bigint-mod-arith/docs/API.md

bigint-mod-arith - v2.1.0

bigint-mod-arith - v2.1.0

Some common functions for modular arithmetic using native JS implementation of BigInt

Table of contents

Interfaces

• Egcd

Functions

• abs
• bitLength
• eGcd
• gcd
• lcm
• max
• min
• modInv
• modPow
• toZn

Functions

abs

▸ abs(a: number | bigint): 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: ts/abs.ts:8

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bitLength

▸ bitLength(a: number | bigint): number

Returns the bitlength of a number

Parameters:

Name	Type
a	number | bigint

Returns: number

The bit length

Defined in: ts/bitLength.ts:7

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eGcd

▸ eGcd(a: number | bigint, b: number | bigint): Egcd

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).

Parameters:

Name	Type
a	number | bigint
b	number | bigint

Returns: Egcd

A triple (g, x, y), such that ax + by = g = gcd(a, b).

Defined in: ts/egcd.ts:15

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gcd

▸ gcd(a: number | bigint, b: number | bigint): 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: ts/gcd.ts:10

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lcm

▸ lcm(a: number | bigint, b: number | bigint): 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: ts/lcm.ts:10

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max

▸ max(a: number | bigint, b: number | bigint): 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: ts/max.ts:9

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min

▸ min(a: number | bigint, b: number | bigint): 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: ts/min.ts:9

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modInv

▸ modInv(a: number | bigint, n: number | bigint): bigint | number

Modular inverse.

Parameters:

Name	Type	Description
a	number | bigint	The number to find an inverse for
n	number | bigint	The modulo

Returns: bigint | number

The inverse modulo n or number NaN if it does not exist

Defined in: ts/modInv.ts:11

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modPow

▸ modPow(b: number | bigint, e: number | bigint, n: number | bigint): bigint | number

Modular exponentiation b**e mod n. Currently using the right-to-left binary method

Parameters:

Name	Type	Description
b	number | bigint	base
e	number | bigint	exponent
n	number | bigint	modulo

Returns: bigint | number

b**e mod n or number NaN if n <= 0

Defined in: ts/modPow.ts:13

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toZn

▸ toZn(a: number | bigint, n: number | bigint): bigint | number

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

Parameters:

Name	Type	Description
a	number | bigint	An integer
n	number | bigint	The modulo

Returns: bigint | number

A bigint with the smallest positive representation of a modulo n or number NaN if n < 0

Defined in: ts/toZn.ts:12