let exit_success = 0 let exit_failure = 1 external random_seed : unit -> int array = "caml_sys_random_seed" let pp_int_array ppf arr = Fmt.pf ppf "[|" ; for i = 0 to pred (Array.length arr) do Fmt.pf ppf "%d;" arr.(i) done ; Fmt.pf ppf "|]" (* XXX(dinosaure): deterministic generation. It appears that some calls of [check/check.exe] does not get same results, mostly about [String.*] functions. As we understand implementation of them, it's an expected behavior but it puts some noises when we try to introspect results on different platforms. So all inputs are generated with this seed to be able to get as much as we can reproducible outputs. *) let seed = "4EygbdYh+v35vvrmD9YYP4byT5E3H7lTeXJiIj+dQnc=" let seed = Base64.decode_exn seed let seed = let res = Array.make (String.length seed / 2) 0 in for i = 0 to (String.length seed / 2) - 1 do res.(i) <- (Char.code seed.[i * 2] lsl 8) lor (Char.code seed.[i * 2 + 1]) done ; res let () = let random_seed = seed in Fmt.pr "Random: %a.\n%!" pp_int_array random_seed ; Random.full_init random_seed let random length = let get _ = match Random.int (10 + 26 + 26) with | n when n < 10 -> Char.(chr (code '0' + n)) | n when n < 10 + 26 -> Char.(chr (code 'a' + n - 10)) | n -> Char.(chr (code 'A' + n - 10 - 26)) in String.init length get let hash_eq_0 = random 4096 let hash_eq_1 = Bytes.to_string (Bytes.of_string hash_eq_0) let chr_into_hash_eq_0 = hash_eq_0.[Random.int 4096] let int32_into_hash_eq_0 = Unsafe.get_int32_ne (Bytes.of_string hash_eq_0) (Random.int (4096-4)) let int32_into_hash_eq_1 = Unsafe.get_int32_ne (Bytes.of_string hash_eq_1) (Random.int (4096-4)) let int14_into_hash_eq_0 = Unsafe.get_int32_ne (Bytes.of_string hash_eq_0) (Random.int (4096-4)) |> (Int32.logand 0xfffl) let int14_into_hash_eq_1 = Unsafe.get_int32_ne (Bytes.of_string hash_eq_1) (Random.int (4096-4)) |> (Int32.logand 0xfffl) let () = assert (hash_eq_0 != hash_eq_1) let () = assert (hash_eq_0 = hash_eq_1) let () = assert (String.contains hash_eq_0 chr_into_hash_eq_0) let hash_neq_0 = random 4096 let hash_neq_1 = let rec go limit = if limit <= 0 then failwith "Impossible to generate different hashes." ; let res = random 4096 in if res = hash_neq_0 then go (pred limit) else res in go 10 let random_chr = let rec go limit = if limit <= 0 then failwith "Impossible to generate a byte which does not appear into hash_neq_0." ; let res = Char.chr (Random.int 256) in if not (String.contains hash_neq_0 res) then res else go (pred limit) in go 10 let () = assert (hash_neq_0 <> hash_neq_1) let () = assert (not (String.contains hash_neq_0 random_chr)) let error_msgf fmt = Fmt.kstrf (fun err -> Error (`Msg err)) fmt let merge m0 m1 = let cons_0 r = [| 0.; r.(0); r.(1) |] in let cons_1 r = [| 1.; r.(0); r.(1) |] in Array.(append (map cons_0 m0) (map cons_1 m1)) let test_spss fn_0 fn_1 = Fmt.pr "> Start benchmarks on [fn⁰].\n%!" ; let m0 = Benchmark.run fn_0 in Fmt.pr "> Start benchmarks on [fn¹].\n%!" ; let m1 = Benchmark.run fn_1 in Fmt.pr "> Merge results.\n%!" ; let m = merge m0 m1 in let m = Array.map (fun r -> [| r.(0); r.(1); r.(2); r.(0) *. r.(1) |]) m in Fmt.pr "> Start linear regression.\n%!" ; match Linear_algebra.ols (fun m -> m.(2)) [|(fun m -> m.(0)); (fun m -> m.(1)); (fun m -> m.(3))|] m with | Ok (estimates, r_square) -> if r_square >= 0.95 then Ok estimates else error_msgf "r² (%f) is bad" r_square | Error (`Msg _) as err -> err let test_ccea fn_0 fn_1 = Fmt.pr "> Start benchmarks on [fn⁰].\n%!" ; let m0 = Benchmark.run fn_0 in Fmt.pr "> Start benchmarks on [fn¹].\n%!" ; let m1 = Benchmark.run fn_1 in match Linear_algebra.ols (fun m -> m.(1)) [|(fun m -> m.(0))|] m0, Linear_algebra.ols (fun m -> m.(1)) [|(fun m -> m.(0))|] m1 with | Ok (estimates_0, r_square_0), Ok (estimates_1, r_square_1) -> Fmt.epr "> Calculating Z.\n%!" ; let z = (estimates_0.(0) -. estimates_1.