Source file loop_domain.ml
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module Log = Tracelog.Make(struct let category = "Domains.Loop" end);;
module TC = Operator.Function_symbol
module In_bits = Units.In_bits
let index_size = In_bits.of_int 32
module Make
(Terms: Terms.Sig.TERMS)
(Sub: Sig.BASE
with type binary = TC.binary Terms.t
and type boolean = TC.boolean Terms.t
and type enum = TC.enum Terms.t)
: Sig.BASE = struct
let name () = "Loop_Domain(" ^ Sub.name () ^ ")";;
let unique_id () = Sig.Fresh_id.fresh @@ name ();;
module Types = struct
type binary = Sub.binary
type boolean = Sub.boolean
type enum = Sub.enum
end
include Types
module Binary = Sub.Binary
module Boolean = Sub.Boolean
module Enum = Sub.Enum
type context =
{
subcontext: Sub.Context.t ;
index: binary option
};;
module Context = struct
type t = context
let copy x = { x with subcontext=Sub.Context.copy x.subcontext }
let assign ctx1 ctx2 =
Sub.Context.assign ctx1.subcontext ctx2.subcontext
let level ctx = Sub.Context.level ctx.subcontext
type 'a in_tuple = 'a Sub.Context.in_tuple
type 'a in_acc = bool * 'a Sub.Context.in_tuple
type 'a out_tuple = 'a Sub.Context.out_tuple
type ('a,'b) result =
Result: bool * 'some in_tuple * (t -> 'some out_tuple -> 'a * 'b out_tuple) -> ('a,'b) result
type empty_tuple = Sub.Context.empty_tuple
let empty_tuple () = Sub.Context.empty_tuple ()
end
open Context
let root_context () =
{
subcontext = Sub.root_context () ;
index = None
}
;;
let context_pretty fmt ctx =
match ctx.index with
| None -> Format.fprintf fmt "Context{sub=%a}" Sub.context_pretty ctx.subcontext
| Some idx -> Format.fprintf fmt "Context{sub=%a,index=%a}" Sub.context_pretty ctx.subcontext (Sub.binary_pretty ~size:index_size ctx.subcontext) idx
let assume ctx cond =
Option.map (fun subctx -> {ctx with subcontext = subctx}) (Sub.assume ctx.subcontext cond)
module Boolean_Forward = struct
let (||) ctx = Sub.Boolean_Forward.(||) ctx.subcontext
let (&&) ctx = Sub.Boolean_Forward.(&&) ctx.subcontext
let not ctx = Sub.Boolean_Forward.not ctx.subcontext
let true_ ctx = Sub.Boolean_Forward.true_ ctx.subcontext
let false_ ctx = Sub.Boolean_Forward.false_ ctx.subcontext
end
module Binary_Forward = struct
let biadd ~size ~flags ctx = Sub.Binary_Forward.biadd ~size ~flags ctx.subcontext
let bisub ~size ~flags ctx = Sub.Binary_Forward.bisub ~size ~flags ctx.subcontext
let bimul ~size ~flags ctx = Sub.Binary_Forward.bimul ~size ~flags ctx.subcontext
let bxor ~size ctx = Sub.Binary_Forward.bxor ~size ctx.subcontext
let band ~size ctx = Sub.Binary_Forward.band ~size ctx.subcontext
let bor ~size ctx = Sub.Binary_Forward.bor ~size ctx.subcontext
let bashr ~size ctx = Sub.Binary_Forward.bashr ~size ctx.subcontext
let blshr ~size ctx = Sub.Binary_Forward.blshr ~size ctx.subcontext
let bshl ~size ~flags ctx = Sub.Binary_Forward.bshl ~size ~flags ctx.subcontext
let bisdiv ~size ctx = Sub.Binary_Forward.bisdiv ~size ctx.subcontext
let biudiv ~size ctx = Sub.Binary_Forward.biudiv ~size ctx.subcontext
let bismod ~size ctx = Sub.Binary_Forward.bismod ~size ctx.subcontext
let biumod ~size ctx = Sub.Binary_Forward.biumod ~size ctx.subcontext
