Chapter 14: Numeric Types

Co-authored-by: Thalia Archibald <thalia@archibald.dev>
Co-authored-by: Tamás Hadházy <85063808+Hels15@users.noreply.github.com>
Co-authored-by: Hsiang-Ying Fu <66062782+fuhsnn@users.noreply.github.com>
Co-authored-by: Dibyendu Majumdar <mobile@majumdar.org.uk>
Co-authored-by: tannal <tannal2409@gmail.com>
Co-authored-by: hadha <helsgithub15@gmail.com>
Co-authored-by: fuhsnn <66062782+fuhsnn@users.noreply.github.com>
Co-authored-by: XmiliaH <45106915+XmiliaH@users.noreply.github.com>
Co-authored-by: RobertObkircher <robert.obkircher@gmail.com>
Co-authored-by: Robert Obkircher <robert.obkircher@gmail.com>
Co-authored-by: Jun Kawasaki <jun784@gmail.com>

33 files changed, 1069 insertions, 152 deletions

diff --git a/src/main/java/com/seaofnodes/simple/Parser.java b/src/main/java/com/seaofnodes/simple/Parser.java
index 3c8d8f40..0602d290 100644
--- a/src/main/java/com/seaofnodes/simple/Parser.java
+++ b/src/main/java/com/seaofnodes/simple/Parser.java
@@ -64,10 +64,19 @@ public class Parser {
      * List of keywords disallowed as identifiers
      */
     private static final HashSet<String> KEYWORDS = new HashSet<>(){{
+            add("bool");
             add("break");
+            add("byte");
             add("continue");
             add("else");
+            add("f32");
+            add("f64");
             add("false");
+            add("flt");
+            add("i16");
+            add("i32");
+            add("i64");
+            add("i8");
             add("if");
             add("int");
             add("new");
@@ -75,6 +84,10 @@ public class Parser {
             add("return");
             add("struct");
             add("true");
+            add("u1");
+            add("u16");
+            add("u32");
+            add("u8");
             add("while");
         }};
 
@@ -96,7 +109,20 @@ public class Parser {
         Node.reset();
         IterPeeps.reset();
         TYPES.clear();
-        TYPES.put("int",TypeInteger.BOT);
+        TYPES.put("bool",TypeInteger.U1 );
+        TYPES.put("byte",TypeInteger.U8 );
+        TYPES.put("f32" ,TypeFloat  .B32);
+        TYPES.put("f64" ,TypeFloat  .BOT);
+        TYPES.put("flt" ,TypeFloat  .BOT);
+        TYPES.put("i16" ,TypeInteger.I16);
+        TYPES.put("i32" ,TypeInteger.I32);
+        TYPES.put("i64" ,TypeInteger.BOT);
+        TYPES.put("i8"  ,TypeInteger.I8 );
+        TYPES.put("int" ,TypeInteger.BOT);
+        TYPES.put("u1"  ,TypeInteger.U1 );
+        TYPES.put("u16" ,TypeInteger.U16);
+        TYPES.put("u32" ,TypeInteger.U32);
+        TYPES.put("u8"  ,TypeInteger.U8 );
         SCHEDULED = false;
         _lexer = new Lexer(source);
         _scope = new ScopeNode();
@@ -200,7 +226,7 @@ public class Parser {
      * Only allowed in top level scope.
      * Structs cannot be redefined.
      *
-     * @return null
+     * @return The statement following the struct
      */
     private Node parseStruct() {
         if (_xScopes.size() > 1) throw errorSyntax("struct declarations can only appear in top level scope");
@@ -220,7 +246,7 @@ public class Parser {
         TYPES.put(typeName, ts); // Insert the struct name in the collection of all struct names
         _aliases.put(typeName,_alias);
         _alias += ts._fields.length;
-        return null;
+        return parseStatement();
     }
 
     /**
@@ -435,6 +461,11 @@ public class Parser {
                 throw error("Undefined name '" + name + "'");
             t = _scope.lookupDeclaredType(name);
         }
+        // Auto-widen int to float
+        if( expr._type instanceof TypeInteger && t instanceof TypeFloat )
+            expr = new ToFloatNode(expr).peephole();
+        // Auto-narrow wide ints to narrow ints
+        expr = zsMask(expr,t);
         // Auto-deepen forward ref types
         Type e = expr._type;
         if( e instanceof TypeMemPtr tmp && tmp._obj._fields==null )
@@ -476,7 +507,29 @@ public class Parser {
      * </pre>
      * @return an expression {@link Node}, never {@code null}
      */
-    private Node parseExpression() { return parseComparison(); }
+    private Node parseExpression() { return parseBitwise(); }
+
+    /**
+     * Parse an bitwise expression
+     *
+     * <pre>
+     *     bitwise : compareExpr (('&' | '|' | '^') compareExpr)*
+     * </pre>
+     * @return a bitwise expression {@link Node}, never {@code null}
+     */
+    private Node parseBitwise() {
+        Node lhs = parseComparison();
+        while( true ) {
+            if( false ) ;
+            else if( match("&") ) lhs = new AndNode(lhs,null);
+            else if( match("|") ) lhs = new  OrNode(lhs,null);
+            else if( match("^") ) lhs = new XorNode(lhs,null);
+            else break;
+            lhs.setDef(2,parseComparison());
+            lhs = lhs.peephole();
+        }
+        return lhs;
+    }
 
     /**
      * Parse an expression of the form:
@@ -487,7 +540,7 @@ public class Parser {
      * @return an comparator expression {@link Node}, never {@code null}
      */
     private Node parseComparison() {
-        var lhs = parseAddition();
+        var lhs = parseShift();
         while( true ) {
             int idx=0;  boolean negate=false;
             // Test for any local nodes made, and "keep" lhs during peepholes
@@ -500,8 +553,8 @@ public class Parser {
             else if( match(">" ) ) { idx=1;  lhs = new BoolNode.LT(null, lhs); }
             else break;
             // Peepholes can fire, but lhs is already "hooked", kept alive
-            lhs.setDef(idx,parseAddition());
-            lhs = lhs.peephole();
+            lhs.setDef(idx,parseShift());
+            lhs = lhs.widen().peephole();
             if( negate )        // Extra negate for !=
                 lhs = new NotNode(lhs).peephole();
         }
@@ -512,6 +565,28 @@ public class Parser {
      * Parse an additive expression
      *
      * <pre>
+     *     shiftExpr : additiveExpr (('<<' | '>>' | '>>>') additiveExpr)*
+     * </pre>
+     * @return a shift expression {@link Node}, never {@code null}
+     */
+    private Node parseShift() {
+        Node lhs = parseAddition();
+        while( true ) {
+            if( false ) ;
+            else if( match("<<") ) lhs = new ShlNode(lhs,null);
+            else if( match(">>>")) lhs = new ShrNode(lhs,null);
+            else if( match(">>") ) lhs = new SarNode(lhs,null);
+            else break;
+            lhs.setDef(2,parseAddition());
+            lhs = lhs.widen().peephole();
+        }
+        return lhs;
+    }
+
+    /**
+     * Parse an additive expression
+     *
+     * <pre>
      *     additiveExpr : multiplicativeExpr (('+' | '-') multiplicativeExpr)*
      * </pre>
      * @return an add expression {@link Node}, never {@code null}
@@ -524,7 +599,7 @@ 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;
     }
@@ -545,7 +620,7 @@ public class Parser {
             else if( match("/") ) lhs = new DivNode(lhs,null);
             else break;
             lhs.setDef(2,parseUnary());
-            lhs = lhs.peephole();
+            lhs = lhs.widen().peephole();
         }
         return lhs;
     }
@@ -559,7 +634,7 @@ 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());
     }
@@ -644,6 +719,8 @@ public class Parser {
             else {
                 Node val = parseExpression();
                 Type glb = base._fields[idx]._type;
+                // Auto-truncate when storing to narrow fields
+                val = zsMask(val,glb);
                 store(name,alias,glb,expr,val,false);
                 return expr;        // "obj.a = expr" returns the expression while updating memory
             }
@@ -653,11 +730,34 @@ public class Parser {
         return parsePostfix(new LoadNode(name, alias, declaredType.glb(), mem(), expr).peephole());
     }
 
