Class ExMMod

See ExM. This class contains functions related to mod (remainder) operations.

Inheritance

System.Object

ExMMod

Inherited Members

System.Object.ToString()

System.Object.Equals(System.Object)

System.Object.Equals(System.Object, System.Object)

System.Object.ReferenceEquals(System.Object, System.Object)

System.Object.GetHashCode()

System.Object.GetType()

System.Object.MemberwiseClone()

Namespace: Danmokou.DMath.Functions

Assembly: cs.temp.dll.dll

Syntax

public static class ExMMod

Methods

FlipXMod(tfloat, tfloat)

Returns v if x is even, and 180-v if x is odd.

Declaration

public static tfloat FlipXMod(tfloat x, tfloat v)

Parameters

Type	Name	Description
tfloat	x
tfloat	v

Returns

Type	Description
tfloat

FlipXPMMod(tfloat, tfloat)

Returns v if x is 1, and 180-v if x is -1.

Declaration

public static tfloat FlipXPMMod(tfloat x, tfloat v)

Parameters

Type	Name	Description
tfloat	x
tfloat	v

Returns

Type	Description
tfloat

HMod(tfloat, tfloat)

Use this to draw "wings" where both go in the same direction.
Odd by: 0 is the center, [1,by/2-0.5] are one wing, and [by/2+0.5,by) are the other.
Even by: [0, by/2) are one wing, [by/2, by) are the other.

Declaration

public static tfloat HMod(tfloat by, tfloat x)

Parameters

Type	Name	Description
tfloat	by	Period (note all values are in the range [0, by/2-0.5]
tfloat	x	Value

Returns

Type	Description
tfloat

Examples

HMod(X(), 9)(0) = HMod(X(), 9)(9) = 0 HMod(X(), 9)(1) = 1 HMod(X(), 9)(5) = 1 HMod(X(), 9)(8) = 4 HMod(X(), 8)(0) = HMod(X(), 8)(8) = HMod(X(), 8)(4) = 0 HMod(X(), 8)(2) = 2 HMod(X(), 8)(6) = 2

HNMod(tfloat, tfloat)

Use this to draw "wings" where both go in opposite directions.
Odd by: 0 is the center, [1,by/2-0.5] are one wing, and [by/2+0.5,by) are the other.
Even by: [0, by/2) are one wing, [by/2, by) are the other.

Declaration

public static tfloat HNMod(tfloat by, tfloat x)

Parameters

Type	Name	Description
tfloat	by	Period
tfloat	x	Target function

Returns

Type	Description
tfloat

Examples

HNMod(X(), 9)(0) = HNMod(X(), 9)(9) = 0 HNMod(X(), 9)(1) = 1 HNMod(X(), 9)(5) = -1 HNMod(X(), 9)(8) = -4 HNMod(X(), 8)(0) = HNMod(X(), 8)(8) = 0.5 HNMod(X(), 8)(3) = 3.5 HNMod(X(), 8)(4) = -0.5

Mod(tfloat, tfloat)

Get the modulo (nonnegative) of one number by another.

Declaration

public static tfloat Mod(tfloat by, tfloat x)

Parameters

Type	Name	Description
tfloat	by	Modulo value
tfloat	x	Target value

Returns

Type	Description
tfloat

Modh(tfloat)

= Mod(1, 1/phi * x)

Declaration

public static tfloat Modh(tfloat x)

Parameters

Type	Name	Description
tfloat	x

Returns

Type	Description
tfloat

ModWithPause(tfloat, tfloat, tfloat, tfloat)

Periodize the return value of the target function with a "pause" at the value pauseAt for pauseLen units. The true period of this function is by + pauseLen, however the output only varies [0, by]. During the pause time, the return value will be stuck at pauseAt.

