Class MathHelper

Provides useful mathematical algorithms and functions.

Inheritance

System.Object

MathHelper

Namespace: Mars.Numerics

Assembly: Mars.Numerics.dll

Syntax

public static class MathHelper : object

Fields

E

Defines the value of E as a System.Single.

Declaration

public const float E = null

Field Value

Type	Description
System.Single

Log10E

Defines the base-10 logarithm of E.

Declaration

public const float Log10E = null

Field Value

Type	Description
System.Single

Log2E

Defines the base-2 logarithm of E.

Declaration

public const float Log2E = null

Field Value

Type	Description
System.Single

Pi

Defines the value of Pi as a System.Single.

Declaration

public const float Pi = null

Field Value

Type	Description
System.Single

PiOver2

Defines the value of Pi divided by two as a System.Single.

Declaration

public const float PiOver2 = null

Field Value

Type	Description
System.Single

PiOver3

Defines the value of Pi divided by three as a System.Single.

Declaration

public const float PiOver3 = null

Field Value

Type	Description
System.Single

PiOver4

Defines the value of Pi divided by four as a System.Single.

Declaration

public const float PiOver4 = null

Field Value

Type	Description
System.Single

PiOver6

Defines the value of Pi divided by six as a System.Single.

Declaration

public const float PiOver6 = null

Field Value

Type	Description
System.Single

ThreePiOver2

Defines the value of Pi multiplied by 3 and divided by two as a System.Single.

Declaration

public const float ThreePiOver2 = null

Field Value

Type	Description
System.Single

ToDegreeFactorD

Gets the double precision factor to convert radian to degree

Declaration

public const double ToDegreeFactorD = null

Field Value

Type	Description
System.Double

ToDegreeFactorF

Gets the single precision factor to convert degree to radian

Declaration

public const float ToDegreeFactorF = null

Field Value

Type	Description
System.Single

ToRadianFactorD

Gets the double precision factor to convert degree to radian.

Declaration

public const double ToRadianFactorD = null

Field Value

Type	Description
System.Double

ToRadianFactorF

Gets the single precision factor to convert degree to radian.

Declaration

public const float ToRadianFactorF = null

Field Value

Type	Description
System.Single

TwoPi

Defines the value of Pi multiplied by two as a System.Single.

Declaration

public const float TwoPi = null

Field Value

Type	Description
System.Single

Methods

BinomialCoefficient(Int32, Int32)

Computes the binomial coefficient of (n, k), also read as "n choose k".

Declaration

public static long BinomialCoefficient(int n, int k)

Parameters

Type	Name	Description
System.Int32	n	n, must be a value equal to or greater than 0.
System.Int32	k	k, a value in the range [0, n].

Returns

Type	Description
System.Int64	The binomial coefficient.

Remarks

This method returns a binomial coefficient. The result is the k'th element in the n'th row of Pascal's triangle (using zero-based indices for k and n). This method returns 0 for negative n.

Bitmask(UInt32)

Creates the smallest bitmask that is greater than or equal to the given value.

Declaration

public static uint Bitmask(uint value)

Parameters

Type	Name	Description
System.UInt32	value	The value.

Returns

Type	Description
System.UInt32	A bitmask where the left bits are 0 and the right bits are 1. The value of the bitmask is ≥ value.

Remarks

This result can also be interpreted as finding the smallest x such that 2^x > value and returning 2^x - 1.

Another useful application: Bitmask(x) + 1 returns the next power of 2 that is greater than x.

Clamp<T>(T, T, T)

Clamps the specified value.

Declaration

public static T Clamp<T>(T value, T min, T max)
    where T : IComparable<T>

Parameters

Type	Name	Description
T	value	The value which should be clamped.
T	min	The min limit.
T	max	The max limit.

Returns

Type	Description
T	value clamped to the interval [min, max].

Type Parameters

Name	Description
T	The type of the value.

Remarks

Values within the limits are not changed. Values exceeding the limits are cut off.

Factorial(Int32)

Calculates the factorial of a given natural number.

Declaration

public static long Factorial(int n)

Parameters

Type	Name	Description
System.Int32	n	The number.

Returns

Type	Description
System.Int64	n!

FastFloor(Double)

Returns the largest integer less than or equal to the specified decimal number.

Declaration

public static int FastFloor(double d)

Parameters

Type	Name	Description
System.Double	d	A decimal number.

Returns

Type	Description
System.Int32	The largest integer less than or equal to d.

Remarks

Note that the method returns an integral value of type System.Math

Frac(Double)

Calculates the fractional part of a specified double-precision floating-point number.

