Class NumberUtil

Provides a comprehensive set of deterministic numeric utility methods covering clamping, range checks, floating-point comparisons, rounding, interpolation, modular arithmetic, safe division, power-of-two alignment, angle operations, and common math helpers across all standard numeric types.

Inheritance

object

NumberUtil

Inherited Members

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Namespace: Scylla.Core.Util

Assembly: ScyllaCore.dll

Syntax

public static class NumberUtil

Remarks

Float-based methods delegate to UnityEngine.Mathf where available, while double and decimal overloads use Math directly. This ensures identical results to Unity's built-in math on float inputs.

All methods are deterministic and contain no randomness. For random number generation see RandomUtil.

Floating-point equality comparisons use Approximately(float, float, float) rather than == to avoid false negatives due to floating-point rounding. The default tolerance constants are EPSILON (1e-6f) for float and EPSILON_D (1e-12) for double.

Fields

EPSILON

Default tolerance used by float comparison helpers such as Approximately(float, float, float) and IsNearlyZero(float, float). Equal to 1e-6.

Declaration

public const float EPSILON = 1E-06

Field Value

Type	Description
float

Remarks

This value is significantly tighter than UnityEngine.Mathf.Epsilon (which is the smallest representable positive float) but loose enough to absorb typical single-precision rounding errors in game math. Increase the tolerance when comparing values that have accumulated over many arithmetic operations.

EPSILON_D

Default tolerance used by double comparison helpers such as Approximately(double, double, double) and IsNearlyZero(double, double). Equal to 1e-12.

Declaration

public const double EPSILON_D = 1E-12

Field Value

Type	Description
double

Remarks

This tolerance is appropriate for double-precision values where roughly 12 significant decimal digits of precision are expected. Tighten or loosen it per-call when the algorithm demands higher or lower accuracy.

Methods

AbsDiff(int, int)

Returns the absolute (unsigned) difference between two integers - equivalent to Math.Abs(a - b) but without the risk of an intermediate overflow when a and b have opposite signs near the bounds of int.

Declaration

public static int AbsDiff(int a, int b)

Parameters

Type	Name	Description
int	a	The first integer value.
int	b	The second integer value.

Returns

Type	Description
int	The absolute difference between the two integers.

AbsDiff(long, long)

Calculates the absolute difference between two long integers.

Declaration

public static long AbsDiff(long a, long b)

Parameters

Type	Name	Description
long	a	The first long integer.
long	b	The second long integer.

Returns

Type	Description
long	The absolute difference between the two long integers.

AbsDiff(uint, uint)

Calculates the absolute difference between two unsigned integers.

Declaration

public static uint AbsDiff(uint a, uint b)

Parameters

Type	Name	Description
uint	a	The first unsigned integer.
uint	b	The second unsigned integer.

Returns

Type	Description
uint	The absolute difference between the two values.

AbsDiff(ulong, ulong)

Calculates the absolute difference between two unsigned long integers.

Declaration

public static ulong AbsDiff(ulong a, ulong b)

Parameters

Type	Name	Description
ulong	a	The first unsigned long integer.
ulong	b	The second unsigned long integer.

Returns

Type	Description
ulong	The absolute difference between the two values.

AlignDown(uint, uint)

Aligns the given value down to the nearest multiple of the specified alignment.

Declaration

public static uint AlignDown(uint value, uint alignment)

Parameters

Type	Name	Description
uint	value	The value to be aligned down.
uint	alignment	The alignment value, which must be greater than 0.

Returns

Type	Description
uint	The largest multiple of the alignment that is less than or equal to the value.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown if the alignment is 0.

AlignDown(ulong, ulong)

Aligns a value down to the nearest multiple of a specified alignment.

Declaration

public static ulong AlignDown(ulong value, ulong alignment)

Parameters

Type	Name	Description
ulong	value	The value to align down.
ulong	alignment	The alignment value, which must be greater than 0.

Returns

Type	Description
ulong	The largest multiple of the alignment less than or equal to the original value.

AlignUp(uint, uint)

Aligns a value up to the nearest multiple of the specified alignment.

Declaration

public static uint AlignUp(uint value, uint alignment)

Parameters

Type	Name	Description
uint	value	The value to align.
uint	alignment	The alignment boundary to which the value will be aligned.

Returns

Type	Description
uint	The value aligned to the nearest multiple of the alignment.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown if alignment is 0.
OverflowException	Thrown if the aligned value would overflow.

AlignUp(ulong, ulong)

Aligns a value up to the nearest multiple of the specified alignment.

Declaration

public static ulong AlignUp(ulong value, ulong alignment)

Parameters

Type	Name	Description
ulong	value	The value to align.
ulong	alignment	The alignment boundary. Must be greater than 0.

Returns

Type	Description
ulong	The aligned value, which is the smallest multiple of the alignment greater than or equal to the input value.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown if alignment is 0.
OverflowException	Thrown if the aligned value exceeds the range of ulong.

Approximately(double, double, double)

Determines whether two double precision floating-point numbers are approximately equal within a specified tolerance.

Declaration

public static bool Approximately(double a, double b, double epsilon = 1E-12)

Parameters

Type	Name	Description
double	a	The first double value to compare.
double	b	The second double value to compare.
double	epsilon	The maximum difference between the two values for them to be considered approximately equal. Must be non-negative.

Returns

Type	Description
bool	True if the absolute difference between a and b is less than or equal to epsilon; otherwise, false.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown if epsilon is negative.

Approximately(float, float, float)

Determines whether two floating-point numbers are approximately equal, within a specified tolerance.

