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bigint-mod-arith
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# Project specific files
dist/bigint-mod-arith-?.?.?.*
# Logs
logs
*.log
npm-debug.log*
yarn-debug.log*
yarn-error.log*
# Runtime data
pids
*.pid
*.seed
*.pid.lock
# Directory for instrumented libs generated by jscoverage/JSCover
lib-cov
# Coverage directory used by tools like istanbul
coverage
# nyc test coverage
.nyc_output
# Grunt intermediate storage (http://gruntjs.com/creating-plugins#storing-task-files)
.grunt
# Bower dependency directory (https://bower.io/)
bower_components
# node-waf configuration
.lock-wscript
# Compiled binary addons (https://nodejs.org/api/addons.html)
build/Release
# Dependency directories
node_modules/
jspm_packages/
# TypeScript v1 declaration files
typings/
# Optional npm cache directory
.npm
# Optional eslint cache
.eslintcache
# Optional REPL history
.node_repl_history
# Output of 'npm pack'
*.tgz
# Yarn Integrity file
.yarn-integrity
# dotenv environment variables file
.env
# next.js build output
.next
# Visual Studio Code
.vscode

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README.hbs
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# bigint-mod-arith
Some extra functions to work with modular arithmetics using native JS (stage 3) implementation of BigInt. It can be used
with Node.js (>=10.4.0) and [Web Browsers supporting
BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility).
Some extra functions to work with modular arithmetics using native JS (stage 3) implementation of BigInt. It can be used by any [Web Browser or webview supporting BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility) and with Node.js (>=10.4.0).
If you are looking for a cryptographically secure random generator and for probale primes (generation and testing), you
If you are looking for a cryptographically-secure random generator and for strong probable primes (generation and testing), you
may be interested in [bigint-secrets](https://github.com/juanelas/bigint-secrets)
_The operations supported on BigInts are not constant time. BigInt can be therefore **[unsuitable for use in
cryptography](https://www.chosenplaintext.ca/articles/beginners-guide-constant-time-cryptography.html)**_
Many platforms provide native support for cryptography, such as
[webcrypto](https://w3c.github.io/webcrypto/Overview.html) or [node
crypto](https://nodejs.org/dist/latest/docs/api/crypto.html).
_The operations supported on BigInts are not constant time. BigInt can be therefore **[unsuitable for use in cryptography](https://www.chosenplaintext.ca/articles/beginners-guide-constant-time-cryptography.html).** Many platforms provide native support for cryptography, such as [Web Cryptography API](https://w3c.github.io/webcrypto/) or [Node.js Crypto](https://nodejs.org/dist/latest/docs/api/crypto.html)._
## Installation
bigint-mod-arith is distributed as both an ES6 and a CJS module.
The ES6 module is built for any [web browser supporting
BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility).
The module only uses native javascript implementations and no polyfills had been applied.
The CJS module is built as a standard node module.
bigint-mod-arith is distributed for [web browsers and/or webviews supporting
BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility)
as an ES6 module or an IIFE file; and for Node.js (>=10.4.0), as a CJS module.
bigint-mod-arith can be imported to your project with `npm`:
```bash
npm install bigint-mod-arith
```
NPM installation defaults to the ES6 module for browsers and the CJS one for Node.js.
For web browsers, you can also [download the bundle from
GitHub](https://raw.githubusercontent.com/juanelas/bigint-mod-arith/master/dist/bigint-mod-arith-latest.browser.mod.min.js).
For web browsers, you can also directly download the minimised version of the [IIFE file](https://raw.githubusercontent.com/juanelas/bigint-mod-arith/master/dist/bigint-mod-arith-latest.browser.min.js) or the [ES6 module](https://raw.githubusercontent.com/juanelas/bigint-mod-arith/master/dist/bigint-mod-arith-latest.browser.mod.min.js) from GitHub.
## Usage examples
## Usage example
With node js:
```javascript
const bigintModArith = require('bigint-mod-arith');
// Stage 3 BigInts with value 666 can be declared as BigInt('666')
// or the shorter no-linter-friendly new syntax 666n
/* Stage 3 BigInts with value 666 can be declared as BigInt('666')
or the shorter new no-so-linter-friendly syntax 666n.
Notice that you can also pass a number, e.g. BigInt(666), but it is not
recommended since values over 2**53 - 1 won't be safe but no warning will
be raised.
*/
let a = BigInt('5');
let b = BigInt('2');
let n = BigInt('19');
console.log(bigintModArith.modPow(a, b, n)); // prints 6
console.log(bigintCryptoUtils.modPow(a, b, n)); // prints 6
console.log(bigintModArith.modInv(BigInt('2'), BigInt('5'))); // prints 3
console.log(bigintCryptoUtils.modInv(BigInt('2'), BigInt('5'))); // prints 3
console.log(bigintModArith.modInv(BigInt('3'), BigInt('5'))); // prints 2
console.log(bigintCryptoUtils.modInv(BigInt('3'), BigInt('5'))); // prints 2
```
From a browser, you can just load the module in a html page as:
```html
<script type="module">
import * as bigintModArith from 'bigint-mod-arith-latest.browser.mod.min.js';
// Stage 3 BigInts with value 666 can be declared as BigInt('666')
// or the shorter no-linter-friendly new syntax 666n
let a = BigInt('5');
let b = BigInt('2');

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README.md
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@ -1,37 +1,52 @@
# bigint-mod-arith
Some extra functions to work with modular arithmetics using native JS (stage 3) implementation of BigInt. It can be used with Node.js (>=10.4.0) and [Web Browsers supporting BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility).
