Commit 6b0f7de247

Andrew Kelley <andrew@ziglang.org>
2020-04-29 03:04:18
ZIR: add cmp and condbr instructions
1 parent fb67a72
Changed files (7)
lib/std/math/big/int.zig
@@ -60,6 +60,13 @@ pub const Int = struct {
         return s;
     }
 
+    /// Hint: use `calcLimbLen` to figure out how big an array to allocate for `limbs`.
+    pub fn initSetFixed(limbs: []Limb, value: var) Int {
+        var s = Int.initFixed(limbs);
+        s.set(value) catch unreachable;
+        return s;
+    }
+
     /// Creates a new Int with a specific capacity. If capacity < default_capacity then the
     /// default capacity will be used instead.
     pub fn initCapacity(allocator: *Allocator, capacity: usize) !Int {
@@ -104,12 +111,11 @@ pub const Int = struct {
     /// Returns an Int backed by a fixed set of limb values.
     /// This is read-only and cannot be used as a result argument. If the Int tries to allocate
     /// memory a runtime panic will occur.
-    pub fn initFixed(limbs: []const Limb) Int {
+    pub fn initFixed(limbs: []Limb) Int {
         var self = Int{
             .allocator = null,
             .metadata = limbs.len,
-            // Cast away the const, invalid use to pass as a pointer argument.
-            .limbs = @intToPtr([*]Limb, @ptrToInt(limbs.ptr))[0..limbs.len],
+            .limbs = limbs,
         };
 
         self.normalize(limbs.len);
@@ -218,7 +224,7 @@ pub const Int = struct {
     /// one greater than the returned value.
     ///
     /// e.g. -127 returns 8 as it will fit in an i8. 127 returns 7 since it fits in a u7.
-    fn bitCountTwosComp(self: Int) usize {
+    pub fn bitCountTwosComp(self: Int) usize {
         var bits = self.bitCountAbs();
 
         // If the entire value has only one bit set (e.g. 0b100000000) then the negation in twos
@@ -267,7 +273,6 @@ pub const Int = struct {
 
     /// Sets an Int to value. Value must be an primitive integer type.
     pub fn set(self: *Int, value: var) Allocator.Error!void {
-        self.assertWritable();
         const T = @TypeOf(value);
 
         switch (@typeInfo(T)) {
@@ -598,6 +603,13 @@ pub const Int = struct {
         }
     }
 
+    /// Same as `cmp` but the right-hand operand is a primitive integer.
+    pub fn orderAgainstScalar(lhs: Int, scalar: var) math.Order {
+        var limbs: [calcLimbLen(scalar)]Limb = undefined;
+        const rhs = initSetFixed(&limbs, scalar);
+        return cmp(lhs, rhs);
+    }
+
     /// Returns true if a == 0.
     pub fn eqZero(a: Int) bool {
         return a.len() == 1 and a.limbs[0] == 0;
@@ -642,6 +654,33 @@ pub const Int = struct {
         };
     }
 
+    /// Returns the number of limbs needed to store `scalar`, which must be a
+    /// primitive integer value.
+    pub fn calcLimbLen(scalar: var) usize {
+        switch (@typeInfo(@TypeOf(scalar))) {
+            .Int => return @sizeOf(scalar) / @sizeOf(Limb),
+            .ComptimeInt => {
+                const w_value = if (scalar < 0) -scalar else scalar;
+                const req_limbs = @divFloor(math.log2(w_value), Limb.bit_count) + 1;
+                return req_limbs;
+            },
+            else => @compileError("parameter must be a primitive integer type"),
+        }
+    }
+
+    /// r = a + scalar
+    ///
+    /// r and a may be aliases.
+    /// scalar is a primitive integer type.
+    ///
+    /// Returns an error if memory could not be allocated.
+    pub fn addScalar(r: *Int, a: Int, scalar: var) Allocator.Error!void {
+        var limbs: [calcLimbLen(scalar)]Limb = undefined;
+        var operand = initFixed(&limbs);
+        operand.set(scalar) catch unreachable;
+        return add(r, a, operand);
+    }
+
     /// r = a + b
     ///
     /// r, a and b may be aliases.
lib/std/math.zig
@@ -986,6 +986,43 @@ pub const Order = enum {
 
     /// Greater than (`>`)
     gt,
+
+    pub fn invert(self: Order) Order {
+        return switch (self) {
+            .lt => .gt,
+            .eq => .eq,
+            .gt => .gt,
+        };
+    }
+
+    pub fn compare(self: Order, op: CompareOperator) bool {
+        return switch (self) {
+            .lt => switch (op) {
+                .lt => true,
+                .lte => true,
+                .eq => false,
+                .gte => false,
+                .gt => false,
+                .neq => true,
+            },
+            .eq => switch (op) {
+                .lt => false,
+                .lte => true,
+                .eq => true,
+                .gte => true,
+                .gt => false,
+                .neq => false,
+            },
+            .gt => switch (op) {
+                .lt => false,
+                .lte => false,
+                .eq => false,
+                .gte => true,
+                .gt => true,
+                .neq => true,
+            },
+        };
+    }
 };
 
 /// Given two numbers, this function returns the order they are with respect to each other.
src-self-hosted/ir/text.zig
@@ -34,6 +34,10 @@ pub const Inst = struct {
         bitcast,
         elemptr,
         add,
+        cmp,
+        condbr,
+        isnull,
+        isnonnull,
     };
 
     pub fn TagToType(tag: Tag) type {
@@ -54,6 +58,10 @@ pub const Inst = struct {
             .bitcast => BitCast,
             .elemptr => ElemPtr,
             .add => Add,
+            .cmp => Cmp,
+            .condbr => CondBr,
+            .isnull => IsNull,
+            .isnonnull => IsNonNull,
         };
     }
 
@@ -157,13 +165,9 @@ pub const Inst = struct {
 
         positionals: struct {
             fn_type: *Inst,
-            body: Body,
+            body: Module.Body,
         },
         kw_args: struct {},
-
-        pub const Body = struct {
-            instructions: []*Inst,
-        };
     };
 
     pub const Export = struct {
@@ -297,6 +301,50 @@ pub const Inst = struct {
         },
         kw_args: struct {},
     };
+
+    pub const Cmp = struct {
+        pub const base_tag = Tag.cmp;
+        base: Inst,
+
+        positionals: struct {
+            lhs: *Inst,
+            op: std.math.CompareOperator,
+            rhs: *Inst,
+        },
+        kw_args: struct {},
+    };
+
+    pub const CondBr = struct {
+        pub const base_tag = Tag.condbr;
+        base: Inst,
+
+        positionals: struct {
+            condition: *Inst,
+            true_body: Module.Body,
+            false_body: Module.Body,
+        },
+        kw_args: struct {},
+    };
+
+    pub const IsNull = struct {
+        pub const base_tag = Tag.isnull;
+        base: Inst,
+
+        positionals: struct {
+            operand: *Inst,
+        },
+        kw_args: struct {},
+    };
+
+    pub const IsNonNull = struct {
+        pub const base_tag = Tag.isnonnull;
+        base: Inst,
+
+        positionals: struct {
+            operand: *Inst,
+        },
+        kw_args: struct {},
+    };
 };
 
 pub const ErrorMsg = struct {
@@ -309,6 +357,10 @@ pub const Module = struct {
     errors: []ErrorMsg,
     arena: std.heap.ArenaAllocator,
 
+    pub const Body = struct {
+        instructions: []*Inst,
+    };
+
     pub fn deinit(self: *Module, allocator: *Allocator) void {
         allocator.free(self.decls);
         allocator.free(self.errors);
@@ -321,7 +373,7 @@ pub const Module = struct {
         self.writeToStream(std.heap.page_allocator, std.io.getStdErr().outStream()) catch {};
     }
 
-    const InstPtrTable = std.AutoHashMap(*Inst, struct { index: usize, fn_body: ?*Inst.Fn.Body });
+    const InstPtrTable = std.AutoHashMap(*Inst, struct { index: usize, fn_body: ?*Module.Body });
 
     /// The allocator is used for temporary storage, but this function always returns
     /// with no resources allocated.
@@ -373,6 +425,10 @@ pub const Module = struct {
             .bitcast => return self.writeInstToStreamGeneric(stream, .bitcast, decl, inst_table),
             .elemptr => return self.writeInstToStreamGeneric(stream, .elemptr, decl, inst_table),
             .add => return self.writeInstToStreamGeneric(stream, .add, decl, inst_table),
+            .cmp => return self.writeInstToStreamGeneric(stream, .cmp, decl, inst_table),
+            .condbr => return self.writeInstToStreamGeneric(stream, .condbr, decl, inst_table),
+            .isnull => return self.writeInstToStreamGeneric(stream, .isnull, decl, inst_table),
+            .isnonnull => return self.writeInstToStreamGeneric(stream, .isnonnull, decl, inst_table),
         }
     }
 
@@ -432,7 +488,7 @@ pub const Module = struct {
                 }
                 try stream.writeByte(']');
             },
-            Inst.Fn.Body => {
+            Module.Body => {
                 try stream.writeAll("{\n");
                 for (param.instructions) |inst, i| {
                     try stream.print("  %{} ", .{i});
@@ -497,7 +553,7 @@ const Parser = struct {
         name_map: std.StringHashMap(usize),
     };
 
-    fn parseBody(self: *Parser) !Inst.Fn.Body {
+    fn parseBody(self: *Parser) !Module.Body {
         var body_context = Body{
             .instructions = std.ArrayList(*Inst).init(self.allocator),
             .name_map = std.StringHashMap(usize).init(self.allocator),
@@ -535,7 +591,7 @@ const Parser = struct {
         // Move the instructions to the arena
         const instrs = try self.arena.allocator.alloc(*Inst, body_context.instructions.items.len);
         mem.copy(*Inst, instrs, body_context.instructions.items);
-        return Inst.Fn.Body{ .instructions = instrs };
+        return Module.Body{ .instructions = instrs };
     }
 
     fn parseStringLiteral(self: *Parser) ![]u8 {
@@ -754,7 +810,7 @@ const Parser = struct {
             };
         }
         switch (T) {
-            Inst.Fn.Body => return parseBody(self),
+            Module.Body => return parseBody(self),
             bool => {
                 const bool_value = switch (self.source[self.i]) {
                     '0' => false,
@@ -880,11 +936,12 @@ const EmitZIR = struct {
     }
 
     fn emitComptimeIntVal(self: *EmitZIR, src: usize, val: Value) !*Inst {
+        const big_int_space = try self.arena.allocator.create(Value.BigIntSpace);
         const int_inst = try self.arena.allocator.create(Inst.Int);
         int_inst.* = .{
             .base = .{ .src = src, .tag = Inst.Int.base_tag },
             .positionals = .{
-                .int = try val.toBigInt(&self.arena.allocator),
+                .int = val.toBigInt(big_int_space),
             },
             .kw_args = .{},
         };
@@ -939,85 +996,7 @@ const EmitZIR = struct {
                 var instructions = std.ArrayList(*Inst).init(self.allocator);
                 defer instructions.deinit();
 
-                for (module_fn.body) |inst| {
-                    const new_inst = switch (inst.tag) {
-                        .unreach => blk: {
-                            const unreach_inst = try self.arena.allocator.create(Inst.Unreachable);
-                            unreach_inst.* = .{
-                                .base = .{ .src = inst.src, .tag = Inst.Unreachable.base_tag },
-                                .positionals = .{},
-                                .kw_args = .{},
-                            };
-                            break :blk &unreach_inst.base;
-                        },
-                        .constant => unreachable, // excluded from function bodies
-                        .assembly => blk: {
-                            const old_inst = inst.cast(ir.Inst.Assembly).?;
-                            const new_inst = try self.arena.allocator.create(Inst.Asm);
-
-                            const inputs = try self.arena.allocator.alloc(*Inst, old_inst.args.inputs.len);
-                            for (inputs) |*elem, i| {
-                                elem.* = try self.emitStringLiteral(inst.src, old_inst.args.inputs[i]);
-                            }
-
-                            const clobbers = try self.arena.allocator.alloc(*Inst, old_inst.args.clobbers.len);
-                            for (clobbers) |*elem, i| {
-                                elem.* = try self.emitStringLiteral(inst.src, old_inst.args.clobbers[i]);
-                            }
-
-                            const args = try self.arena.allocator.alloc(*Inst, old_inst.args.args.len);
-                            for (args) |*elem, i| {
-                                elem.* = try self.resolveInst(&inst_table, old_inst.args.args[i]);
-                            }
-
-                            new_inst.* = .{
-                                .base = .{ .src = inst.src, .tag = Inst.Asm.base_tag },
-                                .positionals = .{
-                                    .asm_source = try self.emitStringLiteral(inst.src, old_inst.args.asm_source),
-                                    .return_type = try self.emitType(inst.src, inst.ty),
-                                },
-                                .kw_args = .{
-                                    .@"volatile" = old_inst.args.is_volatile,
-                                    .output = if (old_inst.args.output) |o|
-                                        try self.emitStringLiteral(inst.src, o)
-                                    else
-                                        null,
-                                    .inputs = inputs,
-                                    .clobbers = clobbers,
-                                    .args = args,
-                                },
-                            };
-                            break :blk &new_inst.base;
-                        },
-                        .ptrtoint => blk: {
-                            const old_inst = inst.cast(ir.Inst.PtrToInt).?;
-                            const new_inst = try self.arena.allocator.create(Inst.PtrToInt);
-                            new_inst.* = .{
-                                .base = .{ .src = inst.src, .tag = Inst.PtrToInt.base_tag },
-                                .positionals = .{
-                                    .ptr = try self.resolveInst(&inst_table, old_inst.args.ptr),
-                                },
-                                .kw_args = .{},
-                            };
-                            break :blk &new_inst.base;
-                        },
-                        .bitcast => blk: {
-                            const old_inst = inst.cast(ir.Inst.BitCast).?;
-                            const new_inst = try self.arena.allocator.create(Inst.BitCast);
-                            new_inst.* = .{
-                                .base = .{ .src = inst.src, .tag = Inst.BitCast.base_tag },
-                                .positionals = .{
-                                    .dest_type = try self.emitType(inst.src, inst.ty),
-                                    .operand = try self.resolveInst(&inst_table, old_inst.args.operand),
-                                },
-                                .kw_args = .{},
-                            };
-                            break :blk &new_inst.base;
-                        },
-                    };
-                    try instructions.append(new_inst);
-                    try inst_table.putNoClobber(inst, new_inst);
-                }
+                try self.emitBody(module_fn.body, &inst_table, &instructions);
 
                 const fn_type = try self.emitType(src, module_fn.fn_type);
 
