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 |
|---|---|---|---|---|---|---|---|---|---|---|
le_finite: forall x y [le x y].
is_finite x /\ is_finite y -> (le x y <-> to_real x <=. to_real y) | axiom | le_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"le",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
le_lt_trans:
forall x y z:t. x .<= y /\ y .< z -> x .< z | lemma | le_lt_trans | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
lt_le_trans:
forall x y z:t. x .< y /\ y .<= z -> x .< z | lemma | lt_le_trans | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
le_ge_asym:
forall x y:t. x .<= y /\ x .>= y -> x .= y | lemma | le_ge_asym | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
not_lt_ge: forall x y:t.
not (x .< y) /\ is_not_nan x /\ is_not_nan y -> x .>= y | lemma | not_lt_ge | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_not_nan"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
not_gt_le: forall x y:t.
not (x .> y) /\ is_not_nan x /\ is_not_nan y -> x .<= y | lemma | not_gt_le | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_not_nan"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
le_special: forall x y [le x y]. le x y ->
((is_finite x /\ is_finite y)
\/ ((is_minus_infinity x /\ is_not_nan y)
\/ (is_not_nan x /\ is_plus_infinity y))) | axiom | le_special | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_minus_infinity",
"is_not_nan",
"is_plus_infinity",
"le"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
lt_special: forall x y [lt x y]. lt x y ->
((is_finite x /\ is_finite 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))) | axiom | lt_special | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_minus_infinity",
"is_not_nan",
"is_plus_infinity",
"lt"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
lt_lt_finite: forall x y z. lt x y -> lt y z -> is_finite y | axiom | lt_lt_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"lt"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
positive_to_real: forall x[is_positive x|to_real x >=. 0.0].
is_finite x -> is_positive x -> to_real x >=. 0.0 | axiom | positive_to_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_positive",
"to_real"
] | lemmas on sign | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
to_real_positive: forall x[is_positive x].
is_finite x -> to_real x >. 0.0 -> is_positive x | axiom | to_real_positive | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_positive",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
negative_to_real: forall x [is_negative x|to_real x <=. 0.0].
is_finite x -> is_negative x -> to_real x <=. 0.0 | axiom | negative_to_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_negative",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
to_real_negative: forall x [is_negative x].
is_finite x -> to_real x <. 0.0 -> is_negative x | axiom | to_real_negative | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_negative",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
negative_xor_positive: forall x.
not (is_positive x /\ is_negative x) | axiom | negative_xor_positive | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_negative",
"is_positive"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
negative_or_positive: forall x.
is_not_nan x -> is_positive x \/ is_negative x | axiom | negative_or_positive | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_negative",
"is_not_nan",
"is_positive"
] | 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/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"diff_sign",
"same_sign"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
diff_sign_product:
forall x y:t.
(is_finite x /\ is_finite y /\ to_real x *. to_real y <. 0.0) ->
diff_sign x y | lemma | diff_sign_product | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"diff_sign",
"is_finite",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
same_sign_product:
forall x y:t.
(is_finite x /\ is_finite y /\ same_sign x y) ->
to_real x *. to_real y >=. 0.0 | lemma | same_sign_product | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"same_sign",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
product_sign (z x y: t) | =
(same_sign x y -> is_positive z) /\ (diff_sign x y -> is_negative z) | predicate | product_sign | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"diff_sign",
"is_negative",
"is_positive",
"same_sign"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
overflow_value (m:mode) (x:t) | =
match m with
| RTN -> if is_positive x then is_finite x /\ to_real x = max_real
else is_infinite x
| RTP -> if is_positive x then is_infinite x
else is_finite x /\ to_real x = -. max_real
| RTZ -> if is_positive x then is_finite x /\ to_real ... | predicate | overflow_value | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_infinite",
"is_positive",
"max_real",
"mode",
"to_real"
] | This predicate is used to tell what is the result of a rounding in case of overflow in the axioms specifying add/sub/mul and fma | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
sign_zero_result (m:mode) (x:t) | =
is_zero x ->
match m with
| RTN -> is_negative x
| _ -> is_positive x
end | predicate | sign_zero_result | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_negative",
"is_positive",
"is_zero",
"mode"
] | This predicate is used to tell what is the sign of zero in the axioms specifying add and sub | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
add_finite: forall m:mode, x y:t [add m x y].
