diff --git a/README.md b/README.md
--- a/README.md
+++ b/README.md
@@ -21,8 +21,6 @@
 | `τ(3018)` | Haskell | 35.87 μs |
 | `ω(91)` | ATS | 282.1 ns |
 | `ω(91)` | Haskell | 1.194 μs |
-| `gcd(201, 67)` | ATS | 8.848 ns |
-| `gcd(201, 67)` | Haskell | 11.26 ns |
 
 ## Building
 
diff --git a/Setup.hs b/Setup.hs
--- a/Setup.hs
+++ b/Setup.hs
@@ -21,9 +21,9 @@
 main = defaultMainWithHooks myHooks
 
     where myHooks = simpleUserHooks { preConf = buildScript
-                                    , postBuild = maybeCleanATS }
+                                    , postReg = maybeCleanATS }
 
-maybeCleanATS :: Args -> BuildFlags -> PackageDescription -> LocalBuildInfo -> IO ()
+maybeCleanATS :: Args -> RegisterFlags -> PackageDescription -> LocalBuildInfo -> IO ()
 maybeCleanATS _ _ _ li =
     let cf = configConfigurationsFlags (configFlags li) in
 
diff --git a/ats-src/combinatorics.dats b/ats-src/combinatorics.dats
--- a/ats-src/combinatorics.dats
+++ b/ats-src/combinatorics.dats
@@ -11,14 +11,7 @@
   case+ k of
     | 0 => int2intinf(1)
     | 1 => int2intinf(1)
-    | k =>> let
-      val x = fact(k - 1) * k
-    in
-      if compare(x, 0) = 1 then
-        x
-      else
-        int2intinf(1)
-    end
+    | k =>> $UN.cast(fact(k - 1) * k)
 
 // double factorial http://mathworld.wolfram.com/DoubleFactorial.html
 fnx dfact {n : nat} .<n>. (k : int(n)) : Intinf =
@@ -29,19 +22,19 @@
 
 // Number of permutations on n objects using k at a time.
 fn permutatsions {n : nat}{ k : nat | k <= n } (n : int(n), k : int(k)) : Intinf =
-  fact(n) / fact(n - k)
+  ndiv(fact(n), fact(n - k))
 
 // Number of permutations on n objects using k at a time.
 fn choose {n : nat}{ m : nat | m <= n } (n : int(n), k : int(m)) : Intinf =
   let
-    fun numerator_loop { m : nat | m > 1 } .<m>. (i : int(m)) : Intinf =
+    fun numerator_loop { m : nat | m > 1 } .<m>. (i : int(m)) : [ n : nat | n > 0 ] intinf(n) =
       case+ i of
         | 1 => int2intinf(n)
-        | 2 => int2intinf(n - 1) * n
-        | i =>> (n + 1 - i) * numerator_loop(i - 1)
+        | 2 => $UN.cast(int2intinf(n - 1) * n)
+        | i =>> $UN.cast((n + 1 - i) * numerator_loop(i - 1))
   in
     case+ k of
       | 0 => int2intinf(1)
       | 1 => int2intinf(n)
-      | k =>> numerator_loop(k) / fact(k)
+      | k =>> ndiv(numerator_loop(k), fact(k))
   end
diff --git a/ats-src/number-theory.dats b/ats-src/number-theory.dats
--- a/ats-src/number-theory.dats
+++ b/ats-src/number-theory.dats
@@ -72,6 +72,7 @@
     loop(n, 1)
   end
 
+// TODO proofs of correctness like HX for fibonacci numbers?
 fn is_perfect(n : intGte(1)) :<> bool =
   sum_divisors(n) = n
 
diff --git a/cbits/number-theory.c b/cbits/number-theory.c
--- a/cbits/number-theory.c
+++ b/cbits/number-theory.c
@@ -1,7 +1,7 @@
 /*
 **
 ** The C code is generated by [ATS/Postiats-0-3-8]
-** The starting compilation time is: 2018-1-4:  0h:59m
+** The starting compilation time is: 2018-1-4:  1h:45m
 **
 */
 