@@ -1039,6 +1018,155 @@ const EmitZIR = struct {
         }
     }
 
+    fn emitBody(
+        self: *EmitZIR,
+        body: ir.Module.Body,
+        inst_table: *std.AutoHashMap(*ir.Inst, *Inst),
+        instructions: *std.ArrayList(*Inst),
+    ) Allocator.Error!void {
+        for (body.instructions) |inst| {
+            const new_inst = switch (inst.tag) {
+                .unreach => blk: {
+                    const unreach_inst = try self.arena.allocator.create(Inst.Unreachable);
+                    unreach_inst.* = .{
+                        .base = .{ .src = inst.src, .tag = Inst.Unreachable.base_tag },
+                        .positionals = .{},
+                        .kw_args = .{},
+                    };
+                    break :blk &unreach_inst.base;
+                },
+                .constant => unreachable, // excluded from function bodies
+                .assembly => blk: {
+                    const old_inst = inst.cast(ir.Inst.Assembly).?;
+                    const new_inst = try self.arena.allocator.create(Inst.Asm);
+
+                    const inputs = try self.arena.allocator.alloc(*Inst, old_inst.args.inputs.len);
+                    for (inputs) |*elem, i| {
+                        elem.* = try self.emitStringLiteral(inst.src, old_inst.args.inputs[i]);
+                    }
+
+                    const clobbers = try self.arena.allocator.alloc(*Inst, old_inst.args.clobbers.len);
+                    for (clobbers) |*elem, i| {
+                        elem.* = try self.emitStringLiteral(inst.src, old_inst.args.clobbers[i]);
+                    }
+
+                    const args = try self.arena.allocator.alloc(*Inst, old_inst.args.args.len);
+                    for (args) |*elem, i| {
+                        elem.* = try self.resolveInst(inst_table, old_inst.args.args[i]);
+                    }
+
+                    new_inst.* = .{
+                        .base = .{ .src = inst.src, .tag = Inst.Asm.base_tag },
+                        .positionals = .{
+                            .asm_source = try self.emitStringLiteral(inst.src, old_inst.args.asm_source),
+                            .return_type = try self.emitType(inst.src, inst.ty),
+                        },
+                        .kw_args = .{
+                            .@"volatile" = old_inst.args.is_volatile,
+                            .output = if (old_inst.args.output) |o|
+                                try self.emitStringLiteral(inst.src, o)
+                            else
+                                null,
+                            .inputs = inputs,
+                            .clobbers = clobbers,
+                            .args = args,
+                        },
+                    };
+                    break :blk &new_inst.base;
+                },
+                .ptrtoint => blk: {
+                    const old_inst = inst.cast(ir.Inst.PtrToInt).?;
+                    const new_inst = try self.arena.allocator.create(Inst.PtrToInt);
+                    new_inst.* = .{
+                        .base = .{ .src = inst.src, .tag = Inst.PtrToInt.base_tag },
+                        .positionals = .{
+                            .ptr = try self.resolveInst(inst_table, old_inst.args.ptr),
+                        },
+                        .kw_args = .{},
+                    };
+                    break :blk &new_inst.base;
+                },
+                .bitcast => blk: {
+                    const old_inst = inst.cast(ir.Inst.BitCast).?;
+                    const new_inst = try self.arena.allocator.create(Inst.BitCast);
+                    new_inst.* = .{
+                        .base = .{ .src = inst.src, .tag = Inst.BitCast.base_tag },
+                        .positionals = .{
+                            .dest_type = try self.emitType(inst.src, inst.ty),
+                            .operand = try self.resolveInst(inst_table, old_inst.args.operand),
+                        },
+                        .kw_args = .{},
+                    };
+                    break :blk &new_inst.base;
+                },
+                .cmp => blk: {
+                    const old_inst = inst.cast(ir.Inst.Cmp).?;
+                    const new_inst = try self.arena.allocator.create(Inst.Cmp);
+                    new_inst.* = .{
+                        .base = .{ .src = inst.src, .tag = Inst.Cmp.base_tag },
+                        .positionals = .{
+                            .lhs = try self.resolveInst(inst_table, old_inst.args.lhs),
+                            .rhs = try self.resolveInst(inst_table, old_inst.args.rhs),
+                            .op = old_inst.args.op,
+                        },
+                        .kw_args = .{},
+                    };
+                    break :blk &new_inst.base;
+                },
+                .condbr => blk: {
+                    const old_inst = inst.cast(ir.Inst.CondBr).?;
+
+                    var true_body = std.ArrayList(*Inst).init(self.allocator);
+                    var false_body = std.ArrayList(*Inst).init(self.allocator);
+
+                    defer true_body.deinit();
+                    defer false_body.deinit();
+
+                    try self.emitBody(old_inst.args.true_body, inst_table, &true_body);
+                    try self.emitBody(old_inst.args.false_body, inst_table, &false_body);
+
+                    const new_inst = try self.arena.allocator.create(Inst.CondBr);
+                    new_inst.* = .{
+                        .base = .{ .src = inst.src, .tag = Inst.CondBr.base_tag },
+                        .positionals = .{
+                            .condition = try self.resolveInst(inst_table, old_inst.args.condition),
+                            .true_body = .{ .instructions = true_body.toOwnedSlice() },
+                            .false_body = .{ .instructions = false_body.toOwnedSlice() },
+                        },
+                        .kw_args = .{},
+                    };
+                    break :blk &new_inst.base;
+                },
+                .isnull => blk: {
+                    const old_inst = inst.cast(ir.Inst.IsNull).?;
+                    const new_inst = try self.arena.allocator.create(Inst.IsNull);
+                    new_inst.* = .{
+                        .base = .{ .src = inst.src, .tag = Inst.IsNull.base_tag },
+                        .positionals = .{
+                            .operand = try self.resolveInst(inst_table, old_inst.args.operand),
+                        },
+                        .kw_args = .{},
+                    };
+                    break :blk &new_inst.base;
+                },
+                .isnonnull => blk: {
+                    const old_inst = inst.cast(ir.Inst.IsNonNull).?;
+                    const new_inst = try self.arena.allocator.create(Inst.IsNonNull);
+                    new_inst.* = .{
+                        .base = .{ .src = inst.src, .tag = Inst.IsNonNull.base_tag },
+                        .positionals = .{
+                            .operand = try self.resolveInst(inst_table, old_inst.args.operand),
+                        },
+                        .kw_args = .{},
+                    };
+                    break :blk &new_inst.base;
+                },
+            };
+            try instructions.append(new_inst);
+            try inst_table.putNoClobber(inst, new_inst);
+        }
+    }
+
     fn emitType(self: *EmitZIR, src: usize, ty: Type) Allocator.Error!*Inst {
         switch (ty.tag()) {
             .isize => return self.emitPrimitiveType(src, .isize),
src-self-hosted/codegen.zig
@@ -501,11 +501,19 @@ fn Reg(comptime arch: Target.Cpu.Arch) type {
             bh,
             ch,
             dh,
+            bph,
+            sph,
+            sih,
+            dih,
 
             al,
             bl,
             cl,
             dl,
+            bpl,
+            spl,
+            sil,
+            dil,
             r8b,
             r9b,
             r10b,
src-self-hosted/ir.zig
@@ -26,6 +26,10 @@ pub const Inst = struct {
         assembly,
         ptrtoint,
         bitcast,
+        cmp,
+        condbr,
+        isnull,
+        isnonnull,
     };
 
     pub fn cast(base: *Inst, comptime T: type) ?*T {
@@ -41,15 +45,11 @@ pub const Inst = struct {
 
     /// Returns `null` if runtime-known.
     pub fn value(base: *Inst) ?Value {
-        return switch (base.tag) {
-            .unreach => Value.initTag(.noreturn_value),
-            .constant => base.cast(Constant).?.val,
-
-            .assembly,
-            .ptrtoint,
-            .bitcast,
-            => null,
-        };
+        if (base.ty.onePossibleValue())
+            return Value.initTag(.the_one_possible_value);
+
+        const inst = base.cast(Constant) orelse return null;
+        return inst.val;
     }
 
     pub const Unreach = struct {
@@ -96,6 +96,46 @@ pub const Inst = struct {
             operand: *Inst,
         },
     };
+
+    pub const Cmp = struct {
+        pub const base_tag = Tag.cmp;
+
+        base: Inst,
+        args: struct {
+            lhs: *Inst,
+            op: std.math.CompareOperator,
+            rhs: *Inst,
+        },
+    };
+
+    pub const CondBr = struct {
+        pub const base_tag = Tag.condbr;
+
+        base: Inst,
+        args: struct {
+            condition: *Inst,
+            true_body: Module.Body,
+            false_body: Module.Body,
+        },
+    };
+
+    pub const IsNull = struct {
+        pub const base_tag = Tag.isnull;
+
+        base: Inst,
+        args: struct {
+            operand: *Inst,
+        },
+    };
+
+    pub const IsNonNull = struct {
+        pub const base_tag = Tag.isnonnull;
+
+        base: Inst,
+        args: struct {
+            operand: *Inst,
+        },
+    };
 };
 
 pub const TypedValue = struct {
@@ -118,15 +158,19 @@ pub const Module = struct {
 
     pub const Fn = struct {
         analysis_status: enum { in_progress, failure, success },
-        body: []*Inst,
+        body: Body,
         fn_type: Type,
     };
 
+    pub const Body = struct {
+        instructions: []*Inst,
+    };
+
     pub fn deinit(self: *Module, allocator: *Allocator) void {
         allocator.free(self.exports);
         allocator.free(self.errors);
         for (self.fns) |f| {
-            allocator.free(f.body);
+            allocator.free(f.body.instructions);
         }
         allocator.free(self.fns);
         self.arena.deinit();
@@ -192,10 +236,15 @@ const Analyze = struct {
     };
 
     const Fn = struct {
-        body: std.ArrayList(*Inst),
-        inst_table: std.AutoHashMap(*text.Inst, NewInst),
         /// Index into Module fns array
         fn_index: usize,
+        inner_block: Block,
+        inst_table: std.AutoHashMap(*text.Inst, NewInst),
+    };
+
+    const Block = struct {
+        func: *Fn,
+        instructions: std.ArrayList(*Inst),
     };
 
     const InnerError = error{ OutOfMemory, AnalysisFail };
@@ -208,9 +257,9 @@ const Analyze = struct {
         }
     }
 
-    fn resolveInst(self: *Analyze, opt_func: ?*Fn, old_inst: *text.Inst) InnerError!*Inst {
-        if (opt_func) |func| {
-            if (func.inst_table.get(old_inst)) |kv| {
+    fn resolveInst(self: *Analyze, opt_block: ?*Block, old_inst: *text.Inst) InnerError!*Inst {
+        if (opt_block) |block| {
+            if (block.func.inst_table.get(old_inst)) |kv| {
                 return kv.value.ptr orelse return error.AnalysisFail;
             }
         }
@@ -230,12 +279,12 @@ const Analyze = struct {
         }
     }
 
-    fn requireFunctionBody(self: *Analyze, func: ?*Fn, src: usize) !*Fn {
-        return func orelse return self.fail(src, "instruction illegal outside function body", .{});
+    fn requireRuntimeBlock(self: *Analyze, block: ?*Block, src: usize) !*Block {
+        return block orelse return self.fail(src, "instruction illegal outside function body", .{});
     }
 
-    fn resolveInstConst(self: *Analyze, func: ?*Fn, old_inst: *text.Inst) InnerError!TypedValue {
-        const new_inst = try self.resolveInst(func, old_inst);
+    fn resolveInstConst(self: *Analyze, block: ?*Block, old_inst: *text.Inst) InnerError!TypedValue {
+        const new_inst = try self.resolveInst(block, old_inst);
         const val = try self.resolveConstValue(new_inst);
         return TypedValue{
             .ty = new_inst.ty,
@@ -244,28 +293,39 @@ const Analyze = struct {
     }
 
     fn resolveConstValue(self: *Analyze, base: *Inst) !Value {
-        return base.value() orelse return self.fail(base.src, "unable to resolve comptime value", .{});
+        return (try self.resolveDefinedValue(base)) orelse
+            return self.fail(base.src, "unable to resolve comptime value", .{});
     }
 
-    fn resolveConstString(self: *Analyze, func: ?*Fn, old_inst: *text.Inst) ![]u8 {
-        const new_inst = try self.resolveInst(func, old_inst);
+    fn resolveDefinedValue(self: *Analyze, base: *Inst) !?Value {
+        if (base.value()) |val| {
+            if (val.isUndef()) {
+                return self.fail(base.src, "use of undefined value here causes undefined behavior", .{});
+            }
+            return val;
+        }
+        return null;
+    }
+
+    fn resolveConstString(self: *Analyze, block: ?*Block, old_inst: *text.Inst) ![]u8 {
+        const new_inst = try self.resolveInst(block, old_inst);
         const wanted_type = Type.initTag(.const_slice_u8);
-        const coerced_inst = try self.coerce(func, wanted_type, new_inst);
+        const coerced_inst = try self.coerce(block, wanted_type, new_inst);
         const val = try self.resolveConstValue(coerced_inst);
         return val.toAllocatedBytes(&self.arena.allocator);
     }
 
