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|
(**************************************************************************)
(* *)
(* The Why platform for program certification *)
(* *)
(* Copyright (C) 2002-2011 *)
(* *)
(* Jean-Christophe FILLIATRE, CNRS & Univ. Paris-sud 11 *)
(* Claude MARCHE, INRIA & Univ. Paris-sud 11 *)
(* Yannick MOY, Univ. Paris-sud 11 *)
(* Romain BARDOU, Univ. Paris-sud 11 *)
(* *)
(* Secondary contributors: *)
(* *)
(* Thierry HUBERT, Univ. Paris-sud 11 (former Caduceus front-end) *)
(* Nicolas ROUSSET, Univ. Paris-sud 11 (on Jessie & Krakatoa) *)
(* Ali AYAD, CNRS & CEA Saclay (floating-point support) *)
(* Sylvie BOLDO, INRIA (floating-point support) *)
(* Jean-Francois COUCHOT, INRIA (sort encodings, hyps pruning) *)
(* Mehdi DOGGUY, Univ. Paris-sud 11 (Why GUI) *)
(* *)
(* This software is free software; you can redistribute it and/or *)
(* modify it under the terms of the GNU Lesser General Public *)
(* License version 2.1, with the special exception on linking *)
(* described in file LICENSE. *)
(* *)
(* This software 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. *)
(* *)
(**************************************************************************)
open Format
(*
t : name of the float type
p : precision
e : minimal exponent (2^e is the smallest subnormal number
eg:
t = "double", p = 53, e = -1074
t = "single", p = 24, e = -149
*)
let rec hex_of_precision p =
match p with
| 0 -> ""
| 1 -> "8"
| 2 -> "C"
| 3 -> "E"
| _ -> "F" ^ hex_of_precision (p-4)
let output_common_part fmt t p e =
fprintf fmt "include \"real.why\"@.@.";
fprintf fmt "(* the different rounding modes *)
type mode
logic nearest_even, to_zero, up, down, nearest_away : mode
axiom no_other_mode : forall m:mode.
m = nearest_even or m = to_zero or m = up or m = down or m = nearest_away
axiom mode_distinct :
nearest_even <> to_zero and nearest_even <> up and nearest_even <> down
and nearest_even <> nearest_away and to_zero <> up and to_zero <> down
and to_zero <> nearest_away and up <> down and up <> nearest_away and
down <> nearest_away
parameter current_rounding_mode : mode ref
@.@.";
fprintf fmt "(* About the %s format *)
type %s@.@." t t;
fprintf fmt "logic round_%s : mode, real -> real@.@." t;
fprintf fmt "logic round_%s_logic : mode, real -> %s@.@." t t;
fprintf fmt "logic %s_value : %s -> real
logic %s_exact : %s -> real
logic %s_model : %s -> real@.@." t t t t t t;
fprintf fmt "function %s_round_error(x:%s) : real =
abs_real(%s_value(x) - %s_exact(x))
function %s_total_error(x:%s) : real =
abs_real(%s_value(x) - %s_model(x))@.@." t t t t t t t t;
fprintf fmt "parameter %s_set_model : x:%s ref -> y:real ->
{ }
unit writes x
{ %s_value(x) = %s_value(x@@)
and %s_exact(x) = %s_exact(x@@)
and %s_model(x) = y }@.@." t t t t t t t;
fprintf fmt "function max_%s() : real = 0x1.%sp%d@.@." t (hex_of_precision (p-1)) (-p-e+2) ;
fprintf fmt "predicate no_overflow_%s(m:mode,x:real) =
abs_real(round_%s(m,x)) <= max_%s@.@." t t t;
fprintf fmt "(* About rounding *)@.";
fprintf fmt "axiom bounded_real_no_overflow_%s : forall m:mode. forall x:real.
abs_real(x) <= max_%s -> no_overflow_%s(m,x)@." t t t;
fprintf fmt "axiom round_%s_down_le: forall x:real.
round_%s(down,x) <= x
axiom round_up_%s_ge: forall x:real.
round_%s(up,x) >= x
axiom round_down_%s_neg: forall x:real.
round_%s(down,-x) = -round_%s(up,x)
axiom round_up_%s_neg: forall x:real.
round_%s(up,-x) = -round_%s(down,x)
axiom round_%s_idempotent:
forall m1:mode. forall m2:mode. forall x:real.
