Class MathHelper

Contains common mathematical functions and constants.

Inheritance

object

MathHelper

Inherited Members

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Namespace: OpenTK.Mathematics

Assembly: OpenTK.Mathematics.dll

Syntax

public static class MathHelper

Fields

E

Defines the value of E as a float.

Declaration

public const float E = 2.7182817

Field Value

Type	Description
float

Log10E

Defines the base-10 logarithm of E.

Declaration

public const float Log10E = 0.4342945

Field Value

Type	Description
float

Log2E

Defines the base-2 logarithm of E.

Declaration

public const float Log2E = 1.442695

Field Value

Type	Description
float

Pi

Defines the value of Pi as a float.

Declaration

public const float Pi = 3.1415927

Field Value

Type	Description
float

PiOver2

Defines the value of Pi divided by two as a float.

Declaration

public const float PiOver2 = 1.5707964

Field Value

Type	Description
float

PiOver3

Defines the value of Pi divided by three as a float.

Declaration

public const float PiOver3 = 1.0471976

Field Value

Type	Description
float

PiOver4

Defines the value of Pi divided by four as a float.

Declaration

public const float PiOver4 = 0.7853982

Field Value

Type	Description
float

PiOver6

Defines the value of Pi divided by six as a float.

Declaration

public const float PiOver6 = 0.5235988

Field Value

Type	Description
float

ThreePiOver2

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

Declaration

public const float ThreePiOver2 = 4.712389

Field Value

Type	Description
float

TwoPi

Defines the value of Pi multiplied by two as a float.

Declaration

public const float TwoPi = 6.2831855

Field Value

Type	Description
float

Methods

Abs(decimal)

Returns the absolute value of a decimal number.

Declaration

[Pure]
public static decimal Abs(decimal n)

Parameters

Type	Name	Description
decimal	n	A number that is greater than or equal to MinValue, but less than or equal to MaxValue.

Returns

Type	Description
decimal	A decimal number, x, such that 0 ≤ x ≤ MaxValue.

Abs(double)

Returns the absolute value of a double number.

Declaration

[Pure]
public static double Abs(double n)

Parameters

Type	Name	Description
double	n	A number that is greater than or equal to MinValue, but less than or equal to MaxValue.

Returns

Type	Description
double	A double number, x, such that 0 ≤ x ≤ MaxValue.

Abs(short)

Returns the absolute value of a short number.

Declaration

[Pure]
public static short Abs(short n)

Parameters

Type	Name	Description
short	n	A number that is greater than or equal to MinValue, but less than or equal to MaxValue.

Returns

Type	Description
short	A short number, x, such that 0 ≤ x ≤ MaxValue.

Abs(int)

Returns the absolute value of a int number.

Declaration

[Pure]
public static int Abs(int n)

Parameters

Type	Name	Description
int	n	A number that is greater than or equal to MinValue, but less than or equal to MaxValue.

Returns

Type	Description
int	A int number, x, such that 0 ≤ x ≤ MaxValue.

Abs(long)

Returns the absolute value of a long number.

Declaration

[Pure]
public static long Abs(long n)

Parameters

Type	Name	Description
long	n	A number that is greater than or equal to MinValue, but less than or equal to MaxValue.

Returns

Type	Description
long	A long number, x, such that 0 ≤ x ≤ MaxValue.

Abs(sbyte)

Returns the absolute value of a sbyte number.

Declaration

[Pure]
public static sbyte Abs(sbyte n)

Parameters

Type	Name	Description
sbyte	n	A number that is greater than or equal to MinValue, but less than or equal to MaxValue.

Returns

Type	Description
sbyte	A sbyte number, x, such that 0 ≤ x ≤ MaxValue.

Abs(float)

Returns the absolute value of a float number.

Declaration

[Pure]
public static float Abs(float n)

Parameters

Type	Name	Description
float	n	A number that is greater than or equal to MinValue, but less than or equal to MaxValue.

Returns

Type	Description
float	A float number, x, such that 0 ≤ x ≤ MaxValue.

Acos(double)

Returns the arc sine of the specified angle.

Declaration

[Pure]
public static double Acos(double radians)

Parameters

Type	Name	Description
double	radians	The specified angle.

Returns

Type	Description
double	Arc sine of the specified angle. If radians is equal to NaN, NegativeInfinity, or PositiveInfinity, this method returns NaN.

ApproximatelyEqual(float, float, int)

Approximates floating point equality with a maximum number of different bits. This is typically used in place of an epsilon comparison. see: https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/ see: https://stackoverflow.com/questions/3874627/floating-point-comparison-functions-for-c-sharp.

Declaration

[Pure]
public static bool ApproximatelyEqual(float a, float b, int maxDeltaBits)

Parameters

Type	Name	Description
float	a	the first value to compare.
float	b	the second value to compare.
int	maxDeltaBits	the number of floating point bits to check.

Returns

Type	Description
bool	true if the values are approximately equal; otherwise, false.

