@ -18,22 +18,33 @@ module L = Logging
exception Not_one_symbol
exception Not_one_symbol
module Symbol = struct
module Symbol = struct
type t = Typ . Procname . t * int [ @@ deriving compare ]
type t = { pname : Typ . Procname . t ; id : int ; unsigned : bool } [ @@ deriving compare ]
let eq = [ % compare . equal : t ]
let eq = [ % compare . equal : t ]
let make : Typ . Procname . t -> int -> t = fun pname i -> ( pname , i )
let make : unsigned : bool -> Typ . Procname . t -> int -> t =
fun ~ unsigned pname id -> { pname ; id ; unsigned }
let pp : F . formatter -> t -> unit =
let pp : F . formatter -> t -> unit =
fun fmt x ->
fun fmt { pname ; id ; unsigned } ->
if Config . bo_debug < = 1 then F . fprintf fmt " s$%d " ( snd x )
let symbol_name = if unsigned then " u " else " s " in
else F . fprintf fmt " %s-s$%d " ( fst x | > Typ . Procname . to_string ) ( snd x )
if Config . bo_debug < = 1 then F . fprintf fmt " %s$%d " symbol_name id
else F . fprintf fmt " %s-%s$%d " ( Typ . Procname . to_string pname ) symbol_name id
let is_unsigned : t -> bool = fun x -> x . unsigned
end
end
module SubstMap = Caml . Map . Make ( Symbol )
module SubstMap = Caml . Map . Make ( Symbol )
module SymLinear = struct
module SymLinear = struct
module M = Caml . Map . Make ( Symbol )
module M = struct
include Caml . Map . Make ( Symbol )
let for_all2 : ( key -> ' a option -> ' b option -> bool ) -> ' a t -> ' b t -> bool =
fun cond x y ->
let merge_function k x y = if cond k x y then None else raise Exit in
match merge merge_function x y with _ -> true | exception Exit -> false
end
type t = int M . t [ @@ deriving compare ]
type t = int M . t [ @@ deriving compare ]
@ -60,10 +71,22 @@ module SymLinear = struct
try M . find s x
try M . find s x
with Not_found -> 0
with Not_found -> 0
let le : t -> t -> bool = fun x y -> M . for_all ( fun s v -> v < = find s y ) x
let is_le_zero : t -> bool =
fun x -> M . for_all ( fun s v -> Int . equal v 0 | | Symbol . is_unsigned s && v < = 0 ) x
let is_ge_zero : t -> bool =
fun x -> M . for_all ( fun s v -> Int . equal v 0 | | Symbol . is_unsigned s && v > = 0 ) x
let le : t -> t -> bool =
fun x y ->
let le_one_pair s v1_opt v2_opt =
let v1 , v2 = ( Option . value v1_opt ~ default : 0 , Option . value v2_opt ~ default : 0 ) in
Int . equal v1 v2 | | Symbol . is_unsigned s && v1 < = v2
in
M . for_all2 le_one_pair x y
let make : Typ . Procname . t -> int -> t = fun pname i -> M . add ( Symbol . make pname i ) 1 empty
let make : unsigned : bool -> Typ . Procname . t -> int -> t =
fun ~ unsigned pname i -> M . add ( Symbol . make ~ unsigned pname i ) 1 empty
let eq : t -> t -> bool = fun x y -> le x y && le y x
let eq : t -> t -> bool = fun x y -> le x y && le y x
@ -195,7 +218,7 @@ module Bound = struct
| PInf
| PInf
-> F . fprintf fmt " +oo "
-> F . fprintf fmt " +oo "
| Linear ( c , x )
| Linear ( c , x )
-> if SymLinear . le x SymLinear . empty then F . fprintf fmt " %d " c
-> if SymLinear . is_zero x then F . fprintf fmt " %d " c
else if Int . equal c 0 then F . fprintf fmt " %a " SymLinear . pp x
else if Int . equal c 0 then F . fprintf fmt " %a " SymLinear . pp x
else F . fprintf fmt " %a + %d " SymLinear . pp x c
else F . fprintf fmt " %a + %d " SymLinear . pp x c
