Collaboration diagram for BGC.Mathematics.GeneralMath:

Static Public Member Functions
static int	Mod (int x, int m)
	x mod m More...

static float	Mod (float x, float m)
	x mod m More...

static double	Tanh (double angle)
	Hyperbolic Tangent in radian More...

static double	Sinh (double angle)
	Hyperbolic Sine More...

static double	Cosh (double angle)
	Hyperbolic Cosine More...

static float	Tanh (float angle)
	Hyperbolic Tangent in radian More...

static float	Sinh (float angle)
	Hyperbolic Sine More...

static float	Cosh (float angle)
	Hyperbolic Cosine More...

static bool	IsPowerOfTwo (this int number)
	Find out whether the provided 32 bit integer is a perfect power of two. More...

static int	ToNextExponentOf2 (this int x)

static int	CeilingToPowerOfTwo (this int v)

static decimal	Clamp (decimal value, decimal min, decimal max)

static double	Clamp (double value, double min, double max)

static float	Clamp (float value, float min, float max)

static long	Clamp (long value, long min, long max)

static ulong	Clamp (ulong value, ulong min, ulong max)

static int	Clamp (int value, int min, int max)

static uint	Clamp (uint value, uint min, uint max)

static short	Clamp (short value, short min, short max)

static ushort	Clamp (ushort value, ushort min, ushort max)

static byte	Clamp (byte value, byte min, byte max)

static sbyte	Clamp (sbyte value, sbyte min, sbyte max)

static decimal	Clamp01 (decimal value)
	Clamps value to range [0, 1] More...

static double	Clamp01 (double value)
	Clamps value to range [0, 1] More...

static float	Clamp01 (float value)
	Clamps value to range [0, 1] More...

static decimal	Lerp (decimal initial, decimal final, decimal t)
	Linearly interpolates between initial and final by t , clamps t to range [0,1] More...

static decimal	LerpUnclamped (decimal initial, decimal final, decimal t)
	Linearly interpolates between initial and final by t without clamping t between 0 and 1 More...

static double	Lerp (double initial, double final, double t)
	Linearly interpolates between initial and final by t , clamps t to range [0,1] More...

static double	LerpUnclamped (double initial, double final, double t)
	Linearly interpolates between initial and final by t without clamping t between 0 and 1 More...

static float	Lerp (float initial, float final, float t)
	Linearly interpolates between initial and final by t , clamps t to range [0,1] More...

static float	LerpUnclamped (float initial, float final, float t)
	Linearly interpolates between initial and final by t without clamping t between 0 and 1 More...

static decimal	Repeat (decimal value, decimal min, decimal max)

static double	Repeat (double value, double min, double max)

static float	Repeat (float value, float min, float max)

static long	Repeat (long value, long min, long max)

static int	Repeat (int value, int min, int max)

static bool	Approximately (float a, float b)

static bool	Approximately (double a, double b)

Private Attributes
const float	FLOAT_MANTISSA_LOWER_BOUND = 1.1920929E-7f

const float	FLOAT_SMALLEST_NORMAL = 1.1754943508E-38f

const float	FLOAT_COMPARISON_MAX_FACTOR = 8 * FLOAT_MANTISSA_LOWER_BOUND

const float	FLOAT_COMPARISON_LOWER_BOUND = 8 * FLOAT_SMALLEST_NORMAL

const double	DOUBLE_MANTISSA_LOWER_BOUND = 2.220446E-16

const double	DOUBLE_SMALLEST_NORMAL = 2.2250738585072014E10-308

const double	DOUBLE_COMPARISON_MAX_FACTOR = 8 * DOUBLE_MANTISSA_LOWER_BOUND

const double	DOUBLE_COMPARISON_LOWER_BOUND = 8 * DOUBLE_SMALLEST_NORMAL

Detailed Description

Definition at line 6 of file GeneralMath.cs.

Member Function Documentation

◆ Approximately() [1/2]

static bool BGC.Mathematics.GeneralMath.Approximately	(	float	a,
		float	b
	)

inlinestatic

Definition at line 326 of file GeneralMath.cs.

