class Maths in Tinman.Core.Math

Provides some commonly used math functions.

static class

Maths

Public / Constants

DegToRad

Factor for converting radians to degrees.

public constant	DegToRad = 0.017453292519943295
type	float64

Log10

The natural logarithm of 10.

public constant	Log10 = 2.302585092994046
type	float64

Log2

The natural logarithm of 2.

public constant	Log2 = 0.6931471805599453
type	float64

LogBase

Base of natural logarithm.

public constant	LogBase = 2.71828182845905
type	float64

See also:

Log

MaxDouble

Maximum value of a 32-bit floating-point.

public constant	MaxDouble = 1.7976931348623157E+308
type	float64

MaxFloat

Maximum value of a 32-bit floating-point.

public constant	MaxFloat = 3.4028235E+38
type	float32

MaxInt

Maximum value of a 32-bit signed integer.

public constant	MaxInt = 2147483647
type	int32

MaxLong

Maximum value of a 64-bit signed integer.

public constant	MaxLong = 9223372036854775807
type	int64

MinDouble

Minimum value of a 32-bit floating-point.

public constant	MinDouble = -1.7976931348623157E+308
type	float64

MinFloat

Minimum value of a 32-bit floating-point.

public constant	MinFloat = -3.4028235E+38
type	float32

MinInt

Minimum value of a 32-bit signed integer.

public constant	MinInt = -2147483648
type	int32

MinLong

Minimum value of a 64-bit signed integer.

public constant	MinLong = -9223372036854775808
type	int64

Pi

The value of PI (i.e. 180°).

public constant	Pi = 3.141592653589793
type	float64

PiHalf

The value of PI / 2 (i.e. 90°).

public constant	PiHalf = 1.5707963267948966
type	float64

PiQuarter

The value of PI / 4 (i.e. 45°).

public constant	PiQuarter = 0.7853981633974483
type	float64

PiTwo

The value of PI * 2 (i.e. 360°).

public constant	PiTwo = 6.283185307179586
type	float64

RadToDeg

Factor for converting radians to degrees.

public constant	RadToDeg = 57.29577951308232
type	float64

Sqrt05

The square root of 0.5.

public constant	Sqrt05 = 0.7071067811865476
type	float64

Sqrt2

The square root of 2.

public constant	Sqrt2 = 1.4142135623730951
type	float64

Sqrt3

The square root of 3.

public constant	Sqrt3 = 1.7320508075688772
type	float64

Public / Attributes

NanD

Returns the 64-bit floating point value for: not-a-number.

public static property	NanD { get }
type	float64
value		The NaN value.

NanF

Returns the 32-bit floating point value for: not-a-number.

public static property	NanF { get }
type	float32
value		The NaN value.

NegInfD

Returns the 64-bit floating point value for: negative infinity.

public static property	NegInfD { get }
type	float64
value		The -Inf value.

NegInfF

Returns the 32-bit floating point value for: negative infinity.

public static property	NegInfF { get }
type	float32
value		The -Inf value.

PosInfD

Returns the 64-bit floating point value for: positive infinity.

public static property	PosInfD { get }
type	float64
value		The +Inf value.

PosInfF

Returns the 32-bit floating point value for: positive infinity.

public static property	PosInfF { get }
type	float32
value		The +Inf value.

Public / Methods

Abs

Returns the absolute of the given value.

[Pure]
public static method	Abs (float64 value)
type	float64
params	value		The value.
returns		[>=0]	The absolute value.

---

Returns the absolute of the given value.

[Pure]
public static method	Abs (float32 value)
type	float32
params	value		The value.
returns		[>=0]	The absolute value.

---

Returns the absolute of the given value.

[Pure]
public static method	Abs (int32 value)
type	int32
params	value		The value.
returns		[>=0]	The absolute value.

---

Returns the absolute of the given value.

[Pure]
public static method	Abs (int64 value)
type	int64
params	value		The value.
returns		[>=0]	The absolute value.

Acos

Returns the angle whose cosine is the specified number.

[Pure]
public static method	Acos (float64 v)
type	float64
params	v		The number.
returns			The angle in radians.

Acosh

Computes the inverse hyperbolic cosine for the given value.