| MinMax ( c , sign , m , d , x )
| MinMax ( c , sign , m , d , x )
@ -249,6 +272,21 @@ module Bound = struct
let is_mone_symbol : t -> bool = fun x -> get_mone_symbol_opt x < > None
let is_mone_symbol : t -> bool = fun x -> get_mone_symbol_opt x < > None
let mk_MinMax ( c , sign , m , d , s ) =
if Symbol . is_unsigned s then
match m with
| Min when d < = 0 -> (
match sign with Plus -> of_int ( c + d ) | Minus -> of_int ( c - d ) )
| Max when d < = 0 -> (
match sign with
| Plus
-> Linear ( c , SymLinear . singleton s 1 )
| Minus
-> Linear ( c , SymLinear . singleton s ( - 1 ) ) )
| _
-> MinMax ( c , sign , m , d , s )
else MinMax ( c , sign , m , d , s )
let use_symbol : Symbol . t -> t -> bool =
let use_symbol : Symbol . t -> t -> bool =
fun s ->
fun s ->
function
function
@ -304,37 +342,35 @@ module Bound = struct
| MinMax ( c1 , Minus , Max , d1 , _ ) , Linear ( c2 , se ) when SymLinear . is_zero se
| MinMax ( c1 , Minus , Max , d1 , _ ) , Linear ( c2 , se ) when SymLinear . is_zero se
-> Linear ( c1 - max d1 c2 , SymLinear . zero )
-> Linear ( c1 - max d1 c2 , SymLinear . zero )
| MinMax ( c , sign , m , d , _ ) , _ when is_one_symbol y
| MinMax ( c , sign , m , d , _ ) , _ when is_one_symbol y
-> MinMax ( c , sign , m , d , get_one_symbol y )
-> mk_ MinMax ( c , sign , m , d , get_one_symbol y )
| MinMax ( c , sign , m , d , _ ) , _ when is_mone_symbol y
| MinMax ( c , sign , m , d , _ ) , _ when is_mone_symbol y
-> MinMax ( c , neg_sign sign , neg_min_max m , - d , get_mone_symbol y )
-> mk_ MinMax ( c , neg_sign sign , neg_min_max m , - d , get_mone_symbol y )
| MinMax ( c1 , Plus , Min , d1 , _ ) , MinMax ( c2 , Plus , Min , d2 , s' )
| MinMax ( c1 , Plus , Min , d1 , _ ) , MinMax ( c2 , Plus , Min , d2 , s' )
-> MinMax ( c1 + c2 , Plus , Min , min ( d1 - c2 ) d2 , s' )
-> mk_ MinMax ( c1 + c2 , Plus , Min , min ( d1 - c2 ) d2 , s' )
| MinMax ( c1 , Plus , Max , d1 , _ ) , MinMax ( c2 , Plus , Max , d2 , s' )
| MinMax ( c1 , Plus , Max , d1 , _ ) , MinMax ( c2 , Plus , Max , d2 , s' )
-> MinMax ( c1 + c2 , Plus , Max , max ( d1 - c2 ) d2 , s' )
-> mk_ MinMax ( c1 + c2 , Plus , Max , max ( d1 - c2 ) d2 , s' )
| MinMax ( c1 , Minus , Min , d1 , _ ) , MinMax ( c2 , Plus , Min , d2 , s' )
| MinMax ( c1 , Minus , Min , d1 , _ ) , MinMax ( c2 , Plus , Min , d2 , s' )
-> MinMax ( c1 - c2 , Minus , Min , min ( d1 - c2 ) d2 , s' )
-> mk_ MinMax ( c1 - c2 , Minus , Min , min ( d1 - c2 ) d2 , s' )
| MinMax ( c1 , Minus , Max , d1 , _ ) , MinMax ( c2 , Plus , Max , d2 , s' )
| MinMax ( c1 , Minus , Max , d1 , _ ) , MinMax ( c2 , Plus , Max , d2 , s' )
-> MinMax ( c1 - c2 , Minus , Max , max ( d1 - c2 ) d2 , s' )
-> mk_ MinMax ( c1 - c2 , Minus , Max , max ( d1 - c2 ) d2 , s' )
| MinMax ( c1 , Plus , Min , d1 , _ ) , MinMax ( c2 , Minus , Max , d2 , s' )
| MinMax ( c1 , Plus , Min , d1 , _ ) , MinMax ( c2 , Minus , Max , d2 , s' )
-> MinMax ( c1 + c2 , Minus , Max , max ( - d1 + c2 ) d2 , s' )
-> mk_ MinMax ( c1 + c2 , Minus , Max , max ( - d1 + c2 ) d2 , s' )
| MinMax ( c1 , Plus , Max , d1 , _ ) , MinMax ( c2 , Minus , Min , d2 , s' )
| MinMax ( c1 , Plus , Max , d1 , _ ) , MinMax ( c2 , Minus , Min , d2 , s' )
-> MinMax ( c1 + c2 , Minus , Min , min ( - d1 + c2 ) d2 , s' )
