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authorDibyendu Majumdar <mobile@majumdar.org.uk>2023-10-20 15:21:08 -0700
committerDibyendu Majumdar <mobile@majumdar.org.uk>2024-10-23 17:51:09 -0700
commit83fdf059150e37c335a86e3dd4547a76a1c588db (patch)
tree7df24a5366647c8f9cf083ead43ca106f1d23430
parent0e8916e1a4ae550357401b37df6fdca683c221f7 (diff)
downloadSimple-83fdf059150e37c335a86e3dd4547a76a1c588db.tar.gz
Simple-83fdf059150e37c335a86e3dd4547a76a1c588db.zip
Chapter 4: External Argument and Comparisonslinear-chapter04
Co-authored-by: Cliff Click <cliffc@acm.org> Co-authored-by: Yichen Yan <oraluben@outlook.com> Co-authored-by: Thalia Archibald <thalia@archibald.dev> Co-authored-by: Tamas Hadhazy <helsgithub15@gmail.com> Co-authored-by: Hels15 <helsgithub15@gmail.com> Co-authored-by: XmiliaH <45106915+XmiliaH@users.noreply.github.com>
-rw-r--r--Makefile98
-rw-r--r--README.md2
-rw-r--r--appendix/dce.md166
-rw-r--r--docs/chapter04/04-arg1.svg84
-rw-r--r--docs/chapter04/04-arg2.svg80
-rw-r--r--docs/chapter04/04-dce1.svg100
-rw-r--r--docs/chapter04/04-dce2.svg59
-rw-r--r--docs/chapter04/04-dce3.svg116
-rw-r--r--docs/chapter04/04-grammar.md76
-rw-r--r--docs/chapter04/04-post-peephole.gv43
-rw-r--r--docs/chapter04/04-post-peephole.svg108
-rw-r--r--docs/chapter04/04-pre-peephole.gv47
-rw-r--r--docs/chapter04/04-pre-peephole.svg134
-rw-r--r--docs/chapter04/Makefile12
-rw-r--r--docs/chapter04/README.md397
-rw-r--r--docs/chapter04/lattice.gv63
-rw-r--r--docs/chapter04/lattice.svg195
-rw-r--r--docs/chapter04/projnode.pngbin0 -> 6061 bytes
-rw-r--r--src/main/java/com/seaofnodes/simple/GraphVisualizer.java65
-rw-r--r--src/main/java/com/seaofnodes/simple/Parser.java57
-rw-r--r--src/main/java/com/seaofnodes/simple/node/AddNode.java64
-rw-r--r--src/main/java/com/seaofnodes/simple/node/BoolNode.java52
-rw-r--r--src/main/java/com/seaofnodes/simple/node/ConstantNode.java3
-rw-r--r--src/main/java/com/seaofnodes/simple/node/DivNode.java8
-rw-r--r--src/main/java/com/seaofnodes/simple/node/MulNode.java19
-rw-r--r--src/main/java/com/seaofnodes/simple/node/MultiNode.java7
-rw-r--r--src/main/java/com/seaofnodes/simple/node/Node.java114
-rw-r--r--src/main/java/com/seaofnodes/simple/node/NotNode.java28
-rw-r--r--src/main/java/com/seaofnodes/simple/node/ProjNode.java40
-rw-r--r--src/main/java/com/seaofnodes/simple/node/ReturnNode.java2
-rw-r--r--src/main/java/com/seaofnodes/simple/node/ScopeNode.java18
-rw-r--r--src/main/java/com/seaofnodes/simple/node/StartNode.java11
-rw-r--r--src/main/java/com/seaofnodes/simple/node/SubNode.java9
-rw-r--r--src/main/java/com/seaofnodes/simple/type/Type.java20
-rw-r--r--src/main/java/com/seaofnodes/simple/type/TypeInteger.java44
-rw-r--r--src/main/java/com/seaofnodes/simple/type/TypeTuple.java26
-rw-r--r--src/test/java/com/seaofnodes/simple/Chapter01Test.java2
-rw-r--r--src/test/java/com/seaofnodes/simple/Chapter03Test.java1
-rw-r--r--src/test/java/com/seaofnodes/simple/Chapter04Test.java127
39 files changed, 2424 insertions, 73 deletions
diff --git a/Makefile b/Makefile
new file mode 100644
index 00000000..c7724bc7
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,98 @@
+SHELL := /bin/bash
+.DELETE_ON_ERROR:
+
+# for printing variable values
+# usage: make print-VARIABLE
+# > VARIABLE = value_of_variable
+print-% : ; @echo $* = $($*)
+
+# literal space
+space := $() $()
+
+# Decide OS-specific questions
+# jar-file seperator
+ifeq ($(OS),Windows_NT)
+ SEP = ;
+else
+ SEP = :
+endif
+# Find a reasonable ctags.
+CTAGS = $(shell which ctags)
+# Hack for MacOS: /usr/bin/ctags is unfriendly, so look for ctags from brew
+ifeq ($(UNAME),Darwin)
+ CTAGS = $(shell brew list ctags 2> /dev/null | grep bin/ctags)
+endif
+
+# Fun Args to javac. Mostly limit to java8 source definitions, and fairly
+# aggressive lint warnings.
+JAVAC_ARGS = -g
+
+# Source code
+SIMPLE := com/seaofnodes/simple
+SRC := src/main/java
+TST := src/test/java
+CLZDIR:= build/classes
+main_javas := $(wildcard $(SRC)/$(SIMPLE)/*java $(SRC)/$(SIMPLE)/*/*java)
+test_javas := $(wildcard $(TST)/$(SIMPLE)/*java $(TST)/$(SIMPLE)/*/*java)
+main_classes := $(patsubst $(SRC)/%java,$(CLZDIR)/main/%class,$(main_javas))
+test_classes := $(patsubst $(TST)/%java,$(CLZDIR)/test/%class,$(test_javas))
+test_cp := $(patsubst $(TST)/$(SIMPLE)/%.java,com.seaofnodes.simple.%,$(wildcard $(TST)/$(SIMPLE)/*Test.java))
+classes = $(main_classes) $(test_classes)
+# All the libraries
+libs = $(wildcard lib/*jar)
+jars = $(subst $(space),$(SEP),$(libs))
+
+
+default_targets := $(main_classes) $(test_classes)
+# Optionally add ctags to the default target if a reasonable one was found.
+ifneq ($(CTAGS),)
+default_targets += tags
+endif
+
+default: $(default_targets)
+
+# Compile just the out-of-date files
+$(main_classes): build/classes/main/%class: $(SRC)/%java
+ @echo "compiling " $@ " because " $?
+ @[ -d $(CLZDIR)/main ] || mkdir -p $(CLZDIR)/main
+ @javac $(JAVAC_ARGS) -cp "$(CLZDIR)/main$(SEP)$(jars)" -sourcepath $(SRC) -d $(CLZDIR)/main $(main_javas)
+
+$(test_classes): $(CLZDIR)/test/%class: $(TST)/%java $(main_classes)
+ @echo "compiling " $@ " because " $?
+ @[ -d $(CLZDIR)/test ] || mkdir -p $(CLZDIR)/test
+ @javac $(JAVAC_ARGS) -cp "$(CLZDIR)/test$(SEP)$(CLZDIR)/main$(SEP)$(jars)" -sourcepath $(TST) -d $(CLZDIR)/test $(test_javas)
+
+# Base launch line for JVM tests
+JVM=nice java -ea -cp "build/classes/main${SEP}${jars}${SEP}$(CLZDIR)/test"
+
+tests: $(default_targets)
+ @echo "testing " $(test_cp)
+ @$(JVM) org.junit.runner.JUnitCore $(test_cp)
+
+fuzzer: $(default_targets)
+ @echo "fuzzing " $(test_cp)
+ @$(JVM) org.junit.runner.JUnitCore com.seaofnodes.simple.FuzzerWrap
+
+
+.PHONY: clean
+clean:
+ rm -rf build
+ rm -f TAGS
+ (find . -name "*~" -exec rm {} \; 2>/dev/null; exit 0)
+
+# Download libs from maven
+lib: lib/junit-4.12.jar lib/hamcrest-core-1.3.jar
+
+# Jars
+lib/junit-4.12.jar:
+ @[ -d lib ] || mkdir -p lib
+ @(cd lib; wget https://repo1.maven.org/maven2/junit/junit/4.12/junit-4.12.jar)
+
+lib/hamcrest-core-1.3.jar:
+ @[ -d lib ] || mkdir -p lib
+ @(cd lib; wget https://repo1.maven.org/maven2/org/hamcrest/hamcrest-core/1.3/hamcrest-core-1.3.jar)
+
+# Build emacs tags (part of a tasty emacs ide experience)
+tags: $(main_javas) $(test_javas)
+ @rm -f TAGS
+ @$(CTAGS) -e --recurse=yes --extra=+q --fields=+fksaiS $(SRC) $(TST)
diff --git a/README.md b/README.md
index 51237054..c4f235e2 100644
--- a/README.md
+++ b/README.md
@@ -31,7 +31,7 @@ The Simple language will be styled after a subset of C or Java
with constants. Peephole optimization / simple constant folding.
* [Chapter 3](docs/chapter03/README.md): Local variables, and assignment statements. Read on RHS, SSA, more peephole optimization if local is a
constant.
-* Chapter 4: A non-constant external variable input named `arg`. Binary and Comparison operators involving constants and `arg`. Non-zero values will be truthy. Peephole optimizations involving algebraic simplifications.
+* [Chapter 4](docs/chapter04/README.md): A non-constant external variable input named `arg`. Binary and Comparison operators involving constants and `arg`. Non-zero values will be truthy. Peephole optimizations involving algebraic simplifications.
* Chapter 5: `if` statement. CFG construction.
* Chapter 6: Peephole optimization around dead control flow.
* Chapter 7: `while` statement. Looping construct - eager phi approach.
diff --git a/appendix/dce.md b/appendix/dce.md
new file mode 100644
index 00000000..ad5be2d0
--- /dev/null
+++ b/appendix/dce.md
@@ -0,0 +1,166 @@
+# Appendix
+## Dead Code Elimination(DCE)
+Dead Code Elimination is the process or removing nodes that are dead(unused).
+
+There are two kinds of dead code eliminations present in this chapter.
+- Delete unused nodes when popping the scope.
+- Delete old nodes after finding a better replacement(after idealize call).
+
+Both of the methods mentioned above delete the nodes recursively. However, the first case happens
+regardless of whether `peephole` is called or not.
+
+### Delete unused nodes when popping the scope
+A node is unused if it has no outputs(users).
+
+### Example 1:
+ ```
+ int a = 12; // the only output it has is the scope itself
+ return 1;
+ ```
+We clearly see `a` is unused.
+This gives us the following graph(without DCE):
+
+![Graph2](../docs/04-dce1.svg)
+
+To remove `a` we introduce the following technique when popping the scope.
+
+ ```java
+ var ret = (ReturnNode) parseBlock();
+ _scope.pop();
+ ```
+As of now the end of the program is hard-wired to return, after finishing parsing we pop the scope.
+The state of the scope before popping it:
+ ```
+ _scope = {ScopeNode@1422} "Scope[$ctrl:null, arg:arg][a:12]"
+ 1 = {ProjNode@1528} "arg"
+ 2 = {ConstantNode@1529} "12"
+ _inputs = {ArrayList@1523} size = 3
+ ```
+The output(s) of `a`
+ ```
+ _outputs = {ArrayList@1544} size = 1
+ 0 = {ScopeNode@1422} "Scope[$ctrl:null, arg:arg][a:12]"
+ ```
+Notice how the only output of `a`is the scope itself. When `a` is introduced, it is added to the
+inputs of the scope, and the scope is added to the outputs of `a`(recall use-def chains).
+
+Since `a` is not being returned - it is unused and can be killed.
+
+`_scope.pop`:
+```java
+public void pop() { popN(_scopes.pop().size()); }
+```
+`_scope.popN`(responsible for killing the unused nodes *recursively*):
+```java
+void popN(int n) {
+ for (int i = 0; i < n; i++) {
+ Node old_def = _inputs.removeLast(); // start from the back
+ if (old_def != null && // If it exists and
+ old_def.delUse(this)) { // If we removed the last use, the old def is now dead
+ old_def.kill(); // Kill the old def
+ }
+ }
+}
+```
+First, we start off by looping through the inputs of the scope(*remember*: scope is just a node like any other, the symbols of the scope are the inputs).
+If the node returned by `removeLast` is not null, and if the only user of `old_def` is the current Node then we can delete it.
+
+`old_def.delUse(this)` - delete *this* from `old_def`'s outputs.
+```java
+protected boolean delUse( Node use ) {
+ Utils.del(_outputs, Utils.find(_outputs, use));
+ return _outputs.isEmpty();
+ }
+```
+Returns true if `_outputs` becomes empty after deleting `use`.
+`old_def.kill()` starts the killing process recursively.
+
+`old_def.kill()`
+```java
+public void kill( ) {
+ assert isUnused(); // Has no uses, so it is dead
+ popN(nIns()); // Set all inputs to null, recursively killing unused Nodes
+ _type=null; // Flag as dead
+ assert isDead(); // Really dead now
+ }
+```
+`popN` is called again, our goal is to look for nodes that might also get deleted once `a` is freed.
+The only input `a` has is the constant node with value 12. As every other node a `ConstantNode` takes in the control node first(`Start`), once we
+drop the `Start` node from the inputs of `ConstantNode`:
+```
+Node old_def = _inputs.removeLast();
+```
+we can also get rid of `ConstantNode`(`this`) from the outputs of `Start`:
+```
+old_def.delUse(this)
+```
+### Example 2:
+```
+int a = 12;
+int b = a + 1;
+return 1;
+```
+- Call `popN` on current scope.
+- Realize that `b = a + 1;` has no uses - so we can kill it.
+- In the kill function we can call `popN` but this time with the inputs of `b = a + 1;`(start killing them recursively)
+- We start the killing process from the back and examine "1" first. This has no output other than the `AddNode`. Since `this = AddNode` calling `delUse` will mark "1" as dead.
+- We now can kill "1" and call the `popN` function with one input(the control node).
+- Now we examine "a" which has 2 uses at this point, the scope and `AddNode`. Since `this = AddNode` we will remove `AddNode` from its outputs, it will still have the scope as a user - so we can't delete it just yet.
+- We move onto`a = 12`, since "a" has only one user left(the scope) and `this = scope` it can get killed easily.
+- Same as before, we go through the inputs of "a" and will delete them from the outputs of the control node.
+
+*A constant node pointing to "Start"(ignored by the graph visualizer) but still maintains a connection:*
+
+![Graph3](../docs/04-dce2.svg)
+
+## Delete old nodes after finding a better replacement
+Consider the following code:
+```
+return (2+1)+3;
+```
+Without DCE after the `idealize` call we would end up with:
+![Graph3](../docs/04-dce3.svg)
+
+After identifying a more optimal replacement value (6) for the expression (2 + 1) + 3,
+we created a constant node to store this value.
+However, we did not remove the original expression,
+resulting in dangling nodes in our structure.
+
+To fix this, we introduce an extra `deadCodeElim` call that is responsible for deleting unused nodes.
+
+
+```java
+public final Node peephole( ) {
+ ...