let beq ~size ctx = Sub.Binary_Forward.beq ~size ctx.subcontext
let biule ~size ctx = Sub.Binary_Forward.biule ~size ctx.subcontext
let bisle ~size ctx = Sub.Binary_Forward.bisle ~size ctx.subcontext
let bsext ~size ~oldsize ctx = Sub.Binary_Forward.bsext ~size ~oldsize ctx.subcontext
let buext ~size ~oldsize ctx = Sub.Binary_Forward.buext ~size ~oldsize ctx.subcontext
let bchoose ~size cond ctx = Sub.Binary_Forward.bchoose ~size cond ctx.subcontext
let bofbool ~size ctx = Sub.Binary_Forward.bofbool ~size ctx.subcontext
let bconcat ~size1 ~size2 ctx = Sub.Binary_Forward.bconcat ~size1 ~size2 ctx.subcontext
let ~size ~index ~oldsize ctx = Sub.Binary_Forward.bextract ~size ~index ~oldsize ctx.subcontext
let biconst ~size k ctx = Sub.Binary_Forward.biconst ~size k ctx.subcontext
let buninit ~size = assert false
let bshift ~size ~offset ~max _ = assert false
let bindex ~size _ = assert false
let valid ~size _ = assert false
let valid_ptr_arith ~size _ = assert false
end
module Enum_Forward = struct
let caseof ~case ctx = Sub.Enum_Forward.caseof ~case ctx.subcontext
let enum_const ~case ctx = Sub.Enum_Forward.enum_const ~case ctx.subcontext
end
let boolean_empty ctx = Sub.boolean_empty ctx.subcontext
let binary_empty ~size ctx = Sub.binary_empty ~size ctx.subcontext
let enum_empty ctx = Sub.enum_empty ctx.subcontext
let boolean_unknown ctx = Sub.boolean_unknown ctx.subcontext
let binary_unknown ~size ctx = Sub.binary_unknown ~size ctx.subcontext
let enum_unknown ~enumsize ctx = Sub.enum_unknown ~enumsize ctx.subcontext
let boolean_pretty ctx fmt x = Sub.boolean_pretty ctx.subcontext fmt x
let binary_pretty ~size ctx fmt x = Sub.binary_pretty ~size ctx.subcontext fmt x
let enum_pretty ctx fmt x = Sub.enum_pretty ctx.subcontext fmt x
let serialize_binary ~widens ~size ctxa a ctxb b acc =
let Sub.Context.Result (included, in_tup, deserialize) = Sub.serialize_binary ~widens ~size ctxa.subcontext a ctxb.subcontext b acc in
Context.Result (included, in_tup, (fun ctx out_tup -> deserialize ctx.subcontext out_tup))
let pretty_index fmt ctx =
match ctx.index with
| None -> Format.fprintf fmt "None"
| Some v -> binary_pretty ~size:index_size ctx fmt v
let serialize_binary ~widens ~(size:In_bits.t) ctxa a ctxb b ((inc, tup) as acc) =
Log.debug (fun p -> p "Loop_domain.serialize_binary ~widens:%b ~size:%d %a %a with index = %a" widens (size:>int)
(binary_pretty ~size ctxa) a
(binary_pretty ~size ctxb) b
(fun fmt index -> match index with None -> Format.fprintf fmt "None" | Some idx -> (binary_pretty ~size ctxa fmt) idx) ctxa.index);
if size <> index_size then serialize_binary ~widens ~size ctxa a ctxb b acc
else if not widens then serialize_binary ~widens ~size ctxa a ctxb b acc
else
let cur_level = Context.level ctxa in
match ctxa.index with
| Some (Terms.Binary{term=T0{tag=TC.Biconst(_size,k)}}) when Z.equal Z.zero k ->
begin
match a,b with
| Terms.(Binary _ as x),
Terms.(Binary{term=T2{tag=TC.Biadd{size=size';flags};
a=Binary{term=T0{tag=TC.Biconst(_size2,k)}};
b=Binary _ as y}})
when Terms.equal x y
&& (Terms.level x) < cur_level ->
Log.debug (fun p -> p "in Loop_domain.serialize, applying substitution 1");
Result (inc, tup, (fun ctx out ->