[Pure]
public static method	Acosh (float64 v)
type	float64
params	v		The value.
returns			The resulting value.

Asin

Returns the angle whose sine is the specified number.

[Pure]
public static method	Asin (float64 v)
type	float64
params	v		The number.
returns			The angle in radians.

Asinh

Computes the inverse hyperbolic sine for the given value.

[Pure]
public static method	Asinh (float64 v)
type	float64
params	v		The value.
returns			The resulting value.

Atan

Returns the angle whose tangent is the specified number.

[Pure]
public static method	Atan (float64 v)
type	float64
params	v		A number representing a tangent.
returns			The angle, in radians.

Atan2

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

[Pure]
public static method	Atan2 (float64 y, float64 x)
type	float64
params	y		The Y-coordinate of a point.
	x		The X-coordinate of a point.
returns		[-Pi..Pi]	An angle, in radians.

Atanh

Computes the inverse hyperbolic tangent for the given value.

[Pure]
public static method	Atanh (float64 v)
type	float64
params	v		The value.
returns			The resulting value.

Cbrt

Computes the cubic root of the given number.

[Pure]
public static method	Cbrt (float64 x)
type	float64
params	x		The number.
returns			The cubic root.

Ceiling

Returns the smallest integer greater than or equal to the specified double-precision floating-point number.

[Pure]
public static method	Ceiling (float64 number)
type	float64
params	number		A double-precision floating-point number.
returns			The smallest integer greater than or equal to number.

---

Returns the smallest integer greater than or equal to the specified single-precision floating-point number.

[Pure]
public static method	Ceiling (float32 number)
type	float32
params	number		A single-precision floating-point number.
returns			The smallest integer greater than or equal to number.

---

Returns the smallest multiple of divisor that is greater than or equal to value.

[Pure]
public static method	Ceiling (int32 value, int32 divisor)
type	int32
params	value		The input value.
	divisor		The divisor value (must be greater than 0).
returns			The resulting value, divided by divisor.

---

Returns the smallest multiple of divisor that is greater than or equal to value.

[Pure]
public static method	Ceiling (int64 value, int64 divisor)
type	int64
params	value		The input value.
	divisor		The divisor value (must be greater than 0).
returns			The resulting value, divided by divisor.

Clamp

Clamps the given value.

[Pure]
public static method	Clamp (float64 value, float64 lower, float64 upper)
type	float64
params	value		The value.
	lower		Lower boundary to clamp to.
	upper		Upper boundary to clamp to.
returns			The clamped value.

---

Clamps the given value.

[Pure]
public static method	Clamp (float32 value, float32 lower, float32 upper)
type	float32
params	value		The value.
	lower		Lower boundary to clamp to.
	upper		Upper boundary to clamp to.
returns			The clamped value.

---

Clamps the given value.

[Pure]
public static method	Clamp (int32 value, int32 lower, int32 upper)
type	int32
params	value		The value.
	lower		Lower boundary to clamp to.
	upper		Upper boundary to clamp to.
returns			The clamped value.

---

Clamps the given value.

[Pure]
public static method	Clamp (int64 value, int64 lower, int64 upper)
type	int64
params	value		The value.
	lower		Lower boundary to clamp to.
	upper		Upper boundary to clamp to.
returns			The clamped value.

Cos

Returns the cosine of the specified angle.

[Pure]
public static method	Cos (float64 radians)
type	float64
params	radians		An angle, measured in radians.
returns			The cosine of radians.

Cosh

Computes the hyperbolic cosine of the given value.

[Pure]
public static method	Cosh (float64 v)
type	float64
params	v		The value.
returns			The hyperbolic cosine of v.

Cot

Returns the co-tangent of the specified angle.

[Pure]
public static method	Cot (float64 radians)
type	float64
params	radians		An angle, measured in radians.
returns			The co-tangent of radians.

Digits10

Returns the number of decimal digits of the given number.

[Pure]
public static method	Digits10 (int64 v)
type	int32
params	v		The number.
returns		[>=1]	The number of decimal digits.

Div

Computes a / b if b is not 0, returns c otherwise.

