diff --git a/ptx/src/translate.rs b/ptx/src/translate.rs
index 02ff958..651f996 100644
--- a/ptx/src/translate.rs
+++ b/ptx/src/translate.rs
@@ -151,7 +151,7 @@ fn ssa_legalize(
     doms: &Vec<BBIndex>,
     dom_fronts: &Vec<HashSet<BBIndex>>,
 ) {
-    let phis = gather_phi_sets(&func, &bbs, dom_fronts);
+    let phis = gather_phi_sets(&func, max_id, &bbs, dom_fronts);
     apply_ssa_renaming(func, &bbs, doms, max_id, &phis);
 }
 
@@ -161,7 +161,7 @@ fn apply_ssa_renaming(
     bbs: &[BasicBlock],
     doms: &[BBIndex],
     max_id: spirv::Word,
-    old_phi: &[Vec<spirv::Word>],
+    old_phi: &[HashSet<spirv::Word>],
 ) {
     let mut dom_tree = vec![Vec::new(); bbs.len()];
     for (bb, idom) in doms.iter().enumerate() {
@@ -251,7 +251,7 @@ fn rename_succesor_phi_src(
     }
 }
 
-fn pop_stacks(ssa_state: &mut SSARewriteState, old_phi: &[spirv::Word], old_ids: &[spirv::Word]) {
+fn pop_stacks(ssa_state: &mut SSARewriteState, old_phi: &HashSet<spirv::Word>, old_ids: &[spirv::Word]) {
     for id in old_phi.iter().chain(old_ids) {
         ssa_state.pop(*id);
     }
@@ -313,12 +313,49 @@ impl SSARewriteState {
     }
 }
 
+// "Modern Compiler Implementation in Java" - Algorithm 19.6
 fn gather_phi_sets(
     func: &[Statement],
+    max_id: spirv::Word,
     bbs: &[BasicBlock],
     dom_fronts: &[HashSet<BBIndex>],
-) -> Vec<Vec<spirv::Word>> {
-    todo!()
+) -> Vec<HashSet<spirv::Word>> {
+    let mut result = vec![HashSet::new(); bbs.len()];
+    let mut bb_dst_definitions = vec![HashSet::new(); bbs.len()];
+    let mut def_sites = vec![(HashSet::new(), Vec::new()); (max_id as usize) + 1];
+    for bb in 0..bbs.len() {
+        let bb = BBIndex(bb);
+        for s in get_bb_body(func, bbs, bb) {
+            s.for_dst_id(&mut |id| {
+                bb_dst_definitions[bb.0].insert(id);
+                let (ref mut set, ref mut stack) = def_sites[id as usize];
+                if set.insert(bb) {
+                    stack.push(bb);
+                }
+            });
+        }
+    }
+    for (id, to_work ) in def_sites.iter_mut().enumerate() {
+        let id = id as spirv::Word;
+        let (ref mut set, ref mut stack) = to_work;
+        loop {
+            if let Some(bb) = stack.pop() {
+                set.remove(&bb);
+                for y_bb in &dom_fronts[bb.0] {
+                    if result[y_bb.0].insert(id) {
+                        if !bb_dst_definitions[y_bb.0].contains(&id) {
+                            if set.insert(*y_bb) {
+                                stack.push(*y_bb);
+                            }
+                        }
+                    }
+                }
+            } else {
+                break;
+            }
+        }
+    }
+    result
 }
 
 fn get_basic_blocks(fun: &Vec<Statement>) -> Vec<BasicBlock> {