Chapter 12: Floats

Co-authored-by: Dibyendu Majumdar <mobile@majumdar.org.uk>
Co-authored-by: Thalia Archibald <thalia@archibald.dev>
Co-authored-by: tannal <tannal2409@gmail.com>
Co-authored-by: hadha <helsgithub15@gmail.com>
Co-authored-by: XmiliaH <45106915+XmiliaH@users.noreply.github.com>
Co-authored-by: Tamás Hadházy <85063808+Hels15@users.noreply.github.com>
Co-authored-by: RobertObkircher <robert.obkircher@gmail.com>
Co-authored-by: Robert Obkircher <robert.obkircher@gmail.com>

36 files changed, 693 insertions, 187 deletions

diff --git a/src/main/java/com/seaofnodes/simple/GlobalCodeMotion.java b/src/main/java/com/seaofnodes/simple/GlobalCodeMotion.java
index 14540d46..4e0a31d5 100644
--- a/src/main/java/com/seaofnodes/simple/GlobalCodeMotion.java
+++ b/src/main/java/com/seaofnodes/simple/GlobalCodeMotion.java
@@ -10,7 +10,6 @@ public abstract class GlobalCodeMotion {
     // Node.use(0) is always a block tail (either IfNode or head of the
     // following block).  There are no unreachable infinite loops.
     public static void buildCFG( StopNode stop ) {
-        fixLoops(stop);
         schedEarly();
         Parser.SCHEDULED = true;
         schedLate(Parser.START);
@@ -20,7 +19,7 @@ public abstract class GlobalCodeMotion {
     // Backwards walk on the CFG only, looking for unreachable code - which has
     // to be an infinite loop.  Insert a bogus never-taken exit to Stop, so the
     // loop becomes reachable.  Also, set loop nesting depth
-    private static void fixLoops(StopNode stop) {
+    static void fixLoops(StopNode stop) {
         // Backwards walk from Stop, looking for unreachable code
         BitSet visit = new BitSet();
         HashSet<CFGNode> unreach = new HashSet<>();
@@ -120,7 +119,7 @@ public abstract class GlobalCodeMotion {
                 ns[i].setDef(0,late[i]);
     }
 
-    // Forwards post-order pass.  Schedule all outputs first, then draw an
+    // Forwards post-order pass.  Schedule all outputs first, then draw a
     // idom-tree line from the LCA of uses to the early schedule.  Schedule is
     // legal anywhere on this line; pick the most control-dependent (largest
     // idepth) in the shallowest loop nest.
@@ -148,13 +147,13 @@ public abstract class GlobalCodeMotion {
         assert early != null;
         CFGNode lca = null;
         for( Node use : n._outputs )
-            lca = use_block(n,use, late).idom(lca);
+            lca = use_block(n,use, late)._idom(lca,null);
 
         // Loads may need anti-dependencies, raising their LCA
         if( n instanceof LoadNode load )
             lca = find_anti_dep(lca,load,early,late);
 
-        // Walk up from the LCA to the early, looking for best place.  This is the
+        // Walk up from the LCA to the early, looking for best place.  This is
         // lowest execution frequency, approximated by least loop depth and
         // deepest control flow.
         CFGNode best = lca;
@@ -214,6 +213,7 @@ public abstract class GlobalCodeMotion {
                 break;
             case LoadNode ld: break; // Loads do not cause anti-deps on other loads
             case ReturnNode ret: break; // Load must already be ahead of Return
+            case NeverNode never: break;
             default: throw Utils.TODO();
             }
         }
@@ -226,7 +226,7 @@ public abstract class GlobalCodeMotion {
         for( ; stblk != defblk.idom(); stblk = stblk.idom() ) {
             // Store and Load overlap, need anti-dependence
             if( stblk._anti==load._nid ) {
-                lca = stblk.idom(lca); // Raise Loads LCA
+                lca = stblk._idom(lca,null); // Raise Loads LCA
                 if( lca == stblk && st != null && Utils.find(st._inputs,load) == -1 ) // And if something moved,
                     st.addDef(load);   // Add anti-dep as well
                 return lca;            // Cap this stores' anti-dep to here
diff --git a/src/main/java/com/seaofnodes/simple/IterPeeps.java b/src/main/java/com/seaofnodes/simple/IterPeeps.java
index b2b76777..121d0233 100644
--- a/src/main/java/com/seaofnodes/simple/IterPeeps.java
+++ b/src/main/java/com/seaofnodes/simple/IterPeeps.java
@@ -92,6 +92,8 @@ public abstract class IterPeeps {
                 n.kill();       // Just plain dead
         }
 
+        // Break infinite loops, forcing a Never-branch to exit
+        GlobalCodeMotion.fixLoops(stop);
         if( show )
             System.out.println(new GraphVisualizer().generateDotOutput(stop,null,null));
         GlobalCodeMotion.buildCFG(stop);
diff --git a/src/main/java/com/seaofnodes/simple/Parser.java b/src/main/java/com/seaofnodes/simple/Parser.java
index e367f499..1a223726 100644
--- a/src/main/java/com/seaofnodes/simple/Parser.java
+++ b/src/main/java/com/seaofnodes/simple/Parser.java
@@ -56,6 +56,7 @@ public class Parser {
             add("continue");
             add("else");
             add("false");
+            add("flt");
             add("if");
             add("int");
             add("new");
@@ -76,13 +77,15 @@ public class Parser {
     ScopeNode _continueScope;
     ScopeNode _breakScope;
 
-    // Mapping from a Struct name to a Struct.
-    public static Map<String, TypeStruct> OBJS = new HashMap<>();
+    // Mapping from a type name to a Type.
+    public static HashMap<String, Type> TYPES = new HashMap<>();
 
     public Parser(String source, TypeInteger arg) {
         Node.reset();
         IterPeeps.reset();
-        OBJS.clear();
+        TYPES.clear();
+        TYPES.put("int",TypeInteger.BOT);
+        TYPES.put("flt",TypeFloat  .BOT);
         SCHEDULED = false;
         _lexer = new Lexer(source);
         _scope = new ScopeNode();
@@ -157,7 +160,6 @@ public class Parser {
     private Node parseStatement() {
         if( false ) return null;
         else if (matchx("return")  ) return parseReturn();
-        else if (matchx("int")     ) return parseDecl(TypeInteger.BOT);
         else if (match ("{")       ) return require(parseBlock(),"}");
         else if (matchx("if")      ) return parseIf();
         else if (matchx("while")   ) return parseWhile();
@@ -174,13 +176,14 @@ public class Parser {
     /**
      * Parse a struct field.
      * <pre>
-     *     int IDENTIFIER ;
+     *     type IDENTIFIER ;
      * </pre>
      */
     private Field parseField(String sname) {
-        if( matchx("int") )     // Currently only parsing "int" type fields
-            return require(Field.make(requireId().intern(),TypeInteger.BOT),";");
-        throw errorSyntax("A field type is expected, only type 'int' is supported at present");
+        Type t = type();
+        if( t==null )
+            throw errorSyntax("Requires a field type, found '"+_lexer.getAnyNextToken()+"'");
+        return require(Field.make(requireId().intern(),t),";");
     }
 
     /**
@@ -193,7 +196,7 @@ public class Parser {
     private Node parseStruct() {
         if (_xScopes.size() > 1) throw errorSyntax("struct declarations can only appear in top level scope");
         String typeName = requireId();
-        if ( OBJS.containsKey(typeName)) throw errorSyntax("struct '" + typeName + "' cannot be redefined");
+        if ( TYPES.containsKey(typeName)) throw errorSyntax("struct '" + typeName + "' cannot be redefined");
         ArrayList<Field> fields = new ArrayList<>();
         require("{");
         while (!peek('}') && !_lexer.isEOF()) {
@@ -204,7 +207,7 @@ public class Parser {
         require("}");
         // Build and install the TypeStruct
         TypeStruct ts = TypeStruct.make(typeName, fields);
-        OBJS.put(typeName, ts); // Insert the struct name in the collection of all struct names
+        TYPES.put(typeName, ts); // Insert the struct name in the collection of all struct names
         START.addMemProj(ts, _scope); // Insert memory edges
         return parseStatement();
     }
@@ -423,15 +426,17 @@ public class Parser {
             if( _scope.define(name,t,expr) == null )
                 throw error("Redefining name '" + name + "'");
         } else {
-            Node n = _scope.lookup(name);
-            t = _scope.lookupDeclaredType(name);
-            if( n==null )
+            if( _scope.lookup(name)==null )
                 throw error("Undefined name '" + name + "'");
-            _scope.update(name,expr);
+            t = _scope.lookupDeclaredType(name);
         }
+        // Auto-widen int to float
+        if( expr._type instanceof TypeInteger && t instanceof TypeFloat )
+            expr = new ToFloatNode(expr).peephole();
+        // Type is sane
         if( !expr._type.isa(t) )
             throw error("Type " + expr._type.str() + " is not of declared type " + t.str());
-        return expr;
+        return _scope.update(name,expr);
     }
 