[Pure]
public static method	Div (int32 a, int32 b, int32 c = 0)
type	int32
params	a		The dividend.
	b		The divisor.
	c		The value to return if b is 0.
returns			The resulting value.

---

Computes a / b if b is not 0, returns c otherwise.

[Pure]
public static method	Div (int64 a, int64 b, int64 c = 0)
type	int64
params	a		The dividend.
	b		The divisor.
	c		The value to return if b is 0.
returns			The resulting value.

EqualOrNan

Tests if the given numbers are equal or if both are 'not-a-number'.

[Pure]
public static method	EqualOrNan (float64 a, float64 b)
type	bool
params	a		First number.
	b		Second number.
returns			true if a and b are equal or both are 'not-a-number', false otherwise.

Exp

Returns e raised to the specified power.

[Pure]
public static method	Exp (float64 power)
type	float64
params	power		A number specifying a power.
returns			The resulting value.

FastFloor

Computes the integer floor value of the given double value.

[Pure]
public static method	FastFloor (float64 x)
type	int64
params	x		The double value.
returns			The integer floor value.

---

Computes the integer floor value of the given float value.

[Pure]
public static method	FastFloor (float32 x)
type	int32
params	x		The float value.
returns			The integer floor value.

Floor

Computes the floor value of the given value.

[Pure]
public static method	Floor (float64 v)
type	float64
params	v		The value.
returns			The floor value.

---

Computes the floor value of the given value.

[Pure]
public static method	Floor (float32 v)
type	float32
params	v		The value.
returns			The floor value.

---

Returns the greatest multiple of divisor that is less than or equal to value.

[Pure]
public static method	Floor (int32 value, int32 divisor)
type	int32
params	value		The input value.
	divisor		The divisor value (must be greater than 0).
returns			The resulting value, divided by divisor.

---

Returns the greatest multiple of divisor that is less than or equal to value.

[Pure]
public static method	Floor (int64 value, int64 divisor)
type	int64
params	value		The input value.
	divisor		The divisor value (must be greater than 0).
returns			The resulting value, divided by divisor.

IsInf

Checks if the given floating point number is +/-Inf (infinity).

[Pure]
public static method	IsInf (float64 number)
type	bool
params	number		The number.
returns			true if number is +/-Inf, false if not.

IsNan

Checks if the given floating point number is NaN (not-a-number).

[Pure]
public static method	IsNan (float64 number)
type	bool
params	number		The number.
returns			true if number is NaN, false if not.

IsNegInf

Checks if the given floating point number is -Inf (negative infinity).

[Pure]
public static method	IsNegInf (float64 number)
type	bool
params	number		The number.
returns			true if number is -Inf, false if not.

IsNumber

Checks if the given floating point number is a regular number (i.e. neither nan nor infinity).

[Pure]
public static method	IsNumber (float64 number)
type	bool
params	number		The floating point number.
returns			true if number is neither nan nor infinity.

IsPosInf

Checks if the given floating point number is +Inf (positive infinity).

[Pure]
public static method	IsPosInf (float64 number)
type	bool
params	number		The number.
returns			true if number is +Inf, false if not.

IsPowerOfTwo

Checks if the given value is a power of two.

[Pure]
public static method	IsPowerOfTwo (int32 v)
type	bool
params	v		An integer value.
returns			true if v is a power of two, false if not.

Remarks:

A value v that satisfies the equation v = 2^n with 0 < n < 31 is said to be a power of two.

---

Checks if the given value is a power of two.

[Pure]
public static method	IsPowerOfTwo (int64 v)
type	bool
params	v		An integer value.
returns			true if v is a power of two, false if not.

Remarks:

A value v that satisfies the equation v = 2^n with 0 < n < 31 is said to be a power of two.

IsPrime

Tests if the given number is prime.

[Pure]
public static method	IsPrime (int32 value)
type	bool
params	value		The number to test.
returns			true if value is prime, false if it is not.

Linear

Returns a linear function that passes through the given points.

public static method	Linear (float64 ax, float64 ay, float64 bx, float64 by)
type	Vec2D
params	ax		X-coordinate of first point.
	ay		Y-coordinate of first point.
	bx		X-coordinate of second point.
	by		Y-coordinate of second point.
returns			The coefficients m and b, returned as X and Y, respectively.