-    fn resolveType(self: *Analyze, func: ?*Fn, old_inst: *text.Inst) !Type {
-        const new_inst = try self.resolveInst(func, old_inst);
+    fn resolveType(self: *Analyze, block: ?*Block, old_inst: *text.Inst) !Type {
+        const new_inst = try self.resolveInst(block, old_inst);
         const wanted_type = Type.initTag(.@"type");
-        const coerced_inst = try self.coerce(func, wanted_type, new_inst);
+        const coerced_inst = try self.coerce(block, wanted_type, new_inst);
         const val = try self.resolveConstValue(coerced_inst);
         return val.toType();
     }
 
-    fn analyzeExport(self: *Analyze, func: ?*Fn, export_inst: *text.Inst.Export) !void {
-        const symbol_name = try self.resolveConstString(func, export_inst.positionals.symbol_name);
-        const typed_value = try self.resolveInstConst(func, export_inst.positionals.value);
+    fn analyzeExport(self: *Analyze, block: ?*Block, export_inst: *text.Inst.Export) !void {
+        const symbol_name = try self.resolveConstString(block, export_inst.positionals.symbol_name);
+        const typed_value = try self.resolveInstConst(block, export_inst.positionals.value);
 
         switch (typed_value.ty.zigTypeTag()) {
             .Fn => {},
@@ -285,18 +345,18 @@ const Analyze = struct {
     /// TODO should not need the cast on the last parameter at the callsites
     fn addNewInstArgs(
         self: *Analyze,
-        func: *Fn,
+        block: *Block,
         src: usize,
         ty: Type,
         comptime T: type,
         args: Inst.Args(T),
     ) !*Inst {
-        const inst = try self.addNewInst(func, src, ty, T);
+        const inst = try self.addNewInst(block, src, ty, T);
         inst.args = args;
         return &inst.base;
     }
 
-    fn addNewInst(self: *Analyze, func: *Fn, src: usize, ty: Type, comptime T: type) !*T {
+    fn addNewInst(self: *Analyze, block: *Block, src: usize, ty: Type, comptime T: type) !*T {
         const inst = try self.arena.allocator.create(T);
         inst.* = .{
             .base = .{
@@ -306,7 +366,7 @@ const Analyze = struct {
             },
             .args = undefined,
         };
-        try func.body.append(&inst.base);
+        try block.instructions.append(&inst.base);
         return inst;
     }
 
@@ -349,7 +409,21 @@ const Analyze = struct {
     fn constVoid(self: *Analyze, src: usize) !*Inst {
         return self.constInst(src, .{
             .ty = Type.initTag(.void),
-            .val = Value.initTag(.void_value),
+            .val = Value.initTag(.the_one_possible_value),
+        });
+    }
+
+    fn constUndef(self: *Analyze, src: usize, ty: Type) !*Inst {
+        return self.constInst(src, .{
+            .ty = ty,
+            .val = Value.initTag(.undef),
+        });
+    }
+
+    fn constBool(self: *Analyze, src: usize, v: bool) !*Inst {
+        return self.constInst(src, .{
+            .ty = Type.initTag(.bool),
+            .val = ([2]Value{ Value.initTag(.bool_false), Value.initTag(.bool_true) })[@boolToInt(v)],
         });
     }
 
@@ -399,7 +473,7 @@ const Analyze = struct {
         });
     }
 
-    fn analyzeInst(self: *Analyze, func: ?*Fn, old_inst: *text.Inst) InnerError!*Inst {
+    fn analyzeInst(self: *Analyze, block: ?*Block, old_inst: *text.Inst) InnerError!*Inst {
         switch (old_inst.tag) {
             .str => {
                 // We can use this reference because Inst.Const's Value is arena-allocated.
@@ -411,35 +485,43 @@ const Analyze = struct {
                 const big_int = old_inst.cast(text.Inst.Int).?.positionals.int;
                 return self.constIntBig(old_inst.src, Type.initTag(.comptime_int), big_int);
             },
-            .ptrtoint => return self.analyzeInstPtrToInt(func, old_inst.cast(text.Inst.PtrToInt).?),
-            .fieldptr => return self.analyzeInstFieldPtr(func, old_inst.cast(text.Inst.FieldPtr).?),
-            .deref => return self.analyzeInstDeref(func, old_inst.cast(text.Inst.Deref).?),
-            .as => return self.analyzeInstAs(func, old_inst.cast(text.Inst.As).?),
-            .@"asm" => return self.analyzeInstAsm(func, old_inst.cast(text.Inst.Asm).?),
-            .@"unreachable" => return self.analyzeInstUnreachable(func, old_inst.cast(text.Inst.Unreachable).?),
-            .@"fn" => return self.analyzeInstFn(func, old_inst.cast(text.Inst.Fn).?),
+            .ptrtoint => return self.analyzeInstPtrToInt(block, old_inst.cast(text.Inst.PtrToInt).?),
+            .fieldptr => return self.analyzeInstFieldPtr(block, old_inst.cast(text.Inst.FieldPtr).?),
+            .deref => return self.analyzeInstDeref(block, old_inst.cast(text.Inst.Deref).?),
+            .as => return self.analyzeInstAs(block, old_inst.cast(text.Inst.As).?),
+            .@"asm" => return self.analyzeInstAsm(block, old_inst.cast(text.Inst.Asm).?),
+            .@"unreachable" => return self.analyzeInstUnreachable(block, old_inst.cast(text.Inst.Unreachable).?),
+            .@"fn" => return self.analyzeInstFn(block, old_inst.cast(text.Inst.Fn).?),
             .@"export" => {
-                try self.analyzeExport(func, old_inst.cast(text.Inst.Export).?);
+                try self.analyzeExport(block, old_inst.cast(text.Inst.Export).?);
                 return self.constVoid(old_inst.src);
             },
-            .primitive => return self.analyzeInstPrimitive(func, old_inst.cast(text.Inst.Primitive).?),
-            .fntype => return self.analyzeInstFnType(func, old_inst.cast(text.Inst.FnType).?),
-            .intcast => return self.analyzeInstIntCast(func, old_inst.cast(text.Inst.IntCast).?),
-            .bitcast => return self.analyzeInstBitCast(func, old_inst.cast(text.Inst.BitCast).?),
-            .elemptr => return self.analyzeInstElemPtr(func, old_inst.cast(text.Inst.ElemPtr).?),
-            .add => return self.analyzeInstAdd(func, old_inst.cast(text.Inst.Add).?),
+            .primitive => return self.analyzeInstPrimitive(old_inst.cast(text.Inst.Primitive).?),
+            .fntype => return self.analyzeInstFnType(block, old_inst.cast(text.Inst.FnType).?),
+            .intcast => return self.analyzeInstIntCast(block, old_inst.cast(text.Inst.IntCast).?),
+            .bitcast => return self.analyzeInstBitCast(block, old_inst.cast(text.Inst.BitCast).?),
+            .elemptr => return self.analyzeInstElemPtr(block, old_inst.cast(text.Inst.ElemPtr).?),
+            .add => return self.analyzeInstAdd(block, old_inst.cast(text.Inst.Add).?),
+            .cmp => return self.analyzeInstCmp(block, old_inst.cast(text.Inst.Cmp).?),
+            .condbr => return self.analyzeInstCondBr(block, old_inst.cast(text.Inst.CondBr).?),
+            .isnull => return self.analyzeInstIsNull(block, old_inst.cast(text.Inst.IsNull).?),
+            .isnonnull => return self.analyzeInstIsNonNull(block, old_inst.cast(text.Inst.IsNonNull).?),
         }
     }
 
-    fn analyzeInstFn(self: *Analyze, opt_func: ?*Fn, fn_inst: *text.Inst.Fn) InnerError!*Inst {
-        const fn_type = try self.resolveType(opt_func, fn_inst.positionals.fn_type);
+    fn analyzeInstFn(self: *Analyze, block: ?*Block, fn_inst: *text.Inst.Fn) InnerError!*Inst {
+        const fn_type = try self.resolveType(block, fn_inst.positionals.fn_type);
 
         var new_func: Fn = .{
-            .body = std.ArrayList(*Inst).init(self.allocator),
-            .inst_table = std.AutoHashMap(*text.Inst, NewInst).init(self.allocator),
             .fn_index = self.fns.items.len,
+            .inner_block = .{
+                .func = undefined,
+                .instructions = std.ArrayList(*Inst).init(self.allocator),
+            },
+            .inst_table = std.AutoHashMap(*text.Inst, NewInst).init(self.allocator),
         };
-        defer new_func.body.deinit();
+        new_func.inner_block.func = &new_func;
+        defer new_func.inner_block.instructions.deinit();
         defer new_func.inst_table.deinit();
         // Don't hang on to a reference to this when analyzing body instructions, since the memory
         // could become invalid.
@@ -449,18 +531,11 @@ const Analyze = struct {
             .body = undefined,
         };
 
-        for (fn_inst.positionals.body.instructions) |src_inst| {
-            const new_inst = self.analyzeInst(&new_func, src_inst) catch |err| {
-                self.fns.items[new_func.fn_index].analysis_status = .failure;
-                try new_func.inst_table.putNoClobber(src_inst, .{ .ptr = null });
-                return err;
-            };
-            try new_func.inst_table.putNoClobber(src_inst, .{ .ptr = new_inst });
-        }
+        try self.analyzeBody(&new_func.inner_block, fn_inst.positionals.body);
 
         const f = &self.fns.items[new_func.fn_index];
         f.analysis_status = .success;
-        f.body = new_func.body.toOwnedSlice();
+        f.body = .{ .instructions = new_func.inner_block.instructions.toOwnedSlice() };
 
         const fn_payload = try self.arena.allocator.create(Value.Payload.Function);
         fn_payload.* = .{ .index = new_func.fn_index };
@@ -471,8 +546,8 @@ const Analyze = struct {
         });
     }
 
-    fn analyzeInstFnType(self: *Analyze, func: ?*Fn, fntype: *text.Inst.FnType) InnerError!*Inst {
-        const return_type = try self.resolveType(func, fntype.positionals.return_type);
+    fn analyzeInstFnType(self: *Analyze, block: ?*Block, fntype: *text.Inst.FnType) InnerError!*Inst {
+        const return_type = try self.resolveType(block, fntype.positionals.return_type);
 
         if (return_type.zigTypeTag() == .NoReturn and
             fntype.positionals.param_types.len == 0 and
@@ -484,30 +559,30 @@ const Analyze = struct {
         return self.fail(fntype.base.src, "TODO implement fntype instruction more", .{});
     }
 
-    fn analyzeInstPrimitive(self: *Analyze, func: ?*Fn, primitive: *text.Inst.Primitive) InnerError!*Inst {
+    fn analyzeInstPrimitive(self: *Analyze, primitive: *text.Inst.Primitive) InnerError!*Inst {
         return self.constType(primitive.base.src, primitive.positionals.tag.toType());
     }
 
-    fn analyzeInstAs(self: *Analyze, func: ?*Fn, as: *text.Inst.As) InnerError!*Inst {
-        const dest_type = try self.resolveType(func, as.positionals.dest_type);
-        const new_inst = try self.resolveInst(func, as.positionals.value);
-        return self.coerce(func, dest_type, new_inst);
+    fn analyzeInstAs(self: *Analyze, block: ?*Block, as: *text.Inst.As) InnerError!*Inst {
+        const dest_type = try self.resolveType(block, as.positionals.dest_type);
+        const new_inst = try self.resolveInst(block, as.positionals.value);
+        return self.coerce(block, dest_type, new_inst);
     }
 
-    fn analyzeInstPtrToInt(self: *Analyze, func: ?*Fn, ptrtoint: *text.Inst.PtrToInt) InnerError!*Inst {
-        const ptr = try self.resolveInst(func, ptrtoint.positionals.ptr);
+    fn analyzeInstPtrToInt(self: *Analyze, block: ?*Block, ptrtoint: *text.Inst.PtrToInt) InnerError!*Inst {
+        const ptr = try self.resolveInst(block, ptrtoint.positionals.ptr);
         if (ptr.ty.zigTypeTag() != .Pointer) {
             return self.fail(ptrtoint.positionals.ptr.src, "expected pointer, found '{}'", .{ptr.ty});
         }
         // TODO handle known-pointer-address
-        const f = try self.requireFunctionBody(func, ptrtoint.base.src);
+        const b = try self.requireRuntimeBlock(block, ptrtoint.base.src);
         const ty = Type.initTag(.usize);
-        return self.addNewInstArgs(f, ptrtoint.base.src, ty, Inst.PtrToInt, Inst.Args(Inst.PtrToInt){ .ptr = ptr });
+        return self.addNewInstArgs(b, ptrtoint.base.src, ty, Inst.PtrToInt, Inst.Args(Inst.PtrToInt){ .ptr = ptr });
     }
 
-    fn analyzeInstFieldPtr(self: *Analyze, func: ?*Fn, fieldptr: *text.Inst.FieldPtr) InnerError!*Inst {
-        const object_ptr = try self.resolveInst(func, fieldptr.positionals.object_ptr);
-        const field_name = try self.resolveConstString(func, fieldptr.positionals.field_name);
+    fn analyzeInstFieldPtr(self: *Analyze, block: ?*Block, fieldptr: *text.Inst.FieldPtr) InnerError!*Inst {
+        const object_ptr = try self.resolveInst(block, fieldptr.positionals.object_ptr);
+        const field_name = try self.resolveConstString(block, fieldptr.positionals.field_name);
 
         const elem_ty = switch (object_ptr.ty.zigTypeTag()) {
             .Pointer => object_ptr.ty.elemType(),
@@ -538,9 +613,9 @@ const Analyze = struct {
         }
     }
 