Declaration

public static bool Approximately(float a, float b, float epsilon = 1E-06)

Parameters

Type	Name	Description
float	a	The first floating-point number to compare.
float	b	The second floating-point number to compare.
float	epsilon	The maximum difference allowed for the two numbers to be considered equal. Defaults to EPSILON.

Returns

Type	Description
bool	true if the absolute difference between a and b is less than or equal to epsilon; otherwise, false.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown if epsilon is negative.

CeilToInt(double)

Rounds the specified floating-point value up to the nearest higher integer.

Declaration

public static int CeilToInt(double value)

Parameters

Type	Name	Description
double	value	The floating-point value to ceil.

Returns

Type	Description
int	The smallest integer value greater than or equal to the specified value.

CeilToInt(float)

Rounds the specified floating-point value to the smallest integer greater than or equal to it.

Declaration

public static int CeilToInt(float value)

Parameters

Type	Name	Description
float	value	The floating-point value to be rounded up.

Returns

Type	Description
int	The smallest integer greater than or equal to the specified value.

Clamp(decimal, decimal, decimal)

Clamps an integer value to the inclusive range [min, max]. If value is below the minimum, the minimum is returned; if it is above the maximum, the maximum is returned; otherwise the value is returned unchanged.

Declaration

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

Parameters

Type	Name	Description
decimal	value	The value to clamp.
decimal	min	The inclusive lower bound of the range.
decimal	max	The inclusive upper bound of the range.

Returns

Type	Description
decimal	The clamped value in the range [min, max].

Exceptions

Type	Condition
ArgumentException	Thrown when min is greater than max.

Clamp(double, double, double)

Clamps a double-precision floating-point value to the inclusive range [min, max].

Declaration

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

Parameters

Type	Name	Description
double	value	The value to clamp.
double	min	The inclusive lower bound of the range.
double	max	The inclusive upper bound of the range.

Returns

Type	Description
double	The clamped value in the range [min, max].

Exceptions

Type	Condition
ArgumentException	Thrown when min is greater than max.

Clamp(int, int, int)

Clamps an integer value to the inclusive range [min, max]. If value is below the minimum, the minimum is returned; if it is above the maximum, the maximum is returned; otherwise the value is returned unchanged.

Declaration

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

Parameters

Type	Name	Description
int	value	The value to clamp.
int	min	The inclusive lower bound of the range.
int	max	The inclusive upper bound of the range.

Returns

Type	Description
int	The clamped value in the range [min, max].

Exceptions

Type	Condition
ArgumentException	Thrown when min is greater than max.

Clamp(long, long, long)

Clamps a 64-bit signed integer value to the inclusive range [min, max].

Declaration

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

Parameters

Type	Name	Description
long	value	The 64-bit signed integer value to clamp.
long	min	The inclusive lower bound of the range.
long	max	The inclusive upper bound of the range.

Returns

Type	Description
long	The clamped value in the range [min, max].

Exceptions

Type	Condition
ArgumentException	Thrown when min is greater than max.

Clamp(float, float, float)

Clamps a single-precision floating-point value to the inclusive range [min, max].

Declaration

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

Parameters

Type	Name	Description
float	value	The value to clamp.
float	min	The inclusive lower bound of the range.
float	max	The inclusive upper bound of the range.

Returns

Type	Description
float	The clamped value in the range [min, max].

Exceptions

Type	Condition
ArgumentException	Thrown when min is greater than max.

Clamp(uint, uint, uint)

Clamps an unsigned 32-bit integer value to the inclusive range [min, max].

Declaration

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

Parameters

Type	Name	Description
uint	value	The unsigned integer value to clamp.
uint	min	The inclusive lower bound of the range.
uint	max	The inclusive upper bound of the range.

Returns

Type	Description
uint	The clamped value in the range [min, max].

Exceptions

Type	Condition
ArgumentException	Thrown when min is greater than max.

Clamp(ulong, ulong, ulong)

Clamps an unsigned 64-bit integer value to the inclusive range [min, max].

Declaration

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

Parameters

Type	Name	Description
ulong	value	The unsigned 64-bit integer value to clamp.
ulong	min	The inclusive lower bound of the range.
ulong	max	The inclusive upper bound of the range.

Returns

Type	Description
ulong	The clamped value in the range [min, max].

Exceptions

Type	Condition
ArgumentException	Thrown when min is greater than max.

Clamp01(double)

Clamps a double-precision floating-point value to the inclusive range [0, 1].

Declaration

public static double Clamp01(double value)

Parameters

Type	Name	Description
double	value	The value to clamp.

Returns

Type	Description
double	The clamped value, which will be within the range [0, 1].

Clamp01(float)

Clamps a given value to the inclusive range of [0, 1].

Declaration

public static float Clamp01(float value)

Parameters

Type	Name	Description
float	value	The value to clamp.

Returns

Type	Description
float	The clamped value, which will be within the range [0, 1].

Cube(decimal)

Returns the cube of the specified decimal value (value * value * value).

Declaration

public static decimal Cube(decimal value)

Parameters

Type	Name	Description
decimal	value	The decimal value to cube. The sign is preserved in the result.

Returns

Type	Description
decimal	value * value * value.

Cube(double)

Returns the cube of the specified double value (value * value * value).

Declaration

public static double Cube(double value)

Parameters

Type	Name	Description
double	value	The double-precision value to cube. The sign is preserved in the result.

Returns

Type	Description
double	value * value * value.

