phanerozoic/Why3 · Datasets at Hugging Face

statement stringlengths 1 15.9k	proof stringlengths 0 44.6k	type stringclasses 18 values	symbolic_name stringlengths 1 61	library stringclasses 21 values	filename stringclasses 502 values	imports listlengths 0 38	deps listlengths 0 64	docstring stringlengths 0 500	source_url stringclasses 1 value	commit stringclasses 1 value
round_error (x : t) : real	= abs (value x - exact x)	function	round_error	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "abs", "exact", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
total_error (x : t) : real	= abs (value x - model x)	function	total_error	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "abs", "model", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
max : real		constant	max	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
no_overflow (m:mode) (x:real)	= abs (round m x) <= max	predicate	no_overflow	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "abs", "max", "mode", "round" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
Bounded_real_no_overflow : forall m:mode, x:real. abs x <= max -> no_overflow m x		axiom	Bounded_real_no_overflow	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "abs", "max", "mode", "no_overflow" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
Round_monotonic : forall m:mode, x y:real. x <= y -> round m x <= round m y		axiom	Round_monotonic	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "mode", "round" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
Round_idempotent : forall m1 m2:mode, x:real. round m1 (round m2 x) = round m2 x		axiom	Round_idempotent	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "mode", "round" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
Round_value : forall m:mode, x:t. round m (value x) = value x		axiom	Round_value	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "mode", "round", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
Bounded_value : forall x:t. abs (value x) <= max		axiom	Bounded_value	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "abs", "max", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
max_representable_integer : int		constant	max_representable_integer	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "int" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
Exact_rounding_for_integers: forall m:mode,i:int. Int.(<=) (Int.(-_) max_representable_integer) i /\ Int.(<=) i max_representable_integer -> round m (from_int i) = from_int i		axiom	Exact_rounding_for_integers	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "from_int", "int", "max_representable_integer", "mode", "round" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
Round_down_le: forall x:real. round Down x <= x		axiom	Round_down_le	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "round" ]	rounding up and down	https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
Round_up_ge: forall x:real. round Up x >= x		axiom	Round_up_ge	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "round" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
Round_down_neg: forall x:real. round Down (-x) = - round Up x		axiom	Round_down_neg	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "round" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
Round_up_neg: forall x:real. round Up (-x) = - round Down x		axiom	Round_up_neg	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "round" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
round_logic mode real : t		function	round_logic	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "mode" ]	rounding into a float instead of a real	https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
Round_logic_def: forall m:mode, x:real. no_overflow m x -> value (round_logic m x) = round m x		axiom	Round_logic_def	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "mode", "no_overflow", "round", "round_logic", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
single		type	single	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
max_single : real	= 0x1.FFFFFEp127	constant	max_single	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
max_int : int	= 16777216	constant	max_int	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "int" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
double		type	double	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
max_double : real	= 0x1.FFFFFFFFFFFFFp1023	constant	max_double	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
max_int : int	= 9007199254740992	constant	max_int	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "int" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
of_real_post (m:mode) (x:real) (res:t)	= value res = round m x /\ exact res = x /\ model res = x	predicate	of_real_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "exact", "mode", "model", "round", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
add_post (m:mode) (x y res:t)	= value res = round m (value x + value y) /\ exact res = exact x + exact y /\ model res = model x + model y	predicate	add_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "exact", "mode", "model", "round", "value" ]	{3 binary operations}	https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
sub_post (m:mode) (x y res:t)	= value res = round m (value x - value y) /\ exact res = exact x - exact y /\ model res = model x - model y	predicate	sub_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "exact", "mode", "model", "round", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
mul_post (m:mode) (x y res:t)	= value res = round m (value x * value y) /\ exact res = exact x * exact y /\ model res = model x * model y	predicate	mul_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "exact", "mode", "model", "round", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
div_post (m:mode) (x y res:t)	= value res = round m (value x / value y) /\ exact res = exact x / exact y /\ model res = model x / model y	predicate	div_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "exact", "mode", "model", "round", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
neg_post (x res:t)	= value res = - value x /\ exact res = - exact x /\ model res = - model x	predicate	neg_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "exact", "model", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
lt (x:t) (y:t)	= value x < value y	predicate	lt	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "value" ]	{3 Comparisons}	https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
