diff options
Diffstat (limited to 'gcc/ada/libgnat/s-imageu.adb')
| -rw-r--r-- | gcc/ada/libgnat/s-imageu.adb | 274 |
1 files changed, 0 insertions, 274 deletions
diff --git a/gcc/ada/libgnat/s-imageu.adb b/gcc/ada/libgnat/s-imageu.adb index 820156b..a6cdfed 100644 --- a/gcc/ada/libgnat/s-imageu.adb +++ b/gcc/ada/libgnat/s-imageu.adb @@ -29,79 +29,8 @@ -- -- ------------------------------------------------------------------------------ -with Ada.Numerics.Big_Numbers.Big_Integers_Ghost; -use Ada.Numerics.Big_Numbers.Big_Integers_Ghost; -with System.Val_Spec; - package body System.Image_U is - -- Ghost code, loop invariants and assertions in this unit are meant for - -- analysis only, not for run-time checking, as it would be too costly - -- otherwise. This is enforced by setting the assertion policy to Ignore. - - pragma Assertion_Policy (Ghost => Ignore, - Loop_Invariant => Ignore, - Assert => Ignore, - Assert_And_Cut => Ignore, - Subprogram_Variant => Ignore); - - package Unsigned_Conversion is new Unsigned_Conversions (Int => Uns); - - function Big (Arg : Uns) return Big_Integer renames - Unsigned_Conversion.To_Big_Integer; - - function From_Big (Arg : Big_Integer) return Uns renames - Unsigned_Conversion.From_Big_Integer; - - Big_10 : constant Big_Integer := Big (10) with Ghost; - - ------------------ - -- Local Lemmas -- - ------------------ - - procedure Lemma_Non_Zero (X : Uns) - with - Ghost, - Pre => X /= 0, - Post => Big (X) /= 0; - - procedure Lemma_Div_Commutation (X, Y : Uns) - with - Ghost, - Pre => Y /= 0, - Post => Big (X) / Big (Y) = Big (X / Y); - - procedure Lemma_Div_Twice (X : Big_Natural; Y, Z : Big_Positive) - with - Ghost, - Post => X / Y / Z = X / (Y * Z); - - --------------------------- - -- Lemma_Div_Commutation -- - --------------------------- - - procedure Lemma_Non_Zero (X : Uns) is null; - procedure Lemma_Div_Commutation (X, Y : Uns) is null; - - --------------------- - -- Lemma_Div_Twice -- - --------------------- - - procedure Lemma_Div_Twice (X : Big_Natural; Y, Z : Big_Positive) is - XY : constant Big_Natural := X / Y; - YZ : constant Big_Natural := Y * Z; - XYZ : constant Big_Natural := X / Y / Z; - R : constant Big_Natural := (XY rem Z) * Y + (X rem Y); - begin - pragma Assert (X = XY * Y + (X rem Y)); - pragma Assert (XY = XY / Z * Z + (XY rem Z)); - pragma Assert (X = XYZ * YZ + R); - pragma Assert ((XY rem Z) * Y <= (Z - 1) * Y); - pragma Assert (R <= YZ - 1); - pragma Assert (X / YZ = (XYZ * YZ + R) / YZ); - pragma Assert (X / YZ = XYZ + R / YZ); - end Lemma_Div_Twice; - -------------------- -- Image_Unsigned -- -------------------- @@ -112,50 +41,10 @@ package body System.Image_U is P : out Natural) is pragma Assert (S'First = 1); - - procedure Prove_Value_Unsigned - with - Ghost, - Pre => S'First = 1 - and then S'Last < Integer'Last - and then P in 2 .. S'Last - and then S (1) = ' ' - and then U_Spec.Only_Decimal_Ghost (S, From => 2, To => P) - and then U_Spec.Scan_Based_Number_Ghost (S, From => 2, To => P) - = U_Spec.Wrap_Option (V), - Post => not System.Val_Spec.Only_Space_Ghost (S, 1, P) - and then