is_finite x -> is_finite y -> no_overflow m (to_real x +. to_real y) ->
is_finite (add m x y) /\
to_real (add m x y) = round m (to_real x +. to_real y) | axiom | add_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"add",
"is_finite",
"mode",
"no_overflow",
"round",
"to_real"
] | {3 binary operations} | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
add_finite_rev: forall m:mode, x y:t [add m x y].
is_finite (add m x y) ->
is_finite x /\ is_finite y | lemma | add_finite_rev | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"add",
"is_finite",
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
add_finite_rev_n: forall m:mode, x y:t [add m x y].
to_nearest m ->
is_finite (add m x y) ->
no_overflow m (to_real x +. to_real y) /\
to_real (add m x y) = round m (to_real x +. to_real y) | lemma | add_finite_rev_n | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"add",
"is_finite",
"mode",
"no_overflow",
"round",
"to_nearest",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
sub_finite: forall m:mode, x y:t [sub m x y].
is_finite x -> is_finite y -> no_overflow m (to_real x -. to_real y) ->
is_finite (sub m x y) /\
to_real (sub m x y) = round m (to_real x -. to_real y) | axiom | sub_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"mode",
"no_overflow",
"round",
"sub",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
sub_finite_rev: forall m:mode, x y:t [sub m x y].
is_finite (sub m x y) ->
is_finite x /\ is_finite y | lemma | sub_finite_rev | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"mode",
"sub"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
sub_finite_rev_n: forall m:mode, x y:t [sub m x y].
to_nearest m ->
is_finite (sub m x y) ->
no_overflow m (to_real x -. to_real y) /\
to_real (sub m x y) = round m (to_real x -. to_real y) | lemma | sub_finite_rev_n | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"mode",
"no_overflow",
"round",
"sub",
"to_nearest",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
mul_finite: forall m:mode, x y:t [mul m x y].
is_finite x -> is_finite y -> no_overflow m (to_real x *. to_real y) ->
is_finite (mul m x y) /\
to_real (mul m x y) = round m (to_real x *. to_real y) | axiom | mul_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"mode",
"mul",
"no_overflow",
"round",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
mul_finite_rev: forall m:mode, x y:t [mul m x y].
is_finite (mul m x y) ->
is_finite x /\ is_finite y | lemma | mul_finite_rev | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"mode",
"mul"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
mul_finite_rev_n: forall m:mode, x y:t [mul m x y].
to_nearest m ->
is_finite (mul m x y) ->
no_overflow m (to_real x *. to_real y) /\
to_real (mul m x y) = round m (to_real x *. to_real y) | lemma | mul_finite_rev_n | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"mode",
"mul",
"no_overflow",
"round",
"to_nearest",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
div_finite: forall m:mode, x y:t [div m x y].
is_finite x -> is_finite y ->
not is_zero y -> no_overflow m (to_real x /. to_real y) ->
is_finite (div m x y) /\
to_real (div m x y) = round m (to_real x /. to_real y) | axiom | div_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"div",
"is_finite",
"is_zero",
"mode",
"no_overflow",
"round",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
div_finite_rev: forall m:mode, x y:t [div m x y].
is_finite (div m x y) ->
(is_finite x /\ is_finite y /\ not is_zero y) \/
(is_finite x /\ is_infinite y /\ to_real (div m x y) = 0.) | lemma | div_finite_rev | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"div",
"is_finite",
"is_infinite",
"is_zero",
"mode",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
div_finite_rev_n: forall m:mode, x y:t [div m x y].