     // Parse a type-or-null
@@ -439,35 +444,13 @@ public class Parser {
         int old = _lexer._position;
         String tname = _lexer.matchId();
         if( tname==null ) return null;
-        if( tname.equals("int") ) return TypeInteger.BOT;
-        TypeStruct obj = OBJS.get(tname);
-        if( obj != null )
-            return TypeMemPtr.make(obj,match("?"));
-        // Not a type; unwind the parse
-        _lexer._position = old;
-        return null;
-    }
-
-    /**
-     * Parses a declStatement
-     *
-     * <pre>
-     *     type name = expression ';'
-     * </pre>
-     * @return an expression {@link Node}
-     */
-    private Node parseDecl(Type t) {
-        var name = requireId();
-        var expr = match(";")
-            // Assign a null value
-            ? new ConstantNode(t.makeInit()).peephole()
-            // Assign "= expr;"
-            : require(require("=").parseExpression(), ";");
-        if( !expr._type.isa(t) )
-            throw error("Type " + expr._type.str() + " is not of declared type " + t.str());
-        if( _scope.define(name,t,expr) == null )
-            throw error("Redefining name '" + name + "'");
-        return expr;
+        Type t = TYPES.get(tname);
+        if( t == null ) {
+            // Not a type; unwind the parse
+            _lexer._position = old;
+            return null;
+        }
+        return t instanceof TypeStruct obj ? TypeMemPtr.make(obj,match("?")) : t;
     }
 
 
@@ -504,7 +487,7 @@ public class Parser {
             else break;
             // Peepholes can fire, but lhs is already "hooked", kept alive
             lhs.setDef(idx,parseAddition());
-            lhs = lhs.peephole();
+            lhs = lhs.widen().peephole();
             if( negate )        // Extra negate for !=
                 lhs = new NotNode(lhs).peephole();
         }
@@ -527,7 +510,7 @@ public class Parser {
             else if( match("-") ) lhs = new SubNode(lhs,null);
             else break;
             lhs.setDef(2,parseMultiplication());
-            lhs = lhs.peephole();
+            lhs = lhs.widen().peephole();
         }
         return lhs;
     }
@@ -541,14 +524,14 @@ public class Parser {
      * @return a multiply expression {@link Node}, never {@code null}
      */
     private Node parseMultiplication() {
-        var lhs = parseUnary();
+        var lhs = parseUnary();  boolean mul;
         while( true ) {
             if( false ) ;
             else if( match("*") ) lhs = new MulNode(lhs,null);
             else if( match("/") ) lhs = new DivNode(lhs,null);
             else break;
             lhs.setDef(2,parseUnary());
-            lhs = lhs.peephole();
+            lhs = lhs.widen().peephole();
         }
         return lhs;
     }
@@ -562,7 +545,7 @@ public class Parser {
      * @return a unary expression {@link Node}, never {@code null}
      */
     private Node parseUnary() {
-        if (match("-")) return new MinusNode(parseUnary()).peephole();
+        if (match("-")) return new MinusNode(parseUnary()).widen().peephole();
         if (match("!")) return new   NotNode(parseUnary()).peephole();
         return parsePostfix(parsePrimary());
     }
@@ -576,15 +559,15 @@ public class Parser {
      * @return a primary {@link Node}, never {@code null}
      */
     private Node parsePrimary() {
-        if( _lexer.isNumber() ) return parseIntegerLiteral();
+        if( _lexer.isNumber(_lexer.peek()) ) return parseLiteral();
         if( match("(") ) return require(parseExpression(), ")");
         if( matchx("true" ) ) return new ConstantNode(TypeInteger.constant(1)).peephole();
         if( matchx("false") ) return ZERO;
         if( matchx("null" ) ) return new ConstantNode(TypeMemPtr.NULLPTR).peephole();
         if( matchx("new") ) {
             String structName = requireId();
-            TypeStruct obj = OBJS.get(structName);
-            if( obj == null) throw errorSyntax("Unknown struct type '" + structName + "'");
+            Type t = TYPES.get(structName);
+            if( t == null || !(t instanceof TypeStruct obj) ) throw errorSyntax("Unknown struct type '" + structName + "'");
             return newStruct(obj);
         }
         String name = _lexer.matchId();
@@ -630,6 +613,7 @@ public class Parser {
             throw error("Expected struct reference but got " + expr._type.str());
 
         String name = requireId().intern();
+        if( expr._type == TypeMemPtr.TOP ) throw error("Accessing field '" + name + "' from null");
         int idx = ptr._obj==null ? -1 : ptr._obj.find(name);
         if( idx == -1 ) throw error("Accessing unknown field '" + name + "' from '" + ptr.str() + "'");
         int alias = START._aliasStarts.get(ptr._obj._name)+idx;
@@ -653,9 +637,10 @@ public class Parser {
      *
      * <pre>
      *     integerLiteral: [1-9][0-9]* | [0]
+     *     floatLiteral: [1-9][0-9]* | [0]
      * </pre>
      */
-    private ConstantNode parseIntegerLiteral() {
+    private ConstantNode parseLiteral() {
         return (ConstantNode) new ConstantNode(_lexer.parseNumber()).peephole();
     }
 
@@ -810,19 +795,37 @@ public class Parser {
             return String.valueOf(peek());
         }
 
-        boolean isNumber() {return isNumber(peek());}
+
         boolean isNumber(char ch) {return Character.isDigit(ch);}
 
+        // Return a constant Type, either TypeInteger or TypeFloat
         private Type parseNumber() {
-            String snum = parseNumberString();
-            if (snum.length() > 1 && snum.charAt(0) == '0')
-                throw error("Syntax error: integer values cannot start with '0'");
-            return TypeInteger.constant(Long.parseLong(snum));
+            int old = _position;
+            int len = isLongOrDouble();
+            if( len > 0 ) {
+                if( len > 1 && _input[old]=='0' )
+                    throw error("Syntax error: integer values cannot start with '0'");
+                return TypeInteger.constant(Long.parseLong(new String(_input,old,len)));
+            }
+            return TypeFloat.constant(Double.parseDouble(new String(_input,old,-len)));
         }
         private String parseNumberString() {
-            int start = _position;
-            while (isNumber(nextChar())) ;
-            return new String(_input, start, --_position - start);
+            int old = _position;
+            int len = Math.abs(isLongOrDouble());
+            _position += len;
+            return new String(_input,old,len);
+        }
+
+        // Return +len that ends a long
+        // Return -len that ends a double
+        private int isLongOrDouble() {
+            int old = _position;
+            char c;
+            while( Character.isDigit(c=nextChar()) ) ;
+            if( !(c=='e' || c=='.') )
+                return --_position - old;
+            while( Character.isDigit(c=nextChar()) || c=='e' || c=='.' ) ;
+            return -(--_position - old);
         }
 
         // First letter of an identifier
diff --git a/src/main/java/com/seaofnodes/simple/node/AddFNode.java b/src/main/java/com/seaofnodes/simple/node/AddFNode.java
new file mode 100644
index 00000000..7d4e2910
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/AddFNode.java
@@ -0,0 +1,44 @@
+package com.seaofnodes.simple.node;
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeFloat;
+
+import java.util.BitSet;
+
+public class AddFNode extends Node {
+    public AddFNode(Node lhs, Node rhs) { super(null, lhs, rhs); }
+
+    @Override public String label() { return "AddF"; }
+
+    @Override public String glabel() { return "+"; }
+
+    @Override
+    StringBuilder _print1(StringBuilder sb, BitSet visited) {
+        in(1)._print0(sb.append("("), visited);
+        in(2)._print0(sb.append("+"), visited);
+        return sb.append(")");
+    }
+
+    @Override
+    public Type compute() {
+        if (in(1)._type instanceof TypeFloat i0 &&
+            in(2)._type instanceof TypeFloat i1) {
+            if (i0.isConstant() && i1.isConstant())
+                return TypeFloat.constant(i0.value()+i1.value());
+        }
+        return in(1)._type.meet(in(2)._type);
+    }
+
+    @Override
+    public Node idealize() {
+        Node lhs = in(1);
+        Type t2 = in(2)._type;
+
+        // Add of 0.
+        if ( t2.isConstant() && t2 instanceof TypeFloat i && i.value()==0 )
+            return lhs;
+
+        return null;
+    }
+    @Override Node copy(Node lhs, Node rhs) { return new AddFNode(lhs,rhs); }
+}
diff --git a/src/main/java/com/seaofnodes/simple/node/AddNode.java b/src/main/java/com/seaofnodes/simple/node/AddNode.java
index 2cc0b465..48350957 100644
--- a/src/main/java/com/seaofnodes/simple/node/AddNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/AddNode.java
@@ -106,6 +106,7 @@ public class AddNode extends Node {
     static Node phiCon(Node op, boolean rotate) {
         Node lhs = op.in(1);
         Node rhs = op.in(2);
+        if( rhs._type==TypeInteger.TOP ) return null;
         // LHS is either a Phi of constants, or another op with Phi of constants
         PhiNode lphi = pcon(lhs,op);
         if( rotate && lphi==null && lhs.nIns() > 2 ) {
@@ -171,4 +172,5 @@ public class AddNode extends Node {
     }
 