Some extra functions to work with modular arithmetics using native JS (stage 3) implementation of BigInt. It can be used by any [Web Browser or webview supporting BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility) and with Node.js (>=10.4.0).
If you are looking for a cryptographically secure random generator and for probale primes (generation and testing), you may be interested in [bigint-secrets](https://github.com/juanelas/bigint-secrets)
If you are looking for a cryptographically-secure random generator and for strong probable primes (generation and testing), you
may be interested in [bigint-secrets](https://github.com/juanelas/bigint-secrets)
_The operations supported on BigInts are not constant time. BigInt can be therefore **[unsuitable for use in cryptography](https://www.chosenplaintext.ca/articles/beginners-guide-constant-time-cryptography.html)**_
Many platforms provide native support for cryptography, such as [webcrypto](https://w3c.github.io/webcrypto/Overview.html) or [node crypto](https://nodejs.org/dist/latest/docs/api/crypto.html).
_The operations supported on BigInts are not constant time. BigInt can be therefore **[unsuitable for use in cryptography](https://www.chosenplaintext.ca/articles/beginners-guide-constant-time-cryptography.html).** Many platforms provide native support for cryptography, such as [Web Cryptography API](https://w3c.github.io/webcrypto/) or [Node.js Crypto](https://nodejs.org/dist/latest/docs/api/crypto.html)._
## Installation
bigint-mod-arith is distributed as both an ES6 and a CJS module.
The ES6 module is built for any [web browser supporting BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility). The module only uses native javascript implementations and no polyfills had been applied.
The CJS module is built as a standard node module.
bigint-mod-arith is distributed for [web browsers and/or webviews supporting
BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility)
as an ES6 module or an IIFE file; and for Node.js (>=10.4.0), as a CJS module.
bigint-mod-arith can be imported to your project with `npm`:
```bash
npm install bigint-mod-arith
```
NPM installation defaults to the ES6 module for browsers and the CJS one for Node.js.
For web browsers, you can also [download the bundle from GitHub](https://raw.githubusercontent.com/juanelas/bigint-mod-arith/master/dist/bigint-mod-arith-latest.browser.mod.min.js) or just hotlink to it:
```html
<script type="module" src="https://raw.githubusercontent.com/juanelas/bigint-mod-arith/master/dist/bigint-mod-arith-latest.browser.mod.min.js"></script>
```
For web browsers, you can also directly download the minimised version of the [IIFE file](https://raw.githubusercontent.com/juanelas/bigint-mod-arith/master/dist/bigint-mod-arith-latest.browser.min.js) or the [ES6 module](https://raw.githubusercontent.com/juanelas/bigint-mod-arith/master/dist/bigint-mod-arith-latest.browser.mod.min.js) from GitHub.
## Usage examples
## Usage example
With node js:
```javascript
const bigintModArith = require('bigint-mod-arith');
// Stage 3 BigInts with value 666 can be declared as BigInt('666')
// or the shorter no-linter-friendly new syntax 666n
/* Stage 3 BigInts with value 666 can be declared as BigInt('666')
or the shorter new no-so-linter-friendly syntax 666n.
Notice that you can also pass a number, e.g. BigInt(666), but it is not
recommended since values over 2**53 - 1 won't be safe but no warning will
be raised.
*/
let a = BigInt('5');
let b = BigInt('2');
let n = BigInt('19');
console.log(bigintCryptoUtils.modPow(a, b, n)); // prints 6
console.log(bigintCryptoUtils.modInv(BigInt('2'), BigInt('5'))); // prints 3
console.log(bigintCryptoUtils.modInv(BigInt('3'), BigInt('5'))); // prints 2
```
From a browser, you can just load the module in a html page as:
```html
<script type="module">
import * as bigintModArith from 'bigint-mod-arith-latest.browser.mod.min.js';
let a = BigInt('5');
let b = BigInt('2');
@ -42,6 +57,7 @@ console.log(bigintModArith.modPow(a, b, n)); // prints 6
console.log(bigintModArith.modInv(BigInt('2'), BigInt('5'))); // prints 3
console.log(bigintModArith.modInv(BigInt('3'), BigInt('5'))); // prints 2
</script>
```
# bigint-mod-arith JS Doc
@ -52,25 +68,25 @@ console.log(bigintModArith.modInv(BigInt('3'), BigInt('5'))); // prints 2
<dt><a href="#abs">abs(a)</a> ⇒ <code>bigint</code></dt>
<dd><p>Absolute value. abs(a)==a if a&gt;=0. abs(a)==-a if a&lt;0</p>
</dd>
<dt><a href="#eGcd">eGcd(a, b)</a> ⇒ <code><a href="#egcdReturn">egcdReturn</a></code></dt>
<dd><p>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).</p>
</dd>
<dt><a href="#gcd">gcd(a, b)</a> ⇒ <code>bigint</code></dt>
<dd><p>Greatest-common divisor of two integers based on the iterative binary algorithm.</p>
</dd>
<dt><a href="#lcm">lcm(a, b)</a> ⇒ <code>bigint</code></dt>
<dd><p>The least common multiple computed as abs(a*b)/gcd(a,b)</p>
</dd>
<dt><a href="#toZn">toZn(a, n)</a> ⇒ <code>bigint</code></dt>
<dd><p>Finds the smallest positive element that is congruent to a in modulo n</p>
</dd>
<dt><a href="#eGcd">eGcd(a, b)</a> ⇒ <code><a href="#egcdReturn">egcdReturn</a></code></dt>
<dd><p>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).</p>
</dd>
<dt><a href="#modInv">modInv(a, n)</a> ⇒ <code>bigint</code></dt>
<dd><p>Modular inverse.</p>
</dd>
<dt><a href="#modPow">modPow(a, b, n)</a> ⇒ <code>bigint</code></dt>
<dd><p>Modular exponentiation a**b mod n</p>
</dd>
<dt><a href="#toZn">toZn(a, n)</a> ⇒ <code>bigint</code></dt>
<dd><p>Finds the smallest positive element that is congruent to a in modulo n</p>
</dd>
</dl>
## Typedefs
@ -93,6 +109,19 @@ Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
| --- | --- |
| a | <code>number</code> \| <code>bigint</code> |
<a name="eGcd"></a>
## eGcd(a, b) ⇒ [<code>egcdReturn</code>](#egcdReturn)
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).
