3.2.1

dist/bundle.esm.js

@@ -0,0 +1,146 @@
+function abs(a) {
+    return (a >= 0) ? a : -a;
+}
+
+function bitLength(a) {
+    if (typeof a === 'number')
+        a = BigInt(a);
+    if (a === 1n) {
+        return 1;
+    }
+    let bits = 1;
+    do {
+        bits++;
+    } while ((a >>= 1n) > 1n);
+    return bits;
+}
+
+function eGcd(a, b) {
+    if (typeof a === 'number')
+        a = BigInt(a);
+    if (typeof b === 'number')
+        b = BigInt(b);
+    if (a <= 0n || b <= 0n)
+        throw new RangeError('a and b MUST be > 0');
+    let x = 0n;
+    let y = 1n;
+    let u = 1n;
+    let v = 0n;
+    while (a !== 0n) {
+        const q = b / a;
+        const r = b % a;
+        const m = x - (u * q);
+        const n = y - (v * q);
+        b = a;
+        a = r;
+        x = u;
+        y = v;
+        u = m;
+        v = n;
+    }
+    return {
+        g: b,
+        x,
+        y
+    };
+}
+
+function gcd(a, b) {
+    let aAbs = (typeof a === 'number') ? BigInt(abs(a)) : abs(a);
+    let bAbs = (typeof b === 'number') ? BigInt(abs(b)) : abs(b);
+    if (aAbs === 0n) {
+        return bAbs;
+    }
+    else if (bAbs === 0n) {
+        return aAbs;
+    }
+    let shift = 0n;
+    while (((aAbs | bAbs) & 1n) === 0n) {
+        aAbs >>= 1n;
+        bAbs >>= 1n;
+        shift++;
+    }
+    while ((aAbs & 1n) === 0n)
+        aAbs >>= 1n;
+    do {
+        while ((bAbs & 1n) === 0n)
+            bAbs >>= 1n;
+        if (aAbs > bAbs) {
+            const x = aAbs;
+            aAbs = bAbs;
+            bAbs = x;
+        }
+        bAbs -= aAbs;
+    } while (bAbs !== 0n);
+    return aAbs << shift;
+}
+
+function lcm(a, b) {
+    if (typeof a === 'number')
+        a = BigInt(a);
+    if (typeof b === 'number')
+        b = BigInt(b);
+    if (a === 0n && b === 0n)
+        return BigInt(0);
+    return abs((a / gcd(a, b)) * b);
+}
+
+function max(a, b) {
+    return (a >= b) ? a : b;
+}
+
+function min(a, b) {
+    return (a >= b) ? b : a;
+}
+
+function toZn(a, n) {
+    if (typeof a === 'number')
+        a = BigInt(a);
+    if (typeof n === 'number')
+        n = BigInt(n);
+    if (n <= 0n) {
+        throw new RangeError('n must be > 0');
+    }
+    const aZn = a % n;
+    return (aZn < 0n) ? aZn + n : aZn;
+}
+
+function modInv(a, n) {
+    const egcd = eGcd(toZn(a, n), n);
+    if (egcd.g !== 1n) {
+        throw new RangeError(`${a.toString()} does not have inverse modulo ${n.toString()}`);
+    }
+    else {
+        return toZn(egcd.x, n);
+    }
+}
+
+function modPow(b, e, n) {
+    if (typeof b === 'number')
+        b = BigInt(b);
+    if (typeof e === 'number')
+        e = BigInt(e);
+    if (typeof n === 'number')
+        n = BigInt(n);
+    if (n <= 0n) {
+        throw new RangeError('n must be > 0');
+    }
+    else if (n === 1n) {
+        return 0n;
+    }
+    b = toZn(b, n);
+    if (e < 0n) {
+        return modInv(modPow(b, abs(e), n), n);
+    }
+    let r = 1n;
+    while (e > 0) {
+        if ((e % 2n) === 1n) {
+            r = r * b % n;
+        }
+        e = e / 2n;
+        b = b ** 2n % n;
+    }
+    return r;
+}
+
+export { abs, bitLength, eGcd, gcd, lcm, max, min, modInv, modPow, toZn };