     @Override Node copy(Node lhs, Node rhs) { return new AddNode(lhs,rhs); }
+    @Override Node copyF() { return new AddFNode(null,null); }
 }
diff --git a/src/main/java/com/seaofnodes/simple/node/BoolNode.java b/src/main/java/com/seaofnodes/simple/node/BoolNode.java
index 9c15f01b..a31bd963 100644
--- a/src/main/java/com/seaofnodes/simple/node/BoolNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/BoolNode.java
@@ -1,7 +1,10 @@
 package com.seaofnodes.simple.node;
 
+import com.seaofnodes.simple.Parser;
+import com.seaofnodes.simple.Utils;
 import com.seaofnodes.simple.type.Type;
 import com.seaofnodes.simple.type.TypeInteger;
+import com.seaofnodes.simple.type.TypeFloat;
 import com.seaofnodes.simple.type.TypeMemPtr;
 
 import java.util.BitSet;
@@ -34,10 +37,16 @@ abstract public class BoolNode extends Node {
             if (i0.isConstant() && i1.isConstant())
                 return TypeInteger.constant(doOp(i0.value(), i1.value()) ? 1 : 0);
         }
-        return in(1)._type.meet(in(2)._type);
+        if( in(1)._type instanceof TypeFloat i0 &&
+            in(2)._type instanceof TypeFloat i1 ) {
+            if (i0.isConstant() && i1.isConstant())
+                return TypeInteger.constant(doOp(i0.value(), i1.value()) ? 1 : 0);
+        }
+        return TypeInteger.BOT;
     }
 
-    abstract boolean doOp(long lhs, long rhs);
+    boolean doOp(long   lhs, long   rhs) { throw Utils.TODO(); }
+    boolean doOp(double lhs, double rhs) { throw Utils.TODO(); }
 
     @Override
     public Node idealize() {
@@ -49,11 +58,9 @@ abstract public class BoolNode extends Node {
         if( this instanceof EQ ) {
             if( !(in(2) instanceof ConstantNode) ) {
                 // con==noncon becomes noncon==con
-                if( in(1) instanceof ConstantNode )
-                    return new EQ(in(2),in(1));
+                if( in(1) instanceof ConstantNode || in(1)._nid > in(2)._nid )
                 // Equals sorts by NID otherwise: non.high == non.low becomes non.low == non.high
-                else if( in(1)._nid > in(2)._nid )
-                    return new EQ(in(2),in(1));
+                    return in(1)._type instanceof TypeFloat ? new EQF(in(2),in(1)) : new EQ(in(2),in(1));
             }
             // Equals X==0 becomes a !X
             if( (in(2)._type == TypeInteger.ZERO || in(2)._type == TypeMemPtr.NULLPTR) )
@@ -69,7 +76,12 @@ abstract public class BoolNode extends Node {
         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; } Node copy(Node lhs, Node rhs) { return new EQ(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; } Node copy(Node lhs, Node rhs) { return new LT(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; } Node copy(Node lhs, Node rhs) { return new LE(lhs,rhs); } }
+    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; } Node copy(Node lhs, Node rhs) { return new EQ(lhs,rhs); } Node copyF() { return new EQF(null,null); } }
+    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; } Node copy(Node lhs, Node rhs) { return new LT(lhs,rhs); } Node copyF() { return new LTF(null,null); }}
+    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; } Node copy(Node lhs, Node rhs) { return new LE(lhs,rhs); } Node copyF() { return new LEF(null,null); } }
+
+    public static class EQF extends EQ { public EQF(Node lhs, Node rhs) { super(lhs,rhs); } boolean doOp(double lhs, double rhs) { return lhs == rhs; } Node copyF() { return null; } }
+    public static class LTF extends LT { public LTF(Node lhs, Node rhs) { super(lhs,rhs); } boolean doOp(double lhs, double rhs) { return lhs <  rhs; } Node copyF() { return null; } }
+    public static class LEF extends LE { public LEF(Node lhs, Node rhs) { super(lhs,rhs); } boolean doOp(double lhs, double rhs) { return lhs <= rhs; } Node copyF() { return null; } }
+
 }
diff --git a/src/main/java/com/seaofnodes/simple/node/CFGNode.java b/src/main/java/com/seaofnodes/simple/node/CFGNode.java
index b605071b..07ba0fa4 100644
--- a/src/main/java/com/seaofnodes/simple/node/CFGNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/CFGNode.java
@@ -52,16 +52,17 @@ public abstract class CFGNode extends Node {
     public int idepth() { return _idepth==0 ? (_idepth=idom().idepth()+1) : _idepth; }
 
     // Return the immediate dominator of this Node and compute dom tree depth.
-    public CFGNode idom() { return cfg(0); }
+    public CFGNode idom(Node dep) { return cfg(0); }
+    public final CFGNode idom() { return idom(null); }
 
     // Return the LCA of two idoms
-    public CFGNode idom(CFGNode rhs) {
+    public CFGNode _idom(CFGNode rhs, Node dep) {
         if( rhs==null ) return this;
         CFGNode lhs = this;
         while( lhs != rhs ) {
             var comp = lhs.idepth() - rhs.idepth();
-            if( comp >= 0 ) lhs = lhs.idom();
-            if( comp <= 0 ) rhs = rhs.idom();
+            if( comp >= 0 ) lhs = ((CFGNode)lhs.addDep(dep)).idom();
+            if( comp <= 0 ) rhs = ((CFGNode)rhs.addDep(dep)).idom();
         }
         return lhs;
     }
diff --git a/src/main/java/com/seaofnodes/simple/node/DivFNode.java b/src/main/java/com/seaofnodes/simple/node/DivFNode.java
new file mode 100644
index 00000000..36fd4524
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/DivFNode.java
@@ -0,0 +1,46 @@
+package com.seaofnodes.simple.node;
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeFloat;
+
+import java.util.BitSet;
+
+public class DivFNode extends Node {
+    public DivFNode(Node lhs, Node rhs) { super(null, lhs, rhs); }
+
+    @Override public String label() { return "DivF"; }
+
+    @Override public String glabel() { return "/"; }
+
+    @Override
+    StringBuilder _print1(StringBuilder sb, BitSet visited) {
+        in(1)._print0(sb.append("("), visited);
+        in(2)._print0(sb.append("/"), visited);
+        return sb.append(")");
+    }
+
+    @Override
+    public Type compute() {
+        if (in(1)._type instanceof TypeFloat i0 &&
+            in(2)._type instanceof TypeFloat i1) {
+            if (i0.isConstant() && i1.isConstant())
+                return TypeFloat.constant(i0.value()/i1.value());
+        }
+        return in(1)._type.meet(in(2)._type);
+    }
+
+    @Override
+    public Node idealize() {
+        Node lhs = in(1);
+        Node rhs = in(2);
+        Type t1 = lhs._type;
+        Type t2 = rhs._type;
+
+        // Div of 1.  
+        if ( t2.isConstant() && t2 instanceof TypeFloat i && i.value()==1 )
+            return lhs;
+
+        return null;
+    }
+    @Override Node copy(Node lhs, Node rhs) { return new DivFNode(lhs,rhs); }
+}
diff --git a/src/main/java/com/seaofnodes/simple/node/DivNode.java b/src/main/java/com/seaofnodes/simple/node/DivNode.java
index 08ce70b8..e0c95019 100644
--- a/src/main/java/com/seaofnodes/simple/node/DivNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/DivNode.java
@@ -40,4 +40,5 @@ public class DivNode extends Node {
     }
 
