diff --git a/basis/db/tuples/tuples-tests.factor b/basis/db/tuples/tuples-tests.factor
index d4a58fa4fc..375ee509bb 100644
--- a/basis/db/tuples/tuples-tests.factor
+++ b/basis/db/tuples/tuples-tests.factor
@@ -411,7 +411,7 @@ TUPLE: exam id name score ;
             T{ exam f 4 "Cartman" 41 }
         }
     ] [
-        T{ exam f T{ interval f { 2 t } { 1.0/0.0 f } } } select-tuples
+        T{ exam f T{ interval f { 2 t } { 1/0. f } } } select-tuples
     ] unit-test
 
     [
@@ -419,7 +419,7 @@ TUPLE: exam id name score ;
             T{ exam f 1 "Kyle" 100 }
         }
     ] [
-        T{ exam f T{ interval f { -1.0/0.0 t } { 2 f } } } select-tuples
+        T{ exam f T{ interval f { -1/0. t } { 2 f } } } select-tuples
     ] unit-test
 
     [
@@ -430,7 +430,7 @@ TUPLE: exam id name score ;
             T{ exam f 4 "Cartman" 41 }
         }
     ] [
-        T{ exam f T{ interval f { -1.0/0.0 t } { 1/0. f } } } select-tuples
+        T{ exam f T{ interval f { -1/0. t } { 1/0. f } } } select-tuples
     ] unit-test
     
     [
diff --git a/basis/furnace/cache/cache.factor b/basis/furnace/cache/cache.factor
index a5308c171e..fe2840c9eb 100644
--- a/basis/furnace/cache/cache.factor
+++ b/basis/furnace/cache/cache.factor
@@ -22,7 +22,7 @@ server-state f
 
 : expire-state ( class -- )
     new
-        -1.0/0.0 millis [a,b] >>expires
+        -1/0. millis [a,b] >>expires
     delete-tuples ;
 
 TUPLE: server-state-manager < filter-responder timeout ;
diff --git a/basis/hints/hints.factor b/basis/hints/hints.factor
index 2534e0121f..d44bf92bf4 100644
--- a/basis/hints/hints.factor
+++ b/basis/hints/hints.factor
@@ -3,7 +3,7 @@
 USING: parser words definitions kernel sequences assocs arrays
 kernel.private fry combinators accessors vectors strings sbufs
 byte-arrays byte-vectors io.binary io.streams.string splitting
-math generic generic.standard generic.standard.engines classes
+math math.parser generic generic.standard generic.standard.engines classes
 hashtables ;
 IN: hints
 
@@ -118,6 +118,8 @@ SYNTAX: HINTS:
 
 \ >be { { bignum fixnum } { fixnum fixnum } } "specializer" set-word-prop
 
+\ base> { string fixnum } "specializer" set-word-prop
+
 M\ hashtable at* { { fixnum object } { word object } } "specializer" set-word-prop
 
 M\ hashtable set-at { { object fixnum object } { object word object } } "specializer" set-word-prop
diff --git a/basis/math/functions/functions-tests.factor b/basis/math/functions/functions-tests.factor
index 4c9d151fd8..397a7cc2f3 100644
--- a/basis/math/functions/functions-tests.factor
+++ b/basis/math/functions/functions-tests.factor
@@ -22,9 +22,9 @@ IN: math.functions.tests
 [ t ] [ e pi i* ^ imaginary-part -0.00001 0.00001 between? ] unit-test
 
 [ t ] [ 0 0 ^ fp-nan? ] unit-test
-[ 1.0/0.0 ] [ 0 -2 ^ ] unit-test
+[ 1/0. ] [ 0 -2 ^ ] unit-test
 [ t ] [ 0 0.0 ^ fp-nan? ] unit-test
-[ 1.0/0.0 ] [ 0 -2.0 ^ ] unit-test
+[ 1/0. ] [ 0 -2.0 ^ ] unit-test
 [ 0 ] [ 0 3.0 ^ ] unit-test
 [ 0 ] [ 0 3 ^ ] unit-test
 