gt (x:t) (y:t)	= value x > value y	predicate	gt	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
class t : class		function	class	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[]	{3 special values}	https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
is_finite (x:t)	= class x = Finite	predicate	is_finite	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "class" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
is_infinite (x:t)	= class x = Infinite	predicate	is_infinite	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "class" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
is_NaN (x:t)	= class x = NaN	predicate	is_NaN	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "class" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
is_not_NaN (x:t)	= is_finite x \/ is_infinite x	predicate	is_not_NaN	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "is_finite", "is_infinite" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
is_not_NaN: forall x:t. is_not_NaN x <-> not (is_NaN x)		lemma	is_not_NaN	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "is_NaN" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
sign t : sign		function	sign	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
same_sign_real (x:t) (y:real)	= SpecialValues.same_sign_real (sign x) y	predicate	same_sign_real	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "sign" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
same_sign (x:t) (y:t)	= sign x = sign y	predicate	same_sign	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "sign" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
diff_sign (x:t) (y:t)	= sign x <> sign y	predicate	diff_sign	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "sign" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
sign_zero_result (m:mode) (x:t)	= value x = 0.0 -> match m with \| Down -> sign x = Neg \| _ -> sign x = Pos end	predicate	sign_zero_result	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "Neg", "mode", "sign", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
is_minus_infinity (x:t)	= is_infinite x /\ sign x = Neg	predicate	is_minus_infinity	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "Neg", "is_infinite", "sign" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
is_plus_infinity (x:t)	= is_infinite x /\ sign x = Pos	predicate	is_plus_infinity	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "is_infinite", "sign" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
is_gen_zero (x:t)	= is_finite x /\ value x = 0.0	predicate	is_gen_zero	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "is_finite", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
is_gen_zero_plus (x:t)	= is_gen_zero x /\ sign x = Pos	predicate	is_gen_zero_plus	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "is_gen_zero", "sign" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
is_gen_zero_minus (x:t)	= is_gen_zero x /\ sign x = Neg	predicate	is_gen_zero_minus	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "Neg", "is_gen_zero", "sign" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
finite_sign : forall x:t. class x = Finite /\ value x <> 0.0 -> same_sign_real x (value x)		lemma	finite_sign	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "class", "same_sign_real", "value" ]	non-zero finite gen_float has the same sign as its float_value	https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
finite_sign_pos1: forall x:t. class x = Finite /\ value x > 0.0 -> sign x = Pos		lemma	finite_sign_pos1	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "class", "sign", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
finite_sign_pos2: forall x:t. class x = Finite /\ value x <> 0.0 /\ sign x = Pos -> value x > 0.0		lemma	finite_sign_pos2	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "class", "sign", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
finite_sign_neg1: forall x:t. class x = Finite /\ value x < 0.0 -> sign x = Neg		lemma	finite_sign_neg1	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "Neg", "class", "sign", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
finite_sign_neg2: forall x:t. class x = Finite /\ value x <> 0.0 /\ sign x = Neg -> value x < 0.0		lemma	finite_sign_neg2	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "Neg", "class", "sign", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
diff_sign_trans: forall x y z:t. diff_sign x y /\ diff_sign y z -> same_sign x z		lemma	diff_sign_trans	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "diff_sign", "same_sign" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
diff_sign_product: forall x y:t. class x = Finite /\ class y = Finite /\ value x * value y < 0.0 -> diff_sign x y		lemma	diff_sign_product	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "class", "diff_sign", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
same_sign_product: forall x y:t. class x = Finite /\ class y = Finite /\ same_sign x y -> value x * value y >= 0.0		lemma	same_sign_product	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "class", "same_sign", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
overflow_value (m:mode) (x:t)	= match m, sign x with \| Down, Neg -> is_infinite x \| Down, Pos -> is_finite x /\ value x = max \| Up, Neg -> is_finite x /\ value x = - max \| Up, Pos -> is_infinite x \| ToZero, Neg -> is_finite x /\ value x = - max \| ToZero, Pos -> is_finite x /\ value x = max \| (NearestTiesToAway \| Near...	predicate	overflow_value	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "Neg", "is_finite", "is_infinite", "max", "mode", "sign", "value" ]	This predicate tells what is the result of a rounding in case of overflow	https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
round1 : forall m:mode, x:real. no_overflow m x -> is_finite (round_logic m x) /\ value(round_logic m x) = round m x		lemma	round1	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "is_finite", "mode", "no_overflow", "round", "round_logic", "value" ]	rounding in logic	https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
round2 : forall m:mode, x:real. not no_overflow m x -> same_sign_real (round_logic m x) x /\ overflow_value m (round_logic m x)		lemma	round2	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "mode", "no_overflow", "overflow_value", "round_logic", "same_sign_real" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