@@ -9950,7 +9950,7 @@
 } /* end of [ATSLIB_056_prelude__eq_g0int_int__7__7] */
 
 /*
-/home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 1918(line=75, offs=4) -- 1976(line=76, offs=22)
+/home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 1979(line=76, offs=4) -- 2037(line=77, offs=22)
 */
 /*
 local: sum_divisors_151$0(level=0)
@@ -9968,16 +9968,16 @@
 /* tmpvardeclst(end) */
 ATSfunbody_beg()
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 1918(line=75, offs=4) -- 1976(line=76, offs=22)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 1979(line=76, offs=4) -- 2037(line=77, offs=22)
 */
 ATSINSflab(__patsflab_is_perfect_155):
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 1957(line=76, offs=3) -- 1971(line=76, offs=17)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2018(line=77, offs=3) -- 2032(line=77, offs=17)
 */
 ATSINSmove(tmp361, sum_divisors_151(arg0)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 1957(line=76, offs=3) -- 1976(line=76, offs=22)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2018(line=77, offs=3) -- 2037(line=77, offs=22)
 */
 ATSINSmove(tmpret358, ATSLIB_056_prelude__eq_g0int_int__7__8(tmp361, arg0)) ;
 
@@ -10027,7 +10027,7 @@
 } /* end of [ATSLIB_056_prelude__eq_g0int_int__7__8] */
 
 /*
-/home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2008(line=79, offs=4) -- 2389(line=94, offs=6)
+/home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2069(line=80, offs=4) -- 2450(line=95, offs=6)
 */
 /*
 local: is_prime_16$0(level=0)
@@ -10044,11 +10044,11 @@
 /* tmpvardeclst(end) */
 ATSfunbody_beg()
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2008(line=79, offs=4) -- 2389(line=94, offs=6)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2069(line=80, offs=4) -- 2450(line=95, offs=6)
 */
 ATSINSflab(__patsflab_little_omega_157):
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2048(line=80, offs=3) -- 2389(line=94, offs=6)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2109(line=81, offs=3) -- 2450(line=95, offs=6)
 */
 /*
 letpush(beg)
@@ -10058,12 +10058,12 @@
 */
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2373(line=93, offs=5) -- 2383(line=93, offs=15)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2434(line=94, offs=5) -- 2444(line=94, offs=15)
 */
 ATSINSmove(tmpret362, loop_158(arg0, ATSPMVi0nt(1))) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2048(line=80, offs=3) -- 2389(line=94, offs=6)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2109(line=81, offs=3) -- 2450(line=95, offs=6)
 */
 /*
 INSletpop()
@@ -10073,7 +10073,7 @@
 } /* end of [little_omega_157] */
 
 /*
-/home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2060(line=81, offs=9) -- 2363(line=91, offs=27)
+/home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2121(line=82, offs=9) -- 2424(line=92, offs=27)
 */
 /*
 local: is_prime_16$0(level=0), loop_158$0(level=1)
@@ -10100,98 +10100,98 @@
 /* tmpvardeclst(end) */
 ATSfunbody_beg()
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2060(line=81, offs=9) -- 2363(line=91, offs=27)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2121(line=82, offs=9) -- 2424(line=92, offs=27)
 */
 ATSINSflab(__patsflab_loop_158):
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2158(line=82, offs=10) -- 2166(line=82, offs=18)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2219(line=83, offs=10) -- 2227(line=83, offs=18)
 */
 ATSINSmove(tmp364, ATSLIB_056_prelude__gte_g1int_int__138__4(arg1, arg0)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2155(line=82, offs=7) -- 2363(line=91, offs=27)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2216(line=83, offs=7) -- 2424(line=92, offs=27)
 */
 ATSif(
 tmp364
 ) ATSthen() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2183(line=83, offs=12) -- 2193(line=83, offs=22)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2244(line=84, offs=12) -- 2254(line=84, offs=22)
 */
 ATSINSmove(tmp367, is_prime_16(arg0)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2180(line=83, offs=9) -- 2236(line=86, offs=12)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2241(line=84, offs=9) -- 2297(line=87, offs=12)
 */
 ATSif(
 tmp367
 ) ATSthen() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2210(line=84, offs=11) -- 2211(line=84, offs=12)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2271(line=85, offs=11) -- 2272(line=85, offs=12)
 */
 ATSINSmove(tmpret363, ATSPMVi0nt(1)) ;
 } ATSelse() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2235(line=86, offs=11) -- 2236(line=86, offs=12)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2296(line=87, offs=11) -- 2297(line=87, offs=12)
 */
 ATSINSmove(tmpret363, ATSPMVi0nt(0)) ;
 } /* ATSendif */
 } ATSelse() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2259(line=88, offs=12) -- 2286(line=88, offs=39)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2320(line=89, offs=12) -- 2347(line=89, offs=39)
 */
 ATSINSmove(tmp372, atspre_g0int_mod_int(arg0, arg1)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2259(line=88, offs=12) -- 2286(line=88, offs=39)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2320(line=89, offs=12) -- 2347(line=89, offs=39)
 */
 ATSINSmove(tmp369, ATSLIB_056_prelude__eq_g0int_int__7__9(tmp372, ATSPMVi0nt(0))) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2259(line=88, offs=12) -- 2286(line=88, offs=39)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2320(line=89, offs=12) -- 2347(line=89, offs=39)
 */
 ATSif(
 tmp369
 ) ATSthen() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2259(line=88, offs=12) -- 2286(line=88, offs=39)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2320(line=89, offs=12) -- 2347(line=89, offs=39)
 */
 ATSINSmove(tmp368, is_prime_16(arg1)) ;
 