+ if (!(this instanceof ConstantNode) && type.isConstant())
+ return new deadCodeElim(ConstantNode(type).peephole());
+
+ ...
+
+ Node n = idealize();
+ if( n != null ) // Something changed
+ // Recursively optimize
+ return deadCodeElim(n.peephole());
+
+ ...
+}
+```
+
+```java
+// m is the new Node, self is the old.
+// Return 'm', which may have zero uses but is alive nonetheless.
+// If self has zero uses (and is not 'm'), {@link #kill} self.
+private Node deadCodeElim(Node m) {
+ // If self is going dead and not being returned here (Nodes returned
+ // from peephole commonly have no uses (yet)), then kill self.
+ if( m != this && isUnused() ) {
+ // Killing self - and since self recursively kills self's inputs we
+ // might end up killing 'm', which we are returning as a live Node.
+ // So we add a bogus extra null output edge to stop kill().
+ m.addUse(null); // Add bogus null use to keep m alive
+ kill(); // Kill self because replacing with 'm'
+ m.delUse(null); // Remove bogus null.
+ }
+ return m;
+}
+``` \ No newline at end of file
diff --git a/docs/chapter04/04-arg1.svg b/docs/chapter04/04-arg1.svg
new file mode 100644
index 00000000..cf4599c5
--- /dev/null
+++ b/docs/chapter04/04-arg1.svg
@@ -0,0 +1,84 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<!-- Generated by graphviz version 2.40.1 (20161225.0304)
+ -->
+<!-- Title: chapter04 Pages: 1 -->
+<svg width="358pt" height="186pt" viewBox="0.00 0.00 358.00 186.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 182)">
+<title>chapter04</title>
+<polygon fill="#ffffff" stroke="transparent" points="-4,4 -4,-182 354,-182 354,4 -4,4"/>
+<g id="clust1" class="cluster">
+<title>cluster_Nodes</title>
+<polygon fill="none" stroke="#000000" points="8,-16 8,-170 154,-170 154,-16 8,-16"/>
+</g>
+<g id="clust2" class="cluster">
+<title>cluster_Scope1_0</title>
+<polygon fill="none" stroke="#000000" points="162,-8 162,-76 342,-76 342,-8 162,-8"/>
+</g>
+<g id="clust3" class="cluster">
+<title>cluster_Scope1_1</title>
+<polygon fill="none" stroke="#000000" points="264,-16 264,-68 334,-68 334,-16 264,-16"/>
+</g>
+<!-- Start2 -->
+<g id="node1" class="node">
+<title>Start2</title>
+<polygon fill="#ffff00" stroke="transparent" points="25,-132 25,-158 66,-158 66,-132 25,-132"/>
+<polygon fill="none" stroke="#000000" points="25,-132 25,-158 66,-158 66,-132 25,-132"/>
+<text text-anchor="start" x="32.2805" y="-140.4" font-family="Times,serif" font-size="14.00" fill="#000000">Start</text>
+<polygon fill="none" stroke="#000000" points="25,-100 25,-132 66,-132 66,-100 25,-100"/>
+<polygon fill="#ffff00" stroke="transparent" points="30,-105 30,-127 61,-127 61,-105 30,-105"/>
+<polygon fill="none" stroke="#000000" points="30,-105 30,-127 61,-127 61,-105 30,-105"/>
+<text text-anchor="start" x="32.6718" y="-111.4" font-family="Times,serif" font-size="14.00" fill="#000000">$ctrl</text>
+</g>
+<!-- Con_5 -->
+<g id="node2" class="node">
+<title>Con_5</title>
+<ellipse fill="none" stroke="#000000" cx="119" cy="-129" rx="27" ry="18"/>
+<text text-anchor="middle" x="119" y="-124.8" font-family="Times,serif" font-size="14.00" fill="#000000">2</text>
+</g>
+<!-- Return6 -->
+<g id="node3" class="node">
+<title>Return6</title>
+<polygon fill="#ffff00" stroke="#000000" points="109.1025,-60 54.8975,-60 54.8975,-24 109.1025,-24 109.1025,-60"/>
+<text text-anchor="middle" x="82" y="-37.8" font-family="Times,serif" font-size="14.00" fill="#000000">Return</text>
+</g>
+<!-- Return6&#45;&gt;Start2 -->
+<g id="edge1" class="edge">
+<title>Return6-&gt;Start2:p0</title>
+<path fill="none" stroke="#ff0000" d="M65.0542,-60.052C57.6135,-69.4899 49.9318,-81.7894 47.1181,-94.8747"/>
+<polygon fill="#ff0000" stroke="#ff0000" points="43.6189,-94.6762 46,-105 50.5766,-95.4446 43.6189,-94.6762"/>
+<text text-anchor="middle" x="62.8306" y="-62.452" font-family="Helvetica,sans-Serif" font-size="8.00" fill="#000000">0</text>
+</g>
+<!-- Return6&#45;&gt;Con_5 -->
+<g id="edge2" class="edge">
+<title>Return6-&gt;Con_5</title>
+<path fill="none" stroke="#000000" d="M89.6664,-60.0265C94.8444,-72.2017 101.7707,-88.4878 107.5926,-102.1772"/>
+<polygon fill="#000000" stroke="#000000" points="104.4613,-103.7577 111.5959,-111.5903 110.903,-101.0181 104.4613,-103.7577"/>
+<text text-anchor="middle" x="87.4428" y="-62.4265" font-family="Helvetica,sans-Serif" font-size="8.00" fill="#000000">1</text>
+</g>
+<!-- Scope1_0 -->
+<g id="node4" class="node">
+<title>Scope1_0</title>
+<polygon fill="#00ffff" stroke="transparent" points="179,-31 179,-53 192,-53 192,-31 179,-31"/>
+<polygon fill="none" stroke="#000000" points="179,-31 179,-53 192,-53 192,-31 179,-31"/>
+<text text-anchor="start" x="182" y="-37.4" font-family="Times,serif" font-size="14.00" fill="#000000">0</text>
+<polygon fill="none" stroke="#000000" points="192,-31 192,-53 223,-53 223,-31 192,-31"/>
+<text text-anchor="start" x="194.6718" y="-37.4" font-family="Times,serif" font-size="14.00" fill="#000000">$ctrl</text>
+<polygon fill="none" stroke="#000000" points="223,-31 223,-53 246,-53 246,-31 223,-31"/>
+<text text-anchor="start" x="225.5624" y="-37.4" font-family="Times,serif" font-size="14.00" fill="#000000">arg</text>
+</g>
+<!-- Scope1_0&#45;&gt;Con_5 -->
+<g id="edge3" class="edge">
+<title>Scope1_0:Scope1_0_arg-&gt;Con_5</title>
+<path fill="none" stroke="#6495ed" stroke-dasharray="5,2" d="M235,-53C235,-91.8959 188.8038,-111.9666 154.717,-121.4819"/>
+<polygon fill="#6495ed" stroke="#6495ed" points="153.8305,-118.0959 145.0327,-123.9992 155.5916,-124.8708 153.8305,-118.0959"/>
+</g>
+<!-- Scope1_1 -->
+<g id="node5" class="node">
+<title>Scope1_1</title>
+<polygon fill="#00ffff" stroke="transparent" points="293,-31 293,-53 306,-53 306,-31 293,-31"/>
+<polygon fill="none" stroke="#000000" points="293,-31 293,-53 306,-53 306,-31 293,-31"/>
+<text text-anchor="start" x="296" y="-37.4" font-family="Times,serif" font-size="14.00" fill="#000000">1</text>
+</g>
+</g>
+</svg> \ No newline at end of file
diff --git a/docs/chapter04/04-arg2.svg b/docs/chapter04/04-arg2.svg
new file mode 100644
index 00000000..2b3b47a3
--- /dev/null
+++ b/docs/chapter04/04-arg2.svg
@@ -0,0 +1,80 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<!-- Generated by graphviz version 2.40.1 (20161225.0304)
+ -->
+<!-- Title: chapter04 Pages: 1 -->
+<svg width="308pt" height="186pt" viewBox="0.00 0.00 308.00 186.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 182)">
+<title>chapter04</title>
+<polygon fill="#ffffff" stroke="transparent" points="-4,4 -4,-182 304,-182 304,4 -4,4"/>
+<g id="clust1" class="cluster">
+<title>cluster_Nodes</title>
+<polygon fill="none" stroke="#000000" points="8,-16 8,-170 104,-170 104,-16 8,-16"/>
+</g>
+<g id="clust2" class="cluster">
+<title>cluster_Scope1_0</title>
+<polygon fill="none" stroke="#000000" points="112,-8 112,-76 292,-76 292,-8 112,-8"/>
+</g>
+<g id="clust3" class="cluster">
+<title>cluster_Scope1_1</title>
+<polygon fill="none" stroke="#000000" points="214,-16 214,-68 284,-68 284,-16 214,-16"/>
+</g>
+<!-- Start2 -->
+<g id="node1" class="node">
+<title>Start2</title>
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+<text text-anchor="middle" x="119" y="-116.8" font-family="Times,serif" font-size="14.00" fill="#000000">6</text>
+</g>
+<!-- Return12 -->
+<g id="node9" class="node">
+<title>Return12</title>
+<polygon fill="#ffff00" stroke="#000000" points="109.1025,-52 54.8975,-52 54.8975,-16 109.1025,-16 109.1025,-52"/>
+<text text-anchor="middle" x="82" y="-29.8" font-family="Times,serif" font-size="14.00" fill="#000000">Return</text>
+</g>
+<!-- Return12&#45;&gt;Start2 -->
+<g id="edge5" class="edge">
+<title>Return12-&gt;Start2:p0</title>
+<path fill="none" stroke="#ff0000" d="M65.0542,-52.052C57.6135,-61.4899 49.9318,-73.7894 47.1181,-86.8747"/>
+<polygon fill="#ff0000" stroke="#ff0000" points="43.6189,-86.6762 46,-97 50.5766,-87.4446 43.6189,-86.6762"/>
+<text text-anchor="middle" x="62.8306" y="-54.452" font-family="Helvetica,sans-Serif" font-size="8.00" fill="#000000">0</text>
+</g>
+<!-- Return12&#45;&gt;Con_11 -->
+<g id="edge6" class="edge">
+<title>Return12-&gt;Con_11</title>
+<path fill="none" stroke="#000000" d="M89.6664,-52.0265C94.8444,-64.2017 101.7707,-80.4878 107.5926,-94.1772"/>
+<polygon fill="#000000" stroke="#000000" points="104.4613,-95.7577 111.5959,-103.5903 110.903,-93.0181 104.4613,-95.7577"/>
+<text text-anchor="middle" x="87.4428" y="-54.4265" font-family="Helvetica,sans-Serif" font-size="8.00" fill="#000000">1</text>
+</g>
+</g>
+</svg> \ No newline at end of file
diff --git a/docs/chapter04/04-grammar.md b/docs/chapter04/04-grammar.md
new file mode 100644
index 00000000..48facd4c
--- /dev/null
+++ b/docs/chapter04/04-grammar.md
@@ -0,0 +1,76 @@
+# Grammar for Chapter 1
+
+```antlrv4
+grammar SimpleLanguage;
+
+program
+ : statement+ EOF
+ ;
+
+statement
+ : returnStatement
+ | declStatement
+ | blockStatment
+ | expressionStatement
+ | metaStatement
+ ;
+
+metaStatement
+ : '#showGraph' ';'
+ ;
+
+expressionStatement
+ : IDENTIFIER '=' expression ';'
+ ;
+
+blockStatement
+ : '{' statement+ '}'
+ ;
+
+declStatement
+ : 'int' IDENTIFIER '=' expression ';'
+ ;
+
+returnStatement
+ : 'return' expression ';'
+ ;
+
+expression
+ : comparisonExpression
+ ;
+
+comparisonExpression
+ : additiveExpression (('==' | '!='| '>'| '<'| '>='| '<=') additiveExpression)*
+ ;
+
+additiveExpression
+ : multiplicativeExpression (('+' | '-') multiplicativeExpression)*
+ ;
+
+multiplicativeExpression
+ : unaryExpression (('*' | '/') unaryExpression)*
+ ;
+
+unaryExpression
+ : ('-') unaryExpression
+ | primaryExpression
+ ;
+
+primaryExpression
+ : IDENTIFIER
+ | INTEGER_LITERAL
+ | '(' expression ')'
+ ;
+
+INTEGER_LITERAL
+ : [1-9][0-9]*
+ | [0]
+ ;
+
+IDENTIFIER
+ : NON_DIGIT (NON_DIGIT | DIGIT)*
+ ;
+
+NON_DIGIT: [a-zA-Z_];
+DEC_DIGIT: [0-9];
+```
diff --git a/docs/chapter04/04-post-peephole.gv b/docs/chapter04/04-post-peephole.gv
new file mode 100644
index 00000000..0a9f8e93
--- /dev/null
+++ b/docs/chapter04/04-post-peephole.gv
@@ -0,0 +1,43 @@
+digraph chapter04 {
+/*
+return 1+arg+2; #showGraph;
+*/
+ rankdir=BT;
+ ordering="in";
+ concentrate="true";
+ subgraph cluster_Nodes {
+ Start2 [ shape=plaintext label=<
+ <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+ <TR><TD BGCOLOR="yellow">Start</TD></TR>
+ <TR><TD>
+ <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+ <TR><TD PORT="p0" BGCOLOR="yellow">$ctrl</TD><TD PORT="p1">arg</TD></TR>
+ </TABLE>
+ </TD></TR>
+ </TABLE>>
+ ];
+ Con_10 [ label="#3" ];
+ Add11 [ label="+" ];
+ Return12 [ shape=box style=filled fillcolor=yellow label="Return" ];
+ }
+ node [shape=plaintext];
+ subgraph cluster_Scope1_0 {
+ Scope1_0 [label=<
+ <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+ <TR><TD BGCOLOR="cyan">0</TD><TD PORT="Scope1_0_$ctrl">$ctrl</TD><TD PORT="Scope1_0_arg">arg</TD></TR>
+ </TABLE>>];
+ subgraph cluster_Scope1_1 {
+ Scope1_1 [label=<
+ <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+ <TR><TD BGCOLOR="cyan">1</TD></TR>
+ </TABLE>>];
+ }
+ }
+ edge [ fontname=Helvetica, fontsize=8 ];
+ Add11 -> Start2:p1[taillabel=1];
+ Add11 -> Con_10[taillabel=2];
+ Return12 -> Start2:p0[taillabel=0; color=red];
+ Return12 -> Add11[taillabel=1];
+ edge [style=dashed color=cornflowerblue];
+ Scope1_0:"Scope1_0_arg" -> Start2:p1;
+}
diff --git a/docs/chapter04/04-post-peephole.svg b/docs/chapter04/04-post-peephole.svg
new file mode 100644
index 00000000..550c16ef
--- /dev/null
+++ b/docs/chapter04/04-post-peephole.svg
@@ -0,0 +1,108 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<!-- Generated by graphviz version 2.43.0 (0)
+ -->
+<!-- Title: chapter04 Pages: 1 -->
+<svg width="417pt" height="248pt"
+ viewBox="0.00 0.00 417.00 248.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 244)">
+<title>chapter04</title>
+<polygon fill="white" stroke="transparent" points="-4,4 -4,-244 413,-244 413,4 -4,4"/>
+<g id="clust1" class="cluster">
+<title>cluster_Nodes</title>
+<polygon fill="none" stroke="black" points="8,-8 8,-232 193,-232 193,-8 8,-8"/>
+</g>
+<g id="clust2" class="cluster">
+<title>cluster_Scope1_0</title>
+<polygon fill="none" stroke="black" points="201,-72 201,-140 401,-140 401,-72 201,-72"/>
+</g>
+<g id="clust3" class="cluster">
+<title>cluster_Scope1_1</title>
+<polygon fill="none" stroke="black" points="323,-80 323,-132 393,-132 393,-80 323,-80"/>
+</g>
+<!-- Start2 -->
+<g id="node1" class="node">
+<title>Start2</title>
+<polygon fill="yellow" stroke="transparent" points="97,-195 97,-220 178,-220 178,-195 97,-195"/>
+<polygon fill="none" stroke="black" points="97,-195 97,-220 178,-220 178,-195 97,-195"/>
+<text text-anchor="start" x="119" y="-203.8" font-family="Times,serif" font-size="14.00">Start</text>
+<polygon fill="none" stroke="black" points="97,-164 97,-195 178,-195 178,-164 97,-164"/>
+<polygon fill="yellow" stroke="transparent" points="102,-169 102,-190 142,-190 142,-169 102,-169"/>
+<polygon fill="none" stroke="black" points="102,-169 102,-190 142,-190 142,-169 102,-169"/>
+<text text-anchor="start" x="105" y="-175.8" font-family="Times,serif" font-size="14.00">$ctrl</text>
+<polygon fill="none" stroke="black" points="142,-169 142,-190 173,-190 173,-169 142,-169"/>
+<text text-anchor="start" x="145" y="-175.8" font-family="Times,serif" font-size="14.00">arg</text>
+</g>
+<!-- Con_10 -->
+<g id="node2" class="node">
+<title>Con_10</title>
