diff --git a/circuit/misc.circom b/circuit/misc.circom
index c9065bc..d249553 100644
--- a/circuit/misc.circom
+++ b/circuit/misc.circom
@@ -1,5 +1,15 @@
 pragma circom 2.0.0;
 
+//------------------------------------------------------------------------------
+
+function FloorLog2(n) {
+  return (n==0) ? -1 : (1 + FloorLog2(n>>1));
+}
+
+function CeilLog2(n) {
+  return (n==0) ? 0 : (1 + FloorLog2(n-1));
+}
+
 //------------------------------------------------------------------------------
 // decompose an n-bit number into bits (least significant bit first)