# run any time after creating the SSA representation. Many quadcode
# transformations update the variables incrementally, using 'addUse',
# 'removeUse' and 'renameUses' to do the job. A few make sufficiently
# violent changes to the control flow that it is more effective simply
# to discard and rebuild the relations.

oo::define quadcode::transformer {


















     
    # ud_du_chain --
    #
    #	Records ud- and du-chains for quadcode in SSA form
    #
    # Results:
    #	None.
................................................................................
    method ud_du_chain {} {

	my debug-duchain {
	    puts "before duchain"
	    my dump-bb
	}

	set duchain {}
	set udchain {}

	# Walk through the basic blocks, and the instructions in each block
	set b -1
	foreach content $bbcontent {
	    incr b
	    set pc -1
	    foreach q $content {

# run any time after creating the SSA representation. Many quadcode
# transformations update the variables incrementally, using 'addUse',
# 'removeUse' and 'renameUses' to do the job. A few make sufficiently
# violent changes to the control flow that it is more effective simply
# to discard and rebuild the relations.

oo::define quadcode::transformer {
     
    # reset_ud_du_chains --
    #
    #	Resets the ud- and du-chains
    #
    # Results:
    #	None.
    #
    # When a pass such as partial redundancy elimination runs, it
    # renames all variables. Rather than unlinking individual variables,
    # it simply blows the ud- and du-chains away and starts afresh.

    method reset_ud_du_chains {} {

	set duchain {}
	set udchain {}

    }
     
    # ud_du_chain --
    #
    #	Records ud- and du-chains for quadcode in SSA form
    #
    # Results:
    #	None.
................................................................................
    method ud_du_chain {} {

	my debug-duchain {
	    puts "before duchain"
	    my dump-bb
	}

	my reset_ud_du_chains


	# Walk through the basic blocks, and the instructions in each block
	set b -1
	foreach content $bbcontent {
	    incr b
	    set pc -1
	    foreach q $content {

# The basic idea behind this optimization is that quadcode results are
# partitioned into a set of equivalence classes, corresponding with
# the values that they compute. Variables in the same class are known
# to be equal, and so code that computes them can be removed if the values
# are already available; loop-invariant values can be hoisted out of the
# corresponding loops, and so on.
#
# Sources of particular note that are cited with procedures that emplooy
# their algorithms include:




#
# [SIMP96] Simpson, Loren Taylor. "Value-driven redundancy elimination."
# PhD thesis, Rice University, Houston, Texas, April 1996.
# https://www.clear.rice.edu/comp512/Lectures/Papers/SimpsonThesis.pdf

namespace eval quadcode {

................................................................................
# Results:
#	Returns 1 if modifications were made, 0 if the method
#	accomplished nothing.
#
# Side effects:
#	Redundant calculations are removed.
#
# Notes:
#	The removal of redundant calculations may expose additional
#	opportunities for optimization. In particular, it is possible
#	that phi operations will have become worthless, either because
#	two such operations become the same operation, or because
#	all inputs to a phi become the same input. It may be necessary
#	to repeat this optimization after cleaning up useless phi's.
























































oo::define quadcode::transformer method partialredundancy {} {

    my debug-pre {
	puts "Before partial redundancy elimination:"
	my dump-bb
    }
    my variable pre_exemplar


    # Compute Global Value Numbering for the values present in the quadcode

    lassign [my pre_gvn] VN pre_exemplar cands
    my debug-pre {
	puts "Value numbering:"
	dict for {k n} [lsort -stride 2 -index 0 -ascii -increasing $VN] {
................................................................................
	    if {[lindex $v 0] ne $k} {
		puts "   found congruence $k -> $n ($v)"
	    }
	}
	puts "Candidates for PRE: [my pre_format_bitset $cands]"
    }

    # Compute the 'defined' predicate for the basic blocks

    set defined [my pre_defined $VN]
    my debug-pre {
	puts "Defined expressions:"
	set b -1
	foreach vset $defined {
	    puts "[incr b]: [my pre_format_bitset $vset]"
................................................................................

