arithmoi-0.2.0.4: Efficient basic number-theoretic functions. Primes, powers, integer logarithms.

Portability Non-portable (GHC extensions) Provisional Daniel Fischer Safe-Infered

Math.NumberTheory.Logarithms

Description

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

Synopsis

# Integer logarithms with input checks

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`.

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

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

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

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

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

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

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