWith("-");e&&(t=t.slice(1));const n=t.match(/^([0-9a-f])(?:\.([0-9a-f])(?:$([0-9a-f]+)$)?)?$/i);if(!n)throw new Error(`Cannot parse number "${t}"`);const i=n[1]??"",o=n[2]??"",s=n[3]??"";if(s.length>0){const t=p(`${i}${o}${s}`,r)-p(`${i}${o}`,r),n=p((r-1).toString(r).repeat(s.length)+"0".repeat(o.length),r),u=new g(t,n).normalize();return e?u.neg():u}const a=p(i,r),c=p(o,r),m=new g(c,BigInt(r)*BigInt(o.length)),d=new g(a,u).add(m).normalize();return e?d.neg():d},b.range=function(t,r,e){const n=b(r),i=b(e??1);let o=b(t);for(;o.lt(n);)yield o,o=o.add(i)},b.gcd=(t,r)=>{const e=b(t).abs(),n=b(r).abs();let i=n.gt(e)?n:e,o=i.eq(e)?n:e;for(;;){if(o.isZero())return i;if(i=i.mod(o),i.isZero())return o;o=o.mod(i)}},b.lcm=(t,r)=>{const e=b(t).abs(),n=b(r).abs(),i=e.mul(n);if(i.isZero())throw new Error("LCM of zero is undefined");const o=b.gcd(e,n);return i.div(o)};const E=(t,r,e)=>{const n=((t,r)=>{let e=r.toNumber();if(Number.isFinite(e)){const r=e<0;r&&(e=-e);let n=e*(1/t);return r&&(n=-n),n.toString()}const n=r.abs().toFixed(0).length,i=Math.ceil(n/t);return`${1===r.sign()?"":"-"}5e${i}`})(t,r);let i=new f("0"!==n?n:"1");const o=new g(t-1,t),s=new g(r,t),u=BigInt(t-1);let a=i.trunc(e+5);for(;i=o.mul(i).add(s.mul(i.pow(u).inv())),i=i.trunc(e+5),!i.isZero()&&!a.eq(i);)a=i;return i.trunc(e)},I=(t,r,e)=>{if(!Number.isSafeInteger(t))throw new Error("Integer is expected for N");if(t<0)throw new Error("Negative N is not supported");if(0===t)throw new Error("N cannot be zero");const n=o(b(r),e);if(1===t)return n.trunc(e);if(t%2==0&&-1===n.sign())throw new Error("Complex numbers are not supported");if(n.isZero())return new f(s).trunc(e);if(n.isOne())return new f(u).trunc(e);return E(t,n,e)},N=(t,r)=>I(2,t,r);class v{constructor(t,r){this.cachedDecimals=0,this.fn=t,this.max=r}get(t){if(t<=this.cachedDecimals)return this.cache.trunc(t);const r=new f(this.fn(t)),e=Math.min(this.max,t);return this.cachedDecimals!==e&&(this.cache=r.trunc(e),this.cachedDecimals=e),r}}const T=(t,r)=>{let e=o(b(t),r);if(e.isOne())return new f(0).trunc(r);if(e.lte(0))throw new Error("Invalid parameter");let n=0;const i=b("0.1");for(;e.sub(u).abs().gt(i);)e=new f(N(e,r+10)),n++;const c=function(t,r){const e=t.pow(a).normalize();let n=t,i=u,o=b(t);for(;;){n=n.mul(e),i+=a;const t=n.div(i).trunc(r+10);o=o.add(t),yield{term:t,sum:o}}}(e.sub(u).div(e.add(u)),r);for(const{term:t,sum:e}of c)if(t.isZero()){return e.mul(a*BigInt(n+1)).trunc(r)}return b(s)},O=new v((t=>T(a,t)),200),R=new v((t=>T(h,t)),200);const P=(t,r)=>{const e=o(b(t),r),n=b(`1e-${r+5}`),i=function(t,r){let e=t.add(1),n=BigInt(6),i=m;const o=t.pow(a);let s=o;for(;;){const c=s.mul(t.add(i-u)).div(n);n=i(i+u),i+=a,s=s.mul(o),e=e.add(c).trunc(r+5),yield{term:c,sum:e}}}(e,r);for(const{term:t,sum:e}of i)if(t.abs().lt(n))return e.trunc(r);return b(s)},_=new v((t=>{if(0===t)return b(c);let r=u,e=chBigInt(t+20),n=e;for(;e!==s;)e=er/((r+u)m),r+=a,n+=e/r;return b(`3.${n.toString().slice(1,t+1)}`)}),1e3),S=t=>0===t?b(c):_.get(t).trunc(t),M=(r,e)=>{let n=r.round(e+5,t.RoundingMode.NEAREST_AWAY_FROM_ZERO);const i=S(e+5),o=((t,r,e)=>{const n=Math.max(3,e),i=t.trunc(n),o=i.div(r).round();return r.mul(o).trunc(n).eq(i)?o:null})(n,i.div(12),e);if(null!==o)return(t=>{let r=t.mod(l).toNumber();r<0&&(r+=24);const e=Math.floor(r/6)+1;let n=15r;return 4===e?n=360-n:3===e?n-=180:2===e&&(n=180-n),{specialCaseDeg:n,quadrant:e,subHalfPiAngle:null}})(o);const s=i.mul(a);n=n.mod(s),-1===n.sign()&&(n=n.add(s));const u=n.mul(a).div(i).floor().toNumber()+1;let c=n;return 4===u?c=s.sub(c):3===u?c=c.sub(i):2===u&&(c=i.sub(c)),{specialCaseDeg:null,quadrant:u,subHalfPiAngle:c}};const A=(t,r,e)=>{let n=b(t);return r&&(n=n.neg()),n.trunc(e)},y=(r,e)=>{const n=e+10,i=o(b(r),e+5),{specialCaseDeg:m,subHalfPiAngle:d,quadrant:h}=M(i,e),l=2===h\|\|3===h;if(null!==m){if(0===m)return A(u,l,e);if(30===m)return A(b(N(c,e+5)).div(a),l,e);if(45===m)return A(b(N(a,e+5)).div(a),l,e);if(60===m)return A("0.5",l,e);if(90===m)return A(s,l,e);throw new Error}const f=b(`1e-${n}`),g=function(r,e){const n=r.round(e+10,t.RoundingMode.NEAREST_AWAY_FROM_ZERO).pow(a);let i=n,o=a,s=b(u).sub(i.div(o).trunc(e+10)),m=c;for(;;){o=m(m+u),m+=a;const t=m(m+u);m+=a,i=i.mul(n),o=t;let r=i.mul(t);i=i.mul(n),r=r.sub(i);const c=r.div(o).trunc(e+10);s=s.add(c),yield{term:c,sum:s}}}(d,e);for(const{term:t,sum:r}of g)if(t.lt(f))return A(r,l,e);return b(0)};const F=(t,r)=>{let e=o(b(t),r);if(e.isZero())return b(0);if(e.abs().isOne())return b(S(r)).div(4e.sign()).trunc(r);let n=0;const i=b("0.42");for(;e.abs().gt(i);){const t=b(N(e.pow(a).add(u),r+10));e=e.div(t.add(u)),n++}const s=b(`1e-${r+10}`),m=function(t,r){const e=t.pow(a).normalize(),n=e.pow(a).normalize();let i=c,o=t.sub(t.mul(e).div(i)),s=t.mul(n);for(;;){i+=a;const t=i+a,u=s.mul(e.mul(-i).add(t)).div(it);i=t,s=s.mul(n),o=o.add(u).trunc(r+10),yield{term:u,sum:o}}}(e,r);for(const{term:t,sum:e}of m)if(t.abs().lt(s)){return e.mul(a*BigInt(n)).trunc(r)}return b(0)},B=(t,r)=>{const e=o(b(t),r);if(e.isZero())return b(s);if(e.abs().isOne())return b(S(r)).mul(e.sign()).div(a).trunc(r);if(e.abs().eq("1/2"))return b(S(r)).mul(e.sign()).div(6).trunc(r);if(e.gt(u)\|\|e.lt(-u))throw new Error("Out of range");const n=b(N(e.pow(a).neg().add(u),r+10));return b(F(e.div(n.add(u)),r+10)).mul(a).trunc(r)};const Z=(t,r)=>{const e=o(b(t),r),n=new f(`1e-${r+5}`),i=function(t,r){const e=t.pow(a).normalize();let n=e,i=a,o=n.div(i).add(u).trunc(r+5),s=c;for(;;){n=n.mul(e),i=s(s+u),s+=a;const t=n.div(i);o=o.add(t).trunc(r+5),yield{term:t,sum:o}}}(e,r);for(const{term:t,sum:e}of i)if(t.abs().lt(n))return e.trunc(r);return b(s)};t.ExactNumber=b,t.PI=S,t.acos=(t,r)=>{const e=o(b(t),r);if(e.isZero())return b(S(r)).div(a).trunc(r);if(e.isOne())return b(s);if(e.abs().isOne())return S(r);if(e.abs().eq("1/2")){const t=b(S(r)).div(c);return-1===e.sign()?t.mul(a).trunc(r):t.trunc(r)}if(e.gt(u)\|\|e.lt(-u))throw new Error("Out of range");return b(S(r+10)).div(a).sub(B(e,r+10)).trunc(r)},t.acosh=(t,r)=>{const e=o(b(t),r);if(e.isOne())return b(s);if(e.lt(u))throw new Error("Out of range");const n=N(e.pow(a).sub(u),r+5);return T(e.add(n),r+5).trunc(r)},t.asin=B,t.asinh=(t,r)=>{const e=o(b(t),r);if(e.isZero())return b(s);const n=N(e.pow(a).add(u),r+5);return T(e.add(n),r+5).trunc(r)},t.atan=F,t.atanh=(t,r)=>{const e=o(b(t),r);if(e.abs().gte(u))throw new Error("Out of range");if(e.isZero())return b(s);const n=T(e.add(u).div(e.neg().add(u)),r+5);return b(n).div(a).trunc(r)},t.cbrt=(t,r)=>I(3,t,r),t.cos=y,t.cosh=Z,t.exp=P,t.log=T,t.log10=(t,r)=>new f(T(t,r+10)).div(R.get(r+10)).trunc(r),t.log2=(t,r)=>new f(T(t,r+10)).div(O.get(r+10)).trunc(r),t.logn=(t,r,e)=>{if(!Number.isSafeInteger(t)\|\|t<2)throw new Error("Invalid parameter for N");const n=T(r,e+10),i=T(t,e+10);return new f(n).div(i).trunc(e)},t.nthroot=I,t.pow=(t,r,e)=>{const n=o(b(t),e),i=o(b(r),e);if(i.isInteger()&&Number.isSafeInteger(i.toNumber()))return n.pow(i).trunc(e);if(-1===n.sign()&&!i.isInteger())throw new Error("Complex numbers are not supported");const s=T(n,e+5),u=i.mul(s);return P(u,e+5).trunc(e)},t.sin=(t,r)=>{const e=new f(S(r+10)),n=o(b(t),r+5);return y(e.div(a).sub(n),r+5).trunc(r)},t.sinh=(t,r)=>{const e=o(b(t),r),n=new f(`1e-${r+5}`),i=function(t,r){let e=t,n=u;const i=t.pow(a).normalize();let o=t.trunc(r+5),s=a;for(;;){e=e.mul(i),n=s*(s+u),s+=a;const t=e.div(n);o=o.add(t).trunc(r+5),yield{term:t,sum:o}}}(e,r);for(const{term:t,sum:e}of i)if(t.abs().lt(n))return e.trunc(r);return b(s)},t.sqrt=N,t.tan=(t,r)=>{const e=o(b(t),r+5),{specialCaseDeg:n,quadrant:i,subHalfPiAngle:s}=M(e,r),m=1===i\|\|3===i;if(null!==n){if(0===n)return A("0",m,r);if(30===n)return A(b(u).div(N(c,r+5)),m,r);if(4===n)return A("1",m,r);if(60===n)return A(N(c,r+5),m,r);if(90===n)throw new Error("Out of range");throw new Error}const d=b(y(s.mul(a),r+5)),h=b(u).sub(d).div(b(u).add(d)).round(r+5),l=N(h,r+5).trunc(r);return m?l:l.neg()},t.tanh=(t,r)=>{const e=o(b(t),r);if(e.isZero())return b(s);const n=Z(e,r+10).abs();return N(n.pow(a).sub(u),r+10).div(n).mul(e.sign()).trunc(r)}}));