 } ATSelse() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2259(line=88, offs=12) -- 2286(line=88, offs=39)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2320(line=89, offs=12) -- 2347(line=89, offs=39)
 */
 ATSINSmove(tmp368, ATSPMVbool_false()) ;
 } /* ATSendif */
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2256(line=88, offs=9) -- 2363(line=91, offs=27)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2317(line=89, offs=9) -- 2424(line=92, offs=27)
 */
 ATSif(
 tmp368
 ) ATSthen() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2315(line=89, offs=23) -- 2322(line=89, offs=30)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2376(line=90, offs=23) -- 2383(line=90, offs=30)
 */
 ATSINSmove(tmp374, atspre_g1int_add_int(arg1, ATSPMVi0nt(1))) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2307(line=89, offs=15) -- 2323(line=89, offs=31)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2368(line=90, offs=15) -- 2384(line=90, offs=31)
 */
 ATSINSmove(tmp373, loop_158(arg0, tmp374)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2303(line=89, offs=11) -- 2323(line=89, offs=31)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2364(line=90, offs=11) -- 2384(line=90, offs=31)
 */
 ATSINSmove(tmpret363, atspre_g0int_add_int(ATSPMVi0nt(1), tmp373)) ;
 
 } ATSelse() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2355(line=91, offs=19) -- 2362(line=91, offs=26)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2416(line=92, offs=19) -- 2423(line=92, offs=26)
 */
 ATSINSmove(tmp375, atspre_g1int_add_int(arg1, ATSPMVi0nt(1))) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2347(line=91, offs=11) -- 2363(line=91, offs=27)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2408(line=92, offs=11) -- 2424(line=92, offs=27)
 */
 ATStailcal_beg()
 ATSINSmove_tlcal(apy0, arg0) ;
@@ -10290,7 +10290,7 @@
 } /* end of [ATSLIB_056_prelude__eq_g0int_int__7__9] */
 
 /*
-/home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2423(line=97, offs=4) -- 2971(line=117, offs=10)
+/home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2484(line=98, offs=4) -- 3032(line=118, offs=10)
 */
 /*
 local: is_prime_16$0(level=0)
@@ -10307,11 +10307,11 @@
 /* tmpvardeclst(end) */
 ATSfunbody_beg()
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2423(line=97, offs=4) -- 2971(line=117, offs=10)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2484(line=98, offs=4) -- 3032(line=118, offs=10)
 */
 ATSINSflab(__patsflab_totient_161):
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2456(line=98, offs=3) -- 2971(line=117, offs=10)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2517(line=99, offs=3) -- 3032(line=118, offs=10)
 */
 ATScaseof_beg()
 /*
@@ -10319,15 +10319,15 @@
 */
 ATSbranch_beg()
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2473(line=99, offs=7) -- 2474(line=99, offs=8)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2534(line=100, offs=7) -- 2535(line=100, offs=8)
 */
 ATSINSlab(__atstmplab6):
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2431(line=97, offs=12) -- 2432(line=97, offs=13)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2492(line=98, offs=12) -- 2493(line=98, offs=13)
 */
 ATSifnthen(ATSCKpat_int(arg0, ATSPMVint(1))) { ATSINSgoto(__atstmplab8) ; } ;
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2474(line=99, offs=8) -- 2474(line=99, offs=8)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2535(line=100, offs=8) -- 2535(line=100, offs=8)
 */
 ATSINSlab(__atstmplab7):
 /*
@@ -10337,14 +10337,14 @@
 ibranch-mbody:
 */
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2478(line=99, offs=12) -- 2479(line=99, offs=13)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2539(line=100, offs=12) -- 2540(line=100, offs=13)
 */
 ATSINSmove(tmpret376, ATSPMVi0nt(1)) ;
 ATSbranch_end()
 