diff --git a/basis/math/libm/libm-docs.factor b/basis/math/libm/libm-docs.factor
index bf4c608d77..a890a59c19 100644
--- a/basis/math/libm/libm-docs.factor
+++ b/basis/math/libm/libm-docs.factor
@@ -6,7 +6,7 @@ ARTICLE: "math.libm" "C standard library math functions"
 $nl
 "They can be called directly, however there is little reason to do so, since they only implement real-valued functions, and in some cases place restrictions on the domain:"
 { $example "USE: math.functions" "2 acos ." "C{ 0.0 1.316957896924817 }" }
-{ $unchecked-example "USE: math.libm" "2 facos ." "0.0/0.0" }
+{ $unchecked-example "USE: math.libm" "2 facos ." "0/0." }
 "Trigonometric functions:"
 { $subsection fcos }
 { $subsection fsin }
diff --git a/basis/stack-checker/transforms/transforms.factor b/basis/stack-checker/transforms/transforms.factor
index c2b348f5f1..dfa46be7e2 100755
--- a/basis/stack-checker/transforms/transforms.factor
+++ b/basis/stack-checker/transforms/transforms.factor
@@ -1,13 +1,13 @@
 ! Copyright (C) 2007, 2009 Slava Pestov, Daniel Ehrenberg.
 ! See http://factorcode.org/license.txt for BSD license.
 USING: fry accessors arrays kernel kernel.private combinators.private
-words sequences generic math math.order namespaces make quotations assocs
-combinators combinators.short-circuit classes.tuple
+words sequences generic math math.order namespaces make quotations
+assocs combinators combinators.short-circuit classes.tuple
 classes.tuple.private effects summary hashtables classes generic sets
 definitions generic.standard slots.private continuations locals
-generalizations stack-checker.backend stack-checker.state
-stack-checker.visitor stack-checker.errors stack-checker.values
-stack-checker.recursive-state ;
+sequences.private generalizations stack-checker.backend
+stack-checker.state stack-checker.visitor stack-checker.errors
+stack-checker.values stack-checker.recursive-state ;
 IN: stack-checker.transforms
 
 : give-up-transform ( word -- )
@@ -106,40 +106,68 @@ IN: stack-checker.transforms
     ] [ drop f ] if
 ] 1 define-transform
 
-! Membership testing
-CONSTANT: bit-member-max 256
+! Fast at for integer maps
+CONSTANT: lookup-table-at-max 256
 
-: bit-member? ( seq -- ? )
+: lookup-table-at? ( assoc -- ? )
     #! Can we use a fast byte array test here?
     {
-        [ length 4 > ]
-        [ [ integer? ] all? ]
-        [ [ 0 bit-member-max between? ] any? ]
+        [ assoc-size 4 > ]
+        [ values [ ] all? ]
+        [ keys [ integer? ] all? ]
+        [ keys [ 0 lookup-table-at-max between? ] all? ]
     } 1&& ;
 
-: bit-member-seq ( seq -- flags )
-    [ supremum 1+ ] keep '[ _ member? 1 0 ? ] B{ } map-as ;
+: lookup-table-seq ( assoc -- table )
+    [ keys supremum 1+ ] keep '[ _ at ] { } map-as ;
 
-: bit-member-quot ( seq -- newquot )
-    bit-member-seq
+: lookup-table-quot ( seq -- newquot )
+    lookup-table-seq
     '[
-        _ {
-            { [ over fixnum? ] [ ?nth 1 eq? ] }
-            { [ over bignum? ] [ ?nth 1 eq? ] }
-            [ 2drop f ]
-        } cond
+        _ over integer? [
+            2dup bounds-check? [
+                nth-unsafe dup >boolean
+            ] [ 2drop f f ] if
+        ] [ 2drop f f ] if
     ] ;
 
-: member-quot ( seq -- newquot )
-    dup bit-member? [
-        bit-member-quot
-    ] [
-        dup length 4 <= [
-            [ drop f ] swap
-            [ literalize [ t ] ] { } map>assoc linear-case-quot
+: fast-lookup-table-at? ( assoc -- ? )
+    values {
+        [ [ integer? ] all? ]
+        [ [ 0 254 between? ] all? ]
+    } 1&& ;
+
+: fast-lookup-table-seq ( assoc -- table )
+    lookup-table-seq [ 255 or ] B{ } map-as ;
+
+: fast-lookup-table-quot ( seq -- newquot )
+    fast-lookup-table-seq
+    '[
+        _ over integer? [
+            2dup bounds-check? [
+                nth-unsafe dup 255 eq? [ drop f f ] [ t ] if
+            ] [ 2drop f f ] if
+        ] [ 2drop f f ] if
+    ] ;
+
+: at-quot ( assoc -- quot )
+    dup lookup-table-at? [
+        dup fast-lookup-table-at? [
+            fast-lookup-table-quot
         ] [
-            unique [ key? ] curry
+            lookup-table-quot
         ] if
+    ] [ drop f ] if ;
+
+\ at* [ at-quot ] 1 define-transform
+
+! Membership testing
+: member-quot ( seq -- newquot )
+    dup length 4 <= [
+        [ drop f ] swap
+        [ literalize [ t ] ] { } map>assoc linear-case-quot
+    ] [
+        unique [ key? ] curry
     ] if ;
 