-> mk_ MinMax ( c1 + c2 , Minus , Min , min ( - d1 + c2 ) d2 , s' )
| MinMax ( c1 , Minus , Min , d1 , _ ) , MinMax ( c2 , Minus , Max , d2 , s' )
| MinMax ( c1 , Minus , Min , d1 , _ ) , MinMax ( c2 , Minus , Max , d2 , s' )
-> MinMax ( c1 - c2 , Minus , Max , max ( - d1 + c2 ) d2 , s' )
-> mk_ MinMax ( c1 - c2 , Minus , Max , max ( - d1 + c2 ) d2 , s' )
| MinMax ( c1 , Minus , Max , d1 , _ ) , MinMax ( c2 , Minus , Min , d2 , s' )
| MinMax ( c1 , Minus , Max , d1 , _ ) , MinMax ( c2 , Minus , Min , d2 , s' )
-> MinMax ( c1 - c2 , Minus , Min , min ( - d1 + c2 ) d2 , s' )
-> mk_ MinMax ( c1 - c2 , Minus , Min , min ( - d1 + c2 ) d2 , s' )
| _
| _
-> default
-> default
in
in
NonBottom res
NonBottom res
(* substitution symbols in ``x'' with respect to ``map'' *)
let subst : default : t -> t -> t bottom_lifted SubstMap . t -> t bottom_lifted =
fun ~ default x map -> SubstMap . fold ( fun s y x -> subst1 ~ default x s y ) map ( NonBottom x )
let int_ub_of_minmax = function
let int_ub_of_minmax = function
| MinMax ( c , Plus , Min , d , _ )
| MinMax ( c , Plus , Min , d , _ )
-> Some ( c + d )
-> Some ( c + d )
| MinMax ( c , Minus , Max , d , s ) when Symbol . is_unsigned s
-> Some ( min c ( c - d ) )
| MinMax ( c , Minus , Max , d , _ )
| MinMax ( c , Minus , Max , d , _ )
-> Some ( c - d )
-> Some ( c - d )
| MinMax _
| MinMax _
@ -343,6 +379,8 @@ module Bound = struct
-> assert false
-> assert false
let int_lb_of_minmax = function
let int_lb_of_minmax = function
| MinMax ( c , Plus , Max , d , s ) when Symbol . is_unsigned s
-> Some ( max c ( c + d ) )
| MinMax ( c , Plus , Max , d , _ )
| MinMax ( c , Plus , Max , d , _ )
-> Some ( c + d )
-> Some ( c + d )
| MinMax ( c , Minus , Min , d , _ )
| MinMax ( c , Minus , Min , d , _ )
@ -387,7 +425,7 @@ module Bound = struct
| _ , MInf | PInf , _
| _ , MInf | PInf , _
-> false
-> false
| Linear ( c0 , x0 ) , Linear ( c1 , x1 )
| Linear ( c0 , x0 ) , Linear ( c1 , x1 )
-> c0 < = c1 && SymLinear . eq x0 x1
-> c0 < = c1 && SymLinear . l e x0 x1
| MinMax ( c1 , sign1 , m1 , d1 , x1 ) , MinMax ( c2 , sign2 , m2 , d2 , x2 )
| MinMax ( c1 , sign1 , m1 , d1 , x1 ) , MinMax ( c2 , sign2 , m2 , d2 , x2 )
when sign_equal sign1 sign2 && min_max_equal m1 m2
when sign_equal sign1 sign2 && min_max_equal m1 m2
-> c1 < = c2 && Int . equal d1 d2 && Symbol . eq x1 x2
-> c1 < = c2 && Int . equal d1 d2 && Symbol . eq x1 x2
@ -396,14 +434,12 @@ module Bound = struct
| MinMax ( c1 , Plus , Min , _ , x1 ) , MinMax ( c2 , Plus , Max , _ , x2 )
| MinMax ( c1 , Plus , Min , _ , x1 ) , MinMax ( c2 , Plus , Max , _ , x2 )
| MinMax ( c1 , Minus , Max , _ , x1 ) , MinMax ( c2 , Minus , Min , _ , x2 )
| MinMax ( c1 , Minus , Max , _ , x1 ) , MinMax ( c2 , Minus , Min , _ , x2 )
-> c1 < = c2 && Symbol . eq x1 x2
-> c1 < = c2 && Symbol . eq x1 x2
| MinMax _ , Linear ( c , se ) when SymLinear . is_zero se
| MinMax _ , Linear ( c , se )
-> le_opt1 ( < = ) ( int_ub_of_minmax x ) c
-> SymLinear . is_ge_zero se && le_opt1 ( < = ) ( int_ub_of_minmax x ) c
| MinMax _ , Linear _
| | le_opt1 le ( linear_ub_of_minmax x ) y
-> le_opt1 le ( linear_ub_of_minmax x ) y
| Linear ( c , se ) , MinMax _
| Linear ( c , se ) , MinMax _ when SymLinear . is_zero se