 ATSbranch_beg()
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2487(line=100, offs=8) -- 2487(line=100, offs=8)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2548(line=101, offs=8) -- 2548(line=101, offs=8)
 */
 ATSINSlab(__atstmplab8):
 /*
@@ -10354,7 +10354,7 @@
 ibranch-mbody:
 */
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2513(line=102, offs=9) -- 2961(line=116, offs=12)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2574(line=103, offs=9) -- 3022(line=117, offs=12)
 */
 /*
 letpush(beg)
@@ -10364,12 +10364,12 @@
 */
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2939(line=115, offs=11) -- 2949(line=115, offs=21)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3000(line=116, offs=11) -- 3010(line=116, offs=21)
 */
 ATSINSmove(tmpret376, loop_162(ATSPMVi0nt(1), arg0)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2513(line=102, offs=9) -- 2961(line=116, offs=12)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2574(line=103, offs=9) -- 3022(line=117, offs=12)
 */
 /*
 INSletpop()
@@ -10386,7 +10386,7 @@
 } /* end of [totient_161] */
 
 /*
-/home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2531(line=103, offs=15) -- 2917(line=113, offs=31)
+/home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2592(line=104, offs=15) -- 2978(line=114, offs=31)
 */
 /*
 local: is_prime_16$0(level=0), loop_162$0(level=1)
@@ -10419,126 +10419,126 @@
 */
 ATSfunbody_beg()
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2531(line=103, offs=15) -- 2917(line=113, offs=31)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2592(line=104, offs=15) -- 2978(line=114, offs=31)
 */
 ATSINSflab(__patsflab_loop_162):
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2642(line=104, offs=16) -- 2648(line=104, offs=22)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2703(line=105, offs=16) -- 2709(line=105, offs=22)
 */
 ATSINSmove(tmp378, ATSLIB_056_prelude__gte_g1int_int__138__5(arg0, arg1)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2639(line=104, offs=13) -- 2917(line=113, offs=31)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2700(line=105, offs=13) -- 2978(line=114, offs=31)
 */
 ATSif(
 tmp378
 ) ATSthen() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2671(line=105, offs=18) -- 2681(line=105, offs=28)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2732(line=106, offs=18) -- 2742(line=106, offs=28)
 */
 ATSINSmove(tmp381, is_prime_16(arg1)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2668(line=105, offs=15) -- 2746(line=108, offs=18)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2729(line=106, offs=15) -- 2807(line=109, offs=18)
 */
 ATSif(
 tmp381
 ) ATSthen() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2704(line=106, offs=17) -- 2709(line=106, offs=22)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2765(line=107, offs=17) -- 2770(line=107, offs=22)
 */
 ATSINSmove(tmpret377, atspre_g1int_sub_int(arg1, ATSPMVi0nt(1))) ;
 
 } ATSelse() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2745(line=108, offs=17) -- 2746(line=108, offs=18)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2806(line=109, offs=17) -- 2807(line=109, offs=18)
 */
 ATSINSmove(tmpret377, arg1) ;
 } /* ATSendif */
 } ATSelse() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2781(line=110, offs=18) -- 2815(line=110, offs=52)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2842(line=111, offs=18) -- 2876(line=111, offs=52)
 */
 ATSINSmove(tmp387, atspre_g0int_mod_int(arg1, arg0)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2781(line=110, offs=18) -- 2815(line=110, offs=52)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2842(line=111, offs=18) -- 2876(line=111, offs=52)
 */
 ATSINSmove(tmp384, ATSLIB_056_prelude__eq_g0int_int__7__10(tmp387, ATSPMVi0nt(0))) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2781(line=110, offs=18) -- 2815(line=110, offs=52)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2842(line=111, offs=18) -- 2876(line=111, offs=52)
 */
 ATSif(
 tmp384
 ) ATSthen() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2781(line=110, offs=18) -- 2815(line=110, offs=52)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2842(line=111, offs=18) -- 2876(line=111, offs=52)
 */
 ATSINSmove(tmp383, is_prime_16(arg0)) ;
 
