diff --git a/aes.js b/aes.js
index 2dc7d69..ea0d080 100644
--- a/aes.js
+++ b/aes.js
@@ -113,14 +113,14 @@ class Aes {
      *
      * @private
      */
-    static shiftRows(s, Nb) {
-        const t = new Array(4);
-        for (let r=1; r<4; r++) {
-            for (let c=0; c<4; c++) t[c] = s[r][(c+r)%Nb];  // shift into temp copy
-            for (let c=0; c<4; c++) s[r][c] = t[c];         // and copy back
-        }          // note that this will work for Nb=4,5,6, but not 7,8 (always 4 for AES):
-        return s;  // see asmaes.sourceforge.net/rijndael/rijndaelImplementation.pdf
+static shiftRows(s, Nb) {
+    const t = new Array(4);
+    for (let r = 1; r < 4; r++) {
+        for (let c = 0; c < 4; c++) t[c] = s[r][(c + r) % Nb];
+        for (let c = 0; c < 4; c++) s[r][c] = t[c];
     }
+    return s;
+}
 
 
     /**
@@ -128,26 +128,28 @@ class Aes {
      *
      * @private
      */
-    static mixColumns(s, Nb) {
-        for (let c=0; c<Nb; c++) {
-            const a = new Array(Nb);  // 'a' is a copy of the current column from 's'
-            const b = new Array(Nb);  // 'b' is a•{02} in GF(2^8)
-            for (let r=0; r<4; r++) {
-                a[r] = s[r][c];
-                b[r] = s[r][c]&0x80 ? s[r][c]<<1 ^ 0x011b : s[r][c]<<1;
-            }
-            // a[n] ^ b[n] is a•{03} in GF(2^8)
-            s[0][c] = b[0] ^ a[1] ^ b[1] ^ a[2] ^ a[3]; // {02}•a0 + {03}•a1 + a2 + a3
-            s[1][c] = a[0] ^ b[1] ^ a[2] ^ b[2] ^ a[3]; // a0 • {02}•a1 + {03}•a2 + a3
-            s[2][c] = a[0] ^ a[1] ^ b[2] ^ a[3] ^ b[3]; // a0 + a1 + {02}•a2 + {03}•a3
-            s[3][c] = a[0] ^ b[0] ^ a[1] ^ a[2] ^ b[3]; // {03}•a0 + a1 + a2 + {02}•a3
+static mixColumns(s, Nb) {
+    const a = new Array(4);
+    const b = new Array(4);
+
+    for (let c = 0; c < Nb; c++) {
+        for (let r = 0; r < 4; r++) {
+            a[r] = s[r][c];
+            b[r] = s[r][c] & 0x80 ? (s[r][c] << 1) ^ 0x011b : s[r][c] << 1;
         }
-        return s;
+
+        s[0][c] = b[0] ^ a[1] ^ b[1] ^ a[2] ^ a[3];
+        s[1][c] = a[0] ^ b[1] ^ a[2] ^ b[2] ^ a[3];
+        s[2][c] = a[0] ^ a[1] ^ b[2] ^ a[3] ^ b[3];
+        s[3][c] = a[0] ^ b[0] ^ a[1] ^ a[2] ^ b[3];
     }
 
+    return s;
+}
+
 
     /**
-     * Xor Round Key into state S [§5.1.4].
+     * Xor Round Key into state S [5.1.4].
      *
      * @private
      */
diff --git a/sha512.js b/sha512.js
index aa1eed4..e2f63a1 100644
--- a/sha512.js
+++ b/sha512.js
@@ -237,13 +237,12 @@ Sha512.Long = class {
         return hi + lo;
     }
 
-    add(that) { // addition modulo 2^64
-        const lo = this.lo + that.lo;
-        const hi = this.hi + that.hi + (lo>0x100000000 ? 1 : 0); // carry top bit if lo > 2^32
-
-        return new Sha512.Long(hi >>> 0, lo >>> 0);
-    }
-
+add(that) {
+    const lo = this.lo + that.lo;
+    const carry = lo >= 0x100000000 ? 1 : 0;
+    const hi = this.hi + that.hi + carry;
+    return new Sha512.Long(hi >>> 0, lo >>> 0);
+}
     and(that) { // &
         return new Sha512.Long(this.hi & that.hi, this.lo & that.lo);
     }
@@ -257,7 +256,7 @@ Sha512.Long = class {
     }
 
     shr(n) { // >>>
-        if (n ==  0) return this;
+        if (n ==  0) return this; // no shit needed
         if (n == 32) return new Sha512.Long(0, this.hi);
         if (n >  32) return new Sha512.Long(0, this.hi >>> n-32);
         /* n < 32 */ return new Sha512.Long(this.hi >>> n, this.lo >>> n | this.hi << (32-n));