ApproximatelyEqualEpsilon(double, double, double)

Approximates double-precision floating point equality by an epsilon (maximum error) value. This method is designed as a "fits-all" solution and attempts to handle as many cases as possible.

Declaration

[Pure]
public static bool ApproximatelyEqualEpsilon(double a, double b, double epsilon)

Parameters

Type	Name	Description
double	a	The first float.
double	b	The second float.
double	epsilon	The maximum error between the two.

Returns

Type	Description
bool	true if the values are approximately equal within the error margin; otherwise, false.

ApproximatelyEqualEpsilon(float, float, float)

Approximates single-precision floating point equality by an epsilon (maximum error) value. This method is designed as a "fits-all" solution and attempts to handle as many cases as possible.

Declaration

[Pure]
public static bool ApproximatelyEqualEpsilon(float a, float b, float epsilon)

Parameters

Type	Name	Description
float	a	The first float.
float	b	The second float.
float	epsilon	The maximum error between the two.

Returns

Type	Description
bool	true if the values are approximately equal within the error margin; otherwise, false.

ApproximatelyEquivalent(double, double, double)

Approximates equivalence between two double-precision floating-point numbers on a direct human scale. It is important to note that this does not approximate equality - instead, it merely checks whether or not two numbers could be considered equivalent to each other within a certain tolerance. The tolerance is inclusive.

Declaration

[Pure]
public static bool ApproximatelyEquivalent(double a, double b, double tolerance)

Parameters

Type	Name	Description
double	a	The first value to compare.
double	b	The second value to compare.
double	tolerance	The tolerance within which the two values would be considered equivalent.

Returns

Type	Description
bool	Whether or not the values can be considered equivalent within the tolerance.

ApproximatelyEquivalent(float, float, float)

Approximates equivalence between two single-precision floating-point numbers on a direct human scale. It is important to note that this does not approximate equality - instead, it merely checks whether or not two numbers could be considered equivalent to each other within a certain tolerance. The tolerance is inclusive.

Declaration

[Pure]
public static bool ApproximatelyEquivalent(float a, float b, float tolerance)

Parameters

Type	Name	Description
float	a	The first value to compare.
float	b	The second value to compare.
float	tolerance	The tolerance within which the two values would be considered equivalent.

Returns

Type	Description
bool	Whether or not the values can be considered equivalent within the tolerance.

Asin(double)

Returns the arc sine of the specified angle.

Declaration

[Pure]
public static double Asin(double radians)

Parameters

Type	Name	Description
double	radians	The specified angle.

Returns

Type	Description
double	Arc sine of the specified angle. If radians is equal to NaN, NegativeInfinity, or PositiveInfinity, this method returns NaN.

Atan(double)

Returns the arc tangent of the specified angle.

Declaration

[Pure]
public static double Atan(double radians)

Parameters

Type	Name	Description
double	radians	The specified angle.

Returns

Type	Description
double	Arc tangent of the specified angle. If radians is equal to NaN, NegativeInfinity, or PositiveInfinity, this method returns NaN.

Atan2(double, double)

Returns the angle whose tangent is the quotient of two specified numbers.

Declaration

[Pure]
public static double Atan2(double y, double x)

Parameters

Type	Name	Description
double	y	The y coordinate of a point.
double	x	The x coordinate of a point.

Returns

Type	Description
double	An angle, θ, measured in radians, such that -π ≤ θ ≤ π, and tan(θ) = y / x, where (x, y) is a point in the Cartesian plane.

BigMul(int, int)

Produces the full product of two 32-bit numbers.

Declaration

[Pure]
public static long BigMul(int a, int b)

Parameters

Type	Name	Description
int	a	The first number to multiply.
int	b	The second number to multiply.

Returns

Type	Description
long	The number containing the product of the specified numbers.

BinomialCoefficient(int, int)

Calculates the binomial coefficient n above k.

Declaration

[Pure]
public static long BinomialCoefficient(int n, int k)

Parameters

Type	Name	Description
int	n	The n.
int	k	The k.

Returns

Type	Description
long	n! / (k! * (n - k)!).

Ceiling(decimal)

Returns the smallest integral value greater than or equal to the specified number.

Declaration

[Pure]
public static decimal Ceiling(decimal n)

Parameters

Type	Name	Description
decimal	n	A decimal number.

Returns

Type	Description
decimal	The smallest integral value that is greater than or equal to n. Note that this method returns a Decimal instead of an integral type.

Ceiling(double)

Returns the smallest integral value greater than or equal to the specified number.

Declaration

[Pure]
public static double Ceiling(double n)

Parameters

Type	Name	Description
double	n	A double-precision floating-point number.

Returns

Type	Description
double	The smallest integral value that is greater than or equal to n. If n is equal to NaN, NegativeInfinity, or PositiveInfinity, that value is returned. Note that this method returns a Double instead of an integral type.

Clamp(double, double, double)

Clamps a number between a minimum and a maximum.