match ctx.index with
| Some idx ->
let offset = Binary_Forward.biconst ~size:index_size k ctx in
let offset = Binary_Forward.bimul ~size:index_size
~flags:(Operator.Flags.Bimul.pack ~nsw:false ~nuw:false) ctx offset idx in
let res = Binary_Forward.biadd ~size:index_size ~flags ctx offset x in
res, out
| _ -> assert false
))
| Terms.(Binary _ as x),
Terms.(Binary{term=T2{tag=TC.Bisub{size=size';flags=flagssub};
a=Binary _ as y;
b=Binary{term=T0{tag=TC.Biconst(_size2,k)}}}})
when Terms.equal x y
&& (Terms.level x) < cur_level ->
Log.debug (fun p -> p "in Loop_domain.serialize, applying substitution 2");
Result (inc, tup, (fun ctx out ->
match ctx.index with
| Some idx ->
Log.debug (fun p -> p "while, applying substitution 2, index = %a" (binary_pretty ~size ctx) idx);
let flags = Operator.Flags.Bimul.pack ~nsw:false ~nuw:false in
let offset = Binary_Forward.biconst ~size:index_size k ctx in
let offset = Binary_Forward.bimul ~size:index_size ~flags ctx offset idx in
let res = Binary_Forward.bisub ~size:index_size ~flags:flagssub ctx x offset in
Log.debug (fun p -> p "Loop_domain.serialize_binary, returning %a" Binary.pretty res);
res, out
| _ -> assert false
))
| Terms.(Binary{term=T0{tag=TC.Biconst(_size1, k)}}),
Terms.(Binary{term=T0{tag=TC.Biconst(_size2, l)}})
when not @@ Z.equal k l ->
let l = Z.signed_extract l 0 (index_size:>int) in
if Z.leq k l then (
Log.debug (fun p -> p "in Loop_domain.serialize, applying substitution 7");
Result (inc, tup, (fun ctx out ->
match ctx.index with
| Some idx ->
let base = Binary_Forward.biconst ~size:index_size k ctx in
let offset = Binary_Forward.biconst ~size:index_size (Z.sub l k) ctx in
let offset = Binary_Forward.bimul ~size:index_size
~flags:(Operator.Flags.Bimul.pack ~nsw:false ~nuw:false) ctx idx offset in
let res = Binary_Forward.biadd ~size:index_size
~flags:(Operator.Flags.Biadd.pack ~nsw:false ~nuw:false ~nusw:false) ctx base offset in
res, out
| _ -> assert false
)))
else (
Log.debug (fun p -> p "in Loop_domain.serialize, applying substitution 8");
Result (inc, tup, (fun ctx out ->
match ctx.index with
| Some idx ->
let base = Binary_Forward.biconst ~size:index_size k ctx in
let offset = Binary_Forward.biconst ~size:index_size (Z.sub k l) ctx in
let offset = Binary_Forward.bimul ~size:index_size
~flags:(Operator.Flags.Bimul.pack ~nsw:false ~nuw:false) ctx offset idx in
let res = Binary_Forward.bisub ~size:index_size ~flags:(Operator.Flags.Bisub.pack ~nsw:false ~nuw:false ~nusw:false) ctx base offset in
res, out
| _ -> assert false
)))
| _ ->
Log.debug (fun p -> p "in Loop_domain.serialize, applying no substituation") ;
serialize_binary ~widens ~size ctxa a ctxb b acc
end
| Some previdx ->
begin
match a,b with
| Terms.(Binary{term=T2{tag=TC.Biadd{size=_size1;flags=flags1};
a=Binary{term=T2{tag=TC.Bimul _size2;
a=Binary{term=T0{tag=TC.Biconst(_size3, i)}};
b=Binary _ as u
}};
b=Binary _ as x;
}}),
Terms.(Binary{term=T2{tag=TC.Biadd{size=_size4;flags=flags4};
a=Binary{term=T0{tag=TC.Biconst(_size5, k)}};
b=Binary{term=T2{tag=TC.Biadd{size=_size6;flags=flags6};
a=Binary{term=T2{tag=TC.Bimul{size=_size7;flags=flags7};