dist/src/approx/trigonometry.d.ts

		import { ExactNumberType } from '../types';
		export declare const PI: (decimals: number) => ExactNumberType;
		declare type EvaluationRes = {
		specialCaseDeg: number \| null;
		quadrant: number;
		subHalfPiAngle: ExactNumberType \| null;
		};
		export declare const evaluateAngle: (x: ExactNumberType, decimals: number) => EvaluationRes;
		export declare const cos: (_angle: number \| bigint \| string \| ExactNumberType, decimals: number) => ExactNumberType;
		export declare const sin: (angle: number \| bigint \| string \| ExactNumberType, decimals: number) => ExactNumberType;
		export declare const tan: (angle: number \| bigint \| string \| ExactNumberType, decimals: number) => ExactNumberType;
		export {};

dist/src/FixedNumber.d.ts

		@@ -14,2 +14,3 @@ import { Fraction } from './Fraction';
		pow(x: number \| bigint \| string \| ExactNumberType): ExactNumberType;
		powm(_exp: number \| bigint \| string \| ExactNumberType, _mod: number \| bigint \| string \| ExactNumberType, modType?: ModType): FixedNumber;
		div(x: number \| bigint \| string \| ExactNumberType): ExactNumberType;
		@@ -57,9 +58,9 @@ divToInt(x: number \| bigint \| string \| ExactNumberType): ExactNumberType;
		toNumber(): number;
		toFixed(decimals: number, roundingMode?: RoundingMode): string;
		toExponential(digits: number, roundingMode?: RoundingMode): string;
		toFixed(decimals: number, roundingMode?: RoundingMode, trimZeros?: boolean): string;
		toExponential(digits: number, roundingMode?: RoundingMode, trimZeros?: boolean): string;
		private toBase;
		toFraction(): string;
		toString(radix?: number, maxDigits?: number): string;
		toPrecision(digits: number, roundingMode?: RoundingMode): string;
		toPrecision(digits: number, roundingMode?: RoundingMode, trimZeros?: boolean): string;
		valueOf(): number;
		}

dist/src/Fraction.d.ts

		@@ -17,2 +17,3 @@ import { ExactNumberType, ModType, RoundingMode } from './types';
		pow(x: number \| bigint \| string \| ExactNumberType): ExactNumberType;
		powm(_exp: number \| bigint \| string \| ExactNumberType, _mod: number \| bigint \| string \| ExactNumberType, modType?: ModType): ExactNumberType;
		inv(): ExactNumberType;
		@@ -56,6 +57,6 @@ floor(decimals?: number): FixedNumber;
		private getDecimalFormat;
		toFixed(decimals: number, roundingMode?: RoundingMode): string;
		toFixed(decimals: number, roundingMode?: RoundingMode, trimZeros?: boolean): string;
		private toRepeatingParts;
		toRepeatingDigits(maxDigits: number \| undefined): string;
		toExponential(digits: number, roundingMode?: RoundingMode): string;
		toExponential(digits: number, roundingMode?: RoundingMode, trimZeros?: boolean): string;
		toFraction(): string;
		@@ -65,4 +66,4 @@ private toFixedNumber;
		toString(radix?: number, maxDigits?: number): string;
		toPrecision(digits: number, roundingMode?: RoundingMode): string;
		toPrecision(digits: number, roundingMode?: RoundingMode, trimZeros?: boolean): string;
		valueOf(): number;
		}

dist/src/index.d.ts

		export { ExactNumber } from './ExactNumber';
		export { RoundingMode, ModType, ExactNumberType, ExactNumberParameter } from './types';
		export { trimTrailingZeros } from './util';
		export * from './approx';
		export { nthroot, sqrt, cbrt } from './approx/roots';
		export { pow, exp } from './approx/exponential';
		export { log, logn, log10, log2 } from './approx/logarithm';
		export { PI, sin, cos, tan } from './approx/trigonometry';
		export { asin, acos, atan } from './approx/inverse_trigonometry';
		export { sinh, cosh, tanh } from './approx/hyperbolic';
		export { asinh, acosh, atanh } from './approx/inverse_hyperbolic';

dist/src/types.d.ts

		@@ -38,3 +38,4 @@ import { Fraction } from './Fraction';
		pow(x: number \| bigint \| string \| ExactNumberType): ExactNumberType;
		/** Returns b^e mod m (modular exponentiation) */
		/** Returns modulo of this number exponentiated to the given value (modular exponentiation) */
		powm(exponent: number \| bigint \| string \| ExactNumberType, modulus: number \| bigint \| string \| ExactNumberType, type?: ModType): ExactNumberType;
		/** Returns the result of the division of this number by the given one. */
		@@ -117,7 +118,7 @@ div(x: number \| bigint \| string \| ExactNumberType): ExactNumberType;
		*/
		toFixed(decimals: number, roundingMode?: RoundingMode): string;
		toFixed(decimals: number, roundingMode?: RoundingMode, trimZeros?: boolean): string;
		/** Returns a string representing the number in exponential notation.
		* Defaults to RoundingMode.TO_ZERO
		*/
		toExponential(digits: number, roundingMode?: RoundingMode): string;
		toExponential(digits: number, roundingMode?: RoundingMode, trimZeros?: boolean): string;
		/** Returns a string representing the number using fixed-point notation, rounded to the specified number of significant digits.
		@@ -127,3 +128,3 @@ * In contrary to JS Number.toPrecision(), this function never returns exponential notation.
		*/
		toPrecision(digits: number, roundingMode?: RoundingMode): string;
		toPrecision(digits: number, roundingMode?: RoundingMode, trimZeros?: boolean): string;
		/** Converts current value to a JavaScript Number */
		@@ -130,0 +131,0 @@ toNumber(): number;

dist/src/util.d.ts

		import { FixedNumber } from './FixedNumber';
		import { ExactNumberType } from './types';
		/** Trims trailing zeros from numbers in fixed-point format (1.23000 -> 1.23) */
		export declare const trimTrailingZeros: (num: string) => string;
		export declare const trimTrailingZerosFromFixed: (num: string) => string;
		export declare const bigIntToStr: (num: bigint, inputDecimals: number, outputDecimals: number, trimZeros: boolean) => string;
		export declare const limitDecimals: (x: ExactNumberType, decimals: number) => ExactNumberType \| FixedNumber;
		export declare const _0N: bigint;
		export declare const _1N: bigint;
		export declare const _2N: bigint;
		export declare const _3N: bigint;
		export declare const _4N: bigint;
		export declare const _5N: bigint;
		export declare const _10N: bigint;
		export declare const _24N: bigint;

package.json

		{
		"name": "exactnumber",
		"description": "Arbitrary-precision decimals. Enables making precise math calculations with rational numbers, without precision loss.",
		"version": "0.11.0",
		"description": "Arbitrary-precision decimals. Enables making math calculations with rational numbers, without precision loss.",
		"version": "1.0.0",
		"main": "dist/index.umd.js",
		@@ -47,2 +47,3 @@ "module": "dist/index.esm.js",
		},
		"sideEffects": false,
		"license": "MIT",
		@@ -55,7 +56,6 @@ "devDependencies": {
		"@types/estree": "^1.0.0",
		"@types/jest": "^29.2.0",
		"@types/node": "^18.11.3",
		"@typescript-eslint/eslint-plugin": "^5.40.1",
		"@typescript-eslint/parser": "^5.40.1",
		"decimal.js": "^10.4.2",
		"@types/jest": "^29.2.2",
		"@types/node": "^18.11.9",
		"@typescript-eslint/eslint-plugin": "^5.42.0",
		"@typescript-eslint/parser": "^5.42.0",
		"eslint": "^8.26.0",
		@@ -65,13 +65,13 @@ "eslint-config-airbnb": "^19.0.4",
		"eslint-config-prettier": "^8.5.0",
		"jest": "29.2.1",
		"jest": "^29.2.2",
		"prettier": "^2.7.1",
		"rollup": "^2.79.1",
		"rollup": "^3.2.5",
		"rollup-plugin-copy": "^3.4.0",
		"rollup-plugin-license": "^2.8.2",
		"rollup-plugin-terser": "^7.0.2",
		"rollup-plugin-license": "^3.0.1",
		"@rollup/plugin-terser": "^0.1.0",
		"ts-jest": "^29.0.3",
		"ts-node": "^10.9.1",
		"typescript": "^4.8.4",
		"typedoc": "^0.23.17"
		"typedoc": "^0.23.20"
		}
		}

126

README.md

		@@ -10,48 +10,40 @@ # ExactNumber

		## Quick comparision with JS floating-point arithmetic

		```js
		console.log(1 + 0.36);
		// returns 1.3599999999999999

		console.log(ExactNumber(1).add('0.36').toString());
		// returns 1.36

		console.log(1 / 3);
		// returns 0.3333333333333333

		console.log(ExactNumber(1).div(3).toString());
		// returns 0.(3)

		console.log((1 / 49) * 49);
		// returns 0.9999999999999999

		console.log(ExactNumber(1).div(49).mul(49).toString());
		// returns 1

		console.log(10e16 + 5);
		// returns 100000000000000000

		console.log(ExactNumber('10e16').add(5).toString());
		// returns 100000000000000005
		```

		## Features

		- Works with arbitrary large numbers without precision loss
		- There is no automatic rounding or truncation. Rounding can be archived by explicit calls to rounding functions
		- All fractions can be represented as repeating decimals like `1.23(45)`
		- This repeating decimal format (`1.23(45)`) can also be parsed back
		- Works with all number bases between `2` and `16`
		- There are no special values like `NaN`, `Infinity` or `-0`.
		- No silent errors: it throws errors immediatelly when a confusing parameter is received.
		- All fractions can be represented as repeating decimals like `1.23(45)`
		- Repeating decimal format can also be parsed back
		- No special values like `NaN`, `Infinity` or `-0`.
		- No silent errors: it throws errors immediatelly when a confusing parameter is received (e.g. 0/0)
		- Supports bitwise operators (`and`, `or`, `xor`, `shiftLeft`, `shiftRight`)
		- Approximation algorithms for irrational numbers (_experimental_)
		- Includes approximation algorithms for irrational numbers like `PI`, `sin(1)`.
		- Supports all modern browsers, web workers, Node.js and Deno
		- Includes TypeScript type definitions: [documentation](https://daninet.github.io/exactnumber)
		- Zero external dependencies
		- Uses `BigInt` type under the hood. It automatically switches back and forth between fixed-precision and fractional representations.
		- Under the hood, it relies on the `BigInt` type. It automatically switches back and forth between fixed-precision and fractional representations.
		- Tries to deliver the best possible performance
		- 100% open source + MIT license

		## Comparision with built-in numbers

		```js
		import { ExactNumber as N } from 'exactnumber';

		1 + 0.36 // 1.3599999999999999
		N(1).add('0.36').toString() // 1.36

		(1 / 49) * 49 // 0.9999999999999999
		N(1).div(49).mul(49).toString() // 1

		10e16 + 5 // 100000000000000000
		N('10e16').add(5).toString() // 100000000000000005

		1 / 3 // 0.3333333333333333
		N(1).div(3).toString() // 0.(3)

		2**32 >> 32 // 0
		N(2).pow(32).shiftRight(32).toString() // 1
		```

