Math.NumberTheory.Logarithms

Integer Logarithms. For efficiency, the internal representation of Integers from integer-gmp is used.

Integer logarithms with input checks

integerLogBase :: Integer -> Integer -> Int

Calculate the integer logarithm for an arbitrary base. The base must be greater than 1, the second argument, the number whose logarithm is sought, must be positive, otherwise an error is thrown. If base == 2, the specialised version is called, which is more efficient than the general algorithm.

Satisfies:

base ^ integerLogBase base m <= m < base ^ (integerLogBase base m + 1)

for base > 1 and m > 0.

integerLog2 :: Integer -> Int

Calculate the integer logarithm of an Integer to base 2. The argument must be positive, otherwise an error is thrown.

integerLog10 :: Integer -> Int

Calculate the integer logarithm of an Integer to base 10. The argument must be positive, otherwise an error is thrown.

naturalLogBase :: Natural -> Natural -> Int

Cacluate the integer logarithm for an arbitrary base. The base must be greater than 1, the second argument, the number whose logarithm is sought, must be positive, otherwise an error is thrown. If base == 2, the specialised version is called, which is more efficient than the general algorithm.

Satisfies:

base ^ integerLogBase base m <= m < base ^ (integerLogBase base m + 1)

for base > 1 and m > 0.

naturalLog2 :: Natural -> Int

Calculate the natural logarithm of an Natural to base 2. The argument must be non-zero, otherwise an error is thrown.

naturalLog10 :: Natural -> Int

Calculate the integer logarithm of an Integer to base 10. The argument must be not zero, otherwise an error is thrown.

intLog2 :: Int -> Int

Calculate the integer logarithm of an Int to base 2. The argument must be positive, otherwise an error is thrown.

wordLog2 :: Word -> Int

Calculate the integer logarithm of a Word to base 2. The argument must be positive, otherwise an error is thrown.

Integer logarithms without input checks

These functions are total, however, don't rely on the values with out-of-domain arguments.

integerLogBase' :: Integer -> Integer -> Int

Same as integerLogBase, but without checks, saves a little time when called often for known good input.

integerLog2' :: Integer -> Int

Same as integerLog2, but without checks, saves a little time when called often for known good input.

integerLog10' :: Integer -> Int

Same as integerLog10, but without a check for a positive argument. Saves a little time when called often for known good input.

intLog2' :: Int -> Int

Same as intLog2, but without checks, saves a little time when called often for known good input.

wordLog2' :: Word -> Int

Same as wordLog2, but without checks, saves a little time when called often for known good input.