a=Binary{term=T0{tag=TC.Biconst(_size8, j)}};
b=Binary _ as v
}};
b=Binary _ as y
}};
}})
when Z.equal i j && Z.equal i k
&& Terms.equal x y && Terms.equal u v && Terms.equal u previdx
&& (Terms.level x) < cur_level
&& flags1 = flags4 ->
Log.debug (fun p -> p "in Loop_domain.serialize, applying substitution 3");
Result (inc, tup, (fun ctx out ->
match ctx.index with
| Some idx ->
let offset = Binary_Forward.biconst ~size:index_size i ctx in
let offset = Binary_Forward.bimul ~size:index_size ~flags:flags7 ctx offset idx in
let res = Binary_Forward.biadd ~size:index_size ~flags:flags1 ctx offset x in
res, out
| _ -> assert false
))
| Terms.(Binary{term=T2{tag=TC.Bisub {size=_size1;flags=flags1};
a=Binary _ as x;
b=Binary{term=T2{tag=TC.Bimul {size=_size2;flags=flags2};
a=Binary{term=T0{tag=TC.Biconst(_size3, i)}};
b=Binary _ as u}
}}
}),
Terms.(Binary{term=T2{tag=TC.Bisub {size=_size4;flags=flags4};
a=Binary{term=T2{tag=TC.Bisub {size=_size5;flags=flags5};
a=Binary _ as y;
b=Binary{term=T2{tag=TC.Bimul {size=_size6;flags=flags6};
a=Binary{term=T0{tag=TC.Biconst(_size7, j)}};
b=Binary _ as v
}}
}};
b=Binary{term=T0{tag=TC.Biconst(_size8, k)}}}
})
when Z.equal i j && Z.equal i k
&& Terms.equal x y && Terms.equal u v && Terms.equal u previdx
&& (Terms.level x) < cur_level
&& flags1 = flags4 && flags2 = flags6 ->
Log.debug (fun p -> p "in Loop_domain.serialize, applying substitution 4");
Result (inc, tup, (fun ctx out ->
match ctx.index with
| Some idx ->
let offset = Binary_Forward.biconst ~size:index_size i ctx in
let offset = Binary_Forward.bimul ~size:index_size ~flags:flags2 ctx offset idx in
let res = Binary_Forward.bisub ~size:index_size ~flags:flags1 ctx x offset in
res, out
| _ -> assert false
))
| Terms.(Binary{term=T2{tag=TC.Biadd {size=_size1;flags=flags1};
a=Binary _ as u;
b=Binary _ as x }}),
Terms.(Binary{term=T2{tag=TC.Biadd {size=_size2;flags=flags2};
a=Binary{term=T0{tag=TC.Biconst(_size3, k)}};
b=Binary{term=T2{tag=TC.Biadd {size=_size4;flags=flags4};
a=Binary _ as v;
b=Binary _ as y
}}
}})
when Z.equal k Z.one
&& Terms.equal x y && Terms.equal u v && Terms.equal u previdx
&& (Terms.level x) < cur_level
&& flags1 = flags2 && flags1 = flags4 ->
Log.debug (fun p -> p "in Loop_domain.serialize, applying substitution 5");
Result (inc, tup, (fun ctx out ->
match ctx.index with
| Some idx ->
let res = Binary_Forward.biadd ~size:index_size ~flags:flags1 ctx idx x in
res, out
| _ -> assert false
))
| Terms.(Binary{term=T2{tag=TC.Bisub {size=_size1;flags=flags1};
a=Binary _ as x;
b=Binary _ as u }}),
Terms.(Binary{term=T2{tag=TC.Bisub {size=_size2;flags=flags2};
a=Binary{term=T2{tag=TC.Bisub {size=_size3;flags=flags3};
a=Binary _ as y;
b=Binary _ as v
}};
b=Binary{term=T0{tag=TC.Biconst(_size4, k)}}
}})
when Z.equal k Z.one
&& Terms.equal x y && Terms.equal u v && Terms.equal u previdx
&& (Terms.level x) < cur_level
&& flags1 = flags2 && flags1 = flags3 ->
Log.debug (fun p -> p "in Loop_domain.serialize, applying substitution 6");
Result (inc, tup, (fun ctx out ->
match ctx.index with
| Some idx ->
let res = Binary_Forward.bisub ~size:index_size ~flags:flags1 ctx x idx in
res, out
| _ -> assert false
))