+<ellipse fill="none" stroke="black" cx="43" cy="-192" rx="27" ry="18"/>
+<text text-anchor="middle" x="43" y="-188.3" font-family="Times,serif" font-size="14.00">#3</text>
+</g>
+<!-- Add11 -->
+<g id="node3" class="node">
+<title>Add11</title>
+<ellipse fill="none" stroke="black" cx="158" cy="-106" rx="27" ry="18"/>
+<text text-anchor="middle" x="158" y="-102.3" font-family="Times,serif" font-size="14.00">+</text>
+</g>
+<!-- Add11&#45;&gt;Start2 -->
+<g id="edge1" class="edge">
+<title>Add11&#45;&gt;Start2:p1</title>
+<path fill="none" stroke="black" d="M158,-124.09C158,-133.55 158,-145.77 158,-157.69"/>
+<polygon fill="black" stroke="black" points="154.5,-158 158,-168 161.5,-158 154.5,-158"/>
+<text text-anchor="middle" x="155" y="-126.69" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Add11&#45;&gt;Con_10 -->
+<g id="edge2" class="edge">
+<title>Add11&#45;&gt;Con_10</title>
+<path fill="none" stroke="black" d="M139.03,-119.12C123,-129.54 99.59,-145.19 80,-160 75.68,-163.26 71.19,-166.85 66.88,-170.4"/>
+<polygon fill="black" stroke="black" points="64.34,-167.96 58.92,-177.06 68.84,-173.32 64.34,-167.96"/>
+<text text-anchor="middle" x="136.03" y="-121.72" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- Return12 -->
+<g id="node4" class="node">
+<title>Return12</title>
+<polygon fill="yellow" stroke="black" points="165,-52 99,-52 99,-16 165,-16 165,-52"/>
+<text text-anchor="middle" x="132" y="-30.3" font-family="Times,serif" font-size="14.00">Return</text>
+</g>
+<!-- Return12&#45;&gt;Start2 -->
+<g id="edge3" class="edge">
+<title>Return12&#45;&gt;Start2:p0</title>
+<path fill="none" stroke="red" d="M126.36,-52.13C124.59,-58.32 122.88,-65.4 122,-72 116.87,-110.66 121.12,-123.21 121.89,-157.66"/>
+<polygon fill="red" stroke="red" points="118.39,-158.04 122,-168 125.39,-157.96 118.39,-158.04"/>
+<text text-anchor="middle" x="123.36" y="-54.73" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- Return12&#45;&gt;Add11 -->
+<g id="edge4" class="edge">
+<title>Return12&#45;&gt;Add11</title>
+<path fill="none" stroke="black" d="M138.43,-52.3C141.4,-60.3 144.99,-69.98 148.29,-78.85"/>
+<polygon fill="black" stroke="black" points="145.06,-80.22 151.83,-88.38 151.63,-77.78 145.06,-80.22"/>
+<text text-anchor="middle" x="135.43" y="-54.9" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Scope1_0 -->
+<g id="node5" class="node">
+<title>Scope1_0</title>
+<polygon fill="cyan" stroke="transparent" points="218,-95 218,-116 234,-116 234,-95 218,-95"/>
+<polygon fill="none" stroke="black" points="218,-95 218,-116 234,-116 234,-95 218,-95"/>
+<text text-anchor="start" x="221" y="-101.8" font-family="Times,serif" font-size="14.00">0</text>
+<polygon fill="none" stroke="black" points="234,-95 234,-116 274,-116 274,-95 234,-95"/>
+<text text-anchor="start" x="237" y="-101.8" font-family="Times,serif" font-size="14.00">$ctrl</text>
+<polygon fill="none" stroke="black" points="274,-95 274,-116 305,-116 305,-95 274,-95"/>
+<text text-anchor="start" x="277" y="-101.8" font-family="Times,serif" font-size="14.00">arg</text>
+</g>
+<!-- Scope1_0&#45;&gt;Start2 -->
+<g id="edge5" class="edge">
+<title>Scope1_0:Scope1_0_arg&#45;&gt;Start2:p1</title>
+<path fill="none" stroke="cornflowerblue" stroke-dasharray="5,2" d="M290,-117C290,-172.03 239,-178.4 184.25,-178.95"/>
+<polygon fill="cornflowerblue" stroke="cornflowerblue" points="183.98,-175.45 174,-179 184.02,-182.45 183.98,-175.45"/>
+</g>
+<!-- Scope1_1 -->
+<g id="node6" class="node">
+<title>Scope1_1</title>
+<polygon fill="cyan" stroke="transparent" points="350,-95 350,-116 366,-116 366,-95 350,-95"/>
+<polygon fill="none" stroke="black" points="350,-95 350,-116 366,-116 366,-95 350,-95"/>
+<text text-anchor="start" x="353" y="-101.8" font-family="Times,serif" font-size="14.00">1</text>
+</g>
+</g>
+</svg>
diff --git a/docs/chapter04/04-pre-peephole.gv b/docs/chapter04/04-pre-peephole.gv
new file mode 100644
index 00000000..aefd81c4
--- /dev/null
+++ b/docs/chapter04/04-pre-peephole.gv
@@ -0,0 +1,47 @@
+digraph chapter04 {
+/*
+return 1+arg+2; #showGraph;
+*/
+ rankdir=BT;
+ ordering="in";
+ concentrate="true";
+ subgraph cluster_Nodes {
+ Start2 [ shape=plaintext label=<
+ <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+ <TR><TD BGCOLOR="yellow">Start</TD></TR>
+ <TR><TD>
+ <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+ <TR><TD PORT="p0" BGCOLOR="yellow">$ctrl</TD><TD PORT="p1">arg</TD></TR>
+ </TABLE>
+ </TD></TR>
+ </TABLE>>
+ ];
+ Con_5 [ label="#1" ];
+ Con_6 [ label="#2" ];
+ Add7 [ label="+" ];
+ Add8 [ label="+" ];
+ Return9 [ shape=box style=filled fillcolor=yellow label="Return" ];
+ }
+ node [shape=plaintext];
+ subgraph cluster_Scope1_0 {
+ Scope1_0 [label=<
+ <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+ <TR><TD BGCOLOR="cyan">0</TD><TD PORT="Scope1_0_$ctrl">$ctrl</TD><TD PORT="Scope1_0_arg">arg</TD></TR>
+ </TABLE>>];
+ subgraph cluster_Scope1_1 {
+ Scope1_1 [label=<
+ <TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0">
+ <TR><TD BGCOLOR="cyan">1</TD></TR>
+ </TABLE>>];
+ }
+ }
+ edge [ fontname=Helvetica, fontsize=8 ];
+ Add7 -> Start2:p1[taillabel=1];
+ Add7 -> Con_6[taillabel=2];
+ Add8 -> Con_5[taillabel=1];
+ Add8 -> Add7[taillabel=2];
+ Return9 -> Start2:p0[taillabel=0; color=red];
+ Return9 -> Add8[taillabel=1];
+ edge [style=dashed color=cornflowerblue];
+ Scope1_0:"Scope1_0_arg" -> Start2:p1;
+}
diff --git a/docs/chapter04/04-pre-peephole.svg b/docs/chapter04/04-pre-peephole.svg
new file mode 100644
index 00000000..9ec38d27
--- /dev/null
+++ b/docs/chapter04/04-pre-peephole.svg
@@ -0,0 +1,134 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<!-- Generated by graphviz version 2.43.0 (0)
+ -->
+<!-- Title: chapter04 Pages: 1 -->
+<svg width="417pt" height="320pt"
+ viewBox="0.00 0.00 417.00 320.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 316)">
+<title>chapter04</title>
+<polygon fill="white" stroke="transparent" points="-4,4 -4,-316 413,-316 413,4 -4,4"/>
+<g id="clust1" class="cluster">
+<title>cluster_Nodes</title>
+<polygon fill="none" stroke="black" points="8,-8 8,-304 193,-304 193,-8 8,-8"/>
+</g>
+<g id="clust2" class="cluster">
+<title>cluster_Scope1_0</title>
+<polygon fill="none" stroke="black" points="201,-144 201,-212 401,-212 401,-144 201,-144"/>
+</g>
+<g id="clust3" class="cluster">
+<title>cluster_Scope1_1</title>
+<polygon fill="none" stroke="black" points="323,-152 323,-204 393,-204 393,-152 323,-152"/>
+</g>
+<!-- Start2 -->
+<g id="node1" class="node">
+<title>Start2</title>
+<polygon fill="yellow" stroke="transparent" points="97,-267 97,-292 178,-292 178,-267 97,-267"/>
+<polygon fill="none" stroke="black" points="97,-267 97,-292 178,-292 178,-267 97,-267"/>
+<text text-anchor="start" x="119" y="-275.8" font-family="Times,serif" font-size="14.00">Start</text>
+<polygon fill="none" stroke="black" points="97,-236 97,-267 178,-267 178,-236 97,-236"/>
+<polygon fill="yellow" stroke="transparent" points="102,-241 102,-262 142,-262 142,-241 102,-241"/>
+<polygon fill="none" stroke="black" points="102,-241 102,-262 142,-262 142,-241 102,-241"/>
+<text text-anchor="start" x="105" y="-247.8" font-family="Times,serif" font-size="14.00">$ctrl</text>
+<polygon fill="none" stroke="black" points="142,-241 142,-262 173,-262 173,-241 142,-241"/>
+<text text-anchor="start" x="145" y="-247.8" font-family="Times,serif" font-size="14.00">arg</text>
+</g>
+<!-- Con_5 -->
+<g id="node2" class="node">
+<title>Con_5</title>
+<ellipse fill="none" stroke="black" cx="115" cy="-178" rx="27" ry="18"/>
+<text text-anchor="middle" x="115" y="-174.3" font-family="Times,serif" font-size="14.00">#1</text>
+</g>
+<!-- Con_6 -->
+<g id="node3" class="node">
+<title>Con_6</title>
+<ellipse fill="none" stroke="black" cx="43" cy="-264" rx="27" ry="18"/>
+<text text-anchor="middle" x="43" y="-260.3" font-family="Times,serif" font-size="14.00">#2</text>
+</g>
+<!-- Add7 -->
+<g id="node4" class="node">
+<title>Add7</title>
+<ellipse fill="none" stroke="black" cx="43" cy="-178" rx="27" ry="18"/>
+<text text-anchor="middle" x="43" y="-174.3" font-family="Times,serif" font-size="14.00">+</text>
+</g>
+<!-- Add7&#45;&gt;Start2 -->
+<g id="edge1" class="edge">
+<title>Add7&#45;&gt;Start2:p1</title>
+<path fill="none" stroke="black" d="M56.63,-193.93C62.95,-200.18 70.86,-207.11 79,-212 107.43,-229.09 147.88,-208.4 156.39,-229.99"/>
+<polygon fill="black" stroke="black" points="152.96,-230.68 158,-240 159.87,-229.57 152.96,-230.68"/>
+<text text-anchor="middle" x="53.63" y="-196.53" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Add7&#45;&gt;Con_6 -->
+<g id="edge2" class="edge">
+<title>Add7&#45;&gt;Con_6</title>
+<path fill="none" stroke="black" d="M43,-196.4C43,-207.74 43,-222.77 43,-235.68"/>
+<polygon fill="black" stroke="black" points="39.5,-235.9 43,-245.9 46.5,-235.9 39.5,-235.9"/>
+<text text-anchor="middle" x="40" y="-199" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- Add8 -->
+<g id="node5" class="node">
+<title>Add8</title>
+<ellipse fill="none" stroke="black" cx="115" cy="-106" rx="27" ry="18"/>
+<text text-anchor="middle" x="115" y="-102.3" font-family="Times,serif" font-size="14.00">+</text>
+</g>
+<!-- Add8&#45;&gt;Con_5 -->
+<g id="edge3" class="edge">
+<title>Add8&#45;&gt;Con_5</title>
+<path fill="none" stroke="black" d="M115,-124.3C115,-132.02 115,-141.29 115,-149.89"/>
+<polygon fill="black" stroke="black" points="111.5,-149.9 115,-159.9 118.5,-149.9 111.5,-149.9"/>
+<text text-anchor="middle" x="112" y="-126.9" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Add8&#45;&gt;Add7 -->
+<g id="edge4" class="edge">
+<title>Add8&#45;&gt;Add7</title>
+<path fill="none" stroke="black" d="M100.43,-121.17C90.25,-131.06 76.48,-144.45 64.97,-155.64"/>
+<polygon fill="black" stroke="black" points="62.53,-153.13 57.8,-162.62 67.41,-158.15 62.53,-153.13"/>
+<text text-anchor="middle" x="97.43" y="-123.77" font-family="Helvetica,sans-Serif" font-size="8.00">2</text>
+</g>
+<!-- Return9 -->
+<g id="node6" class="node">
+<title>Return9</title>
+<polygon fill="yellow" stroke="black" points="166,-52 100,-52 100,-16 166,-16 166,-52"/>
+<text text-anchor="middle" x="133" y="-30.3" font-family="Times,serif" font-size="14.00">Return</text>
+</g>
+<!-- Return9&#45;&gt;Start2 -->
+<g id="edge5" class="edge">
+<title>Return9&#45;&gt;Start2:p0</title>
+<path fill="none" stroke="red" d="M140.48,-52.3C144.47,-62.48 148.97,-75.73 151,-88 159.98,-142.37 172.54,-161.27 151,-212 145.75,-224.37 132.06,-223.86 125.55,-230.39"/>
+<polygon fill="red" stroke="red" points="122.18,-229.41 122,-240 128.74,-231.83 122.18,-229.41"/>
+<text text-anchor="middle" x="137.48" y="-54.9" font-family="Helvetica,sans-Serif" font-size="8.00">0</text>
+</g>
+<!-- Return9&#45;&gt;Add8 -->
+<g id="edge6" class="edge">
+<title>Return9&#45;&gt;Add8</title>
+<path fill="none" stroke="black" d="M128.55,-52.3C126.55,-60.1 124.13,-69.49 121.9,-78.17"/>
+<polygon fill="black" stroke="black" points="118.5,-77.34 119.4,-87.9 125.28,-79.08 118.5,-77.34"/>
+<text text-anchor="middle" x="125.55" y="-54.9" font-family="Helvetica,sans-Serif" font-size="8.00">1</text>
+</g>
+<!-- Scope1_0 -->
+<g id="node7" class="node">
+<title>Scope1_0</title>
+<polygon fill="cyan" stroke="transparent" points="218,-167 218,-188 234,-188 234,-167 218,-167"/>
+<polygon fill="none" stroke="black" points="218,-167 218,-188 234,-188 234,-167 218,-167"/>
+<text text-anchor="start" x="221" y="-173.8" font-family="Times,serif" font-size="14.00">0</text>
+<polygon fill="none" stroke="black" points="234,-167 234,-188 274,-188 274,-167 234,-167"/>
+<text text-anchor="start" x="237" y="-173.8" font-family="Times,serif" font-size="14.00">$ctrl</text>
+<polygon fill="none" stroke="black" points="274,-167 274,-188 305,-188 305,-167 274,-167"/>
+<text text-anchor="start" x="277" y="-173.8" font-family="Times,serif" font-size="14.00">arg</text>
+</g>
+<!-- Scope1_0&#45;&gt;Start2 -->
+<g id="edge7" class="edge">
+<title>Scope1_0:Scope1_0_arg&#45;&gt;Start2:p1</title>
+<path fill="none" stroke="cornflowerblue" stroke-dasharray="5,2" d="M290,-189C290,-244.03 239,-250.4 184.25,-250.95"/>
+<polygon fill="cornflowerblue" stroke="cornflowerblue" points="183.98,-247.45 174,-251 184.02,-254.45 183.98,-247.45"/>
+</g>
+<!-- Scope1_1 -->
+<g id="node8" class="node">
+<title>Scope1_1</title>
+<polygon fill="cyan" stroke="transparent" points="350,-167 350,-188 366,-188 366,-167 350,-167"/>
+<polygon fill="none" stroke="black" points="350,-167 350,-188 366,-188 366,-167 350,-167"/>
+<text text-anchor="start" x="353" y="-173.8" font-family="Times,serif" font-size="14.00">1</text>
+</g>
+</g>
+</svg>
diff --git a/docs/chapter04/Makefile b/docs/chapter04/Makefile
new file mode 100644
index 00000000..12659b8f
--- /dev/null
+++ b/docs/chapter04/Makefile
@@ -0,0 +1,12 @@
+GV := $(wildcard *.gv)
+SVG := $(patsubst %.gv,%.svg,$(GV))
+
+.PHONY: all
+all: $(SVG)
+
+%.svg: %.gv
+ dot -Tsvg $< > $@
+
+.PHONY: clean
+clean:
+ @rm -f $(SVG)
diff --git a/docs/chapter04/README.md b/docs/chapter04/README.md
new file mode 100644
index 00000000..bfb52487
--- /dev/null
+++ b/docs/chapter04/README.md
@@ -0,0 +1,397 @@
+# Chapter 4: External Argument and Comparisons
+
+In this chapter we extend the language grammar with following features:
+
+* The program receives a single argument named `arg` of integer type from external environment.
