Provides additional math functions that are not available in System.Math. More...

Source file:

/Core/Loyc.Essentials/Math/MathEx.cs

Remarks

Provides additional math functions that are not available in System.Math.

Static Public Member Functions
static int	Sign< T > (T num)
	Returns the sign of a number (-1 for negative, 1 for positive, 0 for zero). More...

static int	Sign (int num)
	Returns the sign of a number (-1 for negative, 1 for positive, 0 for zero). More...

static int	Sign (long num)
	Returns the sign of a number (-1 for negative, 1 for positive, 0 for zero). More...

static int	Sign (float num)
	Returns the sign of a number (-1 for negative, 1 for positive, 0 for zero). More...

static int	Sign (double num)
	Returns the sign of a number (-1 for negative, 1 for positive, 0 for zero). More...

static int	MulShift (int a, int mulBy, int shiftBy)
	Multiplies two integers, internally producing a double-size result so that overflow is not possible, then divides the result by the specified power of two using a right shift. More...

static uint	MulShift (uint a, uint mulBy, int shiftBy)

static long	MulShift (long a, long mulBy, int shiftBy)

static ulong	MulShift (ulong a, ulong mulBy, int shiftBy)

static int	MulDiv (int a, int mulBy, int divBy, out int remainder)
	Multiplies two integers, internally producing a double-size result so that overflow is not possible, then divides the result by the specified number. More...

static uint	MulDiv (uint a, uint mulBy, uint divBy, out uint remainder)

static long	MulDiv (long a, long mulBy, long divBy, out long remainder)

static ulong	MulDiv (ulong a, ulong mulBy, ulong divBy, out ulong remainder)

static int	MulDiv (int a, int mulBy, int divBy)

static uint	MulDiv (uint a, uint mulBy, uint divBy)

static long	MulDiv (long a, long mulBy, long divBy)

static ulong	MulDiv (ulong a, ulong mulBy, ulong divBy)

static double	Mod (double x, double y)

static float	Mod (float x, float y)

static int	Mod (int x, int y)

static long	Mod (long x, long y)

static uint	RoL (uint value, int amt)
	Rotates a bit pattern left by the specified number of bits. More...

static int	RoL (int value, int amt)
	Rotates a bit pattern left by the specified number of bits. More...

static ulong	RoL (ulong value, int amt)
	Rotates a bit pattern left by the specified number of bits. More...

static long	RoL (long value, int amt)
	Rotates a bit pattern left by the specified number of bits. More...

static ushort	RoL (ushort value, int amt)
	Rotates a bit pattern left by the specified number of bits. More...

static byte	RoL (byte value, int amt)
	Rotates a bit pattern left by the specified number of bits. More...

static uint	RoR (uint value, int amt)
	Rotates a bit pattern right by the specified number of bits. More...

static int	RoR (int value, int amt)
	Rotates a bit pattern right by the specified number of bits. More...

static ulong	RoR (ulong value, int amt)
	Rotates a bit pattern right by the specified number of bits. More...

static long	RoR (long value, int amt)
	Rotates a bit pattern right by the specified number of bits. More...

static ushort	RoR (ushort value, int amt)
	Rotates a bit pattern right by the specified number of bits. More...

static byte	RoR (byte value, int amt)
	Rotates a bit pattern right by the specified number of bits. More...

static uint	Sqrt (long value)

static uint	Sqrt (ulong value)

static int	Sqrt (int value)

static uint	Sqrt (uint value)

static float	Sqrt (float value)

static double	Sqrt (double value)

static int	CountOnes (uint x)
	Returns the number of '1' bits in x More...

static byte	CountOnes (byte x)

static int	CountOnes (ushort x)

static int	CountOnes (int x)

static int	CountOnes (long x)

static int	CountOnes (ulong x)

static int	Log2Floor (uint x)

static int	Log2Floor (int x)
	Returns the floor of the base-2 logarithm of x. e.g. 1024 -> 10, 1000 -> 9 More...

static int	Log2Floor (ulong x)

static int	Log2Floor (long x)

static uint	NextPowerOf2 (uint x)
	Gets the next higher power of 2, e.g. 4=>8, 13=>16. More...

static ulong	NextPowerOf2 (ulong x)
	Gets the next higher power of 2, e.g. 4=>8, 13=>16. More...