| Terms.(Binary{term=T2{tag=TC.Bimul {size=_size1;flags=flags1};
a=Binary{term=T0{tag=TC.Biconst(_size2, i)}};
b=Binary _ as x}}),
Terms.(Binary{term=T2{tag=TC.Biadd {size=_size3;flags=flags3};
a=Binary{term=T0{tag=TC.Biconst(_size4, j)}};
b=Binary{term=T2{tag=TC.Bimul {size=_size5;flags=flags5};
a=Binary{term=T0{tag=TC.Biconst(_size6, k)}};
b=Binary _ as y
}};
}})
when Terms.equal x y && Terms.equal x previdx && Z.equal i j && Z.equal i k
&& flags1 = flags5 ->
Log.debug (fun p -> p "in Loop_domain.serialize, applying substitution 9");
Result (inc, tup, (fun ctx out ->
match ctx.index with
| Some idx ->
let offset = Binary_Forward.biconst ~size:index_size i ctx in
let res = Binary_Forward.bimul ~size:index_size ~flags:flags5 ctx offset idx in
res, out
| _ -> assert false
))
| Terms.(Binary _ as x),
Terms.(Binary{term=T2{tag=TC.Biadd {size=_size;flags};
a=Binary{term=T0{tag=TC.Biconst(_size2, k)}};
b=Binary _ as y
}})
when Z.equal k Z.one
&& Terms.equal x y && Terms.equal x previdx ->
Log.debug (fun p -> p "in Loop_domain.serialize, applying substitution 11");
Result (inc, tup, (fun ctx out ->
match ctx.index with
| Some idx -> idx, out
| _ -> assert false
))
| Terms.(Binary{term=T2{tag=TC.Biadd {size=_size1;flags=flags1};
a=Binary _ as x;
b=Binary{term=T2{tag=TC.Bimul {size=_size2;flags=flags2};
a=Binary {term=T0{tag=TC.Biconst(_size3, i)}};
b=Binary _ as u
}}
}}),
Terms.(Binary{term=T2{tag=TC.Biadd {size=_size4;flags=flags4};
a=Binary{term=T0{tag=TC.Biconst(_size5, k)}};
b=Binary{term=T2{tag=TC.Biadd {size=_size6;flags=flags6};
a=Binary _ as y;
b=Binary{term=T2{tag=TC.Bimul {size=_size7;flags=flags7};
a=Binary{term=T0{tag=TC.Biconst(_size8, j)}};
b=Binary _ as v
}}
}};
}})
when Z.equal i j && Z.equal i k
&& Terms.equal x y && Terms.equal u v && Terms.equal u previdx
&& (Terms.level x) < cur_level
&& flags1 = flags4 && flags1 = flags6
&& flags2=flags7 ->
Log.debug (fun p -> p "in Loop_domain.serialize, applying substitution 13");
Result (inc, tup, (fun ctx out ->
match ctx.index with
| Some idx ->
let offset = Binary_Forward.biconst ~size:index_size i ctx in
let offset = Binary_Forward.bimul ~size:index_size ~flags:flags2 ctx offset idx in
let res = Binary_Forward.biadd ~size:index_size ~flags:flags1 ctx offset x in
res, out
| _ -> assert false
))
| Terms.(Binary{term=T2{tag=TC.Biadd {size=_size1;flags=flags1};
a=Binary _ as x;
b=Binary _ as u }}),
Terms.(Binary{term=T2{tag=TC.Biadd {size=_size2;flags=flags2};
a=Binary{term=T0{tag=TC.Biconst(_size3, k)}};
b=Binary{term=T2{tag=TC.Biadd {size=_size4;flags=flags4};
a=Binary _ as y;
b=Binary _ as v
}}
}})
when Z.equal k Z.one
&& Terms.equal x y && Terms.equal u v && Terms.equal u previdx
&& (Terms.level x) < cur_level
&& flags1 = flags2 && flags1 = flags4 ->
Log.debug (fun p -> p "in Loop_domain.serialize, applying substitution 14");
Result (inc, tup, (fun ctx out ->
match ctx.index with
| Some idx ->
let res = Binary_Forward.biadd ~size:index_size ~flags:(Operator.Flags.Biadd.pack ~nsw:false ~nuw:false ~nusw:false) ctx x idx in
res, out
| _ -> assert false
))
| _ ->
Log.debug (fun p -> p "in Loop_domain.serialize, applying no substituation") ;