 } ATSelse() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2781(line=110, offs=18) -- 2815(line=110, offs=52)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2842(line=111, offs=18) -- 2876(line=111, offs=52)
 */
 ATSINSmove(tmp383, ATSPMVbool_false()) ;
 } /* ATSendif */
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2781(line=110, offs=18) -- 2815(line=110, offs=52)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2842(line=111, offs=18) -- 2876(line=111, offs=52)
 */
 ATSif(
 tmp383
 ) ATSthen() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2781(line=110, offs=18) -- 2815(line=110, offs=52)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2842(line=111, offs=18) -- 2876(line=111, offs=52)
 */
 ATSINSmove(tmp382, ATSLIB_056_prelude__neq_g1int_int__166__1(arg0, arg1)) ;
 
 } ATSelse() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2781(line=110, offs=18) -- 2815(line=110, offs=52)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2842(line=111, offs=18) -- 2876(line=111, offs=52)
 */
 ATSINSmove(tmp382, ATSPMVbool_false()) ;
 } /* ATSendif */
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2778(line=110, offs=15) -- 2917(line=113, offs=31)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2839(line=111, offs=15) -- 2978(line=114, offs=31)
 */
 ATSif(
 tmp382
 ) ATSthen() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2843(line=111, offs=23) -- 2848(line=111, offs=28)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2904(line=112, offs=23) -- 2909(line=112, offs=28)
 */
 ATSINSmove(tmp394, atspre_g1int_add_int(arg0, ATSPMVi0nt(1))) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2838(line=111, offs=18) -- 2852(line=111, offs=32)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2899(line=112, offs=18) -- 2913(line=112, offs=32)
 */
 ATSINSmove(tmp393, loop_162(tmp394, arg1)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2838(line=111, offs=18) -- 2856(line=111, offs=36)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2899(line=112, offs=18) -- 2917(line=112, offs=36)
 */
 ATSINSmove(tmp392, atspre_g0int_div_int(tmp393, arg0)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2861(line=111, offs=41) -- 2866(line=111, offs=46)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2922(line=112, offs=41) -- 2927(line=112, offs=46)
 */
 ATSINSmove(tmp395, atspre_g1int_sub_int(arg0, ATSPMVi0nt(1))) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2837(line=111, offs=17) -- 2867(line=111, offs=47)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2898(line=112, offs=17) -- 2928(line=112, offs=47)
 */
 ATSINSmove(tmpret377, atspre_g0int_mul_int(tmp392, tmp395)) ;
 
 } ATSelse() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2908(line=113, offs=22) -- 2913(line=113, offs=27)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2969(line=114, offs=22) -- 2974(line=114, offs=27)
 */
 ATSINSmove(tmp396, atspre_g1int_add_int(arg0, ATSPMVi0nt(1))) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2903(line=113, offs=17) -- 2917(line=113, offs=31)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 2964(line=114, offs=17) -- 2978(line=114, offs=31)
 */
 ATStailcal_beg()
 ATSINSmove_tlcal(apy0, tmp396) ;
@@ -10724,7 +10724,7 @@
 } /* end of [ATSLIB_056_prelude__neq_g1int_int__166__1] */
 
 /*
-/home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3024(line=120, offs=5) -- 3319(line=129, offs=6)
+/home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3085(line=121, offs=5) -- 3380(line=130, offs=6)
 */
 /*
 local: witness_12$0(level=0), totient_161$0(level=0)
@@ -10741,11 +10741,11 @@
 /* tmpvardeclst(end) */
 ATSfunbody_beg()
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3024(line=120, offs=5) -- 3319(line=129, offs=6)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3085(line=121, offs=5) -- 3380(line=130, offs=6)
 */
 ATSINSflab(__patsflab_totient_sum_169):
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3064(line=121, offs=3) -- 3319(line=129, offs=6)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3125(line=122, offs=3) -- 3380(line=130, offs=6)
 */
 /*
 letpush(beg)
@@ -10755,12 +10755,12 @@
 */
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3303(line=128, offs=5) -- 3313(line=128, offs=15)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3364(line=129, offs=5) -- 3374(line=129, offs=15)
 */
 ATSINSmove(tmpret397, loop_170(ATSPMVi0nt(1), arg0)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3064(line=121, offs=3) -- 3319(line=129, offs=6)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3125(line=122, offs=3) -- 3380(line=130, offs=6)
 */
 /*
 INSletpop()
@@ -10770,7 +10770,7 @@
 } /* end of [totient_sum_169] */
 