+* Expressions support comparison operators.
+* We introduce a scope sensitive name binding `$ctrl` for the current incoming
+ control node. Thus, our Return is no longer hard-wired to Start, instead it
+ tracks the in scope `$ctrl` binding.
+
+Here is the [complete language grammar](04-grammar.md) for this chapter.
+
+You can also read [this chapter](https://github.com/SeaOfNodes/Simple/tree/linear-chapter04) in a linear Git revision history on the [linear](https://github.com/SeaOfNodes/Simple/tree/linear) branch and [compare](https://github.com/SeaOfNodes/Simple/compare/linear-chapter03...linear-chapter04) it to the previous chapter.
+
+## Extensions to Intermediate Representation
+
+In this chapter we add some new nodes and revise some existing nodes.
+Following are revised or new nodes
+
+| Node Name | Type | Description | Inputs | Value |
+|-----------|----------------|------------------------------------------------|-----------------------|----------------------------------------------------------------------------|
+| MultiNode | Abstract class | A node that has a tuple result | | A tuple |
+| Start | Control | Start of function, now a MultiNode | | A tuple with a ctrl token and an `arg` data node |
+| Proj | Data | Projection nodes extract values from MultiNode | A MultiNode and index | Result is the extracted value from the input MultiNode at offset index |
+| Bool | Data | Represents results of a comparison operator | Two data nodes | Result is a comparison, represented as integer value where 1=true, 0=false |
+| Not | Data | Logical not | One data node | Result converts 0 to 1 and vice versa |
+
+Below is our list of Nodes from [Chapter 3](../chapter03/README.md):
+
+| Node Name | Type | Description | Inputs | Value |
+|-----------|--------------|------------------------------------|------------------------------------------------------------------|------------------------------|
+| Return | Control | End of function | Predecessor control node, Data node value | Return value of the function |
+| Constant | Data | Constants such as integer literals | None, however Start node is set as input to enable graph walking | Value of the constant |
+| Add | Data | Add two values | Two data nodes, values are added, order not important | Result of the add operation |
+| Sub | Data | Subtract a value from another | Two data nodes, values are subtracted, order matters | Result of the subtract |
+| Mul | Data | Multiply two values | Two data nodes, values are multiplied, order not important | Result of the multiply |
+| Div | Data | Divide a value by another | Two data nodes, values are divided, order matters | Result of the division |
+| Minus | Data | Negate a value | One data node, value is negated | Result of the unary minus |
+| Scope | Symbol Table | Represents scopes in the graph | All nodes that define variables | None |
+
+## Projection Nodes
+
+We add projection nodes that are used to extract a specific tuple member from a multi-valued node.
+Each projection node contains an index of the field to extract from its input node.
+Projection nodes allow us to maintain labeled use-def edges as simple Node references.
+
+In the visuals, projection nodes are shown as rectangular boxes inside the node to which they are attached.
+
+### Visualisation
+
+![ProjNode](./projnode.png)
+
+In the visual above, the projection nodes have been tagged by the names
+associated with the outputs of the Start node. Both MultiNode that contain
+Control and Control nodes are yellow. `$ctrl` and `arg` are outputs(users) of
+StartNode(`START`) and have their MultiNode as their only input in slot 0. The
+`label` has no semantics and is used during debug printing.
+
+```java
+public ProjNode(MultiNode ctrl, int idx, String label) {
+ super(ctrl);
+```
+
+```java
+_scope.define(ScopeNode.CTRL, new ProjNode(START, 0, ScopeNode.CTRL).peephole());
+_scope.define(ScopeNode.ARG0, new ProjNode(START, 1, ScopeNode.ARG0).peephole());
+```
+
+These projection nodes are going to extract the types for `CTRL` and `ARG0` from the `START` MultiNode.
+The MultiNode holds the types as a TypeTuple:
+
+```java
+public StartNode(Type[] args) {
+ super();
+ _args = new TypeTuple(args);
+```
+
+Extracting the types is based on the `_idx`:
+```java
+return t instanceof TypeTuple tt ? tt._types[_idx] : Type.BOTTOM;
+```
+
+### Initial values
+
+An argument is always provided, and defaults to `TypeInteger.BOT`. Individual
+tests can (and do) pass in other integer values by calling `new Parser` with
+an argument:
+
+```java
+Parser parser = new Parser("return arg; #showGraph;", TypeInteger.constant(2));
+```
+
+The graph:
+
+![ProjNode](./04-arg1.svg)
+
+- `$ctrl` and `arg` are both defined in the outermost symbol table, at lexical depth 0.
+- There is an empty global-scope symbol table created at depth 1; in the future
+ global variables will be defined here.
+- There is no line for the scope `$ctrl` because control is dead after the
+ return. It is manually set to null, which calls `setDef` to kill the node
+ (and killed nodes are not part of the program and not visualized).
+
+```
+ ctrl(null); // Kill control
+```
+
+- The `arg` projection node is not included in the cluster because arg is a
+ constant. The `arg` was originally defined by a ProjNode; but when peephole
+ is called the computed type is a constant, and the ProjNode gets replaced
+ with a ConstantNode:
+
+```java
+public final Node peephole( ) {
+ Type type = _type = compute();
+ /* type = {TypeInteger@1527} "2" */
+
+ if (_disablePeephole)
+ return this;
+
+ // ProjNode is not a constant unlike its type.
+ if (!(this instanceof ConstantNode) && type.isConstant())
+ /* Create Constant(2) */
+ return deadCodeElim(new ConstantNode(type).peephole());
+
+ /* won't get called */
+ ...
+```
+
+If you don't pass an argument you get `TypeInteger.BOT`
+
+```java
+ Parser parser = new Parser("return arg; #showGraph;");
+ ...
+
+public Parser(String source) {
+ this(source, TypeInteger.BOT);
+}
+
+```
+
+We clearly see this is not a constant:
+
+```java
+public final static TypeInteger BOT = new TypeInteger(false, 1);
+ /* _is_con = false */
+```
+
+So the `arg` projection node remains in the cluster:
+
+![ArgNode](./04-arg2.svg)
+
+
+#### When Is Control Not-Null?
+
+In later chapters, `$ctrl` will point to other control nodes, such as
+`If` and `Region` (and `Loop`), but for now with no other control flow it always gets set to null after a `Return`.
+
+#### Note Regarding Visualizations
+
+From this chapter onwards we omit the edges from Constants to Start node, mainly to reduce
+clutter and help draw reader's attention to the more important aspects of the graph.
+
+
+
+## Changes to Type System
+
+In [Chapter 2](../chapter02/README.md) we introduced the Type System.
+
+We have annotated Nodes with Types and the Type annotation serves two purposes:
+
+* It defines the set of operations allowed on the Node, and
+* it defines the set of values the Node takes on.
+
+We mentioned in [Chapter 2](../chapter02/README.md) that the set of values
+associated with a Type at a specific Node can be conveniently represented as a
+[lattice](https://en.wikipedia.org/wiki/Lattice_(order)).
+
+The type itself is identified by the Java class `Type` and subtypes. The type
+implementation uses Java classes as convenient to deal with a Types' internal
+structure - but the Java classes have no relation to a Type's place in the
+lattice.
+
+In this chapter we extend the Type hierarchy as follows:
+
+```
+Type
++-- TypeControl (New - represents control token)
++-- TypeInteger (Enhanced - now has Top and Bottom types)
++-- TypeBot
++-- TypeTuple (New - represents multi-valued result)
+```
+
+Our enhanced Lattice looks like this:
+
+![Lattice](./lattice.svg)
+
+
+In this chapter we introduce the possibility of a program input variable named
+`arg`; all we know about this variable is that it is some integer value, but we do not know whether it is a constant or not.
+
+To support the requirements for non-constant integer values, we enhance `TypeInteger` to
+allow it to represent `IntTop` and `IntBot` integer types in addition to the earlier constant value.
+
+Now that integer values may be constants or non-constants, we need to introduce the "meet" operator
+in our lattice. The `meet` operator describes rules that define the resulting type when we combine
+integer values.
+
+| | IntBot | Con1 | Con2 | IntTop |
+|--------|--------|--------|--------|--------|
+| IntBot | IntBot | IntBot | IntBot | IntBot |
+| Con1 | IntBot | Con1 | IntBot | Con1 |
+| IntTop | IntBot | Con1 | Con2 | IntTop |
+
+In the table above `Con1` and `Con2` represent two distinct integer values, and serve to explain the rules below.
+
+* The `meet` of `IntTop` with any integer constant is that constant.
+* The `meet` of `IntBot` with any integer value is `IntBot`.
+* The `meet` of any integer with itself is that integer.
+* The `meet` of two unrelated integer constants is `IntBot`.
+
+Currently, all our integer valued nodes are either a constant or a `IntBot` integer type.
+When we start optimizing loops, we will start seeing `IntTop` values.
+
+
+## `$ctrl` name binding
+
+In previous chapters, we had a hard coded control input edge from Start to
+Return. In this chapter we no longer have such a hard-wired edge. Instead, we
+track the current in-scope control node via the name `$ctrl`. This means that
+when we need to create an edge to the predecessor control node, we simply
+look up this name in the current scope.
+
+This introduces the idea that the control flow subgraph is a Petri net model.[^1]
+The control token moves virtually from node to node as execution proceeds. The
+initial control token is in Start, it then moves via the Proj node to Return.
+In later chapters we will see how the token moves across branches.
+
+
+## More Peephole Optimizations
+
+Now that we have non-constant integer values, we can do additional
+optimizations, rearranging algebraic expressions to enable constant
+folding. For example:
+
+```
+return 1 + arg + 2;
+```
+
+We would expect the compiler to output `arg+3` here, but as it stands what we get is:
+
+![Graph1](./04-pre-peephole.svg)
+
+We need to perform some algebraic simplifications to enable better outcome. For
+example, we need to rearrange the expression as follows:
+
+```
+arg + (1 + 2)
+```
+
+This then enables constant folding and the final outcome is shown below. By
+canonicalizing expressions we fold common addressing math constants, remove
+algebraic identities and generally simplify the code.
+
+![Graph1](./04-post-peephole.svg)
+
+Here is a list of peepholes introduced in this Chapter, more will be introduced in later chapters:
+
+| Before | After | Description |
+|-----------------------|-----------------------|------------------------------------------------|
+| (arg + 0 ) | arg | Add of zero identity |
+| (arg * 1 ) | arg | Multiple of one identity |
+| (con + arg) | (arg + con) | Move constants to right, to encourage folding |
+| (con * arg) | (arg * con) | Move constants to right, to encourage folding |
+| (con1 + (arg + con2)) | (arg + (con1 + con2)) | Move constants to right, to encourage folding |
+| ((arg1 + con) + arg2) | ((arg1 + arg2) + con) | Move constants to right, to encourage folding |
+| (arg + arg) | (arg * 2) | Sum-of-products form |
+| (arg - arg) | 0 | Sub of same is 0
+| (con / 1) | con | Division by one
+| (arg == arg) | 1 | Compare of same
+| (arg != arg) | 0 | Compare of same
+| (arg < arg) | 0 | Compare of same
+| (arg > arg) | 0 | Compare of same
+| (arg <= arg) | 1 | Compare of same
+| (arg >= arg) | 1 | Compare of same
+
+
+## Peephole Walkthrough
+
+The peephole optimizations introduced in this chapter are local. They are triggered during parsing
+as new nodes are created, before the newly created node has any uses.