Cube(int)

Returns the cube of the specified int value (value * value * value). Useful as a concise alternative to Math.Pow(value, 3) without a cast or allocation.

Declaration

public static int Cube(int value)

Parameters

Type	Name	Description
int	value	The integer value to cube. The sign is preserved in the result.

Returns

Type	Description
int	value * value * value. Note that overflow is not checked; very large inputs will wrap silently.

Cube(long)

Returns the cube of the specified long value (value * value * value).

Declaration

public static long Cube(long value)

Parameters

Type	Name	Description
long	value	The 64-bit integer value to cube. The sign is preserved in the result.

Returns

Type	Description
long	value * value * value. Note that overflow is not checked; very large inputs will wrap silently.

Cube(float)

Returns the cube of the specified float value (value * value * value).

Declaration

public static float Cube(float value)

Parameters

Type	Name	Description
float	value	The float value to cube. The sign is preserved in the result.

Returns

Type	Description
float	value * value * value.

DegToRad(float)

Converts an angle from degrees to radians.

Declaration

public static float DegToRad(float degrees)

Parameters

Type	Name	Description
float	degrees	The angle in degrees.

Returns

Type	Description
float	The equivalent angle in radians.

DeltaAngleDeg(float, float)

Calculates the shortest signed angle difference (in degrees) from the current angle to the target angle. The result is normalized to the range [-180, 180).

Declaration

public static float DeltaAngleDeg(float current, float target)

Parameters

Type	Name	Description
float	current	The current angle in degrees.
float	target	The target angle in degrees.

Returns

Type	Description
float	The shortest signed angle difference (in degrees) from the current angle to the target angle, within the range [-180, 180).

DeltaAngleRad(float, float)

Calculates the shortest signed angle difference, in radians, between the specified current and target angles. The returned angle will be within the range [-π, π).

Declaration

public static float DeltaAngleRad(float current, float target)

Parameters

Type	Name	Description
float	current	The current angle in radians.
float	target	The target angle in radians.

Returns

Type	Description
float	The shortest signed angle difference in radians, within the range [-π, π).

EnsureFinite(double, string)

Ensures that the provided value is finite (neither NaN nor infinity).

Declaration

public static double EnsureFinite(double value, string name)

Parameters

Type	Name	Description
double	value	The value to validate as finite.
string	name	The name of the parameter being validated, used in exception messages.

Returns

Type	Description
double	The original value if it is finite.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown when the value is NaN or infinity, indicating that it is not a finite number.

EnsureFinite(float, string)

Ensures that the provided value is finite (neither NaN nor infinity).

Declaration

public static float EnsureFinite(float value, string name)

Parameters

Type	Name	Description
float	value	The value to validate as finite.
string	name	The name of the parameter being validated, used in exception messages.

Returns

Type	Description
float	The original value if it is finite.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown when the value is NaN or infinity, indicating that it is not a finite number.

EnsureFiniteNonNegative(double, string)

Ensures that the provided value is finite and non-negative.

Declaration

public static double EnsureFiniteNonNegative(double value, string name)

Parameters

Type	Name	Description
double	value	The value to validate.
string	name	The name of the parameter being validated, used in exception messages.

Returns

Type	Description
double	The validated value, if it is both finite and non-negative.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown if the value is NaN, infinity, or less than 0.

EnsureFiniteNonNegative(float, string)

Ensures that the provided value is finite and non-negative.

Declaration

public static float EnsureFiniteNonNegative(float value, string name)

Parameters

Type	Name	Description
float	value	The value to validate.
string	name	The name of the parameter being validated, used in exception messages.

Returns

Type	Description
float	The validated value, if it is both finite and non-negative.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown if the value is NaN, infinity, or less than 0.

FloorToInt(double)

Floors the specified float value to the nearest lower integer.

Declaration

public static int FloorToInt(double value)

Parameters

Type	Name	Description
double	value	The float value to floor.

Returns

Type	Description
int	The largest integer less than or equal to the specified float value.

FloorToInt(float)

Floors the specified float value to the nearest lower integer.

Declaration

public static int FloorToInt(float value)

Parameters

Type	Name	Description
float	value	The float value to floor.

Returns

Type	Description
int	The largest integer less than or equal to the specified value.

InverseLerp(double, double, double)

Calculates the normalized interpolation factor for a value within a specified range, clamped to the range [0, 1].

Declaration

public static double InverseLerp(double a, double b, double value)

Parameters

Type	Name	Description
double	a	The start of the range.
double	b	The end of the range.
double	value	The value to calculate the interpolation factor for.

Returns

Type	Description
double	The normalized interpolation factor, clamped to the range [0, 1].

InverseLerp(float, float, float)

Computes a clamped interpolation factor t in the range [0, 1] such that Lerp(a, b, t) equals the specified value. Returns 0 when a is equal to b.

Declaration

public static float InverseLerp(float a, float b, float value)

Parameters

Type	Name	Description
float	a	The start value of the range.
float	b	The end value of the range.
float	value	The value for which the interpolation factor is computed.

Returns

Type	Description
float	The interpolated factor t in the range [0, 1].

InverseLerpUnclamped(double, double, double)

Calculates the linear parameter t that produces the interpolant value within an unclamped range. Returns 0 when a is approximately equal to b.

Declaration

public static double InverseLerpUnclamped(double a, double b, double value)

Parameters

Type	Name	Description
double	a	The start of the range.
double	b	The end of the range.
double	value	The value for which to calculate the parameter t within the range.

Returns

Type	Description
double	The linear parameter t that corresponds to the value within the range [a, b].