to_nearest m ->
is_finite (div m x y) -> is_finite y ->
no_overflow m (to_real x /. to_real y) /\
to_real (div m x y) = round m (to_real x /. to_real y) | lemma | div_finite_rev_n | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"div",
"is_finite",
"mode",
"no_overflow",
"round",
"to_nearest",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
neg_finite: forall x:t [neg x].
is_finite x ->
is_finite (neg x) /\
to_real (neg x) = -. to_real x | axiom | neg_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"neg",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
neg_finite_rev: forall x:t [neg x].
is_finite (neg x) ->
is_finite x /\
to_real (neg x) = -. to_real x | lemma | neg_finite_rev | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"neg",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
abs_finite: forall x:t [abs x].
is_finite x ->
is_finite (abs x) /\
to_real (abs x) = Abs.abs (to_real x) /\
is_positive (abs x) | axiom | abs_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"abs",
"is_finite",
"is_positive",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
abs_finite_rev: forall x:t [abs x].
is_finite (abs x) ->
is_finite x /\
to_real (abs x) = Abs.abs (to_real x) | lemma | abs_finite_rev | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"abs",
"is_finite",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
abs_universal : forall x:t [abs x]. not (is_negative (abs x)) | axiom | abs_universal | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"abs",
"is_negative"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
fma_finite: forall m:mode, x y z:t [fma m x y z].
is_finite x -> is_finite y -> is_finite z ->
no_overflow m (to_real x *. to_real y +. to_real z) ->
is_finite (fma m x y z) /\
to_real (fma m x y z) = round m (to_real x *. to_real y +. to_real z) | axiom | fma_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"fma",
"is_finite",
"mode",
"no_overflow",
"round",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
fma_finite_rev: forall m:mode, x y z:t [fma m x y z].
is_finite (fma m x y z) ->
is_finite x /\ is_finite y /\ is_finite z | lemma | fma_finite_rev | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"fma",
"is_finite",
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
fma_finite_rev_n: forall m:mode, x y z:t [fma m x y z].
to_nearest m ->
is_finite (fma m x y z) ->
no_overflow m (to_real x *. to_real y +. to_real z) /\
to_real (fma m x y z) = round m (to_real x *. to_real y +. to_real z) | lemma | fma_finite_rev_n | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"fma",
"is_finite",
"mode",
"no_overflow",
"round",
"to_nearest",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
sqrt_finite: forall m:mode, x:t [sqrt m x].
is_finite x -> to_real x >=. 0. ->
is_finite (sqrt m x) /\
to_real (sqrt m x) = round m (S.sqrt (to_real x)) | axiom | sqrt_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"mode",
"round",
"sqrt",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
sqrt_finite_rev: forall m:mode, x:t [sqrt m x].
is_finite (sqrt m x) ->
is_finite x /\ to_real x >=. 0. /\
to_real (sqrt m x) = round m (S.sqrt (to_real x)) | lemma | sqrt_finite_rev | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"mode",
"round",
"sqrt",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
same_sign_real (x:t) (r:real) | =
(is_positive x /\ r >. 0.0) \/ (is_negative x /\ r <. 0.0) | predicate | same_sign_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_negative",
"is_positive"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
add_special: forall m:mode, x y:t [add m x y].
let r = add m x y in
(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 /\ same_sign x... | axiom | add_special | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"add",
"diff_sign",
"is_finite",
"is_infinite",
"is_nan",
"mode",
"no_overflow",
"overflow_value",
"same_sign",
"same_sign_real",
"sign_zero_result",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
sub_special: forall m:mode, x y:t [sub m x y].
let r = sub m x y in
(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 /\ same_sign x... | axiom | sub_special | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"diff_sign",
"is_finite",
"is_infinite",
"is_nan",
"mode",
"no_overflow",
"overflow_value",
"same_sign",
"same_sign_real",
"sign_zero_result",
"sub",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
mul_special: forall m:mode, x y:t [mul m x y].