Referenced by BGC.Mathematics.Complex64.Equals(), and BGC.Mathematics.Complex32.Equals().

         {
             return Math.Abs(b - a) <= Math.Max(
                 FLOAT_COMPARISON_MAX_FACTOR * Math.Max(Math.Abs(a), Math.Abs(b)),
                 FLOAT_COMPARISON_LOWER_BOUND);
         }

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◆ Approximately() [2/2]

static bool BGC.Mathematics.GeneralMath.Approximately	(	double	a,
		double	b
	)

inlinestatic

Definition at line 338 of file GeneralMath.cs.

         {
             return Math.Abs(b - a) <= Math.Max(
                 DOUBLE_COMPARISON_MAX_FACTOR * Math.Max(Math.Abs(a), Math.Abs(b)),
                 DOUBLE_COMPARISON_LOWER_BOUND);
         }

◆ CeilingToPowerOfTwo()

static int BGC.Mathematics.GeneralMath.CeilingToPowerOfTwo ( this int v )

inlinestatic

Definition at line 124 of file GeneralMath.cs.

         {
             v--;
             v |= v >> 1;
             v |= v >> 2;
             v |= v >> 4;
             v |= v >> 8;
             v |= v >> 16;
             v++;
             return v;
         }

◆ Clamp() [1/11]

static decimal BGC.Mathematics.GeneralMath.Clamp	(	decimal	value,
		decimal	min,
		decimal	max
	)

static

Referenced by BGC.Audio.Spatial.NearestValidOffset(), BGC.Audio.Synthesis.SilenceStream.Read(), BGC.Audio.SimpleAudioClip.Read(), BGC.Audio.InterlacingAudioClip.Read(), BGC.Audio.NormalizedMonoClip.Read(), BGC.Audio.Synthesis.WhiteNoiseStream.Read(), BGC.Audio.CrossFadingRefClip.Read(), BGC.Audio.Synthesis.NoiseAudioClip.Read(), BGC.Audio.Synthesis.SweepAudioClip.Read(), BGC.Audio.Synthesis.STMAudioClip.Read(), BGC.Audio.Filters.SinglePassPhaseReencoder.Read(), BGC.Audio.Filters.MultiConvolutionFilter.ReadBody(), BGC.Audio.Filters.StreamEnveloper.Seek(), BGC.Audio.Filters.StreamTimeShiftFilter.Seek(), BGC.Audio.AnalyticStreams.AnalyticFrequencyModulationFilter.Seek(), BGC.Audio.AnalyticStreams.AnalyticStreamWindower.Seek(), BGC.Audio.AnalyticStreams.AnalyticStreamFrequencyShifter.Seek(), BGC.Audio.AnalyticStreams.AnalyticStreamCenterer.Seek(), BGC.Audio.Filters.AllPassFilter.Seek(), BGC.Audio.Filters.StreamCenterer.Seek(), BGC.Audio.AnalyticStreams.AnalyticStreamConverter.Seek(), BGC.Audio.Filters.StreamTruncator.Seek(), BGC.Audio.Filters.FrequencyModulationFilter.Seek(), BGC.Audio.Filters.StreamWindower.Seek(), BGC.Audio.AnalyticStreams.AnalyticADSREnvelope.Seek(), BGC.IO.SubStream.Seek(), BGC.Audio.Synthesis.ADSREnvelope.Seek(), BGC.Audio.Normalization.SPLToAdjustmentDB(), BGC.Audio.Filters.ContinuousFilter.UpdateCoefficients(), and BGC.UI.ColorUIExtensions.updateColorValue().