    # Compute LATER, which is an indication that an expression
    # may be moved later than an edge (LATER) or the start of
    # a block (LATERIN)

    lassign [my pre_later $antloc $EARLIEST] LATERIN LATER

    # Report on insertion and deletion points


    dict for {edge exprs} $LATER {
	lassign $edge from to






	my debug-pre {
	    puts "Edge $from -> $to: LATER = [my pre_format_bitset $exprs]"
	    puts "Node $to: LATERIN =\





                  [my pre_format_bitset [lindex $LATERIN $to]]"
	}
	set insert [expr {$exprs & ~[lindex $LATERIN $to]}]



	if {$insert != 0} {

	    puts "Insert on edge ($from -> $to): [my pre_format_bitset $insert]"
	}
    }

    set b -1
    foreach exprs $antloc laters $LATERIN {
	incr b
	if {$b == 0} continue
	my debug-pre {
	    puts "Block $b: ANTLOC = [my pre_format_bitset $exprs]"
	    puts "Block $b: LATERIN = [my pre_format_bitset $laters]"
	}
	set delete [expr {$exprs & ~$laters}]
	if {$delete != 0} {
	    puts "Delete from block $b: [my pre_format_bitset $delete]"
	}

    }


    unset pre_exemplar

    return 0

}
 
# quadcode::transformer method pre_gvn --
#
#	Calculates a Global Value Numbering for values in a quadcode
#	sequence.
#
# Results:
#	Returns a tjree-element list.
#
#	The first element is a dictionary whose keys are the names of
#	program variables and whose values are value numbers. Two value
#	numbers are distinct if it cannot be shown that they result
#	from the same computation.
#
#	The second element is a dictionary whose keys are the value
................................................................................
#	that represent the values, and the expressions that compute the
#	values.
#
#	The third element is a bit set containing those values that are
#	candidates - that is, could conceivably be moved from block to block
#
# This procedure implements the 'RPO' algorithm presented in
# Figure 4.3 of [Simpson] (see references in the file header.
# While perhaps not as fast, it is significantly simpler than
# the 'SCC' algorithm and yields the same results.
#
# This procedure assumes that 'deadbb' has been run before it,
# so that it will find basic blocks already in depth-first order.

oo::define quadcode::transformer method pre_gvn {} {
................................................................................
#	AVIN is a list of bit vectors giving the sets of values available
#	at the start of the basic blocks.
#
#	AVOUT is a list of bit vectors giving thes sets of values available
#	at the end of the basic blocks
#
# This procedure solves the data flow equations given in Figure 5.6
# on page 63 of [Simpson].

oo::define quadcode::transformer method pre_avail {defined} {

    my debug-pre {
	puts "Calculate available expressions:"
    }

................................................................................
#	        on exit from the program's blocks
#
# Results:
#	Returns a list indexed by basic block number. The list values
#	are dictionaries whose keys are the exemplars of altered values
#	and whose values are immaterial
#
# This is the algorithm of Figure 7.1 on page 75 of [Simpson]. Simpson
# is quite unclear on the issue that (AVOUT-AVIN) should apply only to
# fixed values, and then the altered candidates appear only as a
# consequence of tracking the dependents on thosed fixed
# values. Nevertheless, if this filtering is not done, nothing ever
# becomes locally anticipable, because its own calculation turns up in
# (AVOUT-AVIN).

................................................................................
#	altered - List of bit sets, indexed by basic block number, indicating
#		  what values are altered within the block
#
# Results:
#	Returns a list of bit sets, indexed by basic block number, indicating
#	what values are locally anticipable within the block. Note that
#
# Page 76 of [Simpson]: antloc_b = defined_b - altered_b
# Simpson does not appear to constrain this to candidates, but it doesn't
# ever make sense to move a non-candidate.

oo::define quadcode::transformer method pre_antloc {cands defined altered} {

    set ANTLOC {}
    set b -1
................................................................................
#	entry into basic blocks.
#
#	ANTOUT is a list indexed by basic block number of bit vectors
#	that enumerate the candidate values that are anticipable on
#	exit from basic blocks
#
# This procedure solves data flow equations given in Figure 6.3
# on page 69 of [Simpson].