Declaration

[Pure]
public static double Clamp(double n, double min, double max)

Parameters

Type	Name	Description
double	n	The number to clamp.
double	min	The minimum allowed value.
double	max	The maximum allowed value.

Returns

Type	Description
double	min, if n is lower than min; max, if n is higher than max; n otherwise.

Clamp(int, int, int)

Clamps a number between a minimum and a maximum.

Declaration

[Pure]
public static int Clamp(int n, int min, int max)

Parameters

Type	Name	Description
int	n	The number to clamp.
int	min	The minimum allowed value.
int	max	The maximum allowed value.

Returns

Type	Description
int	min, if n is lower than min; max, if n is higher than max; n otherwise.

Clamp(float, float, float)

Clamps a number between a minimum and a maximum.

Declaration

[Pure]
public static float Clamp(float n, float min, float max)

Parameters

Type	Name	Description
float	n	The number to clamp.
float	min	The minimum allowed value.
float	max	The maximum allowed value.

Returns

Type	Description
float	min, if n is lower than min; max, if n is higher than max; n otherwise.

ClampAngle(double)

Clamps an angle to the range [0, 360).

Declaration

public static double ClampAngle(double angle)

Parameters

Type	Name	Description
double	angle	The angle to clamp in degrees.

Returns

Type	Description
double	The clamped angle in the range [0, 360).

ClampAngle(float)

Clamps an angle to the range [0, 360).

Declaration

public static float ClampAngle(float angle)

Parameters

Type	Name	Description
float	angle	The angle to clamp in degrees.

Returns

Type	Description
float	The clamped angle in the range [0, 360).

ClampRadians(double)

Clamps an angle to the range [0, 2π).

Declaration

public static double ClampRadians(double angle)

Parameters

Type	Name	Description
double	angle	The angle to clamp in radians.

Returns

Type	Description
double	The clamped angle in the range [0, 2π).

ClampRadians(float)

Clamps an angle to the range [0, 2π).

Declaration

public static float ClampRadians(float angle)

Parameters

Type	Name	Description
float	angle	The angle to clamp in radians.

Returns

Type	Description
float	The clamped angle in the range [0, 2π).

Cos(double)

Returns the cosine of the specified angle.

Declaration

[Pure]
public static double Cos(double radians)

Parameters

Type	Name	Description
double	radians	The specified angle.

Returns

Type	Description
double	Cosine of the angle. If radians is equal to NaN, NegativeInfinity, or PositiveInfinity, this method returns NaN.

Cosh(double)

Returns the hyperbolic cosine of the specified angle.

Declaration

[Pure]
public static double Cosh(double radians)

Parameters

Type	Name	Description
double	radians	The specified angle.

Returns

Type	Description
double	Hyperbolic cosine of the specified angle. If radians is equal to NaN, NegativeInfinity, or PositiveInfinity, this method returns NaN.

DegreesToRadians(double)

Convert degrees to radians.

Declaration

[Pure]
public static double DegreesToRadians(double degrees)

Parameters

Type	Name	Description
double	degrees	An angle in degrees.

Returns

Type	Description
double	The angle expressed in radians.

DegreesToRadians(float)

Convert degrees to radians.

Declaration

[Pure]
public static float DegreesToRadians(float degrees)

Parameters

Type	Name	Description
float	degrees	An angle in degrees.

Returns

Type	Description
float	The angle expressed in radians.

DivRem(int, int, out int)

Calculates the quotient of two integers and also returns the remainder in an output parameter.

Declaration

[Pure]
public static int DivRem(int a, int b, out int result)

Parameters

Type	Name	Description
int	a	The dividend.
int	b	The divisor.
int	result	The remainder.

Returns

Type	Description
int	The quotient of the specified numbers.

Exceptions

Type	Condition
DivideByZeroException	b is zero.

DivRem(long, long, out long)

Calculates the quotient of two longs and also returns the remainder in an output parameter.

Declaration

[Pure]
public static long DivRem(long a, long b, out long result)

Parameters

Type	Name	Description
long	a	The dividend.
long	b	The divisor.
long	result	The remainder.

Returns

Type	Description
long	The quotient of the specified numbers.

Exceptions

Type	Condition
DivideByZeroException	b is zero.

Exp(double)

Returns e raised to the specified power.

Declaration

[Pure]
public static double Exp(double n)

Parameters

Type	Name	Description
double	n	The specified power.

Returns

Type	Description
double	The number e raised to the power n. If n equals NaN or PositiveInfinity, that value is returned. If n equals NegativeInfinity, 0 is returned.

Factorial(int)

Calculates the factorial of a given natural number.

Declaration

[Pure]
public static long Factorial(int n)

Parameters

Type	Name	Description
int	n	The number.

Returns

Type	Description
long	The factorial of n.

Floor(decimal)

Returns the largest integral value less than or equal to the specified number.

Declaration

[Pure]
public static decimal Floor(decimal n)

Parameters

Type	Name	Description
decimal	n	A decimal number.