-> SymLinear . is_le_zero se && le_opt2 ( < = ) c ( int_lb_of_minmax y )
-> le_opt2 ( < = ) c ( int_lb_of_minmax y )
| | le_opt2 le x ( linear_lb_of_minmax y )
| Linear _ , MinMax _
-> le_opt2 le x ( linear_lb_of_minmax y )
| _ , _
| _ , _
-> false
-> false
@ -415,7 +451,7 @@ module Bound = struct
| Linear ( c , x ) , _
| Linear ( c , x ) , _
-> le ( Linear ( c + 1 , x ) ) y
-> le ( Linear ( c + 1 , x ) ) y
| MinMax ( c , sign , min_max , d , x ) , _
| MinMax ( c , sign , min_max , d , x ) , _
-> le ( MinMax ( c + 1 , sign , min_max , d , x ) ) y
-> le ( mk_ MinMax ( c + 1 , sign , min_max , d , x ) ) y
| _ , _
| _ , _
-> false
-> false
@ -453,29 +489,29 @@ module Bound = struct
else
else
match ( x , y ) with
match ( x , y ) with
| Linear ( c1 , x1 ) , Linear ( c2 , x2 ) when SymLinear . is_zero x1 && SymLinear . is_one_symbol x2
| Linear ( c1 , x1 ) , Linear ( c2 , x2 ) when SymLinear . is_zero x1 && SymLinear . is_one_symbol x2
-> MinMax ( c2 , Plus , Min , c1 - c2 , SymLinear . get_one_symbol x2 )
-> mk_ MinMax ( c2 , Plus , Min , c1 - c2 , SymLinear . get_one_symbol x2 )
| Linear ( c1 , x1 ) , Linear ( c2 , x2 ) when SymLinear . is_one_symbol x1 && SymLinear . is_zero x2
| Linear ( c1 , x1 ) , Linear ( c2 , x2 ) when SymLinear . is_one_symbol x1 && SymLinear . is_zero x2
-> MinMax ( c1 , Plus , Min , c2 - c1 , SymLinear . get_one_symbol x1 )
-> mk_ MinMax ( c1 , Plus , Min , c2 - c1 , SymLinear . get_one_symbol x1 )
| Linear ( c1 , x1 ) , Linear ( c2 , x2 ) when SymLinear . is_zero x1 && SymLinear . is_mone_symbol x2
| Linear ( c1 , x1 ) , Linear ( c2 , x2 ) when SymLinear . is_zero x1 && SymLinear . is_mone_symbol x2
-> MinMax ( c2 , Minus , Max , c2 - c1 , SymLinear . get_mone_symbol x2 )
-> mk_ MinMax ( c2 , Minus , Max , c2 - c1 , SymLinear . get_mone_symbol x2 )
| Linear ( c1 , x1 ) , Linear ( c2 , x2 ) when SymLinear . is_mone_symbol x1 && SymLinear . is_zero x2
| Linear ( c1 , x1 ) , Linear ( c2 , x2 ) when SymLinear . is_mone_symbol x1 && SymLinear . is_zero x2
-> MinMax ( c1 , Minus , Max , c1 - c2 , SymLinear . get_mone_symbol x1 )
-> mk_ MinMax ( c1 , Minus , Max , c1 - c2 , SymLinear . get_mone_symbol x1 )
| MinMax ( c1 , Plus , Min , d1 , s ) , Linear ( c2 , se )
| MinMax ( c1 , Plus , Min , d1 , s ) , Linear ( c2 , se )
| Linear ( c2 , se ) , MinMax ( c1 , Plus , Min , d1 , s )
| Linear ( c2 , se ) , MinMax ( c1 , Plus , Min , d1 , s )
when SymLinear . is_zero se
when SymLinear . is_zero se
-> MinMax ( c1 , Plus , Min , min d1 ( c2 - c1 ) , s )
-> mk_ MinMax ( c1 , Plus , Min , min d1 ( c2 - c1 ) , s )
| MinMax ( c1 , Plus , Max , _ , s ) , Linear ( c2 , se )
| MinMax ( c1 , Plus , Max , _ , s ) , Linear ( c2 , se )
| Linear ( c2 , se ) , MinMax ( c1 , Plus , Max , _ , s )
| Linear ( c2 , se ) , MinMax ( c1 , Plus , Max , _ , s )
when SymLinear . is_zero se
when SymLinear . is_zero se
-> MinMax ( c1 , Plus , Min , c2 - c1 , s )
-> mk_ MinMax ( c1 , Plus , Min , c2 - c1 , s )
| MinMax ( c1 , Minus , Min , _ , s ) , Linear ( c2 , se )
| MinMax ( c1 , Minus , Min , _ , s ) , Linear ( c2 , se )
| Linear ( c2 , se ) , MinMax ( c1 , Minus , Min , _ , s )
| Linear ( c2 , se ) , MinMax ( c1 , Minus , Min , _ , s )
when SymLinear . is_zero se