     @Override Node copy(Node lhs, Node rhs) { return new DivNode(lhs,rhs); }
+    @Override Node copyF() { return new DivFNode(null,null); }
 }
diff --git a/src/main/java/com/seaofnodes/simple/node/LoadNode.java b/src/main/java/com/seaofnodes/simple/node/LoadNode.java
index 296237f4..244a0919 100644
--- a/src/main/java/com/seaofnodes/simple/node/LoadNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/LoadNode.java
@@ -61,9 +61,13 @@ public class LoadNode extends MemOpNode {
             if( profit(memphi,2) ||
                 // Else must not be a loop to count profit on LHS.
                 (!(memphi.region() instanceof LoopNode) && profit(memphi,1)) ) {
-                Node ld1 = new LoadNode(_name,_alias,_declaredType,memphi.in(1),ptr()).peephole();
-                Node ld2 = new LoadNode(_name,_alias,_declaredType,memphi.in(2),ptr()).peephole();
-                return new PhiNode(_name,_type,memphi.region(),ld1,ld2);
+                if( ptr() instanceof NewNode || !(ptr() instanceof CastNode) ) {
+                    if( !(ptr() instanceof NewNode) ) throw Utils.TODO(); // Validate
+
+                    Node ld1 = new LoadNode(_name,_alias,_declaredType,memphi.in(1),ptr()).peephole();
+                    Node ld2 = new LoadNode(_name,_alias,_declaredType,memphi.in(2),ptr()).peephole();
+                    return new PhiNode(_name,_type,memphi.region(),ld1,ld2);
+                }
             }
         }
 
diff --git a/src/main/java/com/seaofnodes/simple/node/LoopNode.java b/src/main/java/com/seaofnodes/simple/node/LoopNode.java
index c662dee6..22862cb9 100644
--- a/src/main/java/com/seaofnodes/simple/node/LoopNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/LoopNode.java
@@ -30,7 +30,7 @@ public class LoopNode extends RegionNode {
     // Bypass Region idom, same as the default idom() using use in(1) instead of in(0)
     @Override public int idepth() { return _idepth==0 ? (_idepth=idom().idepth()+1) : _idepth; }
     // Bypass Region idom, same as the default idom() using use in(1) instead of in(0)
-    @Override public CFGNode idom() { return entry(); }
+    @Override public CFGNode idom(Node dep) { return entry(); }
 
     @Override public int loopDepth() {
         if( _loopDepth!=0 ) return _loopDepth; // Was already set
@@ -60,8 +60,11 @@ public class LoopNode extends RegionNode {
         // directly on the If) we found our exit.
         CFGNode x = back();
         while( x != this ) {
-            if( x instanceof CProjNode exit )
-                return;         // Found an exit, not an infinite loop
+            if( x instanceof CProjNode exit && exit.in(0) instanceof IfNode iff ) {
+                Node other = iff.cproj(1-exit._idx);
+                if( !(other.out(0) instanceof LoopNode loop) || loop.entry()==exit )
+                    return;         // Found an exit, not an infinite loop
+            }
             x = x.idom();
         }
         // Found a no-exit loop.  Insert an exit
diff --git a/src/main/java/com/seaofnodes/simple/node/MinusFNode.java b/src/main/java/com/seaofnodes/simple/node/MinusFNode.java
new file mode 100644
index 00000000..9727f58b
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/MinusFNode.java
@@ -0,0 +1,36 @@
+package com.seaofnodes.simple.node;
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeFloat;
+
+import java.util.BitSet;
+
+public class MinusFNode extends Node {
+    public MinusFNode(Node in) { super(null, in); }
+
+    @Override public String label() { return "MinusF"; }
+
+    @Override public String glabel() { return "-"; }
+
+    @Override
+    StringBuilder _print1(StringBuilder sb, BitSet visited) {
+        in(1)._print0(sb.append("(-"), visited);
+        return sb.append(")");
+    }
+
+    @Override
+    public Type compute() {
+        if (in(1)._type instanceof TypeFloat i0)
+            return i0.isConstant() ? TypeFloat.constant(-i0.value()) : i0;
+        return TypeFloat.BOT;
+    }
+
+    @Override
+    public Node idealize() {
+        // -(-x) is x
+        if( in(1) instanceof MinusFNode minus )
+            return minus.in(1);
+
+        return null;
+    }
+}
diff --git a/src/main/java/com/seaofnodes/simple/node/MinusNode.java b/src/main/java/com/seaofnodes/simple/node/MinusNode.java
index 9b687613..ae8e9e1b 100644
--- a/src/main/java/com/seaofnodes/simple/node/MinusNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/MinusNode.java
@@ -33,4 +33,5 @@ public class MinusNode extends Node {
 
         return null;
     }
+    @Override Node copyF() { return new MinusFNode(null); }
 }
diff --git a/src/main/java/com/seaofnodes/simple/node/MulFNode.java b/src/main/java/com/seaofnodes/simple/node/MulFNode.java
new file mode 100644
index 00000000..2d44a9fb
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/MulFNode.java
@@ -0,0 +1,51 @@
+package com.seaofnodes.simple.node;
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeFloat;
+
+import java.util.BitSet;
+
+public class MulFNode extends Node {
+    public MulFNode(Node lhs, Node rhs) { super(null, lhs, rhs); }
+
+    @Override public String label() { return "MulF"; }
+
+    @Override public String glabel() { return "*"; }
+
+    @Override
+    StringBuilder _print1(StringBuilder sb, BitSet visited) {
+        in(1)._print0(sb.append("("), visited);
+        in(2)._print0(sb.append("*"), visited);
+        return sb.append(")");
+    }
+
+    @Override
+    public Type compute() {
+        if (in(1)._type instanceof TypeFloat i0 &&
+            in(2)._type instanceof TypeFloat i1) {
+            if (i0.isConstant() && i1.isConstant())
+                return TypeFloat.constant(i0.value()*i1.value());
+        }
+        return in(1)._type.meet(in(2)._type);
+    }
+
+    @Override
+    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 TypeFloat i && i.value()==1 )
+            return lhs;
+
+        // Move constants to RHS: con*arg becomes arg*con
+        if ( t1.isConstant() && !t2.isConstant() )
+            return swap12();
+
+        return null;
+    }
+    @Override Node copy(Node lhs, Node rhs) { return new MulFNode(lhs,rhs); }
+}
diff --git a/src/main/java/com/seaofnodes/simple/node/MulNode.java b/src/main/java/com/seaofnodes/simple/node/MulNode.java
index 7e9f88a2..8c8a6e0a 100644
--- a/src/main/java/com/seaofnodes/simple/node/MulNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/MulNode.java
@@ -54,4 +54,5 @@ public class MulNode extends Node {
         return null;
     }
     @Override Node copy(Node lhs, Node rhs) { return new MulNode(lhs,rhs); }
+    @Override Node copyF() { return new MulFNode(null,null); }
 }
diff --git a/src/main/java/com/seaofnodes/simple/node/MultiNode.java b/src/main/java/com/seaofnodes/simple/node/MultiNode.java
index 379e140d..ac9c0045 100644
--- a/src/main/java/com/seaofnodes/simple/node/MultiNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/MultiNode.java
@@ -9,4 +9,12 @@ public interface MultiNode extends OutNode {
                 return prj;
         return null;
     }
+
+    // Find a projection by index
+    default CProjNode cproj( int idx ) {
+        for( Node out : outs() )
+            if( out instanceof CProjNode prj && prj._idx==idx )
+                return prj;
+        return null;
+    }
 }
diff --git a/src/main/java/com/seaofnodes/simple/node/NeverNode.java b/src/main/java/com/seaofnodes/simple/node/NeverNode.java
index f50d3503..e77ed653 100644
--- a/src/main/java/com/seaofnodes/simple/node/NeverNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/NeverNode.java
@@ -3,6 +3,8 @@ package com.seaofnodes.simple.node;
 import com.seaofnodes.simple.Parser;
 import com.seaofnodes.simple.type.TypeInteger;
 import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeTuple;
+
 import java.util.BitSet;
 
 // "Never true" for infinite loop exits
@@ -13,7 +15,7 @@ public class NeverNode extends IfNode {
 
     @Override StringBuilder _print1(StringBuilder sb, BitSet visited) { return sb.append("Never"); }
 
-    @Override public Type compute() { return TypeInteger.BOT; }
+    @Override public Type compute() { return TypeTuple.IF_BOTH; }
 
     @Override public Node idealize() { return null; }
 }
diff --git a/src/main/java/com/seaofnodes/simple/node/Node.java b/src/main/java/com/seaofnodes/simple/node/Node.java
index fc49ad6a..52282737 100644
--- a/src/main/java/com/seaofnodes/simple/node/Node.java
+++ b/src/main/java/com/seaofnodes/simple/node/Node.java
@@ -1,10 +1,10 @@
 package com.seaofnodes.simple.node;
 
 import com.seaofnodes.simple.IRPrinter;
-import com.seaofnodes.simple.Parser;
 import com.seaofnodes.simple.IterPeeps;
 import com.seaofnodes.simple.Utils;
 import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeFloat;
 
 import java.util.*;
 import java.util.function.Function;
@@ -236,6 +236,7 @@ public abstract class Node implements OutNode {
      */
     public void kill( ) {
         unlock();
+        moveDepsToWorklist();
         assert isUnused();      // Has no uses, so it is dead
         _type=null;             // Flag as dead
         while( nIns()>0 ) { // Set all inputs to null, recursively killing unused Nodes
@@ -546,6 +547,27 @@ public abstract class Node implements OutNode {
     /** Pinned in the schedule */
     public boolean isPinned() { return false; }
 
