separate peephole optimization out

1 files changed, 84 insertions, 642 deletions

diff --git a/ir.c b/ir.c
index 42691ee..6e91faa 100644
--- a/ir.c
+++ b/ir.c
@@ -6,96 +6,6 @@
 
 extern int no_opt;
 
-/* TODO:
- *
- * Separate normal graph manipulation from peephole optimization code.
- *
- */
-
-/* types */
-
-int type_eql(Type *a, Type *b) {
-	if (a->t != b->t) return 0;
-	if (a->lvl != b->lvl) return 0;
-	if (a->next != b->next) return 0;
-	return a->next ? type_eql(a->next, b->next) : 1;
-}
-
-int type_base_eql(Type *a, Type *b) {
-	if (a->t != b->t) return 0;
-	if (a->next != b->next) return 0;
-	return a->next ? type_base_eql(a->next, b->next) : 1;
-}
-
-int value_eql(Value *a, Value *b) {
-	if (!type_eql(&a->type, &b->type)) return 0;
-	return a->i == b->i;
-}
-
-Str type_desc(Type *t, Arena *arena) {
-	(void)arena;
-	switch (t->lvl) {
-	case T_CTRL: return S("ctrl");
-	case T_XCTRL: return S("~ctrl");
-	default: break;
-	}
-	switch (t->t) {
-	case T_TUPLE: return S("tuple");
-	case T_BOOL: return S("bool");
-	case T_INT: return S("i64");
-	case T_PTR: return str_fmt(arena, "^%S", type_desc(t->next, arena));
-	default: return S("N/A");
-	}
-}
-
-void type_err(Node *n, Lexer *l) {
-	Str s = S("");
-	for (int i = 0; i < n->in.len; i++) {
-		if (i > 0) str_cat(&s, S(", "), &l->arena);
-		str_cat(&s, type_desc(&IN(n, i)->type, &l->arena), &l->arena);
-	}
-	lex_error_at(l, n->src_pos, LE_ERROR, str_fmt(&l->arena, "type error %s (%S)", node_type_name(n->op), s));
-}
-
-int type_check(Node *n) {
-	switch (n->op) {
-	case N_PHI:
-		n->type = (Type) { .lvl = T_TOP, .t = IN(n, 1)->type.t };
-		for (int i = 2; i < n->in.len; i++) {
-			if (!type_base_eql(&IN(n, i)->type, &n->type)) {
-				return 0;
-			}
-		}
-		return 1;
-	case N_OP_NEG:
-		n->type = (Type) { .lvl = T_TOP, .t = T_INT };
-		return CAR(n)->type.t == T_INT;
-	case N_OP_NOT:
-		n->type = (Type) { .lvl = T_TOP, .t = CAR(n)->type.t };
-		return CAR(n)->type.t == T_INT || CAR(n)->type.t == T_BOOL;
-	case N_OP_AND: case N_OP_OR: case N_OP_XOR:
-		n->type = (Type) { .lvl = T_TOP, .t = CAR(n)->type.t };
-		return (CAR(n)->type.t == T_INT && CDR(n)->type.t == T_INT)
-			|| (CAR(n)->type.t == T_BOOL && CDR(n)->type.t == T_BOOL);
-	case N_OP_ADD: case N_OP_SUB: case N_OP_MUL: case N_OP_DIV:
-	case N_OP_SHL: case N_OP_SHR:
-		n->type = (Type) { .lvl = T_TOP, .t = T_INT };
-		return CAR(n)->type.t == T_INT && CDR(n)->type.t == T_INT;
-	case N_CMP_LES: case N_CMP_GTR:
-	case N_CMP_LTE: case N_CMP_GTE:
-		n->type = (Type) { .lvl = T_TOP, .t = T_BOOL };
-		return CAR(n)->type.t == T_INT && CDR(n)->type.t == T_INT;
-	case N_CMP_EQL:
-	case N_CMP_NEQ:
-		n->type = (Type) { .lvl = T_TOP, .t = T_BOOL };
-		return type_base_eql(&CAR(n)->type, &CDR(n)->type);
-			/* (CAR(n)->type.t == T_INT && CDR(n)->type.t == T_INT)
-			|| (CAR(n)->type.t == T_BOOL && CDR(n)->type.t == T_BOOL); */
-	default:
-		return 1;
-	}
-}
-
 /* nodes */
 
 const char *node_type_name(NodeType t) {
@@ -256,558 +166,6 @@ Node *node_new_lit_bool(Proc *p, int b) {