let r = mul m x y in
(is_nan x \/ is_nan y -> is_nan r)
/\ (is_zero x /\ is_infinite y -> is_nan r)
/\ (is_finite x /\ is_infinite y /\ not (is_zero x)
-> is_infinite r)
/\ (is_infinite x /\ is_zero y -> is_nan r)
/\ (is_infinite x /\ is... | axiom | mul_special | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_infinite",
"is_nan",
"is_zero",
"mode",
"mul",
"no_overflow",
"overflow_value",
"product_sign",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
div_special: forall m:mode, x y:t [div m x y].
let r = div m x y in
(is_nan x \/ is_nan y -> is_nan r)
/\ (is_finite x /\ is_infinite y -> is_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 /\ not (is_ze... | axiom | div_special | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"div",
"is_finite",
"is_infinite",
"is_nan",
"is_zero",
"mode",
"no_overflow",
"overflow_value",
"product_sign",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
neg_special: forall x:t [neg x].
(is_nan x -> is_nan (neg x))
/\ (is_infinite x -> is_infinite (neg x))
/\ (not is_nan x -> diff_sign x (neg x)) | axiom | neg_special | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"diff_sign",
"is_infinite",
"is_nan",
"neg"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
abs_special: forall x:t [abs x].
(is_nan x -> is_nan (abs x))
/\ (is_infinite x -> is_infinite (abs x))
/\ (not is_nan x -> is_positive (abs x)) | axiom | abs_special | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"abs",
"is_infinite",
"is_nan",
"is_positive"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
fma_special: forall m:mode, x y z:t [fma m x y z].
let r = fma m x y z in
(is_nan x \/ is_nan y \/ is_nan z -> is_nan r)
/\ (is_zero x /\ is_infinite y -> is_nan r)
/\ (is_infinite x /\ is_zero y -> is_nan r)
/\ (is_finite x /\ not (is_zero x) /\ is_infinite y /\ is_finite z
-> is_infinit... | axiom | fma_special | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"fma",
"is_finite",
"is_infinite",
"is_nan",
"is_negative",
"is_positive",
"is_zero",
"mode",
"no_overflow",
"overflow_value",
"product_sign",
"same_sign",
"same_sign_real",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
sqrt_special: forall m:mode, x:t [sqrt m x].
let r = sqrt m x in
(is_nan x -> is_nan r)
/\ (is_plus_infinity x -> is_plus_infinity r)
/\ (is_minus_infinity x -> is_nan r)
/\ (is_finite x /\ to_real x <. 0.0 -> is_nan r)
/\ (is_zero x -> same_sign r x)
/\ (is_finite x /\ to_real x >. 0.0 -... | axiom | sqrt_special | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_minus_infinity",
"is_nan",
"is_plus_infinity",
"is_positive",
"is_zero",
"mode",
"same_sign",
"sqrt",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_int_add_exact: forall m n, i j.
in_safe_int_range i -> in_safe_int_range j ->
in_safe_int_range (i + j) -> eq (of_int m (i + j)) (add n (of_int m i) (of_int m j)) | axiom | of_int_add_exact | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"add",
"eq",
"in_safe_int_range",
"of_int"
] | exact arithmetic with integers | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
of_int_sub_exact: forall m n, i j.
in_safe_int_range i -> in_safe_int_range j ->
in_safe_int_range (i - j) -> eq (of_int m (i - j)) (sub n (of_int m i) (of_int m j)) | axiom | of_int_sub_exact | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"eq",
"in_safe_int_range",
"of_int",
"sub"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_int_mul_exact: forall m n, i j.