 /*
-/home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3076(line=122, offs=9) -- 3293(line=126, offs=40)
+/home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3137(line=123, offs=9) -- 3354(line=127, offs=40)
 */
 /*
 local: witness_12$0(level=0), totient_161$0(level=0), loop_170$0(level=1)
@@ -10799,58 +10799,58 @@
 */
 ATSfunbody_beg()
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3076(line=122, offs=9) -- 3293(line=126, offs=40)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3137(line=123, offs=9) -- 3354(line=127, offs=40)
 */
 ATSINSflab(__patsflab_loop_170):
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3179(line=123, offs=10) -- 3188(line=123, offs=19)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3240(line=124, offs=10) -- 3249(line=124, offs=19)
 */
 ATSINSmove(tmp399, ATSLIB_056_prelude__lt_g1int_int__18__2(arg0, arg1)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3176(line=123, offs=7) -- 3293(line=126, offs=40)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3237(line=124, offs=7) -- 3354(line=127, offs=40)
 */
 ATSif(
 tmp399
 ) ATSthen() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3207(line=124, offs=14) -- 3212(line=124, offs=19)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3268(line=125, offs=14) -- 3273(line=125, offs=19)
 */
 ATSINSmove(tmp411, atspre_g1int_add_int(arg0, ATSPMVi0nt(1))) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3202(line=124, offs=9) -- 3220(line=124, offs=27)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3263(line=125, offs=9) -- 3281(line=125, offs=27)
 */
 ATSINSmove(tmp410, loop_170(tmp411, arg1)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3231(line=124, offs=38) -- 3240(line=124, offs=47)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3292(line=125, offs=38) -- 3301(line=125, offs=47)
 */
 ATSINSmove(tmp413, totient_161(arg0)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3223(line=124, offs=30) -- 3242(line=124, offs=49)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3284(line=125, offs=30) -- 3303(line=125, offs=49)
 */
 ATSINSmove(tmp412, witness_12(tmp413)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3202(line=124, offs=9) -- 3242(line=124, offs=49)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3263(line=125, offs=9) -- 3303(line=125, offs=49)
 */
 ATSINSmove(tmpret398, ATSCNTRB_056_HX_056_intinf_t__add_intinf_int__42__1(tmp410, tmp412)) ;
 
 } ATSelse() {
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3262(line=126, offs=9) -- 3293(line=126, offs=40)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3323(line=127, offs=9) -- 3354(line=127, offs=40)
 */
 ATSINSmove(tmp421, totient_161(arg0)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3262(line=126, offs=9) -- 3293(line=126, offs=40)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3323(line=127, offs=9) -- 3354(line=127, offs=40)
 */
 ATSINSmove(tmp420, witness_12(tmp421)) ;
 
 /*
-emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3262(line=126, offs=9) -- 3293(line=126, offs=40)
+emit_instr: loc0 = /home/vanessa/programming/haskell/current/fast-combinatorics/ats-src/number-theory.dats: 3323(line=127, offs=9) -- 3354(line=127, offs=40)
 */
 ATSINSmove(tmpret398, ATSCNTRB_056_HX_056_intinf_t__intinf_make_int__27__1(tmp420)) ;
 
diff --git a/cbits/numerics.c b/cbits/numerics.c
--- a/cbits/numerics.c
+++ b/cbits/numerics.c
@@ -1,7 +1,7 @@
 /*
 **
 ** The C code is generated by [ATS/Postiats-0-3-8]
-** The starting compilation time is: 2018-1-4:  0h:59m
+** The starting compilation time is: 2018-1-4:  1h:45m
 **
 */
 
diff --git a/fast-arithmetic.cabal b/fast-arithmetic.cabal
--- a/fast-arithmetic.cabal
+++ b/fast-arithmetic.cabal
@@ -1,5 +1,5 @@
 name:                fast-arithmetic
-version:             0.1.0.0
+version:             0.1.0.1
 synopsis:            Fast number-theoretic functions.
 description:         Fast number-theoretic code with a high level of safety guaranteed by ATS.
 homepage:            https://github.com/vmchale/fast-arithmetic#readme
@@ -40,8 +40,8 @@
                      , cbits/number-theory.c
   include-dirs:        ats-deps/
                      , ats-deps/contrib
-                     , ats-deps/prelude/ATS2-Postiats-include-0.3.8
                      , ats-deps/prelude/ATS2-Postiats-include-0.3.8/ccomp/runtime
+                     , ats-deps/prelude/ATS2-Postiats-include-0.3.8
   hs-source-dirs:      src
   exposed-modules:     Numeric.Pure
                      , Numeric.Integer