-    fn analyzeInstIntCast(self: *Analyze, func: ?*Fn, intcast: *text.Inst.IntCast) InnerError!*Inst {
-        const dest_type = try self.resolveType(func, intcast.positionals.dest_type);
-        const new_inst = try self.resolveInst(func, intcast.positionals.value);
+    fn analyzeInstIntCast(self: *Analyze, block: ?*Block, intcast: *text.Inst.IntCast) InnerError!*Inst {
+        const dest_type = try self.resolveType(block, intcast.positionals.dest_type);
+        const new_inst = try self.resolveInst(block, intcast.positionals.value);
 
         const dest_is_comptime_int = switch (dest_type.zigTypeTag()) {
             .ComptimeInt => true,
@@ -564,22 +639,22 @@ const Analyze = struct {
         }
 
         if (dest_is_comptime_int or new_inst.value() != null) {
-            return self.coerce(func, dest_type, new_inst);
+            return self.coerce(block, dest_type, new_inst);
         }
 
         return self.fail(intcast.base.src, "TODO implement analyze widen or shorten int", .{});
     }
 
-    fn analyzeInstBitCast(self: *Analyze, func: ?*Fn, inst: *text.Inst.BitCast) InnerError!*Inst {
-        const dest_type = try self.resolveType(func, inst.positionals.dest_type);
-        const operand = try self.resolveInst(func, inst.positionals.operand);
-        return self.bitcast(func, dest_type, operand);
+    fn analyzeInstBitCast(self: *Analyze, block: ?*Block, inst: *text.Inst.BitCast) InnerError!*Inst {
+        const dest_type = try self.resolveType(block, inst.positionals.dest_type);
+        const operand = try self.resolveInst(block, inst.positionals.operand);
+        return self.bitcast(block, dest_type, operand);
     }
 
-    fn analyzeInstElemPtr(self: *Analyze, func: ?*Fn, inst: *text.Inst.ElemPtr) InnerError!*Inst {
-        const array_ptr = try self.resolveInst(func, inst.positionals.array_ptr);
-        const uncasted_index = try self.resolveInst(func, inst.positionals.index);
-        const elem_index = try self.coerce(func, Type.initTag(.usize), uncasted_index);
+    fn analyzeInstElemPtr(self: *Analyze, block: ?*Block, inst: *text.Inst.ElemPtr) InnerError!*Inst {
+        const array_ptr = try self.resolveInst(block, inst.positionals.array_ptr);
+        const uncasted_index = try self.resolveInst(block, inst.positionals.index);
+        const elem_index = try self.coerce(block, Type.initTag(.usize), uncasted_index);
 
         if (array_ptr.ty.isSinglePointer() and array_ptr.ty.elemType().zigTypeTag() == .Array) {
             if (array_ptr.value()) |array_ptr_val| {
@@ -607,15 +682,19 @@ const Analyze = struct {
         return self.fail(inst.base.src, "TODO implement more analyze elemptr", .{});
     }
 
-    fn analyzeInstAdd(self: *Analyze, func: ?*Fn, inst: *text.Inst.Add) InnerError!*Inst {
-        const lhs = try self.resolveInst(func, inst.positionals.lhs);
-        const rhs = try self.resolveInst(func, inst.positionals.rhs);
+    fn analyzeInstAdd(self: *Analyze, block: ?*Block, inst: *text.Inst.Add) InnerError!*Inst {
+        const lhs = try self.resolveInst(block, inst.positionals.lhs);
+        const rhs = try self.resolveInst(block, inst.positionals.rhs);
 
         if (lhs.ty.zigTypeTag() == .Int and rhs.ty.zigTypeTag() == .Int) {
             if (lhs.value()) |lhs_val| {
                 if (rhs.value()) |rhs_val| {
-                    const lhs_bigint = try lhs_val.toBigInt(&self.arena.allocator);
-                    const rhs_bigint = try rhs_val.toBigInt(&self.arena.allocator);
+                    // TODO is this a performance issue? maybe we should try the operation without
+                    // resorting to BigInt first.
+                    var lhs_space: Value.BigIntSpace = undefined;
+                    var rhs_space: Value.BigIntSpace = undefined;
+                    const lhs_bigint = lhs_val.toBigInt(&lhs_space);
+                    const rhs_bigint = rhs_val.toBigInt(&rhs_space);
                     var result_bigint = try BigInt.init(&self.arena.allocator);
                     try BigInt.add(&result_bigint, lhs_bigint, rhs_bigint);
 
@@ -637,8 +716,8 @@ const Analyze = struct {
         return self.fail(inst.base.src, "TODO implement more analyze add", .{});
     }
 
-    fn analyzeInstDeref(self: *Analyze, func: ?*Fn, deref: *text.Inst.Deref) InnerError!*Inst {
-        const ptr = try self.resolveInst(func, deref.positionals.ptr);
+    fn analyzeInstDeref(self: *Analyze, block: ?*Block, deref: *text.Inst.Deref) InnerError!*Inst {
+        const ptr = try self.resolveInst(block, deref.positionals.ptr);
         const elem_ty = switch (ptr.ty.zigTypeTag()) {
             .Pointer => ptr.ty.elemType(),
             else => return self.fail(deref.positionals.ptr.src, "expected pointer, found '{}'", .{ptr.ty}),
@@ -653,28 +732,28 @@ const Analyze = struct {
         return self.fail(deref.base.src, "TODO implement runtime deref", .{});
     }
 
-    fn analyzeInstAsm(self: *Analyze, func: ?*Fn, assembly: *text.Inst.Asm) InnerError!*Inst {
-        const return_type = try self.resolveType(func, assembly.positionals.return_type);
-        const asm_source = try self.resolveConstString(func, assembly.positionals.asm_source);
-        const output = if (assembly.kw_args.output) |o| try self.resolveConstString(func, o) else null;
+    fn analyzeInstAsm(self: *Analyze, block: ?*Block, assembly: *text.Inst.Asm) InnerError!*Inst {
+        const return_type = try self.resolveType(block, assembly.positionals.return_type);
+        const asm_source = try self.resolveConstString(block, assembly.positionals.asm_source);
+        const output = if (assembly.kw_args.output) |o| try self.resolveConstString(block, o) else null;
 
         const inputs = try self.arena.allocator.alloc([]const u8, assembly.kw_args.inputs.len);
         const clobbers = try self.arena.allocator.alloc([]const u8, assembly.kw_args.clobbers.len);
         const args = try self.arena.allocator.alloc(*Inst, assembly.kw_args.args.len);
 
         for (inputs) |*elem, i| {
-            elem.* = try self.resolveConstString(func, assembly.kw_args.inputs[i]);
+            elem.* = try self.resolveConstString(block, assembly.kw_args.inputs[i]);
         }
         for (clobbers) |*elem, i| {
-            elem.* = try self.resolveConstString(func, assembly.kw_args.clobbers[i]);
+            elem.* = try self.resolveConstString(block, assembly.kw_args.clobbers[i]);
         }
         for (args) |*elem, i| {
-            const arg = try self.resolveInst(func, assembly.kw_args.args[i]);
-            elem.* = try self.coerce(func, Type.initTag(.usize), arg);
+            const arg = try self.resolveInst(block, assembly.kw_args.args[i]);
+            elem.* = try self.coerce(block, Type.initTag(.usize), arg);
         }
 
-        const f = try self.requireFunctionBody(func, assembly.base.src);
-        return self.addNewInstArgs(f, assembly.base.src, return_type, Inst.Assembly, Inst.Args(Inst.Assembly){
+        const b = try self.requireRuntimeBlock(block, assembly.base.src);
+        return self.addNewInstArgs(b, assembly.base.src, return_type, Inst.Assembly, Inst.Args(Inst.Assembly){
             .asm_source = asm_source,
             .is_volatile = assembly.kw_args.@"volatile",
             .output = output,
@@ -684,19 +763,350 @@ const Analyze = struct {
         });
     }
 