Declaration

public static double Frac(double d)

Parameters

Type	Name	Description
System.Double	d	The number.

Returns

Type	Description
System.Double	The fractional part of d.

Frac(Single)

Calculates the fractional part of a specified single-precision floating-point number.

Declaration

public static float Frac(float f)

Parameters

Type	Name	Description
System.Single	f	The number.

Returns

Type	Description
System.Single	The fractional part of f.

Gaussian(Double, Double, Double, Double)

Computes the Gaussian function y = k * e^( -(x-μ)²/(2σ²) (double-precision).

Declaration

public static double Gaussian(double x, double coefficient, double expectedValue, double standardDeviation)

Parameters

Type	Name	Description
System.Double	x	The argument x.
System.Double	coefficient	The coefficient k.
System.Double	expectedValue	The expected value μ.
System.Double	standardDeviation	The standard deviation σ.

Returns

Type	Description
System.Double	The height of the Gaussian bell curve at x.

Remarks

This method computes the Gaussian bell curve.

Gaussian(Single, Single, Single, Single)

Computes the Gaussian function y = k * e^( -(x-μ)²/(2σ²) (single precision).

Declaration

public static float Gaussian(float x, float coefficient, float expectedValue, float standardDeviation)

Parameters

Type	Name	Description
System.Single	x	The argument x.
System.Single	coefficient	The coefficient k.
System.Single	expectedValue	The expected value μ.
System.Single	standardDeviation	The standard deviation σ.

Returns

Type	Description
System.Single	The height of the Gaussian bell curve at x.

Remarks

This method computes the Gaussian bell curve.

Hypotenuse(Double, Double)

Computes Sqrt(a*a + b*b) without underflow/overflow (double-precision).

Declaration

public static double Hypotenuse(double cathetusA, double cathetusB)

Parameters

Type	Name	Description
System.Double	cathetusA	Cathetus a.
System.Double	cathetusB	Cathetus b.

Returns

Type	Description
System.Double	The hypotenuse c, which is Sqrt(a*a + b*b).

Hypotenuse(Single, Single)

Computes Sqrt(a*a + b*b) without underflow/overflow (single-precision).

Declaration

public static float Hypotenuse(float cathetusA, float cathetusB)

Parameters

Type	Name	Description
System.Single	cathetusA	Cathetus a.
System.Single	cathetusB	Cathetus b.

Returns

Type	Description
System.Single	The hypotenuse c, which is Sqrt(a*a + b*b).

InverseSqrtFast(Double)

Returns an approximation of the inverse square root of left number.

Declaration

public static double InverseSqrtFast(double x)

Parameters

Type	Name	Description
System.Double	x	A number.

Returns

Type	Description
System.Double	An approximation of the inverse square root of the specified number, with an upper error bound of 0.001

Remarks

This is an improved implementation of the the method known as Carmack's inverse square root which is found in the Quake III source code. This implementation comes from http://www.codemaestro.com/reviews/review00000105.html. For the history of this method, see http://www.beyond3d.com/content/articles/8/

InverseSqrtFast(Single)

Returns an approximation of the inverse square root of left number.

Declaration

public static float InverseSqrtFast(float x)

Parameters

Type	Name	Description
System.Single	x	A number.

Returns

Type	Description
System.Single	An approximation of the inverse square root of the specified number, with an upper error bound of 0.001

Remarks

This is an improved implementation of the the method known as Carmack's inverse square root which is found in the Quake III source code. This implementation comes from http://www.codemaestro.com/reviews/review00000105.html. For the history of this method, see http://www.beyond3d.com/content/articles/8/

IsPowerOfTwo(Int32)

Determines whether the specified value is a power of two.

Declaration

public static bool IsPowerOfTwo(int value)

Parameters

Type	Name	Description
System.Int32	value	The value.

Returns

Type	Description
System.Boolean	langword_csharp_true if value is a power of two; otherwise, langword_csharp_false.

Log2GreaterOrEqual(UInt32)

Returns the smallest non-negative integer x such that 2^x ≥ value.

Declaration

public static uint Log2GreaterOrEqual(uint value)

Parameters

Type	Name	Description
System.UInt32	value	The value.

Returns

Type	Description
System.UInt32	The smallest non-negative integer x such that 2x ≥ value. Exception: If value is 0, 0 is returned.

Log2LessOrEqual(UInt32)

Returns the largest non-negative integer x such that 2^x ≤ value.

Declaration

public static uint Log2LessOrEqual(uint value)

Parameters

Type	Name	Description
System.UInt32	value	The value.