+    // zero/sign extend.  "i" is limited to either classic unsigned (min==0) or
+    // classic signed (min=minus-power-of-2); max=power-of-2-minus-1.
+    private Node zsMask(Node val, Type t ) {
+        if( val._type instanceof TypeFloat && t instanceof TypeInteger )
+            val = new ToIntegerNode(val).peephole();
+        if( !(val._type instanceof TypeInteger tval && t instanceof TypeInteger t0 && !tval.isa(t0)) ) {
+            if( !(val._type instanceof TypeFloat tval && t instanceof TypeFloat t0 && !tval.isa(t0)) )
+                return val;
+            // Float rounding
+            return new RoundF32Node(val).peephole();
+        }
+        if( t0._min==0 )        // Unsigned
+            return new AndNode(val,new ConstantNode(TypeInteger.constant(t0._max)).peephole()).peephole();
+        // Signed extension
+        int shift = Long.numberOfLeadingZeros(t0._max)-1;
+        Node shf = new ConstantNode(TypeInteger.constant(shift)).peephole();
+        if( shf._type==TypeInteger.ZERO )
+            return val;
+        return new SarNode(new ShlNode(val,shf.keep()).peephole(),shf.unkeep()).peephole();
+    }
+
+
     /**
      * Parse integer literal
      *
      * <pre>
      *     integerLiteral: [1-9][0-9]* | [0]
+     *     floatLiteral: [digits].[digits]?[e [digits]]?
      * </pre>
      */
     private ConstantNode parseLiteral() {
@@ -815,19 +915,37 @@ 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..fd713156
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/AddFNode.java
@@ -0,0 +1,37 @@
+package com.seaofnodes.simple.node;
+
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeFloat;
+
+
+public class AddFNode extends Node {
+    public AddFNode(Node lhs, Node rhs) { super(null, lhs, rhs); }
+
+    @Override public String label() { return "AddF"; }
+
+    @Override protected String format() { return "(%1+%2)"; }
+
+    @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 eb7e2793..0046bd03 100644
--- a/src/main/java/com/seaofnodes/simple/node/AddNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/AddNode.java
@@ -15,17 +15,23 @@ public class AddNode extends Node {
     @Override
     public Type compute() {
         Type t1 = in(1)._type, t2 = in(2)._type;
-        if( t1==Type.TOP || t1==TypeInteger.TOP ||
-            t2==Type.TOP || t2==TypeInteger.TOP )
-            return TypeInteger.TOP;
-        if( t1 instanceof TypeInteger i0 &&
-            t2 instanceof TypeInteger i1 ) {
-            if (i0.isConstant() && i1.isConstant())
-                return TypeInteger.constant(i0.value()+i1.value());
+        if( t1.isHigh() || t2.isHigh() ) return TypeInteger.TOP;
+        if( t1 instanceof TypeInteger i1 &&
+            t2 instanceof TypeInteger i2 ) {
+            if (i1.isConstant() && i2.isConstant())
+                return TypeInteger.constant(i1.value()+i2.value());
+            // Fold ranges like {0-1} + {2-3} into {2-4}.
+            if( !overflow(i1._min,i2._min) &&
+                !overflow(i1._max,i2._max) )
+                return TypeInteger.make(i1._min+i2._min,i1._max+i2._max);
         }
         return TypeInteger.BOT;
     }
 
+    private static boolean overflow( long x, long y ) {
+        if(    (x ^      y ) < 0 ) return false; // unequal signs, never overflow
+        return (x ^ (x + y)) < 0; // sum has unequal signs, so overflow
+    }
     @Override
     public Node idealize () {
         Node lhs = in(1);
@@ -34,7 +40,7 @@ public class AddNode extends Node {
 
         // 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 )
+        if( t2 instanceof TypeInteger i && i.isConstant() && i.value()==0 && lhs._type instanceof TypeInteger )
             return lhs;
 
         // Add of same to a multiply by 2
@@ -97,7 +103,7 @@ public class AddNode extends Node {
         return null;
     }
 
-    // Rotation is only valid for associative ops, e.g. Add, Mul, And, Or.
+    // Rotation is only valid for associative ops, e.g. Add, Mul, And, Or, Xor.
     // Do we have ((phi cons)|(x + (phi cons)) + con|(phi cons)) ?
     // Push constant up through the phi: x + (phi con0+con0 con1+con1...)
     static Node phiCon(Node op, boolean rotate) {
@@ -169,6 +175,7 @@ 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); }
     @Override public String err() {
         if( !(in(1)._type instanceof TypeInteger) ) return "Cannot '"+label()+"' " + in(1)._type;
         if( !(in(2)._type instanceof TypeInteger) ) return "Cannot '"+label()+"' " + in(2)._type;
diff --git a/src/main/java/com/seaofnodes/simple/node/AndNode.java b/src/main/java/com/seaofnodes/simple/node/AndNode.java
new file mode 100644
index 00000000..e2729e60
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/AndNode.java
@@ -0,0 +1,59 @@
+package com.seaofnodes.simple.node;
+
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeInteger;
+
+
+public class AndNode extends Node {
+    public AndNode(Node lhs, Node rhs) { super(null, lhs, rhs); }
+
+    @Override public String label() { return "And"; }
+
+    @Override protected String format() { return "(%1&%2)"; }
+
+    @Override
+    public Type compute() {
+        if( in(1)._type.isHigh() || in(2)._type.isHigh() )  return TypeInteger.TOP;
+        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());
+            // Sharpen allowed bits if either value is narrowed
+            long mask = i0.mask() & i1.mask();
+            return mask < 0 ? TypeInteger.BOT : TypeInteger.make(0,mask);
+        }
+        return TypeInteger.BOT;
+    }
+
+    @Override
+    public Node idealize() {
+        Node lhs = in(1);
+        Node rhs = in(2);
+        Type t1 = lhs._type;
+        Type t2 = rhs._type;
+
+        // And 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 && lhs._type instanceof TypeInteger )
+            return lhs;
+
+        // Move constants to RHS: con*arg becomes arg*con
+        if ( t1.isConstant() && !t2.isConstant() )
+            return swap12();
+
+        // Do we have ((x & (phi cons)) & con) ?
+        // Do we have ((x & (phi cons)) & (phi cons)) ?
+        // Push constant up through the phi: x & (phi con0&con0 con1&con1...)
+        Node phicon = AddNode.phiCon(this,true);
+        if( phicon!=null ) return phicon;
+
+        return null;
+    }
+    @Override Node copy(Node lhs, Node rhs) { return new AndNode(lhs,rhs); }
+    @Override String err() {
+        if( !(in(1)._type instanceof TypeInteger) ) return "Cannot '&' " + in(1)._type;
+        if( !(in(2)._type instanceof TypeInteger) ) return "Cannot '&' " + in(2)._type;
+        return null;
+    }
+}
diff --git a/src/main/java/com/seaofnodes/simple/node/BoolNode.java b/src/main/java/com/seaofnodes/simple/node/BoolNode.java
index 63452dba..8a25e8d9 100644
--- a/src/main/java/com/seaofnodes/simple/node/BoolNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/BoolNode.java
@@ -2,10 +2,14 @@ package com.seaofnodes.simple.node;
 
 import com.seaofnodes.print.ExprPrinter;
 