round3 : forall m:mode, x:real. exact (round_logic m x) = x		lemma	round3	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "exact", "mode", "round_logic" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
round4 : forall m:mode, x:real. model (round_logic m x) = x		lemma	round4	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "mode", "model", "round_logic" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
round_of_zero : forall m:mode. is_gen_zero (round_logic m 0.0)		lemma	round_of_zero	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "is_gen_zero", "mode", "round_logic" ]	rounding of zero	https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
round_logic_le : forall m:mode, x:real. is_finite (round_logic m x) -> abs (value (round_logic m x)) <= max		lemma	round_logic_le	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "abs", "is_finite", "max", "mode", "round_logic", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
round_no_overflow : forall m:mode, x:real. abs x <= max -> is_finite (round_logic m x) /\ value (round_logic m x) = round m x		lemma	round_no_overflow	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "abs", "is_finite", "max", "mode", "round", "round_logic", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
min : real		constant	min	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
positive_constant : forall m:mode, x:real. min <= x <= max -> is_finite (round_logic m x) /\ value (round_logic m x) > 0.0 /\ sign (round_logic m x) = Pos		lemma	positive_constant	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "is_finite", "max", "min", "mode", "round_logic", "sign", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
negative_constant : forall m:mode, x:real. - max <= x <= - min -> is_finite (round_logic m x) /\ value (round_logic m x) < 0.0 /\ sign (round_logic m x) = Neg		lemma	negative_constant	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "Neg", "is_finite", "max", "min", "mode", "round_logic", "sign", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
is_gen_zero_comp1 : forall x y:t. is_gen_zero x /\ value x = value y /\ is_finite y -> is_gen_zero y		lemma	is_gen_zero_comp1	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "is_finite", "is_gen_zero", "value" ]	lemmas on `gen_zero`	https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
is_gen_zero_comp2 : forall x y:t. is_finite x /\ not (is_gen_zero x) /\ value x = value y -> not (is_gen_zero y)		lemma	is_gen_zero_comp2	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "is_finite", "is_gen_zero", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
add_post (m:mode) (x:t) (y:t) (r:t)	= (is_NaN x \/ is_NaN y -> is_NaN r) /\ (is_finite x /\ is_infinite y -> is_infinite r /\ same_sign r y) /\ (is_infinite x /\ is_finite y -> is_infinite r /\ same_sign r x) /\ (is_infinite x /\ is_infinite y -> if same_sign x y then is_infinite r /\ same_sign r x else is_NaN r) ...	predicate	add_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "exact", "is_NaN", "is_finite", "is_infinite", "mode", "model", "no_overflow", "overflow_value", "round", "same_sign", "same_sign_real", "sign", "sign_zero_result", "value" ]	{3 binary operations}	https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
sub_post (m:mode) (x:t) (y:t) (r:t)	= (is_NaN x \/ is_NaN y -> is_NaN r) /\ (is_finite x /\ is_infinite y -> is_infinite r /\ diff_sign r y) /\ (is_infinite x /\ is_finite y -> is_infinite r /\ same_sign r x) /\ (is_infinite x /\ is_infinite y -> if diff_sign x y then is_infinite r /\ same_sign r x else is_NaN r) ...	predicate	sub_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "diff_sign", "exact", "is_NaN", "is_finite", "is_infinite", "mode", "model", "no_overflow", "overflow_value", "round", "same_sign", "same_sign_real", "sign", "sign_zero_result", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
product_sign (z x y: t)	= (same_sign x y -> sign z = Pos) /\ (diff_sign x y -> sign z = Neg)	predicate	product_sign	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "Neg", "diff_sign", "same_sign", "sign" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
mul_post (m:mode) (x:t) (y:t) (r:t)	= (is_NaN x \/ is_NaN y -> is_NaN r) /\ (is_gen_zero x /\ is_infinite y -> is_NaN r) /\ (is_finite x /\ is_infinite y /\ value x <> 0.0 -> is_infinite r) /\ (is_infinite x /\ is_gen_zero y -> is_NaN r) /\ (is_infinite x /\ is_finite y /\ value y <> 0.0 -> is_infinite r) /\ (is_...	predicate	mul_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "exact", "is_NaN", "is_finite", "is_gen_zero", "is_infinite", "mode", "model", "no_overflow", "overflow_value", "product_sign", "round", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
neg_post (x:t) (r:t)	= (is_NaN x -> is_NaN r) /\ (is_infinite x -> is_infinite r) /\ (is_finite x -> is_finite r /\ value r = - value x) /\ (not is_NaN r -> diff_sign r x) /\ exact r = - exact x /\ model r = - model x	predicate	neg_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "diff_sign", "exact", "is_NaN", "is_finite", "is_infinite", "model", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
div_post (m:mode) (x:t) (y:t) (r:t)	= (is_NaN x \/ is_NaN y -> is_NaN r) /\ (is_finite x /\ is_infinite y -> is_gen_zero r) /\ (is_infinite x /\ is_finite y -> is_infinite r) /\ (is_infinite x /\ is_infinite y -> is_NaN r) /\ (is_finite x /\ is_finite y /\ value y <> 0.0 /\ no_overflow m (value x / value y) -> is_finit...	predicate	div_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "exact", "is_NaN", "is_finite", "is_gen_zero", "is_infinite", "mode", "model", "no_overflow", "overflow_value", "product_sign", "round", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
fma_post (m:mode) (x y z:t) (r:t)	= (is_NaN x \/ is_NaN y \/ is_NaN z -> is_NaN r) /\ (is_gen_zero x /\ is_infinite y -> is_NaN r) /\ (is_infinite x /\ is_gen_zero y -> is_NaN r) /\ (is_finite x /\ value x <> 0.0 /\ is_infinite y /\ is_finite z -> is_infinite r /\ product_sign r x y) /\ (is_finite x /\ value x <> 0.0 /\ is_i...	predicate	fma_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "Neg", "exact", "is_NaN", "is_finite", "is_gen_zero", "is_infinite", "mode", "model", "no_overflow", "overflow_value", "product_sign", "round", "same_sign", "same_sign_real", "sign", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