		## Installation
		@@ -83,2 +75,3 @@
		N('1/7').toString(); // 0.(142857)
		N('1/7').toString(6); // 0.(05)
		N('1/7').toFixed(3); // 0.142
		@@ -93,11 +86,64 @@ N('1/7').trunc(3).toString(); // 0.142

		import { PI, sin } from 'exactnumber';
		PI(10); // 3.1415926535
		// approximations

		const PI_OVER_2 = N(PI(10)).div(2);
		sin(PI_OVER_2, 5); // 1.00000
		import { PI, sin, pow } from 'exactnumber';
		PI(10).toString(); // 3.1415926535

		const PI_OVER_2 = PI(10).div(2);
		sin(PI_OVER_2, 5).toString(); // 1.00000

		// 0.1232323 raised to the power of 2.193333, approximated with 10 decimals
		pow('0.1(23)', '2.19(3)', 10).toString(); // 0.0101310867
		```

		## Supported approximations
		## Functions

		- Addition / subtraction: `add()`, `sub()`
		- Multiplication / division: `mul()`, `div()`, `divToInt()`
		- Exponentiation: `pow()`
		- Modular arithmetic: `mod()`, `powm()`
		- Getting the sign / absolute value: `sign()`, `abs()`
		- Negation / inversion: `neg()`, `inv()`
		- Integer and fractional parts: `intPart()`, `fracPart()`
		- Comparisons: `cmp()`, `eq()`, `lt()`, `lte()`, `gt()`, `gte()`
		- Special comparisons: `isZero()`, `isOne()`
		- Type testing: `isInteger()`
		- Rounding: `round()`, `roundToDigits()`, `floor()`, `ceil()`, `trunc()`
		- Bitwise operators: `bitwiseAnd()`, `bitwiseOr()`, `bitwiseXor()`, `shiftLeft()`, `shiftRight()`
		- Clamping: `clamp()`
		- Fraction helper: `getFractionParts()`
		- Normalization / simplifying fractions: `normalize()`
		- String output: `toFixed()`, `toExponential()`, `toPrecision()`, `toString()`, `toFraction()`
		- Number output: `toNumber()`
		- GCD, LCM: `ExactNumber.gcd()`, `ExactNumber.lcm()`
		- Minimum, maximum: `ExactNumber.min()`, `ExactNumber.max()`
		- Parsing numbers in different bases: `ExactNumber.fromBase()`
		- Range generator: `ExactNumber.range()`

		## Rounding modes

		- `NEAREST_TO_POSITIVE` - Rounds to nearest number, with ties rounded towards +Infinity. Similar to Math.round().
		- `NEAREST_TO_NEGATIVE` - Rounds to nearest number, with ties rounded towards -Infinity.
		- `NEAREST_TO_EVEN` - Rounds to nearest number, with ties rounded towards the nearest even number.
		- `NEAREST_TO_ZERO` - Rounds to nearest number, with ties rounded towards zero.
		- `NEAREST_AWAY_FROM_ZERO` - Rounds to nearest number, with ties rounded away from zero.

		- `TO_POSITIVE` - Rounds towards +Infinity. Similar to Math.ceil().
		- `TO_NEGATIVE` - Rounds towards -Infinity. Similar to Math.floor().
		- `TO_ZERO` - Rounds towards zero. Similar to Math.trunc().
		- `AWAY_FROM_ZERO` - Rounds away from zero

		## Modulo variants

		- `TRUNCATED`
		- `FLOORED`
		- `EUCLIDEAN`

		Read more about them [here](https://en.wikipedia.org/wiki/Modulo_operation).

		## Approximation algorithms

		These functions approximate irrational numbers with arbitrary number of decimals.
		The last parameter is always used to specify the number of correct decimals in the result.

		- Roots: `sqrt()`, `cbrt()`, `nthroot()`
		@@ -104,0 +150,0 @@ - Exponentials: `pow()`, `exp()`

src/approx/exponential.ts

		@@ -1,2 +0,2 @@
		import { limitDecimals } from '../util';
		import { limitDecimals, _0N, _1N, _2N, _4N } from '../util';
		import { ExactNumber } from '../ExactNumber';
		@@ -8,8 +8,8 @@ import { ExactNumberType } from '../types';
		function* expGenerator(x: ExactNumberType, decimals: number) {
		let sum = x.add(1n);
		let sum = x.add(1);

		let denominator = 6n;
		let i = 4n;
		let denominator = BigInt(6);
		let i = _4N;

		const xPow2 = x.pow(2n);
		const xPow2 = x.pow(_2N);

		@@ -22,5 +22,5 @@ let xPow = xPow2;

		const term = xPow.mul(x.add(i - 1n)).div(denominator);
		denominator = i (i + 1n);
		i += 2n;
		const term = xPow.mul(x.add(i - _1N)).div(denominator);
		denominator = i (i + _1N);
		i += _2N;
		xPow = xPow.mul(xPow2);
		@@ -46,3 +46,3 @@ sum = sum.add(term).trunc(decimals + 5);

		return ExactNumber(0);
		return ExactNumber(_0N);
		};
		@@ -49,0 +49,0 @@

src/approx/hyperbolic.ts

		@@ -5,3 +5,3 @@ import { FixedNumber } from '../FixedNumber';
		import { sqrt } from './roots';
		import { limitDecimals } from '../util';
		import { limitDecimals, _0N, _1N, _2N, _3N } from '../util';

		@@ -11,10 +11,10 @@ // sinh x = x + x^3/3! + x^5/5! + ...
		let numerator = x;
		let denominator = 1n;
		const x2 = x.pow(2n).normalize();
		let denominator = _1N;
		const x2 = x.pow(_2N).normalize();
		let sum = x.trunc(decimals + 5);
		let i = 2n;
		let i = _2N;
		while (true) {
		numerator = numerator.mul(x2);
		denominator = i (i + 1n);
		i += 2n;
		denominator = i (i + _1N);
		i += _2N;
		const term = numerator.div(denominator);
		@@ -38,3 +38,3 @@ sum = sum.add(term).trunc(decimals + 5);

		return ExactNumber(0);
		return ExactNumber(_0N);
		};
		@@ -44,15 +44,15 @@
		function* coshGenerator(x: ExactNumberType, decimals: number) {
		const x2 = x.pow(2n).normalize();
		const x2 = x.pow(_2N).normalize();
		let numerator = x2;
		let denominator = 2n;
		let denominator = _2N;
		let sum = numerator
		.div(denominator)
		.add(1n)
		.add(_1N)
		.trunc(decimals + 5);

		let i = 3n;
		let i = _3N;
		while (true) {
		numerator = numerator.mul(x2);
		denominator = i (i + 1n);
		i += 2n;
		denominator = i (i + _1N);
		i += _2N;
		const term = numerator.div(denominator);
		@@ -76,3 +76,3 @@ sum = sum.add(term).trunc(decimals + 5);

		return ExactNumber(0);
		return ExactNumber(_0N);
		};
		@@ -82,3 +82,3 @@
		const angleNum = limitDecimals(ExactNumber(angle), decimals);
		if (angleNum.isZero()) return ExactNumber(0);
		if (angleNum.isZero()) return ExactNumber(_0N);

		@@ -89,3 +89,3 @@ // tanh x = sinh x / cosh x;
		const coshRes = cosh(angleNum, decimals + 10).abs();
		const sinhRes = sqrt(coshRes.pow(2).sub(1), decimals + 10);
		const sinhRes = sqrt(coshRes.pow(_2N).sub(_1N), decimals + 10);

		@@ -92,0 +92,0 @@ const res = sinhRes.div(coshRes).mul(angleNum.sign());

src/approx/inverse_hyperbolic.ts

		@@ -1,2 +0,2 @@
		import { limitDecimals } from '../util';
		import { limitDecimals, _0N, _1N, _2N } from '../util';
		import { ExactNumber } from '../ExactNumber';
		@@ -9,7 +9,7 @@ import { ExactNumberType } from '../types';
		const input = limitDecimals(ExactNumber(x), decimals);
		if (input.isZero()) return ExactNumber(0);
		if (input.isZero()) return ExactNumber(_0N);

		// asinh(x) = ln(x + sqrt(x^2 + 1))

		const root = sqrt(input.pow(2).add(1n), decimals + 5);
		const root = sqrt(input.pow(_2N).add(_1N), decimals + 5);
		const res = log(input.add(root), decimals + 5);
		@@ -22,8 +22,8 @@
		const input = limitDecimals(ExactNumber(x), decimals);
		if (input.isOne()) return ExactNumber(0);
		if (input.lt(1n)) throw new Error('Out of range');
		if (input.isOne()) return ExactNumber(_0N);
		if (input.lt(_1N)) throw new Error('Out of range');

		// acosh(x) = ln(x + sqrt(x^2 - 1))

		const root = sqrt(input.pow(2).sub(1n), decimals + 5);
		const root = sqrt(input.pow(_2N).sub(_1N), decimals + 5);
		const res = log(input.add(root), decimals + 5);
		@@ -36,10 +36,10 @@
		const input = limitDecimals(ExactNumber(x), decimals);
		if (input.abs().gte(1n)) throw new Error('Out of range');
		if (input.isZero()) return ExactNumber(0);
		if (input.abs().gte(_1N)) throw new Error('Out of range');
		if (input.isZero()) return ExactNumber(_0N);

		// atanh(x) = 0.5 * ln((1 + x) / (1 - x))

		const res = log(input.add(1n).div(input.neg().add(1n)), decimals + 5);
		const res = log(input.add(_1N).div(input.neg().add(_1N)), decimals + 5);

		return ExactNumber(res).div(2n).trunc(decimals);
		return ExactNumber(res).div(_2N).trunc(decimals);
		};

src/approx/inverse_trigonometry.ts

		@@ -1,2 +0,2 @@
		import { limitDecimals } from '../util';
		import { limitDecimals, _0N, _1N, _2N, _3N } from '../util';
		import { ExactNumber } from '../ExactNumber';
		@@ -9,5 +9,5 @@ import { ExactNumberType } from '../types';
		function* atanGenerator(x: ExactNumberType, decimals: number) {
		const x2 = x.pow(2n).normalize();
		const x4 = x2.pow(2n).normalize();
		let denominator = 3n;
		const x2 = x.pow(_2N).normalize();
		const x4 = x2.pow(_2N).normalize();
		let denominator = _3N;

		@@ -21,4 +21,4 @@ let sum = x.sub(x.mul(x2).div(denominator));
		// = x^5 * (-ax^2 + (a + 2)) / (a * (a + 2))
		denominator += 2n;
		const denominator2 = denominator + 2n;
		denominator += _2N;
		const denominator2 = denominator + _2N;
		const numerator = xPow.mul(x2.mul(-denominator).add(denominator2));
		@@ -50,4 +50,4 @@ const term = numerator.div(denominator * denominator2);
		while (x.abs().gt(reductionLimit)) {
		const root = ExactNumber(sqrt(x.pow(2n).add(1n), decimals + 10));
		x = x.div(root.add(1n));
		const root = ExactNumber(sqrt(x.pow(_2N).add(_1N), decimals + 10));
		x = x.div(root.add(_1N));
		reductionSteps++;
		@@ -62,3 +62,3 @@ }
		// undo argument reduction
		const res = sum.mul(2n ** BigInt(reductionSteps));
		const res = sum.mul(_2N ** BigInt(reductionSteps));
		return res.trunc(decimals);
		@@ -74,10 +74,10 @@ }

		if (x.isZero()) return ExactNumber(0);
		if (x.isZero()) return ExactNumber(_0N);
		if (x.abs().isOne()) {
		return ExactNumber(PI(decimals)).mul(x.sign()).div(2n).trunc(decimals);
		return ExactNumber(PI(decimals)).mul(x.sign()).div(_2N).trunc(decimals);
		}
		if (x.abs().eq('1/2')) {
		return ExactNumber(PI(decimals)).mul(x.sign()).div(6n).trunc(decimals);
		return ExactNumber(PI(decimals)).mul(x.sign()).div(6).trunc(decimals);
		}
		if (x.gt(1n) \|\| x.lt(-1n)) {
		if (x.gt(_1N) \|\| x.lt(-_1N)) {