+    // Semantic change to the graph (so NOT a peephole), used by the Parser.
+    // If any input is a float, flip to a float-flavored opcode and widen any
+    // non-float input.
+    public final Node widen() {
+        if( !hasFloatInput() ) return this;
+        Node flt = copyF();
+        if( flt==null ) return this;
+        for( int i=1; i<nIns(); i++ )
+            flt.setDef(i, in(i)._type instanceof TypeFloat ? in(i) : new ToFloatNode(in(i)).peephole());
+        kill();
+        return flt;
+    }
+    private boolean hasFloatInput() {
+        for( int i=1; i<nIns(); i++ )
+            if( in(i)._type instanceof TypeFloat )
+                return true;
+        return false;
+    }
+    Node copyF() { return null; }
+
+
     // ------------------------------------------------------------------------
     // Peephole utilities
 
diff --git a/src/main/java/com/seaofnodes/simple/node/NotNode.java b/src/main/java/com/seaofnodes/simple/node/NotNode.java
index 05e44eb0..3cf69520 100644
--- a/src/main/java/com/seaofnodes/simple/node/NotNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/NotNode.java
@@ -21,8 +21,8 @@ public class NotNode extends Node {
     public Type compute() {
         Type t0 = in(1)._type;
         switch( t0 ) {
-        case TypeInteger i0:
-            return i0.isConstant() ? TypeInteger.constant(i0.value()==0 ? 1 : 0) : i0;
+        case TypeInteger i0:  return i0.isConstant() ? TypeInteger.constant(i0.value()==0 ? 1 : 0) : i0;
+        case TypeFloat   i0:  return i0.isConstant() ? TypeInteger.constant(i0.value()==0 ? 1 : 0) : i0;
         case TypeMemPtr p0:
             // top->top, bot->bot, null->1, *void->0, not-null ptr->0, ptr/nil->bot
             // If input in null then true
diff --git a/src/main/java/com/seaofnodes/simple/node/PhiNode.java b/src/main/java/com/seaofnodes/simple/node/PhiNode.java
index a07dc140..ebed8dd1 100644
--- a/src/main/java/com/seaofnodes/simple/node/PhiNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/PhiNode.java
@@ -100,10 +100,10 @@ public class PhiNode extends Node {
             if( in(2)._type == in(2)._type.makeInit() ) nullx = 2;
             if( nullx != -1 ) {
                 Node val = in(3-nullx);
-                if( region().idom() instanceof IfNode iff && iff.pred().addDep(this)==val ) {
+                if( region().idom(this) instanceof IfNode iff && iff.pred().addDep(this)==val ) {
                     // Must walk the idom on the null side to make sure we hit False.
                     CFGNode idom = (CFGNode)region().in(nullx);
-                    while( idom.in(0) != iff ) idom = idom.idom();
+                    while( idom.nIns() > 0 && idom.in(0) != iff ) idom = idom.idom();
                     if( idom instanceof CProjNode proj && proj._idx==1 )
                         return val;
                 }
diff --git a/src/main/java/com/seaofnodes/simple/node/RegionNode.java b/src/main/java/com/seaofnodes/simple/node/RegionNode.java
index dcc7ccef..d5105614 100644
--- a/src/main/java/com/seaofnodes/simple/node/RegionNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/RegionNode.java
@@ -99,12 +99,12 @@ public class RegionNode extends CFGNode {
         return _idepth=d;
     }
 
-    @Override public CFGNode idom() {
+    @Override public CFGNode idom(Node dep) {
         CFGNode lca = null;
         // Walk the LHS & RHS idom trees in parallel until they match, or either fails.
         // Because this does not cache, it can be linear in the size of the program.
         for( int i=1; i<nIns(); i++ )
-            lca = cfg(i).idom(lca);
+            lca = cfg(i)._idom(lca,dep);
         return lca;
     }
 
diff --git a/src/main/java/com/seaofnodes/simple/node/StartNode.java b/src/main/java/com/seaofnodes/simple/node/StartNode.java
index 62fc8a6b..5f205ffd 100644
--- a/src/main/java/com/seaofnodes/simple/node/StartNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/StartNode.java
@@ -75,7 +75,7 @@ public class StartNode extends CFGNode implements MultiNode {
 
     // No immediate dominator, and idepth==0
     @Override public int idepth() { return 0; }
-    @Override public CFGNode idom() { return null; }
+    @Override public CFGNode idom(Node dep) { return null; }
 
     @Override void _walkUnreach( BitSet visit, HashSet<CFGNode> unreach ) { }
 
diff --git a/src/main/java/com/seaofnodes/simple/node/StopNode.java b/src/main/java/com/seaofnodes/simple/node/StopNode.java
index 94b2ad6d..ab567bae 100644
--- a/src/main/java/com/seaofnodes/simple/node/StopNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/StopNode.java
@@ -59,7 +59,7 @@ public class StopNode extends CFGNode {
                 d = Math.max(d,((CFGNode)n).idepth()+1);
         return _idepth=d;
     }
-    @Override public CFGNode idom() { return null; }
+    @Override public CFGNode idom(Node dep) { return null; }
 
     @Override public int loopDepth() { return (_loopDepth=1); }
 
diff --git a/src/main/java/com/seaofnodes/simple/node/SubFNode.java b/src/main/java/com/seaofnodes/simple/node/SubFNode.java
new file mode 100644
index 00000000..b591718d
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/SubFNode.java
@@ -0,0 +1,44 @@
+package com.seaofnodes.simple.node;
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeFloat;
+
+import java.util.BitSet;
+
+public class SubFNode extends Node {
+    public SubFNode(Node lhs, Node rhs) { super(null, lhs, rhs); }
+
+    @Override public String label() { return "SubF"; }
+
+    @Override public String glabel() { return "-"; }
+
+    @Override
+    StringBuilder _print1(StringBuilder sb, BitSet visited) {
+        in(1)._print0(sb.append("("), visited);
+        in(2)._print0(sb.append("-"), visited);
+        return sb.append(")");
+    }
+
+    @Override
+    public Type compute() {
+        if (in(1)._type instanceof TypeFloat i0 &&
+            in(2)._type instanceof TypeFloat i1) {
+            if (i0.isConstant() && i1.isConstant())
+                return TypeFloat.constant(i0.value()-i1.value());
+        }
+        return in(1)._type.meet(in(2)._type);
+    }
+
+    @Override
+    public Node idealize() {
+        Node lhs = in(1);
+        Type t2 = in(2)._type;
+
+        // Sub of 0.
+        if ( t2.isConstant() && t2 instanceof TypeFloat i && i.value()==0 )
+            return lhs;
+
+        return null;
+    }
+    @Override Node copy(Node lhs, Node rhs) { return new SubFNode(lhs,rhs); }
+}
diff --git a/src/main/java/com/seaofnodes/simple/node/SubNode.java b/src/main/java/com/seaofnodes/simple/node/SubNode.java
index 5ddcdb68..f0c77743 100644
--- a/src/main/java/com/seaofnodes/simple/node/SubNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/SubNode.java
@@ -31,6 +31,7 @@ public class SubNode extends Node {
             if (i0.isConstant() && i1.isConstant())
                 return TypeInteger.constant(i0.value()-i1.value());
         }
+
         return in(1)._type.meet(in(2)._type);
     }
 
@@ -48,4 +49,5 @@ public class SubNode extends Node {
     }
 
     @Override Node copy(Node lhs, Node rhs) { return new SubNode(lhs,rhs); }
+    @Override Node copyF() { return new SubFNode(null,null); }
 }
diff --git a/src/main/java/com/seaofnodes/simple/node/ToFloatNode.java b/src/main/java/com/seaofnodes/simple/node/ToFloatNode.java
new file mode 100644
index 00000000..1d147cf6
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/ToFloatNode.java
@@ -0,0 +1,30 @@
+package com.seaofnodes.simple.node;
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeFloat;
+import com.seaofnodes.simple.type.TypeInteger;
+
+import java.util.BitSet;
+
+public class ToFloatNode extends Node {
+    public ToFloatNode(Node lhs) { super(null, lhs); }
+
+    @Override public String label() { return "ToFloat"; }
+
+    @Override public String glabel() { return "(flt)"; }
+
+    @Override
+    StringBuilder _print1(StringBuilder sb, BitSet visited) {
+        return in(1)._print0(sb.append("(flt)"), visited);
+    }
+
+    @Override
+    public Type compute() {
+        if (in(1)._type instanceof TypeInteger i0 && i0.isConstant() )
+            return TypeFloat.constant(i0.value());
+        return TypeFloat.BOT;
+    }
+
+    @Override public Node idealize() { return null; }
+    @Override Node copy(Node lhs, Node rhs) { return new ToFloatNode(lhs); }
+}
diff --git a/src/main/java/com/seaofnodes/simple/type/Type.java b/src/main/java/com/seaofnodes/simple/type/Type.java
index aa0ba1ea..f3152719 100644
--- a/src/main/java/com/seaofnodes/simple/type/Type.java
+++ b/src/main/java/com/seaofnodes/simple/type/Type.java
@@ -33,11 +33,12 @@ public class Type {
     static final byte TXCTRL  = 3; // Ctrl flow top (mini-lattice: any-xctrl-ctrl-all)
     static final byte TSIMPLE = 4; // End of the Simple Types
     static final byte TINT    = 5; // All Integers; see TypeInteger
-    static final byte TTUPLE  = 6; // Tuples; finite collections of unrelated Types, kept in parallel
-    static final byte TMEM    = 7; // All memory (alias 0) or A slice of memory - with specific alias
-    static final byte TMEMPTR = 8; // Memory pointer type
-    static final byte TSTRUCT = 9; // Structs; tuples with named fields
-    static final byte TFLD    =10; // Fields into struct
+    static final byte TFLT    = 6; // All Integers; see TypeInteger
+    static final byte TTUPLE  = 7; // Tuples; finite collections of unrelated Types, kept in parallel
+    static final byte TMEM    = 8; // All memory (alias 0) or A slice of memory - with specific alias
+    static final byte TMEMPTR = 9; // Memory pointer type
+    static final byte TSTRUCT =10; // Structs; tuples with named fields
+    static final byte TFLD    =11; // Fields into struct
 