sqrt_post (m:mode) (x:t) (r:t)	= (is_NaN x -> is_NaN r) /\ (is_plus_infinity x -> is_plus_infinity r) /\ (is_minus_infinity x -> is_NaN r) /\ (is_finite x /\ value x < 0.0 -> is_NaN r) /\ (is_finite x /\ value x = 0.0 -> is_finite r /\ value r = 0.0 /\ same_sign r x) /\ (is_finite x /\ value x > 0.0 -> is_fini...	predicate	sqrt_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "exact", "is_NaN", "is_finite", "is_minus_infinity", "is_plus_infinity", "mode", "model", "round", "same_sign", "sign", "sqrt", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
of_real_exact_post (x:real) (r:t)	= is_finite r /\ value r = x /\ exact r = x /\ model r = x	predicate	of_real_exact_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "exact", "is_finite", "model", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
le (x:t) (y:t)	= (is_finite x /\ is_finite y /\ value x <= value y) \/ (is_minus_infinity x /\ is_not_NaN y) \/ (is_not_NaN x /\ is_plus_infinity y)	predicate	le	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "is_finite", "is_minus_infinity", "is_not_NaN", "is_plus_infinity", "value" ]	{3 Comparisons}	https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
lt (x:t) (y:t)	= (is_finite x /\ is_finite y /\ value x < value y) \/ (is_minus_infinity x /\ is_not_NaN y /\ not (is_minus_infinity y)) \/ (is_not_NaN x /\ not (is_plus_infinity x) /\ is_plus_infinity y)	predicate	lt	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "is_finite", "is_minus_infinity", "is_not_NaN", "is_plus_infinity", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
ge (x:t) (y:t)	= le y x	predicate	ge	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "le" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
gt (x:t) (y:t)	= lt y x	predicate	gt	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "lt" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
eq (x:t) (y:t)	= (is_finite x /\ is_finite y /\ value x = value y) \/ (is_infinite x /\ is_infinite y /\ same_sign x y)	predicate	eq	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "is_finite", "is_infinite", "same_sign", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
ne (x:t) (y:t)	= not (eq x y)	predicate	ne	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "eq" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
le_lt_trans: forall x y z:t. le x y /\ lt y z -> lt x z		lemma	le_lt_trans	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "le", "lt" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
lt_le_trans: forall x y z:t. lt x y /\ le y z -> lt x z		lemma	lt_le_trans	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "le", "lt" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
le_ge_asym: forall x y:t. le x y /\ ge x y -> eq x y		lemma	le_ge_asym	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "eq", "ge", "le" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
not_lt_ge: forall x y:t. not (lt x y) /\ is_not_NaN x /\ is_not_NaN y -> ge x y		lemma	not_lt_ge	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "ge", "is_not_NaN", "lt" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
not_gt_le: forall x y:t. not (gt x y) /\ is_not_NaN x /\ is_not_NaN y -> le x y		lemma	not_gt_le	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "gt", "is_not_NaN", "le" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
min_single : real	= 0x1p-149	constant	min_single	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
min_double : real	= 0x1p-1074	constant	min_double	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
min_normalized : real		constant	min_normalized	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[]	{3 binary operations}	https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
eps_normalized : real		constant	eps_normalized	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
eta_normalized : real		constant	eta_normalized	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
add_post (_m:mode) (x y res:t)	= ((* CASE 1 : normalized numbers ) (abs(value x + value y) >= min_normalized -> abs(value res - (value x + value y)) <= eps_normalized abs(value x + value y)) /\ (CASE 2: denormalized numbers ) (abs(value x + value y) <= min_normalized -> abs(value res - (value x + value y)) <=...	predicate	add_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "abs", "eps_normalized", "eta_normalized", "exact", "min_normalized", "mode", "model", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
sub_post (_m:mode) (x y res:t)	= ((* CASE 1 : normalized numbers ) (abs(value x - value y) >= min_normalized -> abs(value res - (value x - value y)) <= eps_normalized abs(value x - value y)) /\ (CASE 2: denormalized numbers ) (abs(value x - value y) <= min_normalized -> abs(value res - (value x - value y)) <=...	predicate	sub_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "abs", "eps_normalized", "eta_normalized", "exact", "min_normalized", "mode", "model", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
mul_post (_m:mode) (x y res:t)	= ((* CASE 1 : normalized numbers ) (abs(value x value y) >= min_normalized -> abs(value res - (value x * value y)) <= eps_normalized * abs(value x * value y)) /\ (CASE 2: denormalized numbers ) (abs(value x * value y) <= min_normalized -> abs(value res - (value x * value y)) <=...	predicate	mul_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "abs", "eps_normalized", "eta_normalized", "exact", "min_normalized", "mode", "model", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
neg_post (_m:mode) (x res:t)	= ((abs(value x) >= min_normalized -> abs(value res - (- value x)) <= eps_normalized * abs(- value x)) /\ (abs(value x) <= min_normalized -> abs(value res - (- value x)) <= eta_normalized)) /\ exact res = - exact x /\ model res = - model x	predicate	neg_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "abs", "eps_normalized", "eta_normalized", "exact", "min_normalized", "mode", "model", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
of_real_exact_post (x:real) (r:t)	= value r = x /\ exact r = x /\ model r = x	predicate	of_real_exact_post	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[ "exact", "model", "value" ]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
min_normalized_double : real	= 0x1p-1022	constant	min_normalized_double	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784
eps_normalized_double : real	= 0x1.004p-53	constant	eps_normalized_double	stdlib	stdlib/floating_point.mlw	[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]	[]		https://gitlab.inria.fr/why3/why3	7c59064b4eed9a4059292599f3a657716aa34784