-    fn analyzeInstUnreachable(self: *Analyze, func: ?*Fn, unreach: *text.Inst.Unreachable) InnerError!*Inst {
-        const f = try self.requireFunctionBody(func, unreach.base.src);
-        return self.addNewInstArgs(f, unreach.base.src, Type.initTag(.noreturn), Inst.Unreach, {});
+    fn analyzeInstCmp(self: *Analyze, block: ?*Block, inst: *text.Inst.Cmp) InnerError!*Inst {
+        const lhs = try self.resolveInst(block, inst.positionals.lhs);
+        const rhs = try self.resolveInst(block, inst.positionals.rhs);
+        const op = inst.positionals.op;
+
+        const is_equality_cmp = switch (op) {
+            .eq, .neq => true,
+            else => false,
+        };
+        const lhs_ty_tag = lhs.ty.zigTypeTag();
+        const rhs_ty_tag = rhs.ty.zigTypeTag();
+        if (is_equality_cmp and lhs_ty_tag == .Null and rhs_ty_tag == .Null) {
+            // null == null, null != null
+            return self.constBool(inst.base.src, op == .eq);
+        } else if (is_equality_cmp and
+            ((lhs_ty_tag == .Null and rhs_ty_tag == .Optional) or
+            rhs_ty_tag == .Null and lhs_ty_tag == .Optional))
+        {
+            // comparing null with optionals
+            const opt_operand = if (lhs_ty_tag == .Optional) lhs else rhs;
+            if (opt_operand.value()) |opt_val| {
+                const is_null = opt_val.isNull();
+                return self.constBool(inst.base.src, if (op == .eq) is_null else !is_null);
+            }
+            const b = try self.requireRuntimeBlock(block, inst.base.src);
+            switch (op) {
+                .eq => return self.addNewInstArgs(
+                    b,
+                    inst.base.src,
+                    Type.initTag(.bool),
+                    Inst.IsNull,
+                    Inst.Args(Inst.IsNull){ .operand = opt_operand },
+                ),
+                .neq => return self.addNewInstArgs(
+                    b,
+                    inst.base.src,
+                    Type.initTag(.bool),
+                    Inst.IsNonNull,
+                    Inst.Args(Inst.IsNonNull){ .operand = opt_operand },
+                ),
+                else => unreachable,
+            }
+        } else if (is_equality_cmp and
+            ((lhs_ty_tag == .Null and rhs.ty.isCPtr()) or (rhs_ty_tag == .Null and lhs.ty.isCPtr())))
+        {
+            return self.fail(inst.base.src, "TODO implement C pointer cmp", .{});
+        } else if (lhs_ty_tag == .Null or rhs_ty_tag == .Null) {
+            const non_null_type = if (lhs_ty_tag == .Null) rhs.ty else lhs.ty;
+            return self.fail(inst.base.src, "comparison of '{}' with null", .{non_null_type});
+        } else if (is_equality_cmp and
+            ((lhs_ty_tag == .EnumLiteral and rhs_ty_tag == .Union) or
+            (rhs_ty_tag == .EnumLiteral and lhs_ty_tag == .Union)))
+        {
+            return self.fail(inst.base.src, "TODO implement equality comparison between a union's tag value and an enum literal", .{});
+        } else if (lhs_ty_tag == .ErrorSet and rhs_ty_tag == .ErrorSet) {
+            if (!is_equality_cmp) {
+                return self.fail(inst.base.src, "{} operator not allowed for errors", .{@tagName(op)});
+            }
+            return self.fail(inst.base.src, "TODO implement equality comparison between errors", .{});
+        } else if (lhs.ty.isNumeric() and rhs.ty.isNumeric()) {
+            // This operation allows any combination of integer and float types, regardless of the
+            // signed-ness, comptime-ness, and bit-width. So peer type resolution is incorrect for
+            // numeric types.
+            return self.cmpNumeric(block, inst.base.src, lhs, rhs, op);
+        }
+        return self.fail(inst.base.src, "TODO implement more cmp analysis", .{});
+    }
+
+    fn analyzeInstIsNull(self: *Analyze, block: ?*Block, inst: *text.Inst.IsNull) InnerError!*Inst {
+        const operand = try self.resolveInst(block, inst.positionals.operand);
+        return self.analyzeIsNull(block, inst.base.src, operand, true);
+    }
+
+    fn analyzeInstIsNonNull(self: *Analyze, block: ?*Block, inst: *text.Inst.IsNonNull) InnerError!*Inst {
+        const operand = try self.resolveInst(block, inst.positionals.operand);
+        return self.analyzeIsNull(block, inst.base.src, operand, false);
+    }
+
+    fn analyzeInstCondBr(self: *Analyze, block: ?*Block, inst: *text.Inst.CondBr) InnerError!*Inst {
+        const uncasted_cond = try self.resolveInst(block, inst.positionals.condition);
+        const cond = try self.coerce(block, Type.initTag(.bool), uncasted_cond);
+
+        if (try self.resolveDefinedValue(cond)) |cond_val| {
+            const body = if (cond_val.toBool()) &inst.positionals.true_body else &inst.positionals.false_body;
+            try self.analyzeBody(block, body.*);
+            return self.constVoid(inst.base.src);
+        }
+
+        const parent_block = try self.requireRuntimeBlock(block, inst.base.src);
+
+        var true_block: Block = .{
+            .func = parent_block.func,
+            .instructions = std.ArrayList(*Inst).init(self.allocator),
+        };
+        defer true_block.instructions.deinit();
+        try self.analyzeBody(&true_block, inst.positionals.true_body);
+
+        var false_block: Block = .{
+            .func = parent_block.func,
+            .instructions = std.ArrayList(*Inst).init(self.allocator),
+        };
+        defer false_block.instructions.deinit();
+        try self.analyzeBody(&false_block, inst.positionals.false_body);
+
+        // Copy the instruction pointers to the arena memory
+        const true_instructions = try self.arena.allocator.alloc(*Inst, true_block.instructions.items.len);
+        const false_instructions = try self.arena.allocator.alloc(*Inst, false_block.instructions.items.len);
+
+        mem.copy(*Inst, true_instructions, true_block.instructions.items);
+        mem.copy(*Inst, false_instructions, false_block.instructions.items);
+
+        return self.addNewInstArgs(parent_block, inst.base.src, Type.initTag(.void), Inst.CondBr, Inst.Args(Inst.CondBr){
+            .condition = cond,
+            .true_body = .{ .instructions = true_instructions },
+            .false_body = .{ .instructions = false_instructions },
+        });
+    }
+
+    fn analyzeInstUnreachable(self: *Analyze, block: ?*Block, unreach: *text.Inst.Unreachable) InnerError!*Inst {
+        const b = try self.requireRuntimeBlock(block, unreach.base.src);
+        return self.addNewInstArgs(b, unreach.base.src, Type.initTag(.noreturn), Inst.Unreach, {});
+    }
+
+    fn analyzeBody(self: *Analyze, block: ?*Block, body: text.Module.Body) !void {
+        for (body.instructions) |src_inst| {
+            const new_inst = self.analyzeInst(block, src_inst) catch |err| {
+                if (block) |b| {
+                    self.fns.items[b.func.fn_index].analysis_status = .failure;
+                    try b.func.inst_table.putNoClobber(src_inst, .{ .ptr = null });
+                }
+                return err;
+            };
+            if (block) |b| try b.func.inst_table.putNoClobber(src_inst, .{ .ptr = new_inst });
+        }
+    }
+
+    fn analyzeIsNull(
+        self: *Analyze,
+        block: ?*Block,
+        src: usize,
+        operand: *Inst,
+        invert_logic: bool,
+    ) InnerError!*Inst {
+        return self.fail(src, "TODO implement analysis of isnull and isnotnull", .{});
+    }
+
+    /// Asserts that lhs and rhs types are both numeric.
+    fn cmpNumeric(
+        self: *Analyze,
+        block: ?*Block,
+        src: usize,
+        lhs: *Inst,
+        rhs: *Inst,
+        op: std.math.CompareOperator,
+    ) !*Inst {
+        assert(lhs.ty.isNumeric());
+        assert(rhs.ty.isNumeric());
+
+        const lhs_ty_tag = lhs.ty.zigTypeTag();
+        const rhs_ty_tag = rhs.ty.zigTypeTag();
+
+        if (lhs_ty_tag == .Vector and rhs_ty_tag == .Vector) {
+            if (lhs.ty.arrayLen() != rhs.ty.arrayLen()) {
+                return self.fail(src, "vector length mismatch: {} and {}", .{
+                    lhs.ty.arrayLen(),
+                    rhs.ty.arrayLen(),
+                });
+            }
+            return self.fail(src, "TODO implement support for vectors in cmpNumeric", .{});
+        } else if (lhs_ty_tag == .Vector or rhs_ty_tag == .Vector) {
+            return self.fail(src, "mixed scalar and vector operands to comparison operator: '{}' and '{}'", .{
+                lhs.ty,
+                rhs.ty,
+            });
+        }
+
+        if (lhs.value()) |lhs_val| {
+            if (rhs.value()) |rhs_val| {
+                return self.constBool(src, Value.compare(lhs_val, op, rhs_val));
+            }
+        }
+
+        // TODO handle comparisons against lazy zero values
+        // Some values can be compared against zero without being runtime known or without forcing
+        // a full resolution of their value, for example `@sizeOf(@Frame(function))` is known to
+        // always be nonzero, and we benefit from not forcing the full evaluation and stack frame layout
+        // of this function if we don't need to.
+
+        // It must be a runtime comparison.
+        const b = try self.requireRuntimeBlock(block, src);
+        // For floats, emit a float comparison instruction.
+        const lhs_is_float = switch (lhs_ty_tag) {
+            .Float, .ComptimeFloat => true,
+            else => false,
+        };
+        const rhs_is_float = switch (rhs_ty_tag) {
+            .Float, .ComptimeFloat => true,
+            else => false,
+        };
+        if (lhs_is_float and rhs_is_float) {
+            // Implicit cast the smaller one to the larger one.
+            const dest_type = x: {
+                if (lhs_ty_tag == .ComptimeFloat) {
+                    break :x rhs.ty;
+                } else if (rhs_ty_tag == .ComptimeFloat) {
+                    break :x lhs.ty;
+                }
+                if (lhs.ty.floatBits(self.target) >= rhs.ty.floatBits(self.target)) {
+                    break :x lhs.ty;
+                } else {
+                    break :x rhs.ty;
+                }
+            };
+            const casted_lhs = try self.coerce(block, dest_type, lhs);
+            const casted_rhs = try self.coerce(block, dest_type, rhs);
+            return self.addNewInstArgs(b, src, dest_type, Inst.Cmp, Inst.Args(Inst.Cmp){
+                .lhs = casted_lhs,
+                .rhs = casted_rhs,
+                .op = op,
+            });
+        }
+        // For mixed unsigned integer sizes, implicit cast both operands to the larger integer.
+        // For mixed signed and unsigned integers, implicit cast both operands to a signed
+        // integer with + 1 bit.
+        // For mixed floats and integers, extract the integer part from the float, cast that to
+        // a signed integer with mantissa bits + 1, and if there was any non-integral part of the float,
+        // add/subtract 1.
+        const lhs_is_signed = if (lhs.value()) |lhs_val|
+            lhs_val.compareWithZero(.lt)
+        else
+            (lhs.ty.isFloat() or lhs.ty.isSignedInt());
+        const rhs_is_signed = if (rhs.value()) |rhs_val|
+            rhs_val.compareWithZero(.lt)
+        else
+            (rhs.ty.isFloat() or rhs.ty.isSignedInt());
+        const dest_int_is_signed = lhs_is_signed or rhs_is_signed;
+
+        var dest_float_type: ?Type = null;
+
+        var lhs_bits: usize = undefined;
+        if (lhs.value()) |lhs_val| {
+            if (lhs_val.isUndef())
+                return self.constUndef(src, Type.initTag(.bool));
+            const is_unsigned = if (lhs_is_float) x: {
+                var bigint_space: Value.BigIntSpace = undefined;
+                var bigint = lhs_val.toBigInt(&bigint_space);
+                const zcmp = lhs_val.orderAgainstZero();
+                if (lhs_val.floatHasFraction()) {
+                    switch (op) {
+                        .eq => return self.constBool(src, false),
+                        .neq => return self.constBool(src, true),
+                        else => {},
+                    }
+                    if (zcmp == .lt) {
+                        try bigint.addScalar(bigint, -1);
+                    } else {
+                        try bigint.addScalar(bigint, 1);
+                    }
+                }
+                lhs_bits = bigint.bitCountTwosComp();
+                break :x (zcmp != .lt);
+            } else x: {
+                lhs_bits = lhs_val.intBitCountTwosComp();
+                break :x (lhs_val.orderAgainstZero() != .lt);
+            };
+            lhs_bits += @boolToInt(is_unsigned and dest_int_is_signed);
+        } else if (lhs_is_float) {
+            dest_float_type = lhs.ty;
+        } else {
+            const int_info = lhs.ty.intInfo(self.target);
+            lhs_bits = int_info.bits + @boolToInt(!int_info.signed and dest_int_is_signed);
+        }
+
+        var rhs_bits: usize = undefined;
+        if (rhs.value()) |rhs_val| {
+            if (rhs_val.isUndef())
+                return self.constUndef(src, Type.initTag(.bool));
+            const is_unsigned = if (rhs_is_float) x: {
+                var bigint_space: Value.BigIntSpace = undefined;
+                var bigint = rhs_val.toBigInt(&bigint_space);
+                const zcmp = rhs_val.orderAgainstZero();
+                if (rhs_val.floatHasFraction()) {
+                    switch (op) {
+                        .eq => return self.constBool(src, false),
+                        .neq => return self.constBool(src, true),
+                        else => {},
+                    }
+                    if (zcmp == .lt) {
+                        try bigint.addScalar(bigint, -1);
+                    } else {
+                        try bigint.addScalar(bigint, 1);
+                    }
+                }
+                rhs_bits = bigint.bitCountTwosComp();
+                break :x (zcmp != .lt);
+            } else x: {
+                rhs_bits = rhs_val.intBitCountTwosComp();
+                break :x (rhs_val.orderAgainstZero() != .lt);
+            };
+            rhs_bits += @boolToInt(is_unsigned and dest_int_is_signed);
+        } else if (rhs_is_float) {
+            dest_float_type = rhs.ty;
+        } else {
+            const int_info = rhs.ty.intInfo(self.target);
+            rhs_bits = int_info.bits + @boolToInt(!int_info.signed and dest_int_is_signed);
+        }
+
+        const dest_type = if (dest_float_type) |ft| ft else blk: {
+            const max_bits = std.math.max(lhs_bits, rhs_bits);
+            const casted_bits = std.math.cast(u16, max_bits) catch |err| switch (err) {
+                error.Overflow => return self.fail(src, "{} exceeds maximum integer bit count", .{max_bits}),
+            };
+            break :blk try self.makeIntType(dest_int_is_signed, casted_bits);
+        };
+        const casted_lhs = try self.coerce(block, dest_type, lhs);
+        const casted_rhs = try self.coerce(block, dest_type, lhs);
+
+        return self.addNewInstArgs(b, src, dest_type, Inst.Cmp, Inst.Args(Inst.Cmp){
+            .lhs = casted_lhs,
+            .rhs = casted_rhs,
+            .op = op,
+        });
+    }
+
+    fn makeIntType(self: *Analyze, signed: bool, bits: u16) !Type {
+        if (signed) {
+            const int_payload = try self.arena.allocator.create(Type.Payload.IntSigned);
+            int_payload.* = .{ .bits = bits };
+            return Type.initPayload(&int_payload.base);
+        } else {
+            const int_payload = try self.arena.allocator.create(Type.Payload.IntUnsigned);
+            int_payload.* = .{ .bits = bits };
+            return Type.initPayload(&int_payload.base);
+        }
     }
 
-    fn coerce(self: *Analyze, func: ?*Fn, dest_type: Type, inst: *Inst) !*Inst {
+    fn coerce(self: *Analyze, block: ?*Block, dest_type: Type, inst: *Inst) !*Inst {
         // If the types are the same, we can return the operand.
         if (dest_type.eql(inst.ty))
             return inst;
 
         const in_memory_result = coerceInMemoryAllowed(dest_type, inst.ty);
         if (in_memory_result == .ok) {
-            return self.bitcast(func, dest_type, inst);
+            return self.bitcast(block, dest_type, inst);
         }
 
         // *[N]T to []T
@@ -740,14 +1150,14 @@ const Analyze = struct {
         return self.fail(inst.src, "TODO implement type coercion from {} to {}", .{ inst.ty, dest_type });
     }
 
-    fn bitcast(self: *Analyze, func: ?*Fn, dest_type: Type, inst: *Inst) !*Inst {
+    fn bitcast(self: *Analyze, block: ?*Block, dest_type: Type, inst: *Inst) !*Inst {
         if (inst.value()) |val| {
             // Keep the comptime Value representation; take the new type.
             return self.constInst(inst.src, .{ .ty = dest_type, .val = val });
         }
         // TODO validate the type size and other compile errors
-        const f = try self.requireFunctionBody(func, inst.src);
-        return self.addNewInstArgs(f, inst.src, dest_type, Inst.BitCast, Inst.Args(Inst.BitCast){ .operand = inst });
+        const b = try self.requireRuntimeBlock(block, inst.src);
+        return self.addNewInstArgs(b, inst.src, dest_type, Inst.BitCast, Inst.Args(Inst.BitCast){ .operand = inst });
     }
 
     fn coerceArrayPtrToSlice(self: *Analyze, dest_type: Type, inst: *Inst) !*Inst {
@@ -831,17 +1241,31 @@ pub fn main() anyerror!void {
         try bos.flush();
     }
 
+    // executable
+    //const link = @import("link.zig");
+    //var result = try link.updateExecutableFilePath(allocator, analyzed_module, std.fs.cwd(), "a.out");
+    //defer result.deinit(allocator);
+    //if (result.errors.len != 0) {
+    //    for (result.errors) |err_msg| {
+    //        const loc = std.zig.findLineColumn(source, err_msg.byte_offset);
+    //        std.debug.warn("{}:{}:{}: error: {}\n", .{ src_path, loc.line + 1, loc.column + 1, err_msg.msg });
+    //    }
+    //    if (debug_error_trace) return error.LinkFailure;
+    //    std.process.exit(1);
+    //}
+
+    // object file
     const link = @import("link.zig");
-    var result = try link.updateExecutableFilePath(allocator, analyzed_module, std.fs.cwd(), "a.out");
-    defer result.deinit(allocator);
-    if (result.errors.len != 0) {
-        for (result.errors) |err_msg| {
-            const loc = std.zig.findLineColumn(source, err_msg.byte_offset);
-            std.debug.warn("{}:{}:{}: error: {}\n", .{ src_path, loc.line + 1, loc.column + 1, err_msg.msg });
-        }
-        if (debug_error_trace) return error.LinkFailure;
-        std.process.exit(1);
-    }
+    //var result = try link.updateExecutableFilePath(allocator, analyzed_module, std.fs.cwd(), "a.out");
+    //defer result.deinit(allocator);
+    //if (result.errors.len != 0) {
+    //    for (result.errors) |err_msg| {
+    //        const loc = std.zig.findLineColumn(source, err_msg.byte_offset);
+    //        std.debug.warn("{}:{}:{}: error: {}\n", .{ src_path, loc.line + 1, loc.column + 1, err_msg.msg });
+    //    }
+    //    if (debug_error_trace) return error.LinkFailure;
+    //    std.process.exit(1);
+    //}
 }
 
 // Performance optimization ideas:
src-self-hosted/type.zig
@@ -20,35 +20,37 @@ pub const Type = extern union {
 
     pub fn zigTypeTag(self: Type) std.builtin.TypeId {
         switch (self.tag()) {
-            .@"u8",
-            .@"i8",
-            .@"isize",
-            .@"usize",
-            .@"c_short",
-            .@"c_ushort",
-            .@"c_int",
-            .@"c_uint",
-            .@"c_long",
-            .@"c_ulong",
-            .@"c_longlong",
-            .@"c_ulonglong",
-            .@"c_longdouble",
+            .u8,
+            .i8,
+            .isize,
+            .usize,
+            .c_short,
+            .c_ushort,
+            .c_int,
+            .c_uint,
+            .c_long,
+            .c_ulong,
+            .c_longlong,
+            .c_ulonglong,
+            .c_longdouble,
+            .int_signed,
+            .int_unsigned,
             => return .Int,
 
-            .@"f16",
-            .@"f32",
-            .@"f64",
-            .@"f128",
+            .f16,
+            .f32,
+            .f64,
+            .f128,
             => return .Float,
 
-            .@"c_void" => return .Opaque,
-            .@"bool" => return .Bool,
-            .@"void" => return .Void,
-            .@"type" => return .Type,
-            .@"anyerror" => return .ErrorSet,
-            .@"comptime_int" => return .ComptimeInt,
-            .@"comptime_float" => return .ComptimeFloat,
-            .@"noreturn" => return .NoReturn,
+            .c_void => return .Opaque,
+            .bool => return .Bool,
+            .void => return .Void,
+            .type => return .Type,
+            .anyerror => return .ErrorSet,
+            .comptime_int => return .ComptimeInt,
+            .comptime_float => return .ComptimeFloat,
+            .noreturn => return .NoReturn,
 
             .fn_naked_noreturn_no_args => return .Fn,
 
@@ -153,31 +155,31 @@ pub const Type = extern union {
         while (true) {
             const t = ty.tag();
             switch (t) {
-                .@"u8",
-                .@"i8",
-                .@"isize",
-                .@"usize",
-                .@"c_short",
-                .@"c_ushort",
-                .@"c_int",
-                .@"c_uint",
-                .@"c_long",
-                .@"c_ulong",
-                .@"c_longlong",
-                .@"c_ulonglong",
-                .@"c_longdouble",
-                .@"c_void",
-                .@"f16",
-                .@"f32",
-                .@"f64",
-                .@"f128",
-                .@"bool",
-                .@"void",
-                .@"type",
-                .@"anyerror",
-                .@"comptime_int",
-                .@"comptime_float",
-                .@"noreturn",
+                .u8,
+                .i8,
+                .isize,
+                .usize,
+                .c_short,
+                .c_ushort,
+                .c_int,
+                .c_uint,
+                .c_long,
+                .c_ulong,
+                .c_longlong,
+                .c_ulonglong,
+                .c_longdouble,
+                .c_void,
+                .f16,
+                .f32,
+                .f64,
+                .f128,
+                .bool,
+                .void,
+                .type,
+                .anyerror,
+                .comptime_int,
+                .comptime_float,
+                .noreturn,
                 => return out_stream.writeAll(@tagName(t)),
 
                 .const_slice_u8 => return out_stream.writeAll("[]const u8"),
@@ -200,6 +202,14 @@ pub const Type = extern union {
                     ty = payload.pointee_type;
                     continue;
                 },
+                .int_signed => {
+                    const payload = @fieldParentPtr(Payload.IntSigned, "base", ty.ptr_otherwise);
+                    return out_stream.print("i{}", .{payload.bits});
+                },
+                .int_unsigned => {
+                    const payload = @fieldParentPtr(Payload.IntUnsigned, "base", ty.ptr_otherwise);
+                    return out_stream.print("u{}", .{payload.bits});
+                },
             }
             unreachable;
         }
@@ -207,31 +217,31 @@ pub const Type = extern union {
 
     pub fn toValue(self: Type, allocator: *Allocator) Allocator.Error!Value {
         switch (self.tag()) {
-            .@"u8" => return Value.initTag(.u8_type),
-            .@"i8" => return Value.initTag(.i8_type),
-            .@"isize" => return Value.initTag(.isize_type),
-            .@"usize" => return Value.initTag(.usize_type),
-            .@"c_short" => return Value.initTag(.c_short_type),
-            .@"c_ushort" => return Value.initTag(.c_ushort_type),
-            .@"c_int" => return Value.initTag(.c_int_type),
-            .@"c_uint" => return Value.initTag(.c_uint_type),
-            .@"c_long" => return Value.initTag(.c_long_type),
-            .@"c_ulong" => return Value.initTag(.c_ulong_type),
-            .@"c_longlong" => return Value.initTag(.c_longlong_type),
-            .@"c_ulonglong" => return Value.initTag(.c_ulonglong_type),
-            .@"c_longdouble" => return Value.initTag(.c_longdouble_type),
-            .@"c_void" => return Value.initTag(.c_void_type),
-            .@"f16" => return Value.initTag(.f16_type),
-            .@"f32" => return Value.initTag(.f32_type),
-            .@"f64" => return Value.initTag(.f64_type),
-            .@"f128" => return Value.initTag(.f128_type),
-            .@"bool" => return Value.initTag(.bool_type),
-            .@"void" => return Value.initTag(.void_type),
-            .@"type" => return Value.initTag(.type_type),
-            .@"anyerror" => return Value.initTag(.anyerror_type),
-            .@"comptime_int" => return Value.initTag(.comptime_int_type),
-            .@"comptime_float" => return Value.initTag(.comptime_float_type),
-            .@"noreturn" => return Value.initTag(.noreturn_type),
+            .u8 => return Value.initTag(.u8_type),
+            .i8 => return Value.initTag(.i8_type),
+            .isize => return Value.initTag(.isize_type),
+            .usize => return Value.initTag(.usize_type),
+            .c_short => return Value.initTag(.c_short_type),
+            .c_ushort => return Value.initTag(.c_ushort_type),
+            .c_int => return Value.initTag(.c_int_type),
+            .c_uint => return Value.initTag(.c_uint_type),
+            .c_long => return Value.initTag(.c_long_type),
+            .c_ulong => return Value.initTag(.c_ulong_type),
+            .c_longlong => return Value.initTag(.c_longlong_type),
+            .c_ulonglong => return Value.initTag(.c_ulonglong_type),
+            .c_longdouble => return Value.initTag(.c_longdouble_type),
+            .c_void => return Value.initTag(.c_void_type),
+            .f16 => return Value.initTag(.f16_type),
+            .f32 => return Value.initTag(.f32_type),
+            .f64 => return Value.initTag(.f64_type),
+            .f128 => return Value.initTag(.f128_type),
+            .bool => return Value.initTag(.bool_type),
+            .void => return Value.initTag(.void_type),
+            .type => return Value.initTag(.type_type),
+            .anyerror => return Value.initTag(.anyerror_type),
+            .comptime_int => return Value.initTag(.comptime_int_type),
+            .comptime_float => return Value.initTag(.comptime_float_type),
+            .noreturn => return Value.initTag(.noreturn_type),
             .fn_naked_noreturn_no_args => return Value.initTag(.fn_naked_noreturn_no_args_type),
             .single_const_pointer_to_comptime_int => return Value.initTag(.single_const_pointer_to_comptime_int_type),
             .const_slice_u8 => return Value.initTag(.const_slice_u8_type),
@@ -245,35 +255,37 @@ pub const Type = extern union {
 
     pub fn isSinglePointer(self: Type) bool {
         return switch (self.tag()) {
-            .@"u8",
-            .@"i8",
-            .@"isize",
-            .@"usize",
-            .@"c_short",
-            .@"c_ushort",
-            .@"c_int",
-            .@"c_uint",
-            .@"c_long",
-            .@"c_ulong",
-            .@"c_longlong",
-            .@"c_ulonglong",
-            .@"c_longdouble",
-            .@"f16",
-            .@"f32",
-            .@"f64",
-            .@"f128",
-            .@"c_void",
-            .@"bool",
-            .@"void",
-            .@"type",
-            .@"anyerror",
-            .@"comptime_int",
-            .@"comptime_float",
-            .@"noreturn",
+            .u8,
+            .i8,
+            .isize,
+            .usize,
+            .c_short,
+            .c_ushort,
+            .c_int,
+            .c_uint,
+            .c_long,
+            .c_ulong,
+            .c_longlong,
+            .c_ulonglong,
+            .c_longdouble,
+            .f16,
+            .f32,
+            .f64,
+            .f128,
+            .c_void,
+            .bool,
+            .void,
+            .type,
+            .anyerror,
+            .comptime_int,
+            .comptime_float,
+            .noreturn,
             .array,
             .array_u8_sentinel_0,
             .const_slice_u8,
             .fn_naked_noreturn_no_args,
+            .int_unsigned,
+            .int_signed,
             => false,
 
             .single_const_pointer,
@@ -284,36 +296,38 @@ pub const Type = extern union {
 
     pub fn isSlice(self: Type) bool {
         return switch (self.tag()) {
-            .@"u8",
-            .@"i8",
-            .@"isize",
-            .@"usize",
-            .@"c_short",
-            .@"c_ushort",
-            .@"c_int",
-            .@"c_uint",
-            .@"c_long",
-            .@"c_ulong",
-            .@"c_longlong",
-            .@"c_ulonglong",
-            .@"c_longdouble",
-            .@"f16",
-            .@"f32",
-            .@"f64",
-            .@"f128",
-            .@"c_void",
-            .@"bool",
-            .@"void",
-            .@"type",
-            .@"anyerror",
-            .@"comptime_int",
-            .@"comptime_float",
-            .@"noreturn",
+            .u8,
+            .i8,
+            .isize,
+            .usize,
+            .c_short,
+            .c_ushort,
+            .c_int,
+            .c_uint,
+            .c_long,
+            .c_ulong,
+            .c_longlong,
+            .c_ulonglong,
+            .c_longdouble,
+            .f16,
+            .f32,
+            .f64,
+            .f128,
+            .c_void,
+            .bool,
+            .void,
+            .type,
+            .anyerror,
+            .comptime_int,
+            .comptime_float,
+            .noreturn,
             .array,
             .array_u8_sentinel_0,
             .single_const_pointer,
             .single_const_pointer_to_comptime_int,
             .fn_naked_noreturn_no_args,
+            .int_unsigned,
+            .int_signed,
             => false,
 
             .const_slice_u8 => true,
@@ -323,34 +337,36 @@ pub const Type = extern union {
     /// Asserts the type is a pointer type.
     pub fn pointerIsConst(self: Type) bool {
         return switch (self.tag()) {
-            .@"u8",
-            .@"i8",
-            .@"isize",
-            .@"usize",
-            .@"c_short",
-            .@"c_ushort",
-            .@"c_int",
-            .@"c_uint",
-            .@"c_long",
-            .@"c_ulong",
-            .@"c_longlong",
-            .@"c_ulonglong",
-            .@"c_longdouble",
-            .@"f16",
-            .@"f32",
-            .@"f64",
-            .@"f128",
-            .@"c_void",
-            .@"bool",
-            .@"void",
-            .@"type",
-            .@"anyerror",
-            .@"comptime_int",
-            .@"comptime_float",
-            .@"noreturn",
+            .u8,
+            .i8,
+            .isize,
+            .usize,
+            .c_short,
+            .c_ushort,
+            .c_int,
+            .c_uint,
+            .c_long,
+            .c_ulong,
+            .c_longlong,
+            .c_ulonglong,
+            .c_longdouble,
+            .f16,
+            .f32,
+            .f64,
+            .f128,
+            .c_void,
+            .bool,
+            .void,
+            .type,
+            .anyerror,
+            .comptime_int,
+            .comptime_float,
+            .noreturn,
             .array,
             .array_u8_sentinel_0,
             .fn_naked_noreturn_no_args,
+            .int_unsigned,
+            .int_signed,
             => unreachable,
 
             .single_const_pointer,
@@ -363,32 +379,34 @@ pub const Type = extern union {
     /// Asserts the type is a pointer or array type.
     pub fn elemType(self: Type) Type {
         return switch (self.tag()) {
-            .@"u8",
-            .@"i8",
-            .@"isize",
-            .@"usize",
-            .@"c_short",
-            .@"c_ushort",
-            .@"c_int",
-            .@"c_uint",
-            .@"c_long",
-            .@"c_ulong",
-            .@"c_longlong",
-            .@"c_ulonglong",
-            .@"c_longdouble",
-            .@"f16",
-            .@"f32",
-            .@"f64",
-            .@"f128",
-            .@"c_void",
-            .@"bool",
-            .@"void",
-            .@"type",
-            .@"anyerror",
-            .@"comptime_int",
-            .@"comptime_float",
-            .@"noreturn",
+            .u8,
+            .i8,
+            .isize,
+            .usize,
+            .c_short,
+            .c_ushort,
+            .c_int,
+            .c_uint,
+            .c_long,
+            .c_ulong,
+            .c_longlong,
+            .c_ulonglong,
+            .c_longdouble,
+            .f16,
+            .f32,
+            .f64,
+            .f128,
+            .c_void,
+            .bool,
+            .void,
+            .type,
+            .anyerror,
+            .comptime_int,
+            .comptime_float,
+            .noreturn,
             .fn_naked_noreturn_no_args,
+            .int_unsigned,
+            .int_signed,
             => unreachable,
 
             .array => self.cast(Payload.Array).?.elem_type,
@@ -398,7 +416,7 @@ pub const Type = extern union {
         };
     }
 
-    /// Asserts the type is an array.
+    /// Asserts the type is an array or vector.
     pub fn arrayLen(self: Type) u64 {
         return switch (self.tag()) {
             .u8,
@@ -430,6 +448,8 @@ pub const Type = extern union {
             .single_const_pointer,
             .single_const_pointer_to_comptime_int,
             .const_slice_u8,
+            .int_unsigned,
+            .int_signed,
             => unreachable,
 
             .array => self.cast(Payload.Array).?.len,
@@ -437,22 +457,64 @@ pub const Type = extern union {
         };
     }
 