		throw new Error('Out of range');
		@@ -88,5 +88,5 @@ }

		const root = ExactNumber(sqrt(x.pow(2n).neg().add(1), decimals + 10));
		const atangent = ExactNumber(atan(x.div(root.add(1n)), decimals + 10));
		return atangent.mul(2).trunc(decimals);
		const root = ExactNumber(sqrt(x.pow(_2N).neg().add(_1N), decimals + 10));
		const atangent = ExactNumber(atan(x.div(root.add(_1N)), decimals + 10));
		return atangent.mul(_2N).trunc(decimals);
		};
		@@ -97,6 +97,6 @@

		if (x.isZero()) return ExactNumber(PI(decimals)).div(2n).trunc(decimals);
		if (x.isZero()) return ExactNumber(PI(decimals)).div(_2N).trunc(decimals);

		if (x.isOne()) {
		return ExactNumber(0);
		return ExactNumber(_0N);
		}
		@@ -109,7 +109,7 @@
		if (x.abs().eq('1/2')) {
		const PI_OVER_3 = ExactNumber(PI(decimals)).div(3n);
		return x.sign() === -1 ? PI_OVER_3.mul(2n).trunc(decimals) : PI_OVER_3.trunc(decimals);
		const PI_OVER_3 = ExactNumber(PI(decimals)).div(_3N);
		return x.sign() === -1 ? PI_OVER_3.mul(_2N).trunc(decimals) : PI_OVER_3.trunc(decimals);
		}

		if (x.gt(1n) \|\| x.lt(-1n)) {
		if (x.gt(_1N) \|\| x.lt(-_1N)) {
		throw new Error('Out of range');
		@@ -120,5 +120,5 @@ }
		return ExactNumber(PI(decimals + 10))
		.div(2n)
		.div(_2N)
		.sub(asin(x, decimals + 10))
		.trunc(decimals);
		};

src/approx/logarithm.ts

		@@ -1,2 +0,2 @@
		import { limitDecimals } from '../util';
		import { limitDecimals, _0N, _10N, _1N, _2N } from '../util';
		import { ExactNumber } from '../ExactNumber';
		@@ -11,6 +11,6 @@ import { FixedNumber } from '../FixedNumber';
		function* logGenerator(y: ExactNumberType, decimals: number) {
		const y2 = y.pow(2n).normalize();
		const y2 = y.pow(_2N).normalize();

		let numerator = y;
		let denominator = 1n;
		let denominator = _1N;

		@@ -21,3 +21,3 @@ let sum = ExactNumber(y);
		numerator = numerator.mul(y2);
		denominator += 2n;
		denominator += _2N;
		const term = numerator.div(denominator).trunc(decimals + 10);
		@@ -35,3 +35,3 @@ sum = sum.add(term);

		if (input.lte(0n)) {
		if (input.lte(0)) {
		throw new Error('Invalid parameter');
		@@ -44,3 +44,3 @@ }
		const reductionLimit = ExactNumber('0.1');
		while (input.sub(1n).abs().gt(reductionLimit)) {
		while (input.sub(_1N).abs().gt(reductionLimit)) {
		input = new FixedNumber(sqrt(input, decimals + 10));
		@@ -52,3 +52,3 @@ reductions++;
		// y = (x - 1)/(x + 1) (\|y\| < 1)
		const y = input.sub(1n).div(input.add(1n));
		const y = input.sub(_1N).div(input.add(_1N));

		@@ -59,3 +59,3 @@ const gen = logGenerator(y, decimals);
		// undo reductions
		const res = sum.mul(2n ** BigInt(reductions + 1));
		const res = sum.mul(_2N ** BigInt(reductions + 1));
		return res.trunc(decimals);
		@@ -65,3 +65,3 @@ }

		return ExactNumber(0);
		return ExactNumber(_0N);
		};
		@@ -80,3 +80,3 @@

		const LOG_2 = new ConstantCache(decimals => log(2n, decimals), 200);
		const LOG_2 = new ConstantCache(decimals => log(_2N, decimals), 200);

		@@ -89,3 +89,3 @@ export const log2 = (x: number \| bigint \| string \| ExactNumberType, decimals: number): ExactNumberType => {

		const LOG_10 = new ConstantCache(decimals => log(10n, decimals), 200);
		const LOG_10 = new ConstantCache(decimals => log(_10N, decimals), 200);

		@@ -92,0 +92,0 @@ export const log10 = (x: number \| bigint \| string \| ExactNumberType, decimals: number): ExactNumberType => {

src/approx/roots.ts

		@@ -5,3 +5,3 @@ import { FixedNumber } from '../FixedNumber';
		import { ExactNumber } from '../ExactNumber';
		import { limitDecimals } from '../util';
		import { limitDecimals, _0N, _1N } from '../util';

		@@ -73,4 +73,4 @@ const approximateNthRoot = (n: number, x: ExactNumberType): string => {
		if (n % 2 === 0 && xNum.sign() === -1) throw new Error('Complex numbers are not supported');
		if (xNum.isZero()) return new FixedNumber(0n).trunc(decimals);
		if (xNum.isOne()) return new FixedNumber(1n).trunc(decimals);
		if (xNum.isZero()) return new FixedNumber(_0N).trunc(decimals);
		if (xNum.isOne()) return new FixedNumber(_1N).trunc(decimals);

		@@ -77,0 +77,0 @@ const res = nthrootWithNewton(n, xNum, decimals);

src/approx/trigonometry.test.ts

		@@ -0,3 +1,4 @@
		import { ExactNumberType } from '../types';
		import { ExactNumber } from '../ExactNumber';
		import { cos, PI, sin, tan } from './trigonometry';
		import { cos, evaluateAngle, PI, sin, tan } from './trigonometry';
		import { compareError, testStability } from '../testHelper.test';
		@@ -24,4 +25,54 @@

		it('evaluates angles', () => {
		const precision = 10;
		const pi = PI(15);

		const toRad = (x: ExactNumberType) => ExactNumber(x).div(180).mul(pi).trunc(precision);
		const normalizeAngle = (x: ExactNumberType) => {
		let ref = ExactNumber(x).mod(360);
		if (ref.sign() === -1) ref = ref.add(360);
		return ref;
		};

		for (let deg = -3600; deg <= 3600; deg++) {
		const rad = toRad(ExactNumber(deg));
		const ref = normalizeAngle(ExactNumber(deg));
		const quadrant = ref.div(90).floor().toNumber() + 1;
		const res = evaluateAngle(rad, precision);
		expect(res.quadrant).toBe(quadrant);

		if (deg % 15 === 0) {
		expect(res.specialCaseDeg).not.toBe(null);
		expect(res.specialCaseDeg).toBeGreaterThanOrEqual(0);
		expect(res.specialCaseDeg).toBeLessThanOrEqual(90);
		expect(res.subHalfPiAngle).toBe(null);
		} else {
		expect(res.specialCaseDeg).toBe(null);
		expect(res.subHalfPiAngle.gte(0)).toBe(true);
		expect(res.subHalfPiAngle.lte('1.571')).toBe(true);
		}
		}
		});

		it('reduces angles correctly', () => {
		const precision = 10;
		const pi = PI(100);
		const piOver2 = pi.div(2);

		const seq = [ExactNumber(0), pi.div(6), pi.div(4), pi.div(3)];

		for (let base = ExactNumber(0); base.lt(200); base = base.add(pi.mul(2))) {
		for (let quadrant = 1; quadrant <= 4; quadrant++) {
		const basePlusQuadrant = base.add(piOver2.mul(quadrant - 1));
		for (const angle of seq) {
		const x = basePlusQuadrant.add(angle).trunc(precision);
		const res = evaluateAngle(x, precision);
		expect(res.quadrant).toBe(quadrant);
		}
		}
		}
		});

		it('cos reduce to half pi', () => {
		const pi = ExactNumber(PI(100));
		const pi = PI(100);
		const piOverTwo = pi.div(2);
		@@ -53,2 +104,4 @@
		it('tan', () => {
		// expect(tan(PI(12).div(2), 10).toFixed(10)).toBe('3.1415926535');

		const range = [Math.floor(Math.PI * -4), Math.ceil(Math.PI * 4)];
		@@ -55,0 +108,0 @@ for (let i = range[0]; i <= range[1]; i += 0.01) {

172

src/approx/trigonometry.ts

		@@ -6,3 +6,3 @@ import { FixedNumber } from '../FixedNumber';
		import { sqrt } from './roots';
		import { limitDecimals } from '../util';
		import { limitDecimals, _0N, _1N, _2N, _3N, _4N, _10N, _24N } from '../util';

		@@ -14,11 +14,12 @@ // TODO: https://en.wikipedia.org/wiki/Niven%27s_theorem
		const PIcalc = (decimals: number): ExactNumberType => {
		if (decimals === 0) return ExactNumber(3n);
		if (decimals === 0) return ExactNumber(_3N);

		// PI = 3 + 3(1/2)(1/3)(1/4) + 3((1/2)(3/4))(1/5)(1/4^2) + 3((1/2)(3/4)(5/6))(1/7)(1/4^3) + ...
		let i = 1n;
		let x = 3n * 10n ** BigInt(decimals + 20);
		let i = _1N;
		let x = _3N * _10N ** BigInt(decimals + 20);
		let res = x;
		while (x !== 0n) {
		x = (x * i) / ((i + 1n) * 4n);
		i += 2n;

		while (x !== _0N) {
		x = (x * i) / ((i + _1N) * _4N);
		i += _2N;
		res += x / i;
		@@ -33,37 +34,77 @@ }
		export const PI = (decimals: number): ExactNumberType => {
		if (decimals === 0) return ExactNumber(3);
		if (decimals === 0) return ExactNumber(_3N);
		return PI_CACHE.get(decimals).trunc(decimals);
		};

		const evaluateAngle = (x: ExactNumberType, decimals: number) => {
		const pi = new FixedNumber(PI(decimals + 5));
		const twoPi = pi.mul(2n);
		const roundedX = x.round(decimals + 5, RoundingMode.NEAREST_AWAY_FROM_ZERO);
		// a number between (-1, 1)
		let turns = roundedX.div(twoPi).fracPart();
		const getMultiplierOf = (x: ExactNumberType, y: ExactNumberType, decimals: number) => {
		const precision = Math.max(3, decimals);
		const input = x.trunc(precision);
		const closestQuotient = input.div(y).round();
		const ref = y.mul(closestQuotient).trunc(precision);

		// normalize into the [0, 1) interval
		if (turns.lt(0n)) {
		turns = turns.add(1n);
		if (ref.eq(input)) {
		return closestQuotient;
		}

		// limit precision
		turns = turns.round(decimals + 5);
		return null;
		};

		const quadrant = turns.div('0.25').floor().toNumber() + 1;
		type EvaluationRes = { specialCaseDeg: number \| null; quadrant: number; subHalfPiAngle: ExactNumberType \| null };

		let subHalfPiAngle = twoPi.mul(turns);
		let quadrantDegrees = turns.mul(360n);
		const evaluateSpecialAngle = (angleMultiplier: ExactNumberType): EvaluationRes => {
		let multiplier = angleMultiplier.mod(_24N).toNumber();
		if (multiplier < 0) {
		multiplier += 24;
		}
		const quadrant = Math.floor(multiplier / 6) + 1;

		let specialCaseDeg = multiplier * 15;
		if (quadrant === 4) {
		specialCaseDeg = 360 - specialCaseDeg;
		} else if (quadrant === 3) {
		specialCaseDeg -= 180;
		} else if (quadrant === 2) {
		specialCaseDeg = 180 - specialCaseDeg;
		}

		return {
		specialCaseDeg,
		quadrant,
		subHalfPiAngle: null,
		};
		};

		export const evaluateAngle = (x: ExactNumberType, decimals: number): EvaluationRes => {
		let angle = x.round(decimals + 5, RoundingMode.NEAREST_AWAY_FROM_ZERO);
		const pi = PI(decimals + 5);

		const angleMultiplier = getMultiplierOf(angle, pi.div(12), decimals);
		if (angleMultiplier !== null) {
		return evaluateSpecialAngle(angleMultiplier);
		}