in_safe_int_range i -> in_safe_int_range j ->
in_safe_int_range (i * j) -> eq (of_int m (i * j)) (mul n (of_int m i) (of_int m j)) | axiom | of_int_mul_exact | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"eq",
"in_safe_int_range",
"mul",
"of_int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Min_r : forall x y:t. y .<= x -> (min x y) .= y | lemma | Min_r | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"min"
] | min and max | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
Min_l : forall x y:t. x .<= y -> (min x y) .= x | lemma | Min_l | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"min"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Max_r : forall x y:t. y .<= x -> (max x y) .= x | lemma | Max_r | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"max"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Max_l : forall x y:t. x .<= y -> (max x y) .= y | lemma | Max_l | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"max"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
is_int (x:t) | predicate | is_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | This predicate specify if a float is finite and is an integer | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
zeroF_is_int: is_int zeroF | axiom | zeroF_is_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_int",
"zeroF"
] | by construction | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
of_int_is_int: forall m, x.
in_int_range x -> is_int (of_int m x) | axiom | of_int_is_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"in_int_range",
"is_int",
"of_int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
big_float_is_int: forall m i.
is_finite i ->
i .<= neg (of_int m pow2sb) \/ (of_int m pow2sb) .<= i ->
is_int i | axiom | big_float_is_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_int",
"neg",
"of_int",
"pow2sb"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
roundToIntegral_is_int: forall m:mode, x:t. is_finite x ->
is_int (roundToIntegral m x) | axiom | roundToIntegral_is_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_int",
"mode",
"roundToIntegral"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
eq_is_int: forall x y. eq x y -> is_int x -> is_int y | axiom | eq_is_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"eq",
"is_int"
] | by propagation | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
add_int: forall x y m. is_int x -> is_int y ->
is_finite (add m x y) -> is_int (add m x y) | axiom | add_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"add",
"is_finite",
"is_int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
sub_int: forall x y m. is_int x -> is_int y ->
is_finite (sub m x y) -> is_int (sub m x y) | axiom | sub_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_int",
"sub"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
mul_int: forall x y m. is_int x -> is_int y ->
is_finite (mul m x y) -> is_int (mul m x y) | axiom | mul_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_int",
"mul"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
fma_int: forall x y z m. is_int x -> is_int y -> is_int z ->
is_finite (fma m x y z) -> is_int (fma m x y z) | axiom | fma_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"fma",
"is_finite",
"is_int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
neg_int: forall x. is_int x -> is_int (neg x) | axiom | neg_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_int",
"neg"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
abs_int: forall x. is_int x -> is_int (abs x) | axiom | abs_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"abs",
"is_int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
is_int_of_int: forall x m m'.
is_int x -> eq x (of_int m' (to_int m x)) | axiom | is_int_of_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"eq",
"is_int",
"of_int",
"to_int"
] | basic properties of float integers | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
is_int_to_int: forall m x.
is_int x -> in_int_range (to_int m x) | axiom | is_int_to_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"in_int_range",
"is_int",
"to_int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
is_int_is_finite: forall x.
is_int x -> is_finite x | axiom | is_int_is_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
int_to_real: forall m x.
is_int x -> to_real x = FromInt.from_int (to_int m x) | axiom | int_to_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"from_int",
"is_int",
"to_int",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
truncate_int: forall m:mode, i:t. is_int i ->
roundToIntegral m i .= i | axiom | truncate_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_int",
"mode",
"roundToIntegral"
] | rounding ints | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
truncate_neg: forall x:t.
is_finite x -> is_negative x -> roundToIntegral RTZ x = roundToIntegral RTP x | axiom | truncate_neg | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_negative",
"roundToIntegral"
] | truncate | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
truncate_pos: forall x:t.
is_finite x -> is_positive x -> roundToIntegral RTZ x = roundToIntegral RTN x | axiom | truncate_pos | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_positive",
"roundToIntegral"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
ceil_le: forall x:t. is_finite x -> x .<= (roundToIntegral RTP x) | axiom | ceil_le | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"roundToIntegral"
] | ceil | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
ceil_lest: forall x y:t. x .<= y /\ is_int y -> (roundToIntegral RTP x) .<= y | axiom | ceil_lest | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_int",
"roundToIntegral"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
ceil_to_real: forall x:t.