Remarks:

This method computes the coefficients m and b of the linear function

f(x) = m * x + b

so that the following holds true:

f(ax) = ay
f(bx) = by

Log

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

[Pure]
public static method	Log (float64 number)
type	float64
params	number		A number whose logarithm is to be found.
returns			Positive The natural logarithm of number.

See also:

LogBase

Log2_Ceiling

Returns the discrete logarithm of base two of the given value.

[Pure]
public static method	Log2_Ceiling (int64 v)
type	int32
params	v	[>0]	The value.
returns		[0..63]	The discrete logarithm of v.

Remarks:

The discrete logarithm of base two is computed as follows:

log2 := ceiling(log(v) / log(2))

Log2_Floor

Returns the discrete logarithm of base two of the given value.

[Pure]
public static method	Log2_Floor (int64 v)
type	int32
params	v	[>0]	The value.
returns		[0..62]	The discrete logarithm of v.

Remarks:

The discrete logarithm of base two is computed as follows:

log2 := floor(log(v) / log(2))

Max

Returns the maximum of the given values.

[Pure]
public static method	Max (float64 a, float64 b)
type	float64
params	a		First value (can be NaN).
	b		Second value.
returns			The maximum value.

---

Returns the maximum of the given values.

[Pure]
public static method	Max (float32 a, float32 b)
type	float32
params	a		First value (can be NaN).
	b		Second value.
returns			The maximum value.

---

Returns the maximum of the given values.

[Pure]
public static method	Max (int32 a, int32 b)
type	int32
params	a		First value.
	b		Second value.
returns			The maximum value.

---

Returns the maximum of the given values.

[Pure]
public static method	Max (int64 a, int64 b)
type	int64
params	a		First value.
	b		Second value.
returns			The maximum value.

---

Returns the maximum of the given values.

[Pure]
public static method	Max (float64 a, float64 b, float64 c)
type	float64
params	a		First value.
	b		Second value.
	c		Third value.
returns			The maximum value.

---

Returns the maximum of the given values.

[Pure]
public static method	Max (float32 a, float32 b, float32 c)
type	float32
params	a		First value.
	b		Second value.
	c		Third value.
returns			The maximum value.

---

Returns the maximum of the given values.

[Pure]
public static method	Max (int32 a, int32 b, int32 c)
type	int32
params	a		First value.
	b		Second value.
	c		Third value.
returns			The maximum value.

---

Returns the maximum of the given values.

[Pure]
public static method	Max (int64 a, int64 b, int64 c)
type	int64
params	a		First value.
	b		Second value.
	c		Third value.
returns			The maximum value.

Min

Returns the minimum of the given values.

[Pure]
public static method	Min (float64 a, float64 b)
type	float64
params	a		First value (can be NaN).
	b		Second value.
returns			The maximum value.

---

Returns the minimum of the given values.

[Pure]
public static method	Min (float32 a, float32 b)
type	float32
params	a		First value (can be NaN).
	b		Second value.
returns			The maximum value.

---

Returns the minimum of the given values.

[Pure]
public static method	Min (int32 a, int32 b)
type	int32
params	a		First value.
	b		Second value.
returns			The maximum value.

---

Returns the minimum of the given values.

[Pure]
public static method	Min (int64 a, int64 b)
type	int64
params	a		First value.
	b		Second value.
returns			The maximum value.

---

Returns the minimum of the given values.

[Pure]
public static method	Min (float64 a, float64 b, float64 c)
type	float64
params	a		First value.
	b		Second value.
	c		Third value.
returns			The maximum value.

---

Returns the minimum of the given values.

[Pure]
public static method	Min (float32 a, float32 b, float32 c)
type	float32
params	a		First value.
	b		Second value.
	c		Third value.
returns			The maximum value.

---

Returns the minimum of the given values.

[Pure]
public static method	Min (int32 a, int32 b, int32 c)
type	int32
params	a		First value.
	b		Second value.
	c		Third value.
returns			The maximum value.

---

Returns the minimum of the given values.