Returns

Type	Description
decimal	Returns the largest integral value less than or equal to the specified decimal number.

Floor(double)

Returns the largest integral value less than or equal to the specified number.

Declaration

[Pure]
public static double Floor(double n)

Parameters

Type	Name	Description
double	n	A double-precision floating-point number.

Returns

Type	Description
double	Returns the largest integral value less than or equal to the specified double-precision floating-point number.

IEEERemainder(double, double)

Returns the remainder resulting from the division of a specified number by another specified number.

Declaration

[Pure]
public static double IEEERemainder(double a, double b)

Parameters

Type	Name	Description
double	a	A dividend.
double	b	A divisor.

Returns

Type	Description
double	A number equal to a - (b Q), where Q is the quotient of a / b rounded to the nearest integer (if a / b falls halfway between two integers, the even integer is returned). If a - (b Q) is zero, the value +0 is returned if a is positive, or -0 if a is negative. If b = 0, NaN is returned.

InverseSqrtFast(double)

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

Declaration

[Pure]
public static double InverseSqrtFast(double x)

Parameters

Type	Name	Description
double	x	A number.

Returns

Type	Description
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/. double magic number from: https://cs.uwaterloo.ca/~m32rober/rsqrt.pdf chapter 4.8.

InverseSqrtFast(float)

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

Declaration

[Pure]
public static float InverseSqrtFast(float x)

Parameters

Type	Name	Description
float	x	A number.

Returns

Type	Description
float	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/.

Lerp(double, double, double)

Linearly interpolates between a and b by t.

Declaration

[Pure]
public static double Lerp(double start, double end, double t)

Parameters

Type	Name	Description
double	start	Start value.
double	end	End value.
double	t	Value of the interpollation between a and b. Clamped to [0, 1].

Returns

Type	Description
double	The interpolated result between the a and b values.

Lerp(float, float, float)

Linearly interpolates between a and b by t.

Declaration

[Pure]
public static float Lerp(float start, float end, float t)

Parameters

Type	Name	Description
float	start	Start value.
float	end	End value.
float	t	Value of the interpollation between a and b. Clamped to [0, 1].

Returns

Type	Description
float	The interpolated result between the a and b values.

Log(double, double)

Returns the logarithm of a specified number in a specified base.

Declaration

[Pure]
public static double Log(double n, double newBase)

Parameters

Type	Name	Description
double	n	The specified number.
double	newBase	The specified base.

Returns

Type	Description
double	The base newBase logarithm of n.

Log(double)

Returns the natural (base e) logarithm of a specified number.

Declaration

[Pure]
public static double Log(double n)

Parameters

Type	Name	Description
double	n	A number whose logarithm is to be found.

Returns

Type	Description
double	The natural logarithm of n.

Log10(double)

Returns the base 10 logarithm of a specified number.

Declaration

[Pure]
public static double Log10(double n)

Parameters

Type	Name	Description
double	n	The specified number.

Returns

Type	Description
double	The base 10 log of n.

Log2(double)

Returns the base 2 logarithm of a specified number.

Declaration

[Pure]
public static double Log2(double n)

Parameters

Type	Name	Description
double	n	The specified number.

Returns

Type	Description
double	The base 2 log of n.

Remarks

This one will be implemented by System.Math from .netcore 3.0 and onwards.

MapRange(double, double, double, double, double)

Scales the specified number linearly between a minimum and a maximum.

Declaration

[Pure]
public static double MapRange(double value, double valueMin, double valueMax, double resultMin, double resultMax)

Parameters

Type	Name	Description
double	value	The number to scale.
double	valueMin	The minimum expected number (inclusive).
double	valueMax	The maximum expected number (inclusive).
double	resultMin	The minimum output number (inclusive).
double	resultMax	The maximum output number (inclusive).

Returns

Type	Description
double	The number, scaled linearly between min and max.

Remarks

If the value range is zero, this function will throw a divide by zero exception.

MapRange(int, int, int, int, int)

Scales the specified number linearly between a minimum and a maximum.

Declaration

[Pure]
public static int MapRange(int value, int valueMin, int valueMax, int resultMin, int resultMax)

Parameters

Type	Name	Description
int	value	The number to scale.
int	valueMin	The minimum expected number (inclusive).
int	valueMax	The maximum expected number (inclusive).
int	resultMin	The minimum output number (inclusive).
int	resultMax	The maximum output number (inclusive).

Returns

Type	Description
int	The number, scaled linearly between min and max.

Remarks

If the value range is zero, this function will throw a divide by zero exception.

MapRange(float, float, float, float, float)

Scales the specified number linearly between a minimum and a maximum.

Declaration

[Pure]
public static float MapRange(float value, float valueMin, float valueMax, float resultMin, float resultMax)

Parameters

Type	Name	Description
float	value	The number to scale.
float	valueMin	The minimum expected number (inclusive).
float	valueMax	The maximum expected number (inclusive).
float	resultMin	The minimum output number (inclusive).
float	resultMax	The maximum output number (inclusive).