U_Spec.Is_Unsigned_Ghost (S (1 .. P)) - and then U_Spec.Is_Value_Unsigned_Ghost (S (1 .. P), V); - -- Ghost lemma to prove the value of Value_Unsigned from the value of - -- Scan_Based_Number_Ghost on a decimal string. - - -------------------------- - -- Prove_Value_Unsigned -- - -------------------------- - - procedure Prove_Value_Unsigned is - Str : constant String := S (1 .. P); - begin - pragma Assert (Str'First = 1); - pragma Assert (S (2) /= ' '); - pragma Assert - (U_Spec.Only_Decimal_Ghost (Str, From => 2, To => P)); - U_Spec.Prove_Scan_Based_Number_Ghost_Eq - (S, Str, From => 2, To => P); - pragma Assert - (U_Spec.Scan_Based_Number_Ghost (Str, From => 2, To => P) - = U_Spec.Wrap_Option (V)); - U_Spec.Prove_Scan_Only_Decimal_Ghost (Str, V); - end Prove_Value_Unsigned; - - -- Start of processing for Image_Unsigned - begin S (1) := ' '; P := 1; Set_Image_Unsigned (V, S, P); - - Prove_Value_Unsigned; end Image_Unsigned; ------------------------ @@ -169,118 +58,6 @@ package body System.Image_U is is Nb_Digits : Natural := 0; Value : Uns := V; - - -- Local ghost variables - - Pow : Big_Positive := 1 with Ghost; - S_Init : constant String := S with Ghost; - Prev_Value : Uns with Ghost; - Prev_S : String := S with Ghost; - - -- Local ghost lemmas - - procedure Prove_Character_Val (R : Uns) - with - Ghost, - Post => R rem 10 in 0 .. 9 - and then Character'Val (48 + R rem 10) in '0' .. '9'; - -- Ghost lemma to prove the value of a character corresponding to the - -- next figure. - - procedure Prove_Euclidian (Val, Quot, Rest : Uns) - with - Ghost, - Pre => Quot = Val / 10 - and then Rest = Val rem 10, - Post => Uns'Last - Rest >= 10 * Quot and then Val = 10 * Quot + Rest; - -- Ghost lemma to prove the relation between the quotient/remainder of - -- division by 10 and the initial value. - - procedure Prove_Hexa_To_Unsigned_Ghost (R : Uns) - with - Ghost, - Pre => R in 0 .. 9, - Post => U_Spec.Hexa_To_Unsigned_Ghost (Character'Val (48 + R)) = R; - -- Ghost lemma to prove that Hexa_To_Unsigned_Ghost returns the source - -- figure when applied to the corresponding character. - - procedure Prove_Scan_Iter - (S, Prev_S : String; - V, Prev_V, Res : Uns; - P, Max : Natural) - with - Ghost, - Pre => - S'First = Prev_S'First and then S'Last = Prev_S'Last - and then S'Last < Natural'Last and then - Max in S'Range and then P in S'First .. Max and then - (for all I in P + 1 .. Max => Prev_S (I) in '0' .. '9') - and then (for all I in P + 1 .. Max => Prev_S (I) = S (I)) - and then S (P) in '0' .. '9' - and then V <= Uns'Last / 10 - and then Uns'Last - U_Spec.Hexa_To_Unsigned_Ghost (S (P)) - >= 10 * V - and then Prev_V = - V * 10 + U_Spec.Hexa_To_Unsigned_Ghost (S (P)) - and then - (if P = Max then Prev_V = Res - else U_Spec.Scan_Based_Number_Ghost - (Str => Prev_S, - From => P + 1, - To => Max, - Base => 10, - Acc => Prev_V) = U_Spec.Wrap_Option (Res)), - Post => - (for all I in P .. Max => S (I) in '0' .. '9') - and then U_Spec.Scan_Based_Number_Ghost - (Str => S, - From => P, - To => Max, - Base => 10, - Acc => V) = U_Spec.Wrap_Option (Res); - -- Ghost lemma to prove that