		const twoPi = pi.mul(_2N);

		angle = angle.mod(twoPi);

		if (angle.sign() === -1) {
		angle = angle.add(twoPi);
		}

		const quadrant = angle.mul(_2N).div(pi).floor().toNumber() + 1;

		let subHalfPiAngle = angle;
		if (quadrant === 4) {
		subHalfPiAngle = twoPi.sub(subHalfPiAngle);
		quadrantDegrees = ExactNumber(360).sub(quadrantDegrees);
		} else if (quadrant === 3) {
		subHalfPiAngle = subHalfPiAngle.sub(pi);
		quadrantDegrees = quadrantDegrees.sub(180);
		} else if (quadrant === 2) {
		subHalfPiAngle = pi.sub(subHalfPiAngle);
		quadrantDegrees = ExactNumber(180).sub(quadrantDegrees);
		}

		return { quadrantDegrees: quadrantDegrees.round(decimals), quadrant, subHalfPiAngle };
		return {
		specialCaseDeg: null,
		quadrant,
		subHalfPiAngle,
		};
		};
		@@ -73,10 +114,9 @@
		function* cosGenerator(x: ExactNumberType, decimals: number) {
		const x2 = x.round(decimals + 10, RoundingMode.NEAREST_AWAY_FROM_ZERO).pow(2n);
		const x2 = x.round(decimals + 10, RoundingMode.NEAREST_AWAY_FROM_ZERO).pow(_2N);

		let xPow = x2;

		let termDenominator = 2n;
		let sum = ExactNumber(1n).sub(xPow.div(termDenominator).trunc(decimals + 10));
		let i = 3n;
		// let rndErrors = 1;
		let termDenominator = _2N;
		let sum = ExactNumber(_1N).sub(xPow.div(termDenominator).trunc(decimals + 10));
		let i = _3N;

		@@ -86,6 +126,6 @@ while (true) {
		// = (56x^4 - x^6)/6!
		termDenominator = i (i + 1n);
		i += 2n;
		const multiplier = i * (i + 1n);
		i += 2n;
		termDenominator = i (i + _1N);
		i += _2N;
		const multiplier = i * (i + _1N);
		i += _2N;
		xPow = xPow.mul(x2);
		@@ -98,7 +138,5 @@ termDenominator *= multiplier;
		const term = termNumerator.div(termDenominator).trunc(decimals + 10);
		// rndErrors++;

		sum = sum.add(term);
		// max lagrange error = x^(k+1)/(k+1)!
		// const le = xPow.mul(x).div(termDenominator * i);

		@@ -109,3 +147,7 @@ yield { term, sum };

		const resultHandler = (value: string \| ExactNumberType, shouldNegate: boolean, decimals: number): ExactNumberType => {
		const resultHandler = (
		value: bigint \| string \| ExactNumberType,
		shouldNegate: boolean,
		decimals: number,
		): ExactNumberType => {
		let convertedValue = ExactNumber(value);
		@@ -122,15 +164,18 @@ if (shouldNegate) {
		const angle = limitDecimals(ExactNumber(_angle), decimals + 5);
		const { quadrantDegrees, subHalfPiAngle: x, quadrant } = evaluateAngle(angle, decimals);
		const { specialCaseDeg, subHalfPiAngle: x, quadrant } = evaluateAngle(angle, decimals);

		const shouldNegate = quadrant === 2 \|\| quadrant === 3;

		if (quadrantDegrees.isZero()) return resultHandler('1', shouldNegate, decimals);
		if (quadrantDegrees.eq(30n)) {
		return resultHandler(ExactNumber(sqrt(3n, decimals + 5)).div(2n), shouldNegate, decimals);
		if (specialCaseDeg !== null) {
		if (specialCaseDeg === 0) return resultHandler(_1N, shouldNegate, decimals);
		if (specialCaseDeg === 30) {
		return resultHandler(ExactNumber(sqrt(_3N, decimals + 5)).div(_2N), shouldNegate, decimals);
		}
		if (specialCaseDeg === 45) {
		return resultHandler(ExactNumber(sqrt(_2N, decimals + 5)).div(_2N), shouldNegate, decimals);
		}
		if (specialCaseDeg === 60) return resultHandler('0.5', shouldNegate, decimals);
		if (specialCaseDeg === 90) return resultHandler(_0N, shouldNegate, decimals);
		throw new Error();
		}
		if (quadrantDegrees.eq(45n)) {
		return resultHandler(ExactNumber(sqrt(2n, decimals + 5)).div(2n), shouldNegate, decimals);
		}
		if (quadrantDegrees.eq(60n)) return resultHandler('0.5', shouldNegate, decimals);
		if (quadrantDegrees.eq(90n)) return resultHandler('0', shouldNegate, decimals);

		@@ -152,3 +197,3 @@ const maxError = ExactNumber(`1e-${EXTRA_DECIMALS}`);
		const x = limitDecimals(ExactNumber(angle), decimals + 5);
		return cos(pi.div(2n).sub(x), decimals + 5).trunc(decimals);
		return cos(pi.div(_2N).sub(x), decimals + 5).trunc(decimals);
		};
		@@ -159,24 +204,27 @@

		const { quadrantDegrees, quadrant, subHalfPiAngle: x } = evaluateAngle(angleNum, decimals + 5);
		const { specialCaseDeg, quadrant, subHalfPiAngle: x } = evaluateAngle(angleNum, decimals);

		const shouldNegate = quadrant === 1 \|\| quadrant === 3;

		if (quadrantDegrees.isZero()) return resultHandler('0', shouldNegate, decimals);
		if (quadrantDegrees.eq(30n)) {
		return resultHandler(ExactNumber(1n).div(sqrt(3n, decimals + 5)), shouldNegate, decimals);
		if (specialCaseDeg !== null) {
		if (specialCaseDeg === 0) return resultHandler('0', shouldNegate, decimals);
		if (specialCaseDeg === 30) {
		return resultHandler(ExactNumber(_1N).div(sqrt(_3N, decimals + 5)), shouldNegate, decimals);
		}
		if (specialCaseDeg === 4) {
		return resultHandler('1', shouldNegate, decimals);
		}
		if (specialCaseDeg === 60) return resultHandler(sqrt(_3N, decimals + 5), shouldNegate, decimals);
		if (specialCaseDeg === 90) {
		throw new Error('Out of range');
		}
		throw new Error();
		}
		if (quadrantDegrees.eq(45n)) {
		return resultHandler('1', shouldNegate, decimals);
		}
		if (quadrantDegrees.eq(60n)) return resultHandler(sqrt(3n, decimals + 5), shouldNegate, decimals);
		if (quadrantDegrees.eq(90n)) {
		throw new Error('Out of range');
		}

		// tan x = sqrt((1 - cos(2x)) / 1 + cos(2x))
		const cos2x = ExactNumber(cos(x.mul(2n), decimals + 5));
		const cos2x = ExactNumber(cos(x.mul(_2N), decimals + 5));

		const res = ExactNumber(1n)
		const res = ExactNumber(_1N)
		.sub(cos2x)
		.div(ExactNumber(1n).add(cos2x))
		.div(ExactNumber(_1N).add(cos2x))
		.round(decimals + 5);
		@@ -183,0 +231,0 @@

src/ExactNumber.ts

		import { Fraction } from './Fraction';
		import { FixedNumber } from './FixedNumber';
		import { ExactNumberParameter, ExactNumberType } from './types';
		import { _0N, _1N } from './util';

		@@ -23,3 +24,3 @@ export function parseParameter(x: number \| bigint \| string \| ExactNumberType): ExactNumberType {
		if (x.includes('/') \|\| x.includes('(')) {
		return new Fraction(x, 1n);
		return new Fraction(x, _1N);
		}
		@@ -66,3 +67,3 @@ return new FixedNumber(x);
		const yVal = parseParameter(y);
		return new Fraction(xVal, 1n).div(new Fraction(yVal, 1n));
		return new Fraction(xVal, _1N).div(new Fraction(yVal, _1N));
		});
		@@ -103,3 +104,3 @@
		const parseDigitsInBase = (str: string, radix: number) => {
		let res = 0n;
		let res = _0N;
		for (let i = 0; i < str.length; i++) {
		@@ -150,4 +151,4 @@ const c = str.charAt(i);
		const numerator =
		parseDigitsInBase([wholePartStr, nonRepeatingPartStr, repeatingPartStr].join(''), radix) -
		parseDigitsInBase([wholePartStr, nonRepeatingPartStr].join(''), radix);
		parseDigitsInBase(`${wholePartStr}${nonRepeatingPartStr}${repeatingPartStr}`, radix) -
		parseDigitsInBase(`${wholePartStr}${nonRepeatingPartStr}`, radix);

		@@ -168,3 +169,3 @@ const denominator = parseDigitsInBase(

		const res = new Fraction(whole, 1n).add(fracPath).normalize();
		const res = new Fraction(whole, _1N).add(fracPath).normalize();
		return isNegative ? res.neg() : res;
		@@ -171,0 +172,0 @@ });

src/FixedNumber.test.ts

		@@ -180,2 +180,18 @@ import { FixedNumber } from './FixedNumber';

		it('powm()', () => {
		const run = (b: ExactNumberParameter, e: ExactNumberParameter, m: ExactNumberParameter) =>
		new FixedNumber(b).powm(e, m).toString();

		expect(run(3, 4, 5)).toBe('1');
		expect(run(314, 23, 971)).toBe('865');

		for (let b = 2; b <= 25; b++) {
		for (let e = 0; e <= 10; e++) {
		for (let m = 11; m <= 13; m++) {
		expect(run(b, e, m)).toBe((b ** e % m).toString());
		}
		}
		}
		});

		it('div()', () => {
		@@ -232,2 +248,5 @@ const run = (a: ExactNumberParameter, b: ExactNumberParameter) => new FixedNumber(a).div(b).toString();
		expect(run('-3.745', '-1.25')).toBe('-1.245');
		expect(run('17.891', '-1.66')).toBe('1.291');
		expect(run('-712.8929', '-1.79')).toBe('-0.4729');
		expect(run('-2.8', '-1.789')).toBe('-1.011');

		@@ -697,3 +716,4 @@ const values = [
		it('toFixed()', () => {
		const run = (x: string, digits: number, rndMode?: RoundingMode) => new FixedNumber(x).toFixed(digits, rndMode);
		const run = (x: string, digits: number, trimZeros?: boolean) =>
		new FixedNumber(x).toFixed(digits, RoundingMode.TO_ZERO, trimZeros);

		@@ -708,5 +728,7 @@ expect(run('0', 0)).toBe('0');
		expect(run('0.45600', 6)).toBe('0.456000');
		expect(run('0.45600', 6, true)).toBe('0.456');
		expect(run('-123.45600', 0)).toBe('-123');
		expect(run('-123.45600', 1)).toBe('-123.4');
		expect(run('-123.45600', 6)).toBe('-123.456000');
		expect(run('123000', 2, true)).toBe('123000');

		@@ -730,3 +752,4 @@ expect(() => run('-1.45', -1)).toThrow('Invalid parameter');
		it('toPrecision()', () => {
		const run = (x: string, digits: number) => new FixedNumber(x).toPrecision(digits);
		const run = (x: string, digits: number, trimZeros?: boolean) =>
		new FixedNumber(x).toPrecision(digits, RoundingMode.TO_ZERO, trimZeros);

		@@ -744,2 +767,4 @@ expect(run('0', 1)).toBe('0');
		expect(run('0.0045600', 6)).toBe('0.00456000');
		expect(run('0.0045600', 6, true)).toBe('0.00456');
		expect(run('123000', 2, true)).toBe('120000');

		@@ -751,15 +776,21 @@ expect(() => run('-1.45', -1)).toThrow('Invalid parameter');

		// it('toPrecision() rounding modes', () => {
		// for (const rndMode of Object.values(RoundingMode)) {
		// for (let i = 0; i < 10; i++) {
		// let num = new FixedNumber('123.45600');
		// expect(num.toPrecision(i, rndMode)).toBe(num.roundToDigits(rndMode, i).toPrecision(i));
		// num = new FixedNumber('-123.45600');