Returns

Type	Description
float	The number, scaled linearly between min and max.

Remarks

If the value range is zero, this function will throw a divide by zero exception.

Max(byte, byte)

Returns the larger of two bytes.

Declaration

[Pure]
public static byte Max(byte a, byte b)

Parameters

Type	Name	Description
byte	a	The first of two bytes to compare.
byte	b	The second of two bytes to compare.

Returns

Type	Description
byte	Parameter a or b, whichever is larger.

Max(decimal, decimal)

Returns the larger of two decimals.

Declaration

[Pure]
public static decimal Max(decimal a, decimal b)

Parameters

Type	Name	Description
decimal	a	The first of two decimals to compare.
decimal	b	The second of two decimals to compare.

Returns

Type	Description
decimal	Parameter a or b, whichever is larger.

Max(short, short)

Returns the larger of two shorts.

Declaration

[Pure]
public static short Max(short a, short b)

Parameters

Type	Name	Description
short	a	The first of two shorts to compare.
short	b	The second of two shorts to compare.

Returns

Type	Description
short	Parameter a or b, whichever is larger.

Max(int, int)

Returns the larger of two ints.

Declaration

[Pure]
public static int Max(int a, int b)

Parameters

Type	Name	Description
int	a	The first of two ints to compare.
int	b	The second of two ints to compare.

Returns

Type	Description
int	Parameter a or b, whichever is larger.

Max(long, long)

Returns the larger of two longs.

Declaration

[Pure]
public static long Max(long a, long b)

Parameters

Type	Name	Description
long	a	The first of two longs to compare.
long	b	The second of two longs to compare.

Returns

Type	Description
long	Parameter a or b, whichever is larger.

Max(sbyte, sbyte)

Returns the larger of two sbytes.

Declaration

[Pure]
public static sbyte Max(sbyte a, sbyte b)

Parameters

Type	Name	Description
sbyte	a	The first of two sbytes to compare.
sbyte	b	The second of two sbytes to compare.

Returns

Type	Description
sbyte	Parameter a or b, whichever is larger.

Max(float, float)

Returns the larger of two floats.

Declaration

[Pure]
public static float Max(float a, float b)

Parameters

Type	Name	Description
float	a	The first of two floats to compare.
float	b	The second of two floats to compare.

Returns

Type	Description
float	Parameter a or b, whichever is larger.

Max(ushort, ushort)

Returns the larger of two ushorts.

Declaration

[Pure]
public static ushort Max(ushort a, ushort b)

Parameters

Type	Name	Description
ushort	a	The first of two ushorts to compare.
ushort	b	The second of two ushorts to compare.

Returns

Type	Description
ushort	Parameter a or b, whichever is larger.

Max(uint, uint)

Returns the larger of two uints.

Declaration

[Pure]
public static uint Max(uint a, uint b)

Parameters

Type	Name	Description
uint	a	The first of two uints to compare.
uint	b	The second of two uints to compare.

Returns

Type	Description
uint	Parameter a or b, whichever is larger.

Max(ulong, ulong)

Returns the larger of two ulongs.

Declaration

[Pure]
public static ulong Max(ulong a, ulong b)

Parameters

Type	Name	Description
ulong	a	The first of two ulongs to compare.
ulong	b	The second of two ulongs to compare.

Returns

Type	Description
ulong	Parameter a or b, whichever is larger.

Min(byte, byte)

Returns the smaller of two bytes.

Declaration

[Pure]
public static byte Min(byte a, byte b)

Parameters

Type	Name	Description
byte	a	The first of two bytes to compare.
byte	b	The second of two bytes to compare.

Returns

Type	Description
byte	Parameter a or b, whichever is smaller.

Min(decimal, decimal)

Returns the smaller of two decimals.

Declaration

[Pure]
public static decimal Min(decimal a, decimal b)

Parameters

Type	Name	Description
decimal	a	The first of two decimals to compare.
decimal	b	The second of two decimals to compare.

Returns

Type	Description
decimal	Parameter a or b, whichever is smaller.

Min(double, double)

Returns the smaller of two floats.

Declaration

[Pure]
public static double Min(double a, double b)

Parameters

Type	Name	Description
double	a	The first of two floats to compare.
double	b	The second of two floats to compare.

Returns

Type	Description
double	Parameter a or b, whichever is smaller.

Min(short, short)

Returns the smaller of two shorts.

Declaration

[Pure]
public static short Min(short a, short b)

Parameters

Type	Name	Description
short	a	The first of two shorts to compare.
short	b	The second of two shorts to compare.

Returns

Type	Description
short	Parameter a or b, whichever is smaller.

Min(int, int)

Returns the smaller of two ints.

Declaration

[Pure]
public static int Min(int a, int b)

Parameters

Type	Name	Description
int	a	The first of two ints to compare.
int	b	The second of two ints to compare.

Returns

Type	Description
int	Parameter a or b, whichever is smaller.

