ZFnum (Averest)

ZFnum Type

Namespace: TeachingTools
Assembly: TeachingToolsLib.dll
Parent Module: ComputerArithmetic
Base Type: obj
All Interfaces: IEquatable<ZFnum> , IStructuralEquatable , IComparable<ZFnum> , IComparable , IStructuralComparable

SchoenhageStrassen works on the ring ZF[2^{2^n}+1] having elements 0,...,2^{2^n}. We represent its elements as records with a number num and the information about the ring they belong to (the algorithm makes recursive calls to smaller rings ZF[2^{2^k}+1] so to avoid confusion about the rings we are currently working with, the numbers carry the information about the ring they belong to.

Record fields

Record Field	Description
`FermatNum` Full Usage: `FermatNum` Field type: `BigInteger`	Field type: `BigInteger`
`n` Full Usage: `n` Field type: `int`	Field type: `int`
`num` Full Usage: `num` Field type: `BigInteger`	Field type: `BigInteger`

Instance members

Instance member	Description
`this.Negate` Full Usage: `this.Negate` Returns: `ZFnum`	negate a number (compute its additive inverse) Returns: `ZFnum`
`this.Shift` Full Usage: `this.Shift` Parameters: k : `int` Returns: `ZFnum`	shift a number by k bits, i.e., multiply by 2^k k : `int` Returns: `ZFnum`
`this.ToBinary` Full Usage: `this.ToBinary` Returns: `string`	convert the number to its binary representation using 2^n bits where bytes are separated by : and the more significant ones are printed on the left hand side Returns: `string`

Static members

Static member	Description
`x * y` Full Usage: `x * y` Parameters: x : `ZFnum` y : `ZFnum` Returns: `ZFnum`	Multiplication of numbers in ZF[2^{2^n}+1] x : `ZFnum` y : `ZFnum` Returns: `ZFnum`
`x + y` Full Usage: `x + y` Parameters: x : `ZFnum` y : `ZFnum` Returns: `ZFnum`	addition of numbers in ZF[2^{2^n}+1] x : `ZFnum` y : `ZFnum` Returns: `ZFnum`
`x - y` Full Usage: `x - y` Parameters: x : `ZFnum` y : `ZFnum` Returns: `ZFnum`	subtraction of numbers in ZF[2^{2^n}+1] x : `ZFnum` y : `ZFnum` Returns: `ZFnum`
`ZFnum.FromBigInteger(n, b)` Full Usage: `ZFnum.FromBigInteger(n, b)` Parameters: n : `int` b : `BigInteger` Returns: `ZFnum`	convert a BigInteger to a ZFnum n : `int` b : `BigInteger` Returns: `ZFnum`
`ZFnum.FromInteger(n, i)` Full Usage: `ZFnum.FromInteger(n, i)` Parameters: n : `int` i : `int` Returns: `ZFnum`	convert an integer to a ZFnum n : `int` i : `int` Returns: `ZFnum`
`ZFnum.PowerOf2(n) (k)` Full Usage: `ZFnum.PowerOf2(n) (k)` Parameters: n : `int` k : `int` Returns: `ZFnum`	generate the k-th power of 2 n : `int` k : `int` Returns: `ZFnum`