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◆ Clamp() [2/11]

static double BGC.Mathematics.GeneralMath.Clamp	(	double	value,
		double	min,
		double	max
	)

static

◆ Clamp() [3/11]

static float BGC.Mathematics.GeneralMath.Clamp	(	float	value,
		float	min,
		float	max
	)

static

◆ Clamp() [4/11]

static long BGC.Mathematics.GeneralMath.Clamp	(	long	value,
		long	min,
		long	max
	)

static

◆ Clamp() [5/11]

static ulong BGC.Mathematics.GeneralMath.Clamp	(	ulong	value,
		ulong	min,
		ulong	max
	)

static

◆ Clamp() [6/11]

static int BGC.Mathematics.GeneralMath.Clamp	(	int	value,
		int	min,
		int	max
	)

static

◆ Clamp() [7/11]

static uint BGC.Mathematics.GeneralMath.Clamp	(	uint	value,
		uint	min,
		uint	max
	)

static

◆ Clamp() [8/11]

static short BGC.Mathematics.GeneralMath.Clamp	(	short	value,
		short	min,
		short	max
	)

static

◆ Clamp() [9/11]

static ushort BGC.Mathematics.GeneralMath.Clamp	(	ushort	value,
		ushort	min,
		ushort	max
	)

static

◆ Clamp() [10/11]

static byte BGC.Mathematics.GeneralMath.Clamp	(	byte	value,
		byte	min,
		byte	max
	)

static

◆ Clamp() [11/11]

static sbyte BGC.Mathematics.GeneralMath.Clamp	(	sbyte	value,
		sbyte	min,
		sbyte	max
	)

static

◆ Clamp01() [1/3]

static decimal BGC.Mathematics.GeneralMath.Clamp01 ( decimal value )

inlinestatic

Clamps value to range [0, 1]

Definition at line 177 of file GeneralMath.cs.

         {
             if (value < 0)
             {
                 return 0;
             }
             else if (value > 1)
             {
                 return 1;
             }
 
             return value;
         }

◆ Clamp01() [2/3]

static double BGC.Mathematics.GeneralMath.Clamp01 ( double value )

inlinestatic

Clamps value to range [0, 1]

Definition at line 194 of file GeneralMath.cs.

         {
             if (value < 0)
             {
                 return 0;
             }
             else if (value > 1)
             {
                 return 1;
             }
 
             return value;
         }

◆ Clamp01() [3/3]

static float BGC.Mathematics.GeneralMath.Clamp01 ( float value )

inlinestatic

Clamps value to range [0, 1]

Definition at line 211 of file GeneralMath.cs.

         {
             if (value < 0)
             {
                 return 0;
             }
             else if (value > 1)
             {
                 return 1;
             }
 
             return value;
         }

◆ Cosh() [1/2]

static double BGC.Mathematics.GeneralMath.Cosh ( double angle )

static

Hyperbolic Cosine

Parameters

angle The hyperbolic angle, i.e. the area of the hyperbolic sector.

Returns: The hyperbolic Cosine of the angle.

Referenced by BGC.Mathematics.Complex64.Cos(), BGC.Mathematics.Complex32.Cos(), BGC.Mathematics.Complex64.Cosh(), BGC.Mathematics.Complex32.Cosh(), BGC.Mathematics.Complex64.Sin(), BGC.Mathematics.Complex32.Sin(), BGC.Mathematics.Complex64.Sinh(), BGC.Mathematics.Complex32.Sinh(), BGC.Mathematics.Complex64.Tanh(), and BGC.Mathematics.Complex32.Tanh().

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◆ Cosh() [2/2]

static float BGC.Mathematics.GeneralMath.Cosh ( float angle )

static

Hyperbolic Cosine

Parameters

angle The hyperbolic angle, i.e. the area of the hyperbolic sector.

Returns: The hyperbolic Cosine of the angle.

◆ IsPowerOfTwo()

static bool BGC.Mathematics.GeneralMath.IsPowerOfTwo ( this int number )

static

Find out whether the provided 32 bit integer is a perfect power of two.

Parameters

number The number to very whether it's a power of two.

Returns: True if and only if it is a power of two.

◆ Lerp() [1/3]

static decimal BGC.Mathematics.GeneralMath.Lerp	(	decimal	initial,
		decimal	final,
		decimal	t
	)

inlinestatic

Linearly interpolates between initial and final by t , clamps t to range [0,1]

Definition at line 232 of file GeneralMath.cs.

