GHC.Internal.Natural

Natural number

Invariant: numbers <= 0xffffffffffffffff use the NS constructor

A lifted BigNat

Represented as an array of limbs (Word#) stored in little-endian order (Word# themselves use machine order).

Invariant (canonical representation): higher Word# is non-zero.

As a consequence, zero is represented with a WordArray# whose size is 0.

Construct Natural value from list of Words.

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.

Natural Addition

Natural subtraction. May throw Control.Exception.Underflow.

Natural subtraction. Returns Nothings for non-positive results.

Natural multiplication

Compute greatest common divisor.

Compute least common multiple.

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

Construct Natural from Word value.

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