[zarith] [micromega] Bump to 1.10.0 and remove some hacks

In particular, behavior of `Z.gcd` and `Z.lcm` has been fixed in
1.10.0, see

ocaml/Zarith#58

.gitlab-ci.yml

@@ -19,7 +19,7 @@ stages:
 variables:
   # Format: $IMAGE-V$DATE [Cache is not used as of today but kept here
   # for reference]
-  CACHEKEY: "bionic_coq-V2020-08-28-V92"
+  CACHEKEY: "bionic_coq-V2020-09-15-V83"
   IMAGE: "$CI_REGISTRY_IMAGE:$CACHEKEY"
   # By default, jobs run in the base switch; override to select another switch
   OPAM_SWITCH: "base"

INSTALL.md

@@ -18,7 +18,7 @@ To compile Coq yourself, you need:
 - The [num](https://github.com/ocaml/num) library; note that it is
   included in the OCaml distribution for OCaml versions < 4.06.0
 
-- The [ZArith library](https://github.com/ocaml/Zarith) >= 1.8
+- The [ZArith library](https://github.com/ocaml/Zarith) >= 1.10
 
 - The [findlib](http://projects.camlcity.org/projects/findlib.html) library (version >= 1.8.0)
 

azure-pipelines.yml

@@ -80,7 +80,7 @@ jobs:
       opam switch set ocaml-base-compiler.$COMPILER
       eval $(opam env)
       opam update
-      opam install -j "$NJOBS" num ocamlfind${FINDLIB_VER} ounit lablgtk3-sourceview3 zarith.1.9.1
+      opam install -j "$NJOBS" num ocamlfind${FINDLIB_VER} ounit lablgtk3-sourceview3 zarith.1.10.0
       opam list
     displayName: 'Install OCaml dependencies'
     env:

coq.opam

@@ -25,7 +25,7 @@ depends: [
   "dune"      { >= "2.5.0"  }
   "ocamlfind" { build }
   "num"
-  "zarith"    { >= "1.9.1" }
+  "zarith"    { >= "1.10.0" }
 ]
 
 build: [

coq.opam.docker

@@ -24,7 +24,7 @@ depends: [
   "ocaml"     { >= "4.05.0" }
   "ocamlfind" { build }
   "num"
-  "zarith"    { >= "1.9.1" }
+  "zarith"    { >= "1.10.0" }
   "conf-findutils" {build}
 ]
 

dev/build/windows/makecoq_mingw.sh

@@ -1026,7 +1026,7 @@ function make_num {
 
 function make_zarith {
   make_ocaml
-  if build_prep https://github.com/ocaml/Zarith/archive release-1.9.1 tar.gz 1 zarith-1.9.1; then
+  if build_prep https://github.com/ocaml/Zarith/archive release-1.10.0 tar.gz 1 zarith-1.10.0; then
     logn configure ./configure
     log1 make
     log2 make install

dev/ci/docker/bionic_coq/Dockerfile

@@ -1,4 +1,4 @@
-# CACHEKEY: "bionic_coq-V2020-08-28-V92"
+# CACHEKEY: "bionic_coq-V2020-09-15-V83"
 # ^^ Update when modifying this file.
 
 FROM ubuntu:bionic
@@ -43,7 +43,7 @@ ENV COMPILER="4.05.0"
 # Common OPAM packages, num to be removed once the migration to
 # micromega is complete, `num` also does not have a version number as
 # the right version to install varies with the compiler version.
-ENV BASE_OPAM="num zarith.1.9.1 ocamlfind.1.8.1 ounit2.2.2.3 odoc.1.5.0" \
+ENV BASE_OPAM="num zarith.1.10.0 ocamlfind.1.8.1 ounit2.2.2.3 odoc.1.5.0" \
     CI_OPAM="menhir.20190626 ocamlgraph.1.8.8" \
     BASE_ONLY_OPAM="elpi.1.11.0"
 
@@ -59,7 +59,7 @@ RUN opam init -a --disable-sandboxing --compiler="$COMPILER" default https://opa
 
 # base+32bit switch, note the zarith hack
 RUN opam switch create "${COMPILER}+32bit" && eval $(opam env) && \
-        i386 env CC='gcc -m32' opam install zarith.1.9.1 && \
+        i386 env CC='gcc -m32' opam install zarith.1.10.0 && \
         opam install $BASE_OPAM
 
 # EDGE switch

plugins/micromega/numCompat.ml

@@ -31,6 +31,8 @@ module type ZArith = sig
 end
 
 module Z = struct
+  (* Beware this only works fine in ZArith >= 1.10.0 due to
+     https://github.com/ocaml/Zarith/issues/58 *)
   include Z
 
   (* Constants *)
@@ -39,13 +41,8 @@ module Z = struct
   let power_int = Big_int_Z.power_big_int_positive_int
   let quomod = Big_int_Z.quomod_big_int
 
-  (* Workaround https://github.com/ocaml/Zarith/issues/58 , remove
-     the abs when zarith 1.9.2 is released *)
-  let gcd x y = Z.abs (Z.gcd x y)
-
-  (* zarith fails with division by zero if x && y == 0 *)
-  let lcm x y =
-    if Z.equal x zero && Z.equal y zero then zero else Z.abs (Z.lcm x y)
+  (* zarith fails with division by zero if x == 0 && y == 0 *)
+  let lcm x y = if Z.equal x zero && Z.equal y zero then zero else Z.lcm x y
 
   let ppcm x y =
     let g = gcd x y in
@@ -144,7 +141,7 @@ module Q : QArith with module Z = Z = struct
   let ceiling q : t = Z.cdiv (Q.num q) (Q.den q) |> Q.of_bigint
   let half = Q.make Z.one Z.two
 
-  (* Num round is to the nearest *)
+  (* We imitate Num's round which is to the nearest *)
   let round q = floor (Q.add half q)
 
   (* XXX: review / improve *)

plugins/micromega/numCompat.mli

@@ -25,8 +25,15 @@ module type ZArith = sig
   val power_int : t -> int -> t
   val quomod : t -> t -> t * t
   val ppcm : t -> t -> t
+
+  (** [gcd x y] Greatest Common Divisor. Must always return a
+     positive number *)
   val gcd : t -> t -> t
+
+  (** [lcm x y] Least Common Multiplier. Must always return a
+     positive number *)
   val lcm : t -> t -> t
+
   val to_string : t -> string
 end