+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 static com.seaofnodes.simple.type.TypeInteger.*;
 
 abstract public class BoolNode extends Node {
 
@@ -23,52 +27,84 @@ abstract public class BoolNode extends Node {
     }
 
     @Override
-    public Type compute() {
-        Type t1 = in(1)._type, t2 = in(2)._type;
-        if( t1==Type.TOP || t1==TypeInteger.TOP ||
-            t2==Type.TOP || t2==TypeInteger.TOP )
-            return TypeInteger.TOP;
-        if( t1 instanceof TypeInteger i0 &&
-            t2 instanceof TypeInteger i1 ) {
-            if (i0.isConstant() && i1.isConstant())
-                return TypeInteger.constant(doOp(i0.value(), i1.value()) ? 1 : 0);
-        }
-        return TypeInteger.BOT;
+    public TypeInteger compute() {
+        Type t1 = in(1)._type;
+        Type t2 = in(2)._type;
+        if( t1.isHigh() || t2.isHigh() )
+            return BOOL.dual();
+        // Compare of same
+        if( in(1)==in(2) )
+            return doOp(ZERO,ZERO);
+        if( t1 instanceof TypeInteger i1 &&
+            t2 instanceof TypeInteger i2 )
+            return doOp(i1,i2);
+        if( t1 instanceof TypeFloat f1 &&
+            t2 instanceof TypeFloat f2 &&
+            f1.isConstant() && f2.isConstant() )
+            return TypeInteger.constant(doOp(f1.value(), f2.value()) ? 1 : 0);
+        return BOOL;
     }
 
-    abstract boolean doOp(long lhs, long rhs);
+    TypeInteger doOp(TypeInteger t1, TypeInteger t2) { throw Utils.TODO(); }
+    boolean doOp(double lhs, double rhs) { throw Utils.TODO(); }
 
     @Override
     public Node idealize() {
-        // Compare of same
-        if( in(1)==in(2) )
-            return new ConstantNode(TypeInteger.constant(doOp(3,3)?1:0));
-
         // Equals pushes constant to the right; 5==X becomes X==5.
         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) )
+            if( (in(2)._type == ZERO || in(2)._type == TypeMemPtr.NULLPTR) )
                 return new NotNode(in(1));
+            // Equals bool == 1 becomes bool
+            if( in(2)._type == TRUE && in(1)._type == BOOL )
+                return in(1);
         }
 
-        // Do we have ((phi cons) cmp con) ?
-        // Do we have ((phi cons) cmp (phi cons)) ?
-        // Push the compare up through the phi: (phi con0 cmp con, con1 cmp con...)
-        Node phicon = AddNode.phiCon(this,this instanceof EQ);
-        if( phicon!=null ) return phicon;
-
         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 "=="; }
+        TypeInteger doOp(TypeInteger i1, TypeInteger i2) {
+            if( i1==i2 && i1.isConstant() ) return TRUE;
+            if( i1._max < i2._min || i1._min > i2._max ) return FALSE;
+            return BOOL;
+        }
+        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 "<" ; }
+        TypeInteger doOp(TypeInteger i1, TypeInteger i2) {
+            if( i1._max <  i2._min ) return TRUE;
+            if( i1._min >= i2._max ) return FALSE;
+            return BOOL;
+        }
+        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 "<="; }
+        TypeInteger doOp(TypeInteger i1, TypeInteger i2) {
+            if( i1._max <= i2._min ) return TRUE;
+            if( i1._min >  i2._max ) return FALSE;
+            return BOOL;
+        }
+        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 copy(Node lhs, Node rhs) { return new EQF(lhs,rhs); } }
+    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 copy(Node lhs, Node rhs) { return new LTF(lhs,rhs); } }
+    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 copy(Node lhs, Node rhs) { return new LEF(lhs,rhs); } }
+
 }
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..a3f4318d
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/DivFNode.java
@@ -0,0 +1,39 @@
+package com.seaofnodes.simple.node;
+
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeFloat;
+
+
+public class DivFNode extends Node {
+    public DivFNode(Node lhs, Node rhs) { super(null, lhs, rhs); }
+
+    @Override public String label() { return "DivF"; }
+
+    @Override protected String format() { return "(%1/%2)"; }
+
+    @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 d7244ace..e725ace4 100644
--- a/src/main/java/com/seaofnodes/simple/node/DivNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/DivNode.java
@@ -15,15 +15,14 @@ public class DivNode extends Node {
     @Override
     public Type compute() {
         Type t1 = in(1)._type, t2 = in(2)._type;
-        if( t1==Type.TOP || t1==TypeInteger.TOP ||
-            t2==Type.TOP || t2==TypeInteger.TOP )
+        if( t1.isHigh() || t2.isHigh() )
             return TypeInteger.TOP;
-        if (t1 instanceof TypeInteger i0 &&
-            t2 instanceof TypeInteger i1) {
-            if (i0.isConstant() && i1.isConstant())
-                return i1.value() == 0
+        if( t1 instanceof TypeInteger i1 &&
+            t2 instanceof TypeInteger i2 ) {
+            if (i1.isConstant() && i2.isConstant())
+                return i2.value() == 0
                     ? TypeInteger.ZERO
-                    : TypeInteger.constant(i0.value()/i1.value());
+                    : TypeInteger.constant(i1.value()/i2.value());
         }
         return TypeInteger.BOT;
     }
@@ -31,10 +30,11 @@ public class DivNode extends Node {
     @Override
     public Node idealize() {
         // Div of 1.
-        if( in(2)._type.isConstant() && in(2)._type instanceof TypeInteger i && i.value()==1 )
+        if( in(2)._type.isConstant() && in(2)._type instanceof TypeInteger i && i.value()==1 && in(1)._type instanceof TypeInteger )
             return in(1);
         return null;
     }
 
     @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 277644f5..3191061c 100644
--- a/src/main/java/com/seaofnodes/simple/node/LoadNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/LoadNode.java
@@ -96,4 +96,8 @@ public class LoadNode extends MemOpNode {
         Node px = phi.in(idx);
         return px!=null && px.addDep(this) instanceof StoreNode st1 && ptr()==st1.ptr() && _alias==st1._alias;
     }
+
+    Node copy(Node mem, Node ptr) {
+        return new LoadNode(_name,_alias,_declaredType,mem,ptr);
+    }
 }
diff --git a/src/main/java/com/seaofnodes/simple/node/MemOpNode.java b/src/main/java/com/seaofnodes/simple/node/MemOpNode.java
index 7c6afb0c..29d302cb 100644
--- a/src/main/java/com/seaofnodes/simple/node/MemOpNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/MemOpNode.java
@@ -14,7 +14,7 @@ public abstract class MemOpNode extends Node {
     public final Type _declaredType;
 