when SymLinear . is_zero se
-> MinMax ( c1 , Minus , Max , c1 - c2 , s )
-> mk_ MinMax ( c1 , Minus , Max , c1 - c2 , s )
| MinMax ( c1 , Minus , Max , d1 , s ) , Linear ( c2 , se )
| MinMax ( c1 , Minus , Max , d1 , s ) , Linear ( c2 , se )
| Linear ( c2 , se ) , MinMax ( c1 , Minus , Max , d1 , s )
| Linear ( c2 , se ) , MinMax ( c1 , Minus , Max , d1 , s )
when SymLinear . is_zero se
when SymLinear . is_zero se
-> MinMax ( c1 , Minus , Max , max d1 ( c1 - c2 ) , s )
-> mk_ MinMax ( c1 , Minus , Max , max d1 ( c1 - c2 ) , s )
| MinMax ( _ , Plus , Min , _ , _ ) , MinMax ( _ , Plus , Max , _ , _ )
| MinMax ( _ , Plus , Min , _ , _ ) , MinMax ( _ , Plus , Max , _ , _ )
| MinMax ( _ , Plus , Min , _ , _ ) , MinMax ( _ , Minus , Min , _ , _ )
| MinMax ( _ , Plus , Min , _ , _ ) , MinMax ( _ , Minus , Min , _ , _ )
| MinMax ( _ , Minus , Max , _ , _ ) , MinMax ( _ , Plus , Max , _ , _ )
| MinMax ( _ , Minus , Max , _ , _ ) , MinMax ( _ , Plus , Max , _ , _ )
@ -491,22 +527,22 @@ module Bound = struct
| _ , _
| _ , _
-> default
-> default
let ub : t -> t -> t =
let ub : ? default : t -> t -> t -> t =
fun x y ->
fun ? ( default = PInf ) x y ->
if le x y then y
if le x y then y
else if le y x then x
else if le y x then x
else
else
match ( x , y ) with
match ( x , y ) with
| Linear ( c1 , x1 ) , Linear ( c2 , x2 ) when SymLinear . is_zero x1 && SymLinear . is_one_symbol x2
| Linear ( c1 , x1 ) , Linear ( c2 , x2 ) when SymLinear . is_zero x1 && SymLinear . is_one_symbol x2
-> MinMax ( c2 , Plus , Max , c1 - c2 , SymLinear . get_one_symbol x2 )
-> mk_ MinMax ( c2 , Plus , Max , c1 - c2 , SymLinear . get_one_symbol x2 )
| Linear ( c1 , x1 ) , Linear ( c2 , x2 ) when SymLinear . is_one_symbol x1 && SymLinear . is_zero x2
| Linear ( c1 , x1 ) , Linear ( c2 , x2 ) when SymLinear . is_one_symbol x1 && SymLinear . is_zero x2
-> MinMax ( c1 , Plus , Max , c2 - c1 , SymLinear . get_one_symbol x1 )
-> mk_ MinMax ( c1 , Plus , Max , c2 - c1 , SymLinear . get_one_symbol x1 )
| Linear ( c1 , x1 ) , Linear ( c2 , x2 ) when SymLinear . is_zero x1 && SymLinear . is_mone_symbol x2
| Linear ( c1 , x1 ) , Linear ( c2 , x2 ) when SymLinear . is_zero x1 && SymLinear . is_mone_symbol x2
-> MinMax ( c2 , Minus , Min , c2 - c1 , SymLinear . get_mone_symbol x2 )
-> mk_ MinMax ( c2 , Minus , Min , c2 - c1 , SymLinear . get_mone_symbol x2 )
| Linear ( c1 , x1 ) , Linear ( c2 , x2 ) when SymLinear . is_mone_symbol x1 && SymLinear . is_zero x2
| Linear ( c1 , x1 ) , Linear ( c2 , x2 ) when SymLinear . is_mone_symbol x1 && SymLinear . is_zero x2
-> MinMax ( c1 , Minus , Min , c1 - c2 , SymLinear . get_mone_symbol x1 )
-> mk_ MinMax ( c1 , Minus , Min , c1 - c2 , SymLinear . get_mone_symbol x1 )
| _ , _
| _ , _
-> PInf
-> default
let widen_l : t -> t -> t =
let widen_l : t -> t -> t =
fun x y ->
fun x y ->
@ -538,6 +574,21 @@ module Bound = struct
let is_const : t -> int option =
let is_const : t -> int option =
fun x -> match x with Linear ( c , y ) when SymLinear . is_zero y -> Some c | _ -> None
fun x -> match x with Linear ( c , y ) when SymLinear . is_zero y -> Some c | _ -> None
(* substitution symbols in ``x'' with respect to ``map'' *)
let subst : default : t -> t -> t bottom_lifted SubstMap . t -> t bottom_lifted =
