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(*
* Copyright (c) 1997-1999 Massachusetts Institute of Technology
* Copyright (c) 2003, 2007-14 Matteo Frigo
* Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*
*)
(* Here, we define the data type encapsulating a symbolic arithmetic
expression, and provide some routines for manipulating it. *)
(* I will regret this hack : *)
(* NEWS: I did *)
type transcendent = I | MULTI_A | MULTI_B | CONJ
type expr =
| Num of Number.number
| NaN of transcendent
| Plus of expr list
| Times of expr * expr
| CTimes of expr * expr
| CTimesJ of expr * expr (* CTimesJ (a, b) = conj(a) * b *)
| Uminus of expr
| Load of Variable.variable
| Store of Variable.variable * expr
type assignment = Assign of Variable.variable * expr
(* various hash functions *)
let hash_float x =
let (mantissa, exponent) = frexp x
in truncate (float_of_int(exponent) *. 1234.567 +. mantissa *. 10000.0)
let sum_list l = List.fold_right (+) l 0
let transcendent_to_float = function
| I -> 2.718281828459045235360287471 (* any transcendent number will do *)
| MULTI_A -> 0.6931471805599453094172321214
| MULTI_B -> -0.3665129205816643270124391582
| CONJ -> 0.6019072301972345747375400015
let rec hash = function
| Num x -> hash_float (Number.to_float x)
| NaN x -> hash_float (transcendent_to_float x)
| Load v -> 1 + 1237 * Variable.hash v
| Store (v, x) -> 2 * Variable.hash v - 2345 * hash x
| Plus l -> 5 + 23451 * sum_list (List.map Hashtbl.hash l)
| Times (a, b) -> 41 + 31415 * (Hashtbl.hash a + Hashtbl.hash b)
| CTimes (a, b) -> 49 + 3245 * (Hashtbl.hash a + Hashtbl.hash b)
| CTimesJ (a, b) -> 31 + 3471 * (Hashtbl.hash a + Hashtbl.hash b)
| Uminus x -> 42 + 12345 * (hash x)
(* find all variables *)
let rec find_vars x =
match x with
| Load y -> [y]
| Plus l -> List.flatten (List.map find_vars l)
| Times (a, b) -> (find_vars a) @ (find_vars b)
| CTimes (a, b) -> (find_vars a) @ (find_vars b)
| CTimesJ (a, b) -> (find_vars a) @ (find_vars b)
| Uminus a -> find_vars a
| _ -> []
(* TRUE if expression is a constant *)
let is_constant = function
| Num _ -> true
| NaN _ -> true
| Load v -> Variable.is_constant v
| _ -> false
let is_known_constant = function
| Num _ -> true
| NaN _ -> true
| _ -> false
(* expr to string, used for debugging *)
let rec foldr_string_concat l =
match l with
[] -> ""
| [a] -> a
| a :: b -> a ^ " " ^ (foldr_string_concat b)
let string_of_transcendent = function
| I -> "I"
| MULTI_A -> "MULTI_A"
| MULTI_B -> "MULTI_B"
| CONJ -> "CONJ"
let rec to_string = function
| Load v -> Variable.unparse v
| Num n -> string_of_float (Number.to_float n)
| NaN n -> string_of_transcendent n
| Plus x -> "(+ " ^ (foldr_string_concat (List.map to_string x)) ^ ")"
| Times (a, b) -> "(* " ^ (to_string a) ^ " " ^ (to_string b) ^ ")"
| CTimes (a, b) -> "(c* " ^ (to_string a) ^ " " ^ (to_string b) ^ ")"
| CTimesJ (a, b) -> "(cj* " ^ (to_string a) ^ " " ^ (to_string b) ^ ")"
| Uminus a -> "(- " ^ (to_string a) ^ ")"
| Store (v, a) -> "(:= " ^ (Variable.unparse v) ^ " " ^
(to_string a) ^ ")"
let rec to_string_a d x =
if (d = 0) then "..." else match x with
| Load v -> Variable.unparse v
| Num n -> Number.to_konst n
| NaN n -> string_of_transcendent n
| Plus x -> "(+ " ^ (foldr_string_concat (List.map (to_string_a (d - 1)) x)) ^ ")"
| Times (a, b) -> "(* " ^ (to_string_a (d - 1) a) ^ " " ^ (to_string_a (d - 1) b) ^ ")"
| CTimes (a, b) -> "(c* " ^ (to_string_a (d - 1) a) ^ " " ^ (to_string_a (d - 1) b) ^ ")"
| CTimesJ (a, b) -> "(cj* " ^ (to_string_a (d - 1) a) ^ " " ^ (to_string_a (d - 1) b) ^ ")"
| Uminus a -> "(- " ^ (to_string_a (d-1) a) ^ ")"
| Store (v, a) -> "(:= " ^ (Variable.unparse v) ^ " " ^
(to_string_a (d-1) a) ^ ")"
let to_string = to_string_a 10
let assignment_to_string = function
| Assign (v, a) -> "(:= " ^ (Variable.unparse v) ^ " " ^ (to_string a) ^ ")"
let dump print = List.iter (fun x -> print ((assignment_to_string x) ^ "\n"))
(* find all constants in a given expression *)
let rec expr_to_constants = function
| Num n -> [n]
| Plus a -> List.flatten (List.map expr_to_constants a)
| Times (a, b) -> (expr_to_constants a) @ (expr_to_constants b)
| CTimes (a, b) -> (expr_to_constants a) @ (expr_to_constants b)
| CTimesJ (a, b) -> (expr_to_constants a) @ (expr_to_constants b)
| Uminus a -> expr_to_constants a
| _ -> []
let add_float_key_value list_so_far k =
if List.exists (fun k2 -> Number.equal k k2) list_so_far then
list_so_far
else
k :: list_so_far
let unique_constants = List.fold_left add_float_key_value []
|