InverseLerpUnclamped(float, float, float)

Computes an unclamped interpolation factor t such that LerpUnclamped(a, b, t) == value. Returns 0 when a is approximately equal to b.

Declaration

public static float InverseLerpUnclamped(float a, float b, float value)

Parameters

Type	Name	Description
float	a	The start value, corresponding to t = 0.
float	b	The end value, corresponding to t = 1.
float	value	The value to map between a and b.

Returns

Type	Description
float	The unclamped interpolation factor t.

IsBetween(decimal, decimal, decimal, bool)

Determines whether a value lies within the specified range, optionally including the boundaries.

Declaration

public static bool IsBetween(decimal value, decimal min, decimal max, bool inclusive = true)

Parameters

Type	Name	Description
decimal	value	The value to check.
decimal	min	The lower bound of the range.
decimal	max	The upper bound of the range.
bool	inclusive	Specifies whether the boundaries should be included in the range. Defaults to true.

Returns

Type	Description
bool	True if the value lies within the range; otherwise, false.

IsBetween(double, double, double, bool)

Determines whether a value is within the specified range.

Declaration

public static bool IsBetween(double value, double min, double max, bool inclusive = true)

Parameters

Type	Name	Description
double	value	The value to check.
double	min	The lower bound of the range.
double	max	The upper bound of the range.
bool	inclusive	Specifies whether the bounds are inclusive. If true, the range is [min, max]. If false, the range is (min, max).

Returns

Type	Description
bool	True if the value is within the range; otherwise, false.

IsBetween(int, int, int, bool)

Determines if a value is within a specified range, either inclusive or exclusive of the boundaries.

Declaration

public static bool IsBetween(int value, int min, int max, bool inclusive = true)

Parameters

Type	Name	Description
int	value	The value to evaluate.
int	min	The lower boundary of the range.
int	max	The upper boundary of the range.
bool	inclusive	Specifies whether the boundaries are inclusive. If true, the range is inclusive of the boundaries; otherwise, the range is exclusive.

Returns

Type	Description
bool	True if the value is within the specified range, otherwise false.

Exceptions

Type	Condition
ArgumentException	Thrown when the min value is greater than the max value.

IsBetween(long, long, long, bool)

Determines whether a value is within the range defined by the specified minimum and maximum values.

Declaration

public static bool IsBetween(long value, long min, long max, bool inclusive = true)

Parameters

Type	Name	Description
long	value	The value to check.
long	min	The minimum value of the range.
long	max	The maximum value of the range.
bool	inclusive	Indicates whether the check should include the boundary values. If true, the range is inclusive; otherwise, it is exclusive.

Returns

Type	Description
bool	True if the value is within the specified range; otherwise, false.

IsBetween(float, float, float, bool)

Determines whether a value lies within the specified range, with an option to include or exclude the boundaries.

Declaration

public static bool IsBetween(float value, float min, float max, bool inclusive = true)

Parameters

Type	Name	Description
float	value	The value to test.
float	min	The lower bound of the range.
float	max	The upper bound of the range.
bool	inclusive	Determines if the boundary values should be included in the range. If true, the range is inclusive; otherwise, it is exclusive.

Returns

Type	Description
bool	True if the value is within the specified range; otherwise, false.

IsBetween(uint, uint, uint, bool)

Determines if a value lies within the specified range, with an option to include or exclude the boundaries.

Declaration

public static bool IsBetween(uint value, uint min, uint max, bool inclusive = true)

Parameters

Type	Name	Description
uint	value	The value to check.
uint	min	The minimum value of the range.
uint	max	The maximum value of the range.
bool	inclusive	Indicates whether the range includes the boundaries. Defaults to true.

Returns

Type	Description
bool	True if the value lies within the range; otherwise, false.

IsBetween(ulong, ulong, ulong, bool)

Determines whether a value is within the range defined by the specified minimum and maximum values.

Declaration

public static bool IsBetween(ulong value, ulong min, ulong max, bool inclusive = true)

Parameters

Type	Name	Description
ulong	value	The value to check.
ulong	min	The minimum value of the range.
ulong	max	The maximum value of the range.
bool	inclusive	Determines if the boundaries are inclusive. If true, the range includes min and max; otherwise, it excludes them.

Returns

Type	Description
bool	True if the value is within the specified range; otherwise, false.

IsEven(int)

Returns true if the specified int value is even (divisible by 2 with no remainder). Uses a bitwise AND for a branchless, allocation-free check. Correctly handles negative values.

Declaration

public static bool IsEven(int value)

Parameters

Type	Name	Description
int	value	The integer to evaluate.

Returns

Type	Description
bool	true if the value is even; false if it is odd.

IsEven(long)

Returns true if the specified long value is even. Correctly handles negative values.

Declaration

public static bool IsEven(long value)

Parameters

Type	Name	Description
long	value	The 64-bit integer to evaluate.

Returns

Type	Description
bool	true if the value is even; false if it is odd.

IsEven(uint)

Returns true if the specified uint value is even.

Declaration

public static bool IsEven(uint value)

Parameters

Type	Name	Description
uint	value	The unsigned integer to evaluate.

Returns

Type	Description
bool	true if the value is even; false if it is odd.

IsEven(ulong)

Returns true if the specified ulong value is even.

Declaration

public static bool IsEven(ulong value)

Parameters

Type	Name	Description
ulong	value	The unsigned 64-bit integer to evaluate.

Returns

Type	Description
bool	true if the value is even; false if it is odd.