fun ~ default x map ->
let subst_helper s y x =
let y' =
match y with
| Bottom
-> Bottom
| NonBottom r
-> NonBottom ( if Symbol . is_unsigned s then ub ~ default : r zero r else r )
in
subst1 ~ default x s y'
in
SubstMap . fold subst_helper map ( NonBottom x )
let plus_l : t -> t -> t =
let plus_l : t -> t -> t =
fun x y ->
fun x y ->
match ( x , y ) with
match ( x , y ) with
@ -550,7 +601,7 @@ module Bound = struct
| MinMax ( c1 , sign , min_max , d1 , x1 ) , Linear ( c2 , x2 )
| MinMax ( c1 , sign , min_max , d1 , x1 ) , Linear ( c2 , x2 )
| Linear ( c2 , x2 ) , MinMax ( c1 , sign , min_max , d1 , x1 )
| Linear ( c2 , x2 ) , MinMax ( c1 , sign , min_max , d1 , x1 )
when SymLinear . is_zero x2
when SymLinear . is_zero x2
-> MinMax ( c1 + c2 , sign , min_max , d1 , x1 )
-> mk_ MinMax ( c1 + c2 , sign , min_max , d1 , x1 )
| MinMax ( c1 , Plus , Max , d1 , _ ) , Linear ( c2 , x2 )
| MinMax ( c1 , Plus , Max , d1 , _ ) , Linear ( c2 , x2 )
| Linear ( c2 , x2 ) , MinMax ( c1 , Plus , Max , d1 , _ )
| Linear ( c2 , x2 ) , MinMax ( c1 , Plus , Max , d1 , _ )
-> Linear ( c1 + d1 + c2 , x2 )
-> Linear ( c1 + d1 + c2 , x2 )
@ -572,7 +623,7 @@ module Bound = struct
| MinMax ( c1 , sign , min_max , d1 , x1 ) , Linear ( c2 , x2 )
| MinMax ( c1 , sign , min_max , d1 , x1 ) , Linear ( c2 , x2 )
| Linear ( c2 , x2 ) , MinMax ( c1 , sign , min_max , d1 , x1 )
| Linear ( c2 , x2 ) , MinMax ( c1 , sign , min_max , d1 , x1 )
when SymLinear . is_zero x2
when SymLinear . is_zero x2
-> MinMax ( c1 + c2 , sign , min_max , d1 , x1 )
-> mk_ MinMax ( c1 + c2 , sign , min_max , d1 , x1 )
| MinMax ( c1 , Plus , Min , d1 , _ ) , Linear ( c2 , x2 )
| MinMax ( c1 , Plus , Min , d1 , _ ) , Linear ( c2 , x2 )
| Linear ( c2 , x2 ) , MinMax ( c1 , Plus , Min , d1 , _ )
| Linear ( c2 , x2 ) , MinMax ( c1 , Plus , Min , d1 , _ )
-> Linear ( c1 + d1 + c2 , x2 )
-> Linear ( c1 + d1 + c2 , x2 )
@ -619,7 +670,7 @@ module Bound = struct
| Linear ( c , x )
| Linear ( c , x )
-> Some ( Linear ( - c , SymLinear . neg x ) )
-> Some ( Linear ( - c , SymLinear . neg x ) )
| MinMax ( c , sign , min_max , d , x )
| MinMax ( c , sign , min_max , d , x )
-> Some ( MinMax ( - c , neg_sign sign , min_max , d , x ) )
-> Some ( mk_ MinMax ( - c , neg_sign sign , min_max , d , x ) )
let get_symbols : t -> Symbol . t list = function
let get_symbols : t -> Symbol . t list = function
| MInf | PInf
| MInf | PInf
@ -724,12 +775,8 @@ module ItvPure = struct
let make_sym : unsigned : bool -> Typ . Procname . t -> ( unit -> int ) -> t =
let make_sym : unsigned : bool -> Typ . Procname . t -> ( unit -> int ) -> t =
fun ~ unsigned pname new_sym_num ->
fun ~ unsigned pname new_sym_num ->
let lower =
let lower = Bound . of_sym ( SymLinear . make ~ unsigned pname ( new_sym_num () ) ) in
if unsigned then
let upper = Bound . of_sym ( SymLinear . make ~ unsigned pname ( new_sym_num () ) ) in
Bound . MinMax ( 0 , Bound . Plus , Bound . Max , 0 , Symbol . make pname ( new_sym_num () ) )
else Bound . of_sym ( SymLinear . make pname ( new_sym_num () ) )
in
let upper = Bound . of_sym ( SymLinear . make pname ( new_sym_num () ) ) in
( lower , upper )
( lower , upper )
let m1_255 = ( Bound . minus_one , Bound . _255 )