round_error (x : t) : real

= abs (value x - exact x)

function

round_error

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "abs", "exact", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

total_error (x : t) : real

= abs (value x - model x)

function

total_error

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "abs", "model", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

max : real

constant

max

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

no_overflow (m:mode) (x:real)

= abs (round m x) <= max

predicate

no_overflow

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "abs", "max", "mode", "round" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

Bounded_real_no_overflow : forall m:mode, x:real. abs x <= max -> no_overflow m x

axiom

Bounded_real_no_overflow

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "abs", "max", "mode", "no_overflow" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

Round_monotonic : forall m:mode, x y:real. x <= y -> round m x <= round m y

axiom

Round_monotonic

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "mode", "round" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

Round_idempotent : forall m1 m2:mode, x:real. round m1 (round m2 x) = round m2 x

axiom

Round_idempotent

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "mode", "round" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

Round_value : forall m:mode, x:t. round m (value x) = value x

axiom

Round_value

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "mode", "round", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

Bounded_value : forall x:t. abs (value x) <= max

axiom

Bounded_value

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "abs", "max", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

max_representable_integer : int

constant

max_representable_integer

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "int" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

Exact_rounding_for_integers: forall m:mode,i:int. Int.(<=) (Int.(-_) max_representable_integer) i /\ Int.(<=) i max_representable_integer -> round m (from_int i) = from_int i

axiom

Exact_rounding_for_integers

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "from_int", "int", "max_representable_integer", "mode", "round" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

Round_down_le: forall x:real. round Down x <= x

axiom

Round_down_le

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "round" ]

rounding up and down

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

Round_up_ge: forall x:real. round Up x >= x

axiom

Round_up_ge

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "round" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

Round_down_neg: forall x:real. round Down (-x) = - round Up x

axiom

Round_down_neg

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "round" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

Round_up_neg: forall x:real. round Up (-x) = - round Down x

axiom

Round_up_neg

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "round" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

round_logic mode real : t

function

round_logic

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "mode" ]

rounding into a float instead of a real

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

Round_logic_def: forall m:mode, x:real. no_overflow m x -> value (round_logic m x) = round m x

axiom

Round_logic_def

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "mode", "no_overflow", "round", "round_logic", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

single

type

single

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

max_single : real

= 0x1.FFFFFEp127

constant

max_single

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

max_int : int

= 16777216

constant

max_int

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "int" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

double

type

double

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

max_double : real

= 0x1.FFFFFFFFFFFFFp1023

constant

max_double

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

max_int : int

= 9007199254740992

constant

max_int

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "int" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

of_real_post (m:mode) (x:real) (res:t)

= value res = round m x /\ exact res = x /\ model res = x

predicate

of_real_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "exact", "mode", "model", "round", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

add_post (m:mode) (x y res:t)

= value res = round m (value x + value y) /\ exact res = exact x + exact y /\ model res = model x + model y

predicate

add_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "exact", "mode", "model", "round", "value" ]

{3 binary operations}

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

sub_post (m:mode) (x y res:t)

= value res = round m (value x - value y) /\ exact res = exact x - exact y /\ model res = model x - model y

predicate

sub_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "exact", "mode", "model", "round", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

mul_post (m:mode) (x y res:t)

= value res = round m (value x * value y) /\ exact res = exact x * exact y /\ model res = model x * model y

predicate

mul_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "exact", "mode", "model", "round", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

div_post (m:mode) (x y res:t)

= value res = round m (value x / value y) /\ exact res = exact x / exact y /\ model res = model x / model y

predicate

div_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "exact", "mode", "model", "round", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

neg_post (x res:t)

= value res = - value x /\ exact res = - exact x /\ model res = - model x

predicate

neg_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "exact", "model", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

lt (x:t) (y:t)

= value x < value y

predicate

lt

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "value" ]

{3 Comparisons}

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

gt (x:t) (y:t)

= value x > value y

predicate

gt

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

class t : class

function

class

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[]

{3 special values}

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

is_finite (x:t)

= class x = Finite

predicate

is_finite

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "class" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

is_infinite (x:t)

= class x = Infinite

predicate

is_infinite

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "class" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

is_NaN (x:t)

= class x = NaN

predicate

is_NaN

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "class" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

is_not_NaN (x:t)

= is_finite x \/ is_infinite x

predicate

is_not_NaN

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "is_finite", "is_infinite" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

is_not_NaN: forall x:t. is_not_NaN x <-> not (is_NaN x)

lemma

is_not_NaN

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "is_NaN" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

sign t : sign

function

sign

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

same_sign_real (x:t) (y:real)

= SpecialValues.same_sign_real (sign x) y

predicate

same_sign_real

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "sign" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

same_sign (x:t) (y:t)

= sign x = sign y

predicate

same_sign

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "sign" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

diff_sign (x:t) (y:t)

= sign x <> sign y

predicate

diff_sign

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "sign" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

sign_zero_result (m:mode) (x:t)

