code-comments, restructure gfpinv slightly

diff --git a/gf_reference/gfpinv.py b/gf_reference/gfpinv.py
index ba1494e28977ce4b66290d040a0028d7ae1d2bf2..15c1f2c3a60255bfb9346ac56db82f038b721fbc 100644 (file)
--- a/gf_reference/gfpinv.py
+++ b/gf_reference/gfpinv.py
@@ -4,6 +4,7 @@ from .state import ST
 def gfpinv(a):
     # based on Algorithm ExtEucdInv from:
     # https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.90.5233&rep=rep1&type=pdf
+    # designed to be dead-easy (and efficient) to implement in hardware
     p = ST.GFPRIME
     assert p >= 2, "GFPRIME isn't a prime"
     assert a != 0, "TODO: decide what happens for division by zero"
@@ -11,10 +12,13 @@ def gfpinv(a):
     if p == 2:
         return 1  # the only value possible
 
+    # initial values`
     u = p
     v = a
     r = 0
     s = 1
+
+    # main loop
     while v > 0:
         # implementations could use count-zeros on
         # both u and r to save cycles
@@ -23,25 +27,29 @@ def gfpinv(a):
                 r += p
             u >>= 1
             r >>= 1
+            continue # loop again
         # implementations could use count-zeros on
         # both v and s to save cycles
-        elif v & 1 == 0:
+        if v & 1 == 0:
             if s & 1 != 0:
                 s += p
             v >>= 1
             s >>= 1
+            continue # loop again
+        # both LSB of u and v are 1
+        x = u - v
+        if x > 0:
+            u = x
+            r -= s
+            if r < 0:
+                r += p
         else:
-            x = u - v
-            if x > 0:
-                u = x
-                r -= s
-                if r < 0:
-                    r += p
-            else:
-                v = -x
-                s -= r
-                if s < 0:
-                    s += p
+            v = -x
+            s -= r
+            if s < 0:
+                s += p
+
+    # make sure result r within modulo range 0 <= r <= p
     if r > p:
         r -= p
     if r < 0: