diff --git a/evm/src/cpu/kernel/asm/fields/fp6_mul.asm b/evm/src/cpu/kernel/asm/fields/fp6_mul.asm
index db1a7bf6..6ec69192 100644
--- a/evm/src/cpu/kernel/asm/fields/fp6_mul.asm
+++ b/evm/src/cpu/kernel/asm/fields/fp6_mul.asm
@@ -1,55 +1,58 @@
+/// C = C0 + C1t + C2t^2 
+///   = (c0 + c0_i) + (c1 + c1_i)t + (c2 + c2_i)t^2
+///
+/// D = D0 + D1t + D2t^2
+///   = (d0 + d0_i) + (d1 + d1_i)t + (d2 + d2_i)t^2
+///
+/// E = e0 + e1t + e2t^2 = CD
+///
+///
+/// e0 = C0D0 + i9(C1D2 + C2D1)
+///
+/// C0D0 = (c0d0 - c0_d0_) + (c0d0_ + c0_d0)i
+///
+/// C1D2 = (c1d2 - c1_d2_) + (c1d2_ + c1_d2)i
+/// C2D1 = (c2d1 - c2_d1_) + (c2d1_ + c2_d1)i
+///
+/// CD12 = C1D2 + C2D1
+///      = (c1d2 + c2d1 - c1_d2_ - c2_d1_) + (c1d2_ + c1_d2 + c2d1_ + c2_d1)i
+///
+/// i9(CD12) = (9CD12 - CD12_) + (CD12 + 9CD12_)i
+///
+/// e0  = 9CD12  - CD12_ + C0D0
+/// e0_ = 9CD12_ + CD12  + C0D0_
+///
+///
+/// e1 = C0D1 + C1D0 + i9(C2D2)
+///
+/// C0D1 = (c0d1 - c0_d1_) + (c0d1_ + c0_d1)i
+/// C1D0 = (c1d0 - c1_d0_) + (c1d0_ + c1_d0)i
+///
+/// CD01  = c0d1  + c1d0  - (c0_d1_ + c1_d0_)
+/// CD01_ = c0d1_ + c0_d1 +  c1d0_  + c1_d0
+///
+///    C2D2  = (c2d2 - c2_d2_) + (c2d2_ + c2_d2)i
+/// i9(C2D2) = (9C2D2 - C2D2_) + (C2D2 + 9C2D2_)i
+///
+/// e1  = 9C2D2 -  C2D2_ + CD01
+/// e1_ =  C2D2 + 9C2D2_ + CD01_
+///
+///
+/// e2 = C0D2 + C1D1 + C2D0
+///
+/// C0D2 = (c0d2 - c0_d2_) + (c0d2_ + c0_d2)i
+/// C1D1 = (c1d1 - c1_d1_) + (c1d1_ + c1_d1)i
+/// C2D0 = (c2d0 - c2_d0_) + (c2d0_ + c2_d0)i
+///
+/// e2  = c0d2  + c1d1  + c2d0  - (c0_d2_ + c1_d1_ + c2_d0_)
+/// e2_ = c0d2_ + c0_d2 + c1d1_ +  c1_d1  + c2d0_  + c2_d0
+
+/// initial stack: c0, c0_, c1, c1_, c2, c2_, d0, d0_, d1, d1_, d2, d2_, retdest
+/// final   stack: e0, e0_, e1, e1_, e2, e2_
+
 // cost: 157
 global mul_fp6:
-    /// initial stack: c0, c0_, c1, c1_, c2, c2_, d0, d0_, d1, d1_, d2, d2_, retdest
-    /// final   stack: e0, e0_, e1, e1_, e2, e2_
-
-    /// C = C0 + C1t + C2t^2 
-    ///   = (c0 + c0_i) + (c1 + c1_i)t + (c2 + c2_i)t^2
-    ///
-    /// D = D0 + D1t + D2t^2
-    ///   = (d0 + d0_i) + (d1 + d1_i)t + (d2 + d2_i)t^2
-    ///
-    /// E = E0 + E1t + E2t^2 = CD
-    
-    /// E0 = C0D0 + i9(C1D2 + C2D1)
-    ///
-    /// C0D0 = (c0d0 - c0_d0_) + (c0d0_ + c0_d0)i
-    ///
-    /// C1D2 = (c1d2 - c1_d2_) + (c1d2_ + c1_d2)i
-    /// C2D1 = (c2d1 - c2_d1_) + (c2d1_ + c2_d1)i
-    ///
-    /// CD12 = C1D2 + C2D1
-    ///      = (c1d2 + c2d1 - c1_d2_ - c2_d1_) + (c1d2_ + c1_d2 + c2d1_ + c2_d1)i
-    ///
-    /// i9(CD12) = (9CD12 - CD12_) + (CD12 + 9CD12_)i
-    ///
-    /// E0  = 9CD12  - CD12_ + C0D0
-    /// E0_ = 9CD12_ + CD12  + C0D0_
-    ///
-    /// E1 = C0D1 + C1D0 + i9(C2D2)
-    ///
-    /// C0D1 = (c0d1 - c0_d1_) + (c0d1_ + c0_d1)i
-    /// C1D0 = (c1d0 - c1_d0_) + (c1d0_ + c1_d0)i
-    ///
-    /// CD01  = c0d1  + c1d0  - (c0_d1_ + c1_d0_)
-    /// CD01_ = c0d1_ + c0_d1 +  c1d0_  + c1_d0
-    ///
-    ///    C2D2  = (c2d2 - c2_d2_) + (c2d2_ + c2_d2)i
-    /// i9(C2D2) = (9C2D2 - C2D2_) + (C2D2 + 9C2D2_)i
-    ///
-    /// E1  = 9C2D2 -  C2D2_ + CD01
-    /// E1_ =  C2D2 + 9C2D2_ + CD01_
-    ///
-    /// E2 = C0D2 + C1D1 + C2D0
-    ///
-    /// C0D2 = (c0d2 - c0_d2_) + (c0d2_ + c0_d2)i
-    /// C1D1 = (c1d1 - c1_d1_) + (c1d1_ + c1_d1)i
-    /// C2D0 = (c2d0 - c2_d0_) + (c2d0_ + c2_d0)i
-    ///
-    /// E2  = c0d2  + c1d1  + c2d0  - (c0_d2_ + c1_d1_ + c2_d0_)
-    /// E2_ = c0d2_ + c0_d2 + c1d1_ +  c1_d1  + c2d0_  + c2_d0
-
-    // E2
+    // e2
     // make c0_d2_ + c1_d1_ + c2_d0_
     DUP8
     DUP7
@@ -74,11 +77,12 @@ global mul_fp6:
     DUP8
     MULFP254
     ADDFP254
-    // stack: c0d2  + c1d1  + c2d0, c0_d2_ + c1_d1_ + c2_d0_
+    // stack:      c0d2  + c1d1  + c2d0 ,  c0_d2_ + c1_d1_ + c2_d0_
     SUBFP254
+    // stack: e2 = c0d2  + c1d1  + c2d0 - (c0_d2_ + c1_d1_ + c2_d0_)
     SWAP12
 