let m1_255 = ( Bound . minus_one , Bound . _255 )
@ -911,21 +958,21 @@ module ItvPure = struct
| ( l1 , Bound . Linear ( c1 , s1 ) ) , ( _ , Bound . Linear ( c2 , s2 ) ) when SymLinear . eq s1 s2
| ( l1 , Bound . Linear ( c1 , s1 ) ) , ( _ , Bound . Linear ( c2 , s2 ) ) when SymLinear . eq s1 s2
-> ( l1 , Bound . Linear ( min c1 c2 , s1 ) )
-> ( l1 , Bound . Linear ( min c1 c2 , s1 ) )
| ( l1 , Bound . Linear ( c , se ) ) , ( _ , u ) when SymLinear . is_zero se && Bound . is_one_symbol u
| ( l1 , Bound . Linear ( c , se ) ) , ( _ , u ) when SymLinear . is_zero se && Bound . is_one_symbol u
-> ( l1 , Bound . MinMax ( 0 , Bound . Plus , Bound . Min , c , Bound . get_one_symbol u ) )
-> ( l1 , Bound . mk_ MinMax ( 0 , Bound . Plus , Bound . Min , c , Bound . get_one_symbol u ) )
| ( l1 , u ) , ( _ , Bound . Linear ( c , se ) ) when SymLinear . is_zero se && Bound . is_one_symbol u
| ( l1 , u ) , ( _ , Bound . Linear ( c , se ) ) when SymLinear . is_zero se && Bound . is_one_symbol u
-> ( l1 , Bound . MinMax ( 0 , Bound . Plus , Bound . Min , c , Bound . get_one_symbol u ) )
-> ( l1 , Bound . mk_ MinMax ( 0 , Bound . Plus , Bound . Min , c , Bound . get_one_symbol u ) )
| ( l1 , Bound . Linear ( c , se ) ) , ( _ , u ) when SymLinear . is_zero se && Bound . is_mone_symbol u
| ( l1 , Bound . Linear ( c , se ) ) , ( _ , u ) when SymLinear . is_zero se && Bound . is_mone_symbol u
-> ( l1 , Bound . MinMax ( 0 , Bound . Minus , Bound . Max , - c , Bound . get_mone_symbol u ) )
-> ( l1 , Bound . mk_ MinMax ( 0 , Bound . Minus , Bound . Max , - c , Bound . get_mone_symbol u ) )
| ( l1 , u ) , ( _ , Bound . Linear ( c , se ) ) when SymLinear . is_zero se && Bound . is_mone_symbol u
| ( l1 , u ) , ( _ , Bound . Linear ( c , se ) ) when SymLinear . is_zero se && Bound . is_mone_symbol u
-> ( l1 , Bound . MinMax ( 0 , Bound . Minus , Bound . Max , - c , Bound . get_mone_symbol u ) )
-> ( l1 , Bound . mk_ MinMax ( 0 , Bound . Minus , Bound . Max , - c , Bound . get_mone_symbol u ) )
| ( l1 , Bound . Linear ( c1 , se ) ) , ( _ , Bound . MinMax ( c2 , Bound . Plus , Bound . Min , d2 , se' ) )
| ( l1 , Bound . Linear ( c1 , se ) ) , ( _ , Bound . MinMax ( c2 , Bound . Plus , Bound . Min , d2 , se' ) )
| ( l1 , Bound . MinMax ( c2 , Bound . Plus , Bound . Min , d2 , se' ) ) , ( _ , Bound . Linear ( c1 , se ) )
| ( l1 , Bound . MinMax ( c2 , Bound . Plus , Bound . Min , d2 , se' ) ) , ( _ , Bound . Linear ( c1 , se ) )
when SymLinear . is_zero se
when SymLinear . is_zero se
-> ( l1 , Bound . MinMax ( c2 , Bound . Plus , Bound . Min , min ( c1 - c2 ) d2 , se' ) )
-> ( l1 , Bound . mk_ MinMax ( c2 , Bound . Plus , Bound . Min , min ( c1 - c2 ) d2 , se' ) )
| ( ( l1 , Bound . MinMax ( c1 , Bound . Plus , Bound . Min , d1 , se1 ) )
| ( ( l1 , Bound . MinMax ( c1 , Bound . Plus , Bound . Min , d1 , se1 ) )
, ( _ , Bound . MinMax ( c2 , Bound . Plus , Bound . Min , d2 , se2 ) ) )
, ( _ , Bound . MinMax ( c2 , Bound . Plus , Bound . Min , d2 , se2 ) ) )
when Int . equal c1 c2 && Symbol . eq se1 se2
when Int . equal c1 c2 && Symbol . eq se1 se2
-> ( l1 , Bound . MinMax ( c1 , Bound . Plus , Bound . Min , min d1 d2 , se1 ) )
-> ( l1 , Bound . mk_ MinMax ( c1 , Bound . Plus , Bound . Min , min d1 d2 , se1 ) )