Referenced by BGC.MonoUtility.Interpolation.FadeImageAlpha.CallAction(), BGC.Audio.Calibration.GetLevelOffset(), and BGC.Audio.Visualization.SpectralDecomp.Linterp().

         {
             t = Clamp01(t);
             return initial * (1 - t) + final * t;
         }

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◆ Lerp() [2/3]

static double BGC.Mathematics.GeneralMath.Lerp	(	double	initial,
		double	final,
		double	t
	)

inlinestatic

Linearly interpolates between initial and final by t , clamps t to range [0,1]

Definition at line 251 of file GeneralMath.cs.

         {
             t = Clamp01(t);
             return initial * (1 - t) + final * t;
         }

◆ Lerp() [3/3]

static float BGC.Mathematics.GeneralMath.Lerp	(	float	initial,
		float	final,
		float	t
	)

inlinestatic

Linearly interpolates between initial and final by t , clamps t to range [0,1]

Definition at line 270 of file GeneralMath.cs.

         {
             t = Clamp01(t);
             return initial * (1 - t) + final * t;
         }

◆ LerpUnclamped() [1/3]

static decimal BGC.Mathematics.GeneralMath.LerpUnclamped	(	decimal	initial,
		decimal	final,
		decimal	t
	)

inlinestatic

Linearly interpolates between initial and final by t without clamping t between 0 and 1

Definition at line 242 of file GeneralMath.cs.

         {
             return initial * (1 - t) + final * t;
         }

◆ LerpUnclamped() [2/3]

static double BGC.Mathematics.GeneralMath.LerpUnclamped	(	double	initial,
		double	final,
		double	t
	)

inlinestatic

Linearly interpolates between initial and final by t without clamping t between 0 and 1

Definition at line 261 of file GeneralMath.cs.

         {
             return initial * (1 - t) + final * t;
         }

◆ LerpUnclamped() [3/3]

static float BGC.Mathematics.GeneralMath.LerpUnclamped	(	float	initial,
		float	final,
		float	t
	)

inlinestatic

Linearly interpolates between initial and final by t without clamping t between 0 and 1

Definition at line 280 of file GeneralMath.cs.

         {
             return initial * (1 - t) + final * t;
         }

◆ Mod() [1/2]

static int BGC.Mathematics.GeneralMath.Mod	(	int	x,
		int	m
	)

inlinestatic

x mod m

Parameters

x
m

Returns

Definition at line 14 of file GeneralMath.cs.

         {
             // https://stackoverflow.com/questions/1082917/mod-of-negative-number-is-melting-my-brain
             return ((x % m) + m) % m;
         }

◆ Mod() [2/2]

static float BGC.Mathematics.GeneralMath.Mod	(	float	x,
		float	m
	)

inlinestatic

x mod m

Parameters

x
m

Returns

Definition at line 26 of file GeneralMath.cs.

         {
             return ((x % m) + m) % m;
         }

◆ Repeat() [1/5]

static decimal BGC.Mathematics.GeneralMath.Repeat	(	decimal	value,
		decimal	min,
		decimal	max
	)

inlinestatic

Definition at line 288 of file GeneralMath.cs.

Referenced by BGC.Audio.CarrierTone.CarrierTone().

         {
             decimal scanningValue = (value - min) % (max - min);
             return scanningValue >= 0 ? scanningValue + min : scanningValue + max;
         }

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◆ Repeat() [2/5]

static double BGC.Mathematics.GeneralMath.Repeat	(	double	value,
		double	min,
		double	max
	)

inlinestatic

Definition at line 294 of file GeneralMath.cs.

         {
             double scanningValue = (value - min) % (max - min);
             return scanningValue >= 0 ? scanningValue + min : scanningValue + max;
         }

◆ Repeat() [3/5]

static float BGC.Mathematics.GeneralMath.Repeat	(	float	value,
		float	min,
		float	max
	)

inlinestatic

Definition at line 300 of file GeneralMath.cs.

