diff --git a/evm/src/cpu/kernel/asm/fields/fp6.asm b/evm/src/cpu/kernel/asm/fields/fp6.asm
index a6e93a71..d12322b3 100644
--- a/evm/src/cpu/kernel/asm/fields/fp6.asm
+++ b/evm/src/cpu/kernel/asm/fields/fp6.asm
@@ -180,7 +180,7 @@
     // stack:                         h0, h1, h2, h3, h4, h5
 %endmacro
 
-// *backwards order subtraction* cost: 17
+// *reversed argument subtraction* cost: 17
 %macro bus_fp6
     // stack: f0, f1, f2, f3, f4, f5, g0, g1, g2, g3, g4, g5
     SWAP7
@@ -210,14 +210,14 @@
 
 // cost: 156
 %macro mul_fp6
-    /// E = E0 + E1t + E2t^2 = CD
-    ///
     /// 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
+    ///
     /// initial stack: c0, c0_, c1, c1_, c2, c2_, d0, d0_, d1, d1_, d2, d2_
     /// final   stack: e0, e0_, e1, e1_, e2, e2_
 
@@ -236,7 +236,7 @@
     /// E0  = 9CDX  - CDX_ + C0D0
     /// E0_ = 9CDX_ + CDX  + C0D0_
 
-    // CDX_ = c1d2_ + c1_d2 + c2d1_ + c2_d1
+    // make CDX_ = c1d2_ + c1_d2 + c2d1_ + c2_d1
     DUP12
     DUP4
     MULFP254
@@ -252,7 +252,7 @@
     DUP8
     MULFP254
     ADDFP254
-    // C0D0_ = c0d0_ + c0_d0
+    // make C0D0_ = c0d0_ + c0_d0
     DUP9
     DUP3
     MULFP254
@@ -260,7 +260,7 @@
     DUP5
     MULFP254
     ADDFP254
-    // CDX = c1d2 + c2d1 - c1_d2_ - c2_d1_
+    // make CDX = c1d2 + c2d1 - c1_d2_ - c2_d1_
     DUP12
     DUP9
     MULFP254
@@ -276,7 +276,7 @@
     MULFP254
     ADDFP254
     SUBFP254
-    // C0D0 = c0d0 - c0_d0_
+    // make C0D0 = c0d0 - c0_d0_
     DUP11
     DUP6
     MULFP254
@@ -284,23 +284,24 @@
     DUP6
     MULFP254
     SUBFP254
-    // stack:               C0D0 , CDX , C0D0_, CDX_
+
+    // stack:                    C0D0 , CDX , C0D0_, CDX_
     DUP4
     DUP3
-    // stack:  CDX , CDX_ , C0D0 , CDX , C0D0_, CDX_
+    // stack:       CDX , CDX_ , C0D0 , CDX , C0D0_, CDX_
     PUSH 9
     MULFP254
     SUBFP254
     ADDFP254
-    // stack: 9CDX - CDX_ + C0D0 , CDX , C0D0_, CDX_
+    // stack: E0 = 9CDX - CDX_ + C0D0 , CDX , C0D0_, CDX_
     SWAP15
     SWAP3
-    // stack:               CDX_ , CDX , C0D0_
+    // stack:                    CDX_ , CDX , C0D0_
     PUSH 9
     MULFP254
     ADDFP254
     ADDFP254
-    // stack:              9CDX_ + CDX + C0D0_
+    // stack:             E0_ = 9CDX_ + CDX + C0D0_
     SWAP9
     
     /// E1 = C0D1 + C1D0 + i9(C2D2)
@@ -308,13 +309,16 @@
     /// 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_ + c0d1  + c1d0  - (c0_d1_ + c1_d0_)
-    /// E1_ =  C2D2 + 9C2D2_ + c0d1_ + c0_d1 +  c1d0_  + c1_d0
+    /// E1  = 9C2D2 -  C2D2_ + CD01
+    /// E1_ =  C2D2 + 9C2D2_ + CD01_
 