 
-    public MemOpNode(String name, int alias, Type glb, Node... nodes ) {
+    public MemOpNode(String name, int alias, Type glb, Node...  nodes) {
         super(nodes);
         _name  = name;
         _alias = alias;
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..1b45c7c5
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/MinusFNode.java
@@ -0,0 +1,30 @@
+package com.seaofnodes.simple.node;
+
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeFloat;
+
+
+public class MinusFNode extends Node {
+    public MinusFNode(Node in) { super(null, in); }
+
+    @Override public String label() { return "MinusF"; }
+
+    @Override protected String format() { return "(-%1)"; }
+
+    @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 5b65b3fb..f56c423e 100644
--- a/src/main/java/com/seaofnodes/simple/node/MinusNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/MinusNode.java
@@ -14,9 +14,13 @@ public class MinusNode extends Node {
 
     @Override
     public Type compute() {
-        if (in(1)._type instanceof TypeInteger i0)
-            return i0.isConstant() ? TypeInteger.constant(-i0.value()) : i0;
-        return in(1)._type==Type.TOP ? TypeInteger.TOP : TypeInteger.BOT;
+        if( in(1)._type instanceof TypeInteger i0 ) {
+            if( i0.isHigh() ) return TypeInteger.TOP;
+            // Catch overflow wrapping on `-Long.MIN_VALUE`
+            if( i0 == TypeInteger.BOT || i0._min == Long.MIN_VALUE ) return TypeInteger.BOT;
+            return TypeInteger.make(-i0._max,-i0._min);
+        }
+        return in(1)._type.isHigh() ? TypeInteger.TOP : TypeInteger.BOT;
     }
 
     @Override
@@ -27,4 +31,5 @@ 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..6a57f3c5
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/MulFNode.java
@@ -0,0 +1,44 @@
+package com.seaofnodes.simple.node;
+
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeFloat;
+
+
+public class MulFNode extends Node {
+    public MulFNode(Node lhs, Node rhs) { super(null, lhs, rhs); }
+
+    @Override public String label() { return "MulF"; }
+
+    @Override protected String format() { return "(%1*%2)"; }
+
+    @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 b0359a52..c16edb4b 100644
--- a/src/main/java/com/seaofnodes/simple/node/MulNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/MulNode.java
@@ -15,13 +15,12 @@ public class MulNode extends Node {
     @Override
     public Type compute() {
         Type t1 = in(1)._type, t2 = in(2)._type;
-        if( t1==Type.TOP || t1==TypeInteger.TOP ||
-            t2==Type.TOP || t2==TypeInteger.TOP )
+        if( t1.isHigh() || t2.isHigh() )
             return TypeInteger.TOP;
-        if (t1 instanceof TypeInteger i0 &&
-            t2 instanceof TypeInteger i1) {
-            if (i0.isConstant() && i1.isConstant())
-                return TypeInteger.constant(i0.value()*i1.value());
+        if( t1 instanceof TypeInteger i1 &&
+            t2 instanceof TypeInteger i2 ) {
+            if (i1.isConstant() && i2.isConstant())
+                return TypeInteger.constant(i1.value()*i2.value());
         }
         return TypeInteger.BOT;
     }
@@ -35,7 +34,7 @@ public class MulNode extends Node {
 
         // 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 )
+        if ( t2.isConstant() && t2 instanceof TypeInteger i && i.value()==1 && lhs._type instanceof TypeInteger )
             return lhs;
 
         // Move constants to RHS: con*arg becomes arg*con
@@ -51,6 +50,7 @@ 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); }
     @Override public String err() {
         if( !(in(1)._type instanceof TypeInteger) ) return "Cannot '"+label()+"' " + in(1)._type;
         if( !(in(2)._type instanceof TypeInteger) ) return "Cannot '"+label()+"' " + in(2)._type;
diff --git a/src/main/java/com/seaofnodes/simple/node/Node.java b/src/main/java/com/seaofnodes/simple/node/Node.java
index 2c8596fa..4ee82187 100644
--- a/src/main/java/com/seaofnodes/simple/node/Node.java
+++ b/src/main/java/com/seaofnodes/simple/node/Node.java
@@ -8,6 +8,7 @@ import com.seaofnodes.simple.IRPrinter;
 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;
@@ -496,6 +497,26 @@ public abstract class Node extends BaseNode<Node> implements OutNode, Cloneable
     /** Return block start from a isCFG() */
     public Node getBlockStart() { return null; }
 
+    // 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
 
@@ -572,7 +593,12 @@ public abstract class Node extends BaseNode<Node> implements OutNode, Cloneable
         E x = pred.apply(this);
         if( x != null ) return x;
         for( Node def : _inputs  )  if( def != null && (x = def._walk(pred)) != null ) return x;
-        for( Node use : _outputs )  if( use != null && (x = use._walk(pred)) != null ) return x;
+        // Unroll iterator to survive junk CME
+        for( int i=0; i<_outputs.size(); i++ ) {
+            Node use = _outputs.get(i);
+            if( use != null && (x = use._walk(pred)) != null )
+                return x;
+        }
         return null;
     }
 
diff --git a/src/main/java/com/seaofnodes/simple/node/NotNode.java b/src/main/java/com/seaofnodes/simple/node/NotNode.java
index 5e556390..2e89f013 100644
--- a/src/main/java/com/seaofnodes/simple/node/NotNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/NotNode.java
@@ -14,9 +14,11 @@ public class NotNode extends Node {
     @Override
     public Type compute() {
         Type t0 = in(1)._type;
+        if( t0.isHigh() ) return TypeInteger.BOOL.dual();
         switch( t0 ) {
-        case TypeInteger i0:
-            return i0.isConstant() ? TypeInteger.constant(i0.value()==0 ? 1 : 0) : i0;
+        case TypeInteger i0:  return i0._max < 0 || i0._min > 0 ? TypeInteger.FALSE : (i0==TypeInteger.ZERO ? TypeInteger.TRUE : TypeInteger.BOT);
+        case TypeFloat   i0:
+            return i0.isConstant() ? TypeInteger.constant(i0.value()==0 ? 1 : 0) : TypeInteger.BOT;
         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/OrNode.java b/src/main/java/com/seaofnodes/simple/node/OrNode.java
new file mode 100644
index 00000000..67585423
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/OrNode.java
@@ -0,0 +1,56 @@
+package com.seaofnodes.simple.node;
+
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeInteger;
+
+
+public class OrNode extends Node {
+    public OrNode(Node lhs, Node rhs) { super(null, lhs, rhs); }
+
+    @Override public String label() { return "Or"; }
+
+    @Override protected String format() { return "(%1|%2)"; }
+
+    @Override
+    public Type compute() {
+        if( in(1)._type.isHigh() || in(2)._type.isHigh() )  return TypeInteger.TOP;
+        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 TypeInteger.BOT;
+    }
+
+    @Override
+    public Node idealize() {
+        Node lhs = in(1);
+        Node rhs = in(2);
+        Type t1 = lhs._type;
+        Type t2 = rhs._type;
+
+        // Or of 0.  We do not check for (0|x) because this will already
+        // canonicalize to (x|0)
+        if( t2.isConstant() && t2 instanceof TypeInteger i && i.value()==0 && lhs._type instanceof TypeInteger )
+            return lhs;
+
+        // Move constants to RHS: con*arg becomes arg*con
+        if ( t1.isConstant() && !t2.isConstant() )
+            return swap12();
+
+        // Do we have ((x | (phi cons)) | con) ?
+        // Do we have ((x | (phi cons)) | (phi cons)) ?
+        // Push constant up through the phi: x | (phi con0|con0 con1|con1...)
+        Node phicon = AddNode.phiCon(this,true);
+        if( phicon!=null ) return phicon;
+
+        return null;
+    }
+    @Override Node copy(Node lhs, Node rhs) { return new OrNode(lhs,rhs); }
+    @Override String err() {
+        if( !(in(1)._type instanceof TypeInteger) ) return "Cannot '|' " + in(1)._type;
+        if( !(in(2)._type instanceof TypeInteger) ) return "Cannot '|' " + in(2)._type;
+        return null;
+    }
+}
diff --git a/src/main/java/com/seaofnodes/simple/node/PhiNode.java b/src/main/java/com/seaofnodes/simple/node/PhiNode.java
index 8dfa04cf..309cd8b5 100644
--- a/src/main/java/com/seaofnodes/simple/node/PhiNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/PhiNode.java
@@ -12,7 +12,7 @@ public class PhiNode extends Node {
     final String _label;
 