IsFinite(double)

Determines whether the specified double-precision floating-point value is finite.

Declaration

public static bool IsFinite(double value)

Parameters

Type	Name	Description
double	value	The double value to check for finiteness.

Returns

Type	Description
bool	True if the value is finite (neither NaN nor infinity); otherwise, false.

IsFinite(float)

Determines whether the specified floating-point value is finite (not NaN and not ±Infinity).

Declaration

public static bool IsFinite(float value)

Parameters

Type	Name	Description
float	value	The floating-point value to evaluate.

Returns

Type	Description
bool	True if the value is finite; otherwise, false.

IsNearlyZero(double, double)

Determines whether a given double-precision floating-point value is nearly zero, within a specified margin of error.

Declaration

public static bool IsNearlyZero(double value, double epsilon = 1E-12)

Parameters

Type	Name	Description
double	value	The value to check.
double	epsilon	The allowable margin of error to consider the value as nearly zero. Must be greater than or equal to 0.

Returns

Type	Description
bool	True if the absolute value is less than or equal to the specified epsilon; otherwise, false.

IsNearlyZero(float, float)

Determines whether the specified value is within a defined epsilon range of zero.

Declaration

public static bool IsNearlyZero(float value, float epsilon = 1E-06)

Parameters

Type	Name	Description
float	value	The value to evaluate.
float	epsilon	The permissible range for the value to be considered nearly zero. Must be greater than or equal to zero.

Returns

Type	Description
bool	True if the value is within the specified epsilon range of zero; otherwise, false.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown when the epsilon is negative.

IsOdd(int)

Returns true if the specified int value is odd (not divisible by 2 without a remainder). Uses a bitwise AND for a branchless, allocation-free check. Correctly handles negative values.

Declaration

public static bool IsOdd(int value)

Parameters

Type	Name	Description
int	value	The integer value to evaluate.

Returns

Type	Description
bool	true if the value is odd; false if it is even.

IsOdd(long)

Returns true if the specified long value is odd. Correctly handles negative values.

Declaration

public static bool IsOdd(long value)

Parameters

Type	Name	Description
long	value	The 64-bit integer to evaluate.

Returns

Type	Description
bool	true if the value is odd; false if it is even.

IsOdd(uint)

Returns true if the specified uint value is odd.

Declaration

public static bool IsOdd(uint value)

Parameters

Type	Name	Description
uint	value	The unsigned integer to evaluate.

Returns

Type	Description
bool	true if the value is odd; false if it is even.

IsOdd(ulong)

Returns true if the specified ulong value is odd.

Declaration

public static bool IsOdd(ulong value)

Parameters

Type	Name	Description
ulong	value	The unsigned 64-bit integer to evaluate.

Returns

Type	Description
bool	true if the value is odd; false if it is even.

IsPowerOfTwo(uint)

Determines whether the specified value is a power of two.

Declaration

public static bool IsPowerOfTwo(uint value)

Parameters

Type	Name	Description
uint	value	The value to check.

Returns

Type	Description
bool	True if the value is a power of two; otherwise, false.

IsPowerOfTwo(ulong)

Determines whether the specified value is a power of two.

Declaration

public static bool IsPowerOfTwo(ulong value)

Parameters

Type	Name	Description
ulong	value	The value to check.

Returns

Type	Description
bool	True if the value is a power of two; otherwise, false.

Lerp(double, double, double)

Linearly interpolates between two values based on a weight parameter t.

Declaration

public static double Lerp(double a, double b, double t)

Parameters

Type	Name	Description
double	a	The starting value.
double	b	The target value.
double	t	The interpolation factor, typically in the range [0, 1].

Returns

Type	Description
double	The interpolated value, which is a combination of a and b based on t.

Lerp(float, float, float)

Linearly interpolates between two values based on a parameter t, while clamping t to the range [0, 1].

Declaration

public static float Lerp(float a, float b, float t)

Parameters

Type	Name	Description
float	a	The starting value of the interpolation.
float	b	The ending value of the interpolation.
float	t	The parameter that determines the interpolation factor. It is clamped to the range [0, 1].

Returns

Type	Description
float	The interpolated value between a and b.

LerpAngleDeg(float, float, float)

Interpolates between two angles in degrees, taking into account angle wrapping (e.g., -180° to 180° or 0° to 360°) and clamping the interpolation factor to the range [0, 1].

Declaration

public static float LerpAngleDeg(float a, float b, float t)

Parameters

Type	Name	Description
float	a	The starting angle in degrees.
float	b	The target angle in degrees.
float	t	The interpolation factor, where 0 represents the starting angle and 1 represents the target angle.

Returns

Type	Description
float	The interpolated angle in degrees.

LerpUnclamped(double, double, double)

Interpolates between two values without clamping the interpolation factor.

Declaration

public static double LerpUnclamped(double a, double b, double t)

Parameters

Type	Name	Description
double	a	The starting value of the interpolation.
double	b	The ending value of the interpolation.
double	t	The interpolation factor. This value is not clamped and can extend beyond the range [0, 1].

Returns

Type	Description
double	The interpolated value.

LerpUnclamped(float, float, float)

Linearly interpolates between two values without clamping the interpolation factor.

Declaration

public static float LerpUnclamped(float a, float b, float t)

Parameters

Type	Name	Description
float	a	The start value of the interpolation.
float	b	The end value of the interpolation.
float	t	The interpolation factor, which is not clamped. Values less than 0 will extrapolate below a, and values greater than 1 will extrapolate beyond b.

