Rebase.Data.Bits

Bitwise "and"

Bitwise "or"

Bitwise "xor"

Reverse all the bits in the argument

shift x i shifts x left by i bits if i is positive, or right by -i bits otherwise. Right shifts perform sign extension on signed number types; i.e. they fill the top bits with 1 if the x is negative and with 0 otherwise.

An instance can define either this unified shift or shiftL and shiftR, depending on which is more convenient for the type in question.

rotate x i rotates x left by i bits if i is positive, or right by -i bits otherwise.

For unbounded types like Integer, rotate is equivalent to shift.

An instance can define either this unified rotate or rotateL and rotateR, depending on which is more convenient for the type in question.

zeroBits is the value with all bits unset.

The following laws ought to hold (for all valid bit indices n):

• clearBit zeroBits n == zeroBits

• setBit   zeroBits n == bit n

• testBit  zeroBits n == False

• popCount zeroBits   == 0

This method uses clearBit (bit 0) 0 as its default implementation (which ought to be equivalent to zeroBits for types which possess a 0th bit).

bit i is a value with the ith bit set and all other bits clear.

Can be implemented using bitDefault if a is also an instance of Num.

See also zeroBits.

x `setBit` i is the same as x .|. bit i

x `clearBit` i is the same as x .&. complement (bit i)

x `complementBit` i is the same as x `xor` bit i

x `testBit` i is the same as x .&. bit n /= 0

In other words it returns True if the bit at offset @n is set.

Can be implemented using testBitDefault if a is also an instance of Num.

Return the number of bits in the type of the argument. The actual value of the argument is ignored. Returns Nothing for types that do not have a fixed bitsize, like Integer.

Return the number of bits in the type of the argument. The actual value of the argument is ignored. The function bitSize is undefined for types that do not have a fixed bitsize, like Integer.

Default implementation based upon bitSizeMaybe provided since 4.12.0.0.

Return True if the argument is a signed type. The actual value of the argument is ignored

Shift the argument left by the specified number of bits (which must be non-negative). Some instances may throw an Overflow exception if given a negative input.

An instance can define either this and shiftR or the unified shift, depending on which is more convenient for the type in question.

Shift the argument left by the specified number of bits. The result is undefined for negative shift amounts and shift amounts greater or equal to the bitSize.

Defaults to shiftL unless defined explicitly by an instance.

Shift the first argument right by the specified number of bits. The result is undefined for negative shift amounts and shift amounts greater or equal to the bitSize. Some instances may throw an Overflow exception if given a negative input.

Right shifts perform sign extension on signed number types; i.e. they fill the top bits with 1 if the x is negative and with 0 otherwise.

An instance can define either this and shiftL or the unified shift, depending on which is more convenient for the type in question.

Shift the first argument right by the specified number of bits, which must be non-negative and smaller than the number of bits in the type.

Right shifts perform sign extension on signed number types; i.e. they fill the top bits with 1 if the x is negative and with 0 otherwise.

Defaults to shiftR unless defined explicitly by an instance.

Rotate the argument left by the specified number of bits (which must be non-negative).

An instance can define either this and rotateR or the unified rotate, depending on which is more convenient for the type in question.

Rotate the argument right by the specified number of bits (which must be non-negative).

An instance can define either this and rotateL or the unified rotate, depending on which is more convenient for the type in question.

Return the number of set bits in the argument. This number is known as the population count or the Hamming weight.

Can be implemented using popCountDefault if a is also an instance of Num.

Return the number of bits in the type of the argument. The actual value of the argument is ignored. Moreover, finiteBitSize is total, in contrast to the deprecated bitSize function it replaces.

finiteBitSize = bitSize
bitSizeMaybe = Just . finiteBitSize

Count number of zero bits preceding the most significant set bit.

countLeadingZeros (zeroBits :: a) = finiteBitSize (zeroBits :: a)

countLeadingZeros can be used to compute log base 2 via

logBase2 x = finiteBitSize x - 1 - countLeadingZeros x

Note: The default implementation for this method is intentionally naive. However, the instances provided for the primitive integral types are implemented using CPU specific machine instructions.

Count number of zero bits following the least significant set bit.

countTrailingZeros (zeroBits :: a) = finiteBitSize (zeroBits :: a)
countTrailingZeros . negate = countTrailingZeros

The related find-first-set operation can be expressed in terms of countTrailingZeros as follows

findFirstSet x = 1 + countTrailingZeros x

Note: The default implementation for this method is intentionally naive. However, the instances provided for the primitive integral types are implemented using CPU specific machine instructions.