static int	NextPowerOf2 (int x)
	Calls NextPowerOf2(uint). More...

static int	NextPowerOf2 (long x)
	Calls NextPowerOf2(ulong). More...

static int	FindFirstOne (uint i)
	Returns the bit position of the first '1' bit in a uint, or -1 the input is zero. More...

static int	FindFirstZero (uint i)
	Returns the bit position of the first '0' bit in a uint, or -1 if there are no zeros. More...

static int	FindLastOne (uint i)
	Returns the bit position of the first '1' bit in a uint, or -1 the input is zero. More...

static int	FindLastZero (uint i)

static double	Int64BitsToDouble (long bits)

static long	DoubleToInt64Bits (double value)

static double	Int32BitsToSingle (int bits)

static long	SingleToInt32Bits (float value)

static float	NextHigher (float a)

static float	NextLower (float a)

static double	NextHigher (double num)

static double	NextLower (double num)

static double	ShiftLeft (double num, int amount)

static double	ShiftRight (double num, int amount)

static float	ShiftLeft (float num, int amount)

static float	ShiftRight (float num, int amount)

static int	ShiftLeft (int num, int amount)

static long	ShiftLeft (long num, int amount)

static int	ShiftRight (int num, int amount)

static long	ShiftRight (long num, int amount)

static T	ShiftLeft< T > (T num, int amount)

static T	Min< T > (T a, T b)

static T	Max< T > (T a, T b)

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

static bool	SortPair< T > (ref T lo, ref T hi, Comparison< T > comp)

static bool	SortPair< T > (ref T lo, ref T hi)

static int	Average (int x, int y)
	Computes the average of two integers. Will not overflow. More...

static long	Average (long x, long y)
	Computes the average of two integers. Will not overflow. More...

static float	Average (float x, float y)
	Computes the average of two numbers. Will not overflow. More...

static double	Average (double x, double y)
	Computes the average of two numbers. Will not overflow. More...

static T	Average< T > (T x, T y)
	Computes the average of two numbers. Slow. No overflow protection. More...

static int	Square (int x)

static long	Square (long x)

static uint	Square (uint x)

static ulong	Square (ulong x)

static float	Square (float x)

static double	Square (double x)

static int	Cube (int x)

static long	Cube (long x)

static uint	Cube (uint x)

static ulong	Cube (ulong x)

static float	Cube (float x)

static double	Cube (double x)

static bool	IsPrime (int num)
	Returns true if `num` is a prime number, meaning that it is greater than 1 and is divisible only by 1 and itself. More...

Member Function Documentation

static int Loyc.Math.MathEx.Average	(	int	x,
		int	y
	)

inlinestatic

Computes the average of two integers. Will not overflow.

static long Loyc.Math.MathEx.Average	(	long	x,
		long	y
	)

inlinestatic

Computes the average of two integers. Will not overflow.

static float Loyc.Math.MathEx.Average	(	float	x,
		float	y
	)

inlinestatic

Computes the average of two numbers. Will not overflow.

static double Loyc.Math.MathEx.Average	(	double	x,
		double	y
	)

inlinestatic

Computes the average of two numbers. Will not overflow.

static T Loyc.Math.MathEx.Average< T >	(	T	x,
		T	y
	)

inlinestatic

Computes the average of two numbers. Slow. No overflow protection.

static int Loyc.Math.MathEx.CountOnes ( uint x )

inlinestatic

Returns the number of '1' bits in x

For example, CountOnes(0xF0) == 4.

Some processors have a dedicated instruction for this operation, but the .NET framework provides no access to it.

static int Loyc.Math.MathEx.FindFirstOne ( uint i )

inlinestatic

Returns the bit position of the first '1' bit in a uint, or -1 the input is zero.

static int Loyc.Math.MathEx.FindFirstZero ( uint i )

inlinestatic

Returns the bit position of the first '0' bit in a uint, or -1 if there are no zeros.

static int Loyc.Math.MathEx.FindLastOne ( uint i )

inlinestatic

Returns the bit position of the first '1' bit in a uint, or -1 the input is zero.

static bool Loyc.Math.MathEx.IsPrime ( int num )

inlinestatic

Returns true if num is a prime number, meaning that it is greater than 1 and is divisible only by 1 and itself.