 	return node_new_lit(p, (Value) { { .lvl = T_CONST, .t = T_BOOL }, { .i = b } });
 }
 
-static inline int node_op_communative(NodeType t) {
-	return NMASK(t) & (NM_OP_ADD | NM_OP_MUL | NM_OP_AND | NM_OP_XOR | NM_OP_OR | NM_CMP_EQL | NM_CMP_NEQ);
-	/*NodeType ops[] = { N_OP_ADD, N_OP_MUL, N_OP_AND, N_OP_XOR, N_OP_OR, N_CMP_EQL, N_CMP_NEQ };
-	for (unsigned i = 0; i < sizeof ops / sizeof *ops; i++) {
-		if (ops[i] == t) return 1;
-	}
-	return 0;*/
-}
-
-static inline int node_op_associative(NodeType t) {
-	/*NodeType ops[] = { N_OP_ADD, N_OP_MUL, N_OP_AND, N_OP_XOR, N_OP_OR };
-	for (unsigned i = 0; i < sizeof ops / sizeof *ops; i++) {
-		if (ops[i] == t) return 1;
-	}
-	return 0;*/
-	return NMASK(t) & (NM_OP_ADD | NM_OP_MUL | NM_OP_AND | NM_OP_XOR | NM_OP_OR);
-}
-
-static inline int node_op_comparison(NodeType t) {
-	/*NodeType ops[] = { N_CMP_EQL, N_CMP_NEQ, N_CMP_LES, N_CMP_GTR, N_CMP_LTE, N_CMP_GTE };
-	for (unsigned i = 0; i < sizeof ops / sizeof *ops; i++) {
-		if (ops[i] == t) return 1;
-	}
-	return 0;*/
-	return NMASK(t) & (NM_CMP_EQL | NM_CMP_NEQ | NM_CMP_LES | NM_CMP_GTR | NM_CMP_LTE | NM_CMP_GTE);
-}
-
-/* when applied to the same input, at least one must be true */
-static inline NodeType node_cmp_opposite(NodeType a) {
-	switch (a) {
-	case N_CMP_EQL: return N_CMP_NEQ;
-	case N_CMP_NEQ: return N_CMP_EQL;
-	case N_CMP_LES: return N_CMP_GTE;
-	case N_CMP_GTE: return N_CMP_LES;
-	case N_CMP_GTR: return N_CMP_LTE;
-	case N_CMP_LTE: return N_CMP_GTR;
-	default: return N_NONE;
-	}
-}
-
-static inline NodeType node_cmp_flip_sign(NodeType a) {
-	switch (a) {
-	case N_CMP_LES: return N_CMP_GTR;
-	case N_CMP_LTE: return N_CMP_GTE;
-	case N_CMP_GTR: return N_CMP_LES;
-	case N_CMP_GTE: return N_CMP_LTE;
-	default: return a;
-	}
-}
-
-/* when applied to the same input, at least one must be false */
-static inline int node_cmp_incompat(NodeType a, NodeType b) {
-	struct { NodeType l, r; } pairs[] = {
-		{ N_CMP_EQL, N_CMP_NEQ },
-		{ N_CMP_LES, N_CMP_GTE },
-		{ N_CMP_GTR, N_CMP_LTE },
-		{ N_CMP_LES, N_CMP_GTR },
-	};
-	for (unsigned i = 0; i < sizeof pairs / sizeof *pairs; i++) {
-		if ((pairs[i].l == a && pairs[i].r == b) || (pairs[i].l == b && pairs[i].r == a)) {
-			return 1;
-		}
-	}
-	return 0;
-}
-
-Value node_compute(Node *n, Lexer *l) {
-	Type lit_type = { .lvl = T_BOT };
-	for (int i = 1; i < n->in.len; i++) {
-		Node *p = IN(n, i);
-		if (p->type.lvl != T_CONST) {
-			lit_type.lvl = T_BOT;
-			break;
-		}
-		if (!type_eql(&p->type, &lit_type)) {
-			if (lit_type.lvl == T_BOT) {
-				lit_type = p->type;
-			} else {
-				lit_type.lvl = T_BOT;
-				break;
-			}
-		}
-	}
-
-	if (lit_type.lvl != T_CONST) return n->val;
-
-	Value v = { .type = lit_type };
-
-	if (lit_type.t == T_INT) {
-		switch (n->op) {
-		case N_OP_NEG: v.i = -CAR(n)->val.i; break;
-		case N_OP_NOT: v.i = ~CAR(n)->val.i; break;
-		case N_OP_ADD: v.i = CAR(n)->val.i + CDR(n)->val.i; break;
-		case N_OP_SUB: v.i = CAR(n)->val.i - CDR(n)->val.i; break;