| _
| _
-> x
-> x
@ -937,21 +984,21 @@ module ItvPure = struct
| ( Bound . Linear ( c1 , s1 ) , u1 ) , ( Bound . Linear ( c2 , s2 ) , _ ) when SymLinear . eq s1 s2
| ( Bound . Linear ( c1 , s1 ) , u1 ) , ( Bound . Linear ( c2 , s2 ) , _ ) when SymLinear . eq s1 s2
-> ( Bound . Linear ( max c1 c2 , s1 ) , u1 )
-> ( Bound . Linear ( max c1 c2 , s1 ) , u1 )
| ( Bound . Linear ( c , se ) , u1 ) , ( l , _ ) when SymLinear . is_zero se && Bound . is_one_symbol l
| ( Bound . Linear ( c , se ) , u1 ) , ( l , _ ) when SymLinear . is_zero se && Bound . is_one_symbol l
-> ( Bound . MinMax ( 0 , Bound . Plus , Bound . Max , c , Bound . get_one_symbol l ) , u1 )
-> ( Bound . mk_ MinMax ( 0 , Bound . Plus , Bound . Max , c , Bound . get_one_symbol l ) , u1 )
| ( l , u1 ) , ( Bound . Linear ( c , se ) , _ ) when SymLinear . is_zero se && Bound . is_one_symbol l
| ( l , u1 ) , ( Bound . Linear ( c , se ) , _ ) when SymLinear . is_zero se && Bound . is_one_symbol l
-> ( Bound . MinMax ( 0 , Bound . Plus , Bound . Max , c , Bound . get_one_symbol l ) , u1 )
-> ( Bound . mk_ MinMax ( 0 , Bound . Plus , Bound . Max , c , Bound . get_one_symbol l ) , u1 )
| ( Bound . Linear ( c , se ) , u1 ) , ( l , _ ) when SymLinear . is_zero se && Bound . is_mone_symbol l
| ( Bound . Linear ( c , se ) , u1 ) , ( l , _ ) when SymLinear . is_zero se && Bound . is_mone_symbol l
-> ( Bound . MinMax ( 0 , Bound . Minus , Bound . Min , c , Bound . get_mone_symbol l ) , u1 )
-> ( Bound . mk_ MinMax ( 0 , Bound . Minus , Bound . Min , c , Bound . get_mone_symbol l ) , u1 )
| ( l , u1 ) , ( Bound . Linear ( c , se ) , _ ) when SymLinear . is_zero se && Bound . is_mone_symbol l
| ( l , u1 ) , ( Bound . Linear ( c , se ) , _ ) when SymLinear . is_zero se && Bound . is_mone_symbol l
-> ( Bound . MinMax ( 0 , Bound . Minus , Bound . Min , c , Bound . get_mone_symbol l ) , u1 )
-> ( Bound . mk_ MinMax ( 0 , Bound . Minus , Bound . Min , c , Bound . get_mone_symbol l ) , u1 )
| ( Bound . Linear ( c1 , se ) , u1 ) , ( Bound . MinMax ( c2 , Bound . Plus , Bound . Max , d2 , se' ) , _ )
| ( Bound . Linear ( c1 , se ) , u1 ) , ( Bound . MinMax ( c2 , Bound . Plus , Bound . Max , d2 , se' ) , _ )
| ( Bound . MinMax ( c2 , Bound . Plus , Bound . Max , d2 , se' ) , u1 ) , ( Bound . Linear ( c1 , se ) , _ )
| ( Bound . MinMax ( c2 , Bound . Plus , Bound . Max , d2 , se' ) , u1 ) , ( Bound . Linear ( c1 , se ) , _ )
when SymLinear . is_zero se
when SymLinear . is_zero se
-> ( Bound . MinMax ( c2 , Bound . Plus , Bound . Max , max ( c1 - c2 ) d2 , se' ) , u1 )
-> ( Bound . mk_ MinMax ( c2 , Bound . Plus , Bound . Max , max ( c1 - c2 ) d2 , se' ) , u1 )
| ( ( Bound . MinMax ( c1 , Bound . Plus , Bound . Max , d1 , se1 ) , u1 )
| ( ( Bound . MinMax ( c1 , Bound . Plus , Bound . Max , d1 , se1 ) , u1 )
, ( Bound . MinMax ( c2 , Bound . Plus , Bound . Max , d2 , se2 ) , _ ) )
, ( Bound . MinMax ( c2 , Bound . Plus , Bound . Max , d2 , se2 ) , _ ) )
when Int . equal c1 c2 && Symbol . eq se1 se2
when Int . equal c1 c2 && Symbol . eq se1 se2
-> ( Bound . MinMax ( c1 , Bound . Plus , Bound . Max , max d1 d2 , se1 ) , u1 )
-> ( Bound . mk_ MinMax ( c1 , Bound . Plus , Bound . Max , max d1 d2 , se1 ) , u1 )
| _
| _
-> x
-> x