-    // E0, E0_
+    // e0, e0_
     // make CD12_ = c1d2_ + c1_d2 + c2d1_ + c2_d1
     DUP1
     DUP5
@@ -127,26 +131,26 @@ global mul_fp6:
     DUP7
     MULFP254
     SUBFP254
-    // stack:                 C0D0 , CD12 , C0D0_, CD12_
+    // stack:                      C0D0 , CD12 , C0D0_, CD12_
     DUP4
     DUP3
-    // stack:  CD12 , CD12_ , C0D0 , CD12 , C0D0_, CD12_
+    // stack:       CD12 , CD12_ , C0D0 , CD12 , C0D0_, CD12_
     PUSH 9
     MULFP254
     SUBFP254
     ADDFP254
-    // stack: 9CD12 - CD12_ + C0D0 , CD12 , C0D0_, CD12_
+    // stack: e0 = 9CD12 - CD12_ + C0D0 , CD12 , C0D0_, CD12_
     SWAP12
     SWAP3
-    // stack:                CD12_ , CD12 , C0D0_
+    // stack:                     CD12_ , CD12 , C0D0_
     PUSH 9
     MULFP254
     ADDFP254
     ADDFP254
-    // stack:               9CD12_ + CD12 + C0D0_
+    // stack:              e0_ = 9CD12_ + CD12 + C0D0_
     SWAP11
 
-    // E1, E1_
+    // e1, e1_
     // make C2D2_ = c2d2_ + c2_d2
     DUP14
     DUP10
@@ -187,7 +191,7 @@ global mul_fp6:
     MULFP254
     SUBFP254
     ADDFP254
-    // stack: E1 = 9C2D2 - C2D2_ + CD01, C2D2, C2D2_
+    // stack: e1 = 9C2D2 - C2D2_ + CD01, C2D2, C2D2_
     SWAP15
     SWAP2
     // stack:                    C2D2_ , C2D2
@@ -213,10 +217,10 @@ global mul_fp6:
     ADDFP254
     // stack:       CD01_ , 9C2D2_ + C2D2
     ADDFP254
-    // stack: E1_ = CD01_ + 9C2D2_ + C2D2
+    // stack: e1_ = CD01_ + 9C2D2_ + C2D2
     SWAP15
 
-    // E2_
+    // e2_
     // stack: d2, d1_, d1, d0_, d2_, c0, c0_, c1, c1_, c2, c2_, d0
     SWAP7
     MULFP254
@@ -242,6 +246,8 @@ global mul_fp6:
     SWAP2
     MULFP254
     ADDFP254
-    // stack:  E2_ = c2_d0 + c0_d2 + c0d2_ + c2d0_ + c1d1_ + c1_d1
+    // stack:  e2_ = c2_d0 + c0_d2 + c0d2_ + c2d0_ + c1d1_ + c1_d1
     SWAP6
+
+    // stack: retdest, e0, e0_, e1, e1_, e2, e2_
     JUMP