+
+For example, when we parse a unary expression, and create a Node for the parsed expression,
+`peephole()` is invoked on the newly created `MinusNode`:
+
+```java
+private Node parseUnary() {
+ if (match("-")) return new MinusNode(parseUnary()).peephole();
+ return parsePrimary();
+}
+```
+
+As another example, here is the parsing of comparison operators, also introduced in this chapter:
+
+```java
+private Node parseComparison() {
+ var lhs = parseAddition();
+ if (match("==")) return new BoolNode.EQNode(lhs, parseComparison()).peephole();
+ if (match("!=")) return new BoolNode.NENode(lhs, parseComparison()).peephole();
+ if (match("<=")) return new BoolNode.LENode(lhs, parseComparison()).peephole();
+ if (match("<" )) return new BoolNode.LTNode(lhs, parseComparison()).peephole();
+ if (match(">=")) return new BoolNode.GENode(lhs, parseComparison()).peephole();
+ if (match(">" )) return new BoolNode.GTNode(lhs, parseComparison()).peephole();
+ return lhs;
+}
+```
+
+The implementation of `peephole()` is in the main `Node` class, and is thus shared
+by all subclasses of `Node`.
+
+```java
+public final Node peephole( ) {
+ // Compute initial or improved Type
+ Type type = _type = compute();
+
+ // Replace constant computations from non-constants with a constant node
+ if (!(this instanceof ConstantNode) && type.isConstant())
+ return deadCodeElim(new ConstantNode(type).peephole());
+
+ // Ask each node for a better replacement
+ Node n = idealize();
+ if( n != null ) // Something changed
+ // Recursively optimize
+ return deadCodeElim(n.peephole());
+
+ return this; // No progress
+}
+```
+
+The peephole method does following:
+
+- Compute a Type for the node.
+- If the Type is a Constant and the node is not a ConstantNode, replace with a
+ ConstantNode, recursively invoking peephole on the new constant.
+- Otherwise, ask the Node for a better replacement via a call to `idealize()`.
+ The "better replacement" is things like `(1+2)` becomes `3` and `1+(x+2))`
+ becomes `(x+(1+2))`.
+- - Each Node subtype is responsible for deciding what the `idealize()` step
+ should do. If there is a better replacement then the node returns a non
+ `null` value.
+- - If we see a non `null` value, something changed, so we invoke `peephole()`
+ again and then also run dead code elimination on the (now dead and replaced)
+ `this` node.
+
+`peephole()` calls `deadCodeElim()` which is shown below.
+
+
+## Dead Code Elimination(DCE)
+
+We call `kill` every time a Node makes the 1-user-to-0-users transition during
+graph editing. This commonly happens when replacing via peeps and exiting
+scopes. This recursive `kill` amounts to Dead Code Elimination in many other
+compilers; here we call it in a very fine-grained way. Many Nodes will be
+created by the parser, only to be killed before the very next lexeme is parsed.
+
+For more information please read the [appendix section](appendix/dce.md#appendix) on dead code elimination.
+
+The suggestively called `deadCodeElim` function is a thin wrapper over `kill`
+used by `peepholeOpt` to avoid prematurely killing a Node which only briefly
+makes the 1->0 users transition.
+
+```java
+// m is the new Node, self is the old.
+// Return 'm', which may have zero uses but is alive nonetheless.
+// If self has zero uses (and is not 'm'), {@link #kill} self.
+private Node deadCodeElim(Node m) {
+ // If self is going dead and not being returned here (Nodes returned
+ // from peephole commonly have no uses (yet)), then kill self.
+ if( m != this && isUnused() ) {
+ // Killing self - and since self recursively kills self's inputs we
+ // might end up killing 'm', which we are returning as a live Node.
+ // So we add a bogus extra null output edge to stop kill().
+ m.addUse(null); // Add bogus null use to keep m alive
+ kill(); // Kill self because replacing with 'm'
+ m.delUse(null); // Remove bogus null.
+ }
+ return m;
+}
+```
+
+Note the temporary add of a bogus user to the Node `m`. The reason this is
+done is that we know `m` is the new replacement and is alive, but since it is
+not yet hooked into the graph, it has no users yet. By adding a bogus user we
+prevent it being mistaken for dead and being killed.
+
+[^1]: Click, C. (1995).
+ Combining Analyses, Combining Optimizations, 131.
diff --git a/docs/chapter04/lattice.gv b/docs/chapter04/lattice.gv
new file mode 100644
index 00000000..1f286530
--- /dev/null
+++ b/docs/chapter04/lattice.gv
@@ -0,0 +1,63 @@
+digraph Lattice {
+ // Define nodes
+ splines=false;
+ node [shape=circle, style=filled, fillcolor=lightblue];
+ nodesep=0.6;
+
+ TOP [label="⊤"];
+ BOT [label="⊥"];
+
+ CTRL [label="Ctrl"];
+
+ INT_TOP [label="IntTop"];
+ INT_BOT [label="IntBot"];
+
+ INT_MIN [label="-n"];
+ INT_MINDOTS [label="..." shape=none style=none];
+ INT_MINUS [label="-1"];
+ INT_ZERO [label="0"];
+ INT_PLUS [label="1"];
+ INT_MAXDOTS [label="..." shape=none style=none];
+ INT_MAX [label="+n"];
+
+ TUPLE [label="TUPLE"];
+
+ // Define edges
+ edge [arrowhead=none];
+
+ TOP -> INT_TOP;
+ INT_TOP -> INT_MIN;
+ INT_TOP -> INT_MINDOTS;
+ INT_TOP -> INT_MINUS;
+ INT_TOP -> INT_ZERO;
+ INT_TOP -> INT_PLUS;
+ INT_TOP -> INT_MAXDOTS;
+ INT_TOP -> INT_MAX;
+ INT_MIN -> INT_BOT;
+ INT_MINDOTS -> INT_BOT;
+ INT_MINUS -> INT_BOT;
+ INT_ZERO -> INT_BOT;
+ INT_PLUS -> INT_BOT;
+ INT_MAXDOTS -> INT_BOT;
+ INT_MAX -> INT_BOT;
+ INT_BOT -> BOT;
+
+ INT_MIN -> INT_MINDOTS -> INT_MINUS -> INT_ZERO -> INT_PLUS -> INT_MAXDOTS -> INT_MAX [style=invis];
+
+ TOP -> TUPLE;
+ TUPLE -> BOT;
+
+ TOP -> CTRL;
+ CTRL -> BOT;
+
+
+ // Additional customization
+ {rank=same; TOP}
+ {rank=same; INT_TOP}
+ {rank=same; CTRL; INT_MIN; INT_MINDOTS;
+ INT_MINUS; INT_ZERO;
+ INT_PLUS; INT_MAXDOTS;
+ INT_MAX; TUPLE}
+ {rank=same; INT_BOT}
+ {rank=same; BOT;}
+}
diff --git a/docs/chapter04/lattice.svg b/docs/chapter04/lattice.svg
new file mode 100644
index 00000000..0d403c20
--- /dev/null
+++ b/docs/chapter04/lattice.svg
@@ -0,0 +1,195 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<!-- Generated by graphviz version 2.43.0 (0)
+ -->
+<!-- Title: Lattice Pages: 1 -->
+<svg width="802pt" height="478pt"
+ viewBox="0.00 0.00 802.14 478.27" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 474.27)">
+<title>Lattice</title>
+<polygon fill="white" stroke="transparent" points="-4,4 -4,-474.27 798.14,-474.27 798.14,4 -4,4"/>
+<!-- TOP -->
+<g id="node1" class="node">
+<title>TOP</title>
+<ellipse fill="lightblue" stroke="black" cx="377.6" cy="-450.77" rx="19.5" ry="19.5"/>
+<text text-anchor="middle" x="377.6" y="-447.07" font-family="Times,serif" font-size="14.00">⊤</text>
+</g>
+<!-- CTRL -->
+<g id="node3" class="node">
+<title>CTRL</title>
+<ellipse fill="lightblue" stroke="black" cx="28.6" cy="-235.14" rx="28.7" ry="28.7"/>
+<text text-anchor="middle" x="28.6" y="-231.44" font-family="Times,serif" font-size="14.00">Ctrl</text>
+</g>
+<!-- TOP&#45;&gt;CTRL -->
+<g id="edge25" class="edge">
+<title>TOP&#45;&gt;CTRL</title>
+<path fill="none" stroke="black" d="M360.76,-440.37C304.12,-405.37 120.24,-291.76 53.28,-250.38"/>
+</g>
+<!-- INT_TOP -->
+<g id="node4" class="node">
+<title>INT_TOP</title>
+<ellipse fill="lightblue" stroke="black" cx="377.6" cy="-354.98" rx="40.09" ry="40.09"/>
+<text text-anchor="middle" x="377.6" y="-351.28" font-family="Times,serif" font-size="14.00">IntTop</text>
+</g>
+<!-- TOP&#45;&gt;INT_TOP -->
+<g id="edge1" class="edge">
+<title>TOP&#45;&gt;INT_TOP</title>
+<path fill="none" stroke="black" d="M377.6,-431.24C377.6,-420.99 377.6,-407.84 377.6,-395.42"/>
+</g>
+<!-- TUPLE -->
+<g id="node13" class="node">
+<title>TUPLE</title>
+<ellipse fill="lightblue" stroke="black" cx="750.6" cy="-235.14" rx="43.59" ry="43.59"/>
+<text text-anchor="middle" x="750.6" y="-231.44" font-family="Times,serif" font-size="14.00">TUPLE</text>
+</g>
+<!-- TOP&#45;&gt;TUPLE -->
+<g id="edge23" class="edge">
+<title>TOP&#45;&gt;TUPLE</title>
+<path fill="none" stroke="black" d="M394.59,-440.95C451.03,-408.32 633.13,-303.05 712.75,-257.02"/>
+</g>
+<!-- BOT -->
+<g id="node2" class="node">
+<title>BOT</title>
+<ellipse fill="lightblue" stroke="black" cx="377.6" cy="-19.5" rx="19.5" ry="19.5"/>
+<text text-anchor="middle" x="377.6" y="-15.8" font-family="Times,serif" font-size="14.00">⊥</text>
+</g>
+<!-- CTRL&#45;&gt;BOT -->
+<g id="edge26" class="edge">
+<title>CTRL&#45;&gt;BOT</title>
+<path fill="none" stroke="black" d="M53.14,-219.97C120.01,-178.65 304.22,-64.84 360.83,-29.86"/>
+</g>
+<!-- INT_MIN -->
+<g id="node6" class="node">
+<title>INT_MIN</title>
+<ellipse fill="lightblue" stroke="black" cx="119.6" cy="-235.14" rx="19.5" ry="19.5"/>
+<text text-anchor="middle" x="119.6" y="-231.44" font-family="Times,serif" font-size="14.00">&#45;n</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_MIN -->
+<g id="edge2" class="edge">
+<title>INT_TOP&#45;&gt;INT_MIN</title>
+<path fill="none" stroke="black" d="M341.18,-337.34C284.92,-311.65 179.02,-263.28 137.21,-244.18"/>
+</g>
+<!-- INT_MINDOTS -->
+<g id="node7" class="node">
+<title>INT_MINDOTS</title>
+<text text-anchor="middle" x="208.6" y="-231.44" font-family="Times,serif" font-size="14.00">...</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_MINDOTS -->
+<g id="edge3" class="edge">
+<title>INT_TOP&#45;&gt;INT_MINDOTS</title>
+<path fill="none" stroke="black" d="M345.01,-331.26C312.3,-308.45 262.65,-273.83 233.14,-253.25"/>
+</g>
+<!-- INT_MINUS -->
+<g id="node8" class="node">
+<title>INT_MINUS</title>
+<ellipse fill="lightblue" stroke="black" cx="297.6" cy="-235.14" rx="19.5" ry="19.5"/>
+<text text-anchor="middle" x="297.6" y="-231.44" font-family="Times,serif" font-size="14.00">&#45;1</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_MINUS -->
+<g id="edge4" class="edge">
+<title>INT_TOP&#45;&gt;INT_MINUS</title>
+<path fill="none" stroke="black" d="M355.31,-321.15C339.96,-298.54 320.25,-269.51 308.29,-251.89"/>
+</g>
+<!-- INT_ZERO -->
+<g id="node9" class="node">
+<title>INT_ZERO</title>
+<ellipse fill="lightblue" stroke="black" cx="377.6" cy="-235.14" rx="18" ry="18"/>
+<text text-anchor="middle" x="377.6" y="-231.44" font-family="Times,serif" font-size="14.00">0</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_ZERO -->
+<g id="edge5" class="edge">
+<title>INT_TOP&#45;&gt;INT_ZERO</title>
+<path fill="none" stroke="black" d="M377.6,-314.41C377.6,-293.68 377.6,-269.36 377.6,-253.39"/>
+</g>
+<!-- INT_PLUS -->
+<g id="node10" class="node">
+<title>INT_PLUS</title>
+<ellipse fill="lightblue" stroke="black" cx="456.6" cy="-235.14" rx="18" ry="18"/>
+<text text-anchor="middle" x="456.6" y="-231.44" font-family="Times,serif" font-size="14.00">1</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_PLUS -->
+<g id="edge6" class="edge">
+<title>INT_TOP&#45;&gt;INT_PLUS</title>
+<path fill="none" stroke="black" d="M399.6,-321.15C415.13,-298 435.17,-268.1 446.88,-250.63"/>
+</g>
+<!-- INT_MAXDOTS -->
+<g id="node11" class="node">
+<title>INT_MAXDOTS</title>
+<text text-anchor="middle" x="544.6" y="-231.44" font-family="Times,serif" font-size="14.00">...</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_MAXDOTS -->
+<g id="edge7" class="edge">
+<title>INT_TOP&#45;&gt;INT_MAXDOTS</title>
+<path fill="none" stroke="black" d="M410.19,-330.98C442.56,-308.14 491.43,-273.65 520.47,-253.16"/>
+</g>
+<!-- INT_MAX -->
+<g id="node12" class="node">
+<title>INT_MAX</title>
+<ellipse fill="lightblue" stroke="black" cx="639.6" cy="-235.14" rx="24.9" ry="24.9"/>
+<text text-anchor="middle" x="639.6" y="-231.44" font-family="Times,serif" font-size="14.00">+n</text>
+</g>
+<!-- INT_TOP&#45;&gt;INT_MAX -->
+<g id="edge8" class="edge">
+<title>INT_TOP&#45;&gt;INT_MAX</title>
+<path fill="none" stroke="black" d="M414.03,-337.59C469.15,-312.8 572.09,-266.5 617.32,-246.16"/>
+</g>
+<!-- INT_BOT -->
+<g id="node5" class="node">
+<title>INT_BOT</title>
+<ellipse fill="lightblue" stroke="black" cx="377.6" cy="-115.29" rx="40.09" ry="40.09"/>
+<text text-anchor="middle" x="377.6" y="-111.59" font-family="Times,serif" font-size="14.00">IntBot</text>
+</g>
+<!-- INT_BOT&#45;&gt;BOT -->
+<g id="edge16" class="edge">
+<title>INT_BOT&#45;&gt;BOT</title>
+<path fill="none" stroke="black" d="M377.6,-74.79C377.6,-62.37 377.6,-49.25 377.6,-39.01"/>
+</g>
+<!-- INT_MIN&#45;&gt;INT_BOT -->
+<g id="edge9" class="edge">
+<title>INT_MIN&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M137.33,-226.04C179.23,-206.9 285.02,-158.58 341.21,-132.91"/>
+</g>
+<!-- INT_MIN&#45;&gt;INT_MINDOTS -->
+<!-- INT_MINDOTS&#45;&gt;INT_BOT -->
+<g id="edge10" class="edge">
+<title>INT_MINDOTS&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M233.17,-217C262.65,-196.45 312.17,-161.91 344.87,-139.11"/>
+</g>
+<!-- INT_MINDOTS&#45;&gt;INT_MINUS -->
+<!-- INT_MINUS&#45;&gt;INT_BOT -->
+<g id="edge11" class="edge">
+<title>INT_MINUS&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M308.39,-218.24C320.33,-200.65 339.91,-171.81 355.2,-149.29"/>
+</g>
+<!-- INT_MINUS&#45;&gt;INT_ZERO -->
+<!-- INT_ZERO&#45;&gt;INT_BOT -->
+<g id="edge12" class="edge">
+<title>INT_ZERO&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M377.6,-217C377.6,-201.04 377.6,-176.66 377.6,-155.88"/>
+</g>
+<!-- INT_ZERO&#45;&gt;INT_PLUS -->
+<!-- INT_PLUS&#45;&gt;INT_BOT -->
+<g id="edge13" class="edge">
+<title>INT_PLUS&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M446.91,-219.69C435.21,-202.23 415.16,-172.33 399.63,-149.16"/>
+</g>
+<!-- INT_PLUS&#45;&gt;INT_MAXDOTS -->
+<!-- INT_MAXDOTS&#45;&gt;INT_BOT -->
+<g id="edge14" class="edge">
+<title>INT_MAXDOTS&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M520.31,-217C491.28,-196.51 442.55,-162.13 410.24,-139.33"/>
+</g>
+<!-- INT_MAXDOTS&#45;&gt;INT_MAX -->
+<!-- INT_MAX&#45;&gt;INT_BOT -->
+<g id="edge15" class="edge">
+<title>INT_MAX&#45;&gt;INT_BOT</title>
+<path fill="none" stroke="black" d="M617.26,-224.09C572.09,-203.77 469.52,-157.64 414.35,-132.82"/>
+</g>
+<!-- TUPLE&#45;&gt;BOT -->
+<g id="edge24" class="edge">
+<title>TUPLE&#45;&gt;BOT</title>
+<path fill="none" stroke="black" d="M712.78,-213.27C633.14,-167.23 450.85,-61.85 394.51,-29.27"/>
+</g>
+</g>
+</svg>
diff --git a/docs/chapter04/projnode.png b/docs/chapter04/projnode.png
new file mode 100644
index 00000000..bf7493f2
--- /dev/null
+++ b/docs/chapter04/projnode.png
Binary files differ
diff --git a/src/main/java/com/seaofnodes/simple/GraphVisualizer.java b/src/main/java/com/seaofnodes/simple/GraphVisualizer.java
index 9dfac52d..62b434f3 100644
--- a/src/main/java/com/seaofnodes/simple/GraphVisualizer.java
+++ b/src/main/java/com/seaofnodes/simple/GraphVisualizer.java
@@ -17,7 +17,7 @@ public class GraphVisualizer {
// nodes in the graph.
