Copyright	(C) 2014 Herbert Valerio Riedel, (C) 2011 Edward Kmett
License	see libraries/base/LICENSE
Maintainer	[email protected]
Stability	internal
Portability	non-portable (GHC Extensions)
Safe Haskell	Unsafe
Language	Haskell2010

The Natural number type

Warning: The internal implementation of Natural (i.e. which constructors are available) depends on the Integer backend used!

data Natural Source

Type representing arbitrary-precision non-negative integers.

Operations whose result would be negative throw (Underflow :: ArithException).

Since: 4.8.0.0

isValidNatural :: Natural -> Bool Source

Test whether all internal invariants are satisfied by Natural value

This operation is mostly useful for test-suites and/or code which constructs Integer values directly.

Since: 4.8.0.0

Conversions

wordToNatural :: Word -> Natural Source

Construct Natural from Word value.

Since: 4.8.0.0

naturalToWordMaybe :: Natural -> Maybe Word Source

Try downcasting Natural to Word value. Returns Nothing if value doesn't fit in Word.

Since: 4.8.0.0

Checked subtraction

minusNaturalMaybe :: Natural -> Natural -> Maybe Natural Source

Natural subtraction. Returns Nothings for non-positive results.

Since: 4.8.0.0

Modular arithmetic

powModNatural :: Natural -> Natural -> Natural -> Natural Source

"powModNatural b e m" computes base b raised to exponent e modulo m.

Since: 4.8.0.0