238 lines
5.2 KiB
Markdown
238 lines
5.2 KiB
Markdown
bigint-mod-arith - v2.1.0
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# bigint-mod-arith - v2.1.0
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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*): *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:** *number* \| *bigint*
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The absolute value of a
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Defined in: [ts/abs.ts:8](https://github.com/juanelas/bigint-mod-arith/blob/6131edd/src/ts/abs.ts#L8)
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___
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### bitLength
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▸ **bitLength**(`a`: *number* \| *bigint*): *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:** *number*
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The bit length
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Defined in: [ts/bitLength.ts:7](https://github.com/juanelas/bigint-mod-arith/blob/6131edd/src/ts/bitLength.ts#L7)
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___
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### eGcd
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▸ **eGcd**(`a`: *number* \| *bigint*, `b`: *number* \| *bigint*): [*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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#### 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:** [*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: [ts/egcd.ts:15](https://github.com/juanelas/bigint-mod-arith/blob/6131edd/src/ts/egcd.ts#L15)
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___
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### gcd
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▸ **gcd**(`a`: *number* \| *bigint*, `b`: *number* \| *bigint*): *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:** *bigint*
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The greatest common divisor of a and b
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Defined in: [ts/gcd.ts:10](https://github.com/juanelas/bigint-mod-arith/blob/6131edd/src/ts/gcd.ts#L10)
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___
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### lcm
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▸ **lcm**(`a`: *number* \| *bigint*, `b`: *number* \| *bigint*): *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:** *bigint*
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The least common multiple of a and b
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Defined in: [ts/lcm.ts:10](https://github.com/juanelas/bigint-mod-arith/blob/6131edd/src/ts/lcm.ts#L10)
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___
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### max
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▸ **max**(`a`: *number* \| *bigint*, `b`: *number* \| *bigint*): *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:** *number* \| *bigint*
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Maximum of numbers a and b
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Defined in: [ts/max.ts:9](https://github.com/juanelas/bigint-mod-arith/blob/6131edd/src/ts/max.ts#L9)
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___
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### min
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▸ **min**(`a`: *number* \| *bigint*, `b`: *number* \| *bigint*): *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:** *number* \| *bigint*
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Minimum of numbers a and b
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Defined in: [ts/min.ts:9](https://github.com/juanelas/bigint-mod-arith/blob/6131edd/src/ts/min.ts#L9)
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___
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### modInv
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▸ **modInv**(`a`: *number* \| *bigint*, `n`: *number* \| *bigint*): *bigint* \| *number*
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Modular inverse.
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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:** *bigint* \| *number*
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The inverse modulo n or number NaN if it does not exist
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Defined in: [ts/modInv.ts:11](https://github.com/juanelas/bigint-mod-arith/blob/6131edd/src/ts/modInv.ts#L11)
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___
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### modPow
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▸ **modPow**(`b`: *number* \| *bigint*, `e`: *number* \| *bigint*, `n`: *number* \| *bigint*): *bigint* \| *number*
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Modular exponentiation b**e mod n. Currently using the right-to-left binary method
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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:** *bigint* \| *number*
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b**e mod n or number NaN if n <= 0
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Defined in: [ts/modPow.ts:13](https://github.com/juanelas/bigint-mod-arith/blob/6131edd/src/ts/modPow.ts#L13)
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___
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### toZn
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▸ **toZn**(`a`: *number* \| *bigint*, `n`: *number* \| *bigint*): *bigint* \| *number*
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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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#### 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:** *bigint* \| *number*
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A bigint with the smallest positive representation of a modulo n or number NaN if n < 0
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Defined in: [ts/toZn.ts:12](https://github.com/juanelas/bigint-mod-arith/blob/6131edd/src/ts/toZn.ts#L12)
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