**Kind**: global function
| Param | Type |
| --- | --- |
| a | <code>number</code> \| <code>bigint</code> |
| b | <code>number</code> \| <code>bigint</code> |
<a name="gcd"></a>
## gcd(a, b) ⇒ <code>bigint</code>
@ -119,32 +148,6 @@ The least common multiple computed as abs(a*b)/gcd(a,b)
| a | <code>number</code> \| <code>bigint</code> |
| b | <code>number</code> \| <code>bigint</code> |
<a name="toZn"></a>
## toZn(a, n) ⇒ <code>bigint</code>
Finds the smallest positive element that is congruent to a in modulo n
**Kind**: global function
**Returns**: <code>bigint</code> - The smallest positive representation of a in modulo n
| Param | Type | Description |
| --- | --- | --- |
| a | <code>number</code> \| <code>bigint</code> | An integer |
| n | <code>number</code> \| <code>bigint</code> | The modulo |
<a name="eGcd"></a>
## eGcd(a, b) ⇒ [<code>egcdReturn</code>](#egcdReturn)
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).
**Kind**: global function
| Param | Type |
| --- | --- |
| a | <code>number</code> \| <code>bigint</code> |
| b | <code>number</code> \| <code>bigint</code> |
<a name="modInv"></a>
## modInv(a, n) ⇒ <code>bigint</code>
@ -172,6 +175,19 @@ Modular exponentiation a**b mod n
| b | <code>number</code> \| <code>bigint</code> | exponent |
| n | <code>number</code> \| <code>bigint</code> | modulo |
<a name="toZn"></a>
## toZn(a, n) ⇒ <code>bigint</code>
Finds the smallest positive element that is congruent to a in modulo n
**Kind**: global function
**Returns**: <code>bigint</code> - The smallest positive representation of a in modulo n
| Param | Type | Description |
| --- | --- | --- |
| a | <code>number</code> \| <code>bigint</code> | An integer |
| n | <code>number</code> \| <code>bigint</code> | The modulo |
<a name="egcdReturn"></a>
## egcdReturn : <code>Object</code>

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@ -1,48 +1,73 @@
'use strict';
const rollup = require('rollup');
const commonjs = require('rollup-plugin-commonjs');
const minify = require('rollup-plugin-babel-minify');
const fs = require('fs');
const path = require('path');
const pkgJson = require('../package.json');
const rootDir = path.join(__dirname, '..');
const srcDir = path.join(rootDir, 'src');
const dstDir = path.join(rootDir, 'dist');
const buildOptions = [
{ // Browser
input: {
input: path.join(__dirname, '..', 'src', 'main.js'),
plugins: [
commonjs()
],
input: path.join(srcDir, 'main.js')
},
output: {
file: path.join(__dirname, '..', 'dist', `${pkgJson.name}-${pkgJson.version}.browser.mod.js`),
format: 'esm'
file: path.join(dstDir, `${pkgJson.name}-${pkgJson.version}.browser.js`),
format: 'iife',
name: camelise(pkgJson.name)
}
},
{ // Browser minified
input: {
input: path.join(__dirname, '..', 'src', 'main.js'),
input: path.join(srcDir, 'main.js'),
plugins: [
commonjs(),
minify({
'comments': false
})
],
},
output: {
file: path.join(__dirname, '..', 'dist', `${pkgJson.name}-${pkgJson.version}.browser.mod.min.js`),
file: path.join(dstDir, `${pkgJson.name}-${pkgJson.version}.browser.min.js`),
format: 'iife',
name: camelise(pkgJson.name)
}
},
{ // Browser esm
input: {
input: path.join(srcDir, 'main.js')
},
output: {
file: path.join(dstDir, `${pkgJson.name}-${pkgJson.version}.browser.mod.js`),
format: 'esm'
}
},
{ // Browser esm minified
input: {
input: path.join(srcDir, 'main.js'),
plugins: [
minify({
'comments': false
})
],
},
output: {
file: path.join(dstDir, `${pkgJson.name}-${pkgJson.version}.browser.mod.min.js`),
format: 'esm'
}
},
{ // Node
input: {
input: path.join(__dirname, '..', 'src', 'main.js'),
input: path.join(srcDir, 'main.js'),
},
output: {
file: path.join(__dirname, '..', 'dist', `${pkgJson.name}-${pkgJson.version}.node.js`),
file: path.join(dstDir, `${pkgJson.name}-${pkgJson.version}.node.js`),
format: 'cjs'
}
},
}
];
for (const options of buildOptions) {
@ -50,7 +75,6 @@ for (const options of buildOptions) {
}
/* --- HELPLER FUNCTIONS --- */
async function build(options) {
@ -69,3 +93,10 @@ async function build(options) {
options.output.file.replace(`${pkgJson.name}-${pkgJson.version}.`, `${pkgJson.name}-latest.`)
);
}
function camelise(str) {
return str.replace(/-([a-z])/g,
function (m, w) {
return w.toUpperCase();
});
}

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@ -1,3 +1,7 @@
const _ZERO = BigInt(0);
const _ONE = BigInt(1);
const _TWO = BigInt(2);
/**
* Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
*
@ -5,68 +9,10 @@
*
* @returns {bigint} the absolute value of a
*/
const abs = function (a) {
function abs(a) {
a = BigInt(a);
return (a >= BigInt(0)) ? a : -a;
};
/**
* Greatest-common divisor of two integers based on the iterative binary algorithm.