-		case N_OP_MUL: v.i = CAR(n)->val.i * CDR(n)->val.i; break;
-		case N_OP_DIV:
-		       if (CDR(n)->val.i == 0) {
-			       lex_error_at(l, CDR(n)->src_pos, LE_ERROR, S("divisor always evaluates to zero"));
-		       }
-		       v.i = CAR(n)->val.i / CDR(n)->val.i;
-		       break;
-		case N_OP_AND: v.i = CAR(n)->val.i & CDR(n)->val.i; break;
-		case N_OP_OR: v.i = CAR(n)->val.i | CDR(n)->val.i; break;
-		case N_OP_XOR: v.i = CAR(n)->val.i ^ CDR(n)->val.i; break;
-		case N_OP_SHL: v.i = CAR(n)->val.u << CDR(n)->val.u; break;
-		case N_OP_SHR: v.i = CAR(n)->val.u >> CDR(n)->val.u; break;
-		case N_CMP_EQL: v.type.t = T_BOOL; v.i = CAR(n)->val.i == CDR(n)->val.i; break;
-		case N_CMP_NEQ: v.type.t = T_BOOL; v.i = CAR(n)->val.i != CDR(n)->val.i; break;
-		case N_CMP_LES: v.type.t = T_BOOL; v.i = CAR(n)->val.i < CDR(n)->val.i; break;
-		case N_CMP_GTR: v.type.t = T_BOOL; v.i = CAR(n)->val.i > CDR(n)->val.i; break;
-		case N_CMP_LTE: v.type.t = T_BOOL; v.i = CAR(n)->val.i <= CDR(n)->val.i; break;
-		case N_CMP_GTE: v.type.t = T_BOOL; v.i = CAR(n)->val.i >= CDR(n)->val.i; break;
-		default: return n->val;
-		}
-		return v;
-	} else if (lit_type.t == T_BOOL) {
-		switch (n->op) {
-		case N_OP_NOT: v.i = !CAR(n)->val.i; break;
-		case N_CMP_EQL: v.i = CAR(n)->val.i == CDR(n)->val.i; break;
-		case N_CMP_NEQ: v.i = CAR(n)->val.i != CDR(n)->val.i; break;
-		case N_OP_AND: v.i = CAR(n)->val.i && CDR(n)->val.i; break;
-		case N_OP_OR: v.i = CAR(n)->val.i || CDR(n)->val.i; break;
-		case N_OP_XOR: v.i = CAR(n)->val.i ^ CDR(n)->val.i; break;
-		default: return n->val;
-		}
-		return v;
-	}
-
-	return n->val;
-}
-
-#include <stdio.h>
-
-#define NODE(t, ...) node_peephole(node_new(p, t, CTRL(n), __VA_ARGS__), p, l)
-#define OP(...) NODE(n->op, __VA_ARGS__)
-
-static inline int node_eql_i64(Node *n, int64_t i) {
-	return n->op == N_LIT && n->type.t == T_INT && n->val.i == i;
-}
-
-static inline int u64_power_of_2(uint64_t x) {
-	int ldz = 0, tlz = 0;
-	for (int i = 0; i < 64; i++) {
-		if ((x >> i) & 1) break;
-		else tlz++;
-	}
-	for (int i = 0; i < 64; i++) {
-		if ((x << i) & (1UL << 63)) break;
-		else ldz++;
-	}
-	if (ldz + tlz != 63) return 0;
-	return tlz;
-}
-
-/* functions to query the compile-time equivalence of nodes */
-/* fairly conservative of necessity */
-
-static int node_equiv(Node *a, Node *b);
-static int node_known_neg_of(Node *a, Node *b) {
-	if (T(b, N_OP_NEG) && node_equiv(a, CAR(b))) return 1;
-	if (T(a, N_OP_NEG) && node_equiv(CAR(a), b)) return 1;
-	if (T(a, N_LIT) && T(b, N_LIT) && (a->type.t == b->type.t) && b->val.i == -a->val.i) return 1;
-	return 0;
-}
-
-static inline int node_sub_add_equiv(Node *a, Node *b) {
-	if (node_equiv(CAR(a), CAR(b)) && !node_known_neg_of(CDR(a), CDR(b))) return 1;
-	if (node_equiv(CAR(a), CDR(b)) && !node_known_neg_of(CDR(a), CAR(b))) return 1;
-	return 0;
-}
-
-static int node_equiv_input(Node *a, Node *b);
-
-static int node_equiv(Node *a, Node *b) {
-	/* will doing this recursively be too slow? */