is_finite x ->
to_real (roundToIntegral RTP x) = FromInt.from_int (Truncate.ceil (to_real x)) | axiom | ceil_to_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"ceil",
"from_int",
"is_finite",
"roundToIntegral",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
ceil_to_int: forall m:mode, x:t.
is_finite x ->
to_int m (roundToIntegral RTP x) = Truncate.ceil (to_real x) | axiom | ceil_to_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"ceil",
"is_finite",
"mode",
"roundToIntegral",
"to_int",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
floor_le: forall x:t. is_finite x -> (roundToIntegral RTN x) .<= x | axiom | floor_le | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"roundToIntegral"
] | floor | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
floor_lest: forall x y:t. y .<= x /\ is_int y -> y .<= (roundToIntegral RTN x) | axiom | floor_lest | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_int",
"roundToIntegral"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
floor_to_real: forall x:t.
is_finite x ->
to_real (roundToIntegral RTN x) = FromInt.from_int (Truncate.floor (to_real x)) | axiom | floor_to_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"floor",
"from_int",
"is_finite",
"roundToIntegral",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
floor_to_int: forall m:mode, x:t.
is_finite x ->
to_int m (roundToIntegral RTN x) = Truncate.floor (to_real x) | axiom | floor_to_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"floor",
"is_finite",
"mode",
"roundToIntegral",
"to_int",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
RNA_down:
forall x:t. (x .- (roundToIntegral RTN x)) .< ((roundToIntegral RTP x) .- x) ->
roundToIntegral RNA x = roundToIntegral RTN x | axiom | RNA_down | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"roundToIntegral"
] | Rna | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
RNA_up:
forall x:t. (x .- (roundToIntegral RTN x)) .> ((roundToIntegral RTP x) .- x) ->
roundToIntegral RNA x = roundToIntegral RTP x | axiom | RNA_up | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"roundToIntegral"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
RNA_down_tie:
forall x:t. (x .- (roundToIntegral RTN x)) .= ((roundToIntegral RTP x) .- x) ->
is_negative x -> roundToIntegral RNA x = roundToIntegral RTN x | axiom | RNA_down_tie | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_negative",
"roundToIntegral"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
RNA_up_tie:
forall x:t. ((roundToIntegral RTP x) .- x) .= (x .- (roundToIntegral RTN x)) ->
is_positive x -> roundToIntegral RNA x = roundToIntegral RTP x | axiom | RNA_up_tie | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_positive",
"roundToIntegral"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
to_int_roundToIntegral: forall m:mode, x:t.
to_int m x = to_int m (roundToIntegral m x) | axiom | to_int_roundToIntegral | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode",
"roundToIntegral",
"to_int"
] | to_int | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
to_int_monotonic: forall m:mode, x y:t.
is_finite x -> is_finite y -> le x y -> to_int m x <= to_int m y | axiom | to_int_monotonic | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"le",
"mode",
"to_int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
to_int_of_int: forall m:mode, i:int.
in_safe_int_range i ->
to_int m (of_int m i) = i | axiom | to_int_of_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"in_safe_int_range",
"int",
"mode",
"of_int",
"to_int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
eq_to_int: forall m, x y. is_finite x -> x .= y ->
to_int m x = to_int m y | axiom | eq_to_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"to_int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
neg_to_int: forall m x.
is_int x -> to_int m (neg x) = - (to_int m x) | axiom | neg_to_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_int",
"neg",
"to_int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
roundToIntegral_is_finite : forall m:mode, x:t. is_finite x ->
is_finite (roundToIntegral m x) | axiom | roundToIntegral_is_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"mode",
"roundToIntegral"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
is_finite t | predicate | is_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | the underlying float type, to be cloned | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
to_real t : real | function | to_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
round mode real : real | function | round | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_sbv8 mode BV8.t : t | val function | of_sbv8 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | convert from signed bitvector | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
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