# bigint-mod-arith Some extra functions to work with modular arithmetics using native JS (stage 3) implementation of BigInt. ## Usage examples ```javascript const modArith = require('bigint-mod-arith'); let a = 5n; let b = 2n; let n = 19n; console.log(modArith.modPow(a, b, n)); // prints 13 console.log(modArith.modInv(2n, 5n)); // prints 3 console.log(modArith.modInv(3n, 5n)); // prints 2 ``` ## Functions
bigint
Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
bigint
Greatest-common divisor of two integers based on the iterative binary algorithm.
bigint
The least common multiple computed as abs(a*b)/gcd(a,b)
bigint
Finds the smallest positive element that is congruent to a in modulo n
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).
bigint
Modular inverse.
bigint
Modular exponentiation a**b mod n
Object
A triple (g, x, y), such that ax + by = g = gcd(a, b).
bigint
Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
**Kind**: global function
**Returns**: bigint
- the absolute value of a
| Param | Type |
| --- | --- |
| a | number
\| bigint
|
## gcd(a, b) ⇒ bigint
Greatest-common divisor of two integers based on the iterative binary algorithm.
**Kind**: global function
**Returns**: bigint
- The greatest common divisor of a and b
| Param | Type |
| --- | --- |
| a | number
\| bigint
|
| b | number
\| bigint
|
## lcm(a, b) ⇒ bigint
The least common multiple computed as abs(a*b)/gcd(a,b)
**Kind**: global function
**Returns**: bigint
- The least common multiple of a and b
| Param | Type |
| --- | --- |
| a | number
\| bigint
|
| b | number
\| bigint
|
## toZn(a, n) ⇒ bigint
Finds the smallest positive element that is congruent to a in modulo n
**Kind**: global function
**Returns**: bigint
- The smallest positive representation of a in modulo n
| Param | Type | Description |
| --- | --- | --- |
| a | number
\| bigint
| An integer |
| n | number
\| bigint
| The modulo |
## eGcd(a, b) ⇒ [egcdReturn
](#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 | number
\| bigint
|
| b | number
\| bigint
|
## modInv(a, n) ⇒ bigint
Modular inverse.
**Kind**: global function
**Returns**: bigint
- the inverse modulo n
| Param | Type | Description |
| --- | --- | --- |
| a | number
\| bigint
| The number to find an inverse for |
| n | number
\| bigint
| The modulo |
## modPow(a, b, n) ⇒ bigint
Modular exponentiation a**b mod n
**Kind**: global function
**Returns**: bigint
- a**b mod n
| Param | Type | Description |
| --- | --- | --- |
| a | number
\| bigint
| base |
| b | number
\| bigint
| exponent |
| n | number
\| bigint
| modulo |
## egcdReturn : Object
A triple (g, x, y), such that ax + by = g = gcd(a, b).
**Kind**: global typedef
**Properties**
| Name | Type |
| --- | --- |
| g | bigint
|
| x | bigint
|
| y | bigint
|
* * *