oo::define quadcode::transformer method pre_ant_global {altered antloc} {

    my debug-pre {
	puts "Calculate global anticipable expressions:"
    }

................................................................................
#	Returns a dictionary whose keys are ordered pairs {from to}
#	representing edges in the control flow graph (where 'from' and
#	'to' are basic block numbers), and whose values are bit vectors
#	representing the sets of values for which the edges are the
#	earliest points where the values may be computed.
#
# This analysis is part of the data flow equations in Figure 6.3 on
# page 69 of [Simpson].

oo::define quadcode::transformer method pre_earliest {AVOUT altered
						      ANTIN ANTOUT} {

    set EARLIEST {}

    # Walk through flowgraph edges (i -> j)
................................................................................
#	in the program.
#
#	LATERIN is a list indexed by basic block number of bit vectors
#	that enumerate the candidate values that may be calculated
#	on entry to the corresponding basic block or later in the program.
#
# This procedure solves part of the dataflow equations shown in
# Figure 6.4 on page 70 of [Simpson].

oo::define quadcode::transformer method pre_later {ANTLOC EARLIEST} {

    my debug-pre {
	puts "Calculate LATER:"
    }

................................................................................
    }

    $worklist destroy

    return [list $LATERIN $LATER]
    
}













































































































 
# quadcode::transformer method pre_format_bitset --
#
#	Formats a set of values for debug printing
#
# Parameters:
#	vset - Set of values to be printed

# The basic idea behind this optimization is that quadcode results are
# partitioned into a set of equivalence classes, corresponding with
# the values that they compute. Variables in the same class are known
# to be equal, and so code that computes them can be removed if the values
# are already available; loop-invariant values can be hoisted out of the
# corresponding loops, and so on.
#
# Sources of particular note that are cited with procedures that employ
# their algorithms include:
#
# [DRES93] Drechsler, Karl-Heinz, and Manfred P. Stadel. "A variation of
# Knoop, Rüthing and Steffen's _Lazy Code Motion._ _SIGPLAN Notices_ 28:5
# (May, 1993), pp. 29-38.
#
# [SIMP96] Simpson, Loren Taylor. "Value-driven redundancy elimination."
# PhD thesis, Rice University, Houston, Texas, April 1996.
# https://www.clear.rice.edu/comp512/Lectures/Papers/SimpsonThesis.pdf

namespace eval quadcode {

................................................................................
# Results:
#	Returns 1 if modifications were made, 0 if the method
#	accomplished nothing.
#
# Side effects:
#	Redundant calculations are removed.
#

# The removal of redundant calculations may expose additional
# opportunities for optimization. In particular, it is possible
# that phi operations will have become worthless, either because
# two such operations become the same operation, or because
# all inputs to a phi become the same input. It may be necessary
# to repeat this optimization after cleaning up useless phi's.
#
# The partial redundancy elimination done here is a combination of the
# 'lazy code motion' of [DRES93] (and explained again in [SIMP96] and
# straigntforward available expression analysis. It follows the general
# plan:
#
#	Identify expressions that can be proven to compute the same value.
#	(Global Value Numbering - https://en.wikipedia.org/wiki/Value_numbering)
#
#	Calculate 'defined' - a function from basic blocks to sets of values
#	that enumerates the values that have values assigned in a block
#
#	Calculate 'available expressions' - a pair of functions from
#	basic blocks to sets of values that enumerate the values that
#	are known to be in quadcode registers at the start and the end of
#	the blocks. https://en.wikipedia.org/wiki/Available_expression
#
#	Calculate the 'altered' function, which enumerates the set of
#	values that are changed in a basic block and therefore may
#	not flow through it. ([DRES93] uses the function TRANSP, which
#	is the complement of 'altered').
#
#	Calculate the 'ANTLOC' function, which is the set of computations
#	in a basic block that do not depend on fixed values assigned in the
#	block and could therefore be moved to a predecessor block.
#
#	Using ANTLOC and 'altered' calculate the 'ANTIN' and 'ANTOUT'
#	functions. ANTIN is the set of values anywhere later in the program
#	that could be moved to a point before a basic block. ANTOUT is
#	the set of values anywhere later in the program that could be
#	pulled up into the basic block.
#
#	Calculate EARLIEST, which is a function on flowgraph edges
#	rather than basic blocks, and identifies the set of values for which
#	the edge is the earliest point at which the calculation might appear.
#
#	Calculate LATER, which is a function on flowgraph edges, and
#	LATERIN, which is a function on basic blocks. They are sets of
#	computations that could be done on the given edge or at the start
#	of the given basic block with the same effect as if they were
#	done at EARLIEST.
#
#	Calculate INSERT, which is a function from flowgraph edges to sets
#	of values, that enumerates the places to insert computations that
#	have been moved upward.
#
#	Calculate DELETE, which is a function from basic blocks to sets of
#	values, that enumerates the places to remove values that have
#	been covered by INSERT (or naturally by being computed redundantly
#	in an earler block.)
#
#	Finally, rewrite all the variable names in the program, while
#	performing the required insertions and deletions. In addition to
#	deleting the calculations identified by DELETE, delete any that
#	are performed redundantly within a single basic block.