dist/bundle.esm.min.js

@@ -0,0 +1 @@
+function n(n){return n>=0?n:-n}function t(n){if("number"==typeof n&&(n=BigInt(n)),1n===n)return 1;let t=1;do{t++}while((n>>=1n)>1n);return t}function r(n,t){if("number"==typeof n&&(n=BigInt(n)),"number"==typeof t&&(t=BigInt(t)),n<=0n||t<=0n)throw new RangeError("a and b MUST be > 0");let r=0n,e=1n,o=1n,u=0n;for(;0n!==n;){const i=t/n,f=t%n,g=r-o*i,b=e-u*i;t=n,n=f,r=o,e=u,o=g,u=b}return{g:t,x:r,y:e}}function e(t,r){let e="number"==typeof t?BigInt(n(t)):n(t),o="number"==typeof r?BigInt(n(r)):n(r);if(0n===e)return o;if(0n===o)return e;let u=0n;for(;0n===(1n&(e|o));)e>>=1n,o>>=1n,u++;for(;0n===(1n&e);)e>>=1n;do{for(;0n===(1n&o);)o>>=1n;if(e>o){const n=e;e=o,o=n}o-=e}while(0n!==o);return e<<u}function o(t,r){return"number"==typeof t&&(t=BigInt(t)),"number"==typeof r&&(r=BigInt(r)),0n===t&&0n===r?BigInt(0):n(t/e(t,r)*r)}function u(n,t){return n>=t?n:t}function i(n,t){return n>=t?t:n}function f(n,t){if("number"==typeof n&&(n=BigInt(n)),"number"==typeof t&&(t=BigInt(t)),t<=0n)throw new RangeError("n must be > 0");const r=n%t;return r<0n?r+t:r}function g(n,t){const e=r(f(n,t),t);if(1n!==e.g)throw new RangeError(`${n.toString()} does not have inverse modulo ${t.toString()}`);return f(e.x,t)}function b(t,r,e){if("number"==typeof t&&(t=BigInt(t)),"number"==typeof r&&(r=BigInt(r)),"number"==typeof e&&(e=BigInt(e)),e<=0n)throw new RangeError("n must be > 0");if(1n===e)return 0n;if(t=f(t,e),r<0n)return g(b(t,n(r),e),e);let o=1n;for(;r>0;)r%2n===1n&&(o=o*t%e),r/=2n,t=t**2n%e;return o}export{n as abs,t as bitLength,r as eGcd,e as gcd,o as lcm,u as max,i as min,g as modInv,b as modPow,f as toZn};

dist/bundle.iife.js

@@ -0,0 +1 @@
+var bigintModArith=function(n){"use strict";function t(n){return n>=0?n:-n}function r(n,t){if("number"==typeof n&&(n=BigInt(n)),"number"==typeof t&&(t=BigInt(t)),n<=0n||t<=0n)throw new RangeError("a and b MUST be > 0");let r=0n,e=1n,o=1n,i=0n;for(;0n!==n;){const u=t/n,f=t%n,g=r-o*u,m=e-i*u;t=n,n=f,r=o,e=i,o=g,i=m}return{g:t,x:r,y:e}}function e(n,r){let e="number"==typeof n?BigInt(t(n)):t(n),o="number"==typeof r?BigInt(t(r)):t(r);if(0n===e)return o;if(0n===o)return e;let i=0n;for(;0n===(1n&(e|o));)e>>=1n,o>>=1n,i++;for(;0n===(1n&e);)e>>=1n;do{for(;0n===(1n&o);)o>>=1n;if(e>o){const n=e;e=o,o=n}o-=e}while(0n!==o);return e<<i}function o(n,t){if("number"==typeof n&&(n=BigInt(n)),"number"==typeof t&&(t=BigInt(t)),t<=0n)throw new RangeError("n must be > 0");const r=n%t;return r<0n?r+t:r}function i(n,t){const e=r(o(n,t),t);if(1n!==e.g)throw new RangeError(`${n.toString()} does not have inverse modulo ${t.toString()}`);return o(e.x,t)}return n.abs=t,n.bitLength=function(n){if("number"==typeof n&&(n=BigInt(n)),1n===n)return 1;let t=1;do{t++}while((n>>=1n)>1n);return t},n.eGcd=r,n.gcd=e,n.lcm=function(n,r){return"number"==typeof n&&(n=BigInt(n)),"number"==typeof r&&(r=BigInt(r)),0n===n&&0n===r?BigInt(0):t(n/e(n,r)*r)},n.max=function(n,t){return n>=t?n:t},n.min=function(n,t){return n>=t?t:n},n.modInv=i,n.modPow=function n(r,e,u){if("number"==typeof r&&(r=BigInt(r)),"number"==typeof e&&(e=BigInt(e)),"number"==typeof u&&(u=BigInt(u)),u<=0n)throw new RangeError("n must be > 0");if(1n===u)return 0n;if(r=o(r,u),e<0n)return i(n(r,t(e),u),u);let f=1n;for(;e>0;)e%2n===1n&&(f=f*r%u),e/=2n,r=r**2n%u;return f},n.toZn=o,n}({});