Returns

Type	Description
float	The interpolated value between a and b based on t.

Mod(decimal, decimal)

Computes the modulus of the given value and divisor, ensuring the result is always non-negative.

Declaration

public static decimal Mod(decimal value, decimal m)

Parameters

Type	Name	Description
decimal	value	The value to compute the modulus for.
decimal	m	The divisor. Must be greater than zero.

Returns

Type	Description
decimal	The modulus result, which is always a non-negative value.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown when the divisor is less than or equal to zero.

Mod(double, double)

Computes the remainder of a division operation, ensuring the result is always non-negative.

Declaration

public static double Mod(double value, double m)

Parameters

Type	Name	Description
double	value	The dividend in the division operation.
double	m	The divisor in the division operation. Must be greater than 0.

Returns

Type	Description
double	The remainder of the division operation, always in the range [0, m).

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown when the divisor (m) is less than or equal to 0.

Mod(int, int)

Computes the true modulo (always in the range [0, m)) for the specified integer value and divisor.

Declaration

public static int Mod(int value, int m)

Parameters

Type	Name	Description
int	value	The integer value to compute the modulo for.
int	m	The divisor, which must be greater than 0.

Returns

Type	Description
int	The result of the modulo operation, always in the range [0, m).

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown when m is less than or equal to 0.

Mod(long, long)

Calculates the modulus of a value, ensuring the result is always non-negative.

Declaration

public static long Mod(long value, long m)

Parameters

Type	Name	Description
long	value	The value to calculate the modulus for.
long	m	The modulus base, which must be greater than 0.

Returns

Type	Description
long	The non-negative remainder of the division of the value by the modulus base.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown when the modulus base is less than or equal to 0.

Mod(float, float)

Computes the modulo of a value, ensuring the result is always within the range [0, m).

Declaration

public static float Mod(float value, float m)

Parameters

Type	Name	Description
float	value	The value to compute the modulo for.
float	m	The divisor, which must be greater than 0.

Returns

Type	Description
float	The result of the modulo operation, always within the range [0, m).

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown if m is less than or equal to 0.

NextPowerOfTwo(uint)

Returns the next power of two greater than or equal to the specified value.

Declaration

public static uint NextPowerOfTwo(uint value)

Parameters

Type	Name	Description
uint	value	The value to compute the next power of two for.

Returns

Type	Description
uint	The next power of two greater than or equal to the specified value.

Exceptions

Type	Condition
OverflowException	Thrown if the next power of two exceeds the maximum value of the type.

NextPowerOfTwo(ulong)

Calculates the next power of two greater than or equal to the specified value.

Declaration

public static ulong NextPowerOfTwo(ulong value)

Parameters

Type	Name	Description
ulong	value	The value for which to calculate the next power of two.

Returns

Type	Description
ulong	The next power of two greater than or equal to the specified value.

Exceptions

Type	Condition
OverflowException	Thrown if the next power of two would exceed the maximum value of ulong.

NormalizeAngleDeg180(float)

Normalizes an angle in degrees to the range [-180, 180).

Declaration

public static float NormalizeAngleDeg180(float angle)

Parameters

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

Returns

Type	Description
float	The normalized angle, which will be within the range [-180, 180).

NormalizeAngleDeg360(float)

Normalizes an angle in degrees to the range [0, 360).

Declaration

public static float NormalizeAngleDeg360(float angle)

Parameters

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

Returns

Type	Description
float	The normalized angle within the range [0, 360).

NormalizeAngleRad2Pi(float)

Normalizes an angle in radians to the range [0, 2π).

Declaration

public static float NormalizeAngleRad2Pi(float angle)

Parameters

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

Returns

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

NormalizeAngleRadPi(float)

Normalizes an angle in radians to the range [-π, π).

Declaration

public static float NormalizeAngleRadPi(float angle)

Parameters

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

Returns

Type	Description
float	The normalized angle within the range [-π, π).

RadToDeg(float)

Converts a value from radians to degrees.

Declaration

public static float RadToDeg(float radians)

Parameters

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

Returns

Type	Description
float	The equivalent angle in degrees.

Remap(double, double, double, double, double, bool)

Remaps a value from one range to another, with an option to clamp the result to the target range.

Declaration

public static double Remap(double value, double inMin, double inMax, double outMin, double outMax, bool clamp = false)

Parameters

Type	Name	Description
double	value	The value to remap.
double	inMin	The lower bound of the input range.
double	inMax	The upper bound of the input range.
double	outMin	The lower bound of the output range.
double	outMax	The upper bound of the output range.
bool	clamp	Indicates whether the output value should be clamped to the output range.

Returns

Type	Description
double	The remapped value, scaled to the range [outMin, outMax].

Remap(float, float, float, float, float, bool)

Remaps a specified value from one range to another.

Declaration

public static float Remap(float value, float inMin, float inMax, float outMin, float outMax, bool clamp = false)

Parameters

Type	Name	Description
float	value	The value to be remapped.
float	inMin	The lower bound of the input range.
float	inMax	The upper bound of the input range.
float	outMin	The lower bound of the output range.
float	outMax	The upper bound of the output range.
bool	clamp	Determines whether the interpolation factor should be clamped to the output range.

Returns

Type	Description
float	The value remapped to the output range.

Repeat(double, double)

Repeats a value within the range [0, length). Effectively, it wraps the input value to stay within the specified range.

Declaration

public static double Repeat(double t, double length)

Parameters

Type	Name	Description
double	t	The value to repeat.
double	length	The length of the range. Must be greater than 0.