round_%s(m1,round_%s(m2,x)) = round_%s(m2,x)@.@." t t t t t t t t t t t t t t;
fprintf fmt "(* Specification of operations (from the strict model) *)@.";
fprintf fmt "predicate %s_of_real_post(m:mode,x:real,res:%s) =
%s_value(res) = round_%s(m,x)
and
%s_exact(res) = x
and
%s_model(res) = x@.@." t t t t t t;
fprintf fmt "predicate add_%s_post(m:mode,x:%s,y:%s,res:%s) =
%s_value(res) = round_%s(m,%s_value(x) + %s_value(y))
and
%s_exact(res) = %s_exact(x) + %s_exact(y)
and
%s_model(res) = %s_model(x) + %s_model(y)@.@." t t t t t t t t t t t t t t;
fprintf fmt "predicate sub_%s_post(m:mode,x:%s,y:%s,res:%s) =
%s_value(res) = round_%s(m,%s_value(x) - %s_value(y))
and
%s_exact(res) = %s_exact(x) - %s_exact(y)
and
%s_model(res) = %s_model(x) - %s_model(y)@.@." t t t t t t t t t t t t t t;
fprintf fmt "predicate mul_%s_post(m:mode,x:%s,y:%s,res:%s) =
%s_value(res) = round_%s(m,%s_value(x) * %s_value(y))
and
%s_exact(res) = %s_exact(x) * %s_exact(y)
and
%s_model(res) = %s_model(x) * %s_model(y)@.@." t t t t t t t t t t t t t t;
fprintf fmt "predicate div_%s_post(m:mode,x:%s,y:%s,res:%s) =
%s_value(res) = round_%s(m,%s_value(x) / %s_value(y))
and
%s_exact(res) = %s_exact(x) / %s_exact(y)
and
%s_model(res) = %s_model(x) / %s_model(y)@.@." t t t t t t t t t t t t t t;
fprintf fmt "predicate sqrt_%s_post(m:mode,x:%s,res:%s) =
%s_value(res) = round_%s(m,sqrt_real(%s_value(x)))
and
%s_exact(res) = sqrt_real(%s_exact(x))
and
%s_model(res) = sqrt_real(%s_model(x))@.@." t t t t t t t t t t;
fprintf fmt "predicate neg_%s_post(x:%s,res:%s) =
%s_value(res) = -%s_value(x)
and
%s_exact(res) = -%s_exact(x)
and
%s_model(res) = -%s_model(x)@.@." t t t t t t t t t;
fprintf fmt "predicate abs_%s_post(x:%s,res:%s) =
%s_value(res) = abs_real(%s_value(x))
and
%s_exact(res) = abs_real(%s_exact(x))
and
%s_model(res) = abs_real(%s_model(x))@.@." t t t t t t t t t;
();;
(* Strict model *)
let output_strict_part fmt t _p _e =
fprintf fmt "include \"%s_model.why\"@.@." t;
fprintf fmt "(* Parameters for the strict model for %s format *)@.@." t;
fprintf fmt "parameter %s_of_real : m:mode -> x:real ->
{ no_overflow_%s(m,x) }
%s
{ %s_of_real_post(m,x,result) }@." t t t t;
fprintf fmt "parameter %s_of_real_safe : m:mode -> x:real ->
{ }
%s
{ no_overflow_%s(m,x) and
%s_of_real_post(m,x,result) }@.@." t t t t;
fprintf fmt "parameter add_%s : m:mode -> x:%s -> y:%s ->
{ no_overflow_%s(m,%s_value(x) + %s_value(y)) }
%s
{ add_%s_post(m,x,y,result) }@." t t t t t t t t;
fprintf fmt "parameter add_%s_safe : m:mode -> x:%s -> y:%s ->
{ }
%s
{ no_overflow_%s(m,%s_value(x) + %s_value(y)) and
add_%s_post(m,x,y,result) }@.@." t t t t t t t t;
fprintf fmt "parameter sub_%s : m:mode -> x:%s -> y:%s ->
{ no_overflow_%s(m,%s_value(x) - %s_value(y)) }
%s
{ sub_%s_post(m,x,y,result) }@." t t t t t t t t;
fprintf fmt "parameter sub_%s_safe : m:mode -> x:%s -> y:%s ->
{ }
%s
{ no_overflow_%s(m,%s_value(x) - %s_value(y)) and
sub_%s_post(m,x,y,result) }@.@." t t t t t t t t;