Collection<Node> all = findAll(parser);
StringBuilder sb = new StringBuilder();
- sb.append("digraph chapter03 {\n");
+ sb.append("digraph chapter04 {\n");
sb.append("/*\n");
sb.append(parser.src());
sb.append("\n*/\n");
@@ -57,15 +57,45 @@ public class GraphVisualizer {
// Just the Nodes first, in a cluster no edges
sb.append("\tsubgraph cluster_Nodes {\n"); // Magic "cluster_" in the subgraph name
for( Node n : all ) {
- if( n instanceof ScopeNode )
- continue; // Do not emit, rolled into Scope cluster already
+ if( n instanceof ProjNode || n instanceof ScopeNode )
+ continue; // Do not emit, rolled into MultiNode or Scope cluster already
sb.append("\t\t").append(n.uniqueName()).append(" [ ");
String lab = n.glabel();
- // control nodes have box shape
- // other nodes are ellipses, i.e. default shape
- if( n.isCFG() )
- sb.append("shape=box style=filled fillcolor=yellow ");
- sb.append("label=\"").append(lab).append("\" ");
+ if( n instanceof MultiNode ) {
+ // Make a box with the MultiNode on top, and all the projections on the bottom
+ sb.append("shape=plaintext label=<\n");
+ sb.append("\t\t\t<TABLE BORDER=\"0\" CELLBORDER=\"1\" CELLSPACING=\"0\" CELLPADDING=\"4\">\n");
+ sb.append("\t\t\t<TR><TD BGCOLOR=\"yellow\">").append(lab).append("</TD></TR>\n");
+ sb.append("\t\t\t<TR>");
+ boolean doProjTable = false;
+ for( Node use : n._outputs ) {
+ if( use instanceof ProjNode proj ) {
+ if (!doProjTable) {
+ doProjTable = true;
+ sb.append("<TD>").append("\n");
+ sb.append("\t\t\t\t<TABLE BORDER=\"0\" CELLBORDER=\"1\" CELLSPACING=\"0\">").append("\n");
+ sb.append("\t\t\t\t<TR>");
+ }
+ sb.append("<TD PORT=\"p").append(proj._idx).append("\"");
+ if( proj.isCFG() ) sb.append(" BGCOLOR=\"yellow\"");
+ sb.append(">").append(proj.glabel()).append("</TD>");
+ }
+ }
+ if (doProjTable) {
+ sb.append("</TR>").append("\n");
+ sb.append("\t\t\t\t</TABLE>").append("\n");
+ sb.append("\t\t\t</TD>");
+ }
+ sb.append("</TR>\n");
+ sb.append("\t\t\t</TABLE>>\n\t\t");
+
+ } else {
+ // control nodes have box shape
+ // other nodes are ellipses, i.e. default shape
+ if( n.isCFG() )
+ sb.append("shape=box style=filled fillcolor=yellow ");
+ sb.append("label=\"").append(lab).append("\" ");
+ }
sb.append("];\n");
}
sb.append("\t}\n"); // End Node cluster
@@ -101,22 +131,24 @@ public class GraphVisualizer {
// All them edge labels
sb.append("\tedge [ fontname=Helvetica, fontsize=8 ];\n");
for( Node n : all ) {
- // In this chapter we do display the Constant->Start edge;
+ // Do not display the Constant->Start edge;
+ // ProjNodes handled by Multi;
// ScopeNodes are done separately
- if( n instanceof ScopeNode )
+ if( n instanceof ConstantNode || n instanceof ProjNode || n instanceof ScopeNode )
continue;
int i=0;
for( Node def : n._inputs ) {
if( def != null ) {
// Most edges land here use->def
sb.append('\t').append(n.uniqueName()).append(" -> ");
- sb.append(def.uniqueName());
+ if( def instanceof ProjNode proj ) {
+ String mname = proj.ctrl().uniqueName();
+ sb.append(mname).append(":p").append(proj._idx);
+ } else sb.append(def.uniqueName());
// Number edges, so we can see how they track
sb.append("[taillabel=").append(i);
- if( n instanceof ConstantNode && def instanceof StartNode )
- sb.append(" style=dotted");
// control edges are colored red
- else if( def.isCFG() )
+ if( def.isCFG() )
sb.append(" color=red");
sb.append("];\n");
}
@@ -138,7 +170,10 @@ public class GraphVisualizer {
.append(scopeName).append(":")
.append('"').append(makePortName(scopeName, name)).append('"') // wrap port name with quotes because $ctrl is not valid unquoted
.append(" -> ");
- sb.append(def.uniqueName());
+ if( def instanceof ProjNode proj ) {
+ String mname = proj.ctrl().uniqueName();
+ sb.append(mname).append(":p").append(proj._idx);
+ } else sb.append(def.uniqueName());
sb.append(";\n");
}
level++;
diff --git a/src/main/java/com/seaofnodes/simple/Parser.java b/src/main/java/com/seaofnodes/simple/Parser.java
index fa1a852c..ff2c0504 100644
--- a/src/main/java/com/seaofnodes/simple/Parser.java
+++ b/src/main/java/com/seaofnodes/simple/Parser.java
@@ -14,6 +14,7 @@ import java.util.*;
*/
public class Parser {
+
/**
* A Global Static, unique to each compilation. This is a public, so we
* can make constants everywhere without having to thread the StartNode
@@ -27,7 +28,7 @@ public class Parser {
private final Lexer _lexer;
/**
- * Stack of lexical scopes, each scope is a symbol table that binds
+ * A ScopeNode contains a stack of lexical scopes, each scope is a symbol table that binds
* variable names to Nodes. The top of this stack represents current scope.
*/
public ScopeNode _scope;
@@ -41,18 +42,38 @@ public class Parser {
}};
- public Parser(String source) {
- _lexer = new Lexer(source);
+ public Parser(String source, TypeInteger arg) {
Node.reset();
+ _lexer = new Lexer(source);
_scope = new ScopeNode();
- START = new StartNode();
+ START = new StartNode(new Type[]{ Type.CONTROL, arg });
+ START.peephole();
+ }
+
+ public Parser(String source) {
+ this(source, TypeInteger.BOT);
}
+ @Override
+ public String toString() { return _lexer.toString(); }
+
String src() { return new String( _lexer._input ); }
+ // Debugging utility to find a Node by index
+ public static Node find(int nid) { return START.find(nid); }
+
+ private Node ctrl() { return _scope.ctrl(); }
+
+ private Node ctrl(Node n) { return _scope.ctrl(n); }
+
public ReturnNode parse() { return parse(false); }
public ReturnNode parse(boolean show) {
+ // Enter a new scope for the initial control and arguments
+ _scope.push();
+ _scope.define(ScopeNode.CTRL, new ProjNode(START, 0, ScopeNode.CTRL).peephole());
+ _scope.define(ScopeNode.ARG0, new ProjNode(START, 1, ScopeNode.ARG0).peephole());
var ret = (ReturnNode) parseBlock();
+ _scope.pop();
if (!_lexer.isEOF()) throw error("Syntax error, unexpected " + _lexer.getAnyNextToken());
if( show ) showGraph();
return ret;
@@ -99,6 +120,7 @@ public class Parser {
/**
* Parses a return statement; "return" already parsed.
+ * The $ctrl edge is killed.
*
* <pre>
* 'return' expr ;
@@ -107,7 +129,9 @@ public class Parser {
*/
private Node parseReturn() {
var expr = require(parseExpression(), ";");
- return new ReturnNode(START, expr).peephole();
+ Node ret = new ReturnNode(ctrl(), expr).peephole();
+ ctrl(null); // Kill control
+ return ret;
}
/**
@@ -158,11 +182,30 @@ public class Parser {
* Parse an expression of the form:
*
* <pre>
- * expr : additiveExpr
+ * expr : compareExpr
* </pre>
* @return an expression {@link Node}, never {@code null}
*/
- private Node parseExpression() { return parseAddition(); }
+ private Node parseExpression() { return parseComparison(); }
+
+ /**
+ * Parse an expression of the form:
+ *
+ * <pre>
+ * expr : additiveExpr op additiveExpr
+ * </pre>
+ * @return an comparator expression {@link Node}, never {@code null}
+ */
+ private Node parseComparison() {
+ var lhs = parseAddition();
+ if (match("==")) return new BoolNode.EQ(lhs, parseComparison()).peephole();
+ if (match("!=")) return new NotNode(new BoolNode.EQ(lhs, parseComparison()).peephole()).peephole();
+ if (match("<=")) return new BoolNode.LE(lhs, parseComparison()).peephole();
+ if (match("<" )) return new BoolNode.LT(lhs, parseComparison()).peephole();
+ if (match(">=")) return new BoolNode.LE(parseComparison(), lhs).peephole();
+ if (match(">" )) return new BoolNode.LT(parseComparison(), lhs).peephole();
+ return lhs;
+ }
/**
* Parse an additive expression
diff --git a/src/main/java/com/seaofnodes/simple/node/AddNode.java b/src/main/java/com/seaofnodes/simple/node/AddNode.java
index 7c1968c5..5720aca4 100644
--- a/src/main/java/com/seaofnodes/simple/node/AddNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/AddNode.java
@@ -23,14 +23,76 @@ public class AddNode extends Node {
in(2)._type instanceof TypeInteger i1 ) {
if (i0.isConstant() && i1.isConstant())
return TypeInteger.constant(i0.value()+i1.value());
+ return i0.meet(i1);
}
return Type.BOTTOM;
}
@Override
public Node idealize () {
- // TODO: add of 0, and many other peepholes added in Chaper04
+ Node lhs = in(1);
+ Node rhs = in(2);
+ Type t1 = lhs._type;
+ Type t2 = rhs._type;
+
+ // Already handled by peephole constant folding
+ assert !(t1.isConstant() && t2.isConstant());
+
+ // Add of 0. We do not check for (0+x) because this will already
+ // canonicalize to (x+0)
+ if( t2 instanceof TypeInteger i && i.value()==0 )
+ return lhs;
+
+ // Add of same to a multiply by 2
+ if( lhs==rhs )
+ return new MulNode(lhs,new ConstantNode(TypeInteger.constant(2)).peephole());
+
+ // Goal: a left-spine set of adds, with constants on the rhs (which then fold).
+
+ // Move non-adds to RHS
+ if( !(lhs instanceof AddNode) && rhs instanceof AddNode )
+ return swap12();
+
+ // Now we might see (add add non) or (add non non) or (add add add) but never (add non add)
+
+ // Do we have x + (y + z) ?
+ // Swap to (x + y) + z
+ // Rotate (add add add) to remove the add on RHS
+ if( rhs instanceof AddNode add )
+ return new AddNode(new AddNode(lhs,add.in(1)).peephole(), add.in(2));
+
+ // Now we might see (add add non) or (add non non) but never (add non add) nor (add add add)
+ if( !(lhs instanceof AddNode) )
+ return spline_cmp(lhs,rhs) ? swap12() : null;
+
+ // Now we only see (add add non)
+
+ // Do we have (x + con1) + con2?
+ // Replace with (x + (con1+con2) which then fold the constants
+ if( lhs.in(2)._type.isConstant() && t2.isConstant() )
+ return new AddNode(lhs.in(1),new AddNode(lhs.in(2),rhs).peephole());
+
+ // Now we sort along the spline via rotates, to gather similar things together.
+
+ // Do we rotate (x + y) + z
+ // into (x + z) + y ?
+ if( spline_cmp(lhs.in(2),rhs) )
+ return new AddNode(new AddNode(lhs.in(1),rhs).peephole(),lhs.in(2));
+
return null;
}
+ // Compare two off-spline nodes and decide what order they should be in.
+ // Do we rotate ((x + hi) + lo) into ((x + lo) + hi) ?
+ // Generally constants always go right, then others.
+ // Ties with in a category sort by node ID.
+ // TRUE if swapping hi and lo.
