[GHC] #10711: Defining mapM_ in terms of traverse_ causes substantial blow-up in ByteCodeAsm

[GHC]

#10711: Defining mapM_ in terms of traverse_ causes substantial blow-up in
ByteCodeAsm
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        Reporter:  bgamari           |                   Owner:  bgamari
            Type:  bug               |                  Status:  new
        Priority:  normal            |               Milestone:
       Component:  Compiler          |                 Version:
      Resolution:                    |                Keywords:
Operating System:  Unknown/Multiple  |            Architecture:
 Type of failure:  Compile-time      |  Unknown/Multiple
  performance bug                    |               Test Case:  ghcirun004
      Blocked By:                    |                Blocking:
 Related Tickets:                    |  Differential Revisions:
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Comment (by akio):

 I think the quadratic behavior comes from the fact that the `>>=` linearly
 traverses its LHS.

 Let's define the size of an `Assembler` value with:

 {{{#!hs
 size :: Assembler a -> Integer
 size (Pure _) = 1
 size (Thing i k) = 1 + size (k i)
 }}}

 `m >>= f` performs `O(size(m))` operations because `>>=` is recursive on
 its LHS. Most of the cost is hidden inside a lambda, but you will have to
 pay it eventually, namely when `run` is finally applied.

 Now we can analyze the cost of other operations:

 * `m >> n` needs `O(size(m))` operations, because it's `m >>= \_ -> n`.
 * `f <$> m` needs `O(size(m))` operations, because it's `m >>= return .
 f`.
 * `m <*> n` needs `O(size(m) + size(n))` operations, because it's `m >>=
 \v -> n >>= \w -> return v w`.
 * `m *> n` needs `O(size(m) + size(n))` operations, because it's `const
 <$> m <*> n`.

 If you use `mapM_` with a `N`-element list of 2-sized `Assembler`s, each
 application of `>>` costs `O(1)`, so the total cost is `O(N)`.

 If you use `mapA_` instead, the LHS of an application of `*>` is `O(1)`
 large but the RHS is `O(N)` large on average. This means it needs `O(N)`
 operations on average, so the total cost is `O(N*N)`.

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Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/10711#comment:10>
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