diff --git a/basis/math/functions/functions-tests.factor b/basis/math/functions/functions-tests.factor
index cbaf37daf8..a06a67e4a1 100644
--- a/basis/math/functions/functions-tests.factor
+++ b/basis/math/functions/functions-tests.factor
@@ -134,3 +134,6 @@ IN: math.functions.tests
 [ -4.0 ] [ -4.4 round ] unit-test
 [ 5.0 ] [ 4.5 round ] unit-test
 [ 4.0 ] [ 4.4 round ] unit-test
+
+[ 6 59967 ] [ 3837888 factor-2s ] unit-test
+[ 6 -59967 ] [ -3837888 factor-2s ] unit-test
diff --git a/basis/math/functions/functions.factor b/basis/math/functions/functions.factor
index 8516292e9d..0444998bec 100644
--- a/basis/math/functions/functions.factor
+++ b/basis/math/functions/functions.factor
@@ -1,7 +1,7 @@
-! Copyright (C) 2004, 2007 Slava Pestov.
+! Copyright (C) 2004, 2008 Slava Pestov.
 ! See http://factorcode.org/license.txt for BSD license.
 USING: math kernel math.constants math.private
-math.libm combinators math.order ;
+math.libm combinators math.order math.ratios sequences ;
 IN: math.functions
 
 <PRIVATE
@@ -30,14 +30,35 @@ M: real sqrt
         2dup >r >r >r odd? r> call r> 2/ r> each-bit
     ] if ; inline recursive
 
-: ^n ( z w -- z^w )
-    1 swap [
-        [ dupd * ] when >r sq r>
-    ] each-bit nip ; inline
+: map-bits ( n quot: ( ? -- obj ) -- seq )
+    accumulator [ each-bit ] dip ; inline
+
+: factor-2s ( n -- r s )
+    #! factor an integer into 2^r * s
+    dup 0 = [ 1 ] [
+        0 swap [ dup even? ] [ [ 1+ ] [ 2/ ] bi* ] [ ] while
+    ] if ; inline
+
+<PRIVATE
+
+GENERIC# ^n 1 ( z w -- z^w )
+
+: (^n) 1 swap [ [ dupd * ] when [ sq ] dip ] each-bit nip ; inline
+
+M: integer ^n
+    [ factor-2s ] dip [ (^n) ] keep rot * shift ;
+
+M: ratio ^n
+    [ >fraction ] dip tuck [ ^n ] 2bi@ / ;
+
+M: float ^n
+    (^n) ;
 
 : integer^ ( x y -- z )
     dup 0 > [ ^n ] [ neg ^n recip ] if ; inline
 
+PRIVATE>
+
 : >rect ( z -- x y )
     [ real-part ] [ imaginary-part ] bi ; inline
 
@@ -52,6 +73,8 @@ M: real sqrt
 
 : polar> ( abs arg -- z ) cis * ; inline
 
+<PRIVATE
+
 : ^mag ( w abs arg -- magnitude )
     >r >r >float-rect swap r> swap fpow r> rot * fexp /f ;
     inline
@@ -68,6 +91,8 @@ M: real sqrt
 : 0^ ( x -- z )
     dup zero? [ drop 0./0. ] [ 0 < 1./0. 0 ? ] if ; inline
 
+PRIVATE>
+
 : ^ ( x y -- z )
     {
         { [ over zero? ] [ nip 0^ ] }
diff --git a/extra/math/miller-rabin/miller-rabin.factor b/extra/math/miller-rabin/miller-rabin.factor
index 3045a35836..def8a04738 100755
--- a/extra/math/miller-rabin/miller-rabin.factor
+++ b/extra/math/miller-rabin/miller-rabin.factor
@@ -11,13 +11,6 @@ IN: math.miller-rabin
 
 TUPLE: positive-even-expected n ;
 
-: (factor-2s) ( r s -- r s )
-    dup even? [ -1 shift [ 1+ ] dip (factor-2s) ] when ;
-
-: factor-2s ( n -- r s )
-    #! factor an integer into s * 2^r
-    0 swap (factor-2s) ;
-
 :: (miller-rabin) ( n trials -- ? )
     [let | r [ n 1- factor-2s drop ]
            s [ n 1- factor-2s nip ]