     public final byte _type;
 
diff --git a/src/main/java/com/seaofnodes/simple/type/TypeFloat.java b/src/main/java/com/seaofnodes/simple/type/TypeFloat.java
new file mode 100644
index 00000000..36bc61f5
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/type/TypeFloat.java
@@ -0,0 +1,101 @@
+package com.seaofnodes.simple.type;
+
+import java.util.ArrayList;
+
+/**
+ * Float Type
+ */
+public class TypeFloat extends Type {
+
+    public final static TypeFloat TOP = make(false, 0);
+    public final static TypeFloat BOT = make(false, 1);
+    public final static TypeFloat ZERO= make(true , 0);
+
+    public final boolean _is_con;
+
+    /**
+     * The constant value or
+     * if not constant then 1=bottom, 0=top.
+     */
+    public final double _con;
+
+    private TypeFloat(boolean is_con, double con) {
+        super(TFLT);
+        _is_con = is_con;
+        _con = con;
+    }
+    public static TypeFloat make(boolean is_con, double con) {
+        return new TypeFloat(is_con,con).intern();
+    }
+
+    public static TypeFloat constant(double con) { return make(true, con); }
+
+    public static void gather(ArrayList<Type> ts) { ts.add(ZERO); ts.add(BOT); }
+
+    // FIXME this display format is problematic
+    // In visualizer '#' gets prepended if its a constant
+    @Override
+    public StringBuilder _print(StringBuilder sb) {
+        if( this==TOP ) return sb.append("FltTop");
+        if( this==BOT ) return sb.append("FltBot");
+        return sb.append(_con);
+    }
+
+    @Override public String str() {
+        if( this==TOP ) return "~flt";
+        if( this==BOT ) return  "flt";
+        return ""+_con;
+    }
+
+    /**
+     * Display Type name in a format that's good for IR printer
+     */
+    @Override
+    public StringBuilder typeName(StringBuilder sb) {
+        if( this==TOP ) return sb.append("FltTop");
+        if( this==BOT ) return sb.append("FltBot");
+        return sb.append("Int");
+    }
+
+    @Override
+    public boolean isHighOrConst() { return _is_con || _con==0; }
+
+    @Override
+    public boolean isConstant() { return _is_con; }
+
+    public double value() { return _con; }
+
+    @Override
+    public Type xmeet(Type other) {
+        // Invariant from caller: 'this' != 'other' and same class (TypeFloat)
+        TypeFloat i = (TypeFloat)other; // Contract
+        // BOT wins
+        if ( this==BOT ) return this;
+        if ( i   ==BOT ) return i   ;
+        // TOP loses
+        if ( i   ==TOP ) return this;
+        if ( this==TOP ) return i   ;
+        // Since both are constants, and are never equals (contract) unequals
+        // constants fall to bottom
+        return BOT;
+    }
+
+    @Override
+    public Type dual() {
+        if( isConstant() ) return this; // Constants are a self-dual
+        return _con==0 ? BOT : TOP;
+    }
+
+    @Override
+    public Type glb() { return BOT; }
+
+    @Override public TypeFloat makeInit() { return ZERO; }
+
+    @Override
+    int hash() { return (int)(Double.hashCode(_con) ^ (_is_con ? 0 : 0x4000)); }
+    @Override
+    public boolean eq( Type t ) {
+        TypeFloat i = (TypeFloat)t; // Contract
+        return _con==i._con && _is_con==i._is_con;
+    }
+}
diff --git a/src/test/java/com/seaofnodes/simple/Chapter08Test.java b/src/test/java/com/seaofnodes/simple/Chapter08Test.java
index 98fd181b..6aa74125 100644
--- a/src/test/java/com/seaofnodes/simple/Chapter08Test.java
+++ b/src/test/java/com/seaofnodes/simple/Chapter08Test.java
@@ -2,7 +2,6 @@ package com.seaofnodes.simple;
 
 import com.seaofnodes.simple.evaluator.Evaluator;
 import com.seaofnodes.simple.node.*;
-import com.seaofnodes.simple.type.TypeInteger;
 import org.junit.Assert;
 import org.junit.Test;
 
diff --git a/src/test/java/com/seaofnodes/simple/Chapter09Test.java b/src/test/java/com/seaofnodes/simple/Chapter09Test.java
index 2abce3cb..64bbf245 100644
--- a/src/test/java/com/seaofnodes/simple/Chapter09Test.java
+++ b/src/test/java/com/seaofnodes/simple/Chapter09Test.java
@@ -5,7 +5,6 @@ import com.seaofnodes.simple.node.*;
 import com.seaofnodes.simple.type.Type;
 import com.seaofnodes.simple.type.TypeInteger;
 import org.junit.Assert;
-import org.junit.BeforeClass;
 import org.junit.Test;
 import org.junit.Ignore;
 
diff --git a/src/test/java/com/seaofnodes/simple/Chapter10Test.java b/src/test/java/com/seaofnodes/simple/Chapter10Test.java
index 7371ff18..4a9521b9 100644
--- a/src/test/java/com/seaofnodes/simple/Chapter10Test.java
+++ b/src/test/java/com/seaofnodes/simple/Chapter10Test.java
@@ -1,7 +1,12 @@
 package com.seaofnodes.simple;
 
+import com.seaofnodes.simple.node.Node;
 import com.seaofnodes.simple.node.StopNode;
+import com.seaofnodes.simple.type.*;
 import org.junit.Test;
+
+import java.util.Arrays;
+
 import static org.junit.Assert.assertEquals;
 import static org.junit.Assert.fail;
 
@@ -259,7 +264,6 @@ while(arg) {
     v0.v0 = arg;
     arg = arg-1;
     if (arg==5) ret=v0;
-
 }
 return ret;
 """);
diff --git a/src/test/java/com/seaofnodes/simple/Chapter11Test.java b/src/test/java/com/seaofnodes/simple/Chapter11Test.java
index fdf56b56..a8b09226 100644
--- a/src/test/java/com/seaofnodes/simple/Chapter11Test.java
+++ b/src/test/java/com/seaofnodes/simple/Chapter11Test.java
@@ -292,7 +292,7 @@ else {
 }
 """);
         StopNode stop = parser.parse().iterate();
-        assertEquals("Stop[ return 9; return 0; return 0; ]", stop.toString());
+        assertEquals("Stop[ return 9; return 0; return 0; return 0; return 0; ]", stop.toString());
     }
 
 
@@ -434,7 +434,7 @@ while(1)
   arg = arg+ptr.v;
 """);
         StopNode stop = parser.parse().iterate();
-        assertEquals("return 0;", stop.toString());
+        assertEquals("Stop[ return 0; return 0; ]", stop.toString());
     }
 
