Module "Integer.curry"

A collection of common operations on integer numbers. Most operations make no assumption on the precision of integers. Operation bitNot is necessarily an exception.

Author: Sergio Antoy

Version: March 20, 2006

Functions:
abs | binomial | bitAnd | bitNot | bitOr | bitTrunc | bitXor | even | factorial | ilog | isqrt | max3 | maxlist | min3 | minlist | odd | pow

pow  :: Int -> Int -> Int              The value of pow a b is a raised to the power of b.

ilog  :: Int -> Int              The value of ilog n is the floor of the logarithm in the base 10 of n.

isqrt  :: Int -> Int              The value of isqrt n is the floor of the square root of n.

factorial  :: Int -> Int              The value of factorial n is the factorial of n.

binomial  :: Int -> Int -> Int              The value of binomial n m is n*(n-1)*...*(n-m+1)/m*(m-1)*...1 Fails if m <= 0 or n < m.

abs  :: Int -> Int              The value of abs n is the absolute value of n.

max3  :: a -> a -> a -> a              Returns the maximum of the three arguments.

min3  :: a -> a -> a -> a              Returns the minimum of the three arguments.

maxlist  :: [a] -> a              Returns the maximum of a list of integer values.

minlist  :: [a] -> a              Returns the minimum of a list of integer values.

bitTrunc  :: Int -> Int -> Int              The value of bitTrunc n m is the value of the n least significant bits of m.

bitAnd  :: Int -> Int -> Int              Returns the bitwise AND of the two arguments.

bitOr  :: Int -> Int -> Int              Returns the bitwise inclusive OR of the two arguments.

bitNot  :: Int -> Int              Returns the bitwise NOT of the argument.

bitXor  :: Int -> Int -> Int              Returns the bitwise exclusive OR of the two arguments.

even  :: Int -> Bool              Returns whether an integer is even

odd  :: Int -> Bool              Returns whether an integer is odd

The value of pow a b is a raised to the power of b. Fails if b < 0. Executes in O(log b) steps.

Example call:  (pow a b)

Parameters:

a - The base.

b - The exponent.

Returns:

a raised to the power of b.

Further infos:

• incompletely defined

The value of ilog n is the floor of the logarithm in the base 10 of n. Fails if n <= 0. For positive integers, the returned value is 1 less the number of digits in the decimal representation of n.

Example call:  (ilog n)

Parameters:

n - The argument.

Returns:

the floor of the logarithm in the base 10 of n.

Further infos:

• incompletely defined

The value of isqrt n is the floor of the square root of n. Fails if n < 0. Executes in O(log n) steps, but there must be a better way.

Example call:  (isqrt n)

Parameters:

n - The argument.

Returns:

the floor of the square root of n.

Further infos:

• incompletely defined

The value of factorial n is the factorial of n. Fails if n < 0.

Example call:  (factorial n)

Parameters:

n - The argument.

Returns:

the factorial of n.

Further infos:

• incompletely defined

The value of binomial n m is n*(n-1)*...*(n-m+1)/m*(m-1)*...1 Fails if m <= 0 or n < m.

Example call:  (binomial n m)

Parameters:

n - Argument.

m - Argument.

Returns:

the binomial coefficient of n over m.

Further infos:

• incompletely defined

The value of abs n is the absolute value of n.

Example call:  (abs n)

Parameters:

n - The argument.

Returns:

the absolute value of n.

Further infos:

• incompletely defined

Returns the maximum of the three arguments.

Example call:  (max3 n m p)

Parameters:

n - Argument.

m - Argument.

p - Argument.

Returns:

the maximum among n, m and p.

Returns the minimum of the three arguments.

Example call:  (min3 n m p)

Parameters:

n - Argument.

m - Argument.

p - Argument.

Returns:

the minimum among n, m and p.

Returns the maximum of a list of integer values. Fails if the list is empty.

Example call:  (maxlist l)

Parameters:

l - The list of values.

Returns:

the maximum element of l.

Further infos:

• incompletely defined

Returns the minimum of a list of integer values. Fails if the list is empty.

Example call:  (minlist l)

Parameters:

l - The list of values.

Returns:

the minimum element of l.

Further infos:

• incompletely defined

The value of bitTrunc n m is the value of the n least significant bits of m.

Example call:  (bitTrunc n m)

Parameters:

n - Argument.

m - Argument.

Returns:

m truncated to the n least significant bits.

Returns the bitwise AND of the two arguments.

Example call:  (bitAnd n m)

Parameters:

n - Argument.

m - Argument.

Returns:

the bitwise and of n and m.

Further infos:

• incompletely defined

Returns the bitwise inclusive OR of the two arguments.

Example call:  (bitOr n m)

Parameters:

n - Argument.

m - Argument.

Returns:

the bitwise inclusive or of n and m.

Further infos:

• incompletely defined

Returns the bitwise NOT of the argument. Since integers have unlimited precision, only the 32 least significant bits are computed.

Example call:  (bitNot n)

Parameters:

n - Argument.

Returns:

the bitwise negation of n truncated to 32 bits.

Returns the bitwise exclusive OR of the two arguments.

Example call:  (bitXor n m)

Parameters:

n - Argument.

m - Argument.

Returns:

the bitwise exclusive of n and m.

Further infos:

• incompletely defined

Returns whether an integer is even

Example call:  (even n)

Parameters:

n - Argument.

Returns:

whether n is even.

Returns whether an integer is odd

Example call:  (odd n)

Parameters:

n - Argument.

Returns:

whether n is odd.