Updates

fftw-3.3.10/genfft/expr.ml

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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 []