     @Test
@@ -496,7 +496,7 @@ return v;
     @Test
     public void testExample2() {
         Parser parser = new Parser(
-                                   """
+                """
 struct S { int f; }
 S v = new S;
 int i = arg;
@@ -507,7 +507,7 @@ while (arg > 0) {
     arg = arg - 1;
 }
 return v;
-""");
+                """);
         StopNode stop = parser.parse().iterate();
         //assertEquals("return new S;", stop.toString());
     }
@@ -528,38 +528,4 @@ return s.f;
         assertEquals(1L, Evaluator.evaluate(stop,  1));
         assertEquals(0L, Evaluator.evaluate(stop,  2));
     }
-
-    @Test
-    public void testScheduleUse() {
-        Parser parser = new Parser(
-"""
-int v0=0;
-while(0>=0) {
-    int v1=0;
-    v1=v0;
-    if(v1*0)
-        v0=-v1;
-}
-return 0;
-""");
-        StopNode stop = parser.parse().iterate();
-        assertEquals("return 0;", stop.toString());
-    }
-
-    @Test
-    public void testLoopCarriedDep() {
-        Parser parser = new Parser(
-"""
-int v0=0;
-{
-    int v1=0;
-    while(v1) {
-        v1=1+(v0!=0);
-        v0=v1/0;
-    }
-}
-""");
-        StopNode stop = parser.parse().iterate();
-        assertEquals("return 0;", stop.toString());
-    }
 }
diff --git a/src/test/java/com/seaofnodes/simple/Chapter12Test.java b/src/test/java/com/seaofnodes/simple/Chapter12Test.java
new file mode 100644
index 00000000..af8fdfe9
--- /dev/null
+++ b/src/test/java/com/seaofnodes/simple/Chapter12Test.java
@@ -0,0 +1,64 @@
+package com.seaofnodes.simple;
+
+import com.seaofnodes.simple.evaluator.Evaluator;
+import com.seaofnodes.simple.node.StopNode;
+import org.junit.Test;
+
+
+import static org.junit.Assert.assertEquals;
+import static org.junit.Assert.fail;
+
+public class Chapter12Test {
+    @Test
+    public void testJig() {
+        Parser parser = new Parser(
+"""
+return 3.14;
+""");
+        StopNode stop = parser.parse(false).iterate(false);
+        assertEquals("return 3.14;", stop.toString());
+        assertEquals(3.14, Evaluator.evaluate(stop,  0));
+    }
+
+    @Test
+    public void testFloat() {
+        Parser parser = new Parser(
+"""
+return 3.14;
+""");
+        StopNode stop = parser.parse(false).iterate(false);
+        assertEquals("return 3.14;", stop.toString());
+        assertEquals(3.14, Evaluator.evaluate(stop,  0));
+    }
+
+    @Test
+    public void testSquareRoot() {
+        Parser parser = new Parser(
+"""
+flt guess = arg;
+while( 1 ) {
+    flt next = (arg/guess + guess)/2;
+    if( next == guess ) break;
+    guess = next;
+}
+return guess;
+""");
+        StopNode stop = parser.parse(false).iterate(false);
+        assertEquals("return Phi(Loop9,(flt)arg,(((ToFloat/Phi_guess)+Phi_guess)/2.0));", stop.toString());
+        assertEquals(3.0, Evaluator.evaluate(stop,  9));
+        assertEquals(1.414213562373095, Evaluator.evaluate(stop,  2));
+    }
+
+    @Test
+    public void testFPOps() {
+        Parser parser = new Parser(
+"""
+flt x = arg;
+return x+1==x;
+""");
+        StopNode stop = parser.parse(false).iterate(false);
+        assertEquals("return ((flt)arg==(ToFloat+1.0));", stop.toString());
+        assertEquals(0L, Evaluator.evaluate(stop, 1));
+    }
+
+}
diff --git a/src/test/java/com/seaofnodes/simple/SchedulerTest.java b/src/test/java/com/seaofnodes/simple/SchedulerTest.java
index 32c9c0c5..5def2782 100644
--- a/src/test/java/com/seaofnodes/simple/SchedulerTest.java
+++ b/src/test/java/com/seaofnodes/simple/SchedulerTest.java
@@ -46,7 +46,7 @@ S v0=new S;
 if(arg) v0.f=1;
 return v0;
 """);
-        StopNode stop = parser.parse(false).iterate();
+        StopNode stop = parser.parse().iterate();
         var eval = new Evaluator(stop);
         assertObj(eval.evaluate(0, 10), "S", 0L);
         assertObj(eval.evaluate(1, 10), "S", 1L);
@@ -65,7 +65,7 @@ i=v.f;
 if (arg) v.f=1;
 return i;
 """);
-        StopNode stop = parser.parse(false).iterate();
+        StopNode stop = parser.parse().iterate();
         var eval = new Evaluator(stop);
         assertEquals(2L, eval.evaluate(0, 10));
         assertEquals(2L, eval.evaluate(1, 10));
diff --git a/src/test/java/com/seaofnodes/simple/evaluator/Evaluator.java b/src/test/java/com/seaofnodes/simple/evaluator/Evaluator.java
index 4a405a3b..3512d2e9 100644
--- a/src/test/java/com/seaofnodes/simple/evaluator/Evaluator.java
+++ b/src/test/java/com/seaofnodes/simple/evaluator/Evaluator.java
@@ -2,10 +2,7 @@ package com.seaofnodes.simple.evaluator;
 
 import com.seaofnodes.simple.Utils;
 import com.seaofnodes.simple.node.*;
-import com.seaofnodes.simple.type.Field;
-import com.seaofnodes.simple.type.TypeInteger;
-import com.seaofnodes.simple.type.TypeMemPtr;
-import com.seaofnodes.simple.type.TypeStruct;
+import com.seaofnodes.simple.type.*;
 
 import java.lang.invoke.MethodHandle;
 import java.lang.invoke.MethodHandles;
@@ -80,6 +77,10 @@ public class Evaluator {
         long in2 = vall(div.in(2));
         return in2 == 0 ? 0 : vall(div.in(1)) / in2;
     }
+    private double div(DivFNode div) {
+        double in2 = vald(div.in(2));
+        return in2 == 0 ? 0 : vald(div.in(1)) / in2;
+    }
 
     private Object alloc(NewNode alloc) {
         var type = ((TypeMemPtr)alloc.compute())._obj;
@@ -115,10 +116,16 @@ public class Evaluator {
         if (v instanceof Number n) return n.longValue();
         throw new AssertionError("Not a long " + v);
     }
+    private double vald(Node node) {
+        var v = val(node);
+        if (v instanceof Number n) return n.doubleValue();
+        throw new AssertionError("Not a double " + v);
+    }
 
     private Object cons(ConstantNode cons) {
         var type = cons.compute();
         if (type instanceof TypeInteger i) return i.value();
+        if (type instanceof TypeFloat i) return i.value();
         assert type instanceof TypeMemPtr;
         return null;
     }
@@ -127,15 +134,24 @@ public class Evaluator {
         return switch (node) {
             case ConstantNode cons  -> cons(cons);
             case AddNode      add   -> vall(add.in(1)) + vall(add.in(2));
+            case AddFNode     add   -> vald(add.in(1)) + vald(add.in(2));
+            case BoolNode.EQF eq    -> vald(eq.in(1)) == vald(eq.in(2)) ? 1L : 0L;
+            case BoolNode.LEF le    -> vald(le.in(1)) <= vald(le.in(2)) ? 1L : 0L;
+            case BoolNode.LTF lt    -> vald(lt.in(1)) <  vald(lt.in(2)) ? 1L : 0L;
             case BoolNode.EQ  eq    -> Objects.equals(val(eq.in(1)), val(eq.in(2))) ? 1L : 0L;
             case BoolNode.LE  le    -> vall(le.in(1)) <= vall(le.in(2)) ? 1L : 0L;
             case BoolNode.LT  lt    -> vall(lt.in(1)) <  vall(lt.in(2)) ? 1L : 0L;
             case DivNode      div   -> div(div);
+            case DivFNode     div   -> div(div);
             case MinusNode    minus -> -vall(minus.in(1));
+            case MinusFNode   minus -> -vald(minus.in(1));
             case MulNode      mul   -> vall(mul.in(1)) * vall(mul.in(2));
+            case MulFNode     mul   -> vald(mul.in(1)) * vald(mul.in(2));
             case NotNode      not   -> isTrue(val(not.in(1))) ? 0L : 1L;
             case SubNode      sub   -> vall(sub.in(1)) - vall(sub.in(2));
+            case SubFNode     sub   -> vald(sub.in(1)) - vald(sub.in(2));
             case CastNode     cast  -> val(cast.in(1));
+            case ToFloatNode  cast  -> (double)vall(cast.in(1));
             case LoadNode     load  -> load(load);
             case StoreNode    store -> store(store);
             case NewNode      alloc -> alloc(alloc);
diff --git a/src/test/java/com/seaofnodes/simple/fuzzer/ScriptGenerator.java b/src/test/java/com/seaofnodes/simple/fuzzer/ScriptGenerator.java
index 155063ab..b8437b50 100644
--- a/src/test/java/com/seaofnodes/simple/fuzzer/ScriptGenerator.java
+++ b/src/test/java/com/seaofnodes/simple/fuzzer/ScriptGenerator.java
@@ -22,6 +22,7 @@ public class ScriptGenerator {
     private static final int MAX_NAME_LENGTH = 10;
     private static final int MAX_BLOCK_DEPTH = 4;
     private static final int MAX_EXPRESSION_DEPTH = 10;
+    private static final int MAX_SUFFIX_RECURSIVE_DEPTH = 10;
 
     /**
      * Number of spaces per indentation
@@ -68,7 +69,7 @@ public class ScriptGenerator {
     }
 
     private static class TypeStruct extends Type {
-        record Field (String name, Type type) {}
+        record Field (String name, Type type, TypeStruct struct) {}
         final Field[] fields;
         final TypeNullable nullable = new TypeNullable(this);
         TypeStruct(String name, Field[] fields) {
@@ -89,7 +90,21 @@ public class ScriptGenerator {
 