+    /// Returns true if and only if the type is a fixed-width, signed integer.
+    pub fn isSignedInt(self: Type) bool {
+        return switch (self.tag()) {
+            .f16,
+            .f32,
+            .f64,
+            .f128,
+            .c_longdouble,
+            .c_void,
+            .bool,
+            .void,
+            .type,
+            .anyerror,
+            .comptime_int,
+            .comptime_float,
+            .noreturn,
+            .fn_naked_noreturn_no_args,
+            .array,
+            .single_const_pointer,
+            .single_const_pointer_to_comptime_int,
+            .array_u8_sentinel_0,
+            .const_slice_u8,
+            .int_unsigned,
+            .u8,
+            .usize,
+            .c_ushort,
+            .c_uint,
+            .c_ulong,
+            .c_ulonglong,
+            => false,
+
+            .int_signed,
+            .i8,
+            .isize,
+            .c_short,
+            .c_int,
+            .c_long,
+            .c_longlong,
+            => true,
+        };
+    }
+
     /// Asserts the type is a fixed-width integer.
     pub fn intInfo(self: Type, target: Target) struct { signed: bool, bits: u16 } {
         return switch (self.tag()) {
-            .@"f16",
-            .@"f32",
-            .@"f64",
-            .@"f128",
-            .@"c_longdouble",
-            .@"c_void",
-            .@"bool",
-            .@"void",
-            .@"type",
-            .@"anyerror",
-            .@"comptime_int",
-            .@"comptime_float",
-            .@"noreturn",
+            .f16,
+            .f32,
+            .f64,
+            .f128,
+            .c_longdouble,
+            .c_void,
+            .bool,
+            .void,
+            .type,
+            .anyerror,
+            .comptime_int,
+            .comptime_float,
+            .noreturn,
             .fn_naked_noreturn_no_args,
             .array,
             .single_const_pointer,
@@ -461,18 +523,46 @@ pub const Type = extern union {
             .const_slice_u8,
             => unreachable,
 
-            .@"u8" => .{ .signed = false, .bits = 8 },
-            .@"i8" => .{ .signed = true, .bits = 8 },
-            .@"usize" => .{ .signed = false, .bits = target.cpu.arch.ptrBitWidth() },
-            .@"isize" => .{ .signed = true, .bits = target.cpu.arch.ptrBitWidth() },
-            .@"c_short" => .{ .signed = true, .bits = CInteger.short.sizeInBits(target) },
-            .@"c_ushort" => .{ .signed = false, .bits = CInteger.ushort.sizeInBits(target) },
-            .@"c_int" => .{ .signed = true, .bits = CInteger.int.sizeInBits(target) },
-            .@"c_uint" => .{ .signed = false, .bits = CInteger.uint.sizeInBits(target) },
-            .@"c_long" => .{ .signed = true, .bits = CInteger.long.sizeInBits(target) },
-            .@"c_ulong" => .{ .signed = false, .bits = CInteger.ulong.sizeInBits(target) },
-            .@"c_longlong" => .{ .signed = true, .bits = CInteger.longlong.sizeInBits(target) },
-            .@"c_ulonglong" => .{ .signed = false, .bits = CInteger.ulonglong.sizeInBits(target) },
+            .int_unsigned => .{ .signed = false, .bits = self.cast(Payload.IntUnsigned).?.bits },
+            .int_signed => .{ .signed = true, .bits = self.cast(Payload.IntSigned).?.bits },
+            .u8 => .{ .signed = false, .bits = 8 },
+            .i8 => .{ .signed = true, .bits = 8 },
+            .usize => .{ .signed = false, .bits = target.cpu.arch.ptrBitWidth() },
+            .isize => .{ .signed = true, .bits = target.cpu.arch.ptrBitWidth() },
+            .c_short => .{ .signed = true, .bits = CType.short.sizeInBits(target) },
+            .c_ushort => .{ .signed = false, .bits = CType.ushort.sizeInBits(target) },
+            .c_int => .{ .signed = true, .bits = CType.int.sizeInBits(target) },
+            .c_uint => .{ .signed = false, .bits = CType.uint.sizeInBits(target) },
+            .c_long => .{ .signed = true, .bits = CType.long.sizeInBits(target) },
+            .c_ulong => .{ .signed = false, .bits = CType.ulong.sizeInBits(target) },
+            .c_longlong => .{ .signed = true, .bits = CType.longlong.sizeInBits(target) },
+            .c_ulonglong => .{ .signed = false, .bits = CType.ulonglong.sizeInBits(target) },
+        };
+    }
+
+    pub fn isFloat(self: Type) bool {
+        return switch (self.tag()) {
+            .f16,
+            .f32,
+            .f64,
+            .f128,
+            .c_longdouble,
+            => true,
+
+            else => false,
+        };
+    }
+
+    /// Asserts the type is a fixed-size float.
+    pub fn floatBits(self: Type, target: Target) u16 {
+        return switch (self.tag()) {
+            .f16 => 16,
+            .f32 => 32,
+            .f64 => 64,
+            .f128 => 128,
+            .c_longdouble => CType.longdouble.sizeInBits(target),
+
+            else => unreachable,
         };
     }
 
@@ -511,6 +601,8 @@ pub const Type = extern union {
             .c_ulong,
             .c_longlong,
             .c_ulonglong,
+            .int_unsigned,
+            .int_signed,
             => unreachable,
         };
     }
@@ -551,6 +643,8 @@ pub const Type = extern union {
             .c_ulong,
             .c_longlong,
             .c_ulonglong,
+            .int_unsigned,
+            .int_signed,
             => unreachable,
         }
     }
@@ -590,6 +684,8 @@ pub const Type = extern union {
             .c_ulong,
             .c_longlong,
             .c_ulonglong,
+            .int_unsigned,
+            .int_signed,
             => unreachable,
         };
     }
@@ -629,10 +725,145 @@ pub const Type = extern union {
             .c_ulong,
             .c_longlong,
             .c_ulonglong,
+            .int_unsigned,
+            .int_signed,
             => unreachable,
         };
     }
 
+    pub fn isNumeric(self: Type) bool {
+        return switch (self.tag()) {
+            .f16,
+            .f32,
+            .f64,
+            .f128,
+            .c_longdouble,
+            .comptime_int,
+            .comptime_float,
+            .u8,
+            .i8,
+            .usize,
+            .isize,
+            .c_short,
+            .c_ushort,
+            .c_int,
+            .c_uint,
+            .c_long,
+            .c_ulong,
+            .c_longlong,
+            .c_ulonglong,
+            .int_unsigned,
+            .int_signed,
+            => true,
+
+            .c_void,
+            .bool,
+            .void,
+            .type,
+            .anyerror,
+            .noreturn,
+            .fn_naked_noreturn_no_args,
+            .array,
+            .single_const_pointer,
+            .single_const_pointer_to_comptime_int,
+            .array_u8_sentinel_0,
+            .const_slice_u8,
+            => false,
+        };
+    }
+
+    pub fn onePossibleValue(self: Type) bool {
+        var ty = self;
+        while (true) switch (ty.tag()) {
+            .f16,
+            .f32,
+            .f64,
+            .f128,
+            .c_longdouble,
+            .comptime_int,
+            .comptime_float,
+            .u8,
+            .i8,
+            .usize,
+            .isize,
+            .c_short,
+            .c_ushort,
+            .c_int,
+            .c_uint,
+            .c_long,
+            .c_ulong,
+            .c_longlong,
+            .c_ulonglong,
+            .bool,
+            .type,
+            .anyerror,
+            .fn_naked_noreturn_no_args,
+            .single_const_pointer_to_comptime_int,
+            .array_u8_sentinel_0,
+            .const_slice_u8,
+            => return false,
+
+            .c_void,
+            .void,
+            .noreturn,
+            => return true,
+
+            .int_unsigned => return ty.cast(Payload.IntUnsigned).?.bits == 0,
+            .int_signed => return ty.cast(Payload.IntSigned).?.bits == 0,
+            .array => {
+                const array = ty.cast(Payload.Array).?;
+                if (array.len == 0)
+                    return true;
+                ty = array.elem_type;
+                continue;
+            },
+            .single_const_pointer => {
+                const ptr = ty.cast(Payload.SingleConstPointer).?;
+                ty = ptr.pointee_type;
+                continue;
+            },
+        };
+    }
+
+    pub fn isCPtr(self: Type) bool {
+        return switch (self.tag()) {
+            .f16,
+            .f32,
+            .f64,
+            .f128,
+            .c_longdouble,
+            .comptime_int,
+            .comptime_float,
+            .u8,
+            .i8,
+            .usize,
+            .isize,
+            .c_short,
+            .c_ushort,
+            .c_int,
+            .c_uint,
+            .c_long,
+            .c_ulong,
+            .c_longlong,
+            .c_ulonglong,
+            .bool,
+            .type,
+            .anyerror,
+            .fn_naked_noreturn_no_args,
+            .single_const_pointer_to_comptime_int,
+            .array_u8_sentinel_0,
+            .const_slice_u8,
+            .c_void,
+            .void,
+            .noreturn,
+            .int_unsigned,
+            .int_signed,
+            .array,
+            .single_const_pointer,
+            => return false,
+        };
+    }
+
     /// This enum does not directly correspond to `std.builtin.TypeId` because
     /// it has extra enum tags in it, as a way of using less memory. For example,
     /// even though Zig recognizes `*align(10) i32` and `*i32` both as Pointer types
@@ -674,6 +905,8 @@ pub const Type = extern union {
         array_u8_sentinel_0,
         array,
         single_const_pointer,
+        int_signed,
+        int_unsigned,
 
         pub const last_no_payload_tag = Tag.const_slice_u8;
         pub const no_payload_count = @enumToInt(last_no_payload_tag) + 1;
@@ -700,10 +933,22 @@ pub const Type = extern union {
 
             pointee_type: Type,
         };
+
+        pub const IntSigned = struct {
+            base: Payload = Payload{ .tag = .int_signed },
+
+            bits: u16,
+        };
+
+        pub const IntUnsigned = struct {
+            base: Payload = Payload{ .tag = .int_unsigned },
+
+            bits: u16,
+        };
     };
 };
 
-pub const CInteger = enum {
+pub const CType = enum {
     short,
     ushort,
     int,
@@ -712,8 +957,9 @@ pub const CInteger = enum {
     ulong,
     longlong,
     ulonglong,
+    longdouble,
 
-    pub fn sizeInBits(self: CInteger, target: Target) u16 {
+    pub fn sizeInBits(self: CType, target: Target) u16 {
         const arch = target.cpu.arch;
         switch (target.os.tag) {
             .freestanding, .other => switch (target.cpu.arch) {
@@ -729,6 +975,7 @@ pub const CInteger = enum {
                     .longlong,
                     .ulonglong,
                     => return 64,
+                    .longdouble => @panic("TODO figure out what kind of float `long double` is on this target"),
                 },
                 else => switch (self) {
                     .short,
@@ -743,6 +990,7 @@ pub const CInteger = enum {
                     .longlong,
                     .ulonglong,
                     => return 64,
+                    .longdouble => @panic("TODO figure out what kind of float `long double` is on this target"),
                 },
             },
 
@@ -767,6 +1015,7 @@ pub const CInteger = enum {
                 .longlong,
                 .ulonglong,
                 => return 64,
+                .longdouble => @panic("TODO figure out what kind of float `long double` is on this target"),
             },
 
             .windows, .uefi => switch (self) {
@@ -781,6 +1030,7 @@ pub const CInteger = enum {
                 .longlong,
                 .ulonglong,
                 => return 64,
+                .longdouble => @panic("TODO figure out what kind of float `long double` is on this target"),
             },
 
             .ios => switch (self) {
@@ -795,6 +1045,7 @@ pub const CInteger = enum {
                 .longlong,
                 .ulonglong,
                 => return 64,
+                .longdouble => @panic("TODO figure out what kind of float `long double` is on this target"),
             },
 
             .ananas,
@@ -821,7 +1072,7 @@ pub const CInteger = enum {
             .amdpal,
             .hermit,
             .hurd,
-            => @panic("TODO specify the C integer type sizes for this OS"),
+            => @panic("TODO specify the C integer and float type sizes for this OS"),
         }
     }
 };
src-self-hosted/value.zig
@@ -48,9 +48,10 @@ pub const Value = extern union {
         single_const_pointer_to_comptime_int_type,
         const_slice_u8_type,
 
+        undef,
         zero,
-        void_value,
-        noreturn_value,
+        the_one_possible_value, // when the type only has one possible value
+        null_value,
         bool_true,
         bool_false, // See last_no_payload_tag below.
         // After this, the tag requires a payload.
@@ -63,6 +64,7 @@ pub const Value = extern union {
         ref,
         ref_val,
         bytes,
+        repeated, // the value is a value repeated some number of times
 
         pub const last_no_payload_tag = Tag.bool_false;
         pub const no_payload_count = @enumToInt(last_no_payload_tag) + 1;
@@ -135,9 +137,10 @@ pub const Value = extern union {
             .single_const_pointer_to_comptime_int_type => return out_stream.writeAll("*const comptime_int"),
             .const_slice_u8_type => return out_stream.writeAll("[]const u8"),
 
+            .null_value => return out_stream.writeAll("null"),
+            .undef => return out_stream.writeAll("undefined"),
             .zero => return out_stream.writeAll("0"),
-            .void_value => return out_stream.writeAll("{}"),
-            .noreturn_value => return out_stream.writeAll("unreachable"),
+            .the_one_possible_value => return out_stream.writeAll("(one possible value)"),
             .bool_true => return out_stream.writeAll("true"),
             .bool_false => return out_stream.writeAll("false"),
             .ty => return val.cast(Payload.Ty).?.ty.format("", options, out_stream),
@@ -152,6 +155,10 @@ pub const Value = extern union {
                 continue;
             },
             .bytes => return std.zig.renderStringLiteral(self.cast(Payload.Bytes).?.data, out_stream),
+            .repeated => {
+                try out_stream.writeAll("(repeated) ");
+                val = val.cast(Payload.Repeated).?.val;
+            },
         };
     }
 
@@ -198,11 +205,12 @@ pub const Value = extern union {
             .single_const_pointer_to_comptime_int_type => Type.initTag(.single_const_pointer_to_comptime_int),
             .const_slice_u8_type => Type.initTag(.const_slice_u8),
 