Returns

Type	Description
System.UInt32	The largest non-negative integer x such that 2x ≤ value. Exception: If value is 0 then 0 is returned.

Magnitude(IList<Single>)

Calculates magnitude of the vector.

Declaration

public static float Magnitude(IList<float> vector)

Parameters

Type	Name	Description
IList<System.Single>	vector	The vector to calculate magnitude for.

Returns

Type	Description
System.Single	The magnitude.

MagnitudeSimd(Single[])

Calculates magnitude of the vector using SIMD (single instruction multiple data parallelism).

Declaration

public static float MagnitudeSimd(float[] vector)

Parameters

Type	Name	Description
System.Single[]	vector	The vector to calculate magnitude for.

Returns

Type	Description
System.Single	The magnitude.

NextPowerOf2(UInt32)

Returns the smallest power of two that is greater than the given value.

Declaration

public static uint NextPowerOf2(uint value)

Parameters

Type	Name	Description
System.UInt32	value	The value.

Returns

Type	Description
System.UInt32	The smallest power of two (2x) that is greater than value.

Remarks

For example, NextPowerOf2(7) is 8 and NextPowerOf2(8) is 16.

NextPowerOfTwo(Double)

Returns the next power of two that is larger than the specified number.

Declaration

public static double NextPowerOfTwo(double n)

Parameters

Type	Name	Description
System.Double	n	The specified number.

Returns

Type	Description
System.Double	The next power of two.

NextPowerOfTwo(Int32)

Returns the next power of two that is larger than the specified number.

Declaration

public static int NextPowerOfTwo(int n)

Parameters

Type	Name	Description
System.Int32	n	The specified number.

Returns

Type	Description
System.Int32	The next power of two.

NextPowerOfTwo(Int64)

Returns the next power of two that is larger than the specified number.

Declaration

public static long NextPowerOfTwo(long n)

Parameters

Type	Name	Description
System.Int64	n	The specified number.

Returns

Type	Description
System.Int64	The next power of two.

NextPowerOfTwo(Single)

Returns the next power of two that is larger than the specified number.

Declaration

public static float NextPowerOfTwo(float n)

Parameters

Type	Name	Description
System.Single	n	The specified number.

Returns

Type	Description
System.Single	The next power of two.

NormalizeSimd(Single[])

Calculates normalization of the vector using SIMD (single instruction multiple data).

Declaration

public static void NormalizeSimd(float[] vector)

Parameters

Type	Name	Description
System.Single[]	vector	The vector to calculate magnitude for.

Swap(ref Double, ref Double)

Swaps two double values.

Declaration

public static void Swap(ref double a, ref double b)

Parameters

Type	Name	Description
System.Double	a	The first value.
System.Double	b	The second value.

Swap(ref Single, ref Single)

Swaps two float values.

Declaration

public static void Swap(ref float a, ref float b)

Parameters

Type	Name	Description
System.Single	a	The first value.
System.Single	b	The second value.

Swap<T>(ref T, ref T)

Swaps the content of two variables.

Declaration

public static void Swap<T>(ref T obj1, ref T obj2)

Parameters

Type	Name	Description
T	obj1	First variable.
T	obj2	Second variable.

Type Parameters

Name	Description
T	The type of the objects.

ToBearing(Double)

Gets the compass-bearing in degree for the specified radian

Declaration

public static double ToBearing(double radian)

Parameters

Type	Name	Description
System.Double	radian	The radian, getting the bearing.

Returns

Type	Description
System.Double	The compass-bearing

ToDegrees(Double)

Converts an angle value from radians to degrees (double-precision).

Declaration

public static double ToDegrees(double radians)

Parameters

Type	Name	Description
System.Double	radians	The angle in radians.

Returns

Type	Description
System.Double	The angle in degrees.

ToDegrees(Single)

Converts an angle value from radians to degrees (single-precision).

Declaration

public static float ToDegrees(float radians)

Parameters

Type	Name	Description
System.Single	radians	The angle in radians.

Returns

Type	Description
System.Single	The angle in degrees.

ToRadians(Double)

Converts an angle value from degrees to radians (double-precision).

Declaration

public static double ToRadians(double degree)

Parameters

Type	Name	Description
System.Double	degree	The angle in degrees.

Returns

Type	Description
System.Double	The angle in radians.

ToRadians(Single)

Converts an angle value from degrees to radians (single-precision).

Declaration

public static float ToRadians(float degree)

Parameters

Type	Name	Description
System.Single	degree	The angle in degrees.

Returns

Type	Description
System.Single	The angle in radians.