Min(long, long)

Returns the smaller of two longs.

Declaration

[Pure]
public static long Min(long a, long b)

Parameters

Type	Name	Description
long	a	The first of two longs to compare.
long	b	The second of two longs to compare.

Returns

Type	Description
long	Parameter a or b, whichever is smaller.

Min(sbyte, sbyte)

Returns the smaller of two sbytes.

Declaration

[Pure]
public static sbyte Min(sbyte a, sbyte b)

Parameters

Type	Name	Description
sbyte	a	The first of two sbytes to compare.
sbyte	b	The second of two sbytes to compare.

Returns

Type	Description
sbyte	Parameter a or b, whichever is smaller.

Min(float, float)

Returns the smaller of two floats.

Declaration

[Pure]
public static float Min(float a, float b)

Parameters

Type	Name	Description
float	a	The first of two floats to compare.
float	b	The second of two floats to compare.

Returns

Type	Description
float	Parameter a or b, whichever is smaller.

Min(ushort, ushort)

Returns the smaller of two ushorts.

Declaration

[Pure]
public static ushort Min(ushort a, ushort b)

Parameters

Type	Name	Description
ushort	a	The first of two ushorts to compare.
ushort	b	The second of two ushorts to compare.

Returns

Type	Description
ushort	Parameter a or b, whichever is smaller.

Min(uint, uint)

Returns the smaller of two uints.

Declaration

[Pure]
public static uint Min(uint a, uint b)

Parameters

Type	Name	Description
uint	a	The first of two uints to compare.
uint	b	The second of two uints to compare.

Returns

Type	Description
uint	Parameter a or b, whichever is smaller.

Min(ulong, ulong)

Returns the smaller of two ulongs.

Declaration

[Pure]
public static ulong Min(ulong a, ulong b)

Parameters

Type	Name	Description
ulong	a	The first of two ulongs to compare.
ulong	b	The second of two ulongs to compare.

Returns

Type	Description
ulong	Parameter a or b, whichever is smaller.

NextPowerOfTwo(double)

Returns the next power of two that is greater than or equal to the specified number.

Declaration

[Pure]
public static double NextPowerOfTwo(double n)

Parameters

Type	Name	Description
double	n	The specified number.

Returns

Type	Description
double	The next power of two.

NextPowerOfTwo(int)

Returns the next power of two that is greater than or equal to the specified number.

Declaration

[Pure]
public static int NextPowerOfTwo(int n)

Parameters

Type	Name	Description
int	n	The specified number.

Returns

Type	Description
int	The next power of two.

NextPowerOfTwo(long)

Returns the next power of two that is greater than or equal to the specified number.

Declaration

[Pure]
public static long NextPowerOfTwo(long n)

Parameters

Type	Name	Description
long	n	The specified number.

Returns

Type	Description
long	The next power of two.

NextPowerOfTwo(float)

Returns the next power of two that is greater than or equal to the specified number.

Declaration

[Pure]
public static float NextPowerOfTwo(float n)

Parameters

Type	Name	Description
float	n	The specified number.

Returns

Type	Description
float	The next power of two.

NormalizeAngle(double)

Normalizes an angle to the range (-180, 180].

Declaration

public static double NormalizeAngle(double angle)

Parameters

Type	Name	Description
double	angle	The angle in degrees to normalize.

Returns

Type	Description
double	The normalized angle in the range (-180, 180].

NormalizeAngle(float)

Normalizes an angle to the range (-180, 180].

Declaration

public static float NormalizeAngle(float angle)

Parameters

Type	Name	Description
float	angle	The angle in degrees to normalize.

Returns

Type	Description
float	The normalized angle in the range (-180, 180].

NormalizeRadians(double)

Normalizes an angle to the range (-π, π].

Declaration

public static double NormalizeRadians(double angle)

Parameters

Type	Name	Description
double	angle	The angle in radians to normalize.

Returns

Type	Description
double	The normalized angle in the range (-π, π].

NormalizeRadians(float)

Normalizes an angle to the range (-π, π].

Declaration

public static float NormalizeRadians(float angle)

Parameters

Type	Name	Description
float	angle	The angle in radians to normalize.

Returns

Type	Description
float	The normalized angle in the range (-π, π].

Pow(double, double)

Returns a specified number raised to the specified power.

Declaration

[Pure]
public static double Pow(double x, double y)

Parameters

Type	Name	Description
double	x	A double-precision floating-point number to be raised to a power.
double	y	A double-precision floating-point number that specifies a power.

Returns

Type	Description
double	The number x raised to the power y.

RadiansToDegrees(double)

Convert radians to degrees.

Declaration

[Pure]
public static double RadiansToDegrees(double radians)

Parameters

Type	Name	Description
double	radians	An angle in radians.

Returns

Type	Description
double	The angle expressed in degrees.

RadiansToDegrees(float)

Convert radians to degrees.

Declaration

[Pure]
public static float RadiansToDegrees(float radians)

Parameters

Type	Name	Description
float	radians	An angle in radians.

