Reduce path formatting allocations

internal/engine/path.go

@@ -86,7 +86,20 @@ func (p Path) String() string {
 		return ""
 	}
 
+	// Include each separator and the extra byte introduced by escaping a token.
+	// Use stack storage for sizing indexes without allocating another string.
+	size := len(p.segments)
+	var indexText [20]byte
+	for _, segment := range p.segments {
+		if segment.kind == pathSegmentIndex {
+			size += len(strconv.AppendInt(indexText[:0], int64(segment.index), 10))
+		} else {
+			size += len(segment.key) + strings.Count(segment.key, "~") + strings.Count(segment.key, "/")
+		}
+	}
+
 	var b strings.Builder
+	b.Grow(size)
 	for _, segment := range p.segments {
 		b.WriteByte('/')
 		if segment.kind == pathSegmentIndex {

internal/engine/path_test.go

@@ -1,6 +1,9 @@
 package engine
 
-import "testing"
+import (
+	"strconv"
+	"testing"
+)
 
 func TestPathRoundTripsSemanticKeys(t *testing.T) {
 	t.Parallel()
@@ -36,6 +39,13 @@ func TestPathRoundTripsSemanticKeys(t *testing.T) {
 	if got := Keys("items").Index(12).Key("name").String(); got != "/items/12/name" {
 		t.Fatalf("indexed path = %q", got)
 	}
+	maximum := int(^uint(0) >> 1)
+	for _, index := range []int{100, maximum, -1, -maximum - 1} {
+		want := "/items/" + strconv.Itoa(index)
+		if got := Keys("items").Index(index).String(); got != want {
+			t.Fatalf("indexed path = %q, want %q", got, want)
+		}
+	}
 }
 
 func TestPathPreservesSegmentIntentAndImmutability(t *testing.T) {