		// expect(num.toPrecision(i, rndMode)).toBe(num.roundToDigits(rndMode, i).toPrecision(i));
		// }
		// }
		// });
		it('toPrecision() rounding modes', () => {
		for (const rndMode of Object.values(RoundingMode)) {
		if (!Number.isInteger(rndMode)) continue;
		for (let i = 1; i < 10; i++) {
		let num = new FixedNumber('123.45600');
		expect(num.toPrecision(i, rndMode as RoundingMode)).toBe(
		num.roundToDigits(i, rndMode as RoundingMode).toPrecision(i),
		);
		num = num.neg();
		expect(num.toPrecision(i, rndMode as RoundingMode)).toBe(
		num.roundToDigits(i, rndMode as RoundingMode).toPrecision(i),
		);
		}
		}
		});

		it('toExponential()', () => {
		const run = (a: string, digits: number) => new FixedNumber(a).toExponential(digits);
		const run = (a: string, digits: number, trimZeros?: boolean) =>
		new FixedNumber(a).toExponential(digits, RoundingMode.TO_ZERO, trimZeros);

		@@ -791,2 +822,7 @@ expect(run('0', 0)).toBe('0e+0');

		expect(run('0.0045600', 6, true)).toBe('4.56e-3');
		expect(run('123000', 2, true)).toBe('1.23e+5');
		expect(run('123000', 10, false)).toBe('1.2300000000e+5');
		expect(run('123000', 10, true)).toBe('1.23e+5');

		expect(() => run('-1.45', -1)).toThrow('Invalid parameter');
		@@ -807,3 +843,3 @@ expect(() => run('-1.45', 0.5)).toThrow('Invalid parameter');
		expect(run('0.4', 3)).toBe('0.(1012)');
		expect(run('0.3', 16)).toBe('0.4(c)');
		expect(run('0.300', 16)).toBe('0.4(c)');
		expect(run('0.013', 7)).toBe('0.(00431330261442015456)');
		@@ -813,2 +849,5 @@ expect(run('0.012', 6)).toBe('0.0(0233151220401052455413443)');
		expect(run('-15.012', 6)).toBe('-23.0(0233151220401052455413443)');
		expect(run('-123.500', 6)).toBe('-323.3');
		expect(run('1234.88', 16)).toBe('4d2.(e147a)');
		expect(run('-1234.2000', 15)).toBe('-574.3');

		@@ -815,0 +854,0 @@ expect(run('100', 5)).toBe('400');

151

src/FixedNumber.ts

		@@ -1,2 +0,2 @@
		import { bigIntToStr } from './util';
		import { bigIntToStr, trimTrailingZerosFromFixed, _0N, _10N, _1N, _24N, _2N } from './util';
		import { Fraction } from './Fraction';
		@@ -80,4 +80,4 @@ import { ExactNumber, parseParameter } from './ExactNumber';
		const maxPos = Math.max(this.decimalPos, decimalPos);
		const a = maxPos === this.decimalPos ? this.number : this.number * 10n ** BigInt(maxPos - this.decimalPos);
		const b = maxPos === decimalPos ? number : number * 10n ** BigInt(maxPos - decimalPos);
		const a = maxPos === this.decimalPos ? this.number : this.number * _10N ** BigInt(maxPos - this.decimalPos);
		const b = maxPos === decimalPos ? number : number * _10N ** BigInt(maxPos - decimalPos);
		return { a, b, decimalPos: maxPos };
		@@ -127,2 +127,27 @@ }

		powm(
		_exp: number \| bigint \| string \| ExactNumberType,
		_mod: number \| bigint \| string \| ExactNumberType,
		modType?: ModType,
		): FixedNumber {
		let exp = parseParameter(_exp).toNumber();
		if (!Number.isSafeInteger(exp)) {
		throw new Error('Unsupported parameter');
		}

		const mod = parseParameter(_mod);
		let base = this as FixedNumber;

		let res = new FixedNumber(_1N);
		while (exp !== 0) {
		if (exp % 2 !== 0) {
		res = res.mul(base).mod(mod, modType) as FixedNumber;
		}
		base = base.pow(_2N).mod(mod, modType) as FixedNumber;
		exp = Math.floor(exp / 2);
		}

		return res;
		}

		div(x: number \| bigint \| string \| ExactNumberType): ExactNumberType {
		@@ -162,7 +187,7 @@ const frac = this.convertToFraction();
		if (type === ModType.FLOORED) {
		return Number(a < 0) ^ Number(b < 0) ? res.add(b) : res;
		return Number(a < _0N) ^ Number(b < _0N) ? res.add(b) : res;
		}

		if (type === ModType.EUCLIDEAN) {
		return mod < 0 ? res.add(b < 0 ? -b : b) : res;
		return mod < _0N ? res.add(b < _0N ? -b : b) : res;
		}
		@@ -174,3 +199,3 @@
		abs(): FixedNumber {
		const res = new FixedNumber(this.number < 0 ? -this.number : this.number, this.decimalPos);
		const res = new FixedNumber(this.number < _0N ? -this.number : this.number, this.decimalPos);
		return res;
		@@ -180,3 +205,3 @@ }
		neg() {
		return this.mul(-1n) as FixedNumber;
		return this.mul(-_1N) as FixedNumber;
		}
		@@ -222,3 +247,3 @@

		const exp = 10n ** BigInt(shift);
		const exp = _10N ** BigInt(shift);
		const outDigits = this.number / exp;
		@@ -231,3 +256,3 @@
		const extraDigits = this.number % exp;
		if (extraDigits === 0n) {
		if (extraDigits === _0N) {
		return new FixedNumber(outDigits, decimals);
		@@ -237,3 +262,3 @@ }
		if (roundingMode === RoundingMode.AWAY_FROM_ZERO) {
		const res = this.number < 0n ? outDigits - 1n : outDigits + 1n;
		const res = this.number < _0N ? outDigits - _1N : outDigits + _1N;
		return new FixedNumber(res, decimals);
		@@ -243,3 +268,3 @@ }
		if (roundingMode === RoundingMode.TO_POSITIVE) {
		const res = this.number < 0n ? outDigits : outDigits + 1n;
		const res = this.number < _0N ? outDigits : outDigits + _1N;
		return new FixedNumber(res, decimals);
		@@ -249,3 +274,3 @@ }
		if (roundingMode === RoundingMode.TO_NEGATIVE) {
		const res = this.number >= 0n ? outDigits : outDigits - 1n;
		const res = this.number >= _0N ? outDigits : outDigits - _1N;
		return new FixedNumber(res, decimals);
		@@ -267,3 +292,3 @@ }

		let extraDigitsStr = (extraDigits < 0n ? -extraDigits : extraDigits).toString();
		let extraDigitsStr = (extraDigits < _0N ? -extraDigits : extraDigits).toString();
		// '00123' extra part will appear in extraDigitsStr as '123'
		@@ -281,3 +306,3 @@ // -> in this case we can exclude the tie case by setting the extra part to zero
		if (roundingMode === RoundingMode.NEAREST_AWAY_FROM_ZERO) {
		const res = this.number < 0n ? outDigits - 1n : outDigits + 1n;
		const res = this.number < _0N ? outDigits - _1N : outDigits + _1N;
		return new FixedNumber(res, decimals);
		@@ -287,3 +312,3 @@ }
		if (roundingMode === undefined \|\| roundingMode === RoundingMode.NEAREST_TO_POSITIVE) {
		const res = this.number < 0n ? outDigits : outDigits + 1n;
		const res = this.number < _0N ? outDigits : outDigits + _1N;
		return new FixedNumber(res, decimals);
		@@ -293,3 +318,3 @@ }
		if (roundingMode === RoundingMode.NEAREST_TO_NEGATIVE) {
		const res = this.number >= 0n ? outDigits : outDigits - 1n;
		const res = this.number >= _0N ? outDigits : outDigits - _1N;
		return new FixedNumber(res, decimals);
		@@ -299,7 +324,7 @@ }
		if (roundingMode === RoundingMode.NEAREST_TO_EVEN) {
		if (outDigits % 2n === 0n) {
		if (outDigits % _2N === _0N) {
		return new FixedNumber(outDigits, decimals);
		}

		const res = outDigits < 0n ? outDigits - 1n : outDigits + 1n;
		const res = outDigits < _0N ? outDigits - _1N : outDigits + _1N;
		return new FixedNumber(res, decimals);
		@@ -313,3 +338,3 @@ }

		const res = this.number < 0 ? outDigits - 1n : outDigits + 1n;
		const res = this.number < _0N ? outDigits - _1N : outDigits + _1N;
		return new FixedNumber(res, decimals);
		@@ -340,3 +365,3 @@ }
		if (rem > 0) {
		newNumber = 10n * BigInt(rem);
		newNumber = _10N * BigInt(rem);
		}
		@@ -349,7 +374,7 @@ }
		private countDigits() {
		if (this.number === 0n) return 1;
		if (this.number === _0N) return 1;
		let digits = 0;
		let x = this.number < 0 ? -this.number : this.number;
		while (x > 0n) {
		x /= 10n;
		let x = this.number < _0N ? -this.number : this.number;
		while (x > _0N) {
		x /= _10N;
		digits++;
		@@ -389,3 +414,3 @@ }
		sign(): -1 \| 1 {
		return this.number < 0n ? -1 : 1;
		return this.number < _0N ? -1 : 1;
		}
		@@ -404,9 +429,9 @@

		const pow = 2n ** 24n;
		const pow = _2N ** _24N;
		let an = this.normalize().number;
		let bn = (x.trunc().normalize() as FixedNumber).number;
		let res = 0n;
		let shift = 1n;
		let res = _0N;
		let shift = _1N;

		while (an > 0 && bn > 0) {
		while (an > _0N && bn > _0N) {
		const modA = BigInt.asUintN(24, an);
		@@ -434,9 +459,9 @@ const modB = BigInt.asUintN(24, bn);

		const pow = 2n ** 24n;
		const pow = _2N ** _24N;
		let an = this.normalize().number;
		let bn = (x.trunc().normalize() as FixedNumber).number;
		let res = 0n;
		let shift = 1n;
		let res = _0N;
		let shift = _1N;

		while (an > 0 \|\| bn > 0) {
		while (an > _0N \|\| bn > _0N) {
		const modA = BigInt.asUintN(24, an);
		@@ -464,9 +489,9 @@ const modB = BigInt.asUintN(24, bn);

		const pow = 2n ** 24n;
		const pow = _2N ** _24N;
		let an = this.normalize().number;
		let bn = (x.trunc().normalize() as FixedNumber).number;
		let res = 0n;
		let shift = 1n;
		let res = _0N;
		let shift = _1N;

		while (an > 0 \|\| bn > 0) {
		while (an > _0N \|\| bn > _0N) {
		const modA = BigInt.asUintN(24, an);
		@@ -492,3 +517,3 @@ const modB = BigInt.asUintN(24, bn);

		const pow = 2n ** BigInt(bitCount);
		const pow = _2N ** BigInt(bitCount);
		return this.mul(pow);
		@@ -506,3 +531,3 @@ }

		const pow = 2n ** BigInt(bitCount);
		const pow = _2N ** BigInt(bitCount);
		return new FixedNumber(this.normalize().number / pow);
		@@ -557,3 +582,3 @@ }
		isZero() {
		return this.number === 0n;
		return this.number === _0N;
		}
		@@ -563,8 +588,8 @@
		if (this.decimalPos === 0) {
		return this.number === 1n;
		return this.number === _1N;
		}

		const exp = 10n ** BigInt(this.decimalPos);
		const exp = _10N ** BigInt(this.decimalPos);
		const q = this.number / exp;
		return q === 1n && q * exp === this.number;
		return q === _1N && q * exp === this.number;
		}
		@@ -574,3 +599,3 @@
		if (this.decimalPos === 0) return true;
		return this.number % 10n ** BigInt(this.decimalPos) === 0n;
		return this.number % _10N ** BigInt(this.decimalPos) === _0N;
		}
		@@ -590,5 +615,5 @@
		let n = this.number;
