Module Fval

module Fval: sig .. end

Floating-point intervals, used to construct arithmetic lattices. The interfaces of this module may change between Frama-C versions. Contact us if you need stable APIs.


type kind = Float_sig.prec = 
| Single (*

32 bits float (a.k.a 'float' C type)

*)
| Double (*

64 bits float (a.k.a 'double' C type)

*)
| Long_Double
| Real (*

set of real

*)
val pretty_kind : Stdlib.Format.formatter -> kind -> unit
module F: sig .. end
include Float_interval_sig.S
val round_to_single_precision_float : t -> t
val inject : ?nan:bool -> kind -> F.t -> F.t -> t

inject creates an abstract float interval. It handles infinities, flush-to-zero (rounding subnormals if needed) and NaN. Inputs must be compatible with float_kind. Raises no exceptions (unless values are not compatible with float_kind, in which case execution is aborted). The two floating point numbers must be ordered (so not NaN). ~nan indicates if NaN is present.

val inject_singleton : F.t -> t
val top : t
val plus_zero : t
val minus_zero : t
val zeros : t

Both positive and negative zero

val pi : t

Real representation of \pi.

val e : t

Real representation of \e.

val contains_plus_zero : t -> bool
val meet : t -> t -> t Lattice_bounds.or_bottom
val is_singleton : t -> bool

Returns true on NaN. We expect this function to be e.g. to perform subdivisions/enumerations. The size of the concretization is less interesting to us. (And it is also possible to consider that there is only one NaN value in the concrete anyway.)

exception Not_Singleton_Float
val project_float : t -> F.t
val subdiv_float_interval : kind -> t -> t * t

Raise Can_not_subdiv if it can't be subdivided

Discussion regarding kind and the 3 functions below.

Support for fesetround(FE_UPWARD) and fesetround(FE_DOWNWARD) seems to be especially poor, including in not-so-old versions of Glibc (https://sourceware.org/bugzilla/show_bug.cgi?id=3976). The code for Fval.exp, Fval.log and Fval.log10 is correct wrt. kind=Reak ONLY if the C implementation of these functions is correct in directed rounding modes. Otherwise, anything could happen, including crashes. For now, unless the Libc is known to be reliable, these functions should be called with rounding_mode=Nearest_Even only. Also note that there the Glibc does not guarantee that f(FE_DOWNWARD) <= f(FE_TONEAREST) <= f(FE_UPWARD), which implies that using different rounding modes to bound the final result does not ensure correct bounds. Here's an example where it does not hold (glibc 2.21): log10f(3, FE_TONEAREST) < log10f(3, FE_DOWNWARD).

Also, we have observed bugs in powf, which is called when kind=Float32.

val exp : kind -> t -> t
val log : kind -> t -> t
val log10 : kind -> t -> t
val floor : kind -> t -> t
val ceil : kind -> t -> t
val trunc : kind -> t -> t
val fround : kind -> t -> t
val backward_cast_float_to_double : t -> t Lattice_bounds.or_bottom

backward_cast_float_to_double d return all possible float32 f such that (double)f = d. The double of d that have no float32 equivalent are discarded.

val backward_cast_double_to_real : t -> t
val kind : Cil_types.fkind -> kind

Classify a Cil_types.fkind as either a 32 or 64 floating-point type. Long double are over approximated by Reals