         {
             float scanningValue = (value - min) % (max - min);
             return scanningValue >= 0 ? scanningValue + min : scanningValue + max;
         }

◆ Repeat() [4/5]

static long BGC.Mathematics.GeneralMath.Repeat	(	long	value,
		long	min,
		long	max
	)

inlinestatic

Definition at line 306 of file GeneralMath.cs.

         {
             long scanningValue = (value - min) % (max - min);
             return scanningValue >= 0 ? scanningValue + min : scanningValue + max;
         }

◆ Repeat() [5/5]

static int BGC.Mathematics.GeneralMath.Repeat	(	int	value,
		int	min,
		int	max
	)

inlinestatic

Definition at line 312 of file GeneralMath.cs.

         {
             int scanningValue = (value - min) % (max - min);
             return scanningValue >= 0 ? scanningValue + min : scanningValue + max;
         }

◆ Sinh() [1/2]

static double BGC.Mathematics.GeneralMath.Sinh ( double angle )

static

Hyperbolic Sine

Parameters

angle The hyperbolic angle, i.e. the area of the hyperbolic sector.

Returns: The hyperbolic sine of the angle.

Referenced by BGC.Mathematics.Complex64.Cos(), BGC.Mathematics.Complex32.Cos(), BGC.Mathematics.Complex64.Cosh(), BGC.Mathematics.Complex32.Cosh(), BGC.Mathematics.Complex64.Sin(), BGC.Mathematics.Complex32.Sin(), BGC.Mathematics.Complex64.Sinh(), BGC.Mathematics.Complex32.Sinh(), BGC.Mathematics.Complex64.Tanh(), and BGC.Mathematics.Complex32.Tanh().

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◆ Sinh() [2/2]

static float BGC.Mathematics.GeneralMath.Sinh ( float angle )

static

Hyperbolic Sine

Parameters

angle The hyperbolic angle, i.e. the area of the hyperbolic sector.

Returns: The hyperbolic sine of the angle.

◆ Tanh() [1/2]

static double BGC.Mathematics.GeneralMath.Tanh ( double angle )

inlinestatic

Hyperbolic Tangent in radian

Parameters

angle The hyperbolic angle, i.e. the area of the hyperbolic sector.

Returns: The hyperbolic tangent of the angle.

Definition at line 38 of file GeneralMath.cs.

Referenced by BGC.Audio.Envelopes.SigmoidEnvelope.Read(), BGC.Audio.Envelopes.SigmoidEnvelope.ReadNextSample(), BGC.Mathematics.Complex64.Tanh(), and BGC.Mathematics.Complex32.Tanh().

         {
             if (angle > 19.1)
             {
                 return 1.0;
             }
 
             if (angle < -19.1)
             {
                 return -1.0;
             }
 
             double e1 = Math.Exp(angle);
             double e2 = Math.Exp(-angle);
             return (e1 - e2) / (e1 + e2);
         }

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◆ Tanh() [2/2]

static float BGC.Mathematics.GeneralMath.Tanh ( float angle )

inlinestatic

Hyperbolic Tangent in radian

Parameters

angle The hyperbolic angle, i.e. the area of the hyperbolic sector.

Returns: The hyperbolic tangent of the angle.

Definition at line 79 of file GeneralMath.cs.

         {
             if (angle > 19.1f)
             {
                 return 1.0f;
             }
 
             if (angle < -19.1f)
             {
                 return -1f;
             }
 
             float e1 = Mathf.Exp(angle);
             float e2 = Mathf.Exp(-angle);
             return (e1 - e2) / (e1 + e2);
         }

◆ ToNextExponentOf2()

static int BGC.Mathematics.GeneralMath.ToNextExponentOf2 ( this int x )

static

Field Documentation

◆ DOUBLE_COMPARISON_LOWER_BOUND

const double BGC.Mathematics.GeneralMath.DOUBLE_COMPARISON_LOWER_BOUND = 8 * DOUBLE_SMALLEST_NORMAL

private

Definition at line 336 of file GeneralMath.cs.