     // The Phi type we compute must stay within the domain of the Phi.
-    // Example Int stays Int, Ptr stays Ptr, Control stays Control, Mem stays Mem.
+    // Example Int stays Int, Ptr stays Ptr, Mem stays Mem.
     final Type _declaredType;
 
     public PhiNode(String label, Type declaredType, Node... inputs) { super(inputs); _label = label;  assert declaredType!=null; _declaredType = declaredType; }
diff --git a/src/main/java/com/seaofnodes/simple/node/RoundF32Node.java b/src/main/java/com/seaofnodes/simple/node/RoundF32Node.java
new file mode 100644
index 00000000..6be071a2
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/RoundF32Node.java
@@ -0,0 +1,34 @@
+package com.seaofnodes.simple.node;
+
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeFloat;
+
+
+public class RoundF32Node extends Node {
+    public RoundF32Node(Node lhs) { super(null, lhs); }
+
+    @Override public String label() { return "RoundF32"; }
+
+    @Override protected String format() { return "((f32)%1)"; }
+
+    @Override
+    public Type compute() {
+        if (in(1)._type instanceof TypeFloat i0 && i0.isConstant() )
+            return TypeFloat.constant((float)i0.value());
+        if( in(1)._type==TypeFloat.BOT ) return TypeFloat.B32;
+        return in(1)._type;
+    }
+
+    @Override
+    public Node idealize() {
+        Node lhs = in(1);
+        Type t1 = lhs._type;
+
+        // RoundF32 of float
+        if( t1 instanceof TypeFloat tf && tf._sz==32 )
+            return lhs;
+
+        return null;
+    }
+}
diff --git a/src/main/java/com/seaofnodes/simple/node/SarNode.java b/src/main/java/com/seaofnodes/simple/node/SarNode.java
new file mode 100644
index 00000000..6ab7141f
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/SarNode.java
@@ -0,0 +1,49 @@
+package com.seaofnodes.simple.node;
+
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeInteger;
+
+
+public class SarNode extends Node {
+    public SarNode(Node lhs, Node rhs) { super(null, lhs, rhs); }
+
+    @Override public String label() { return "Sar"; }
+
+    @Override protected String format() { return "(%1>>%2)"; }
+
+    @Override
+    public Type compute() {
+        if( in(1)._type.isHigh() || in(2)._type.isHigh() )  return TypeInteger.TOP;
+        if (in(1)._type instanceof TypeInteger i1 &&
+            in(2)._type instanceof TypeInteger i2) {
+            if( i1.isConstant() && i2.isConstant() )
+                return TypeInteger.constant(i1.value()>>i2.value());
+            if( i2._min < 0 || i2._max >= 64 )
+                return TypeInteger.BOT;
+            return TypeInteger.make(i1._min>>i2._min,i1._max>>i2._min);
+        }
+        return TypeInteger.BOT;
+    }
+
+    @Override
+    public Node idealize() {
+        Node lhs = in(1);
+        Node rhs = in(2);
+        Type t2 = rhs._type;
+
+        // Sar of 0.
+        if( t2.isConstant() && t2 instanceof TypeInteger i && (i.value()&63)==0 && lhs._type instanceof TypeInteger )
+            return lhs;
+
+        // TODO: x >> 3 >> (y ? 1 : 2) ==> x >> (y ? 4 : 5)
+
+        return null;
+    }
+    @Override Node copy(Node lhs, Node rhs) { return new SarNode(lhs,rhs); }
+    @Override String err() {
+        if( !(in(1)._type instanceof TypeInteger) ) return "Cannot '>>' " + in(1)._type;
+        if( !(in(2)._type instanceof TypeInteger) ) return "Cannot '>>' " + in(2)._type;
+        return null;
+    }
+}
diff --git a/src/main/java/com/seaofnodes/simple/node/ShlNode.java b/src/main/java/com/seaofnodes/simple/node/ShlNode.java
new file mode 100644
index 00000000..999fc7da
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/ShlNode.java
@@ -0,0 +1,46 @@
+package com.seaofnodes.simple.node;
+
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeInteger;
+
+
+public class ShlNode extends Node {
+    public ShlNode(Node lhs, Node rhs) { super(null, lhs, rhs); }
+
+    @Override public String label() { return "Shl"; }
+
+    @Override protected String format() { return "(%1<<%2)"; }
+
+    @Override
+    public Type compute() {
+        if( in(1)._type.isHigh() || in(2)._type.isHigh() )  return TypeInteger.TOP;
+        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 TypeInteger.BOT;
+    }
+
+    @Override
+    public Node idealize() {
+        Node lhs = in(1);
+        Node rhs = in(2);
+        Type t2 = rhs._type;
+
+        // Shl of 0.
+        if( t2.isConstant() && t2 instanceof TypeInteger i && (i.value()&63)==0 && lhs._type instanceof TypeInteger )
+            return lhs;
+
+        // TODO: x << 3 << (y ? 1 : 2) ==> x << (y ? 4 : 5)
+
+        return null;
+    }
+    @Override Node copy(Node lhs, Node rhs) { return new ShlNode(lhs,rhs); }
+    @Override String err() {
+        if( !(in(1)._type instanceof TypeInteger) ) return "Cannot '<<' " + in(1)._type;
+        if( !(in(2)._type instanceof TypeInteger) ) return "Cannot '<<' " + in(2)._type;
+        return null;
+    }
+}
diff --git a/src/main/java/com/seaofnodes/simple/node/ShrNode.java b/src/main/java/com/seaofnodes/simple/node/ShrNode.java
new file mode 100644
index 00000000..b89f5191
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/ShrNode.java
@@ -0,0 +1,49 @@
+package com.seaofnodes.simple.node;
+
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeInteger;
+
+
+public class ShrNode extends Node {
+    public ShrNode(Node lhs, Node rhs) { super(null, lhs, rhs); }
+
+    @Override public String label() { return "Shr"; }
+
+    @Override protected String format() { return "(%1>>>%2)"; }
+
+    @Override
+    public Type compute() {
+        if( in(1)._type.isHigh() || in(2)._type.isHigh() )  return TypeInteger.TOP;
+        if (in(1)._type instanceof TypeInteger i1 &&
+            in(2)._type instanceof TypeInteger i2) {
+            if( i1.isConstant() && i2.isConstant() )
+                return TypeInteger.constant(i1.value()>>>i2.value());
+            if( i2._min < 0 || i2._max >= 64 )
+                return TypeInteger.BOT;
+            // Zero shifting a negative makes a larger positive
+            // so get the endpoints correct.
+            long s1 = i1._min>>>i2._min;
+            long s2 = i1._max>>>i2._min;
+            boolean wrap = i1._min < 0 && i1._max >=0;
+            return TypeInteger.make(wrap ? 0 : Math.min(s1,s2),Math.max(s1,s2));
+        }
+        return TypeInteger.BOT;
+    }
+
+    @Override
+    public Node idealize() {
+        Node lhs = in(1);
+        Node rhs = in(2);
+        Type t2 = rhs._type;
+
+        // Shr of 0.
+        if( t2.isConstant() && t2 instanceof TypeInteger i && (i.value()&63)==0 && lhs._type instanceof TypeInteger )
+            return lhs;
+
+        // TODO: x >>> 3 >>> (y ? 1 : 2) ==> x >>> (y ? 4 : 5)
+
+        return null;
+    }
+    @Override Node copy(Node lhs, Node rhs) { return new ShrNode(lhs,rhs); }
+}
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..2d218a03
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/SubFNode.java
@@ -0,0 +1,37 @@
+package com.seaofnodes.simple.node;
+
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeFloat;
+
+
+public class SubFNode extends Node {
+    public SubFNode(Node lhs, Node rhs) { super(null, lhs, rhs); }
+
+    @Override public String label() { return "SubF"; }
+
+    @Override protected String format() { return "(%1-%2)"; }
+
+    @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 1589abe7..d5e54e73 100644
--- a/src/main/java/com/seaofnodes/simple/node/SubNode.java
+++ b/src/main/java/com/seaofnodes/simple/node/SubNode.java
@@ -15,18 +15,17 @@ public class SubNode extends Node {
 