		while (pos > 0 && n % 10n === 0n) {
		while (pos > 0 && n % _10N === _0N) {
		pos--;
		n /= 10n;
		n /= _10N;
		}
		@@ -600,5 +625,5 @@ return new FixedNumber(n, pos);
		if (this.decimalPos === 0) {
		return new Fraction(this.number, 1n);
		return new Fraction(this.number, _1N);
		}
		const denominator = 10n ** BigInt(this.decimalPos);
		const denominator = _10N ** BigInt(this.decimalPos);
		return new Fraction(this.number, denominator);
		@@ -611,3 +636,3 @@ }

		toFixed(decimals: number, roundingMode = RoundingMode.TO_ZERO): string {
		toFixed(decimals: number, roundingMode = RoundingMode.TO_ZERO, trimZeros = false): string {
		if (!Number.isSafeInteger(decimals) \|\| decimals < 0) throw new Error('Invalid parameter');
		@@ -617,6 +642,6 @@

		return bigIntToStr(rounded.number, rounded.decimalPos, decimals, false);
		return bigIntToStr(rounded.number, rounded.decimalPos, decimals, trimZeros);
		}

		toExponential(digits: number, roundingMode = RoundingMode.TO_ZERO): string {
		toExponential(digits: number, roundingMode = RoundingMode.TO_ZERO, trimZeros = false): string {
		if (!Number.isSafeInteger(digits) \|\| digits < 0) throw new Error('Invalid parameter');
		@@ -633,5 +658,11 @@

		const strWithPoint =
		slicedString.length > 1 ? `${slicedString.slice(0, 1)}.${slicedString.slice(1)}` : slicedString;
		let strWithPoint = slicedString;

		if (slicedString.length > 1) {
		strWithPoint = `${slicedString.slice(0, 1)}.${slicedString.slice(1)}`;
		if (trimZeros) {
		strWithPoint = trimTrailingZerosFromFixed(strWithPoint);
		}
		}

		const fractionalDigitsBefore = absNumber.decimalPos;
		@@ -689,3 +720,7 @@ const fractionalDigitsAfter = str.length - 1;

		return [isNegative ? '-' : '', intPart.number.toString(radix), digits.length ? '.' : '', ...digits].join('');
		const digitsStr = digits.join('');

		const res = `${isNegative ? '-' : ''}${intPart.number.toString(radix)}${digits.length ? '.' : ''}${digitsStr}`;

		return res;
		}
		@@ -706,6 +741,7 @@

		toPrecision(digits: number, roundingMode = RoundingMode.TO_ZERO): string {
		toPrecision(digits: number, roundingMode = RoundingMode.TO_ZERO, trimZeros = false): string {
		if (!Number.isSafeInteger(digits) \|\| digits < 1) throw new Error('Invalid parameter');

		const rounded = this.roundToDigits(digits, roundingMode);

		const { subZeroNum, exponentDiff } = rounded.toSubZeroNum();
		@@ -724,3 +760,2 @@
		const suffixLength = Math.max(0, digits - whole.length - frac.length);
		const suffix = '0'.repeat(suffixLength);
		const prefix = '0'.repeat(exponentDiff < 0 ? -exponentDiff : 0);
		@@ -730,3 +765,7 @@
		if (frac.length + prefix.length + suffixLength > 0) {
		const suffix = '0'.repeat(suffixLength);
		res += `.${prefix}${frac}${suffix}`;
		if (trimZeros) {
		res = trimTrailingZerosFromFixed(res);
		}
		}
		@@ -733,0 +772,0 @@

src/Fraction.test.ts

		@@ -213,2 +213,18 @@ import { Fraction } from './Fraction';

		it('powm()', () => {
		const run = (b: ExactNumberParameter, e: ExactNumberParameter, m: ExactNumberParameter) =>
		new Fraction(b, 1n).powm(e, m).toString();

		expect(run(3, 4, 5)).toBe('1');
		expect(run(314, 23, 971)).toBe('865');

		for (let b = 2; b <= 25; b++) {
		for (let e = 0; e <= 10; e++) {
		for (let m = 11; m <= 13; m++) {
		expect(run(b, e, m)).toBe((b ** e % m).toString());
		}
		}
		}
		});

		it('round()', () => {
		@@ -215,0 +231,0 @@ const run = (a: string, decimals?: number, rndMode?: RoundingMode) =>

133

src/Fraction.ts

		import { CommonNumberFields, ExactNumberType, ModType, RoundingMode } from './types';
		import { FixedNumber } from './FixedNumber';
		import { trimTrailingZeros } from './util';
		import { trimTrailingZerosFromFixed, _0N, _10N, _1N, _2N, _5N } from './util';
		import { ExactNumber } from './ExactNumber';
		@@ -35,3 +35,3 @@
		const isNegativeExp = exponent.startsWith('-');
		const exp = 10n ** BigInt(isNegativeExp ? exponent.slice(1) : exponent);
		const exp = _10N ** BigInt(isNegativeExp ? exponent.slice(1) : exponent);
		if (isNegativeExp) {
		@@ -59,7 +59,7 @@ return fraction.div(exp).normalize() as Fraction;
		}
		return new Fraction(BigInt(x), 1n);
		return new Fraction(BigInt(x), _1N);
		}

		if (typeof x === 'bigint') {
		return new Fraction(x, 1n);
		return new Fraction(x, _1N);
		}
		@@ -71,3 +71,3 @@
		const numerator = this.parseRepeatingDecimal(parts[0]);
		const denominator = parts[1] ? this.parseRepeatingDecimal(parts[1]) : new Fraction(1n, 1n);
		const denominator = parts[1] ? this.parseRepeatingDecimal(parts[1]) : new Fraction(_1N, _1N);
		const res = numerator.div(denominator) as CommonNumberFields;
		@@ -95,3 +95,3 @@ const fraction = res.convertToFraction();
		}
		if (this.denominator === 0n) {
		if (this.denominator === _0N) {
		throw new Error('Division by zero');
		@@ -161,3 +161,3 @@ }
		if (type === ModType.EUCLIDEAN) {
		return res.sign() < 0 ? res.add(rFrac.sign() < 0 ? rFrac.neg() : rFrac) : res;
		return res.sign() === -1 ? res.add(rFrac.sign() === -1 ? rFrac.neg() : rFrac) : res;
		}
		@@ -175,8 +175,35 @@
		const exp = param.numerator / param.denominator;
		const absExp = exp < 0 ? -exp : exp;
		const absExp = exp < _0N ? -exp : exp;

		const res = new Fraction(this.numerator absExp, this.denominator absExp);
		return exp < 0 ? res.inv() : res;
		return exp < _0N ? res.inv() : res;
		}

		powm(
		_exp: number \| bigint \| string \| ExactNumberType,
		_mod: number \| bigint \| string \| ExactNumberType,
		modType?: ModType,
		): ExactNumberType {
		const exp = this.parseParameter(_exp);
		if (!exp.isInteger()) {
		throw new Error('Unsupported parameter');
		}

		let expInt = exp.toNumber();

		const mod = this.parseParameter(_mod);
		let base = this as Fraction;

		let res = new Fraction(_1N, _1N);
		while (expInt !== 0) {
		if (expInt % 2 !== 0) {
		res = res.mul(base).mod(mod, modType) as Fraction;
		}
		base = base.pow(_2N).mod(mod, modType) as Fraction;
		expInt = Math.floor(expInt / 2);
		}

		return res;
		}

		inv(): ExactNumberType {
		@@ -188,3 +215,3 @@ const res = new Fraction(this.denominator, this.numerator);
		floor(decimals?: number) {
		if (this.denominator === 1n) return new FixedNumber(this.numerator);
		if (this.denominator === _1N) return new FixedNumber(this.numerator);

		@@ -195,3 +222,3 @@ return this.round(decimals, RoundingMode.TO_NEGATIVE);
		ceil(decimals?: number) {
		if (this.denominator === 1n) return new FixedNumber(this.numerator);
		if (this.denominator === _1N) return new FixedNumber(this.numerator);

		@@ -202,3 +229,3 @@ return this.round(decimals, RoundingMode.TO_POSITIVE);
		trunc(decimals?: number) {
		if (this.denominator === 1n) return new FixedNumber(this.numerator);
		if (this.denominator === _1N) return new FixedNumber(this.numerator);

		@@ -240,3 +267,3 @@ return this.round(decimals, RoundingMode.TO_ZERO);

		if (this.isZero()) return new FixedNumber(0n);
		if (this.isZero()) return new FixedNumber(_0N);

		@@ -248,10 +275,10 @@ let x = this.abs();

		while (x.gte(1n)) {
		x = x.div(10n);
		while (x.gte(_1N)) {
		x = x.div(_10N);
		divisions++;
		}

		const zeroPointOne = new Fraction(1n, 10n);
		const zeroPointOne = new Fraction(_1N, _10N);
		while (x.lt(zeroPointOne)) {
		x = x.mul(10n);
		x = x.mul(_10N);
		divisions--;
		@@ -268,4 +295,4 @@ }
		private gcd(numerator: bigint, denominator: bigint): bigint {
		let a = numerator < 0 ? -numerator : numerator;
		let b = denominator < 0 ? -denominator : denominator;
		let a = numerator < _0N ? -numerator : numerator;
		let b = denominator < _0N ? -denominator : denominator;

		@@ -279,5 +306,5 @@ if (b > a) {
		while (true) {
		if (b === 0n) return a;
		if (b === _0N) return a;
		a %= b;
		if (a === 0n) return b;
		if (a === _0N) return b;
		b %= a;
		@@ -295,3 +322,3 @@ }
		const gcd = this.gcd(numerator, denominator);
		if (gcd > 1n) {
		if (gcd > _1N) {
		numerator /= gcd;
		@@ -301,3 +328,3 @@ denominator /= gcd;

		if (denominator < 0n) {
		if (denominator < _0N) {
		numerator = -numerator;
		@@ -313,3 +340,3 @@ denominator = -denominator;

		if (denominator === 1n) {
		if (denominator === _1N) {
		return new FixedNumber(numerator, 0);
		@@ -339,4 +366,4 @@ }
		sign(): -1 \| 1 {
		const numeratorSign = this.numerator < 0n ? -1 : 1;
		const denominatorSign = this.denominator < 0n ? -1 : 1;
		const numeratorSign = this.numerator < _0N ? -1 : 1;
		const denominatorSign = this.denominator < _0N ? -1 : 1;
		return (numeratorSign * denominatorSign) as -1 \| 1;
		@@ -347,4 +374,4 @@ }
		const res = new Fraction(
		this.numerator < 0n ? -this.numerator : this.numerator,
		this.denominator < 0n ? -this.denominator : this.denominator,
		this.numerator < _0N ? -this.numerator : this.numerator,
		this.denominator < _0N ? -this.denominator : this.denominator,
		);
		@@ -355,3 +382,3 @@ return res;
		neg() {
		return this.mul(-1n);
		return this.mul(-_1N);
		}
		@@ -412,3 +439,3 @@
		isZero() {
		return this.numerator === 0n;
		return this.numerator === _0N;
		}
		@@ -421,3 +448,3 @@
		isInteger() {
		return this.numerator % this.denominator === 0n;
		return this.numerator % this.denominator === _0N;
		}
		@@ -467,7 +494,7 @@

		let d = this.denominator < 0 ? -this.denominator : this.denominator;
		let d = this.denominator < _0N ? -this.denominator : this.denominator;

		let twoExp = 0;
		while (d % 2n === 0n) {
		d /= 2n;
		while (d % _2N === _0N) {
		d /= _2N;
		twoExp++;
		@@ -477,4 +504,4 @@ }
		let fiveExp = 0;
		while (d % 5n === 0n) {
		d /= 5n;
		while (d % _5N === _0N) {
		d /= _5N;