Returns

Type	Description
float	The angle expressed in degrees.

Round(decimal, int, MidpointRounding)

Rounds a decimal value to a specified number of fractional digits, and uses the specified rounding convention for midpoint values.

Declaration

[Pure]
public static decimal Round(decimal d, int digits, MidpointRounding mode)

Parameters

Type	Name	Description
decimal	d	A decimal number to be rounded.
int	digits	The number of decimal places in the return value.
MidpointRounding	mode	Specification for how to round d if it is midway between two other numbers.

Returns

Type	Description
decimal	The number nearest to d that contains a number of fractional digits equal to digits. If d has fewer fractional digits than digits, d is returned unchanged.

Exceptions

Type	Condition
ArgumentOutOfRangeException	digits is less than 0 or greater than 28.
ArgumentException	mode is not a valid value of MidpointRounding.
OverflowException	The result is outside the range of a Decimal.

Round(decimal, int)

Rounds a decimal value to a specified number of fractional digits, and rounds midpoint values to the nearest even number.

Declaration

[Pure]
public static decimal Round(decimal d, int digits)

Parameters

Type	Name	Description
decimal	d	A decimal number to be rounded.
int	digits	The number of fractional digits in the return value.

Returns

Type	Description
decimal	The number nearest to d that contains a number of fractional digits equal to digits.

Exceptions

Type	Condition
ArgumentOutOfRangeException	digits is less than 0 or greater than 15.
OverflowException	The result is outside the range of a Decimal.

Round(decimal, MidpointRounding)

Rounds a decimal value to the nearest integer, and uses the specified rounding convention for midpoint values.

Declaration

[Pure]
public static decimal Round(decimal d, MidpointRounding mode)

Parameters

Type	Name	Description
decimal	d	A decimal number to be rounded.
MidpointRounding	mode	Specification for how to round d if it is midway between two other numbers.

Returns

Type	Description
decimal	The integer nearest d. If d is halfway between two numbers, one of which is even and the other odd, then mode determines which of the two is returned. Note that this method returns a Decimal instead of an integral type.

Exceptions

Type	Condition
ArgumentException	mode is not a valid value of MidpointRounding.
OverflowException	The result is outside the range of a Decimal.

Round(decimal)

Rounds a decimal value to the nearest integral value, and rounds midpoint values to the nearest even number.

Declaration

[Pure]
public static decimal Round(decimal d)

Parameters

Type	Name	Description
decimal	d	A decimal number to be rounded.

Returns

Type	Description
decimal	The integer nearest the d parameter. If the fractional component of d is halfway between two integers, one of which is even and the other odd, the even number is returned. Note that this method returns a Decimal instead of an integral type.

Exceptions

Type	Condition
OverflowException	The result is outside the range of a Decimal.

Round(double, int, MidpointRounding)

Rounds a double-precision floating-point value to a specified number of fractional digits, and uses the specified rounding convention for midpoint values.

Declaration

[Pure]
public static double Round(double d, int digits, MidpointRounding mode)

Parameters

Type	Name	Description
double	d	A double-precision floating-point number to be rounded.
int	digits	The number of fractional digits in the return value.
MidpointRounding	mode	Specification for how to round d if it is midway between two other numbers.

Returns

Type	Description
double	The number nearest to d that has a number of fractional digits equal to digits. If d has fewer fractional digits than digits, d is returned unchanged.

Exceptions

Type	Condition
ArgumentOutOfRangeException	digits is less than 0 or greater than 15.
ArgumentException	mode is not a valid value of MidpointRounding.

Round(double, int)

Rounds a double-precision floating-point value to a specified number of fractional digits, and rounds midpoint values to the nearest even number.

Declaration

[Pure]
public static double Round(double d, int digits)

Parameters

Type	Name	Description
double	d	A double-precision floating-point number to be rounded.
int	digits	The number of fractional digits in the return value.

Returns

Type	Description
double	The number nearest to value that contains a number of fractional digits equal to digits.

Exceptions

Type	Condition
ArgumentOutOfRangeException	digits is less than 0 or greater than 15.

Round(double, MidpointRounding)

Rounds a double-precision floating-point value to the nearest integer, and uses the specified rounding convention for midpoint values.

Declaration

[Pure]
public static double Round(double d, MidpointRounding mode)

Parameters

Type	Name	Description
double	d	A double-precision floating-point number to be rounded.
MidpointRounding	mode	Specification for how to round d if it is midway between two other numbers.

Returns

Type	Description
double	The integer nearest d. If d is halfway between two integers, one of which is even and the other odd, then mode determines which of the two is returned. Note that this method returns a Double instead of an integral type.

Exceptions

Type	Condition
ArgumentException	mode is not a valid value of MidpointRounding.

Round(double)

Rounds a double-precision floating-point value to the nearest integral value, and rounds midpoint values to the nearest even number.

Declaration

[Pure]
public static double Round(double d)

Parameters

Type	Name	Description
double	d	A double-precision floating-point number to be rounded.