= value x = 0.0 -> match m with | Down -> sign x = Neg | _ -> sign x = Pos end

predicate

sign_zero_result

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "Neg", "mode", "sign", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

is_minus_infinity (x:t)

= is_infinite x /\ sign x = Neg

predicate

is_minus_infinity

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "Neg", "is_infinite", "sign" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

is_plus_infinity (x:t)

= is_infinite x /\ sign x = Pos

predicate

is_plus_infinity

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "is_infinite", "sign" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

is_gen_zero (x:t)

= is_finite x /\ value x = 0.0

predicate

is_gen_zero

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "is_finite", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

is_gen_zero_plus (x:t)

= is_gen_zero x /\ sign x = Pos

predicate

is_gen_zero_plus

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "is_gen_zero", "sign" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

is_gen_zero_minus (x:t)

= is_gen_zero x /\ sign x = Neg

predicate

is_gen_zero_minus

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "Neg", "is_gen_zero", "sign" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

finite_sign : forall x:t. class x = Finite /\ value x <> 0.0 -> same_sign_real x (value x)

lemma

finite_sign

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "class", "same_sign_real", "value" ]

non-zero finite gen_float has the same sign as its float_value

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

finite_sign_pos1: forall x:t. class x = Finite /\ value x > 0.0 -> sign x = Pos

lemma

finite_sign_pos1

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "class", "sign", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

finite_sign_pos2: forall x:t. class x = Finite /\ value x <> 0.0 /\ sign x = Pos -> value x > 0.0

lemma

finite_sign_pos2

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "class", "sign", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

finite_sign_neg1: forall x:t. class x = Finite /\ value x < 0.0 -> sign x = Neg

lemma

finite_sign_neg1

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "Neg", "class", "sign", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

finite_sign_neg2: forall x:t. class x = Finite /\ value x <> 0.0 /\ sign x = Neg -> value x < 0.0

lemma

finite_sign_neg2

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "Neg", "class", "sign", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

diff_sign_trans: forall x y z:t. diff_sign x y /\ diff_sign y z -> same_sign x z

lemma

diff_sign_trans

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "diff_sign", "same_sign" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

diff_sign_product: forall x y:t. class x = Finite /\ class y = Finite /\ value x * value y < 0.0 -> diff_sign x y

lemma

diff_sign_product

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "class", "diff_sign", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

same_sign_product: forall x y:t. class x = Finite /\ class y = Finite /\ same_sign x y -> value x * value y >= 0.0

lemma

same_sign_product

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "class", "same_sign", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

overflow_value (m:mode) (x:t)

predicate

overflow_value

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "Neg", "is_finite", "is_infinite", "max", "mode", "sign", "value" ]

This predicate tells what is the result of a rounding in case of overflow

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

round1 : forall m:mode, x:real. no_overflow m x -> is_finite (round_logic m x) /\ value(round_logic m x) = round m x

lemma

round1

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "is_finite", "mode", "no_overflow", "round", "round_logic", "value" ]

rounding in logic

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

round2 : forall m:mode, x:real. not no_overflow m x -> same_sign_real (round_logic m x) x /\ overflow_value m (round_logic m x)

lemma

round2

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "mode", "no_overflow", "overflow_value", "round_logic", "same_sign_real" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

round3 : forall m:mode, x:real. exact (round_logic m x) = x

lemma

round3

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "exact", "mode", "round_logic" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

round4 : forall m:mode, x:real. model (round_logic m x) = x

lemma

round4

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "mode", "model", "round_logic" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

round_of_zero : forall m:mode. is_gen_zero (round_logic m 0.0)

lemma

round_of_zero

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "is_gen_zero", "mode", "round_logic" ]

rounding of zero

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

round_logic_le : forall m:mode, x:real. is_finite (round_logic m x) -> abs (value (round_logic m x)) <= max

lemma

round_logic_le

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "abs", "is_finite", "max", "mode", "round_logic", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

round_no_overflow : forall m:mode, x:real. abs x <= max -> is_finite (round_logic m x) /\ value (round_logic m x) = round m x

lemma

round_no_overflow

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "abs", "is_finite", "max", "mode", "round", "round_logic", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

min : real

constant

min

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

positive_constant : forall m:mode, x:real. min <= x <= max -> is_finite (round_logic m x) /\ value (round_logic m x) > 0.0 /\ sign (round_logic m x) = Pos

lemma

positive_constant

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "is_finite", "max", "min", "mode", "round_logic", "sign", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

negative_constant : forall m:mode, x:real. - max <= x <= - min -> is_finite (round_logic m x) /\ value (round_logic m x) < 0.0 /\ sign (round_logic m x) = Neg

lemma

negative_constant

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "Neg", "is_finite", "max", "min", "mode", "round_logic", "sign", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

is_gen_zero_comp1 : forall x y:t. is_gen_zero x /\ value x = value y /\ is_finite y -> is_gen_zero y

lemma

is_gen_zero_comp1

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "is_finite", "is_gen_zero", "value" ]

lemmas on `gen_zero`

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

is_gen_zero_comp2 : forall x y:t. is_finite x /\ not (is_gen_zero x) /\ value x = value y -> not (is_gen_zero y)

lemma

is_gen_zero_comp2

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "is_finite", "is_gen_zero", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

add_post (m:mode) (x:t) (y:t) (r:t)