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The greatest common divisor of a and b
*/
const gcd = function (a, b) {
a = abs(a);
b = abs(b);
let shift = BigInt(0);
while (!((a | b) & BigInt(1))) {
a >>= BigInt(1);
b >>= BigInt(1);
shift++;
return (a >= _ZERO) ? a : -a;
}
while (!(a & BigInt(1))) a >>= BigInt(1);
do {
while (!(b & BigInt(1))) b >>= BigInt(1);
if (a > b) {
let x = a;
a = b;
b = x;
}
b -= a;
} while (b);
// rescale
return a << shift;
};
/**
* The least common multiple computed as abs(a*b)/gcd(a,b)
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The least common multiple of a and b
*/
const lcm = function (a, b) {
a = BigInt(a);
b = BigInt(b);
return abs(a * b) / gcd(a, b);
};
/**
* Finds the smallest positive element that is congruent to a in modulo n
* @param {number|bigint} a An integer
* @param {number|bigint} n The modulo
*
* @returns {bigint} The smallest positive representation of a in modulo n
*/
const toZn = function (a, n) {
n = BigInt(n);
a = BigInt(a) % n;
return (a < 0) ? a + n : a;
};
/**
* @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b).
@ -83,15 +29,15 @@ const toZn = function (a, n) {
*
* @returns {egcdReturn}
*/
const eGcd = function (a, b) {
function eGcd(a, b) {
a = BigInt(a);
b = BigInt(b);
let x = BigInt(0);
let y = BigInt(1);
let u = BigInt(1);
let v = BigInt(0);
let x = _ZERO;
let y = _ONE;
let u = _ONE;
let v = _ZERO;
while (a !== BigInt(0)) {
while (a !== _ZERO) {
let q = b / a;
let r = b % a;
let m = x - (u * q);
@ -108,7 +54,52 @@ const eGcd = function (a, b) {
x: x,
y: y
};
};
}
/**
* Greatest-common divisor of two integers based on the iterative binary algorithm.
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The greatest common divisor of a and b
*/
function gcd(a, b) {
a = abs(a);
b = abs(b);
let shift = _ZERO;
while (!((a | b) & _ONE)) {
a >>= _ONE;
b >>= _ONE;
shift++;
}
while (!(a & _ONE)) a >>= _ONE;
do {
while (!(b & _ONE)) b >>= _ONE;
if (a > b) {
let x = a;
a = b;
b = x;
}
b -= a;
} while (b);
// rescale
return a << shift;
}
/**
* The least common multiple computed as abs(a*b)/gcd(a,b)
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The least common multiple of a and b
*/
function lcm(a, b) {
a = BigInt(a);
b = BigInt(b);
return abs(a * b) / gcd(a, b);
}
/**
* Modular inverse.
@ -118,14 +109,14 @@ const eGcd = function (a, b) {
*
* @returns {bigint} the inverse modulo n
*/
const modInv = function (a, n) {
function modInv(a, n) {
let egcd = eGcd(a, n);
if (egcd.b !== BigInt(1)) {
if (egcd.b !== _ONE) {
return null; // modular inverse does not exist
} else {
return toZn(egcd.x, n);
}
};
}
/**
* Modular exponentiation a**b mod n
@ -135,20 +126,20 @@ const modInv = function (a, n) {
*
* @returns {bigint} a**b mod n
*/
const modPow = function (a, b, n) {
function modPow(a, b, n) {
// See Knuth, volume 2, section 4.6.3.