-	if (a == b) return 1;
-	if (a->op != b->op) return 0;
-	if (a->in.len != b->in.len) return 0;
-	if (!value_eql(&a->val, &b->val)) return 0;
-	if (!node_equiv_input(a, b)) return 0;
-	return 1;
-}
-
-/* TODO: figure out a more thorough way of comparing node graphs */
-
-static inline int node_known_not_equiv_ord(Node *a, Node *b) {
-	if ((b->op & (NM_OP_ADD | NM_OP_SUB)) && node_equiv(a, CAR(b))
-			&& T(CDR(b), N_LIT) && !node_eql_i64(CDR(b), 0)) return 1;
-	if ((a->op & (NM_OP_ADD | NM_OP_SUB)) && node_sub_add_equiv(a, b)) return 1;
-	return 0;
-}
-static inline int node_known_not_equiv(Node *a, Node *b) {
-	return node_known_not_equiv_ord(a, b) || node_known_not_equiv_ord(b, a);
-}
-
-static int node_equiv_input(Node *a, Node *b) {
-	if (a->in.len != b->in.len) return 0;
-	if (CTRL(a) != CTRL(b)) return 0;
-	/* note that this means the order of inputs isn't guaranteed, so be
-	 * careful what you use this procedure for */
-	if ((node_op_communative(a->op) || node_op_communative(b->op))
-			&& node_equiv(CDR(a), CAR(b))
-			&& node_equiv(CAR(a), CDR(b))) {
-		/* assuming input count is 2 */
-		return 1;
-	}
-	for (int i = 1; i < a->in.len; i++) {
-		if (!node_equiv(IN(a, i), IN(b, i))) return 0;
-	}
-	return 1;
-}
-
-Node *node_new_zero(Proc *p, Node *n) {
-	Value v = {
-		.type = {
-			.lvl = T_CONST,
-			.t = n->type.t,
-		},
-		.i = 0
-	};
-	Node *r = node_new_lit(p, v);
-	return r;
-}
-
-static inline int is_zero(Node *n) {
-	return n->type.lvl == T_CONST && (n->type.t == T_INT || n->type.t == T_BOOL) && !n->val.i;
-}
-
-/* needs lexer for error reporting */
-Node *node_idealize(Node *n, Proc *p, Lexer *l) {
-	if (!type_check(n)) {
-		type_err(n, l);
-	}
-
-	if (no_opt) return NULL;
-
-	/* try to compute a literal value */
-
-	if (n->op != N_LIT) {
-		Value v = node_compute(n, l);
-		if (v.type.lvl == T_CONST) {
-			Node *t = node_dedup_lit(p, v);
-			if (t) return t;
-			Node *r = node_new(p, N_LIT, NULL, p->start);
-			r->val = v;
-			r->src_pos = n->src_pos;
-			return r;
-		}
-	}
-
-	/* try to trim duplicate inputs from the graph */
-
-	int same = 1, same_ptr = 1;
-	for (int i = 1; i < n->in.len; i++) {
-		if (IN(n, i) == CAR(n)) continue;
-		same_ptr = 0;
-		if (!node_equiv(IN(n, i), CAR(n))) {
-			same = 0;
-			break;
-		}
-	}
-
-	if (n->in.len > 2 && same && !same_ptr) {
-		Node *r = node_new(p, n->op, NULL);
-		for (int i = 0; i < n->in.len; i++) {
-			node_add(p, CAR(n), r);
-		}
-		return node_peephole(r, p, l);
-	}
-
-	/* transformations to help encourage constant folding */
-	/* the overall trend is to move them rightwards */
-
-	/* need to check for type compatibility */
-	#define C(a, b) type_base_eql(&(a)->type, &(b)->type)
-	if (node_op_communative(n->op)) {
-		/* op(lit, X) -> op(X, lit) */
-		if (T(CAR(n), N_LIT) && !T(CDR(n), N_LIT)) return OP(CDR(n), CAR(n));
-
-		/* op(X, not(Y)) -> op(not(Y), X) */
-		/* shuffle not left to avoid conflict w/ literals */
-		if (T(CDR(n), N_OP_NOT) && !T(CAR(n), N_OP_NOT)) {
-			return NODE(n->op, CDR(n), CAR(n));
