288 lines
5.0 KiB
Markdown
288 lines
5.0 KiB
Markdown
# bigint-mod-arith - v3.0.1
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Some common functions for modular arithmetic using native JS implementation of BigInt
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## Table of contents
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### Interfaces
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- [Egcd](interfaces/Egcd.md)
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### Functions
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- [abs](API.md#abs)
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- [bitLength](API.md#bitlength)
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- [eGcd](API.md#egcd)
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- [gcd](API.md#gcd)
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- [lcm](API.md#lcm)
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- [max](API.md#max)
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- [min](API.md#min)
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- [modInv](API.md#modinv)
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- [modPow](API.md#modpow)
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- [toZn](API.md#tozn)
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## Functions
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### abs
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▸ **abs**(`a`): `number` \| `bigint`
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Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
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#### Parameters
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| Name | Type |
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| :------ | :------ |
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| `a` | `number` \| `bigint` |
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#### Returns
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`number` \| `bigint`
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The absolute value of a
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#### Defined in
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[abs.ts:8](https://github.com/juanelas/bigint-mod-arith/blob/09f1243/src/ts/abs.ts#L8)
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___
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### bitLength
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▸ **bitLength**(`a`): `number`
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Returns the bitlength of a number
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#### Parameters
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| Name | Type |
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| :------ | :------ |
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| `a` | `number` \| `bigint` |
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#### Returns
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`number`
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The bit length
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#### Defined in
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[bitLength.ts:7](https://github.com/juanelas/bigint-mod-arith/blob/09f1243/src/ts/bitLength.ts#L7)
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___
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### eGcd
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▸ **eGcd**(`a`, `b`): [`Egcd`](interfaces/Egcd.md)
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An iterative implementation of the extended euclidean algorithm or extended greatest common divisor algorithm.
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Take positive integers a, b as input, and return a triple (g, x, y), such that ax + by = g = gcd(a, b).
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**`throws`** {RangeError}
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This excepction is thrown if a or b are less than 0
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#### Parameters
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| Name | Type |
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| :------ | :------ |
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| `a` | `number` \| `bigint` |
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| `b` | `number` \| `bigint` |
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#### Returns
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[`Egcd`](interfaces/Egcd.md)
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A triple (g, x, y), such that ax + by = g = gcd(a, b).
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#### Defined in
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[egcd.ts:18](https://github.com/juanelas/bigint-mod-arith/blob/09f1243/src/ts/egcd.ts#L18)
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___
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### gcd
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▸ **gcd**(`a`, `b`): `bigint`
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Greatest-common divisor of two integers based on the iterative binary algorithm.
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#### Parameters
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| Name | Type |
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| :------ | :------ |
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| `a` | `number` \| `bigint` |
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| `b` | `number` \| `bigint` |
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#### Returns
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`bigint`
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The greatest common divisor of a and b
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#### Defined in
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[gcd.ts:10](https://github.com/juanelas/bigint-mod-arith/blob/09f1243/src/ts/gcd.ts#L10)
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___
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### lcm
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▸ **lcm**(`a`, `b`): `bigint`
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The least common multiple computed as abs(a*b)/gcd(a,b)
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#### Parameters
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| Name | Type |
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| :------ | :------ |
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| `a` | `number` \| `bigint` |
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| `b` | `number` \| `bigint` |
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#### Returns
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`bigint`
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The least common multiple of a and b
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#### Defined in
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[lcm.ts:10](https://github.com/juanelas/bigint-mod-arith/blob/09f1243/src/ts/lcm.ts#L10)
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___
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### max
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▸ **max**(`a`, `b`): `number` \| `bigint`
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Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b
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#### Parameters
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| Name | Type |
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| :------ | :------ |
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| `a` | `number` \| `bigint` |
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| `b` | `number` \| `bigint` |
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#### Returns
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`number` \| `bigint`
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Maximum of numbers a and b
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#### Defined in
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[max.ts:9](https://github.com/juanelas/bigint-mod-arith/blob/09f1243/src/ts/max.ts#L9)
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___
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### min
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▸ **min**(`a`, `b`): `number` \| `bigint`
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Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b
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#### Parameters
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| Name | Type |
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| :------ | :------ |
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| `a` | `number` \| `bigint` |
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| `b` | `number` \| `bigint` |
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#### Returns
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`number` \| `bigint`
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Minimum of numbers a and b
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#### Defined in
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[min.ts:9](https://github.com/juanelas/bigint-mod-arith/blob/09f1243/src/ts/min.ts#L9)
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___
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### modInv
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▸ **modInv**(`a`, `n`): `bigint`
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Modular inverse.
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**`throws`** {RangeError}
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Excpeption thorwn when a does not have inverse modulo n
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#### Parameters
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| Name | Type | Description |
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| :------ | :------ | :------ |
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| `a` | `number` \| `bigint` | The number to find an inverse for |
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| `n` | `number` \| `bigint` | The modulo |
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#### Returns
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`bigint`
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The inverse modulo n
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#### Defined in
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[modInv.ts:14](https://github.com/juanelas/bigint-mod-arith/blob/09f1243/src/ts/modInv.ts#L14)
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___
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### modPow
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▸ **modPow**(`b`, `e`, `n`): `bigint`
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Modular exponentiation b**e mod n. Currently using the right-to-left binary method
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**`throws`** {RangeError}
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Excpeption thrown when n is not > 0
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#### Parameters
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| Name | Type | Description |
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| :------ | :------ | :------ |
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| `b` | `number` \| `bigint` | base |
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| `e` | `number` \| `bigint` | exponent |
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| `n` | `number` \| `bigint` | modulo |
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#### Returns
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`bigint`
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b**e mod n
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#### Defined in
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[modPow.ts:16](https://github.com/juanelas/bigint-mod-arith/blob/09f1243/src/ts/modPow.ts#L16)
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___
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### toZn
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▸ **toZn**(`a`, `n`): `bigint`
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Finds the smallest positive element that is congruent to a in modulo n
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**`remarks`**
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a and b must be the same type, either number or bigint
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**`throws`** {RangeError}
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Excpeption thrown when n is not > 0
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#### Parameters
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| Name | Type | Description |
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| :------ | :------ | :------ |
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| `a` | `number` \| `bigint` | An integer |
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| `n` | `number` \| `bigint` | The modulo |
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#### Returns
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`bigint`
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A bigint with the smallest positive representation of a modulo n
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#### Defined in
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[toZn.ts:15](https://github.com/juanelas/bigint-mod-arith/blob/09f1243/src/ts/toZn.ts#L15)
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