(0)) /. sqrt ((r_square_0 ** 2.) +. (r_square_1 ** 2.)) in Ok z | (Error (`Msg _) as err), Ok _ -> err | Ok _, (Error (`Msg _) as err) -> err | Error (`Msg err0), Error (`Msg err1) -> Fmt.epr "Got errors for while processing both.\n%!" ; Fmt.epr "B¹: %s.\n%!" err0 ; Fmt.epr "B²: %s.\n%!" err1 ; exit exit_failure let ccea ~reset ~switch ~name_of_fns_0 ~name_of_fns_1 fns_0 fns_1 = Fmt.pr "> Start to test %s (B¹).\n%!" name_of_fns_0 ; reset () ; let eqaf = test_ccea (fst fns_0) (snd fns_0) in switch () ; Fmt.pr "> Start to test %s (B²).\n%!" name_of_fns_1 ; let stdlib = test_ccea (fst fns_1) (snd fns_1) in match eqaf, stdlib with | Ok eqaf, Ok stdlib -> Ok (eqaf, stdlib) | Error (`Msg err), Ok _ -> Fmt.epr "Got an error while processing %s: %s\n%!" name_of_fns_0 err ; Error () | Ok _, Error (`Msg err) -> Fmt.epr "Got an error while processing %s: %s\n%!" name_of_fns_1 err ; Error () | Error (`Msg err0), Error (`Msg err1) -> Fmt.epr "Got errors while processing both:\n%!" ; Fmt.epr "B¹> %s.\n%!" err0 ; Fmt.epr "B²> %s.\n%!" err1 ; Error () let spss ~reset ~switch ~name_of_fns_0 ~name_of_fns_1 fns_0 fns_1 = Fmt.pr "> Start to test %s (B¹).\n%!" name_of_fns_0 ; reset () ; let eqaf = test_spss (fst fns_0) (snd fns_0) in switch () ; Fmt.pr "> Start to test %s (B²).\n%!" name_of_fns_1 ; let stdlib = test_spss (fst fns_1) (snd fns_1) in match eqaf, stdlib with | Ok eqaf, Ok stdlib -> Fmt.pr "%s: %f ns/run.\n%!" name_of_fns_0 eqaf.(1) ; Fmt.pr "%s: %f ns/run.\n%!" name_of_fns_1 stdlib.(1) ; Ok (eqaf.(2), stdlib.(2)) | Error (`Msg err), Ok _ -> Fmt.epr "Got an error while processing %s: %s\n%!" name_of_fns_0 err ; Error () | Ok _, Error (`Msg err) -> Fmt.epr "Got an error while processing %s: %s\n%!" name_of_fns_1 err ; Error () | Error (`Msg err0), Error (`Msg err1) -> Fmt.epr "Got errors while processing both:\n%!" ; Fmt.epr "B¹> %s.\n%!" err0 ; Fmt.epr "B²> %s.\n%!" err1 ; Error () (* XXX(dinosaure): this program try to compute diff between 2 coefficient regressions: - 1: time needed to compute equal function on 2 same values ([_eq]) - 2: time needed to compute equal function on 2 different values ([_neq]) ### Samples We have 2 ways to compute it. The first is to compute a regression equation which includes group 1 and group 2. A initial regression equation can be done to know how long [equal] lasts: regression /dep time // m.(1) /method = enter run // m.(0) It's a basic linear regression where we run 1..N times the function with same inputs. Then, we have a matrix such as: m.(n).(0) <- time m.(n).(1) <- run Obviously, if our function is /constant-time/, you should have something like: y = m.(x).(0) = a * m.(x).(1) + b To infer the curve, we use the linear regression for each points. Then, we collect same samples but with [_neq] values. Now, the goal is to see that [_eq]: y = a * x + b and [_neq]: y = a * x + b are ~ equals. For that, we have 2 ways. ### SPSS The first way to compare group 1 ([_eq]) and group 2 ([_neq]): we need to insert a dummy variable [kind] where it is equal to [0.0] when it's owned by the group 1 and [1.1] is owned by the group 2 (see [cons_*] function). Finally, we had a new variable which is the product between [kind] ([m.(0)]) and [run] ([m.(1)]). Finally, we can start to compute a regression equation where [time] will be the responder and [kind], [run] and [kind * run] will be predictors: regression /dep time // m.(2) /method = enter kind run (kind * run) // m.(0) m.(1) m.(3) Time of [equal] will be available on [estimates.(1)] and diff will be available on [estimates.