-		}
-
-		if (T(CAR(n), N_PHI) && T(CDR(n), N_PHI) && CTRL(CAR(n)) == CTRL(CDR(n))
-				&& ((node_equiv(CAAR(n), CDAR(n)) && node_equiv(CADR(n), CDDR(n)))
-				|| (node_equiv(CADR(n), CDAR(n)) && node_equiv(CAAR(n), CDDR(n))))) {
-			return OP(CAAR(n), CDAR(n));
-		}
-	}
-
-	if (node_op_associative(n->op)) {
-		/* op(X, op(Y,Z)) -> op(op(Y,Z), X) */
-		if (!T(CAR(n), n->op) && T(CDR(n), n->op)
-				&& C(CAR(n), CDAR(n))) return OP(CDR(n), CAR(n));
-
-		/* op(op(X,Y), op(Z, lit)) -> op(op(X, op(Y, Z)), lit) */
-		if (T2(CAR(n), CDR(n), n->op) && T(CDDR(n), N_LIT)
-				&& C(CAAR(n), CDAR(n)) && C(CAR(n), CDR(n))) {
-			return OP(OP(CAAR(n), OP(CADR(n), CDAR(n))), CDDR(n));
-		}
-
-		/* op(op(X, lit), lit) -> op(X, op(lit, lit)) */
-		if (T(CDR(n), N_LIT) && T(CAR(n), n->op)
-				&& !T(CAAR(n), N_LIT) && T(CADR(n), N_LIT)
-				&& C(CADR(n), CDR(n))) {
-			return OP(CAAR(n), OP(CADR(n), CDR(n)));
-		}
-
-		/* op(op(X, lit), Y) -> op(op(X, Y), lit) */
-		if (T(CAR(n), n->op) && !T(CAAR(n), N_LIT)
-				&& T(CADR(n), N_LIT) && !T(CDR(n), N_LIT)
-				&& C(CADR(n), CDR(n))) {
-			return OP(OP(CAAR(n), CDR(n)), CADR(n));
-		}
-	}
-
-	/* optimize based on situations where the input is partly known (e.g.
-	 * one constant input and one not, or identical inputs) */
-
-#define INT_EQ(n, v) ((n)->type.lvl == T_CONST && (n)->type.t == T_INT && (n)->val.i == v)
-#define BOOL_EQ(n, v) ((n)->type.lvl == T_CONST && (n)->type.t == T_BOOL && (n)->val.i == v)
-
-	switch (n->op) {
-	case N_OP_NOT:
-		{
-			NodeType op = node_cmp_opposite(CAR(n)->op);
-			if (op != N_NONE) return NODE(op, CAAR(n), CADR(n));
-		}
-		/* fallthrough */
-	case N_OP_NEG:
-		if (T(CAR(n), n->op)) return CAAR(n);
-		break;
-	case N_OP_ADD:
-		if (same) return NODE(N_OP_MUL, CAR(n), node_new_lit_i64(p, 2));
-		if (CAR(n)->type.t == T_INT) {
-			/* a + ~a = -1 */
-			if (T(CAR(n), N_OP_NOT) && node_equiv(CAAR(n), CDR(n))) return node_new_lit_i64(p, -1);
-			if (T(CDR(n), N_LIT) && CDR(n)->val.i < 0) return NODE(N_OP_SUB, CAR(n), node_new_lit_i64(p, -CDR(n)->val.i));
-		}
-		if (T(CAR(n), N_OP_NEG)) return NODE(N_OP_SUB, CDR(n), CAAR(n));
-		if (T(CDR(n), N_OP_NEG)) return NODE(N_OP_SUB, CAR(n), CDAR(n));
-		if (T(CAR(n), N_OP_SUB) && T(CDR(n), N_OP_SUB)
-			&& node_equiv(CAAR(n), CDDR(n)) && node_equiv(CADR(n), CDAR(n))) {
-			return node_new_lit_i64(p, 0);
-		}
-		goto zero_no_effect;
-	case N_OP_SUB:
-		if (same) return node_new_lit_i64(p, 0);
-		if (node_eql_i64(CAR(n), 0)) return NODE(N_OP_NEG, CDR(n));
-		if (node_eql_i64(CDR(n), 0)) return CAR(n);
-		break;
-	case N_OP_MUL:
-		if (node_eql_i64(CDR(n), 0)) return CDR(n);
-		if (node_eql_i64(CDR(n), 1)) return CAR(n);
-		{
-			int po2;
-			if (T(CDR(n), N_LIT) && CDR(n)->type.t == T_INT && (po2 = u64_power_of_2(CDR(n)->val.u))) {;
-				return NODE(N_OP_SHL, CAR(n), node_new_lit_i64(p, po2));
-			}
-		}
-		break;
-	case N_OP_DIV:
-		if (node_eql_i64(CDR(n), 0)) {
-		       lex_error_at(l, CDR(n)->src_pos, LE_ERROR, S("divisor always evaluates to zero"));
