Module Int_val

module Int_val: sig .. end

Integer values abstractions: an abstraction represents a set of integers. Provided with a lattice structure and over-approximations of arithmetic operations.

Abstractions do not represent the empty set. Instead, operations creating empty sets return `Bottom.

include Datatype.S_with_collections

module Widen_Hints: Datatype.Integer.Set

type size_widen_hint = Integer.t

type generic_widen_hint = Widen_Hints.t

include Eva_lattice_type.Full_AI_Lattice_with_cardinality

val zero : t

val one : t

val minus_one : t

val zero_or_one : t

val positive_integers : t

All positive integers, including 0.

val negative_integers : t

All negative integers, including 0.

Building.

val inject_singleton : Integer.t -> t

Returns an exact abstraction of the given integer.

val inject_range : Integer.t option -> Integer.t option -> t

inject_range min max returns an abstraction of all integers between min and max included. None means that the abstraction is unbounded.

val inject_interval : min:Integer.t option ->
       max:Integer.t option -> rem:Integer.t -> modu:Integer.t -> t

Builds an abstraction of all integers between min and max included and congruent to rem modulo modu. For min and max, None is the corresponding infinity. Checks that min <= max, modu > 0 and 0 <= rest < modu, and fails otherwise. If possible, reduces min and max according to the modulo.

val make : min:Integer.t option ->
       max:Integer.t option -> rem:Integer.t -> modu:Integer.t -> t

As inject_interval, but also checks that min and max are congruent to rem modulo modu.

Accessors.

val min_int : t -> Integer.t option

Returns the smallest integer represented by an abstraction. Returns None if it does not exist, i.e. if the abstraction is unbounded.

val max_int : t -> Integer.t option

Returns the highest integer represented by an abstraction. Returns None if it does not exist, i.e. if the abstraction is unbouded.

val min_and_max : t -> Integer.t option * Integer.t option

Returns the smallest and highest integers represented by an abstraction.

val min_max_rem_modu : t -> Integer.t option * Integer.t option * Integer.t * Integer.t

Returns min, max, rem, modu such that for all integers i represented by the given abstraction, i satisfies min ≤ i ≤ max and i ≅ rem modu.

exception Not_Singleton

val project_int : t -> Integer.t

Projects a singleton abstraction into an integer.

Raises Not_Singleton if the cardinal of the argument is not 1.

val is_small_set : t -> bool

Is an abstraction internally represented as a small integer set?

val project_small_set : t -> Integer.t list option

Cardinality.

val is_singleton : t -> bool

val cardinal_zero_or_one : t -> bool

val cardinal : t -> Integer.t option

val cardinal_estimate : size:Integer.t -> t -> Integer.t

val cardinal_less_than : t -> int -> int

val cardinal_is_less_than : t -> int -> bool

val is_zero : t -> bool

val contains_zero : t -> bool

val contains_non_zero : t -> bool

Arithmetics.

val add : t -> t -> t

Addition of two integer abstractions.

val add_under : t -> t -> t Lattice_bounds.or_bottom

Under-approximation of the addition of two integer abstractions

val add_singleton : Integer.t -> t -> t

Addition of an integer abstraction with a singleton integer. Exact operation.

val neg : t -> t

Negation of an integer abstraction.

val abs : t -> t

Absolute value of an integer abstraction.

val scale : Integer.t -> t -> t

scale f v returns an abstraction of the integers f * x for all x in v. This operation is exact.

val scale_div : pos:bool -> Integer.t -> t -> t

scale_div f v is an over-approximation of the elements x / f for all elements x in v. Uses the computer division (like in C99) if pos is false, and the euclidean division if pos is true.

val scale_div_under : pos:bool -> Integer.t -> t -> t Lattice_bounds.or_bottom

Under-approximation of the division.

val scale_rem : pos:bool -> Integer.t -> t -> t

Over-approximation of the remainder of the division. Uses the computer division (like in C99) if pos is false, and the euclidean division if pos is true.

val mul : t -> t -> t

val div : t -> t -> t Lattice_bounds.or_bottom

val c_rem : t -> t -> t Lattice_bounds.or_bottom

val shift_left : t -> t -> t Lattice_bounds.or_bottom

val shift_right : t -> t -> t Lattice_bounds.or_bottom

val bitwise_and : t -> t -> t

val bitwise_or : t -> t -> t

val bitwise_xor : t -> t -> t

val bitwise_signed_not : t -> t

val bitwise_unsigned_not : size:int -> t -> t

Misc

val cast_int_to_int : size:Integer.t -> signed:bool -> t -> t

val subdivide : t -> t * t

Splits an abstraction into two abstractions.

val extract_bits : start:Integer.t -> stop:Integer.t -> t -> t

Extracts bits from start to stop from the given integer abstraction, start and stop being included.

val create_all_values : signed:bool -> size:int -> t

Builds an abstraction of all integers in a C integer type.

val all_values : size:Integer.t -> t -> bool

all_values ~size v returns true iff v contains all integer values representable in size bits.

val overlaps : partial:bool -> size:Integer.t -> t -> t -> bool

val complement_under : size:int -> signed:bool -> t -> t Lattice_bounds.or_bottom

Returns an under-approximation of the integers of the given size and signedness that are *not* represented by the given value.

val fold_int : ?increasing:bool -> (Integer.t -> 'a -> 'a) -> t -> 'a -> 'a

Iterates on all integers represented by an abstraction, in increasing order by default. If increasing is set to false, iterate by decreasing order.

Raises Abstract_interp.Error_Top if the abstraction is unbounded.