integer-logarithms-1.0.3.1: Integer logarithms.
Copyright(c) 2011 Daniel Fischer
LicenseMIT
MaintainerDaniel Fischer <daniel.is.fischer@googlemail.com>
StabilityProvisional
PortabilityNon-portable (GHC extensions)
Safe HaskellTrustworthy
LanguageHaskell2010

Math.NumberTheory.Logarithms

Description

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

Synopsis

Integer logarithms with input checks

integerLogBase :: Integer -> Integer -> Int Source #

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 Source #

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

integerLog10 :: Integer -> Int Source #

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

naturalLogBase :: Natural -> Natural -> Int Source #

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 Source #

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

naturalLog10 :: Natural -> Int Source #

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

intLog2 :: Int -> Int Source #

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

wordLog2 :: Word -> Int Source #

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 Source #

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

integerLog2' :: Integer -> Int Source #

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

integerLog10' :: Integer -> Int Source #

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 Source #

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

wordLog2' :: Word -> Int Source #

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