-		}
-		{
-			int po2;
-			if (T(CDR(n), N_LIT) && CDR(n)->type.t == T_INT && (po2 = u64_power_of_2(CDR(n)->val.u))) {;
-				return NODE(N_OP_SHR, CAR(n), node_new_lit_i64(p, po2));
-			}
-		}
-		break;
-	case N_OP_OR:
-		if (same) return CAR(n);
-		if (is_zero(CDR(n))) return CAR(n);
-		if (BOOL_EQ(CDR(n), 1)) return CDR(n);
-		if (CDR(n)->op == node_cmp_opposite(CAR(n)->op) && node_equiv_input(CAR(n), CDR(n))) {
-			return node_new_lit_bool(p, 1);
-		}
-		if (T(CAR(n), N_CMP_LES) && T(CDR(n), N_CMP_EQL) && node_equiv_input(CAR(n), CDR(n))) {
-			return NODE(N_CMP_LTE, CAAR(n), CADR(n));
-		}
-		if (T(CAR(n), N_CMP_EQL) && T(CDR(n), N_CMP_LES) && node_equiv_input(CAR(n), CDR(n))) {
-			return NODE(N_CMP_LTE, CDAR(n), CDDR(n));
-		}
-		if (T(CAR(n), N_CMP_GTR) && T(CDR(n), N_CMP_EQL) && node_equiv_input(CAR(n), CDR(n))) {
-			return NODE(N_CMP_GTE, CAAR(n), CADR(n));
-		}
-		if (T(CAR(n), N_CMP_EQL) && T(CDR(n), N_CMP_GTR) && node_equiv_input(CAR(n), CDR(n))) {
-			return NODE(N_CMP_GTE, CDAR(n), CDDR(n));
-		}
-		goto zero_no_effect;
-	case N_OP_AND:
-		if (same) return CAR(n);
-		if (BOOL_EQ(CDR(n), 1)) return CAR(n);
-		if (is_zero(CDR(n))) return node_new_zero(p, CDR(n));
-		if (T(CAR(n), N_OP_NOT) && node_equiv(CAAR(n), CDR(n))) return node_new_zero(p, CDR(n));
-		if (node_cmp_incompat(CAR(n)->op, CDR(n)->op) && node_equiv_input(CAR(n), CDR(n))) {
-			return node_new_lit_bool(p, 0);
-		}
-		break;
-	case N_OP_XOR:
-		if (same) return node_new_zero(p, CAR(n));
-		if (CDR(n)->op == node_cmp_opposite(CAR(n)->op) && node_equiv_input(CAR(n), CDR(n))) {
-			return node_new_lit_bool(p, 1);
-		}
-		/* ~bool ^ bool = 1 */
-		/* ~i64 ^ i64 = -1 */
-		if (T(CAR(n), N_OP_NOT) && node_equiv(CAAR(n), CDR(n))) {
-			if (CDR(n)->type.t == T_INT) return node_new_lit_i64(p, -1);
-			if (CDR(n)->type.t == T_BOOL) return node_new_lit_bool(p, 1);
-		}
-zero_no_effect:	if (node_eql_i64(CAR(n), 0)) return CDR(n);
-		if (node_eql_i64(CDR(n), 0)) return CAR(n);
-		break;
-	case N_CMP_EQL:
-		if (same) return node_new_lit_bool(p, 1);
-		if (node_known_not_equiv(CAR(n), CDR(n))) return node_new_lit_bool(p, 0);
-		if (BOOL_EQ(CDR(n), 1)) return CAR(n);
-		if (BOOL_EQ(CDR(n), 0)) return NODE(N_OP_NOT, CAR(n));
-		if (T(CAR(n), N_OP_NOT) && node_equiv(CDR(n), CAAR(n))) return node_new_lit_bool(p, 0);
-		break;
-	case N_CMP_NEQ:
-		if (same) return node_new_lit_bool(p, 0);
-		if (node_known_not_equiv(CAR(n), CDR(n))) return node_new_lit_bool(p, 1);
-		if (BOOL_EQ(CDR(n), 0)) return CAR(n);
-		if (BOOL_EQ(CDR(n), 1)) return NODE(N_OP_NOT, CAR(n));
-		break;
-	case N_CMP_LES:
-		if (same) return node_new_lit_bool(p, 0);
-		break;
-	case N_CMP_GTR:
-		if (same) return node_new_lit_bool(p, 0);
-		break;
-	case N_CMP_LTE:
-		if (same) return node_new_lit_bool(p, 1);
-		break;
-	case N_CMP_GTE:
-		if (same) return node_new_lit_bool(p, 1);
-		break;
-
-	case N_IF_ELSE:
-		if (T(CAR(n), N_LIT)) {
-			if (CAR(n)->val.i) {
-				n->val.tuple.data[1].type.lvl = T_XCTRL;