		fiveExp++;
		@@ -485,3 +512,3 @@ }

		if (d === 1n) {
		if (d === _1N) {
		return { cycleLen: 0, cycleStart };
		@@ -492,7 +519,7 @@ }

		let rem = 10n % d;
		let rem = _10N % d;
		let cycleLen = 1;

		// 10^l ≡ 1 (mod d)
		while (rem !== 1n) {
		while (rem !== _1N) {
		if (cycleLen === end) {
		@@ -502,3 +529,3 @@ // abort calculation
		}
		rem = (rem * 10n) % d;
		rem = (rem * _10N) % d;
		cycleLen++;
		@@ -510,6 +537,6 @@ }

		toFixed(decimals: number, roundingMode = RoundingMode.TO_ZERO): string {
		toFixed(decimals: number, roundingMode = RoundingMode.TO_ZERO, trimZeros = false): string {
		if (!Number.isSafeInteger(decimals) \|\| decimals < 0) throw new Error('Invalid parameter');

		return this.round(decimals, roundingMode).toFixed(decimals);
		return this.round(decimals, roundingMode).toFixed(decimals, RoundingMode.TO_ZERO, trimZeros);
		}
		@@ -528,3 +555,3 @@
		const str = this.toFixed(outputDigits);
		const parts = trimTrailingZeros(str).split('.');
		const parts = trimTrailingZerosFromFixed(str).split('.');
		return [parts[0], parts[1] ?? '', ''];
		@@ -555,7 +582,7 @@ }

		toExponential(digits: number, roundingMode = RoundingMode.TO_ZERO): string {
		toExponential(digits: number, roundingMode = RoundingMode.TO_ZERO, trimZeros = false): string {
		if (!Number.isSafeInteger(digits) \|\| digits < 0) throw new Error('Invalid parameters');

		const fixedNum = this.toFixedNumber(digits);
		return fixedNum.toExponential(digits, roundingMode);
		return fixedNum.toExponential(digits, roundingMode, trimZeros);
		}
		@@ -570,3 +597,3 @@
		private toFixedNumber(digits: number): FixedNumber {
		const numerator = this.numerator * 10n ** BigInt(digits);
		const numerator = this.numerator * _10N ** BigInt(digits);
		const fixedNum = new FixedNumber(numerator / this.denominator, digits);
		@@ -584,3 +611,5 @@ return fixedNum;
		if (radix === 10) {
		return maxDigits === undefined ? this.toRepeatingDigits(maxDigits) : trimTrailingZeros(this.toFixed(maxDigits));
		return maxDigits === undefined
		? this.toRepeatingDigits(maxDigits)
		: trimTrailingZerosFromFixed(this.toFixed(maxDigits));
		}
		@@ -627,3 +656,7 @@

		return [isNegative ? '-' : '', intPart.toString(radix), digits.length ? '.' : '', ...digits].join('');
		const digitsStr = digits.join('');

		const res = `${isNegative ? '-' : ''}${intPart.toString(radix)}${digits.length ? '.' : ''}${digitsStr}`;

		return res;
		}
		@@ -639,6 +672,6 @@

		toPrecision(digits: number, roundingMode = RoundingMode.TO_ZERO): string {
		toPrecision(digits: number, roundingMode = RoundingMode.TO_ZERO, trimZeros = false): string {
		if (!Number.isSafeInteger(digits) \|\| digits < 1) throw new Error('Invalid parameter');

		return this.roundToDigits(digits, roundingMode).toPrecision(digits);
		return this.roundToDigits(digits, roundingMode).toPrecision(digits, RoundingMode.TO_ZERO, trimZeros);
		}
		@@ -645,0 +678,0 @@

src/index.test.ts

		@@ -9,3 +9,2 @@ import * as API from '.';
		'ModType',
		'trimTrailingZeros',
		'nthroot',
		@@ -12,0 +11,0 @@ 'sqrt',

src/index.ts

		@@ -5,4 +5,8 @@ export { ExactNumber } from './ExactNumber';

		export { trimTrailingZeros } from './util';

		export * from './approx';
		export { nthroot, sqrt, cbrt } from './approx/roots';
		export { pow, exp } from './approx/exponential';
		export { log, logn, log10, log2 } from './approx/logarithm';
		export { PI, sin, cos, tan } from './approx/trigonometry';
		export { asin, acos, atan } from './approx/inverse_trigonometry';
		export { sinh, cosh, tanh } from './approx/hyperbolic';
		export { asinh, acosh, atanh } from './approx/inverse_hyperbolic';

src/types.ts

		@@ -50,8 +50,8 @@ import { Fraction } from './Fraction';

		/** Returns b^e mod m (modular exponentiation) */
		// modpow(
		// exponent: number \| bigint \| string \| ExactNumberType,
		// modulus: number \| bigint \| string \| ExactNumberType,
		// type?: ModType,
		// ): ExactNumberType;
		/** Returns modulo of this number exponentiated to the given value (modular exponentiation) */
		powm(
		exponent: number \| bigint \| string \| ExactNumberType,
		modulus: number \| bigint \| string \| ExactNumberType,
		type?: ModType,
		): ExactNumberType;

		@@ -166,3 +166,3 @@ /** Returns the result of the division of this number by the given one. */
		*/
		toFixed(decimals: number, roundingMode?: RoundingMode): string;
		toFixed(decimals: number, roundingMode?: RoundingMode, trimZeros?: boolean): string;

		@@ -172,3 +172,3 @@ /** Returns a string representing the number in exponential notation.
		*/
		toExponential(digits: number, roundingMode?: RoundingMode): string;
		toExponential(digits: number, roundingMode?: RoundingMode, trimZeros?: boolean): string;

		@@ -179,3 +179,3 @@ /** Returns a string representing the number using fixed-point notation, rounded to the specified number of significant digits.
		*/
		toPrecision(digits: number, roundingMode?: RoundingMode): string;
		toPrecision(digits: number, roundingMode?: RoundingMode, trimZeros?: boolean): string;

		@@ -182,0 +182,0 @@ /** Converts current value to a JavaScript Number */

src/util.test.ts

		@@ -1,24 +0,24 @@
		import { trimTrailingZeros } from './util';
		import { trimTrailingZerosFromFixed } from './util';

		describe('Util functions', () => {
		it('trimTrailingZeros()', () => {
		expect(trimTrailingZeros('0')).toBe('0');
		expect(trimTrailingZeros('-0')).toBe('-0');
		expect(trimTrailingZeros('00000')).toBe('00000');
		expect(trimTrailingZeros('0.0000')).toBe('0');
		expect(trimTrailingZeros('.0000')).toBe('0');
		expect(trimTrailingZeros('.0001')).toBe('.0001');
		expect(trimTrailingZeros('-.00010')).toBe('-.0001');
		expect(trimTrailingZeros('-123.0000')).toBe('-123');
		expect(trimTrailingZeros('-123.002')).toBe('-123.002');
		expect(trimTrailingZeros('-123.0020')).toBe('-123.002');
		expect(trimTrailingZeros('100.00')).toBe('100');
		expect(trimTrailingZeros('1231.')).toBe('1231');
		expect(trimTrailingZeros('1230.0')).toBe('1230');
		expect(trimTrailingZeros('1230.2304')).toBe('1230.2304');
		expect(trimTrailingZeros('001230.0')).toBe('001230');
		expect(trimTrailingZeros('-001230.01')).toBe('-001230.01');
		expect(trimTrailingZeros('001230.010')).toBe('001230.01');
		expect(trimTrailingZeros('001230.01000000')).toBe('001230.01');
		it('trimTrailingZerosFromFixed()', () => {
		expect(trimTrailingZerosFromFixed('0')).toBe('0');
		expect(trimTrailingZerosFromFixed('-0')).toBe('-0');
		expect(trimTrailingZerosFromFixed('00000')).toBe('00000');
		expect(trimTrailingZerosFromFixed('0.0000')).toBe('0');
		expect(trimTrailingZerosFromFixed('.0000')).toBe('0');
		expect(trimTrailingZerosFromFixed('.0001')).toBe('.0001');
		expect(trimTrailingZerosFromFixed('-.00010')).toBe('-.0001');
		expect(trimTrailingZerosFromFixed('-123.0000')).toBe('-123');
		expect(trimTrailingZerosFromFixed('-123.002')).toBe('-123.002');
		expect(trimTrailingZerosFromFixed('-123.0020')).toBe('-123.002');
		expect(trimTrailingZerosFromFixed('100.00')).toBe('100');
		expect(trimTrailingZerosFromFixed('1231.')).toBe('1231');
		expect(trimTrailingZerosFromFixed('1230.0')).toBe('1230');
		expect(trimTrailingZerosFromFixed('1230.2304')).toBe('1230.2304');
		expect(trimTrailingZerosFromFixed('001230.0')).toBe('001230');
		expect(trimTrailingZerosFromFixed('-001230.01')).toBe('-001230.01');
		expect(trimTrailingZerosFromFixed('001230.010')).toBe('001230.01');
		expect(trimTrailingZerosFromFixed('001230.01000000')).toBe('001230.01');
		});
		});

src/util.ts

		@@ -0,1 +1,2 @@
		/* eslint-disable @typescript-eslint/naming-convention */
		import { FixedNumber } from './FixedNumber';
		@@ -5,3 +6,3 @@ import { ExactNumberType, RoundingMode } from './types';
		/** Trims trailing zeros from numbers in fixed-point format (1.23000 -> 1.23) */
		export const trimTrailingZeros = (num: string): string => {
		export const trimTrailingZerosFromFixed = (num: string): string => {
		const pointPos = num.indexOf('.');
		@@ -43,3 +44,3 @@ if (pointPos === -1) return num;
		if (trimZeros) {
		str = trimTrailingZeros(str);
		str = trimTrailingZerosFromFixed(str);
		}
		@@ -49,3 +50,3 @@ } else {
		}
		} else if (outputDecimals > 0) {
		} else if (outputDecimals > 0 && !trimZeros) {
		str = `${str}.${'0'.repeat(outputDecimals)}`;
		@@ -67,12 +68,11 @@ }

		// export const modpow = (base: bigint, exp: bigint, mod: bigint) => {
		// let res = 1n;
		// while (exp > 0n) {
		// if (exp % 2n) {
		// res = (res * base) % mod;
		// }
		// base = base ** 2n % mod;
		// exp /= 2n;
		// }
		// return res;
		// };
		// BigInt literals (1n) are not supported by all parsers
		// also, the BigInt() constructor is still too slow to call in a loop
		export const _0N = BigInt(0);
		export const _1N = BigInt(1);
		export const _2N = BigInt(2);
		export const _3N = BigInt(3);
		export const _4N = BigInt(4);
		export const _5N = BigInt(5);
		export const _10N = BigInt(10);
		export const _24N = BigInt(24);

test/convergence.ts

		/* eslint-disable no-console */
		import { ExactNumberType } from 'src';
		import { sin, cos, tan, sqrt, cbrt } from '../src/approx';
		import { ExactNumberType, sin, cos, tan, sqrt, cbrt } from 'src';

		@@ -5,0 +4,0 @@ function run(name: string, fn: (digits: number) => ExactNumberType) {

dist/src/approx/index.d.ts

rollup.config.js

src/approx/index.ts

dist/index.esm.js

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dist/index.umd.js

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