5.3 KiB
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
Functions
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
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
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).
throws {RangeError}
This excepction is thrown if a or b are less than 0
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:18
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
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
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
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
modInv
▸ modInv(a: number | bigint, n: number | bigint): bigint
Modular inverse.
throws {RangeError}
Excpeption thorwn when 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: ts/modInv.ts:14
modPow
▸ modPow(b: number | bigint, e: number | bigint, n: number | bigint): bigint
Modular exponentiation b**e mod n. Currently using the right-to-left binary method
throws {RangeError}
Excpeption thrown when n is not > 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: ts/modPow.ts:16
toZn
▸ toZn(a: number | bigint, n: number | bigint): 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}
Excpeption thrown when n is not > 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: ts/toZn.ts:15