oo::define quadcode::transformer method partialredundancy {} {

    my debug-pre {
	puts "Before partial redundancy elimination:"
	my dump-bb

	my variable pre_exemplar
    }

    # Compute Global Value Numbering for the values present in the quadcode

    lassign [my pre_gvn] VN pre_exemplar cands
    my debug-pre {
	puts "Value numbering:"
	dict for {k n} [lsort -stride 2 -index 0 -ascii -increasing $VN] {
................................................................................
	    if {[lindex $v 0] ne $k} {
		puts "   found congruence $k -> $n ($v)"
	    }
	}
	puts "Candidates for PRE: [my pre_format_bitset $cands]"
    }

    # Compute the 'defined' function for the basic blocks

    set defined [my pre_defined $VN]
    my debug-pre {
	puts "Defined expressions:"
	set b -1
	foreach vset $defined {
	    puts "[incr b]: [my pre_format_bitset $vset]"
................................................................................

    # Compute LATER, which is an indication that an expression
    # may be moved later than an edge (LATER) or the start of
    # a block (LATERIN)

    lassign [my pre_later $antloc $EARLIEST] LATERIN LATER

    # Compute INSERT, which records where we want to insert new
    # definitions of values


    set INSERT [my pre_insert $LATER $LATERIN]

    # Compute DELETE, which records where we want to remove existing
    # definitions of values

    set DELETE [my pre_delete $antloc $LATERIN]

    my debug-pre {


	puts "Actions to take:"
	set b -1
	foreach del $DELETE {
	    incr b
	    if {$del != 0} {
		puts "Basic block $b:\n    delete [my pre_format_bitset $del]"
	    }

	    foreach s [my bbsucc $b] {
		set edge [list $b $s]
		set ins [dict get $INSERT $edge]
		if {$ins != 0} {
		    puts "Graph edge $b->$s:\n   \
                          insert [my pre_format_bitset $ins]"
		}
	    }
	}







    }




    # OK, we're ready to do the variable rewriting

    set changed [my pre_rewrite_vars $INSERT $DELETE $pre_exemplar]

    unset pre_exemplar

    return $changed

}
 
# quadcode::transformer method pre_gvn --
#
#	Calculates a Global Value Numbering for values in a quadcode
#	sequence.
#
# Results:
#	Returns a three-element list.
#
#	The first element is a dictionary whose keys are the names of
#	program variables and whose values are value numbers. Two value
#	numbers are distinct if it cannot be shown that they result
#	from the same computation.
#
#	The second element is a dictionary whose keys are the value
................................................................................
#	that represent the values, and the expressions that compute the
#	values.
#
#	The third element is a bit set containing those values that are
#	candidates - that is, could conceivably be moved from block to block
#
# This procedure implements the 'RPO' algorithm presented in
# Figure 4.3 of [SIMP96] (see references in the file header.
# While perhaps not as fast, it is significantly simpler than
# the 'SCC' algorithm and yields the same results.
#
# This procedure assumes that 'deadbb' has been run before it,
# so that it will find basic blocks already in depth-first order.