n = BigInt(n);
a = toZn(a, n);
b = BigInt(b);
if (b < BigInt(0)) {
if (b < _ZERO) {
return modInv(modPow(a, abs(b), n), n);
}
let result = BigInt(1);
let result = _ONE;
let x = a;
while (b > 0) {
var leastSignificantBit = b % BigInt(2);
b = b / BigInt(2);
if (leastSignificantBit == BigInt(1)) {
var leastSignificantBit = b % _TWO;
b = b / _TWO;
if (leastSignificantBit == _ONE) {
result = result * x;
result = result % n;
}
@ -156,20 +147,19 @@ const modPow = function (a, b, n) {
x = x % n;
}
return result;
};
}
var main = {
abs: abs,
gcd: gcd,
lcm: lcm,
modInv: modInv,
modPow: modPow
};
var main_1 = main.abs;
var main_2 = main.gcd;
var main_3 = main.lcm;
var main_4 = main.modInv;
var main_5 = main.modPow;
/**
* Finds the smallest positive element that is congruent to a in modulo n
* @param {number|bigint} a An integer
* @param {number|bigint} n The modulo
*
* @returns {bigint} The smallest positive representation of a in modulo n
*/
function toZn(a, n) {
n = BigInt(n);
a = BigInt(a) % n;
return (a < 0) ? a + n : a;
}
export default main;
export { main_1 as abs, main_2 as gcd, main_3 as lcm, main_4 as modInv, main_5 as modPow };
export { abs, eGcd, gcd, lcm, modInv, modPow, toZn };

2
dist/bigint-mod-arith-latest.browser.mod.min.js vendored
View File

@ -1 +1 @@
const abs=function(b){return b=BigInt(b),b>=BigInt(0)?b:-b},gcd=function(c,d){c=abs(c),d=abs(d);let e=BigInt(0);for(;!((c|d)&BigInt(1));)c>>=BigInt(1),d>>=BigInt(1),e++;for(;!(c&BigInt(1));)c>>=BigInt(1);do{for(;!(d&BigInt(1));)d>>=BigInt(1);if(c>d){let a=c;c=d,d=a}d-=c}while(d);return c<<e},lcm=function(c,d){return c=BigInt(c),d=BigInt(d),abs(c*d)/gcd(c,d)},toZn=function(b,c){return c=BigInt(c),b=BigInt(b)%c,0>b?b+c:b},eGcd=function(c,d){c=BigInt(c),d=BigInt(d);let e=BigInt(0),f=BigInt(1),g=BigInt(1),h=BigInt(0);for(;c!==BigInt(0);){let a=d/c,b=d%c,i=e-g*a,j=f-h*a;d=c,c=b,e=g,f=h,g=i,h=j}return{b:d,x:e,y:f}},modInv=function(b,a){let c=eGcd(b,a);return c.b===BigInt(1)?toZn(c.x,a):null},modPow=function(c,d,e){if(e=BigInt(e),c=toZn(c,e),d=BigInt(d),d<BigInt(0))return modInv(modPow(c,abs(d),e),e);let f=BigInt(1),g=c;for(;0<d;){var h=d%BigInt(2);d/=BigInt(2),h==BigInt(1)&&(f*=g,f%=e),g*=g,g%=e}return f};var main={abs:abs,gcd:gcd,lcm:lcm,modInv:modInv,modPow:modPow},main_1=main.abs,main_2=main.gcd,main_3=main.lcm,main_4=main.modInv,main_5=main.modPow;export default main;export{main_1 as abs,main_2 as gcd,main_3 as lcm,main_4 as modInv,main_5 as modPow};
const _ZERO=BigInt(0),_ONE=BigInt(1),_TWO=BigInt(2);function abs(b){return b=BigInt(b),b>=_ZERO?b:-b}function eGcd(c,d){c=BigInt(c),d=BigInt(d);let e=_ZERO,f=_ONE,g=_ONE,h=_ZERO;for(;c!==_ZERO;){let a=d/c,b=d%c,i=e-g*a,j=f-h*a;d=c,c=b,e=g,f=h,g=i,h=j}return{b:d,x:e,y:f}}function gcd(c,d){c=abs(c),d=abs(d);let e=_ZERO;for(;!((c|d)&_ONE);)c>>=_ONE,d>>=_ONE,e++;for(;!(c&_ONE);)c>>=_ONE;do{for(;!(d&_ONE);)d>>=_ONE;if(c>d){let a=c;c=d,d=a}d-=c}while(d);return c<<e}function lcm(c,d){return c=BigInt(c),d=BigInt(d),abs(c*d)/gcd(c,d)}function modInv(b,a){let c=eGcd(b,a);return c.b===_ONE?toZn(c.x,a):null}function modPow(c,d,e){if(e=BigInt(e),c=toZn(c,e),d=BigInt(d),d<_ZERO)return modInv(modPow(c,abs(d),e),e);let f=_ONE,g=c;for(;0<d;){var h=d%_TWO;d/=_TWO,h==_ONE&&(f*=g,f%=e),g*=g,g%=e}return f}function toZn(b,c){return c=BigInt(c),b=BigInt(b)%c,0>b?b+c:b}export{abs,eGcd,gcd,lcm,modInv,modPow,toZn};

174
dist/bigint-mod-arith-latest.node.js vendored
View File

@ -1,5 +1,11 @@
'use strict';
Object.defineProperty(exports, '__esModule', { value: true });
const _ZERO = BigInt(0);
const _ONE = BigInt(1);
const _TWO = BigInt(2);
/**
* Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
*
@ -7,68 +13,10 @@
*
* @returns {bigint} the absolute value of a
*/
const abs = function (a) {
function abs(a) {
a = BigInt(a);
return (a >= BigInt(0)) ? a : -a;
};
/**
* Greatest-common divisor of two integers based on the iterative binary algorithm.