(2)]. [compare_spss] checks r² ([>= 0.95]) and main program checks if the diff is between [-30.0] and [30.0]. ### CCEA The second way to compare group 1 and group 2: it consists to compute basic regression equation to know how long [equal] lasts. Then, we will compute [Z] which is equal to: B¹-B² --------------- sqrt(r¹² + r²²) Where B¹ and B² are regression coefficients for [_eq] and [_neq] and r¹ and r² are standard error of B¹ and B². Then, main program, as the first way, checks if [Z] is between [-30.0] and [30.0]. NOTE about SPSS: This is the name of a software which explain how to compare results of linear regression. NOTE about CCEA: I don't remmember when I got this name but it seems close to Vuong test. NOTE about virtualization: Virtual context (VirtualBox, VMWare, Xen or qemu) can delayed CPU instructions and tricks on the time spended to execute them. By this fact, time counter lies about time needed to compute [equal] function. So, in a virtual context we can have some noises when we record measures (in [Benchmark]). NOTE about bare-metal: In a bare-metal context, results are more determinists (but they are not completely fixed). In fact, it depends on the system-scheduler which can prioritize an other process while [check/check.exe] is executed. For all of these reasons, [check/check.exe] is really fragile and can not work in your context - however, a CI with [eqaf] is provided is we surely are aware of it and results. *) module Make (Check : sig type ret val eqaf_name : string val stdlib_name : string val reset : unit -> unit val switch : unit -> unit val eqaf_true : unit -> ret val eqaf_false : unit -> ret val stdlib_true : unit -> ret val stdlib_false : unit -> ret end) = struct open Check let last_chance () = let open Benchmark in match ccea ~reset:Check.reset ~switch:Check.switch ~name_of_fns_0:eqaf_name ~name_of_fns_1:stdlib_name (V eqaf_true, V eqaf_false) (V stdlib_true, V stdlib_false) with | Error () -> exit_failure | Ok (eqaf, stdlib) -> if eqaf >= -30. && eqaf <= 30. then ( Fmt.pr "Z¹ = %f, Z² = %f.\n%!" eqaf stdlib ; exit_success ) else ( Fmt.pr "Z¹ = %f, Z² = %f.\n%!" eqaf stdlib ; exit_failure ) let test () = let open Benchmark in match spss ~reset:Check.reset ~switch:Check.switch ~name_of_fns_0:eqaf_name ~name_of_fns_1:stdlib_name (V eqaf_true, V eqaf_false) (V stdlib_true, V stdlib_false) with | Error () -> last_chance () | Ok (eqaf, stdlib) -> if eqaf >= -30. && eqaf <= 30. then ( Fmt.pr "B¹ = %f, B² = %f.\n%!" eqaf stdlib ; exit_success ) else ( Fmt.pr "Fail with B¹ = %f, B² = %f.\n%!" eqaf stdlib ; Fmt.pr "> Start to compute Z.\n%!" ; last_chance () ) end module Equal = Make(struct type ret = bool let eqaf_name = "Eqaf.equal" let stdlib_name = "String.equal" let reset = ignore and switch = ignore let stdlib_true () = String.equal hash_eq_0 hash_eq_1 let stdlib_false () = for _ = 1 to 100 do let _ = String.equal hash_neq_0 hash_neq_1 in () done ; String.equal hash_neq_0 hash_neq_1 let eqaf_true () = Eqaf.equal hash_eq_0 hash_eq_1 let eqaf_false () = Eqaf.equal hash_neq_0 hash_neq_1 end) module Compare = Make(struct type ret = int let eqaf_name = "Eqaf.compare" let stdlib_name = "String.compare" let reset = ignore and switch = ignore let stdlib_true () = String.compare hash_eq_0 hash_eq_1 let stdlib_false () = for _ = 1 to 100 do let _ = String.compare hash_neq_0 hash_neq_1 in () done ; String.compare hash_neq_0 hash_neq_1 let eqaf_true () = Eqaf.compare_be hash_eq_0 hash_eq_1 let eqaf_false () = Eqaf.compare_be hash_neq_0 hash_neq_1 end) module Exists = Make(struct type ret = bool let eqaf_name = "Eqaf.exists_uint8" let stdlib_name = "String.contains" let constant = ref (Char.code chr_into_hash_eq_0) let reset () = constant := Char.code chr_into_hash_eq_0 let switch () = constant := Char.code random_chr let stdlib_true () = String.contains hash_eq_0 chr_into_hash_eq_0 let stdlib_false () = String.contains hash_neq_0 random_chr let f (v : int) = v = !constant let eqaf_true () = Eqaf.exists_uint8 ~f hash_eq_0 let eqaf_false () = Eqaf.exists_uint8 ~f hash_neq_0 end) module Find = Make(struct type ret = int let eqaf_name = "Eqaf.find_uint8" let stdlib_name = "String.index" let switch () = () let reset () = () let stdlib_true () = String.index hash_eq_0 chr_into_hash_eq_0 let stdlib_false () = try String.index hash_neq_0 random_chr with Not_found -> (-1) let f_hash_eq_0 (v : int) = v = Char.code chr_into_hash_eq_0 let f_random (v : int) = v = Char.code random_chr let eqaf_true () = Eqaf.find_uint8 ~f:f_hash_eq_0 hash_eq_0 let eqaf_false () = Eqaf.find_uint8 ~f:f_random hash_neq_0 end) module Divmod32 = Make(struct type ret = int32 * int32 let eqaf_name = "Eqaf.divmod" let stdlib_name = "Int32.unsigned_div,Int32.unsigned_rem" let switch () = () let reset () = () (* These are here for compat with OCaml <= 4.09 from >= they can be replaced by Int32.unsigned_div Int32.unsigned_rem *) let int32_div_unsigned n d = let sub,min_int = Int32.(sub,min_int)in let int32_unsigned_compare n m = Int32.compare (sub n min_int) (sub m min_int) in if d < 0_l then if int32_unsigned_compare n d < 0 then 0_l else 1_l else let q = let open Int32 in shift_left (Int32.div (Int32.shift_right_logical n 1) d) 1 in let r = sub n (Int32.mul q d) in if int32_unsigned_compare r d >= 0 then Int32.succ q else q let int32_rem_unsigned n d = Int32.sub n (Int32.mul (int32_div_unsigned n d) d) (* TODO *) let stdlib_true () = let x, m = int32_into_hash_eq_0, int14_into_hash_eq_0 in int32_div_unsigned x m, int32_rem_unsigned x m let stdlib_false () = let x, m = int32_into_hash_eq_1, int14_into_hash_eq_1 in int32_div_unsigned x m, int32_rem_unsigned x m let eqaf_true () = Eqaf.divmod ~x:int32_into_hash_eq_0 ~m:int14_into_hash_eq_0 let eqaf_false () = Eqaf.divmod ~x:int32_into_hash_eq_1 ~m:int14_into_hash_eq_1 end) module Ascii_int32 = Make(struct type ret = string let eqaf_name = "Eqaf.ascii_of_int32" let stdlib_name = "Int32.to_string" let switch () = () let reset () = () (* TODO setting 0x8000 bit ensures five digits. We need a constant amount of digits to specify ~digits because we don't have a [Int32.to_string] that left-pads. Maybe we can use [Format.sprintf] ? *) let true_int = Int32.logand 0x8000l int14_into_hash_eq_0 let false_int = Int32.logand 0x8000l int14_into_hash_eq_1 let stdlib_true () = Int32.to_string true_int let stdlib_false () = Int32.to_string false_int let eqaf_true () = Eqaf.ascii_of_int32 ~digits:5 true_int let eqaf_false () = Eqaf.ascii_of_int32 ~digits:5 false_int end) let limit = 20 let () = let rec _0 tried = if tried > 20 then invalid_arg "Too many tried for Eqaf.equal" ; let res = Equal.test () in if res = exit_success then tried else _0 (succ tried) in let rec _1 tried = if tried > 20 then invalid_arg "Too many tried for Eqaf.compare" ; let res = Compare.test () in if res = exit_success then tried else _1 (succ tried) in let rec _2 tried = if tried > 20 then invalid_arg "Too many tried for Eqaf.exists" ; let res = Exists.test () in if res = exit_success then tried else _2 (succ tried) in let rec _3 tried = if tried > 20 then invalid_arg "Too many tried for Eqaf.find_uint8" ; let res = Find.test () in if res = exit_success then tried else _3 (succ tried) in let rec _4 tried = if tried > 20 then invalid_arg "Too many tried for Eqaf.divmod" ; let res = Divmod32.test () in if res = exit_success then tried else _4 (succ tried) in let pr_bench name value = Fmt.pr {|{"results": [{"name": "check", "metrics": [{"name": "%s", "value": %d}]}]}@.|} name value in let _0 = _0 1 in Fmt.pr "%d trial(s) for Eqaf.equal.\n%!" _0 ; pr_bench "equal" _0 ; let _1 = _1 1 in Fmt.pr "%d trial(s) for Eqaf.compare.\n%!" _1 ; pr_bench "compare" _1 ; let _2 = _2 1 in Fmt.pr "%d trial(s) for Eqaf.exists.\n%!" _2 ; pr_bench "exists" _2 ; let _3 = _3 1 in Fmt.pr "%d trial(s) for Eqaf.find_uint8.\n%!" _3 ; pr_bench "find_uint8" _3 ; let _4 = _4 1 in Fmt.pr "%d trial(s) for Eqaf.divmod.\n%!" _4 ; pr_bench "divmod" _4 ; exit exit_success