     }
 
-    private static final Type TYPE_INT = new Type("int");
+    private static final Type TYPE_FLT = new Type("flt");
+
+    private static class TypeInt extends Type {
+
+        TypeInt() {
+            super("int");
+        }
+
+        @Override
+        boolean isa(Type other) {
+            return super.isa(other) || other == TYPE_FLT;
+        }
+    }
+
+    private static final Type TYPE_INT = new TypeInt();
 
 
     private static class Variable {
@@ -343,7 +358,9 @@ public class ScriptGenerator {
      * @return A random type
      */
     private Type getType() {
-        if (structs.isEmpty() || random.nextBoolean()) return TYPE_INT;
+        int t = random.nextInt(10);
+        if( t<5 || structs.isEmpty() ) return TYPE_INT;
+        if( t<7 ) return TYPE_FLT;
         var idx = random.nextInt(structs.size());
         TypeStruct struct = structs.get(idx);
         if (random.nextBoolean()) return struct.nullable;
@@ -411,17 +428,18 @@ public class ScriptGenerator {
     public int genStruct() {
         var name = getStructName();
         var fields = new TypeStruct.Field[generateInvalid() ? 0 : random.nextInt(10)];
+        var struct = new TypeStruct(name, fields);
         sb.append("struct ").append(name).append(" {\n");
         indentation += INDENTATION;
         for (int i=0; i<fields.length; i++) {
             var fieldName = getRandomName();
-            var type = generateInvalid() ? getType() : TYPE_INT;
+            var type = getType();
             printIndentation().append(type.name).append(" ").append(fieldName).append(";\n");
-            fields[i] = new TypeStruct.Field(fieldName.toString(), type);
+            fields[i] = new TypeStruct.Field(fieldName.toString(), type, struct);
         }
         indentation -= INDENTATION;
         printIndentation().append("}");
-        structs.add(new TypeStruct(name, fields));
+        structs.add(struct);
         return 0;
     }
 
@@ -515,7 +533,7 @@ public class ScriptGenerator {
      */
     public int genIf() {
         sb.append("if(");
-        genExpression(TYPE_INT);
+        genExpression(TYPE_INT, true);
         sb.append(") ");
         var stop = genStatementBlock();
         if ((stop & FLAG_IF_WITHOUT_ELSE) == 0 && random.nextInt(10) > 3) {
@@ -561,7 +579,7 @@ public class ScriptGenerator {
      */
     public int genWhile() {
         sb.append("while(");
-        genExpression(TYPE_INT);
+        genExpression(TYPE_INT, true);
         sb.append(") ");
         loopDepth++;
         genStatementBlock();
@@ -587,17 +605,17 @@ public class ScriptGenerator {
         indentation += INDENTATION;
         String name = getVarName();
         printIndentation().append("int ").append(name).append("=");
-        genExpression(TYPE_INT);
+        genExpression(TYPE_INT, true);
         sb.append(";\n");
         addVariable(name, TYPE_INT);
         printIndentation().append("while(").append(name).append("<");
-        genExpression(TYPE_INT);
+        genExpression(TYPE_INT, true);
         sb.append(") {\n");
         indentation += INDENTATION;
         depth--;
         loopDepth++;
         printIndentation().append(name).append("=").append(name).append("+");
-        genExpression(TYPE_INT);
+        genExpression(TYPE_INT, true);
         sb.append(";\n");
         genStatements();
         loopDepth--;
@@ -621,7 +639,7 @@ public class ScriptGenerator {
         sb.append(generateInvalid() ? getRandomName() : type.name).append(" ").append(name);
         if (!(type instanceof TypeNullable) || random.nextBoolean()) {
             sb.append("=");
-            genExpression(type);
+            genExpression(type, true);
         }
         sb.append(";");
         addVariable(name, type);
@@ -656,7 +674,7 @@ public class ScriptGenerator {
             declared = field.type;
         }
         sb.append("=");
-        genExpression(declared);
+        genExpression(declared, true);
         sb.append(";");
         return 0;
     }
@@ -668,7 +686,7 @@ public class ScriptGenerator {
     public int genReturn() {
         var type = getType();
         sb.append("return ");
-        genExpression(type);
+        genExpression(type, true);
         sb.append(";");
         return FLAG_STOP;
     }
@@ -677,70 +695,91 @@ public class ScriptGenerator {
      * Generate a binary expression.
      * This method does not care about operator precedence.
      */
-    public void genExpression(Type type) {
-        if (generateInvalid()) type = getType();
-        if (type != TYPE_INT) {
-            genUnary(type);
+    public void genExpression(Type type, boolean change) {
+        if (change && generateInvalid()) type = getType();
+        if (type != TYPE_INT && type != TYPE_FLT) {
+            genUnary(type, false);
             return;
         }
         var num = randLog(MAX_BINARY_EXPRESSIONS_PER_EXPRESSION);
         while(num-->0) {
-            genUnary(TYPE_INT);
+            genUnary(type, false);
             sb.append(BINARY_OP[random.nextInt(BINARY_OP.length)]);
         }
-        genUnary(TYPE_INT);
+        genUnary(type, false);
     }
 
     /**
      * Generate a unary expression.
      */
-    public void genUnary(Type type) {
-        if (generateInvalid()) type = getType();
-        if (type != TYPE_INT) {
-            genSuffix(type);
+    public void genUnary(Type type, boolean change) {
+        if (change && generateInvalid()) type = getType();
+        if (type != TYPE_INT && type != TYPE_FLT) {
+            genSuffix(type, false);
             return;
         }
         var num = randLog(MAX_UNARY_EXPRESSIONS_PER_EXPRESSION);
         while(num-->0) {
             sb.append(UNARY_OP[random.nextInt(UNARY_OP.length)]);
         }
-        genSuffix(TYPE_INT);
+        genSuffix(type, false);
+    }
+
+    public TypeStruct.Field getField(Type type) {
+        int n=0;
+        for (var s: structs) {
+            for (var f: s.fields) {
+                if (f.type.isa(type)) n++;
+            }
+        }
+        if (n==0) return null;
+        n = random.nextInt(n);
+        for (var s: structs) {
+            for (var f: s.fields) {
+                if (f.type.isa(type)) if (n--==0) return f;
+            }
+        }
+        throw new AssertionError();
     }
 
     /**
      * Generate
      */
-    public void genSuffix(Type type) {
-        if (generateInvalid()) type = getType();
-        if (type == TYPE_INT && random.nextBoolean()) {
-            var t = getType();
+    public void genSuffix(Type type, boolean change) {
+        genSuffixRecursive(type, change, MAX_SUFFIX_RECURSIVE_DEPTH);
+    }
+
+    public void genSuffixRecursive(Type type, boolean change, int depth) {
+        if (change && generateInvalid()) type = getType();
+        if (depth > 0 && random.nextBoolean()) {
             if (generateInvalid()) {
                 var field = getRandomName();
-                genPrimary(t);
+                var t = getType();
+                genSuffixRecursive(t, true, depth-1);
                 sb.append(".").append(field);
                 return;
-            } else if (t instanceof TypeStruct s && s.fields.length > 0) {
-                var field = s.fields[random.nextInt(s.fields.length)];
-                if (field.type == TYPE_INT) {
-                    genPrimary(t);
+            } else {
+                var field = getField(type);
+                if (field != null) {
+                    genSuffixRecursive(field.struct, true, depth-1);
                     sb.append(".").append(field.name);
                     return;
                 }
             }
         }
-        genPrimary(type);
+        genPrimary(type, false);
     }
 
     /**
      * Generate a primary expression.
      */
-    public void genPrimary(Type type) {
-        if (generateInvalid()) type = getType();
+    public void genPrimary(Type type, boolean change) {
+        if (change && generateInvalid()) type = getType();
         var rand = random.nextInt(10);
         if (rand == 0 && exprDepth != 0) {
             sb.append("(");
             exprDepth--;
-            genExpression(type);
+            genExpression(type, false);
             exprDepth++;
             sb.append(")");
         } else if (rand < 6) {
@@ -755,13 +794,15 @@ public class ScriptGenerator {
      */
     public void genConst(Type type) {
         if (generateInvalid()) type = getType();
-        if (type == TYPE_INT) {
+        if (type == TYPE_INT || (type == TYPE_FLT && random.nextBoolean())) {
             var rand = random.nextInt(10);
             switch (rand) {
                 case 0 -> sb.append("true");
                 case 1 -> sb.append("false");
                 default -> sb.append(random.nextInt(1<<(rand-2)));
             }
+        } else if (type == TYPE_FLT) {
+            sb.append(random.nextFloat());
         } else if (type instanceof TypeNullable n) {
             if (random.nextBoolean()) {
                 sb.append("null");