= (is_NaN x \/ is_NaN y -> is_NaN r) /\ (is_finite x /\ is_infinite y -> is_infinite r /\ same_sign r y) /\ (is_infinite x /\ is_finite y -> is_infinite r /\ same_sign r x) /\ (is_infinite x /\ is_infinite y -> if same_sign x y then is_infinite r /\ same_sign r x else is_NaN r) ...

predicate

add_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "exact", "is_NaN", "is_finite", "is_infinite", "mode", "model", "no_overflow", "overflow_value", "round", "same_sign", "same_sign_real", "sign", "sign_zero_result", "value" ]

{3 binary operations}

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

sub_post (m:mode) (x:t) (y:t) (r:t)

= (is_NaN x \/ is_NaN y -> is_NaN r) /\ (is_finite x /\ is_infinite y -> is_infinite r /\ diff_sign r y) /\ (is_infinite x /\ is_finite y -> is_infinite r /\ same_sign r x) /\ (is_infinite x /\ is_infinite y -> if diff_sign x y then is_infinite r /\ same_sign r x else is_NaN r) ...

predicate

sub_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "diff_sign", "exact", "is_NaN", "is_finite", "is_infinite", "mode", "model", "no_overflow", "overflow_value", "round", "same_sign", "same_sign_real", "sign", "sign_zero_result", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

product_sign (z x y: t)

= (same_sign x y -> sign z = Pos) /\ (diff_sign x y -> sign z = Neg)

predicate

product_sign

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "Neg", "diff_sign", "same_sign", "sign" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

mul_post (m:mode) (x:t) (y:t) (r:t)

= (is_NaN x \/ is_NaN y -> is_NaN r) /\ (is_gen_zero x /\ is_infinite y -> is_NaN r) /\ (is_finite x /\ is_infinite y /\ value x <> 0.0 -> is_infinite r) /\ (is_infinite x /\ is_gen_zero y -> is_NaN r) /\ (is_infinite x /\ is_finite y /\ value y <> 0.0 -> is_infinite r) /\ (is_...

predicate

mul_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "exact", "is_NaN", "is_finite", "is_gen_zero", "is_infinite", "mode", "model", "no_overflow", "overflow_value", "product_sign", "round", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

neg_post (x:t) (r:t)

= (is_NaN x -> is_NaN r) /\ (is_infinite x -> is_infinite r) /\ (is_finite x -> is_finite r /\ value r = - value x) /\ (not is_NaN r -> diff_sign r x) /\ exact r = - exact x /\ model r = - model x

predicate

neg_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "diff_sign", "exact", "is_NaN", "is_finite", "is_infinite", "model", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

div_post (m:mode) (x:t) (y:t) (r:t)

= (is_NaN x \/ is_NaN y -> is_NaN r) /\ (is_finite x /\ is_infinite y -> is_gen_zero r) /\ (is_infinite x /\ is_finite y -> is_infinite r) /\ (is_infinite x /\ is_infinite y -> is_NaN r) /\ (is_finite x /\ is_finite y /\ value y <> 0.0 /\ no_overflow m (value x / value y) -> is_finit...

predicate

div_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "exact", "is_NaN", "is_finite", "is_gen_zero", "is_infinite", "mode", "model", "no_overflow", "overflow_value", "product_sign", "round", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

fma_post (m:mode) (x y z:t) (r:t)

= (is_NaN x \/ is_NaN y \/ is_NaN z -> is_NaN r) /\ (is_gen_zero x /\ is_infinite y -> is_NaN r) /\ (is_infinite x /\ is_gen_zero y -> is_NaN r) /\ (is_finite x /\ value x <> 0.0 /\ is_infinite y /\ is_finite z -> is_infinite r /\ product_sign r x y) /\ (is_finite x /\ value x <> 0.0 /\ is_i...

predicate

fma_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "Neg", "exact", "is_NaN", "is_finite", "is_gen_zero", "is_infinite", "mode", "model", "no_overflow", "overflow_value", "product_sign", "round", "same_sign", "same_sign_real", "sign", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

sqrt_post (m:mode) (x:t) (r:t)

= (is_NaN x -> is_NaN r) /\ (is_plus_infinity x -> is_plus_infinity r) /\ (is_minus_infinity x -> is_NaN r) /\ (is_finite x /\ value x < 0.0 -> is_NaN r) /\ (is_finite x /\ value x = 0.0 -> is_finite r /\ value r = 0.0 /\ same_sign r x) /\ (is_finite x /\ value x > 0.0 -> is_fini...

predicate

sqrt_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "exact", "is_NaN", "is_finite", "is_minus_infinity", "is_plus_infinity", "mode", "model", "round", "same_sign", "sign", "sqrt", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

of_real_exact_post (x:real) (r:t)

= is_finite r /\ value r = x /\ exact r = x /\ model r = x

predicate

of_real_exact_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "exact", "is_finite", "model", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

le (x:t) (y:t)

