GMP notes
=========

need
----

canonical place for high-level GMP types (mpz, mpq, mpf, gmp_randstate)
(low-level types (limb type, etc) are exposed by 'integer-gmp')

helpers for FFI to high-level GMP code (whether in gmp or 3rd-party libraries)
(users of low-level GMP probably don't need much help)


want
----

fast BigFloat type
("There are no reallocations during a calculation, only in a change of
precision with mpf_set_prec."
<https://gmplib.org/manual/Float-Internals.html>)


later
-----

BigFloat Num instances (with type-level precision ala 'rounded')


FFI helper sketch
-----------------

appropriate use of safe vs unsafe ffi can't be decided by a binding library..


> peekInteger           :: mpz_srcptr_t -> IO Integer

straightforward enough?


> withIntegerSrc        :: Integer -> (mpz_srcptr_t -> IO r) -> IO r

for safe foreign call: alloca struct + limbs and copy data?


> unsafeWithIntegerSrc  :: Integer -> (mpz_srcptr_t -> IO r) -> IO r

for unsafe foreign call: alloca struct
is it possible and safe to reuse Integer limb array (if it has one)?


> pokeInteger           :: mpz_ptr_t -> Integer -> IO ()
> pokeInteger p i       =  unsafeWithIntegerSrc i $ mpz_set p

straightforward, assumes mpz_ptr_t already init'd
this mpz_set is foreign imported unsafe


> peekRational          :: mpq_srcptr_t -> IO Rational

could return a pair of Integer in case the mpq isn't canonical?


> withRationalSrc       :: Rational -> (mpq_srcptr_t -> IO r) -> IO r
> unsafeWithRationalSrc :: Rational -> (mpq_srcptr_t -> IO r) -> IO r
> pokeRational          :: mpq_ptr_t -> Rational -> IO ()

as Integer versions


similarly for BigFloat


BigFloat primops
----------------

> addBigFloat :: BigFloat -> BigFloat -> prec -> BigFloat

ie, specify output precision explicitly instead of guessing from input


> setPrecBigFloat :: BigFloat -> prec -> BigFloat

immutability means limb array could be reused if prec is smaller?