Scan_Based_Number_Ghost is preserved - -- through an iteration of the loop. - - ----------------------------- - -- Local lemma null bodies -- - ----------------------------- - - procedure Prove_Character_Val (R : Uns) is null; - procedure Prove_Euclidian (Val, Quot, Rest : Uns) is null; - procedure Prove_Hexa_To_Unsigned_Ghost (R : Uns) is null; - - --------------------- - -- Prove_Scan_Iter -- - --------------------- - - procedure Prove_Scan_Iter - (S, Prev_S : String; - V, Prev_V, Res : Uns; - P, Max : Natural) - is - pragma Unreferenced (Res); - begin - U_Spec.Lemma_Scan_Based_Number_Ghost_Step - (Str => S, - From => P, - To => Max, - Base => 10, - Acc => V); - if P < Max then - U_Spec.Prove_Scan_Based_Number_Ghost_Eq - (Prev_S, S, P + 1, Max, 10, Prev_V); - else - U_Spec.Lemma_Scan_Based_Number_Ghost_Base - (Str => S, - From => P + 1, - To => Max, - Base => 10, - Acc => Prev_V); - end if; - end Prove_Scan_Iter; - - -- Start of processing for Set_Image_Unsigned - begin pragma Assert (P >= S'First - 1 and then P < S'Last and then P < Natural'Last); @@ -290,70 +67,19 @@ package body System.Image_U is -- First we compute the number of characters needed for representing -- the number. loop - Lemma_Div_Commutation (Value, 10); - Lemma_Div_Twice (Big (V), Big_10 ** Nb_Digits, Big_10); - Value := Value / 10; Nb_Digits := Nb_Digits + 1; - Pow := Pow * 10; - - pragma Loop_Invariant (Nb_Digits in 1 .. Unsigned_Width_Ghost - 1); - pragma Loop_Invariant (Pow = Big_10 ** Nb_Digits); - pragma Loop_Invariant (Big (Value) = Big (V) / Pow); - pragma Loop_Variant (Decreases => Value); exit when Value = 0; - - Lemma_Non_Zero (Value); - pragma Assert (Pow <= Big (Uns'Last)); end loop; - pragma Assert (Big (V) / (Big_10 ** Nb_Digits) = 0); Value := V; - Pow := 1; - - pragma Assert (Value = From_Big (Big (V) / Big_10 ** 0)); -- We now populate digits from the end of the string to the beginning for J in reverse 1 .. Nb_Digits loop - Lemma_Div_Commutation (Value, 10); - Lemma_Div_Twice (Big (V), Big_10 ** (Nb_Digits - J), Big_10); - Prove_Character_Val (Value); - Prove_Hexa_To_Unsigned_Ghost (Value rem 10); - - Prev_Value := Value; - Prev_S := S; - Pow := Pow * 10; S (P + J) := Character'Val (48 + (Value rem 10)); Value := Value / 10; - - Prove_Euclidian - (Val => Prev_Value, - Quot => Value, - Rest => U_Spec.Hexa_To_Unsigned_Ghost (S (P + J))); - - Prove_Scan_Iter - (S, Prev_S, Value, Prev_Value, V, P + J, P + Nb_Digits); - - pragma Loop_Invariant (Value <= Uns'Last / 10); - pragma Loop_Invariant - (for all K in S'First .. P => S (K) = S_Init (K)); - pragma Loop_Invariant - (U_Spec.Only_Decimal_Ghost - (S, From => P + J, To => P + Nb_Digits)); - pragma Loop_Invariant (Pow = Big_10 ** (Nb_Digits - J + 1)); - pragma Loop_Invariant (Big (Value) = Big (V) / Pow); - pragma Loop_Invariant - (U_Spec.Scan_Based_Number_Ghost - (Str => S, - From => P + J, - To => P + Nb_Digits, - Base => 10, - Acc => Value) - = U_Spec.Wrap_Option (V)); end loop; - pragma Assert (Big (Value) = Big (V) / (Big_10 ** Nb_Digits)); - pragma Assert (Value = 0); P := P + Nb_Digits; end Set_Image_Unsigned; |