[Pure]
public static method	Min (int64 a, int64 b, int64 c)
type	int64
params	a		First value.
	b		Second value.
	c		Third value.
returns			The maximum value.

Mod

Computes the remainder of x / y.

[Pure]
public static method	Mod (float64 x, float64 y)
type	float64
params	x		The dividend.
	y		The divisor.
returns			The value of x-(y*R), where R is equal to x/y, rounded towards zero.

---

Computes the remainder of x / y.

[Pure]
public static method	Mod (float32 x, float32 y)
type	float32
params	x		The dividend.
	y		The divisor.
returns			The value of x-(y*R), where R is equal to x/y, rounded towards zero.

NextPowerOfTwo

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

[Pure]
public static method	NextPowerOfTwo (int32 v)
type	int64
params	v		The value.
returns		[>=1]	The next power of two.

Pack3

Packs the given 8-bit integer values into a 32-bit floating-point value.

[Pure]
public static method	Pack3 (int32 a, int32 b, int32 c)
type	float32
params	a	[0..255]	First integer value to pack.
	b	[0..255]	Second integer value to pack.
	c	[0..255]	Third integer value to pack.
returns			The packed floating-point value.

See also:

Unpack3

Pack4

Packs the given 6-bit integer values into a 32-bit floating-point value.

[Pure]
public static method	Pack4 (int32 a, int32 b, int32 c, int32 d)
type	float32
params	a	[0..63]	First integer value to pack.
	b	[0..63]	Second integer value to pack.
	c	[0..63]	Third integer value to pack.
	d	[0..63]	Third integer value to pack.
returns			The packed floating-point value.

See also:

Unpack3

Pow

Raises the given value by the specified power.

[Pure]
public static method	Pow (float64 value, float64 power)
type	float64
params	value		The value.
	power		The power.
returns			The resulting value.

Pow10

Returns a discrete power of 10.

[Pure]
public static method	Pow10 (int32 v)
type	int64
params	v		The power.
returns			The discrete power of 10 or 0 if v is outside of the range [0..18].

Round

Rounds the given number.

[Pure]
public static method	Round (float64 value, int32 digits = 0)
type	float64
params	value		The number value to round.
	digits	[>=0]	The number of fractional digits to keep. Defaults to 0.
returns			The resulting number.

Sign

Returns the sign of the given value.

[Pure]
public static method	Sign (int64 v)
type	int32
params	v		The value.
returns			-1 if v is less than zero. 1 if v is greater than zero or 0 if v is equal to zero.

---

Returns the sign of the given value.

[Pure]
public static method	Sign (float64 v)
type	int32
params	v		The value.
returns			-1 if v is less than zero. 1 if v is greater than zero or 0 if v is equal to zero.

Similar

Checks if the given floating-point values are similar.

[Pure]
public static method	Similar (float32 a, float32 b)
type	bool
params	a		First value.
	b		Second value.
returns			true if both values are similar but not necessarily equal, false if they are different.

---

Checks if the given floating-point values are similar.

[Pure]
public static method	Similar (float64 a, float64 b)
type	bool
params	a		First value.
	b		Second value.
returns			true if both values are similar but not necessarily equal, false if they are different.

Sin

Returns the sine of the specified angle.

[Pure]
public static method	Sin (float64 radians)
type	float64
params	radians		An angle, measured in radians.
returns			The sine of radians.

Sinh

Computes the hyperbolic sine of the given value.

[Pure]
public static method	Sinh (float64 v)
type	float64
params	v		The value.
returns			The hyperbolic sine of v.

SmootherStep

Applies a smoothstep function to the given value.

[Pure]
public static method	SmootherStep (float64 x)
type	float64
params	x		Interpolation factor in the range [0..1].
returns			The smoother interpolation factor f(x).

Remarks:

This method uses the following polynomial:

f(x) = 6 * x^5 - 15 * x^4 + 10 * x^3
f(0) = 0
f(1) = 1
f'(0) = f''(0) = f'(1) = f''(1) = 0
F(0.5) - F(0) = 0.5

---

Applies a smoothstep function to the given value.

[Pure]
public static method	SmootherStep (float64 a, float64 b, float64 f)
type	float64
params	a		First value.
	b		Second value.
	f		Interpolation factor in the range [0..1].
returns			The interpolated value.