dist/bundle.umd.js

@@ -0,0 +1 @@
+!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).bigintModArith={})}(this,(function(n){"use strict";function t(n){return n>=0?n:-n}function e(n,t){if("number"==typeof n&&(n=BigInt(n)),"number"==typeof t&&(t=BigInt(t)),n<=0n||t<=0n)throw new RangeError("a and b MUST be > 0");let e=0n,r=1n,o=1n,i=0n;for(;0n!==n;){const f=t/n,u=t%n,g=e-o*f,b=r-i*f;t=n,n=u,e=o,r=i,o=g,i=b}return{g:t,x:e,y:r}}function r(n,e){let r="number"==typeof n?BigInt(t(n)):t(n),o="number"==typeof e?BigInt(t(e)):t(e);if(0n===r)return o;if(0n===o)return r;let i=0n;for(;0n===(1n&(r|o));)r>>=1n,o>>=1n,i++;for(;0n===(1n&r);)r>>=1n;do{for(;0n===(1n&o);)o>>=1n;if(r>o){const n=r;r=o,o=n}o-=r}while(0n!==o);return r<<i}function o(n,t){if("number"==typeof n&&(n=BigInt(n)),"number"==typeof t&&(t=BigInt(t)),t<=0n)throw new RangeError("n must be > 0");const e=n%t;return e<0n?e+t:e}function i(n,t){const r=e(o(n,t),t);if(1n!==r.g)throw new RangeError(`${n.toString()} does not have inverse modulo ${t.toString()}`);return o(r.x,t)}n.abs=t,n.bitLength=function(n){if("number"==typeof n&&(n=BigInt(n)),1n===n)return 1;let t=1;do{t++}while((n>>=1n)>1n);return t},n.eGcd=e,n.gcd=r,n.lcm=function(n,e){return"number"==typeof n&&(n=BigInt(n)),"number"==typeof e&&(e=BigInt(e)),0n===n&&0n===e?BigInt(0):t(n/r(n,e)*e)},n.max=function(n,t){return n>=t?n:t},n.min=function(n,t){return n>=t?t:n},n.modInv=i,n.modPow=function n(e,r,f){if("number"==typeof e&&(e=BigInt(e)),"number"==typeof r&&(r=BigInt(r)),"number"==typeof f&&(f=BigInt(f)),f<=0n)throw new RangeError("n must be > 0");if(1n===f)return 0n;if(e=o(e,f),r<0n)return i(n(e,t(r),f),f);let u=1n;for(;r>0;)r%2n===1n&&(u=u*e%f),r/=2n,e=e**2n%f;return u},n.toZn=o}));