+            .undef,
             .zero,
-            .void_value,
-            .noreturn_value,
+            .the_one_possible_value,
             .bool_true,
             .bool_false,
+            .null_value,
             .int_u64,
             .int_i64,
             .int_big,
@@ -210,12 +218,13 @@ pub const Value = extern union {
             .ref,
             .ref_val,
             .bytes,
+            .repeated,
             => unreachable,
         };
     }
 
     /// Asserts the value is an integer.
-    pub fn toBigInt(self: Value, allocator: *Allocator) Allocator.Error!BigInt {
+    pub fn toBigInt(self: Value, space: *BigIntSpace) BigInt {
         switch (self.tag()) {
             .ty,
             .u8_type,
@@ -246,20 +255,23 @@ pub const Value = extern union {
             .fn_naked_noreturn_no_args_type,
             .single_const_pointer_to_comptime_int_type,
             .const_slice_u8_type,
-            .void_value,
-            .noreturn_value,
             .bool_true,
             .bool_false,
+            .null_value,
             .function,
             .ref,
             .ref_val,
             .bytes,
+            .undef,
+            .repeated,
             => unreachable,
 
-            .zero => return BigInt.initSet(allocator, 0),
+            .the_one_possible_value, // An integer with one possible value is always zero.
+            .zero,
+            => return BigInt.initSetFixed(&space.limbs, 0),
 
-            .int_u64 => return BigInt.initSet(allocator, self.cast(Payload.Int_u64).?.int),
-            .int_i64 => return BigInt.initSet(allocator, self.cast(Payload.Int_i64).?.int),
+            .int_u64 => return BigInt.initSetFixed(&space.limbs, self.cast(Payload.Int_u64).?.int),
+            .int_i64 => return BigInt.initSetFixed(&space.limbs, self.cast(Payload.Int_i64).?.int),
             .int_big => return self.cast(Payload.IntBig).?.big_int,
         }
     }
@@ -296,17 +308,20 @@ pub const Value = extern union {
             .fn_naked_noreturn_no_args_type,
             .single_const_pointer_to_comptime_int_type,
             .const_slice_u8_type,
-            .void_value,
-            .noreturn_value,
             .bool_true,
             .bool_false,
+            .null_value,
             .function,
             .ref,
             .ref_val,
             .bytes,
+            .undef,
+            .repeated,
             => unreachable,
 
-            .zero => return 0,
+            .zero,
+            .the_one_possible_value, // an integer with one possible value is always zero
+            => return 0,
 
             .int_u64 => return self.cast(Payload.Int_u64).?.int,
             .int_i64 => return @intCast(u64, self.cast(Payload.Int_u64).?.int),
@@ -314,6 +329,66 @@ pub const Value = extern union {
         }
     }
 
+    /// Asserts the value is an integer and not undefined.
+    /// Returns the number of bits the value requires to represent stored in twos complement form.
+    pub fn intBitCountTwosComp(self: Value) usize {
+        switch (self.tag()) {
+            .ty,
+            .u8_type,
+            .i8_type,
+            .isize_type,
+            .usize_type,
+            .c_short_type,
+            .c_ushort_type,
+            .c_int_type,
+            .c_uint_type,
+            .c_long_type,
+            .c_ulong_type,
+            .c_longlong_type,
+            .c_ulonglong_type,
+            .c_longdouble_type,
+            .f16_type,
+            .f32_type,
+            .f64_type,
+            .f128_type,
+            .c_void_type,
+            .bool_type,
+            .void_type,
+            .type_type,
+            .anyerror_type,
+            .comptime_int_type,
+            .comptime_float_type,
+            .noreturn_type,
+            .fn_naked_noreturn_no_args_type,
+            .single_const_pointer_to_comptime_int_type,
+            .const_slice_u8_type,
+            .bool_true,
+            .bool_false,
+            .null_value,
+            .function,
+            .ref,
+            .ref_val,
+            .bytes,
+            .undef,
+            .repeated,
+            => unreachable,
+
+            .the_one_possible_value, // an integer with one possible value is always zero
+            .zero,
+            => return 0,
+
+            .int_u64 => {
+                const x = self.cast(Payload.Int_u64).?.int;
+                if (x == 0) return 0;
+                return std.math.log2(x) + 1;
+            },
+            .int_i64 => {
+                @panic("TODO implement i64 intBitCountTwosComp");
+            },
+            .int_big => return self.cast(Payload.IntBig).?.big_int.bitCountTwosComp(),
+        }
+    }
+
     /// Asserts the value is an integer, and the destination type is ComptimeInt or Int.
     pub fn intFitsInType(self: Value, ty: Type, target: Target) bool {
         switch (self.tag()) {
@@ -346,17 +421,20 @@ pub const Value = extern union {
             .fn_naked_noreturn_no_args_type,
             .single_const_pointer_to_comptime_int_type,
             .const_slice_u8_type,
-            .void_value,
-            .noreturn_value,
             .bool_true,
             .bool_false,
+            .null_value,
             .function,
             .ref,
             .ref_val,
             .bytes,
+            .repeated,
             => unreachable,
 
-            .zero => return true,
+            .zero,
+            .undef,
+            .the_one_possible_value, // an integer with one possible value is always zero
+            => return true,
 
             .int_u64 => switch (ty.zigTypeTag()) {
                 .Int => {
@@ -392,9 +470,148 @@ pub const Value = extern union {
         }
     }
 
+    /// Asserts the value is a float
+    pub fn floatHasFraction(self: Value) bool {
+        return switch (self.tag()) {
+            .ty,
+            .u8_type,
+            .i8_type,
+            .isize_type,
+            .usize_type,
+            .c_short_type,
+            .c_ushort_type,
+            .c_int_type,
+            .c_uint_type,
+            .c_long_type,
+            .c_ulong_type,
+            .c_longlong_type,
+            .c_ulonglong_type,
+            .c_longdouble_type,
+            .f16_type,
+            .f32_type,
+            .f64_type,
+            .f128_type,
+            .c_void_type,
+            .bool_type,
+            .void_type,
+            .type_type,
+            .anyerror_type,
+            .comptime_int_type,
+            .comptime_float_type,
+            .noreturn_type,
+            .fn_naked_noreturn_no_args_type,
+            .single_const_pointer_to_comptime_int_type,
+            .const_slice_u8_type,
+            .bool_true,
+            .bool_false,
+            .null_value,
+            .function,
+            .ref,
+            .ref_val,
+            .bytes,
+            .repeated,
+            .undef,
+            .int_u64,
+            .int_i64,
+            .int_big,
+            .the_one_possible_value,
+            => unreachable,
+
+            .zero => false,
+        };
+    }
+
+    pub fn orderAgainstZero(lhs: Value) std.math.Order {
+        switch (lhs.tag()) {
+            .ty,
+            .u8_type,
+            .i8_type,
+            .isize_type,
+            .usize_type,
+            .c_short_type,
+            .c_ushort_type,
+            .c_int_type,
+            .c_uint_type,
+            .c_long_type,
+            .c_ulong_type,
+            .c_longlong_type,
+            .c_ulonglong_type,
+            .c_longdouble_type,
+            .f16_type,
+            .f32_type,
+            .f64_type,
+            .f128_type,
+            .c_void_type,
+            .bool_type,
+            .void_type,
+            .type_type,
+            .anyerror_type,
+            .comptime_int_type,
+            .comptime_float_type,
+            .noreturn_type,
+            .fn_naked_noreturn_no_args_type,
+            .single_const_pointer_to_comptime_int_type,
+            .const_slice_u8_type,
+            .bool_true,
+            .bool_false,
+            .null_value,
+            .function,
+            .ref,
+            .ref_val,
+            .bytes,
+            .repeated,
+            .undef,
+            => unreachable,
+
+            .zero,
+            .the_one_possible_value, // an integer with one possible value is always zero
+            => return .eq,
+
+            .int_u64 => return std.math.order(lhs.cast(Payload.Int_u64).?.int, 0),
+            .int_i64 => return std.math.order(lhs.cast(Payload.Int_i64).?.int, 0),
+            .int_big => return lhs.cast(Payload.IntBig).?.big_int.orderAgainstScalar(0),
+        }
+    }
+
+    /// Asserts the value is comparable.
+    pub fn order(lhs: Value, rhs: Value) std.math.Order {
+        const lhs_tag = lhs.tag();
+        const rhs_tag = lhs.tag();
+        const lhs_is_zero = lhs_tag == .zero or lhs_tag == .the_one_possible_value;
+        const rhs_is_zero = rhs_tag == .zero or rhs_tag == .the_one_possible_value;
+        if (lhs_is_zero) return rhs.orderAgainstZero().invert();
+        if (rhs_is_zero) return lhs.orderAgainstZero();
+
+        // TODO floats
+
+        var lhs_bigint_space: BigIntSpace = undefined;
+        var rhs_bigint_space: BigIntSpace = undefined;
+        const lhs_bigint = lhs.toBigInt(&lhs_bigint_space);
+        const rhs_bigint = rhs.toBigInt(&rhs_bigint_space);
+        return BigInt.cmp(lhs_bigint, rhs_bigint);
+    }
+
+    /// Asserts the value is comparable.
+    pub fn compare(lhs: Value, op: std.math.CompareOperator, rhs: Value) bool {
+        return order(lhs, rhs).compare(op);
+    }
+
+    /// Asserts the value is comparable.
+    pub fn compareWithZero(lhs: Value, op: std.math.CompareOperator) bool {
+        return orderAgainstZero(lhs).compare(op);
+    }
+
+    pub fn toBool(self: Value) bool {
+        return switch (self.tag()) {
+            .bool_true => true,
+            .bool_false => false,
+            else => unreachable,
+        };
+    }
+
     /// Asserts the value is a pointer and dereferences it.
     pub fn pointerDeref(self: Value) Value {
-        switch (self.tag()) {
+        return switch (self.tag()) {
             .ty,
             .u8_type,
             .i8_type,
@@ -425,20 +642,22 @@ pub const Value = extern union {
             .single_const_pointer_to_comptime_int_type,
             .const_slice_u8_type,
             .zero,
-            .void_value,
-            .noreturn_value,
             .bool_true,
             .bool_false,
+            .null_value,
             .function,
             .int_u64,
             .int_i64,
             .int_big,
             .bytes,
+            .undef,
+            .repeated,
             => unreachable,
 
-            .ref => return self.cast(Payload.Ref).?.cell.contents,
-            .ref_val => return self.cast(Payload.RefVal).?.val,
-        }
+            .the_one_possible_value => Value.initTag(.the_one_possible_value),
+            .ref => self.cast(Payload.Ref).?.cell.contents,
+            .ref_val => self.cast(Payload.RefVal).?.val,
+        };
     }
 
     /// Asserts the value is a single-item pointer to an array, or an array,
@@ -475,14 +694,15 @@ pub const Value = extern union {
             .single_const_pointer_to_comptime_int_type,
             .const_slice_u8_type,
             .zero,
-            .void_value,
-            .noreturn_value,
+            .the_one_possible_value,
             .bool_true,
             .bool_false,
+            .null_value,
             .function,
             .int_u64,
             .int_i64,
             .int_big,
+            .undef,
             => unreachable,
 
             .ref => @panic("TODO figure out how MemoryCell works"),
@@ -493,9 +713,68 @@ pub const Value = extern union {
                 int_payload.* = .{ .int = self.cast(Payload.Bytes).?.data[index] };
                 return Value.initPayload(&int_payload.base);
             },
+
+            // No matter the index; all the elements are the same!
+            .repeated => return self.cast(Payload.Repeated).?.val,
         }
     }
 
+    pub fn isUndef(self: Value) bool {
+        return self.tag() == .undef;
+    }
+
+    /// Valid for all types. Asserts the value is not undefined.
+    /// `.the_one_possible_value` is reported as not null.
+    pub fn isNull(self: Value) bool {
+        return switch (self.tag()) {
+            .ty,
+            .u8_type,
+            .i8_type,
+            .isize_type,
+            .usize_type,
+            .c_short_type,
+            .c_ushort_type,
+            .c_int_type,
+            .c_uint_type,
+            .c_long_type,
+            .c_ulong_type,
+            .c_longlong_type,
+            .c_ulonglong_type,
+            .c_longdouble_type,
+            .f16_type,
+            .f32_type,
+            .f64_type,
+            .f128_type,
+            .c_void_type,
+            .bool_type,
+            .void_type,
+            .type_type,
+            .anyerror_type,
+            .comptime_int_type,
+            .comptime_float_type,
+            .noreturn_type,
+            .fn_naked_noreturn_no_args_type,
+            .single_const_pointer_to_comptime_int_type,
+            .const_slice_u8_type,
+            .zero,
+            .the_one_possible_value,
+            .bool_true,
+            .bool_false,
+            .function,
+            .int_u64,
+            .int_i64,
+            .int_big,
+            .ref,
+            .ref_val,
+            .bytes,
+            .repeated,
+            => false,
+
+            .undef => unreachable,
+            .null_value => true,
+        };
+    }
+
     /// This type is not copyable since it may contain pointers to its inner data.
     pub const Payload = struct {
         tag: Tag,
@@ -550,6 +829,20 @@ pub const Value = extern union {
             base: Payload = Payload{ .tag = .ty },
             ty: Type,
         };
+
+        pub const Repeated = struct {
+            base: Payload = Payload{ .tag = .ty },
+            /// This value is repeated some number of times. The amount of times to repeat
+            /// is stored externally.
+            val: Value,
+        };
+    };
+
+    /// Big enough to fit any non-BigInt value
+    pub const BigIntSpace = struct {
+        /// The +1 is headroom so that operations such as incrementing once or decrementing once
+        /// are possible without using an allocator.
+        limbs: [(@sizeOf(u64) / @sizeOf(std.math.big.Limb)) + 1]std.math.big.Limb,
     };
 };