     @Override
     public Type compute() {
-        Type t1 = in(1)._type, t2 = in(2)._type;
-        if( t1==Type.TOP || t1==TypeInteger.TOP ||
-            t2==Type.TOP || t2==TypeInteger.TOP )
-            return TypeInteger.TOP;
         // Sub of same is 0
         if( in(1)==in(2) )
             return TypeInteger.ZERO;
 
-        if (t1 instanceof TypeInteger i0 &&
-            t2 instanceof TypeInteger i1) {
-            if (i0.isConstant() && i1.isConstant())
-                return TypeInteger.constant(i0.value()-i1.value());
+        Type t1 = in(1)._type, t2 = in(2)._type;
+        if( t1.isHigh() || t2.isHigh() )
+            return TypeInteger.TOP;
+        if( t1 instanceof TypeInteger i1 &&
+            t2 instanceof TypeInteger i2 ) {
+            if (i1.isConstant() && i2.isConstant())
+                return TypeInteger.constant(i1.value()-i2.value());
         }
 
         return TypeInteger.BOT;
@@ -57,4 +56,5 @@ 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..26cf50e1
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/ToFloatNode.java
@@ -0,0 +1,25 @@
+package com.seaofnodes.simple.node;
+
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeFloat;
+import com.seaofnodes.simple.type.TypeInteger;
+
+
+public class ToFloatNode extends Node {
+    public ToFloatNode(Node lhs) { super(null, lhs); }
+
+    @Override public String label() { return "ToFloat"; }
+
+    @Override protected String format() { return "(flt)%1"; }
+
+    @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/node/ToIntegerNode.java b/src/main/java/com/seaofnodes/simple/node/ToIntegerNode.java
new file mode 100644
index 00000000..df740202
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/ToIntegerNode.java
@@ -0,0 +1,23 @@
+package com.seaofnodes.simple.node;
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeFloat;
+import com.seaofnodes.simple.type.TypeInteger;
+
+// Truncate toward zero, saturating overflow; NaN converts to zero.
+public class ToIntegerNode extends Node {
+    public ToIntegerNode(Node lhs) { super(null,lhs); }
+    @Override public String label() { return "ToInteger"; }
+    @Override protected String format() { return "(int)%1"; }
+
+    @Override public Type compute() {
+        Type t = in(1)._type;
+        if( t.isHigh() ) return TypeInteger.TOP;
+        if( t instanceof TypeFloat tf && tf.isConstant() )
+            return TypeInteger.constant((long)tf.value());
+        return TypeInteger.BOT;
+    }
+
+    @Override public Node idealize() { return null; }
+    @Override Node copy(Node lhs, Node rhs) { return new ToIntegerNode(lhs); }
+}
diff --git a/src/main/java/com/seaofnodes/simple/node/XorNode.java b/src/main/java/com/seaofnodes/simple/node/XorNode.java
new file mode 100644
index 00000000..720fb8e4
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/node/XorNode.java
@@ -0,0 +1,56 @@
+package com.seaofnodes.simple.node;
+
+
+import com.seaofnodes.simple.type.Type;
+import com.seaofnodes.simple.type.TypeInteger;
+
+
+public class XorNode extends Node {
+    public XorNode(Node lhs, Node rhs) { super(null, lhs, rhs); }
+
+    @Override public String label() { return "Xor"; }
+
+    @Override protected String format() { return "(%1^%2)"; }
+
+    @Override
+    public Type compute() {
+        if( in(1)._type.isHigh() || in(2)._type.isHigh() )  return TypeInteger.TOP;
+        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 TypeInteger.BOT;
+    }
+
+    @Override
+    public Node idealize() {
+        Node lhs = in(1);
+        Node rhs = in(2);
+        Type t1 = lhs._type;
+        Type t2 = rhs._type;
+
+        // Xor of 0.  We do not check for (0^x) because this will already
+        // canonicalize to (x^0)
+        if( t2.isConstant() && t2 instanceof TypeInteger i && i.value()==0 && lhs._type instanceof TypeInteger )
+            return lhs;
+
+        // Move constants to RHS: con*arg becomes arg*con
+        if ( t1.isConstant() && !t2.isConstant() )
+            return swap12();
+
+        // Do we have ((x ^ (phi cons)) ^ con) ?
+        // Do we have ((x ^ (phi cons)) ^ (phi cons)) ?
+        // Push constant up through the phi: x ^ (phi con0^con0 con1^con1...)
+        Node phicon = AddNode.phiCon(this,true);
+        if( phicon!=null ) return phicon;
+
+        return null;
+    }
+    @Override Node copy(Node lhs, Node rhs) { return new XorNode(lhs,rhs); }
+    @Override String err() {
+        if( !(in(1)._type instanceof TypeInteger) ) return "Cannot '^' " + in(1)._type;
+        if( !(in(2)._type instanceof TypeInteger) ) return "Cannot '^' " + in(2)._type;
+        return null;
+    }
+}
diff --git a/src/main/java/com/seaofnodes/simple/print/SimpleGraphAdapter.java b/src/main/java/com/seaofnodes/simple/print/SimpleGraphAdapter.java
index e65963db..26897a7c 100644
--- a/src/main/java/com/seaofnodes/simple/print/SimpleGraphAdapter.java
+++ b/src/main/java/com/seaofnodes/simple/print/SimpleGraphAdapter.java
@@ -6,7 +6,7 @@ import com.seaofnodes.simple.node.*;
 import com.seaofnodes.simple.node.Node;
 import com.seaofnodes.simple.type.TypeMem;
 