 \ member? [
@@ -170,4 +198,4 @@ CONSTANT: bit-member-max 256
 
 \ shuffle [
     shuffle-mapping nths-quot
-] 1 define-transform
\ No newline at end of file
+] 1 define-transform
diff --git a/basis/wrap/wrap.factor b/basis/wrap/wrap.factor
index 58957ba8e7..482d50ab5f 100644
--- a/basis/wrap/wrap.factor
+++ b/basis/wrap/wrap.factor
@@ -30,7 +30,7 @@ SYMBOL: line-ideal
     { [ lines>> car 1list? ] [ top-fits? ] } 1|| ;
 
 :: min-by ( seq quot -- elt )
-    f 1.0/0.0 seq [| key value new |
+    f 1/0. seq [| key value new |
         new quot call :> newvalue
         newvalue value < [ new newvalue ] [ key value ] if
     ] each drop ; inline
diff --git a/core/math/floats/floats-tests.factor b/core/math/floats/floats-tests.factor
index 27cc510ea2..9f8f7b06fc 100644
--- a/core/math/floats/floats-tests.factor
+++ b/core/math/floats/floats-tests.factor
@@ -56,8 +56,6 @@ unit-test
 [ t ] [ 0.0 zero? ] unit-test
 [ t ] [ -0.0 zero? ] unit-test
 
-! [ f ] [ 0.0/0.0 0.0/0.0 number= ] unit-test
-
 [ 0 ] [ 1/0. >bignum ] unit-test
 
 [ t ] [ 64 [ 2^ 0.5 * ] map [ < ] monotonic? ] unit-test
diff --git a/core/math/integers/integers.factor b/core/math/integers/integers.factor
index e88caa7703..868d9fc02e 100644
--- a/core/math/integers/integers.factor
+++ b/core/math/integers/integers.factor
@@ -122,7 +122,7 @@ M: bignum (log2) bignum-log2 ;
         2drop 0.0
     ] [
         dup zero? [
-            2drop 1.0/0.0
+            2drop 1/0.
         ] [
             pre-scale
             /f-loop over odd?
diff --git a/core/math/parser/parser-tests.factor b/core/math/parser/parser-tests.factor
index 0fb2559854..c655965e35 100644
--- a/core/math/parser/parser-tests.factor
+++ b/core/math/parser/parser-tests.factor
@@ -95,17 +95,17 @@ unit-test
 [ 1 0 >base ] must-fail
 [ 1 -1 >base ] must-fail
 
-[ "0.0/0.0" ] [ 0.0 0.0 / number>string ] unit-test
+[ "0/0." ] [ 0.0 0.0 / number>string ] unit-test
 
-[ "1.0/0.0" ] [ 1.0 0.0 / number>string ] unit-test
+[ "1/0." ] [ 1.0 0.0 / number>string ] unit-test
 
-[ "-1.0/0.0" ] [ -1.0 0.0 / number>string ] unit-test
+[ "-1/0." ] [ -1.0 0.0 / number>string ] unit-test
 
 [ t ] [ "0/0." string>number fp-nan? ] unit-test
 
-[ 1.0/0.0 ] [ "1/0." string>number ] unit-test
+[ 1/0. ] [ "1/0." string>number ] unit-test
 
-[ -1.0/0.0 ] [ "-1/0." string>number ] unit-test
+[ -1/0. ] [ "-1/0." string>number ] unit-test
 
 [ "-0.0" ] [ -0.0 number>string ] unit-test
 
diff --git a/core/math/parser/parser.factor b/core/math/parser/parser.factor
index 0d8f0c0b08..0a637c2eab 100644
--- a/core/math/parser/parser.factor
+++ b/core/math/parser/parser.factor
@@ -1,7 +1,7 @@
-! Copyright (C) 2004, 2008 Slava Pestov.
+! Copyright (C) 2004, 2009 Slava Pestov.
 ! See http://factorcode.org/license.txt for BSD license.
-USING: kernel math.private namespaces sequences strings
-arrays combinators splitting math assocs make ;
+USING: kernel math.private namespaces sequences sequences.private
+strings arrays combinators splitting math assocs make ;
 IN: math.parser
 
 : digit> ( ch -- n )
@@ -28,13 +28,19 @@ IN: math.parser
         { CHAR: d 13 }
         { CHAR: e 14 }
         { CHAR: f 15 }
-    } at ;
+    } at 255 or ; inline
 