oo::define quadcode::transformer method pre_gvn {} {
................................................................................
#	AVIN is a list of bit vectors giving the sets of values available
#	at the start of the basic blocks.
#
#	AVOUT is a list of bit vectors giving thes sets of values available
#	at the end of the basic blocks
#
# This procedure solves the data flow equations given in Figure 5.6
# on page 63 of [SIMP96].

oo::define quadcode::transformer method pre_avail {defined} {

    my debug-pre {
	puts "Calculate available expressions:"
    }

................................................................................
#	        on exit from the program's blocks
#
# Results:
#	Returns a list indexed by basic block number. The list values
#	are dictionaries whose keys are the exemplars of altered values
#	and whose values are immaterial
#
# This is the algorithm of Figure 7.1 on page 75 of [SIMP96]. Simpson
# is quite unclear on the issue that (AVOUT-AVIN) should apply only to
# fixed values, and then the altered candidates appear only as a
# consequence of tracking the dependents on thosed fixed
# values. Nevertheless, if this filtering is not done, nothing ever
# becomes locally anticipable, because its own calculation turns up in
# (AVOUT-AVIN).

................................................................................
#	altered - List of bit sets, indexed by basic block number, indicating
#		  what values are altered within the block
#
# Results:
#	Returns a list of bit sets, indexed by basic block number, indicating
#	what values are locally anticipable within the block. Note that
#
# Page 76 of [SIMP96]: antloc_b = defined_b - altered_b
# Simpson does not appear to constrain this to candidates, but it doesn't
# ever make sense to move a non-candidate.

oo::define quadcode::transformer method pre_antloc {cands defined altered} {

    set ANTLOC {}
    set b -1
................................................................................
#	entry into basic blocks.
#
#	ANTOUT is a list indexed by basic block number of bit vectors
#	that enumerate the candidate values that are anticipable on
#	exit from basic blocks
#
# This procedure solves data flow equations given in Figure 6.3
# on page 69 of [SIMP96].

oo::define quadcode::transformer method pre_ant_global {altered antloc} {

    my debug-pre {
	puts "Calculate global anticipable expressions:"
    }

................................................................................
#	Returns a dictionary whose keys are ordered pairs {from to}
#	representing edges in the control flow graph (where 'from' and
#	'to' are basic block numbers), and whose values are bit vectors
#	representing the sets of values for which the edges are the
#	earliest points where the values may be computed.
#
# This analysis is part of the data flow equations in Figure 6.3 on
# page 69 of [SIMP96].

oo::define quadcode::transformer method pre_earliest {AVOUT altered
						      ANTIN ANTOUT} {

    set EARLIEST {}

    # Walk through flowgraph edges (i -> j)
................................................................................
#	in the program.
#
#	LATERIN is a list indexed by basic block number of bit vectors
#	that enumerate the candidate values that may be calculated
#	on entry to the corresponding basic block or later in the program.
#
# This procedure solves part of the dataflow equations shown in
# Figure 6.4 on page 70 of [SIMP96].

oo::define quadcode::transformer method pre_later {ANTLOC EARLIEST} {

    my debug-pre {
	puts "Calculate LATER:"
    }

................................................................................
    }

    $worklist destroy

    return [list $LATERIN $LATER]
    
