Commit dd1dfdbf authored by Michael D. Adams's avatar Michael D. Adams
Browse files

Formatted documentation for compiler/cmm/Dataflow.hs

parent 8bae799d
......@@ -2,21 +2,8 @@ module Dataflow (
fixedpoint
) where
--------------------------------------------------------------------------------
-- Solve a fixed-point of a dataflow problem.
--
-- dependants: map from nodes to those who's value depend on the argument node
-- update:
-- Given the node which needs to be updated, and
-- which node caused that node to need to be updated,
-- update the state.
-- (The causing node will be 'Nothing' if this is the initial update.)
-- Must return 'Nothing' if no change,
-- otherwise returrn 'Just' of the new state
-- nodes: a set of nodes that initially need updating
-- state: some sort of state (usually a map)
-- containing the initial value for each node
-----------------------------------------------------------------------------
-- | Solve the fixed-point of a dataflow problem.
--
-- Complexity: O(N+H*E) calls to 'update' where
-- N = number of nodes,
......@@ -26,19 +13,39 @@ module Dataflow (
-- Sketch for proof of complexity:
-- Note that the state is threaded through the entire execution.
-- Also note that the height of the latice at any particular node
-- is the number of times 'update' can return non-Nothing for a particular node.
-- Every call (except for the top level one) must be caused by a non-Nothing
-- result and each non-Nothing result causes as many calls as it has
-- out-going edges. Thus any particular node, n, may cause in total
-- at most H*out(n) further calls. When summed over all nodes,
-- is the number of times 'update' can return non-Nothing for a
-- particular node. Every call (except for the top level one)
-- must be caused by a non-Nothing result and each non-Nothing
-- result causes as many calls as it has out-going edges.
-- Thus any particular node, n, may cause in total at
-- most H*out(n) further calls. When summed over all nodes,
-- that is H*E. The N term of the complexity is from the initial call
-- when 'update' will be passed 'Nothing'.
fixedpoint ::
(node -> [node])
(node -> [node]) -- ^ map from nodes to those who's
-- value depend on the argument node
-> (node -> Maybe node -> s -> Maybe s)
-> [node] -> s -> s
-- ^ Given the node which needs to be
-- updated, and which node caused that node
-- to need to be updated, update the state.
--
-- The causing node will be 'Nothing' if
-- this is the initial/bootstrapping update.
--
-- Must return 'Nothing' if no change,
-- otherwise returrn 'Just' of the new state.
-> [node] -- ^ Nodes that should initially be updated
-> s -- ^ Initial state
-- (usually a map from node to
-- the value for that node)
-> s -- ^ Final state
fixedpoint dependants update nodes state =
foldr (fixedpoint' Nothing) state nodes where
-- Use a depth first traversal of nodes based on the update graph.
-- Terminate the traversal when the update doesn't change anything.
fixedpoint' cause node state =
case update node cause state of
Nothing -> state
......
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