fprintf fmt "parameter mul_%s : m:mode -> x:%s -> y:%s ->
{ no_overflow_%s(m,%s_value(x) * %s_value(y)) }
%s
{ mul_%s_post(m,x,y,result) }@." t t t t t t t t;
fprintf fmt "parameter mul_%s_safe : m:mode -> x:%s -> y:%s ->
{ }
%s
{ no_overflow_%s(m,%s_value(x) * %s_value(y)) and
mul_%s_post(m,x,y,result) }@.@." t t t t t t t t;
fprintf fmt "parameter div_%s : m:mode -> x:%s -> y:%s ->
{ %s_value(y) <> 0.0
and
no_overflow_%s(m,%s_value(x) / %s_value(y)) }
%s
{ div_%s_post(m,x,y,result) }@." t t t t t t t t t;
fprintf fmt "parameter div_%s_safe : m:mode -> x:%s -> y:%s ->
{ }
%s
{ %s_value(y) <> 0.0 and
no_overflow_%s(m,%s_value(x) / %s_value(y)) and
div_%s_post(m,x,y,result) }@.@." t t t t t t t t t;
fprintf fmt "parameter sqrt_%s : m:mode -> x:%s ->
{ %s_value(x) >= 0.0 }
%s
{ sqrt_%s_post(m,x,result) }@." t t t t t;
fprintf fmt "parameter sqrt_%s_safe : m:mode -> x:%s ->
{ }
%s
{ %s_value(x) >= 0.0 and
sqrt_%s_post(m,x,result) }@.@." t t t t t;
fprintf fmt "parameter neg_%s : x:%s ->
{ }
%s
{ neg_%s_post(x,result) }@." t t t t;
fprintf fmt "parameter abs_%s : x:%s ->
{ }
%s
{ abs_%s_post(x,result) }@." t t t t;
fprintf fmt "(* Comparisons for the strict model for %s format *)@.@." t;
fprintf fmt "parameter lt_%s : x:%s -> y:%s ->
{} bool { if result then %s_value(x) < %s_value(y)
else %s_value(x) >= %s_value(y) }@." t t t t t t t;
fprintf fmt "parameter le_%s : x:%s -> y:%s ->
{} bool { if result then %s_value(x) <= %s_value(y)
else %s_value(x) > %s_value(y) }@." t t t t t t t;
fprintf fmt "parameter gt_%s : x:%s -> y:%s ->
{} bool { if result then %s_value(x) > %s_value(y)
else %s_value(x) <= %s_value(y) }@." t t t t t t t;
fprintf fmt "parameter ge_%s : x:%s -> y:%s ->
{} bool { if result then %s_value(x) >= %s_value(y)
else %s_value(x) < %s_value(y) }@." t t t t t t t;
fprintf fmt "parameter eq_%s : x:%s -> y:%s ->
{} bool { if result then %s_value(x) = %s_value(y)
else %s_value(x) <> %s_value(y) }@." t t t t t t t;
fprintf fmt "parameter neq_%s : x:%s -> y:%s ->
{} bool { if result then %s_value(x) <> %s_value(y)
else %s_value(x) = %s_value(y) }@.@." t t t t t t t;
fprintf fmt "(* Any %s *)
parameter any_%s : { } %s { }" t t t;
();;
(* Coq model *)
let output_coq_model fmt t p e =
fprintf fmt "(* Coq model for float type '%s'
* with precision = %d and min exponent = %d
*)@.@." t p e;
();;
(* main program *)
let type_name = Sys.argv.(1)
let precision = int_of_string Sys.argv.(2)
let exponent = int_of_string Sys.argv.(3)
let main =
let f = "lib/why/" ^ type_name ^ "_model.why" in
let c = open_out f in
output_common_part (formatter_of_out_channel c) type_name precision exponent;
close_out c;
let f = "lib/why/" ^ type_name ^ "_strict.why" in
let c = open_out f in
output_strict_part (formatter_of_out_channel c) type_name precision exponent;
close_out c;
let f = "lib/coq/" ^ type_name ^ "_model.v" in
let c = open_out f in
output_coq_model (formatter_of_out_channel c) type_name precision exponent;
close_out c;
|