Declaration

public static tfloat ModWithPause(tfloat by, tfloat pauseAt, tfloat pauseLen, tfloat x)

Parameters

Type	Name	Description
tfloat	by	Naive period
tfloat	pauseAt	Time at which to pause
tfloat	pauseLen	Length for which to pause
tfloat	x	Target function

Returns

Type	Description
tfloat

MP1Mod(tfloat)

Returns -1 if the value is even, and 1 if the value is odd.

Declaration

public static tfloat MP1Mod(tfloat x)

Parameters

Type	Name	Description
tfloat	x

Returns

Type	Description
tfloat

PM1Mod(tfloat)

Returns 1 if the value is even, and -1 if the value is odd.

Declaration

public static tfloat PM1Mod(tfloat x)

Parameters

Type	Name	Description
tfloat	x

Returns

Type	Description
tfloat

PMZ1(tfloat)

Convert a value 1,-1 to 1,0.

Declaration

public static tfloat PMZ1(tfloat x)

Parameters

Type	Name	Description
tfloat	x

Returns

Type	Description
tfloat

RangeMod(tfloat, tfloat)

Periodize a value around a positive and negative endpoint.

Declaration

public static tfloat RangeMod(tfloat by, tfloat x)

Parameters

Type	Name	Description
tfloat	by
tfloat	x

Returns

Type	Description
tfloat

Examples

FSoftMod(X(), 4)(3.95) = 3.95 FSoftMod(X(), 4)(4.05) = -3.95 FSoftMod(X(), 4)(11) = 3 FSoftMod(X(), 4)(12.05) = -3.95

RangeModh(tfloat)

= RangeMod(1, 2/phi * x)

Declaration

public static tfloat RangeModh(tfloat x)

Parameters

Type	Name	Description
tfloat	x

Returns

Type	Description
tfloat

RangeSoftMod(tfloat, tfloat)

Periodize a value, bouncing it off a positive and negative endpoint.

Declaration

public static tfloat RangeSoftMod(tfloat by, tfloat x)

Parameters

Type	Name	Description
tfloat	by
tfloat	x

Returns

Type	Description
tfloat

Examples

FSoftMod(X(), 4)(3.95) = 3.95 FSoftMod(X(), 4)(4.05) = 3.95 FSoftMod(X(), 4)(11) = -3 FSoftMod(X(), 4)(12.05) = -3.95

RemapIndex(tfloat, tfloat)

Use Fermat's Little Theorem to reindex integers around a prime number mod.

Declaration

public static tfloat RemapIndex(tfloat mod, tfloat index)

Parameters

Type	Name	Description
tfloat	mod
tfloat	index

Returns

Type	Description
tfloat

RemapIndexLoop(tfloat, tfloat)

Use Fermat's Little Theorem to reindex integers around a prime number mod, localized to the region [mod*floor(index/mod), mod+mod*floor(index/mod)].

Declaration

public static tfloat RemapIndexLoop(tfloat mod, tfloat index)

Parameters

Type	Name	Description
tfloat	mod
tfloat	index

Returns

Type	Description
tfloat

SoftMod(tfloat, tfloat)

Periodize a value, "bouncing off" the endpoint instead of wrapping around.

Declaration

public static tfloat SoftMod(tfloat by, tfloat x)

Parameters

Type	Name	Description
tfloat	by	Period
tfloat	x	Value

Returns

Type	Description
tfloat

Examples

FSoftMod(X(), 4)(3.95) = 3.95 FSoftMod(X(), 4)(4.05) = 3.95 FSoftMod(X(), 4)(4.15) = 3.85

z1Mod(tfloat)

Returns 0 if the value is even, and 1 if the value is odd.

Declaration

public static tfloat z1Mod(tfloat x)

Parameters

Type	Name	Description
tfloat	x

Returns

Type	Description
tfloat

Z1PM(tfloat)

Convert a value 1,0 to 1,-1.

Declaration

public static tfloat Z1PM(tfloat x)

Parameters

Type	Name	Description
tfloat	x

Returns

Type	Description
tfloat