-			} else {
-				n->val.tuple.data[0].type.lvl = T_XCTRL;
-			}
-		}
-		break;
-
-	case N_RETURN:
-		if (CTRL(n)->type.lvl == T_XCTRL) return CTRL(n);
-		break;
-
-	case N_PROJ:
-		if (T(CTRL(n), N_IF_ELSE) && CTRL(n)->type.t == T_TUPLE) {
-			/*if (CTRL(n)->val.tuple.data[n->val.i].type.lvl == T_XCTRL) {
-				return node_new_lit(p, (Value) {
-					.type = { .lvl = T_XCTRL, .t = T_NONE }
-				});
-			}*/
-			if (CTRL(n)->val.tuple.data[(n->val.i + 1) % CTRL(n)->val.tuple.len].type.lvl == T_XCTRL) {
-				return CTRL(CTRL(n));
-			}
-		}
-		break;
-
-	case N_PHI:
-		if (same) return CAR(n);
-		if (CTRL(n)->in.len == 2) {
-			fprintf(stderr, "ctrl: %s\n", node_type_name(CTRL(n)->op));
-			fprintf(stderr, "left: %p\n", (void*)IN(CTRL(n), 0));
-			fprintf(stderr, "right: %p\n", (void*)IN(CTRL(n), 1));
-			if (IN(CTRL(n), 1)->type.lvl == T_XCTRL) return CAR(n);
-			if (IN(CTRL(n), 0)->type.lvl == T_XCTRL) return CDR(n);
-		}
-		break;
-
-	case N_REGION: if (0) {
-		int live_in = 0;
-		for (int i = 0; i < n->in.len; i++) {
-			if (IN(n, i)->type.lvl != T_XCTRL) live_in++;
-		}
-		if (live_in == 1) {
-			for (int i = 0; i < n->in.len; i++) {
-				if (IN(n, i)->type.lvl != T_XCTRL) {
-					return IN(n, i);
-				}
-			}
-		}
-		if (live_in == 0) {
-			return node_new_lit(p, (Value) {
-				.type = { .lvl = T_XCTRL, .t = T_NONE }
-			});
-		}
-	} break;
-
-	default:
-		break;
-	}
-
-	if (node_op_comparison(n->op)) {
-		/* cmp(2a, a + b) -> cmp(a, b) */
-		if (T(CAR(n), N_OP_SHL) && T(CDR(n), N_OP_ADD) && node_eql_i64(CADR(n), 1)) {
-			if (node_equiv(CAAR(n), CDAR(n))) return NODE(n->op, CAAR(n), CDDR(n));
-			if (node_equiv(CAAR(n), CDDR(n))) return NODE(n->op, CAAR(n), CDAR(n));
-		}
-		if (T(CDR(n), N_OP_SHL) && T(CAR(n), N_OP_ADD) && node_eql_i64(CDDR(n), 1)) {
-			if (node_equiv(CDAR(n), CAAR(n))) return NODE(n->op, CDAR(n), CADR(n));
-			if (node_equiv(CDAR(n), CADR(n))) return NODE(n->op, CDAR(n), CAAR(n));
-		}
-		/* cmp(a + b, a + c) -> cmp(b, c) */
-		if (node_op_associative(CAR(n)->op) && T(CAR(n), CDR(n)->op)) {
-			if (node_equiv(CAAR(n), CDAR(n))) return NODE(n->op, CADR(n), CDDR(n));
-			if (node_equiv(CADR(n), CDAR(n))) return NODE(n->op, CAAR(n), CDDR(n));
-			if (node_equiv(CAAR(n), CDDR(n))) return NODE(n->op, CADR(n), CDAR(n));
-			if (node_equiv(CADR(n), CDDR(n))) return NODE(n->op, CAAR(n), CDAR(n));
-		}
-		if (T2(CAR(n), CDR(n), N_OP_SUB)) {
-			/* cmp(a - b, b - a) -> cmp(a, b) */
-			if (node_equiv(CAAR(n), CDDR(n)) && node_equiv(CADR(n), CDAR(n))) {
-				return NODE(n->op, CAAR(n), CDAR(n));
-			}
-			/* cmp(a - b, c - b) -> flipcmp(a, c) */
-			if (node_equiv(CAAR(n), CDAR(n))) {
-				return NODE(node_cmp_flip_sign(n->op), CADR(n), CDDR(n));
-			}
-		}
-		/* cmp(-a, -b) -> flipcmp(a, b) */
-		if (T2(CAR(n), CDR(n), N_OP_NEG)) {
-			return NODE(node_cmp_flip_sign(n->op), CAAR(n), CDAR(n));
-		}
-	}
-
-	return NULL;
-}
-
-Node *node_peephole(Node *n, Proc *p, Lexer *l) {
-	assert(n->refs > 0);
-	Node *r = node_idealize(n, p, l);
-	if (r) {
