[GHC] #15622: Generalize `E{0,1,2,3,6,9,12}` from `Data.Fixed`

[GHC]

#15622: Generalize `E{0,1,2,3,6,9,12}` from `Data.Fixed`
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           Reporter:  rockbmb        |             Owner:  (none)
               Type:  feature        |            Status:  new
  request                            |
           Priority:  normal         |         Milestone:  8.6.1
          Component:  Core           |           Version:  8.4.3
  Libraries                          |
           Keywords:  base,          |  Operating System:  Unknown/Multiple
  Data.Fixed                         |
       Architecture:                 |   Type of failure:  None/Unknown
  Unknown/Multiple                   |
          Test Case:                 |        Blocked By:
           Blocking:                 |   Related Tickets:
Differential Rev(s):                 |         Wiki Page:
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 Hello;

 I'm creating this email to propose a change to `Data.Fixed`. Full credit
 for this idea goes to Bhavik Mehta (@b-mehta on GitHub), who implemented
 it in this [https://github.com/dmcclean/exact-pi/pull/8 PR] for `exact-
 pi`.

 In `Data.Fixed` there are several `E`-prefixed datatypes used to represent
 a certain number of digits of precision in fixed-precision arithmetic. For
 example, `E1` has 1 decimal place, `E12` has 12. Each of them,
 `E{0,1,2,3,6,9,12}` is hardcoded. If more precision types are to be
 provided, they have to be hardcoded as well, and all of these types
 resemble each other. I think there is room for improvement here.

 Instead of having

 {{{#!hs
 data E0

 instance HasResolution E0 where
     resolution _ = 1
 }}}

 and repeating it as many times as there are `E` datatypes, I propose to
 add the following type:

 {{{#!hs
 {-# LANGUAGE DataKinds      #-}
 {-# LANGUAGE KindSignatures #-}

 import GHC.TypeLits (Nat, KnownNat, natVal)

 data E (n :: Nat)
 }}}

 and then do

 {{{#!hs
 instance KnownNat n => HasResolution (E n) where
     resolution _ = 10^natVal (undefined :: E n)
 }}}

 just once, replacing `data E0` with `type E0 = E 0` (and the same for the
 rest of them) to continue reexporting these types. `E` should also be
 exported.

 I've sent an email to the Core Libraries Committee regarding this issue.
 This is my first contribution to GHC, if I'm doing something incorrectly
 please tell me.

-- 
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/15622>
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