Returns

Type	Description
double	The value wrapped within the range [0, length).

Repeat(float, float)

Loops a given value so that it is constrained within the range [0, length).

Declaration

public static float Repeat(float t, float length)

Parameters

Type	Name	Description
float	t	The value to loop.
float	length	The length of the range. Must be greater than 0.

Returns

Type	Description
float	A value in the range [0, length).

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown if length is less than or equal to 0.

RoundToDecimals(decimal, int)

Rounds a decimal value to the specified number of decimal places.

Declaration

public static decimal RoundToDecimals(decimal value, int decimals)

Parameters

Type	Name	Description
decimal	value	The decimal value to be rounded.
int	decimals	The number of decimal places to round to. Must be greater than or equal to 0.

Returns

Type	Description
decimal	The rounded decimal value.

RoundToDecimals(double, int)

Rounds a double-precision floating-point value to the specified number of fractional decimal places.

Declaration

public static double RoundToDecimals(double value, int decimals)

Parameters

Type	Name	Description
double	value	The double value to round.
int	decimals	The number of decimal places to round to. Must be 0 or greater.

Returns

Type	Description
double	The rounded double value, rounded to the specified number of decimal places.

RoundToDecimals(float, int)

Rounds the specified value to the given number of decimal places using midpoint rounding away from zero.

Declaration

public static float RoundToDecimals(float value, int decimals)

Parameters

Type	Name	Description
float	value	The float value to round.
int	decimals	The number of decimal places to round to. Must be greater than or equal to zero.

Returns

Type	Description
float	The rounded float value.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown when decimals is negative.

RoundToInt(double)

Rounds a double value to the nearest integer, with midpoint values rounding away from zero.

Declaration

public static int RoundToInt(double value)

Parameters

Type	Name	Description
double	value	The double value to be rounded.

Returns

Type	Description
int	The rounded integer value.

Exceptions

Type	Condition
OverflowException	Thrown if the rounded value exceeds the range of the int type.

RoundToInt(float)

Rounds the specified floating-point value to the nearest integer, with midpoint values rounded away from zero.

Declaration

public static int RoundToInt(float value)

Parameters

Type	Name	Description
float	value	The floating-point value to round.

Returns

Type	Description
int	The rounded integer value.

SafeDivide(decimal, decimal, decimal)

Safely divides a numerator by a denominator, returning a fallback value if the denominator is zero.

Declaration

public static decimal SafeDivide(decimal numerator, decimal denominator, decimal fallback = 0)

Parameters

Type	Name	Description
decimal	numerator	The value to be divided.
decimal	denominator	The value to divide the numerator by.
decimal	fallback	The value to return if the denominator is zero.

Returns

Type	Description
decimal	The result of the division if the denominator is non-zero; otherwise, the fallback value.

SafeDivide(double, double, double)

Safely divides a numerator by a denominator, returning a fallback value if the denominator is zero.

Declaration

public static double SafeDivide(double numerator, double denominator, double fallback = 0)

Parameters

Type	Name	Description
double	numerator	The value to be divided.
double	denominator	The value by which to divide the numerator.
double	fallback	The value to return if the denominator is zero. Defaults to 0.

Returns

Type	Description
double	The result of the division if the denominator is not zero; otherwise, the fallback value.

SafeDivide(float, float, float)

Divides the specified numerator by the specified denominator. Returns the fallback value if the denominator is zero.

Declaration

public static float SafeDivide(float numerator, float denominator, float fallback = 0)

Parameters

Type	Name	Description
float	numerator	The value to be divided.
float	denominator	The value by which the numerator is divided.
float	fallback	The value to return if the denominator is zero. Defaults to 0.

Returns

Type	Description
float	The result of the division if the denominator is not zero, otherwise the fallback value.

SignNonZero(double, double)

Returns -1 if the specified double value is strictly less than -epsilon, or +1 for any value greater than or equal to -epsilon. Values in the near-zero tolerance band are treated as positive.

Declaration

public static int SignNonZero(double value, double epsilon = 1E-12)

Parameters

Type	Name	Description
double	value	The double-precision value to evaluate.
double	epsilon	The tolerance that defines the zero-band. Must be non-negative. Defaults to EPSILON_D.

Returns

Type	Description
int	-1 if value < -epsilon; +1 otherwise.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown if epsilon is negative.

SignNonZero(int)

Returns -1 if the specified integer value is negative, or +1 if the value is zero or positive. Unlike Math.Sign(int), this method never returns 0, making it safe to use as a divisor or direction multiplier without an additional zero-check.

Declaration

public static int SignNonZero(int value)

Parameters

Type	Name	Description
int	value	The integer value to evaluate.

Returns

Type	Description
int	-1 if value is negative; +1 otherwise.

SignNonZero(long)

Returns -1 if the specified 64-bit integer value is negative, or +1 if the value is zero or positive. Unlike Math.Sign(long), this method never returns 0.

Declaration

public static int SignNonZero(long value)

Parameters

Type	Name	Description
long	value	The 64-bit integer value to evaluate.

Returns

Type	Description
int	-1 if value is negative; +1 otherwise.

SignNonZero(float, float)

Returns -1 if the specified float value is strictly less than -epsilon, or +1 for any value greater than or equal to -epsilon (including zero and near-zero values within the tolerance band). This ensures zero and values within the epsilon band are always treated as positive, making the result safe to use as a non-zero direction multiplier.