◆ DOUBLE_COMPARISON_MAX_FACTOR

const double BGC.Mathematics.GeneralMath.DOUBLE_COMPARISON_MAX_FACTOR = 8 * DOUBLE_MANTISSA_LOWER_BOUND

private

Definition at line 335 of file GeneralMath.cs.

◆ DOUBLE_MANTISSA_LOWER_BOUND

const double BGC.Mathematics.GeneralMath.DOUBLE_MANTISSA_LOWER_BOUND = 2.220446E-16

private

Definition at line 333 of file GeneralMath.cs.

◆ DOUBLE_SMALLEST_NORMAL

const double BGC.Mathematics.GeneralMath.DOUBLE_SMALLEST_NORMAL = 2.2250738585072014E10-308

private

Definition at line 334 of file GeneralMath.cs.

◆ FLOAT_COMPARISON_LOWER_BOUND

const float BGC.Mathematics.GeneralMath.FLOAT_COMPARISON_LOWER_BOUND = 8 * FLOAT_SMALLEST_NORMAL

private

Definition at line 324 of file GeneralMath.cs.

◆ FLOAT_COMPARISON_MAX_FACTOR

const float BGC.Mathematics.GeneralMath.FLOAT_COMPARISON_MAX_FACTOR = 8 * FLOAT_MANTISSA_LOWER_BOUND

private

Definition at line 323 of file GeneralMath.cs.

◆ FLOAT_MANTISSA_LOWER_BOUND

const float BGC.Mathematics.GeneralMath.FLOAT_MANTISSA_LOWER_BOUND = 1.1920929E-7f

private

Definition at line 321 of file GeneralMath.cs.

◆ FLOAT_SMALLEST_NORMAL

const float BGC.Mathematics.GeneralMath.FLOAT_SMALLEST_NORMAL = 1.1754943508E-38f

private

Definition at line 322 of file GeneralMath.cs.

The documentation for this class was generated from the following file:

Mathematics/GeneralMath.cs

Static Public Member Functions

Private Attributes

Detailed Description

Member Function Documentation

◆ Approximately() [1/2]

◆ Approximately() [2/2]

◆ CeilingToPowerOfTwo()

◆ Clamp() [1/11]

◆ Clamp() [2/11]

◆ Clamp() [3/11]

◆ Clamp() [4/11]

◆ Clamp() [5/11]

◆ Clamp() [6/11]

◆ Clamp() [7/11]

◆ Clamp() [8/11]

◆ Clamp() [9/11]

◆ Clamp() [10/11]

◆ Clamp() [11/11]

◆ Clamp01() [1/3]

◆ Clamp01() [2/3]

◆ Clamp01() [3/3]

◆ Cosh() [1/2]

◆ Cosh() [2/2]

◆ IsPowerOfTwo()

◆ Lerp() [1/3]

◆ Lerp() [2/3]

◆ Lerp() [3/3]

◆ LerpUnclamped() [1/3]

◆ LerpUnclamped() [2/3]

◆ LerpUnclamped() [3/3]

◆ Mod() [1/2]

◆ Mod() [2/2]

◆ Repeat() [1/5]

◆ Repeat() [2/5]

◆ Repeat() [3/5]

◆ Repeat() [4/5]

◆ Repeat() [5/5]

◆ Sinh() [1/2]

◆ Sinh() [2/2]

◆ Tanh() [1/2]

◆ Tanh() [2/2]

◆ ToNextExponentOf2()

Field Documentation

◆ DOUBLE_COMPARISON_LOWER_BOUND

◆ DOUBLE_COMPARISON_MAX_FACTOR

◆ DOUBLE_MANTISSA_LOWER_BOUND

◆ DOUBLE_SMALLEST_NORMAL

◆ FLOAT_COMPARISON_LOWER_BOUND

◆ FLOAT_COMPARISON_MAX_FACTOR

◆ FLOAT_MANTISSA_LOWER_BOUND

◆ FLOAT_SMALLEST_NORMAL