dist/index.browser.esm.js

@@ -0,0 +1,2 @@
+function n(n){return n>=0?n:-n}function t(n){if("number"==typeof n&&(n=BigInt(n)),1n===n)return 1;let t=1;do{t++}while((n>>=1n)>1n);return t}function r(n,t){if("number"==typeof n&&(n=BigInt(n)),"number"==typeof t&&(t=BigInt(t)),n<=0n||t<=0n)throw new RangeError("a and b MUST be > 0");let r=0n,e=1n,o=1n,u=0n;for(;0n!==n;){const i=t/n,f=t%n,g=r-o*i,b=e-u*i;t=n,n=f,r=o,e=u,o=g,u=b}return{g:t,x:r,y:e}}function e(t,r){let e="number"==typeof t?BigInt(n(t)):n(t),o="number"==typeof r?BigInt(n(r)):n(r);if(0n===e)return o;if(0n===o)return e;let u=0n;for(;0n===(1n&(e|o));)e>>=1n,o>>=1n,u++;for(;0n===(1n&e);)e>>=1n;do{for(;0n===(1n&o);)o>>=1n;if(e>o){const n=e;e=o,o=n}o-=e}while(0n!==o);return e<<u}function o(t,r){return"number"==typeof t&&(t=BigInt(t)),"number"==typeof r&&(r=BigInt(r)),0n===t&&0n===r?BigInt(0):n(t/e(t,r)*r)}function u(n,t){return n>=t?n:t}function i(n,t){return n>=t?t:n}function f(n,t){if("number"==typeof n&&(n=BigInt(n)),"number"==typeof t&&(t=BigInt(t)),t<=0n)throw new RangeError("n must be > 0");const r=n%t;return r<0n?r+t:r}function g(n,t){const e=r(f(n,t),t);if(1n!==e.g)throw new RangeError(`${n.toString()} does not have inverse modulo ${t.toString()}`);return f(e.x,t)}function b(t,r,e){if("number"==typeof t&&(t=BigInt(t)),"number"==typeof r&&(r=BigInt(r)),"number"==typeof e&&(e=BigInt(e)),e<=0n)throw new RangeError("n must be > 0");if(1n===e)return 0n;if(t=f(t,e),r<0n)return g(b(t,n(r),e),e);let o=1n;for(;r>0;)r%2n===1n&&(o=o*t%e),r/=2n,t=t**2n%e;return o}export{n as abs,t as bitLength,r as eGcd,e as gcd,o as lcm,u as max,i as min,g as modInv,b as modPow,f as toZn};
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dist/index.d.ts

@@ -0,0 +1,26 @@
+declare function abs(a: number | bigint): number | bigint;
+
+declare function bitLength(a: number | bigint): number;
+
+interface Egcd {
+    g: bigint;
+    x: bigint;
+    y: bigint;
+}
+declare function eGcd(a: number | bigint, b: number | bigint): Egcd;
+
+declare function gcd(a: number | bigint, b: number | bigint): bigint;
+
+declare function lcm(a: number | bigint, b: number | bigint): bigint;
+
+declare function max(a: number | bigint, b: number | bigint): number | bigint;
+
+declare function min(a: number | bigint, b: number | bigint): number | bigint;
+
+declare function modInv(a: number | bigint, n: number | bigint): bigint;
+
+declare function modPow(b: number | bigint, e: number | bigint, n: number | bigint): bigint;
+
+declare function toZn(a: number | bigint, n: number | bigint): bigint;
+
+export { Egcd, abs, bitLength, eGcd, gcd, lcm, max, min, modInv, modPow, toZn };

dist/index.node.cjs

@@ -0,0 +1,2 @@
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dist/index.node.esm.js

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docs/.nojekyll

@@ -0,0 +1 @@
+TypeDoc added this file to prevent GitHub Pages from using Jekyll. You can turn off this behavior by setting the `githubPages` option to false.