-/** Chapter 12's view of the IR; browser, transport and layout are shared. */
+/** Chapter 14's view of the IR; browser, transport and layout are shared. */
 public class SimpleGraphAdapter extends GraphAdapter<Node> {
 
     @Override protected String[] edgeNames(Node n) {
diff --git a/src/main/java/com/seaofnodes/simple/print/SimpleGraphObserver.java b/src/main/java/com/seaofnodes/simple/print/SimpleGraphObserver.java
index 3aabd79f..202aa9d9 100644
--- a/src/main/java/com/seaofnodes/simple/print/SimpleGraphObserver.java
+++ b/src/main/java/com/seaofnodes/simple/print/SimpleGraphObserver.java
@@ -7,7 +7,7 @@ import com.seaofnodes.simple.node.Node;
 import java.util.ArrayList;
 import java.io.IOException;
 
-/** Chapter 13's compilation context; capture and event bookkeeping are shared. */
+/** Chapter 14's compilation context; capture and event bookkeeping are shared. */
 public class SimpleGraphObserver extends GraphCapture<Node> {
     private Parser _parser;
     private Node _ret;
diff --git a/src/main/java/com/seaofnodes/simple/type/Type.java b/src/main/java/com/seaofnodes/simple/type/Type.java
index 93e27c76..49dc090a 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;
 
@@ -55,6 +56,7 @@ public class Type {
         ts.add(CONTROL);
         Field.gather(ts);
         TypeInteger.gather(ts);
+        TypeFloat.gather(ts);
         TypeMem.gather(ts);
         TypeMemPtr.gather(ts);
         TypeStruct.gather(ts);
@@ -66,6 +68,7 @@ public class Type {
     }
 
     // Is high or on the lattice centerline.
+    public boolean isHigh       () { return _type==TTOP || _type==TXCTRL; }
     public boolean isHighOrConst() { return _type==TTOP || _type==TXCTRL; }
 
     // Strict constant values, things on the lattice centerline.
@@ -81,14 +84,16 @@ public class Type {
 
     // ----------------------------------------------------------
 
-    // Notes on Type interning.
-    // At the moment it is not easy to reset the interned types
-    // because we hold static references to several types and these are scattered
-    // around. This means the INTERN cache will retain all types from
-    // every run of the Parser. For this to work correctly types must be
-    // rigorous about defining when they are the same. Also types need to be
-    // immutable once defined.
-    // The rationale for interning is performance.
+    // Notes on Type interning: At the moment it is not easy to reset the
+    // interned types because we hold static references to several types and
+    // these are scattered around.  This means the INTERN cache will retain all
+    // types from every run of the Parser.  For this to work correctly types
+    // must be rigorous about defining when they are the same.  Also types need
+    // to be immutable once defined.  The rationale for interning is
+    // *correctness* with cyclic type definitions.  Simple structural recursive
+    // checks go exponential with merely sharing, but with cycles they will
+    // stack overflow and crash.  Intering means we do not need to have sharing
+    // checks with every type compare, only during interning.
 
     // Factory method which interns "this"
     public  <T extends Type> T intern() {
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..975c1a9e
--- /dev/null
+++ b/src/main/java/com/seaofnodes/simple/type/TypeFloat.java
@@ -0,0 +1,114 @@
+package com.seaofnodes.simple.type;
+
+import java.util.ArrayList;
+
+/**
+ * Float Type
+ */
+public class TypeFloat extends Type {
+
+    public final static TypeFloat TOP = make((byte)-64, 0);
+    public final static TypeFloat T32 = make((byte)-32, 0);
+    public final static TypeFloat ZERO= make((byte)  0, 0);
+    public final static TypeFloat B32 = make((byte) 32, 0);
+    public final static TypeFloat BOT = make((byte) 64, 0);
+
+    /** +/-64 for double; +/-32 for float, or 0 for constants */
+    public final byte _sz;
+
+    /**
+     * The constant value or 0
+     */
+    public final double _con;
+
+    private TypeFloat(byte sz, double con) {
+        super(TFLT);
+        _sz  = sz ;
+        _con = con;
+    }
+    private static TypeFloat make(byte sz, double con) {
+        return new TypeFloat(sz,con).intern();
+    }
+
+    public static TypeFloat constant(double con) { return make((byte)0, con); }
+
+    public static void gather(ArrayList<Type> ts) { ts.add(ZERO); ts.add(BOT); ts.add(B32); ts.add(constant(3.141592653589793)); }
+
+    // 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==T32 ) return sb.append("F32Top");
+        if( this==B32 ) return sb.append("F32Bot");
+        if( this==BOT ) return sb.append("FltBot");
+        return sb.append(_con);
+    }
+
+    @Override public String str() {
+        if( this==TOP ) return "~flt";
+        if( this==T32 ) return "~f32";
+        if( this==B32 ) return  "f32";
+        if( this==BOT ) return  "flt";
+        return ""+_con+(isF32() ? "f" : "");
+    }
+
+    /**
+     * 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==T32 ) return sb.append("F32Top");
+        if( this==B32 ) return sb.append("F32Bot");
+        if( this==BOT ) return sb.append("FltBot");
+        return sb.append(isF32() ? "F32" : "Flt");
+    }
+
+    boolean isF32() { return ((float)_con)==_con; }
+    @Override public boolean isHigh()        { return _sz< 0; }
+    @Override public boolean isHighOrConst() { return _sz<=0; }
+    @Override public boolean isConstant()    { return _sz==0; }
+
+    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
+        // Larger size in i1, smaller in i0
+        TypeFloat i0 = _sz < i._sz ? this : i;
+        TypeFloat i1 = _sz < i._sz ? i : this;
+
+        if( i1._sz== 64 ) return BOT;
+        if( i0._sz==-64 ) return i1;
+        if( i1._sz== 32 )
+            return i0._sz==0 && !i0.isF32() ? BOT : B32;
+        if( i1._sz!=  0 ) return i1;
+        // i1 is a constant
+        if( i0._sz==-32 )
+            return i1.isF32() ? i1 : BOT;
+        // Since both are constants, and are never equals (contract) unequals
+        // constants fall to bottom
+        return i0.isF32() && i1.isF32() ? B32 : BOT;
+    }
+
+    @Override
+    public Type dual() {
+        if( _sz==0 ) return this; // Constants are a self-dual
+        return make((byte)-_sz,0);
+    }
+
+    @Override
+    public Type glb() { return BOT; }
+
+    @Override public TypeFloat makeInit() { return ZERO; }
+
+    @Override
+    int hash() { return (int)(Double.hashCode(_con) ^ _sz); }
+    @Override
+    public boolean eq( Type t ) {
+        TypeFloat i = (TypeFloat)t; // Contract
+        return _con==i._con && _sz==i._sz;
+    }
+}
diff --git a/src/main/java/com/seaofnodes/simple/type/TypeInteger.java b/src/main/java/com/seaofnodes/simple/type/TypeInteger.java
index 8c77672b..aca3e06b 100644
--- a/src/main/java/com/seaofnodes/simple/type/TypeInteger.java
+++ b/src/main/java/com/seaofnodes/simple/type/TypeInteger.java
@@ -9,42 +9,56 @@ public class TypeInteger extends Type {
 
     public final static TypeInteger TOP = make(false, 0);
     public final static TypeInteger BOT = make(false, 1);
-    public final static TypeInteger ZERO= make(true , 0);
-
-    public final boolean _is_con;
+    public final static TypeInteger ZERO= make(0,0);
+    public final static TypeInteger U1  = make(0,1);
+    public final static TypeInteger BOOL= U1;
+    public final static TypeInteger FALSE=ZERO;
+    public final static TypeInteger TRUE= make(1,1);
+    public final static TypeInteger I8  = make(-128,127);
+    public final static TypeInteger I16 = make(-32768,32767);
+    public final static TypeInteger I32 = make(-1L<<31,(1L<<31)-1);
+
+    public final static TypeInteger U8  = make(0,255);
+    public final static TypeInteger U16 = make(0,65535);
+    public final static TypeInteger U32 = make(0,(1L<<32)-1);
 