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The greatest common divisor of a and b
*/
const gcd = function (a, b) {
a = abs(a);
b = abs(b);
let shift = BigInt(0);
while (!((a | b) & BigInt(1))) {
a >>= BigInt(1);
b >>= BigInt(1);
shift++;
return (a >= _ZERO) ? a : -a;
}
while (!(a & BigInt(1))) a >>= BigInt(1);
do {
while (!(b & BigInt(1))) b >>= BigInt(1);
if (a > b) {
let x = a;
a = b;
b = x;
}
b -= a;
} while (b);
// rescale
return a << shift;
};
/**
* The least common multiple computed as abs(a*b)/gcd(a,b)
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The least common multiple of a and b
*/
const lcm = function (a, b) {
a = BigInt(a);
b = BigInt(b);
return abs(a * b) / gcd(a, b);
};
/**
* Finds the smallest positive element that is congruent to a in modulo n
* @param {number|bigint} a An integer
* @param {number|bigint} n The modulo
*
* @returns {bigint} The smallest positive representation of a in modulo n
*/
const toZn = function (a, n) {
n = BigInt(n);
a = BigInt(a) % n;
return (a < 0) ? a + n : a;
};
/**
* @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b).
@ -85,15 +33,15 @@ const toZn = function (a, n) {
*
* @returns {egcdReturn}
*/
const eGcd = function (a, b) {
function eGcd(a, b) {
a = BigInt(a);
b = BigInt(b);
let x = BigInt(0);
let y = BigInt(1);
let u = BigInt(1);
let v = BigInt(0);
let x = _ZERO;
let y = _ONE;
let u = _ONE;
let v = _ZERO;
while (a !== BigInt(0)) {
while (a !== _ZERO) {
let q = b / a;
let r = b % a;
let m = x - (u * q);
@ -110,7 +58,52 @@ const eGcd = function (a, b) {
x: x,
y: y
};
};
}
/**
* Greatest-common divisor of two integers based on the iterative binary algorithm.
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The greatest common divisor of a and b
*/
function gcd(a, b) {
a = abs(a);
b = abs(b);
let shift = _ZERO;
while (!((a | b) & _ONE)) {
a >>= _ONE;
b >>= _ONE;
shift++;
}
while (!(a & _ONE)) a >>= _ONE;
do {
while (!(b & _ONE)) b >>= _ONE;
if (a > b) {
let x = a;
a = b;
b = x;
}
b -= a;
} while (b);
// rescale
return a << shift;
}
/**
* The least common multiple computed as abs(a*b)/gcd(a,b)
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The least common multiple of a and b
*/
function lcm(a, b) {
a = BigInt(a);
b = BigInt(b);
return abs(a * b) / gcd(a, b);
}
/**
* Modular inverse.
@ -120,14 +113,14 @@ const eGcd = function (a, b) {
*
* @returns {bigint} the inverse modulo n
*/
const modInv = function (a, n) {
function modInv(a, n) {
let egcd = eGcd(a, n);
if (egcd.b !== BigInt(1)) {
if (egcd.b !== _ONE) {
return null; // modular inverse does not exist
} else {
return toZn(egcd.x, n);
}
};
}
/**
* Modular exponentiation a**b mod n
@ -137,20 +130,20 @@ const modInv = function (a, n) {
*
* @returns {bigint} a**b mod n
*/
const modPow = function (a, b, n) {
function modPow(a, b, n) {
// See Knuth, volume 2, section 4.6.3.
