diff --git a/contrib/math/utils.factor b/contrib/math/utils.factor
index 688af5b1ae..43148ba917 100644
--- a/contrib/math/utils.factor
+++ b/contrib/math/utils.factor
@@ -1,5 +1,5 @@
 IN: math-contrib
-USING: errors kernel sequences math sequences-internals ;
+USING: errors kernel sequences math sequences-internals namespaces arrays ;
 
 : deg>rad pi * 180 / ; inline
 : rad>deg 180 * pi / ; inline
@@ -32,28 +32,86 @@ USING: errors kernel sequences math sequences-internals ;
     #! Complex inner product.
     0 [ ** + ] 2reduce ;
 
+: minmax ( seq -- min max )
+    #! find the min and max of a seq in one pass
+    inf -inf rot [ dup pick max -rot nip pick min -rot nip ] each ;
+
+: absminmax ( seq -- min max )
+    #! find the min and max of a seq in one pass
+    inf -inf rot [ dup pick max -rot nip pick min -rot nip ] each
+    2dup [ abs ] 2apply > [ swap ] when ;
+
+SYMBOL: almost=-precision .000001 almost=-precision set
+: almost= ( a b -- bool )
+    2dup - abs almost=-precision get < [
+            2drop t
+        ] [
+            2array absminmax dup almost=-precision get * >r - abs r>
+            dup 0 < [ >= ] [ <= ] if
+    ] if ;
+
 TUPLE: frange from step length ;
 
 C: frange ( from step to -- seq )
     #! example: 0 .01 10 <frange> >array
-    >r pick - swap [ / ] keep -rot swapd >fixnum 1+ r> 
+    >r pick - swap [ / ceiling 1+ ] keep -rot swapd r> 
     [ set-frange-length ] keep
     [ set-frange-step ] keep
     [ set-frange-from ] keep ;
 
-M: frange length ( frange -- n )
-    frange-length ;
-
 : decrement-length ( frange -- )
     [ frange-length 1- ] keep set-frange-length ;
 
+: <frange-no-endpt> ( from step length -- seq )
+    <frange> dup decrement-length ;
+
+M: frange length ( frange -- n )
+    frange-length ;
+
 : increment-start ( frange -- )
     [ [ frange-from ] keep frange-step + ] keep set-frange-from ;
 
+: exclude-last ( frange -- )
+    ;
+
 : frange-range ( frange -- range )
     [ frange-step ] keep frange-length 1- * ;
 
 M: frange nth ( n frange -- obj ) [ frange-step * ] keep frange-from + ;
 M: frange nth-unsafe ( n frange -- obj ) nth ;
 
+: nseq-swap ( a b seq -- seq )
+    #! swap indices a,b in seq
+    3dup [ nth ] keep swapd [ nth ] keep
+    >r >r rot r> r> swapd set-nth -rot set-nth ;
+
+! : pivot ( left right index seq -- )
+    ! [ nth ] keep [ nseq-swap ] 3keep ;
+
+SYMBOL: step-size .01 step-size set  ! base on arguments
+: (limit) ( count diff quot -- x quot )
+    pick 10 > [ "Not converging fast enough" throw ] when
+    [ call ] keep >r 2dup swap - 0 < [ "not converging" throw ] when
+    2dup almost= rot drop r>
+    swap [ step-size [ 2 / ] change rot 1+ -rot (limit) ] unless ;
+
+: limit ( quot -- x )
+    .1 step-size set [ call ] keep step-size [ 2 / ] change 0 -rot (limit) 2drop ;
+
+! take elements n at a time and apply the quotation, forming a new seq
+: group-map ( seq n quot -- seq )
+    pick length pick /
+    [ [ >r pick pick r> -rot pick over * [ + ] keep swap rot <slice> pick call
+    , ] repeat ] { } make 2nip nip ;
+
+: nths ( start n seq -- seq )
+    -rot pick length <frange-no-endpt> [ over nth ] map nip ;
+
+! take a set of every nth element and apply the quotation, forming a new seq
+! { 1 2 3 4 5 6 } 3 [ sum ] skip-map ->  { 1 4 } { 2 5 } { 3 6 } -> { 5 7 9 }
+: skip-map ( seq n quot -- seq )
+    pick length pick /mod 
+    0 = [ "seq length must be a multiple of n" throw ] unless
+    1 <= [ "seq must be 2n or longer" throw ] when 
+    over [ [ dup >r >r pick pick r> rot swapd nths over call , r> ] repeat ] { } make 2nip nip ;