Declaration

public static int SignNonZero(float value, float epsilon = 1E-06)

Parameters

Type	Name	Description
float	value	The float value to evaluate.
float	epsilon	The tolerance that defines the zero-band. Values in the range [-epsilon, +epsilon] are treated as positive. Must be non-negative. Defaults to EPSILON.

Returns

Type	Description
int	-1 if value < -epsilon; +1 otherwise.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown if epsilon is negative.

Snap(decimal, decimal)

Snaps a value to the nearest multiple of the specified step.

Declaration

public static decimal Snap(decimal value, decimal step)

Parameters

Type	Name	Description
decimal	value	The value to be snapped.
decimal	step	The step size to which the value should be snapped. Must be greater than 0.

Returns

Type	Description
decimal	The value snapped to the nearest multiple of the step.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown if step is less than or equal to 0.

Snap(double, double)

Rounds the given value to the nearest multiple of the specified step.

Declaration

public static double Snap(double value, double step)

Parameters

Type	Name	Description
double	value	The value to round.
double	step	The step size to which the value will be rounded. Must be greater than 0.

Returns

Type	Description
double	The value rounded to the nearest multiple of the specified step.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown if step is less than or equal to 0.

Snap(float, float)

Rounds the specified value to the nearest multiple of the specified step (midpoint rounds away from zero).

Declaration

public static float Snap(float value, float step)

Parameters

Type	Name	Description
float	value	The value to be rounded.
float	step	The step size to which the value will be rounded. Must be greater than 0.

Returns

Type	Description
float	The rounded value, as a multiple of the specified step.

Exceptions

Type	Condition
ArgumentOutOfRangeException	Thrown if the step is less than or equal to 0.

Sqr(decimal)

Returns the square of the specified decimal value (value * value).

Declaration

public static decimal Sqr(decimal value)

Parameters

Type	Name	Description
decimal	value	The decimal value to square. May be negative; the result is always non-negative.

Returns

Type	Description
decimal	value * value.

Sqr(double)

Returns the square of the specified double value (value * value).

Declaration

public static double Sqr(double value)

Parameters

Type	Name	Description
double	value	The double-precision value to square. May be negative; the result is always non-negative for finite inputs.

Returns

Type	Description
double	value * value.

Sqr(int)

Returns the square of the specified int value (value * value). Useful as a concise alternative to Math.Pow(value, 2) without a cast or allocation.

Declaration

public static int Sqr(int value)

Parameters

Type	Name	Description
int	value	The integer value to square. May be negative; the result is always non-negative.

Returns

Type	Description
int	value * value. Note that overflow is not checked; very large inputs will wrap silently.

Sqr(long)

Returns the square of the specified long value (value * value).

Declaration

public static long Sqr(long value)

Parameters

Type	Name	Description
long	value	The 64-bit integer value to square. May be negative; the result is always non-negative.

Returns

Type	Description
long	value * value. Note that overflow is not checked; very large inputs will wrap silently.

Sqr(float)

Returns the square of the specified float value (value * value).

Declaration

public static float Sqr(float value)

Parameters

Type	Name	Description
float	value	The float value to square. May be negative; the result is always non-negative for finite inputs.

Returns

Type	Description
float	value * value.

Wrap(int, int, int)

Wraps a value into the half-open interval defined by the specified minimum (inclusive) and maximum (exclusive) bounds.

Declaration

public static int Wrap(int value, int minInclusive, int maxExclusive)

Parameters

Type	Name	Description
int	value	The value to be wrapped.
int	minInclusive	The inclusive lower bound of the interval.
int	maxExclusive	The exclusive upper bound of the interval.

Returns

Type	Description
int	The wrapped value, constrained within the interval [minInclusive, maxExclusive).

Exceptions

Type	Condition
ArgumentException	Thrown if maxExclusive is less than or equal to minInclusive.

Wrap(long, long, long)

Wraps a given value such that it falls within the inclusive lower bound and exclusive upper bound, cycling back to the lower bound if it exceeds the upper bound.

Declaration

public static long Wrap(long value, long minInclusive, long maxExclusive)

Parameters

Type	Name	Description
long	value	The value to wrap.
long	minInclusive	The inclusive lower bound of the range.
long	maxExclusive	The exclusive upper bound of the range.

Returns

Type	Description
long	The wrapped value within the range [minInclusive, maxExclusive).

Wrap(uint, uint, uint)

Wraps a value to fit within a specified range, ensuring that the resulting value lies within [minInclusive, maxExclusive).

Declaration

public static uint Wrap(uint value, uint minInclusive, uint maxExclusive)

Parameters

Type	Name	Description
uint	value	The value to wrap.
uint	minInclusive	The inclusive lower bound of the range.
uint	maxExclusive	The exclusive upper bound of the range. Must be greater than minInclusive.

Returns

Type	Description
uint	The wrapped value, guaranteed to be within the range [minInclusive, maxExclusive).

Wrap(ulong, ulong, ulong)

Wraps a value such that it falls within the specified range [minInclusive, maxExclusive). If the value is outside the range, it is adjusted to "wrap around" within the range.

Declaration

public static ulong Wrap(ulong value, ulong minInclusive, ulong maxExclusive)

Parameters

Type	Name	Description
ulong	value	The value to be wrapped.
ulong	minInclusive	The inclusive lower bound of the range.
ulong	maxExclusive	The exclusive upper bound of the range.

Returns

Type	Description
ulong	The wrapped value, adjusted to lie within the range [minInclusive, maxExclusive).

Exceptions

Type	Condition
ArgumentException	Thrown when maxExclusive is less than or equal to minInclusive, or when the range is zero.