Parameters

num	A number to test.

This test takes O(sqrt(num)) time and it is moderately optimized, although faster algorithms exist (e.g. the Sieve of Eratosthenes can be faster per number, but is designed to find a list of all the prime numbers rather than to test a single number.

static int Loyc.Math.MathEx.Log2Floor ( int x )

inlinestatic

Returns the floor of the base-2 logarithm of x. e.g. 1024 -> 10, 1000 -> 9

The return value is -1 for an input that is zero or negative.

Some processors have a dedicated instruction for this operation, but the .NET framework provides no access to it.

static int Loyc.Math.MathEx.MulDiv	(	int	a,
		int	mulBy,
		int	divBy,
		out int	remainder
	)

inlinestatic

Multiplies two integers, internally producing a double-size result so that overflow is not possible, then divides the result by the specified number.

Parameters

remainder The remainder of the division is placed here. The remainder is computed properly even if the main result overflows.

Returns: a * mulBy / divBy, without overflow during multiplication.

If the final result does not fit in the original data type, this method returns largest possible value of the result type (int.MaxValue, or int.MinValue if the overflowing result is negative).

static uint Loyc.Math.MathEx.MulDiv	(	uint	a,
		uint	mulBy,
		uint	divBy,
		out uint	remainder
	)

inlinestatic

If the final result does not fit in the original data type, this method returns largest possible value of the result type (uint.MaxValue).

static long Loyc.Math.MathEx.MulDiv	(	long	a,
		long	mulBy,
		long	divBy,
		out long	remainder
	)

inlinestatic

If the final result does not fit in the original data type, this method returns largest possible value of the result type (long.MaxValue, or long.MinValue if the overflowing result is negative).

static ulong Loyc.Math.MathEx.MulDiv	(	ulong	a,
		ulong	mulBy,
		ulong	divBy,
		out ulong	remainder
	)

inlinestatic

If the final result does not fit in the original data type, this method returns largest possible value of the result type (ulong.MaxValue).

static int Loyc.Math.MathEx.MulShift	(	int	a,
		int	mulBy,
		int	shiftBy
	)

inlinestatic

Multiplies two integers, internally producing a double-size result so that overflow is not possible, then divides the result by the specified power of two using a right shift.

Returns: a * mulBy >> shiftBy, without overflow during multiplication.

This method does not handle the case that the result is too large to fit in the original data type.

static uint Loyc.Math.MathEx.NextPowerOf2 ( uint x )

inlinestatic

Gets the next higher power of 2, e.g. 4=>8, 13=>16.

For negative values of x, NextPowerOf2((uint)x) is 0.

static ulong Loyc.Math.MathEx.NextPowerOf2 ( ulong x )

inlinestatic

Gets the next higher power of 2, e.g. 4=>8, 13=>16.

For negative values of (long)x, NextPowerOf2((ulong)x) is 0.

static int Loyc.Math.MathEx.NextPowerOf2 ( int x )

inlinestatic

Calls NextPowerOf2(uint).

static int Loyc.Math.MathEx.NextPowerOf2 ( long x )

inlinestatic

Calls NextPowerOf2(ulong).

static uint Loyc.Math.MathEx.RoL	(	uint	value,
		int	amt
	)

inlinestatic

Rotates a bit pattern left by the specified number of bits.

static int Loyc.Math.MathEx.RoL	(	int	value,
		int	amt
	)

inlinestatic

Rotates a bit pattern left by the specified number of bits.

static ulong Loyc.Math.MathEx.RoL	(	ulong	value,
		int	amt
	)

inlinestatic

Rotates a bit pattern left by the specified number of bits.

static long Loyc.Math.MathEx.RoL	(	long	value,
		int	amt
	)

inlinestatic

Rotates a bit pattern left by the specified number of bits.

static ushort Loyc.Math.MathEx.RoL	(	ushort	value,
		int	amt
	)

inlinestatic

Rotates a bit pattern left by the specified number of bits.

static byte Loyc.Math.MathEx.RoL	(	byte	value,
		int	amt
	)

inlinestatic

Rotates a bit pattern left by the specified number of bits.

static uint Loyc.Math.MathEx.RoR	(	uint	value,
		int	amt
	)

inlinestatic