 : string>digits ( str -- digits )
-    [ digit> ] { } map-as ;
+    [ digit> ] B{ } map-as ; inline
 
-: digits>integer ( seq radix -- n )
-    0 swap [ swapd * + ] curry reduce ;
+: (digits>integer) ( valid? accum digit radix -- valid? accum )
+    2dup < [ swapd * + ] [ 2drop 2drop f 0 ] if ; inline
+
+: each-digit ( seq radix quot -- n/f )
+    [ t 0 ] 3dip curry each swap [ drop f ] unless ; inline
+
+: digits>integer ( seq radix -- n/f )
+    [ (digits>integer) ] each-digit ; inline
 
 DEFER: base>
 
@@ -43,6 +49,9 @@ DEFER: base>
 SYMBOL: radix
 SYMBOL: negative?
 
+: string>natural ( seq radix -- n/f )
+    [ [ digit> ] dip (digits>integer) ] each-digit ; inline
+
 : sign ( -- str ) negative? get "-" "+" ? ;
 
 : with-radix ( radix quot -- )
@@ -54,37 +63,30 @@ SYMBOL: negative?
     sign split1 [ (base>) ] dip
     dup [ (base>) ] [ drop 0 swap ] if ;
 
-: string>ratio ( str -- a/b )
-    "-" ?head dup negative? set swap
-    "/" split1 (base>) [ whole-part ] dip
-    3dup and and [ / + swap [ neg ] when ] [ 2drop 2drop f ] if ;
+: string>ratio ( str radix -- a/b )
+    [
+        "-" ?head dup negative? set swap
+        "/" split1 (base>) [ whole-part ] dip
+        3dup and and [ / + swap [ neg ] when ] [ 2drop 2drop f ] if
+    ] with-radix ;
 
-: valid-digits? ( seq -- ? )
-    {
-        { [ dup empty? ] [ drop f ] }
-        { [ f over memq? ] [ drop f ] }
-        [ radix get [ < ] curry all? ]
-    } cond ;
-
-: string>integer ( str -- n/f )
-    "-" ?head swap
-    string>digits dup valid-digits?
-    [ radix get digits>integer swap [ neg ] when ] [ 2drop f ] if ;
+: string>integer ( str radix -- n/f )
+    over first-unsafe CHAR: - = [
+        [ rest-slice ] dip string>natural dup [ neg ] when
+    ] [
+        string>natural
+    ] if ; inline
 
 PRIVATE>
 
 : base> ( str radix -- n/f )
-    [
-        CHAR: / over member? [
-            string>ratio
-        ] [
-            CHAR: . over member? [
-                string>float
-            ] [
-                string>integer
-            ] if
-        ] if
-    ] with-radix ;
+    over empty? [ 2drop f ] [
+        over [ "/." member? ] find nip {
+            { CHAR: / [ string>ratio ] }
+            { CHAR: . [ drop string>float ] }
+            [ drop string>integer ]
+        } case
+    ] if ;
 
 : string>number ( str -- n/f ) 10 base> ;
 : bin> ( str -- n/f ) 2 base> ;
@@ -147,9 +149,9 @@ M: ratio >base
 
 M: float >base
     drop {
-        { [ dup fp-nan? ] [ drop "0.0/0.0" ] }
-        { [ dup 1.0/0.0 = ] [ drop "1.0/0.0" ] }
-        { [ dup -1.0/0.0 = ] [ drop "-1.0/0.0" ] }
+        { [ dup fp-nan? ] [ drop "0/0." ] }
+        { [ dup 1/0. = ] [ drop "1/0." ] }
+        { [ dup -1/0. = ] [ drop "-1/0." ] }
         { [ dup double>bits HEX: 8000000000000000 = ] [ drop "-0.0" ] }
         [ float>string fix-float ]
     } cond ;
diff --git a/extra/benchmark/raytracer/raytracer.factor b/extra/benchmark/raytracer/raytracer.factor
index a4df1fe04d..642b3dbb93 100755
--- a/extra/benchmark/raytracer/raytracer.factor
+++ b/extra/benchmark/raytracer/raytracer.factor
@@ -53,7 +53,7 @@ C: <sphere> sphere
 
 : sphere-t ( b d -- t )
     -+ dup 0.0 <
-    [ 2drop 1.0/0.0 ] [ [ [ 0.0 > ] keep ] dip ? ] if ; inline
+    [ 2drop 1/0. ] [ [ [ 0.0 > ] keep ] dip ? ] if ; inline
 
 : sphere-b&v ( sphere ray -- b v )
     [ sphere-v ] [ nip ] 2bi