n = BigInt(n);
a = toZn(a, n);
b = BigInt(b);
if (b < BigInt(0)) {
if (b < _ZERO) {
return modInv(modPow(a, abs(b), n), n);
}
let result = BigInt(1);
let result = _ONE;
let x = a;
while (b > 0) {
var leastSignificantBit = b % BigInt(2);
b = b / BigInt(2);
if (leastSignificantBit == BigInt(1)) {
var leastSignificantBit = b % _TWO;
b = b / _TWO;
if (leastSignificantBit == _ONE) {
result = result * x;
result = result % n;
}
@ -158,12 +151,25 @@ const modPow = function (a, b, n) {
x = x % n;
}
return result;
};
}
module.exports = {
abs: abs,
gcd: gcd,
lcm: lcm,
modInv: modInv,
modPow: modPow
};
/**
* Finds the smallest positive element that is congruent to a in modulo n
* @param {number|bigint} a An integer
* @param {number|bigint} n The modulo
*
* @returns {bigint} The smallest positive representation of a in modulo n
*/
function toZn(a, n) {
n = BigInt(n);
a = BigInt(a) % n;
return (a < 0) ? a + n : a;
}
exports.abs = abs;
exports.eGcd = eGcd;
exports.gcd = gcd;
exports.lcm = lcm;
exports.modInv = modInv;
exports.modPow = modPow;
exports.toZn = toZn;

34
package-lock.json generated
View File

@ -188,9 +188,9 @@
"dev": true
},
"@types/node": {
"version": "11.13.0",
"resolved": "https://registry.npmjs.org/@types/node/-/node-11.13.0.tgz",
"integrity": "sha512-rx29MMkRdVmzunmiA4lzBYJNnXsW/PhG4kMBy2ATsYaDjGGR75dCFEVVROKpNwlVdcUX3xxlghKQOeDPBJobng==",
"version": "11.13.7",
"resolved": "https://registry.npmjs.org/@types/node/-/node-11.13.7.tgz",
"integrity": "sha512-suFHr6hcA9mp8vFrZTgrmqW2ZU3mbWsryQtQlY/QvwTISCw7nw/j+bCQPPohqmskhmqa5wLNuMHTTsc+xf1MQg==",
"dev": true
},
"acorn": {
@ -774,9 +774,9 @@
}
},
"commander": {
"version": "2.19.0",
"resolved": "https://registry.npmjs.org/commander/-/commander-2.19.0.tgz",
"integrity": "sha512-6tvAOO+D6OENvRAh524Dh9jcfKTYDQAqvqezbCW82xj5X0pSrcpxtvRKHLG0yBY6SD7PSDrJaj+0AiOcKVd1Xg==",
"version": "2.20.0",
"resolved": "https://registry.npmjs.org/commander/-/commander-2.20.0.tgz",
"integrity": "sha512-7j2y+40w61zy6YC2iRNpUe/NwhNyoXrYpHMrSunaMG64nRnaf96zO/KMQR4OyN/UnE5KLyEBnKHd4aG3rskjpQ==",
"dev": true,
"optional": true
},
@ -1169,9 +1169,9 @@
"dev": true
},
"handlebars": {
"version": "4.1.1",
"resolved": "https://registry.npmjs.org/handlebars/-/handlebars-4.1.1.tgz",
"integrity": "sha512-3Zhi6C0euYZL5sM0Zcy7lInLXKQ+YLcF/olbN010mzGQ4XVm50JeyBnMqofHh696GrciGruC7kCcApPDJvVgwA==",
"version": "4.1.2",
"resolved": "https://registry.npmjs.org/handlebars/-/handlebars-4.1.2.tgz",
"integrity": "sha512-nvfrjqvt9xQ8Z/w0ijewdD/vvWDTOweBUm96NTr66Wfvo1mJenBLwcYmPs3TIBP5ruzYGD7Hx/DaM9RmhroGPw==",
"dev": true,
"requires": {
"neo-async": "^2.6.0",
@ -1891,13 +1891,13 @@
"dev": true
},
"rollup": {
"version": "1.9.0",
"resolved": "https://registry.npmjs.org/rollup/-/rollup-1.9.0.tgz",
"integrity": "sha512-cNZx9MLpKFMSaObdVFeu8nXw8gfw6yjuxWjt5mRCJcBZrAJ0NHAYwemKjayvYvhLaNNkf3+kS2DKRKS5J6NRVg==",
"version": "1.10.1",
"resolved": "https://registry.npmjs.org/rollup/-/rollup-1.10.1.tgz",
"integrity": "sha512-pW353tmBE7QP622ITkGxtqF0d5gSRCVPD9xqM+fcPjudeZfoXMFW2sCzsTe2TU/zU1xamIjiS9xuFCPVT9fESw==",
"dev": true,
"requires": {
"@types/estree": "0.0.39",
"@types/node": "^11.13.0",
"@types/node": "^11.13.5",
"acorn": "^6.1.1"
}
},
@ -2328,13 +2328,13 @@
"dev": true
},
"uglify-js": {
"version": "3.4.10",
"resolved": "https://registry.npmjs.org/uglify-js/-/uglify-js-3.4.10.tgz",
"integrity": "sha512-Y2VsbPVs0FIshJztycsO2SfPk7/KAF/T72qzv9u5EpQ4kB2hQoHlhNQTsNyy6ul7lQtqJN/AoWeS23OzEiEFxw==",
"version": "3.5.8",
"resolved": "https://registry.npmjs.org/uglify-js/-/uglify-js-3.5.8.tgz",
"integrity": "sha512-GFSjB1nZIzoIq70qvDRtWRORHX3vFkAnyK/rDExc0BN7r9+/S+Voz3t/fwJuVfjppAMz+ceR2poE7tkhvnVwQQ==",
"dev": true,
"optional": true,
"requires": {
"commander": "~2.19.0",
"commander": "~2.20.0",
"source-map": "~0.6.1"
}
},

9
package.json
View File

@ -8,7 +8,9 @@
"lcm",
"gcd",
"egcd",
"modinv",
"modular inverse",
"modpow",
"modular exponentiation"
],
"license": "MIT",
@ -26,13 +28,14 @@
"src": "./src"
},
"scripts": {
"docs:build": "jsdoc2md --template=README.hbs --files ./src/main.js > README.md",
"build": "node build/build.rollup.js",
"prepublishOnly": "npm run build && npm run docs:build"
"build:docs": "jsdoc2md --template=README.hbs --files ./src/main.js > README.md",
"build:all": "npm run build && npm run build:docs",
"prepublishOnly": "npm run build && npm run build:docs"
},
"devDependencies": {
"jsdoc-to-markdown": "^4.0.1",
"rollup": "^1.9.0",
"rollup": "^1.10.1",
"rollup-plugin-babel-minify": "^8.0.0",
"rollup-plugin-commonjs": "^9.3.4"
}

164
src/main.js
View File

@ -1,5 +1,9 @@
'use strict';
const _ZERO = BigInt(0);
const _ONE = BigInt(1);
const _TWO = BigInt(2);
/**
* Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
*
@ -7,68 +11,10 @@
*
* @returns {bigint} the absolute value of a
*/
const abs = function (a) {
export function abs(a) {
a = BigInt(a);
return (a >= BigInt(0)) ? a : -a;
};
/**
* Greatest-common divisor of two integers based on the iterative binary algorithm.