= (is_finite x /\ is_finite y /\ value x <= value y) \/ (is_minus_infinity x /\ is_not_NaN y) \/ (is_not_NaN x /\ is_plus_infinity y)

predicate

le

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "is_finite", "is_minus_infinity", "is_not_NaN", "is_plus_infinity", "value" ]

{3 Comparisons}

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

lt (x:t) (y:t)

= (is_finite x /\ is_finite y /\ value x < value y) \/ (is_minus_infinity x /\ is_not_NaN y /\ not (is_minus_infinity y)) \/ (is_not_NaN x /\ not (is_plus_infinity x) /\ is_plus_infinity y)

predicate

lt

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "is_finite", "is_minus_infinity", "is_not_NaN", "is_plus_infinity", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

ge (x:t) (y:t)

= le y x

predicate

ge

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "le" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

gt (x:t) (y:t)

= lt y x

predicate

gt

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "lt" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

eq (x:t) (y:t)

= (is_finite x /\ is_finite y /\ value x = value y) \/ (is_infinite x /\ is_infinite y /\ same_sign x y)

predicate

eq

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "is_finite", "is_infinite", "same_sign", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

ne (x:t) (y:t)

= not (eq x y)

predicate

ne

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "eq" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

le_lt_trans: forall x y z:t. le x y /\ lt y z -> lt x z

lemma

le_lt_trans

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "le", "lt" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

lt_le_trans: forall x y z:t. lt x y /\ le y z -> lt x z

lemma

lt_le_trans

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "le", "lt" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

le_ge_asym: forall x y:t. le x y /\ ge x y -> eq x y

lemma

le_ge_asym

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "eq", "ge", "le" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

not_lt_ge: forall x y:t. not (lt x y) /\ is_not_NaN x /\ is_not_NaN y -> ge x y

lemma

not_lt_ge

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "ge", "is_not_NaN", "lt" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

not_gt_le: forall x y:t. not (gt x y) /\ is_not_NaN x /\ is_not_NaN y -> le x y

lemma

not_gt_le

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "gt", "is_not_NaN", "le" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

min_single : real

= 0x1p-149

constant

min_single

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

min_double : real

= 0x1p-1074

constant

min_double

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

min_normalized : real

constant

min_normalized

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[]

{3 binary operations}

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

eps_normalized : real

constant

eps_normalized

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

eta_normalized : real

constant

eta_normalized

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

add_post (_m:mode) (x y res:t)

= ((* CASE 1 : normalized numbers *) (abs(value x + value y) >= min_normalized -> abs(value res - (value x + value y)) <= eps_normalized * abs(value x + value y)) /\ (*CASE 2: denormalized numbers *) (abs(value x + value y) <= min_normalized -> abs(value res - (value x + value y)) <=...

predicate

add_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "abs", "eps_normalized", "eta_normalized", "exact", "min_normalized", "mode", "model", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

sub_post (_m:mode) (x y res:t)

= ((* CASE 1 : normalized numbers *) (abs(value x - value y) >= min_normalized -> abs(value res - (value x - value y)) <= eps_normalized * abs(value x - value y)) /\ (*CASE 2: denormalized numbers *) (abs(value x - value y) <= min_normalized -> abs(value res - (value x - value y)) <=...

predicate

sub_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "abs", "eps_normalized", "eta_normalized", "exact", "min_normalized", "mode", "model", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

mul_post (_m:mode) (x y res:t)

= ((* CASE 1 : normalized numbers *) (abs(value x * value y) >= min_normalized -> abs(value res - (value x * value y)) <= eps_normalized * abs(value x * value y)) /\ (*CASE 2: denormalized numbers *) (abs(value x * value y) <= min_normalized -> abs(value res - (value x * value y)) <=...

predicate

mul_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "abs", "eps_normalized", "eta_normalized", "exact", "min_normalized", "mode", "model", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

neg_post (_m:mode) (x res:t)

= ((abs(value x) >= min_normalized -> abs(value res - (- value x)) <= eps_normalized * abs(- value x)) /\ (abs(value x) <= min_normalized -> abs(value res - (- value x)) <= eta_normalized)) /\ exact res = - exact x /\ model res = - model x

predicate

neg_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "abs", "eps_normalized", "eta_normalized", "exact", "min_normalized", "mode", "model", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

of_real_exact_post (x:real) (r:t)

= value r = x /\ exact r = x /\ model r = x

predicate

of_real_exact_post

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[ "exact", "model", "value" ]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

min_normalized_double : real

= 0x1p-1022

constant

min_normalized_double

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784

eps_normalized_double : real

= 0x1.004p-53

constant

eps_normalized_double

stdlib

stdlib/floating_point.mlw

[ "DoubleFormat", "GenFloat", "GenFloatFull", "GenFloatSpecFull", "GenFloatSpecMultiRounding", "GenFloatSpecStrict", "Rounding", "SingleFormat", "SpecialValues", "int.Int", "real.Abs", "real.FromInt", "real.Real", "real.Square" ]

[]

https://gitlab.inria.fr/why3/why3

7c59064b4eed9a4059292599f3a657716aa34784