Remarks:

This method uses the following polynomial:

f(x) = 6 * x^5 - 15 * x^4 + 10 * x^3
f(0) = 0
f(1) = 1
f'(0) = f''(0) = f'(1) = f''(1) = 0
F(0.5) - F(0) = 0.5

SplineCatmullRom

Mixes the first and second value using a Catmull-Rom spline.

[Pure]
public static method	SplineCatmullRom (float64 a, float64 b, float64 c, float64 d, float64 f)
type	float64
params	a		Zeroth value.
	b		First value.
	c		Second value.
	d		Third value.
	f		Mix factor.
returns			The mixed value.

SplineUniformB

Mixes the first and second value using an Uniform-B spline.

[Pure]
public static method	SplineUniformB (float64 a, float64 b, float64 c, float64 d, float64 f)
type	float64
params	a		Zeroth value.
	b		First value.
	c		Second value.
	d		Third value.
	f		Mix factor.
returns			The mixed value.

Sqr

Returns the square of the given number.

[Pure]
public static method	Sqr (float64 number)
type	float64
params	number		The number.
returns			The square value.

---

Returns the square of the given number.

[Pure]
public static method	Sqr (float32 number)
type	float32
params	number		The number.
returns			The square value.

Sqrt

Returns the square root of a specified number.

[Pure]
public static method	Sqrt (float64 number)
type	float64
params	number		A number.
returns			The positive square root of number.

---

Returns the square root of a specified number.

[Pure]
public static method	Sqrt (float32 number)
type	float32
params	number		A number.
returns			The positive square root of number.

Sqrt_Int

Computes the integer square root of the given value.

[Pure]
public static method	Sqrt_Int (int32 value)
type	int32
params	value		The input value.
returns			The integer square root of value.

Remarks:

The integer square root is defined as floor(sqrt(v)).

---

Computes the integer square root of the given value.

[Pure]
public static method	Sqrt_Int (int64 value)
type	int64
params	value		The input value.
returns			The integer square root of value.

Remarks:

The integer square root is defined as floor(sqrt(v)).

Tan

Returns the tangent of the specified angle.

[Pure]
public static method	Tan (float64 radians)
type	float64
params	radians		An angle, measured in radians.
returns			The tangent of radians.

Tanh

Computes the hyperbolic tangent of the given value.

[Pure]
public static method	Tanh (float64 v)
type	float64
params	v		The value.
returns			The hyperbolic tangent of v.

Truncate

Removes all fractional digits from the given number.

[Pure]
public static method	Truncate (float64 number)
type	float64
params	number		The number.
returns			The truncated number.

---

Removes all fractional digits from the given number.

[Pure]
public static method	Truncate (float32 number)
type	float32
params	number		The number.
returns			The truncated number.

Unpack3

Unpacks the given 32-bit floating-point value to three 8-bit integer values.

[Pure]
public static method	Unpack3 (float32 v)
type	Vec3I
params	v		The packed floating-point value.
returns			The unpacked integer values.

See also:

Pack3

Unpack4

Unpacks the given 32-bit floating-point value to four 6-bit integer values.

[Pure]
public static method	Unpack4 (float32 v)
type	Vec4I
params	v		The packed floating-point value.
returns			The unpacked integer values.

See also:

Pack4

UnsignedCompare

Compares the given values, treating them as unsigned integers.

[Pure]
public static method	UnsignedCompare (int64 first, int64 second)
type	int32
params	first		The first value.
	second		The second value.
returns			-1 if first is less than second 0 if first is equal to second 1 if first is greater than second

UnsignedDivide

Divides the given integers while treating them as unsigned: dividend / divisor.

[Pure]
public static method	UnsignedDivide (int64 dividend, int64 divisor)
type	int64
params	dividend		The dividend value.
	divisor		The divisor value.
returns			The quotient.

UnsignedModulo

Divides the given integers while treating them as unsigned: dividend % divisor.

[Pure]
public static method	UnsignedModulo (int64 dividend, int64 divisor)
type	int64
params	dividend		The dividend value.
	divisor		The divisor value.
returns			The remainder.