+ static boolean spline_cmp( Node hi, Node lo ) {
+ if( lo._type.isConstant() ) return false;
+ if( hi._type.isConstant() ) return true ;
+
+ // Same category of "others"
+ return lo._nid > hi._nid;
+ }
+
}
diff --git a/src/main/java/com/seaofnodes/simple/node/BoolNode.java b/src/main/java/com/seaofnodes/simple/node/BoolNode.java
new file mode 100644
index 00000000..05495790
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/BoolNode.java
@@ -0,0 +1,52 @@
+package com.seaofnodes.simple.node;
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeInteger;
+
+abstract public class BoolNode extends Node {
+
+ public BoolNode(Node lhs, Node rhs) {
+ super(null, lhs, rhs);
+ }
+
+ abstract String op(); // String opcode name
+
+ @Override
+ public String label() { return getClass().getSimpleName(); }
+
+ @Override
+ public String glabel() { return op(); }
+
+ @Override
+ StringBuilder _print1(StringBuilder sb) {
+ in(1)._print0(sb.append("("));
+ in(2)._print0(sb.append(op()));
+ return sb.append(")");
+ }
+
+ @Override
+ public Type compute() {
+ if( in(1)._type instanceof TypeInteger i0 &&
+ in(2)._type instanceof TypeInteger i1 ) {
+ if (i0.isConstant() && i1.isConstant())
+ return TypeInteger.constant(doOp(i0.value(), i1.value()) ? 1 : 0);
+ return i0.meet(i1);
+ }
+ return Type.BOTTOM;
+ }
+
+ abstract boolean doOp(long lhs, long rhs);
+
+ @Override
+ public Node idealize() {
+ // Compare of same
+ if( in(1)==in(2) )
+ return new ConstantNode(TypeInteger.constant(doOp(3,3)?1:0));
+
+ return null;
+ }
+
+ public static class EQ extends BoolNode { public EQ(Node lhs, Node rhs) { super(lhs,rhs); } String op() { return "=="; } boolean doOp(long lhs, long rhs) { return lhs == rhs; } }
+ public static class LT extends BoolNode { public LT(Node lhs, Node rhs) { super(lhs,rhs); } String op() { return "<" ; } boolean doOp(long lhs, long rhs) { return lhs < rhs; } }
+ public static class LE extends BoolNode { public LE(Node lhs, Node rhs) { super(lhs,rhs); } String op() { return "<="; } boolean doOp(long lhs, long rhs) { return lhs <= rhs; } }
+}
diff --git a/src/main/java/com/seaofnodes/simple/node/ConstantNode.java b/src/main/java/com/seaofnodes/simple/node/ConstantNode.java
index e4d7f412..1086037d 100644
--- a/src/main/java/com/seaofnodes/simple/node/ConstantNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/ConstantNode.java
@@ -23,7 +23,7 @@ public class ConstantNode extends Node {
}
@Override
- public String label() { return "#"+_con; }
+ public String label() { return ""+_con; }
@Override
public String uniqueName() { return "Con_" + _nid; }
@@ -38,5 +38,4 @@ public class ConstantNode extends Node {
@Override
public Node idealize() { return null; }
-
}
diff --git a/src/main/java/com/seaofnodes/simple/node/DivNode.java b/src/main/java/com/seaofnodes/simple/node/DivNode.java
index e3c3616a..3b3a4436 100644
--- a/src/main/java/com/seaofnodes/simple/node/DivNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/DivNode.java
@@ -25,10 +25,16 @@ public class DivNode extends Node {
return i1.value() == 0
? TypeInteger.ZERO
: TypeInteger.constant(i0.value()/i1.value());
+ return i0.meet(i1);
}
return Type.BOTTOM;
}
@Override
- public Node idealize() { return null; }
+ public Node idealize() {
+ // Div of 1.
+ if( in(2)._type.isConstant() && in(2)._type instanceof TypeInteger i && i.value()==1 )
+ return in(1);
+ return null;
+ }
}
diff --git a/src/main/java/com/seaofnodes/simple/node/MulNode.java b/src/main/java/com/seaofnodes/simple/node/MulNode.java
index 26c28281..36d5eb3e 100644
--- a/src/main/java/com/seaofnodes/simple/node/MulNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/MulNode.java
@@ -23,10 +23,27 @@ public class MulNode extends Node {
in(2)._type instanceof TypeInteger i1) {
if (i0.isConstant() && i1.isConstant())
return TypeInteger.constant(i0.value()*i1.value());
+ return i0.meet(i1);
}
return Type.BOTTOM;
}
@Override
- public Node idealize() { return null; }
+ public Node idealize() {
+ Node lhs = in(1);
+ Node rhs = in(2);
+ Type t1 = lhs._type;
+ Type t2 = rhs._type;
+
+ // Mul of 1. We do not check for (1*x) because this will already
+ // canonicalize to (x*1)
+ if ( t2.isConstant() && t2 instanceof TypeInteger i && i.value()==1 )
+ return lhs;
+
+ // Move constants to RHS: con*arg becomes arg*con
+ if ( t1.isConstant() && !t2.isConstant() )
+ return swap12();
+
+ return null;
+ }
}
diff --git a/src/main/java/com/seaofnodes/simple/node/MultiNode.java b/src/main/java/com/seaofnodes/simple/node/MultiNode.java
new file mode 100644
index 00000000..7ba1aa19
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/MultiNode.java
@@ -0,0 +1,7 @@
+package com.seaofnodes.simple.node;
+
+public abstract class MultiNode extends Node {
+
+ public MultiNode(Node... inputs) { super(inputs); }
+
+}
diff --git a/src/main/java/com/seaofnodes/simple/node/Node.java b/src/main/java/com/seaofnodes/simple/node/Node.java
index 82357f9b..9fa0a95a 100644
--- a/src/main/java/com/seaofnodes/simple/node/Node.java
+++ b/src/main/java/com/seaofnodes/simple/node/Node.java
@@ -81,14 +81,7 @@ public abstract class Node {
// line (because this is what a debugger typically displays by default) and
// has to be robust with broken graph/nodes.
@Override
- public final String toString() {
- // TODO: The print evolves in later chapters. For now, a simple
- // recursive print does well. Later with control flow and later still
- // with loops, we need some serious algorithm work to get a decent
- // print. So you should consider the "print" to always be a work-in-
- // progress as we march through the chapters.
- return print();
- }
+ public final String toString() { return print(); }
// This is a *deep* print. This version will fail on cycles, which we will
// correct later when we can parse programs with loops. We print with a
@@ -125,8 +118,6 @@ public abstract class Node {
public boolean isCFG() { return false; }
-
-
/**
* Change a <em>def</em> into a Node. Keeps the edges correct, by removing
* the corresponding <em>use->def</em> edge. This may make the original
@@ -184,11 +175,11 @@ public abstract class Node {
// Error is 'use' does not exist; ok for 'use' to be null.
protected boolean delUse( Node use ) {
Utils.del(_outputs, Utils.find(_outputs, use));
- return _outputs.size() == 0;
+ return _outputs.isEmpty();
}
// Shortcut for "popping" n nodes. A "pop" is basically a
- // set_def(last,null) followed by lowering the nIns() count.
+ // setDef(last,null) followed by lowering the nIns() count.
void popN(int n) {
for( int i=0; i<n; i++ ) {
Node old_def = _inputs.removeLast();
@@ -212,6 +203,15 @@ public abstract class Node {
// Mostly used for asserts and printing.
boolean isDead() { return isUnused() && nIns()==0 && _type==null; }
+
+ // Shortcuts to stop DCE mid-parse
+ // Add bogus null use to keep node alive
+ public <N extends Node> N keep() { return addUse(null); }
+ // Remove bogus null.
+ public <N extends Node> N unkeep() { delUse(null); return (N)this; }
+ // ------------------------------------------------------------------------
+ // Graph-based optimizations
+
/**
* We allow disabling peephole opt so that we can observe the
* full graph, vs the optimized graph.
@@ -226,7 +226,11 @@ public abstract class Node {
* <li>in a future chapter we will look for a
* <a href="https://en.wikipedia.org/wiki/Common_subexpression_elimination">Common Subexpression</a>
* to eliminate.</li>
- * <li>we ask the Node for a better replacement (again, none enabled in this chapter)</li>
+ * <li>we ask the Node for a better replacement. The "better replacement"
+ * is things like {@code (1+2)} becomes {@code 3} and {@code (1+(x+2))} becomes
+ * {@code (x+(1+2))}. By canonicalizing expressions we fold common addressing
+ * math constants, remove algebraic identities and generally simplify the
+ * code. </li>
* </ul>
*/
public final Node peephole( ) {
@@ -237,20 +241,37 @@ public abstract class Node {
return this; // Peephole optimizations turned off
// Replace constant computations from non-constants with a constant node
- if (!(this instanceof ConstantNode) && type.isConstant()) {
- kill(); // Kill `this` because replacing with a Constant
- return new ConstantNode(type).peephole();
- }
+ if (!(this instanceof ConstantNode) && type.isConstant())
+ return deadCodeElim(new ConstantNode(type).peephole());
// Future chapter: Global Value Numbering goes here
// Ask each node for a better replacement
Node n = idealize();
- if( n != null ) return n;
+ if( n != null ) // Something changed
+ // Recursively optimize
+ return deadCodeElim(n.peephole());
return this; // No progress
}
+ // m is the new Node, self is the old.
+ // Return 'm', which may have zero uses but is alive nonetheless.
+ // If self has zero uses (and is not 'm'), {@link #kill} self.
+ private Node deadCodeElim(Node m) {
+ // If self is going dead and not being returned here (Nodes returned
+ // from peephole commonly have no uses (yet)), then kill self.
+ if( m != this && isUnused() ) {
+ // Killing self - and since self recursively kills self's inputs we
+ // might end up killing 'm', which we are returning as a live Node.
+ // So we add a bogus extra null output edge to stop kill().
+ m.keep(); // Keep m alive
+ kill(); // Kill self because replacing with 'm'
+ m.unkeep(); // Okay to peephole m
+ }
+ return m;
+ }
+
/**
* This function needs to be
* <a href="https://en.wikipedia.org/wiki/Monotonic_function">Monotonic</a>
@@ -269,8 +290,65 @@ public abstract class Node {
*/
public abstract Type compute();
+ /**
+ * This function rewrites the current Node into a more "idealized" form.
+ * This is the bulk of our peephole rewrite rules, and we use this to
+ * e.g. turn arbitrary collections of adds and multiplies with mixed
+ * constants into a normal form that's easy for hardware to implement.
+ * Example: An array addressing expression:
+ * <pre> ary[idx+1]</pre>
+ * might turn into Sea-of-Nodes IR:
+ * <pre> (ary+12)+((idx+1) * 4)</pre>
+ * This expression can then be idealized into:
+ * <pre> ary + ((idx*4) + (12 + (1*4)))</pre>
+ * And more folding:
+ * <pre> ary + ((idx<<2) + 16)</pre>
+ * And during code-gen:
+ * <pre> MOV4 Rary,Ridx,16 // or some such hardware-specific notation </pre>
+ * <p>
+ * {@link #idealize} has a very specific calling convention:
+ * <ul>
+ * <li>If NO change is made, return {@code null}
+ * <li>If ANY change is made, return not-null; this can be {@code this}
+ * <li>The returned Node does NOT call {@link #peephole} on itself; the {@link #peephole} call will recursively peephole it.
+ * <li>Any NEW nodes that are not directly returned DO call {@link #peephole}.
+ * </ul>
+ * <p>
+ * Examples:
+ * <table border="3">
+ * <tr><th> before </th><th> after </th><th>return </th><th>comment </th></tr>
+ * <tr><td>{@code (x+5) }</td><td>{@code (x+5) }</td><td>{@code null }</td><td>No change</td></tr>
+ * <tr><td>{@code (5+x) }</td><td>{@code (x+5) }</td><td>{@code this }</td><td>Swapped arguments</td></tr>
+ * <tr><td>{@code ((x+1)+2)}</td><td>{@code (x+(1+2))}</td><td>{@code (x+_) }</td><td>Returns 2 new Nodes</td></tr>
+ * </table>
+ *
+ * The last entry deserves more discussion. The new Node {@code (1+2)}
+ * created in {@link #idealize} calls {@link #peephole} (which then folds
+ * into a constant). The other new Node {@code (x+3)} does not call
+ * peephole, because it is returned and peephole itself will recursively
+ * call peephole.
+ * <p>
+ * Since idealize calls peephole and peephole calls idealize, you must be
+ * careful that all idealizations are <em>monotonic</em>: all transforms remove
+ * some feature, so that the set of available transforms always shrinks.
+ * If you don't, you risk an infinite peephole loop!
+ *
+ * @return Either a new or changed node, or null for no changes.
+ */
public abstract Node idealize();
+
+ // ------------------------------------------------------------------------
+ // Peephole utilities
+
+ // Swap inputs without letting either input go dead during the swap.
+ Node swap12() {
+ Node tmp = in(1);
+ _inputs.set(1,in(2));
+ _inputs.set(2,tmp);
+ return this;
+ }
+
/**
* Used to allow repeating tests in the same JVM. This just resets the
* Node unique id generator, and is done as part of making a new Parser.
diff --git a/src/main/java/com/seaofnodes/simple/node/NotNode.java b/src/main/java/com/seaofnodes/simple/node/NotNode.java
new file mode 100644
index 00000000..e3683646
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/NotNode.java
@@ -0,0 +1,28 @@
+package com.seaofnodes.simple.node;
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeInteger;
+
+public class NotNode extends Node {
+ public NotNode(Node in) { super(null, in); }
+
+ @Override public String label() { return "Not"; }
+
+ @Override public String glabel() { return "!"; }
+
+ @Override
+ StringBuilder _print1(StringBuilder sb) {
+ in(1)._print0(sb.append("(!"));
+ return sb.append(")");
+ }
+
+ @Override
+ public Type compute() {
+ if( in(1)._type instanceof TypeInteger i0 )
+ return i0.isConstant() ? TypeInteger.constant(i0.value()==0 ? 1 : 0) : i0;
+ return Type.BOTTOM;
+ }
+
+ @Override
+ public Node idealize() { return null; }
+}
diff --git a/src/main/java/com/seaofnodes/simple/node/ProjNode.java b/src/main/java/com/seaofnodes/simple/node/ProjNode.java
new file mode 100644
index 00000000..2f49fe91
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/ProjNode.java
@@ -0,0 +1,40 @@
+package com.seaofnodes.simple.node;
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeTuple;
+
+public class ProjNode extends Node {
+
+ // Which slice of the incoming multi-part value
+ public final int _idx;
+
+ // Debugging label
+ public final String _label;
+
+ public ProjNode(MultiNode ctrl, int idx, String label) {
+ super(ctrl);
+ _idx = idx;
+ _label = label;
+ }
+
+ @Override
+ public String label() { return _label; }
+
+ @Override
+ StringBuilder _print1(StringBuilder sb) { return sb.append(_label); }
+
+ @Override public boolean isCFG() { return _idx==0; }
+
+ public MultiNode ctrl() { return (MultiNode)in(0); }
+
+ @Override
+ public Type compute() {
+ Type t = ctrl()._type;
+ return t instanceof TypeTuple tt ? tt._types[_idx] : Type.BOTTOM;
+ }
+
+ @Override
+ public Node idealize() {
+ return null;
+ }
+}
diff --git a/src/main/java/com/seaofnodes/simple/node/ReturnNode.java b/src/main/java/com/seaofnodes/simple/node/ReturnNode.java
index 7fa470f8..c9d6c9c8 100644
--- a/src/main/java/com/seaofnodes/simple/node/ReturnNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/ReturnNode.java
@@ -32,7 +32,7 @@ public class ReturnNode extends Node {
@Override
public Type compute() {
- return Type.BOTTOM;
+ return new TypeTuple(ctrl()._type,expr()._type);
}
@Override
diff --git a/src/main/java/com/seaofnodes/simple/node/ScopeNode.java b/src/main/java/com/seaofnodes/simple/node/ScopeNode.java
index 379ef033..8ffeac64 100644
--- a/src/main/java/com/seaofnodes/simple/node/ScopeNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/ScopeNode.java
@@ -7,12 +7,18 @@ import java.util.*;
/**
* The Scope node is purely a parser helper - it tracks names to nodes with a
* stack of scopes.
