145 lines
4.2 KiB
OCaml
145 lines
4.2 KiB
OCaml
(*
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* Copyright (c) 1997-1999 Massachusetts Institute of Technology
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* Copyright (c) 2003, 2007-14 Matteo Frigo
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* Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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*
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*)
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(*
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* the oracle decrees whether the sign of an expression should
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* be changed.
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*
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* Say the expression (A - B) appears somewhere. Elsewhere in the
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* expression dag the expression (B - A) may appear.
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* The oracle determines which of the two forms is canonical.
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*
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* Algorithm: evaluate the expression at a random input, and
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* keep the expression with the positive sign.
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*)
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let make_memoizer hash equal =
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let table = ref Assoctable.empty
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in
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(fun f k ->
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match Assoctable.lookup hash equal k !table with
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Some value -> value
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| None ->
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let value = f k in
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begin
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table := Assoctable.insert hash k value !table;
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value
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end)
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let almost_equal x y =
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let epsilon = 1.0E-8 in
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(abs_float (x -. y) < epsilon) ||
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(abs_float (x -. y) < epsilon *. (abs_float x +. abs_float y))
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let absid = make_memoizer
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(fun x -> Expr.hash_float (abs_float x))
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(fun a b -> almost_equal a b || almost_equal (-. a) b)
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(fun x -> x)
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let make_random_oracle () = make_memoizer
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Variable.hash
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Variable.same
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(fun _ -> (float (Random.bits())) /. 1073741824.0)
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let the_random_oracle = make_random_oracle ()
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let sum_list l = List.fold_right (+.) l 0.0
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let eval_aux random_oracle =
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let memoizing = make_memoizer Expr.hash (==) in
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let rec eval x =
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memoizing
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(function
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| Expr.Num x -> Number.to_float x
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| Expr.NaN x -> Expr.transcendent_to_float x
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| Expr.Load v -> random_oracle v
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| Expr.Store (v, x) -> eval x
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| Expr.Plus l -> sum_list (List.map eval l)
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| Expr.Times (a, b) -> (eval a) *. (eval b)
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| Expr.CTimes (a, b) ->
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1.098612288668109691395245236 +.
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1.609437912434100374600759333 *. (eval a) *. (eval b)
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| Expr.CTimesJ (a, b) ->
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0.9102392266268373936142401657 +.
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0.6213349345596118107071993881 *. (eval a) *. (eval b)
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| Expr.Uminus x -> -. (eval x))
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x
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in eval
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let eval = eval_aux the_random_oracle
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let should_flip_sign node =
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let v = eval node in
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let v' = absid v in
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not (almost_equal v v')
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(*
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* determine with high probability if two expressions are equal.
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*
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* The test is randomized: if the two expressions have the
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* same value for NTESTS random inputs, then they are proclaimed
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* equal. (Note that two distinct linear functions L1(x0, x1, ..., xn)
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* and L2(x0, x1, ..., xn) have the same value with probability
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* 0 for random x's, and thus this test is way more paranoid than
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* necessary.)
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*)
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let likely_equal a b =
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let tolerance = 1.0e-8
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and ntests = 20
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in
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let rec loop n =
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if n = 0 then
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true
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else
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let r = make_random_oracle () in
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let va = eval_aux r a
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and vb = eval_aux r b
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in
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if (abs_float (va -. vb)) >
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tolerance *. (abs_float va +. abs_float vb +. 0.0001)
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then
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false
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else
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loop (n - 1)
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in
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match (a, b) with
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(*
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* Because of the way eval is constructed, we have
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* eval (Store (v, x)) == eval x
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* However, we never consider the two expressions equal
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*)
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| (Expr.Store _, _) -> false
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| (_, Expr.Store _) -> false
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(*
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* Expressions of the form ``Uminus (Store _)''
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* are artifacts of algsimp
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*)
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| ((Expr.Uminus (Expr.Store _)), _) -> false
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| (_, Expr.Uminus (Expr.Store _)) -> false
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| _ -> loop ntests
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let hash x =
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let f = eval x in
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truncate (f *. 65536.0)
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