}
 
# quadcode::transformer method pre_insert --
#
#	Calculates where new definitions of values must be inserted
#	in partial redundancy elimination.
#
# Parameters:
#	LATER - Dictionary whose keys are ordered pairs {i j}
#	        identifying edges {i -> j} in the control flow graph.
#	        The values are bit sets that enumerate the candidate values
#	        that may be computed on the corresponding edge or a later
#               point in the program.
#
#	LATERIN - List indexed by basic block number of bit vectors
#	          that enumerate the candidate values that may be calculated
#	          on entry to the corresponding basic block or later in the
#                 program.
#
# Results:
#	Returns a dictionary whose keys are ordered pairs {i j} identifying
#	edges (i -> j) in the control flow graph. The values are bit sets
#	that enumerate candidate values that need newly-created assignments
#	on those edges

oo::define quadcode::transformer method pre_insert {LATER LATERIN} {

    set INSERT {}

    # Walk through the edges and set INSERT on any edge for which
    # the value is evaluated LATER, but not LATER-IN on the following node
    
    dict for {edge exprs} $LATER {
	lassign $edge from to
	dict set INSERT $edge [expr {$exprs & ~[lindex $LATERIN $to]}]
    }
    
    return $INSERT
}
 
# quadcode::transformer method pre_delete --
#
#	Calculates the points in the program where assignments to a given
#	value must be deleted when performing partial redundancy elimination.
#
# Parameters:
#	ANTLOC - List of bit sets, indexed by basic block number, indicating
#	         what values are locally anticipable within the block.
#	LATERIN - List indexed by basic block number of bit vectors
#	          that enumerate the candidate values that may be calculated
#	          on entry to the corresponding basic block or later in the
#                 program.
#
# Results:
#	Returns a list indexed by basic block number whose values are
#	bit vectors identifying values whose assignments in the given
#	block are superfluous.

oo::define quadcode::transformer method pre_delete {ANTLOC LATERIN} {

    set DELETE {}
    
    set b -1
    foreach antloc $ANTLOC laterin $LATERIN {
	incr b
	if {$b == 0} {
	    lappend DELETE 0
	} else {
	    lappend DELETE [expr {$antloc & ~$laterin}]
	}
    }

    return $DELETE

}
 
# quadcode::transformer method pre_rewrite_vars
#
#	Once all the information is available, rewrites the variables
#	in a program, inserting and deleting computations of values,
#	to perform partial redundancy elimination.
#
# Parameters:
#	INSERT - Dictionary whose keys are ordered pairs {from to}
#	         identifying flowgraph edges and whose values are
#	         bit sets identifying the values whose computation should
#	         be inserted onto the edges.
#	DELETE - List indexed by basic block number whose values are bit
#	         sets identifying the values whose computation may be
#	         removed from the blocks.
#	exemplar - List indexed by value number containing ordered pairs,
#                  {exemplar signature} that give an exemplar variable name
#	           and the signature of a quadcode instruction that computes
#	           the value. 
#
# Results:
#	Returns 1 if the program has been rewritten in any substantial way,
#	0 if only renamings have been performed
#
# Side effects:
#	All program variables are renumbered, redundant computations are
#	removed, and invariant computations are hoisted.
#
# Note that this transformation can leave meaningless phi operations
# behind, which will be tidied up in dead code elimination.

oo::define quadcode::transformer method pre_rewrite_vars {INSERT DELETE
							  exemplar} {
    return 0
}
 
# quadcode::transformer method pre_format_bitset --
#
#	Formats a set of values for debug printing
#
# Parameters:
#	vset - Set of values to be printed

    if {[dict exists $r $v]} {
	return [dict get $r $v]
    }
    set nv  [my newVarInstance $v]
    dict set r $v $nv
    return $nv
}
















 
# quadcode::transformer method newVarInstance
#
#	Creates a new instance of the given variable
#
# Parameters:
#	name - Name of the variable or of an existing instance

    if {[dict exists $r $v]} {
	return [dict get $r $v]
    }
    set nv  [my newVarInstance $v]
    dict set r $v $nv
    return $nv
}
 
# quadcode::transformer method resetVarCounts
#
#	Resets all instance counts of all variables.
#
# Results:
#	None.
#
# When a pass such as partial redundancy elimination runs, it rewrites
# all variable names throughout the program. Rather than having runaway
# variable indices, it calls this routine to reset all counts for
# variable names.

oo::define quadcode::transformer method resetVarCounts {} {
    unset varcount
}
 
# quadcode::transformer method newVarInstance
#
#	Creates a new instance of the given variable
#
# Parameters:
#	name - Name of the variable or of an existing instance