- * @see <a href="file:../../../../../../../../chapter03/README.md">chapter03/README.md</a>
*/
public class ScopeNode extends Node {
/**
- * A Stack of symbol tables; a symbol table is a map from names to node indices.
+ * The control is a name that binds to the currently active control
+ * node in the graph
+ */
+ public static final String CTRL = "$ctrl";
+ public static final String ARG0 = "arg";
+
+ /**
+ * Names for every input edge
*/
public final Stack<HashMap<String, Integer>> _scopes;
@@ -49,7 +55,7 @@ public class ScopeNode extends Node {
* Recover the names for all variable bindings.
* The result is an array of names that is aligned with the
* inputs to the Node.
- * <p>
+ *
* This is an expensive operation.
*/
public String[] reverseNames() {
@@ -78,21 +84,21 @@ public class ScopeNode extends Node {
}
/**
* Lookup a name in all scopes starting from most deeply nested.
- * <p>
+ *
* @param name Name to be looked up
* @see #update(String, Node, int)
*/
public Node lookup( String name ) { return update(name,null,_scopes.size()-1); }
/**
* If the name is present in any scope, then redefine else null
- * <p>
+ *
* @param name Name being redefined
* @param n The node to bind to the name
*/
public Node update( String name, Node n ) { return update(name,n,_scopes.size()-1); }
/**
* Both recursive lookup and update.
- * <p>
+ *
* A shared implementation allows us to create lazy phis both during
* lookups and updates; the lazy phi creation is part of chapter 8.
*
diff --git a/src/main/java/com/seaofnodes/simple/node/StartNode.java b/src/main/java/com/seaofnodes/simple/node/StartNode.java
index 99e240ad..022e276d 100644
--- a/src/main/java/com/seaofnodes/simple/node/StartNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/StartNode.java
@@ -1,6 +1,7 @@
package com.seaofnodes.simple.node;
import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeTuple;
/**
* The Start node represents the start of the function. For now, we do not
@@ -9,10 +10,14 @@ import com.seaofnodes.simple.type.Type;
* will require Projections to extract the values. We discuss this in detail
* in Chapter 9: Functions and Calls.
*/
-public class StartNode extends Node {
+public class StartNode extends MultiNode {
- public StartNode(/*arguments go here*/) {
+ final TypeTuple _args;
+
+ public StartNode(Type[] args) {
super();
+ _args = new TypeTuple(args);
+ _type = _args;
}
@Override
@@ -26,7 +31,7 @@ public class StartNode extends Node {
@Override public boolean isCFG() { return true; }
@Override
- public Type compute() { return Type.BOTTOM; }
+ public TypeTuple compute() { return _args; }
@Override
public Node idealize() { return null; }
diff --git a/src/main/java/com/seaofnodes/simple/node/SubNode.java b/src/main/java/com/seaofnodes/simple/node/SubNode.java
index d2e32c61..58d757ea 100644
--- a/src/main/java/com/seaofnodes/simple/node/SubNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/SubNode.java
@@ -19,15 +19,22 @@ public class SubNode extends Node {
@Override
public Type compute() {
+ // Sub of same is 0
+ if( in(1)==in(2) )
+ return TypeInteger.ZERO;
+
if (in(1)._type instanceof TypeInteger i0 &&
in(2)._type instanceof TypeInteger i1) {
if (i0.isConstant() && i1.isConstant())
return TypeInteger.constant(i0.value()-i1.value());
+ return i0.meet(i1);
}
return Type.BOTTOM;
}
@Override
- public Node idealize() { return null; }
+ public Node idealize() {
+ return null;
+ }
}
diff --git a/src/main/java/com/seaofnodes/simple/type/Type.java b/src/main/java/com/seaofnodes/simple/type/Type.java
index 89f6c715..1687f65a 100644
--- a/src/main/java/com/seaofnodes/simple/type/Type.java
+++ b/src/main/java/com/seaofnodes/simple/type/Type.java
@@ -24,17 +24,29 @@ public class Type {
// type hierarchy are simple, not that the Type is conceptually simple.
static final byte TBOT = 0; // Bottom (ALL)
static final byte TTOP = 1; // Top (ANY)
- static final byte TSIMPLE = 2; // End of the Simple Types
- static final byte TINT = 3; // All Integers; see TypeInteger
+ static final byte TCTRL = 2; // Ctrl flow bottom
+ static final byte TSIMPLE = 3; // End of the Simple Types
+ static final byte TINT = 4; // All Integers; see TypeInteger
+ static final byte TTUPLE = 5; // Tuples; finite collections of unrelated Types, kept in parallel
+
public final byte _type;
public boolean is_simple() { return _type < TSIMPLE; }
- private static final String[] STRS = new String[]{"Bot","Top"};
+ private static final String[] STRS = new String[]{"Bot","Top","Ctrl"};
protected Type(byte type) { _type = type; }
- public static final Type BOTTOM = new Type( TBOT ); // ALL
+ public static final Type BOTTOM = new Type( TBOT ); // ALL
+ public static final Type TOP = new Type( TTOP ); // ANY
+ public static final Type CONTROL = new Type( TCTRL ); // Ctrl
public boolean isConstant() { return _type == TTOP; }
public StringBuilder _print(StringBuilder sb) {return is_simple() ? sb.append(STRS[_type]) : sb;}
+
+ public Type meet(Type other) { return Type.BOTTOM; }
+
+ @Override
+ public final String toString() {
+ return _print(new StringBuilder()).toString();
+ }
}
diff --git a/src/main/java/com/seaofnodes/simple/type/TypeInteger.java b/src/main/java/com/seaofnodes/simple/type/TypeInteger.java
index 13f816bf..9fb4b853 100644
--- a/src/main/java/com/seaofnodes/simple/type/TypeInteger.java
+++ b/src/main/java/com/seaofnodes/simple/type/TypeInteger.java
@@ -5,37 +5,59 @@ package com.seaofnodes.simple.type;
*/
public class TypeInteger extends Type {
- public final static TypeInteger ZERO= new TypeInteger(0);
+ public final static TypeInteger TOP = new TypeInteger(false, 0);
+ public final static TypeInteger BOT = new TypeInteger(false, 1);
+ public final static TypeInteger ZERO= new TypeInteger(true, 0);
+
+ private final boolean _is_con;
/**
- * The constant value observed for this type
+ * The constant value or
+ * if not constant then 0=bottom, 1=top.
*/
private final long _con;
- public TypeInteger(long con) {
+ public TypeInteger(boolean is_con, long con) {
super(TINT);
+ _is_con = is_con;
_con = con;
}
- public static TypeInteger constant(long con) { return new TypeInteger(con); }
+ public static TypeInteger constant(long con) { return new TypeInteger(true, con); }
- @Override
- public String toString() {
- return _print(new StringBuilder()).toString();
- }
+ public boolean isTop() { return !_is_con && _con==0; }
+ public boolean isBot() { return !_is_con && _con==1; }
@Override
- public StringBuilder _print(StringBuilder sb) { return sb.append(_con); }
+ public StringBuilder _print(StringBuilder sb) {
+ if (isTop()) return sb.append("IntTop");
+ if (isBot()) return sb.append("IntBot");
+ return sb.append(_con);
+ }
@Override
- public boolean isConstant() { return true; }
+ public boolean isConstant() { return _is_con; }
public long value() { return _con; }
@Override
+ public Type meet(Type other) {
+ if( this==other ) return this;
+ if (!(other instanceof TypeInteger i)) return super.meet(other);
+ // BOT wins
+ if ( isBot() ) return this;
+ if ( i.isBot() ) return i ;
+ // TOP loses
+ if ( i.isTop() ) return this;
+ if ( isTop() ) return i ;
+ assert isConstant() && i.isConstant();
+ return _con==i._con ? this : TypeInteger.BOT;
+ }
+
+ @Override
public boolean equals( Object o ) {
if( o==this ) return true;
if( !(o instanceof TypeInteger i) ) return false;
- return _con==i._con;
+ return _con==i._con && _is_con==i._is_con;
}
}
diff --git a/src/main/java/com/seaofnodes/simple/type/TypeTuple.java b/src/main/java/com/seaofnodes/simple/type/TypeTuple.java
new file mode 100644
index 00000000..25663dda
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/type/TypeTuple.java
@@ -0,0 +1,26 @@
+package com.seaofnodes.simple.type;
+
+public class TypeTuple extends Type {
+
+ public final Type[] _types;
+
+ public TypeTuple(Type... _types) {
+ super(TTUPLE);
+ this._types = _types;
+ }
+
+ @Override
+ public Type meet(Type other) {
+ throw new UnsupportedOperationException("Meet on Tuple Type not yet implemented");
+ }
+
+ @Override
+ public StringBuilder _print(StringBuilder sb) {
+ sb.append("[ ");
+ for( Type t : _types )
+ t._print(sb).append(",");
+ sb.setLength(sb.length()-1);
+ sb.append("]");
+ return sb;
+ }
+}
diff --git a/src/test/java/com/seaofnodes/simple/Chapter01Test.java b/src/test/java/com/seaofnodes/simple/Chapter01Test.java
index 311ca23b..3d568337 100644
--- a/src/test/java/com/seaofnodes/simple/Chapter01Test.java
+++ b/src/test/java/com/seaofnodes/simple/Chapter01Test.java
@@ -14,7 +14,7 @@ public class Chapter01Test {
ReturnNode ret = parser.parse();
StartNode start = Parser.START;
- assertEquals(start, ret.ctrl());
+ assertTrue(ret.ctrl() instanceof ProjNode);
Node expr = ret.expr();
if( expr instanceof ConstantNode con ) {
assertEquals(start,con.in(0));
diff --git a/src/test/java/com/seaofnodes/simple/Chapter03Test.java b/src/test/java/com/seaofnodes/simple/Chapter03Test.java
index bdb1d9ea..950d87fe 100644
--- a/src/test/java/com/seaofnodes/simple/Chapter03Test.java
+++ b/src/test/java/com/seaofnodes/simple/Chapter03Test.java
@@ -1,6 +1,7 @@
package com.seaofnodes.simple;
import com.seaofnodes.simple.node.*;
+import com.seaofnodes.simple.type.TypeInteger;
import org.junit.Test;
import static org.junit.Assert.*;
diff --git a/src/test/java/com/seaofnodes/simple/Chapter04Test.java b/src/test/java/com/seaofnodes/simple/Chapter04Test.java
new file mode 100644
index 00000000..9f1535b3
--- /dev/null
+++ b/src/test/java/com/seaofnodes/simple/Chapter04Test.java
@@ -0,0 +1,127 @@
+package com.seaofnodes.simple;
+
+import com.seaofnodes.simple.node.*;
+import com.seaofnodes.simple.type.TypeInteger;
+import org.junit.Test;
+
+import static org.junit.Assert.*;
+
+public class Chapter04Test {
+
+ @Test
+ public void testPeephole() {
+ Parser parser = new Parser("return 1+arg+2; #showGraph;");
+ ReturnNode ret = parser.parse();
+ assertEquals("return (arg+3);", ret.print());
+ }
+
+ @Test
+ public void testPeephole2() {
+ Parser parser = new Parser("return (1+arg)+2;");
+ ReturnNode ret = parser.parse();
+ assertEquals("return (arg+3);", ret.print());
+ }
+
+ @Test
+ public void testAdd0() {
+ Parser parser = new Parser("return 0+arg;");
+ ReturnNode ret = parser.parse();
+ assertEquals("return arg;", ret.print());
+ }
+
+ @Test
+ public void testAddAddMul() {
+ Parser parser = new Parser("return arg+0+arg;");
+ ReturnNode ret = parser.parse();
+ assertEquals("return (arg*2);", ret.print());
+ }
+
+ @Test
+ public void testPeephole3() {
+ Parser parser = new Parser("return 1+arg+2+arg+3; #showGraph;");
+ ReturnNode ret = parser.parse();
+ assertEquals("return ((arg*2)+6);", ret.print());
+ }
+
+ @Test
+ public void testMul1() {
+ Parser parser = new Parser("return 1*arg;");
+ ReturnNode ret = parser.parse();
+ assertEquals("return arg;", ret.print());
+ }
+
+ @Test
+ public void testVarArg() {
+ Parser parser = new Parser("return arg; #showGraph;", TypeInteger.BOT);
+ ReturnNode ret = parser.parse();
+ assertTrue(ret.in(0) instanceof ProjNode);
+ assertTrue(ret.in(1) instanceof ProjNode);
+ }
+
+ @Test
+ public void testConstantArg() {
+ Parser parser = new Parser("return arg; #showGraph;", TypeInteger.constant(2));
+ ReturnNode ret = parser.parse();
+ assertEquals("return 2;", ret.print());
+ }
+
+ @Test
+ public void testCompEq() {
+ Parser parser = new Parser("return 3==3; #showGraph;");
+ ReturnNode ret = parser.parse();
+ assertEquals("return 1;", ret.print());
+ }
+
+ @Test
+ public void testCompEq2() {
+ Parser parser = new Parser("return 3==4; #showGraph;");
+ ReturnNode ret = parser.parse();
+ assertEquals("return 0;", ret.print());
+ }
+
+ @Test
+ public void testCompNEq() {
+ Parser parser = new Parser("return 3!=3; #showGraph;");
+ ReturnNode ret = parser.parse();
+ assertEquals("return 0;", ret.print());
+ }
+
+ @Test
+ public void testCompNEq2() {
+ Parser parser = new Parser("return 3!=4; #showGraph;");
+ ReturnNode ret = parser.parse();
+ assertEquals("return 1;", ret.print());
+ }
+
+ @Test
+ public void testBug1() {
+ Parser parser = new Parser("int a=arg+1; int b=a; b=1; return a+2; #showGraph;");
+ ReturnNode ret = parser.parse();
+ assertEquals("return (arg+3);", ret.print());
+ }
+
+ @Test
+ public void testBug2() {
+ Parser parser = new Parser("int a=arg+1; a=a; return a; #showGraph;");
+ ReturnNode ret = parser.parse();
+ assertEquals("return (arg+1);", ret.print());
+ }
+
+ @Test
+ public void testBug3() {
+ try {
+ new Parser("inta=1; return a;").parse();
+ fail();
+ } catch( RuntimeException e ) {
+ assertEquals("Undefined name 'inta'",e.getMessage());
+ }
+ }
+
+ @Test
+ public void testBug4() {
+ Parser parser = new Parser("return -arg;");
+ ReturnNode ret = parser.parse();
+ assertEquals("return (-arg);", ret.print());
+ }
+
+}