-    // C2D2_ = c2d2_ + c2_d2
+    // make C2D2_ = c2d2_ + c2_d2
     DUP13
     DUP9
     MULFP254
@@ -322,7 +326,7 @@
     DUP9
     MULFP254
     ADDFP254
-    // C2D2  = c2d2  - c2_d2_
+    // make C2D2  = c2d2  - c2_d2_
     DUP3
     DUP10
     MULFP254
@@ -330,8 +334,7 @@
     DUP10
     MULFP254
     SUBFP254
-    // stack:                                                   C2D2, C2D2_
-    // c0d1 + c1d0 - (c0_d1_ + c1_d0_)
+    // make C0D0 = c0d1 + c1d0 - (c0_d1_ + c1_d0_)
     DUP3
     DUP9
     MULFP254
@@ -347,23 +350,23 @@
     MULFP254
     ADDFP254
     SUBFP254
-    // stack:                 c0d1  + c1d0 - (c0_d1_ + c1_d0_), C2D2, C2D2_
+    // stack:                      C0D0, C2D2, C2D2_
     DUP3
     DUP3
-    // stack:  C2D2 , C2D2_ , c0d1  + c1d0 - (c0_d1_ + c1_d0_), C2D2, C2D2_
+    // stack:       C2D2 , C2D2_ , C0D0, C2D2, C2D2_
     PUSH 9
     MULFP254
     SUBFP254
     ADDFP254
-    // stack: 9C2D2 - C2D2_ + c0d1  + c1d0 - (c0_d1_ + c1_d0_), C2D2, C2D2_
+    // stack: E1 = 9C2D2 - C2D2_ + C0D0, C2D2, C2D2_
     SWAP13
     SWAP2
-    // stack:                                           C2D2_ , C2D2
+    // stack:                     C2D2_, C2D2
     PUSH 9
     MULFP254
     ADDFP254
     // stack: 9C2D2_ + C2D2
-    // c0d1_ + c0_d1 +  c1d0_  + c1_d0
+    // make CD01_ = c0d1_ + c0_d1 +  c1d0_  + c1_d0
     DUP11
     DUP9
     MULFP254
@@ -379,7 +382,9 @@
     DUP7
     MULFP254
     ADDFP254
+    // stack:       CD01_ , 9C2D2_ + C2D2
     ADDFP254
+    // stack: E1_ = CD01_ + 9C2D2_ + C2D2
     SWAP13
 
     /// E2 = C0D2 + C1D1 + C2D0
@@ -391,7 +396,7 @@
     /// E2  = c0d2  + c1d1  + c2d0  - (c0_d2_ + c1_d1_ + c2_d0_)
     /// E2_ = c0d2_ + c0_d2 + c1d1_ +  c1_d1  + c2d0_  + c2_d0
 
-    // c0_d2_ + c1_d1_ + c2_d0_
+    // make c0_d2_ + c1_d1_ + c2_d0_
     DUP3
     DUP11
     MULFP254
@@ -403,7 +408,7 @@
     DUP8
     MULFP254
     ADDFP254
-    // c0d2  + c1d1  + c2d0
+    // make c0d2  + c1d1  + c2d0
     DUP16
     DUP7
     MULFP254
@@ -415,10 +420,11 @@
     DUP12
     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_)
     SWAP15
-    // c0d2_ + c0_d2 + c1d1_ +  c1_d1  + c2d0_  + c2_d0
+    // make c0d2_ + c0_d2 + c1d1_ +  c1_d1  + c2d0_  + c2_d0
     SWAP7
     MULFP254
     SWAP7
@@ -436,5 +442,6 @@
     SWAP2
     MULFP254
     ADDFP254
+    // stack: E2_ = c0d2_ + c0_d2 + c1d1_ +  c1_d1  + c2d0_  + c2_d0
     SWAP5
 %endmacro