# Replacing GMP with a Haskell integer arithmetic library

One possiblity is to replace GMP with an arbitrary-precision integer arithmetic library written entirely in Haskell. There is at least one available:

- HIntegerByInt by Isaac Dupree

The downside is speed, of course. The upside is that (a) you don't need GMP and (b) it's relatively easy to do.

Because of the speed issue we can't abandon GMP. So there are two possibilities:

**Easy**: add a build-time option so that you can build GHC with GMP, or instead build GHC with a Haskell Integer library. Disadvantage: there would be two versions of (say)`ghc-6.8`:- vanilla
`ghc-6.8`using GMP `ghc-6.8-special`with Haskell Integer library

- vanilla

**Harder**: give a new flag to GHC, say`-integer-package=my-integer-2.0`. The intention would be that the compiler would then use the`Integer`library in package`my-integer-2.0`instead of GMP. Advantage: only one version of GHC.

Here are some notes on what you'd need to do to achieve this. You'll have to change three bits:

- The libraries
- The compiler
- The runtime system

## The libraries

Currently `Integer` is defined in the module `GHC.Num`. It would not be hard to pull out the `Integer` stuff, into a separate module `GHC.Integer` (exporting a well-defined interface, and not exposing the representation of `Integer`) that `GHC.Num` imported. `GHC.Num` is where class `Num` is defined, and `Num` uses `Integer` in the type of the class method `fromInteger`; that's why `GHC.Num` has to import `Integer` and not the other way round.

Then for the "easy" plan, you could simply change the import so that instead of `GHC.Num` importing `GHC.Integer` it imported `MyIntegerModule` or whatever. Now recompile all libraries.

The tricky bit about the "harder" plan is that you'll need to build the libraries twice; once with `GHC.Num` importing `GHC.Integer`, and once with `GHC.Num` importing your `MyIntegerModule` instead. You'd need to ship GHC with both sets of libraries; the `-integer-package` flag would select which set of libraries you use when compiling and linking. It's rather unclear exactly how to do this so that it works nicely with Cabal etc.

## The compiler

GHC knows relatively little about the `Integer` type. Look in `prelude/PrelNames` and search for `Integer`. These `Names` "know" which module the functions are defined in; look at the defn of `plusIntegerName` for example.

Currently, then, GHC expects the type `Integer` and the value `plusInteger` to be defined in `GHC.Num`. That's fine: just add defns like this:

module GHC.Num where import GHC.Integer( Integer, plusInteger, ... ) as I -- or import MyIntegerModule(...) as I type Integer = I.Integer plusInteger = I.plusInteger ...etc...

Now GHC will still find `GHC.Num.Integer` but it'll find a type synonym that will tell it where `Integer` is *really* defined. Similarly `plusInteger`.

Integer *literals* are built by the desugarer in `DsUtils.mkIntegerExpr`. All it assumes is that there are functions:

smallIntegerDataCon :: Int -> Integer plusInteger, timesInteger :: Integer -> Integer -> Integer

It uses these functions to construct big integer literals using arithmetic. Despite the name, it's not important that `smallIntegerDataCon` is bound to a data constructor. All the library needs to provide is a way to convert an `Int` to an `Integer`. So that can be handled just the same way as above.

In short, the compiler can be untouched EXCEPT for any jiggery pokery to do with finding the right libraries when using the "harder" approach.

## The runtime system

You'd need to build two versions of the runtime system too, one omitting all the GMP goop.