docs/API.md

@@ -0,0 +1,292 @@
+# bigint-mod-arith - v3.2.1
+
+Some common functions for modular arithmetic using native JS implementation of BigInt
+
+## Table of contents
+
+### Interfaces
+
+- [Egcd](interfaces/Egcd.md)
+
+### Functions
+
+- [abs](API.md#abs)
+- [bitLength](API.md#bitlength)
+- [eGcd](API.md#egcd)
+- [gcd](API.md#gcd)
+- [lcm](API.md#lcm)
+- [max](API.md#max)
+- [min](API.md#min)
+- [modInv](API.md#modinv)
+- [modPow](API.md#modpow)
+- [toZn](API.md#tozn)
+
+## Functions
+
+### abs
+
+▸ **abs**(`a`): `number` \| `bigint`
+
+Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
+
+#### Parameters
+
+| Name | Type |
+| :------ | :------ |
+| `a` | `number` \| `bigint` |
+
+#### Returns
+
+`number` \| `bigint`
+
+The absolute value of a
+
+#### Defined in
+
+[abs.ts:8](https://github.com/juanelas/bigint-mod-arith/blob/84ebe88/src/ts/abs.ts#L8)
+
+___
+
+### bitLength
+
+▸ **bitLength**(`a`): `number`
+
+Returns the (minimum) length of a number expressed in bits.
+
+#### Parameters
+
+| Name | Type |
+| :------ | :------ |
+| `a` | `number` \| `bigint` |
+
+#### Returns
+
+`number`
+
+The bit length
+
+#### Defined in
+
+[bitLength.ts:7](https://github.com/juanelas/bigint-mod-arith/blob/84ebe88/src/ts/bitLength.ts#L7)
+
+___
+
+### eGcd
+
+▸ **eGcd**(`a`, `b`): [`Egcd`](interfaces/Egcd.md)
+
+An iterative implementation of the extended euclidean algorithm or extended greatest common divisor algorithm.
+Take positive integers a, b as input, and return a triple (g, x, y), such that ax + by = g = gcd(a, b).
+
+**`Throws`**
+
+RangeError if a or b are <= 0
+
+#### Parameters
+
+| Name | Type |
+| :------ | :------ |
+| `a` | `number` \| `bigint` |
+| `b` | `number` \| `bigint` |
+
+#### Returns
+
+[`Egcd`](interfaces/Egcd.md)
+
+A triple (g, x, y), such that ax + by = g = gcd(a, b).
+
+#### Defined in
+
+[egcd.ts:17](https://github.com/juanelas/bigint-mod-arith/blob/84ebe88/src/ts/egcd.ts#L17)
+
+___
+
+### gcd
+
+▸ **gcd**(`a`, `b`): `bigint`
+
+Greatest common divisor of two integers based on the iterative binary algorithm.
+
+#### Parameters
+
+| Name | Type |
+| :------ | :------ |
+| `a` | `number` \| `bigint` |
+| `b` | `number` \| `bigint` |
+
+#### Returns
+
+`bigint`
+
+The greatest common divisor of a and b
+
+#### Defined in
+
+[gcd.ts:10](https://github.com/juanelas/bigint-mod-arith/blob/84ebe88/src/ts/gcd.ts#L10)
+
+___
+
+### lcm
+
+▸ **lcm**(`a`, `b`): `bigint`
+
+The least common multiple computed as abs(a*b)/gcd(a,b)
+
+#### Parameters
+
+| Name | Type |
+| :------ | :------ |
+| `a` | `number` \| `bigint` |
+| `b` | `number` \| `bigint` |
+
+#### Returns
+
+`bigint`
+
+The least common multiple of a and b
+
+#### Defined in
+
+[lcm.ts:10](https://github.com/juanelas/bigint-mod-arith/blob/84ebe88/src/ts/lcm.ts#L10)
+
+___
+
+### max
+
+▸ **max**(`a`, `b`): `number` \| `bigint`
+
+Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<b
+
+#### Parameters
+
+| Name | Type |
+| :------ | :------ |
+| `a` | `number` \| `bigint` |
+| `b` | `number` \| `bigint` |
+
+#### Returns
+
+`number` \| `bigint`
+
+Maximum of numbers a and b
+
+#### Defined in
+
+[max.ts:9](https://github.com/juanelas/bigint-mod-arith/blob/84ebe88/src/ts/max.ts#L9)
+
+___
+
+### min
+
+▸ **min**(`a`, `b`): `number` \| `bigint`
+
+Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<b
+
+#### Parameters
+
+| Name | Type |
+| :------ | :------ |
+| `a` | `number` \| `bigint` |
+| `b` | `number` \| `bigint` |
+
+#### Returns
+
+`number` \| `bigint`
+
+Minimum of numbers a and b
+
+#### Defined in
+
+[min.ts:9](https://github.com/juanelas/bigint-mod-arith/blob/84ebe88/src/ts/min.ts#L9)
+
+___
+
+### modInv
+
+▸ **modInv**(`a`, `n`): `bigint`
+
+Modular inverse.
+
+**`Throws`**
+
+RangeError if a does not have inverse modulo n
+
+#### Parameters
+
+| Name | Type | Description |
+| :------ | :------ | :------ |
+| `a` | `number` \| `bigint` | The number to find an inverse for |
+| `n` | `number` \| `bigint` | The modulo |
+
+#### Returns
+
+`bigint`
+
+The inverse modulo n
+
+#### Defined in
+
+[modInv.ts:13](https://github.com/juanelas/bigint-mod-arith/blob/84ebe88/src/ts/modInv.ts#L13)
+
+___
+
+### modPow
+
+▸ **modPow**(`b`, `e`, `n`): `bigint`
+
+Modular exponentiation b**e mod n. Currently using the right-to-left binary method
+
+**`Throws`**
+
+RangeError if n <= 0
+
+#### Parameters
+
+| Name | Type | Description |
+| :------ | :------ | :------ |
+| `b` | `number` \| `bigint` | base |
+| `e` | `number` \| `bigint` | exponent |
+| `n` | `number` \| `bigint` | modulo |
+
+#### Returns
+
+`bigint`
+
+b**e mod n
+
+#### Defined in
+
+[modPow.ts:15](https://github.com/juanelas/bigint-mod-arith/blob/84ebe88/src/ts/modPow.ts#L15)
+
+___
+
+### toZn
+
+▸ **toZn**(`a`, `n`): `bigint`
+
+Finds the smallest positive element that is congruent to a in modulo n
+
+**`Remarks`**
+
+a and b must be the same type, either number or bigint
+
+**`Throws`**
+
+RangeError if n <= 0
+
+#### Parameters
+
+| Name | Type | Description |
+| :------ | :------ | :------ |
+| `a` | `number` \| `bigint` | An integer |
+| `n` | `number` \| `bigint` | The modulo |
+
+#### Returns
+
+`bigint`
+
+A bigint with the smallest positive representation of a modulo n
+
+#### Defined in
+
+[toZn.ts:14](https://github.com/juanelas/bigint-mod-arith/blob/84ebe88/src/ts/toZn.ts#L14)