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The greatest common divisor of a and b
*/
const gcd = function (a, b) {
a = abs(a);
b = abs(b);
let shift = BigInt(0);
while (!((a | b) & BigInt(1))) {
a >>= BigInt(1);
b >>= BigInt(1);
shift++;
return (a >= _ZERO) ? a : -a;
}
while (!(a & BigInt(1))) a >>= BigInt(1);
do {
while (!(b & BigInt(1))) b >>= BigInt(1);
if (a > b) {
let x = a;
a = b;
b = x;
}
b -= a;
} while (b);
// rescale
return a << shift;
};
/**
* The least common multiple computed as abs(a*b)/gcd(a,b)
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The least common multiple of a and b
*/
const lcm = function (a, b) {
a = BigInt(a);
b = BigInt(b);
return abs(a * b) / gcd(a, b);
};
/**
* Finds the smallest positive element that is congruent to a in modulo n
* @param {number|bigint} a An integer
* @param {number|bigint} n The modulo
*
* @returns {bigint} The smallest positive representation of a in modulo n
*/
const toZn = function (a, n) {
n = BigInt(n);
a = BigInt(a) % n;
return (a < 0) ? a + n : a;
};
/**
* @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b).
@ -85,15 +31,15 @@ const toZn = function (a, n) {
*
* @returns {egcdReturn}
*/
const eGcd = function (a, b) {
export function eGcd(a, b) {
a = BigInt(a);
b = BigInt(b);
let x = BigInt(0);
let y = BigInt(1);
let u = BigInt(1);
let v = BigInt(0);
let x = _ZERO;
let y = _ONE;
let u = _ONE;
let v = _ZERO;
while (a !== BigInt(0)) {
while (a !== _ZERO) {
let q = b / a;
let r = b % a;
let m = x - (u * q);
@ -110,7 +56,52 @@ const eGcd = function (a, b) {
x: x,
y: y
};
};
}
/**
* Greatest-common divisor of two integers based on the iterative binary algorithm.
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The greatest common divisor of a and b
*/
export function gcd(a, b) {
a = abs(a);
b = abs(b);
let shift = _ZERO;
while (!((a | b) & _ONE)) {
a >>= _ONE;
b >>= _ONE;
shift++;
}
while (!(a & _ONE)) a >>= _ONE;
do {
while (!(b & _ONE)) b >>= _ONE;
if (a > b) {
let x = a;
a = b;
b = x;
}
b -= a;
} while (b);
// rescale
return a << shift;
}
/**
* The least common multiple computed as abs(a*b)/gcd(a,b)
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The least common multiple of a and b
*/
export function lcm(a, b) {
a = BigInt(a);
b = BigInt(b);
return abs(a * b) / gcd(a, b);
}
/**
* Modular inverse.
@ -120,14 +111,14 @@ const eGcd = function (a, b) {
*
* @returns {bigint} the inverse modulo n
*/
const modInv = function (a, n) {
export function modInv(a, n) {
let egcd = eGcd(a, n);
if (egcd.b !== BigInt(1)) {
if (egcd.b !== _ONE) {
return null; // modular inverse does not exist
} else {
return toZn(egcd.x, n);
}
};
}
/**
* Modular exponentiation a**b mod n
@ -137,20 +128,20 @@ const modInv = function (a, n) {
*
* @returns {bigint} a**b mod n
*/
const modPow = function (a, b, n) {
export function modPow(a, b, n) {
// See Knuth, volume 2, section 4.6.3.
n = BigInt(n);
a = toZn(a, n);
b = BigInt(b);
if (b < BigInt(0)) {
if (b < _ZERO) {
return modInv(modPow(a, abs(b), n), n);
}
let result = BigInt(1);
let result = _ONE;
let x = a;
while (b > 0) {
var leastSignificantBit = b % BigInt(2);
b = b / BigInt(2);
if (leastSignificantBit == BigInt(1)) {
var leastSignificantBit = b % _TWO;
b = b / _TWO;
if (leastSignificantBit == _ONE) {
result = result * x;
result = result % n;
}
@ -158,12 +149,17 @@ const modPow = function (a, b, n) {
x = x % n;
}
return result;
};
}
module.exports = {
abs: abs,
gcd: gcd,
lcm: lcm,
modInv: modInv,
modPow: modPow
};
/**
* Finds the smallest positive element that is congruent to a in modulo n
* @param {number|bigint} a An integer
* @param {number|bigint} n The modulo
*
* @returns {bigint} The smallest positive representation of a in modulo n
*/
export function toZn(a, n) {
n = BigInt(n);
a = BigInt(a) % n;
return (a < 0) ? a + n : a;
}