[GHC] #5615: ghc produces poor code for `div` with constant powers of 2.

[GHC]

#5615: ghc produces poor code for `div` with constant powers of 2.
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        Reporter:  Lennart           |            Owner:  daniel.is.fischer
            Type:  bug               |           Status:  new
        Priority:  normal            |        Milestone:  7.6.2
       Component:  Compiler          |          Version:  7.4.1-rc1
      Resolution:                    |         Keywords:
Operating System:  Unknown/Multiple  |     Architecture:  x86
 Type of failure:  None/Unknown      |       Difficulty:  Unknown
       Test Case:                    |       Blocked By:
        Blocking:                    |  Related Tickets:
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Comment (by thomie):

 How about implementing Euclidean division?

 [http://legacy.cs.uu.nl/daan/download/papers/divmodnote.pdf Division and
 Modulus for Computer Scientists] (6 pages pdf) by
 [http://research.microsoft.com/en-us/people/daan/ Daan Leijen].

 "Boute argues that Euclidean division is superior  to the other ones in
 terms of regularity and useful mathematical properties, allthough floored
 division, promoted by Knuth, is also a good definition. Despite its
 widespread use, truncated division is shown to be inferior to the other
 definitions.

 An interesting mathematical property that is only satisfied by Euclidean
 division is the shift-rule. A compiler can use this to optimize divisions
 by a power of two into an arithmetical shift or a bitwise-and operation."

     D '''div''',,E,, (2^n^) = D '''asr''' n
     D '''mod''',,E,, (2^n^) = D '''and''' (2^n - 1^)

 Note: [https://api.dartlang.org/apidocs/channels/stable/dartdoc-viewer
 /dart-core.num Dart]'s modulo operator (%) uses Euclidean division.

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Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/5615#comment:17>
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