docs/interfaces/Egcd.md

@@ -0,0 +1,39 @@
+# Interface: Egcd
+
+## Table of contents
+
+### Properties
+
+- [g](Egcd.md#g)
+- [x](Egcd.md#x)
+- [y](Egcd.md#y)
+
+## Properties
+
+### g
+
+• **g**: `bigint`
+
+#### Defined in
+
+[egcd.ts:2](https://github.com/juanelas/bigint-mod-arith/blob/84ebe88/src/ts/egcd.ts#L2)
+
+___
+
+### x
+
+• **x**: `bigint`
+
+#### Defined in
+
+[egcd.ts:3](https://github.com/juanelas/bigint-mod-arith/blob/84ebe88/src/ts/egcd.ts#L3)
+
+___
+
+### y
+
+• **y**: `bigint`
+
+#### Defined in
+
+[egcd.ts:4](https://github.com/juanelas/bigint-mod-arith/blob/84ebe88/src/ts/egcd.ts#L4)

package-lock.json

@@ -1,12 +1,12 @@
 {
   "name": "bigint-mod-arith",
-  "version": "3.2.0",
+  "version": "3.2.1",
   "lockfileVersion": 3,
   "requires": true,
   "packages": {
     "": {
       "name": "bigint-mod-arith",
-      "version": "3.2.0",
+      "version": "3.2.1",
       "license": "MIT",
       "devDependencies": {
         "@rollup/plugin-commonjs": "^24.0.1",

package.json

@@ -1,6 +1,6 @@
 {
   "name": "bigint-mod-arith",
-  "version": "3.2.0",
+  "version": "3.2.1",
   "description": "Some common functions for modular arithmetic using native JS implementation of BigInt",
   "keywords": [
     "modular arithmetics",