     /**
-     * The constant value or
-     * if not constant then 1=bottom, 0=top.
+     * Describes an integer *range* - everything from min to max; both min and
+     * max are inclusive.  If min==max, this is a constant.
+     *
+     * If min <= max, this is a  below center (towards bottom).
+     * If min >  max, this is an above center (towards top).
      */
-    public final long _con;
+    public final long _min, _max;
 
-    private TypeInteger(boolean is_con, long con) {
-        super(TINT);
-        _is_con = is_con;
-        _con = con;
-    }
+    private TypeInteger(long min, long max) { super(TINT); _min = min; _max = max; }
+    public static TypeInteger make(long lo, long hi) {  return new TypeInteger(lo,hi).intern();  }
     public static TypeInteger make(boolean is_con, long con) {
-        return new TypeInteger(is_con,con).intern();
+        return make(is_con ? con : (con==0 ? Long.MAX_VALUE : Long.MIN_VALUE),
+                    is_con ? con : (con==0 ? Long.MIN_VALUE : Long.MAX_VALUE));
     }
 
     public static TypeInteger constant(long con) { return make(true, con); }
 
-    public static void gather(ArrayList<Type> ts) { ts.add(ZERO); ts.add(BOT); }
+    public static void gather(ArrayList<Type> ts) { ts.add(ZERO); ts.add(BOT); ts.add(U1); ts.add(U8); }
 
     // 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("IntTop");
-        if( this==BOT ) return sb.append("IntBot");
-        return sb.append(_con);
-    }
+    public StringBuilder print(StringBuilder sb) { return sb.append(str()); }
 
     @Override public String str() {
         if( this==TOP ) return "~int";
         if( this==BOT ) return  "int";
-        return ""+_con;
+        if( this==BOOL) return ("bool");
+        if( this==I8  ) return ("i8");
+        if( this==I16 ) return ("i16");
+        if( this==I32 ) return ("i32");
+        if( this==U8  ) return ("u8");
+        if( this==U16 ) return ("u16");
+        if( this==U32 ) return ("u32");
+        if( isConstant() ) return ""+_min;
+        return "["+_min+"-"+_max+"]";
     }
 
     /**
@@ -57,45 +71,45 @@ public class TypeInteger extends Type {
         return sb.append("Int");
     }
 
-    @Override
-    public boolean isHighOrConst() { return _is_con || _con==0; }
-
-    @Override
-    public boolean isConstant() { return _is_con; }
-
-    public long value() { return _con; }
+    @Override public boolean isHigh       () { return _min >  _max; }
+    @Override public boolean isHighOrConst() { return _min >= _max; }
+    @Override public boolean isConstant   () { return _min == _max; }
+
+    public long value() { assert isConstant(); return _min; }
+
+    // AND-mask of forced zeros.  e.g. unsigned types will return their mask;
+    // u8 will return 0xFF.  But also a range of 16-18 (0x10-0x12) will return
+    // 0x13 - no value in the range {16,17,18} will allow bit 0x04 to be set.
+    public long mask() {
+        if( isHigh() ) return 0;
+        if( isConstant() ) return _min;
+        //if( _min<0 ) return -1L;
+        //if( _max==Long.MAX_VALUE ) return -1L;
+        // Those bit positions which differ min to max
+        long x = _min ^ _max;
+        // Highest '1' bit in the differ set.  Since the range is from min to
+        // max, all values below here are possible.
+        long ff1 = Long.highestOneBit(x);
+        // Make a all-1's mask from ff1, and set over the same bits (either min
+        // or max is ok).
+        long mask = _min | (ff1-1) | ff1;
+        return mask;
+    }
 
     @Override
     public Type xmeet(Type other) {
         // Invariant from caller: 'this' != 'other' and same class (TypeInteger)
         TypeInteger i = (TypeInteger)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;
+        return make(Math.min(_min,i._min), Math.max(_max,i._max));
     }
 
-    @Override
-    public Type glb() { return BOT; }
-
+    @Override public TypeInteger dual() { return make(_max,_min); }
+    @Override public Type glb() { return BOT; }
     @Override public TypeInteger makeInit() { return ZERO; }
-
-    @Override
-    int hash() { return (int)(_con ^ (_is_con ? 0 : 0x4000)); }
+    @Override int hash() { return (int)((_min ^ (_min>>32)) *(_max ^ (_max>>32))); }
     @Override
     public boolean eq( Type t ) {
         TypeInteger i = (TypeInteger)t; // Contract
-        return _con==i._con && _is_con==i._is_con;
+        return _min==i._min && _max==i._max;
     }
 }
diff --git a/src/main/java/com/seaofnodes/simple/type/TypeMemPtr.java b/src/main/java/com/seaofnodes/simple/type/TypeMemPtr.java
index 5caa816d..e6e40fe2 100644
--- a/src/main/java/com/seaofnodes/simple/type/TypeMemPtr.java
+++ b/src/main/java/com/seaofnodes/simple/type/TypeMemPtr.java
@@ -55,6 +55,8 @@ public class TypeMemPtr extends Type {
     public Type glb() { return make(_obj.glb(),true); }
     @Override public TypeMemPtr makeInit() { return NULLPTR; }
 
+    @Override public boolean isHigh() { return this==TOP; }
+
     @Override
     int hash() { return _obj.hashCode() ^ (_nil ? 1024 : 0); }
 
diff --git a/src/main/java/com/seaofnodes/simple/type/TypeStruct.java b/src/main/java/com/seaofnodes/simple/type/TypeStruct.java
index 02de7cc8..8ad59a39 100644
--- a/src/main/java/com/seaofnodes/simple/type/TypeStruct.java
+++ b/src/main/java/com/seaofnodes/simple/type/TypeStruct.java
@@ -38,7 +38,7 @@ public class TypeStruct extends Type {
     private static final TypeStruct S1F = make("S1");
     private static final TypeStruct S2F = make("S2");
     public  static final TypeStruct S1  = make("S1", new Field[]{ Field.make("a", TypeInteger.BOT), Field.make("s2",TypeMemPtr.make(S2F,false)) });
-    private static final TypeStruct S2  = make("S2", new Field[]{ Field.make("b", TypeInteger.BOT), Field.make("s1",TypeMemPtr.make(S1F,false)) });
+    private static final TypeStruct S2  = make("S2", new Field[]{ Field.make("b", TypeFloat  .BOT), Field.make("s1",TypeMemPtr.make(S1F,false)) });
     public static void gather(ArrayList<Type> ts) { ts.add(TEST); ts.add(BOT); ts.add(S1); ts.add(S2); }
 
     public int find(String fname) {