Returns

Type	Description
double	The integer nearest d. If the fractional component of d is halfway between two integers, one of which is even and the other odd, then the even number is returned. Note that this method returns a Double instead of an integral type.

Sign(decimal)

Returns an integer that indicates the sign of a decimal.

Declaration

[Pure]
public static int Sign(decimal d)

Parameters

Type	Name	Description
decimal	d	A signed number.

Returns

Type	Description
int	If d ≤ -1 returns -1, if 1 ≤ d returns 1 and if d = 0 returns 0.

Sign(double)

Returns an integer that indicates the sign of a double.

Declaration

[Pure]
public static int Sign(double d)

Parameters

Type	Name	Description
double	d	A signed number.

Returns

Type	Description
int	If d ≤ -1 returns -1, if 1 ≤ d returns 1 and if d = 0 returns 0.

Sign(short)

Returns an integer that indicates the sign of a short.

Declaration

[Pure]
public static int Sign(short d)

Parameters

Type	Name	Description
short	d	A signed number.

Returns

Type	Description
int	If d ≤ -1 returns -1, if 1 ≤ d returns 1 and if d = 0 returns 0.

Sign(int)

Returns an integer that indicates the sign of a int.

Declaration

[Pure]
public static int Sign(int d)

Parameters

Type	Name	Description
int	d	A signed number.

Returns

Type	Description
int	If d ≤ -1 returns -1, if 1 ≤ d returns 1 and if d = 0 returns 0.

Sign(long)

Returns an integer that indicates the sign of a long.

Declaration

[Pure]
public static int Sign(long d)

Parameters

Type	Name	Description
long	d	A signed number.

Returns

Type	Description
int	If d ≤ -1 returns -1, if 1 ≤ d returns 1 and if d = 0 returns 0.

Sign(sbyte)

Returns an integer that indicates the sign of a sbyte.

Declaration

[Pure]
public static int Sign(sbyte d)

Parameters

Type	Name	Description
sbyte	d	A signed number.

Returns

Type	Description
int	If d ≤ -1 returns -1, if 1 ≤ d returns 1 and if d = 0 returns 0.

Sign(float)

Returns an integer that indicates the sign of a float.

Declaration

[Pure]
public static int Sign(float d)

Parameters

Type	Name	Description
float	d	A signed number.

Returns

Type	Description
int	If d ≤ -1 returns -1, if 1 ≤ d returns 1 and if d = 0 returns 0.

Sin(double)

Returns the sine of the specified angle.

Declaration

[Pure]
public static double Sin(double radians)

Parameters

Type	Name	Description
double	radians	The specified angle.

Returns

Type	Description
double	Sine of the angle. If radians is equal to NaN, NegativeInfinity, or PositiveInfinity, this method returns NaN.

Sinh(double)

Returns the hyperbolic sine of the specified angle.

Declaration

[Pure]
public static double Sinh(double radians)

Parameters

Type	Name	Description
double	radians	The specified angle.

Returns

Type	Description
double	Hyperbolic sine of the specified angle. If radians is equal to NaN, NegativeInfinity, or PositiveInfinity, this method returns NaN.

Sqrt(double)

Returns the square root of a specified number.

Declaration

[Pure]
public static double Sqrt(double n)

Parameters

Type	Name	Description
double	n	The number whose square root is to be found.

Returns

Type	Description
double	The positive square root of n.

Swap<T>(ref T, ref T)

Swaps two values.

Declaration

public static void Swap<T>(ref T a, ref T b)

Parameters

Type	Name	Description
T	a	The first value.
T	b	The second value.

Type Parameters

Name	Description
T	The type of the values to swap.

Tan(double)

Returns the tangent of the specified angle.

Declaration

[Pure]
public static double Tan(double radians)

Parameters

Type	Name	Description
double	radians	The specified angle.

Returns

Type	Description
double	Tangent of the specified angle. If radians is equal to NaN, NegativeInfinity, or PositiveInfinity, this method returns NaN.

Tanh(double)

Returns the hyperbolic tangent of the specified angle.

Declaration

[Pure]
public static double Tanh(double radians)

Parameters

Type	Name	Description
double	radians	The specified angle.

Returns

Type	Description
double	Hyperbolic tangent of the specified angle. If radians is equal to NaN, NegativeInfinity, or PositiveInfinity, this method returns NaN.

Truncate(decimal)

Calculates the integral part of a specified decimal number.

Declaration

[Pure]
public static decimal Truncate(decimal d)

Parameters

Type	Name	Description
decimal	d	A number to truncate.

Returns

Type	Description
decimal	The integral part of d; that is, the number that remains after any fractional digits have been discarded.

Truncate(double)

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

Declaration

[Pure]
public static double Truncate(double d)

Parameters

Type	Name	Description
double	d	A number to truncate.

Returns

Type	Description
double	The integral part of d; that is, the number that remains after any fractional digits have been discarded, or one of the values listed in the following table.