-		r->src_pos = n->src_pos;
-		NODE_KEEP(p, r, node_kill(n, p));
-		return r;
-	}
-	/* FIXME: figure out why this shows the wrong position when in an assignment */
-	return n;
-}
-
 /* procedures */
 
 void proc_init(Proc *proc, Str name) {
@@ -913,3 +271,87 @@ void scope_uncollect(Scope *scope, Proc *proc, ScopeNameList *nl) {
 		node_remove(proc, nl->data[i].node, proc->keepalive);
 	}
 }
+
+/* types */
+
+int type_eql(Type *a, Type *b) {
+	if (a->t != b->t) return 0;
+	if (a->lvl != b->lvl) return 0;
+	if (a->next != b->next) return 0;
+	return a->next ? type_eql(a->next, b->next) : 1;
+}
+
+int type_base_eql(Type *a, Type *b) {
+	if (a->t != b->t) return 0;
+	if (a->next != b->next) return 0;
+	return a->next ? type_base_eql(a->next, b->next) : 1;
+}
+
+int value_eql(Value *a, Value *b) {
+	if (!type_eql(&a->type, &b->type)) return 0;
+	return a->i == b->i;
+}
+
+Str type_desc(Type *t, Arena *arena) {
+	(void)arena;
+	switch (t->lvl) {
+	case T_CTRL: return S("ctrl");
+	case T_XCTRL: return S("~ctrl");
+	default: break;
+	}
+	switch (t->t) {
+	case T_TUPLE: return S("tuple");
+	case T_BOOL: return S("bool");
+	case T_INT: return S("i64");
+	case T_PTR: return str_fmt(arena, "^%S", type_desc(t->next, arena));
+	default: return S("N/A");
+	}
+}
+
+void type_err(Node *n, Lexer *l) {
+	Str s = S("");
+	for (int i = 0; i < n->in.len; i++) {
+		if (i > 0) str_cat(&s, S(", "), &l->arena);
+		str_cat(&s, type_desc(&IN(n, i)->type, &l->arena), &l->arena);
+	}
+	lex_error_at(l, n->src_pos, LE_ERROR, str_fmt(&l->arena, "type error %s (%S)", node_type_name(n->op), s));
+}
+
+int type_check(Node *n) {
+	switch (n->op) {
+	case N_PHI:
+		n->type = (Type) { .lvl = T_TOP, .t = IN(n, 1)->type.t };
+		for (int i = 2; i < n->in.len; i++) {
+			if (!type_base_eql(&IN(n, i)->type, &n->type)) {
+				return 0;
+			}
+		}
+		return 1;
+	case N_OP_NEG:
+		n->type = (Type) { .lvl = T_TOP, .t = T_INT };
+		return CAR(n)->type.t == T_INT;
+	case N_OP_NOT:
+		n->type = (Type) { .lvl = T_TOP, .t = CAR(n)->type.t };
+		return CAR(n)->type.t == T_INT || CAR(n)->type.t == T_BOOL;
+	case N_OP_AND: case N_OP_OR: case N_OP_XOR:
+		n->type = (Type) { .lvl = T_TOP, .t = CAR(n)->type.t };
+		return (CAR(n)->type.t == T_INT && CDR(n)->type.t == T_INT)
+			|| (CAR(n)->type.t == T_BOOL && CDR(n)->type.t == T_BOOL);
+	case N_OP_ADD: case N_OP_SUB: case N_OP_MUL: case N_OP_DIV:
+	case N_OP_SHL: case N_OP_SHR:
+		n->type = (Type) { .lvl = T_TOP, .t = T_INT };
+		return CAR(n)->type.t == T_INT && CDR(n)->type.t == T_INT;
+	case N_CMP_LES: case N_CMP_GTR:
+	case N_CMP_LTE: case N_CMP_GTE:
+		n->type = (Type) { .lvl = T_TOP, .t = T_BOOL };
+		return CAR(n)->type.t == T_INT && CDR(n)->type.t == T_INT;
+	case N_CMP_EQL:
+	case N_CMP_NEQ:
+		n->type = (Type) { .lvl = T_TOP, .t = T_BOOL };
+		return type_base_eql(&CAR(n)->type, &CDR(n)->type);
+			/* (CAR(n)->type.t == T_INT && CDR(n)->type.t == T_INT)
+			|| (CAR(n)->type.t == T_BOOL && CDR(n)->type.t == T_BOOL); */
+	default:
+		return 1;
+	}
+}