serialize_binary ~widens ~size ctxa a ctxb b acc
end
| _ ->
Log.debug (fun p -> p "in Loop_domain.serialize, unable to substitute without an adequate loop index") ;
serialize_binary ~widens ~size ctxa a ctxb b acc
let serialize_boolean ctxa a ctxb b acc =
let Sub.Context.Result (included, in_tup, deserialize) = Sub.serialize_boolean ctxa.subcontext a ctxb.subcontext b acc in
Context.Result (included, in_tup, (fun ctx out_tup -> deserialize ctx.subcontext out_tup))
let serialize_enum ctxa a ctxb b acc =
let Sub.Context.Result (included, in_tup, deserialize) = Sub.serialize_enum ctxa.subcontext a ctxb.subcontext b acc in
Context.Result (included, in_tup, (fun ctx out_tup -> deserialize ctx.subcontext out_tup))
let nondet_same_context ctx in_tup = Sub.nondet_same_context ctx.subcontext in_tup
let union cond ctx in_tup = Sub.union cond ctx.subcontext in_tup
let typed_nondet2 ctxa ctxb in_tup =
match ctxa.index, ctxb.index with
| Some ia, Some ib when Terms.equal ia ib ->
let subctx, out = Sub.typed_nondet2 ctxa.subcontext ctxb.subcontext in_tup in
{subcontext = subctx; index = Some ia}, out
| _ ->
let subctx, out = Sub.typed_nondet2 ctxa.subcontext ctxb.subcontext in_tup in
{subcontext = subctx; index = None}, out
let typed_fixpoint_step ~iteration ~init ~arg ~body (inc, tup) =
let bool, continuef = Sub.typed_fixpoint_step ~iteration ~init:init.subcontext ~arg:arg.subcontext ~body:body.subcontext (inc, tup) in
let continuef ~close =
let out, ctx = continuef ~close in
out, {subcontext = ctx; index = None}
in bool, continuef
let typed_fixpoint_step ~iteration ~init ~arg ~body ((inc, tup) : bool * 'a in_tuple) : bool * (close:bool -> 'a out_tuple * Context.t) =
match arg.index with
| Some idx ->
let one = Sub.Binary_Forward.biconst ~size:index_size Z.one init.subcontext in
let next_idx = Sub.Binary_Forward.biadd ~size:index_size ~flags:(Operator.Flags.Biadd.pack ~nsw:false ~nuw:false ~nusw:false) body.subcontext idx one in
let Sub.Context.Result(inc, tup, deserialize) = Sub.serialize_binary ~widens:true ~size:index_size arg.subcontext idx body.subcontext next_idx (inc, tup) in
let bool, continuef = Sub.typed_fixpoint_step ~iteration ~init:init.subcontext ~arg:arg.subcontext ~body:body.subcontext (inc, tup) in
let continuef ~close =
let out, ctx = continuef ~close in
let new_index, out = deserialize ctx out in
out, {subcontext = ctx; index = Some new_index}
in bool, continuef
| _ -> typed_fixpoint_step ~iteration ~init ~arg ~body (inc, tup)
let widened_fixpoint_step ~widening_id ~previous ~next = assert false
let mu_context_open parent_ctx =
let subctx = Sub.mu_context_open parent_ctx.subcontext in
let zero = Sub.Binary_Forward.biconst ~size:index_size Z.zero parent_ctx.subcontext in
{subcontext = subctx; index = Some zero}
module Query = struct
include Sub.Query
let binary ~size ctx = Sub.Query.binary ~size ctx.subcontext
let enum ctx = Sub.Query.enum ctx.subcontext
end
let query_boolean ctx b = Sub.query_boolean ctx.subcontext b
let assume_binary ~size = assert false
let satisfiable ctx cond = Sub.satisfiable ctx.subcontext cond
let binary_unknown_typed ~size ctx typ = Sub.binary_unknown_typed ~size ctx.subcontext typ
end