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From: Pierre-Marie de Rodat <pmderodat@gcc.gnu.org> To: gcc-cvs@gcc.gnu.org Subject: [gcc r12-6462] [Ada] Adapt proof of System.Arith_Double Date: Tue, 11 Jan 2022 13:27:55 +0000 (GMT) [thread overview] Message-ID: <20220111132755.7DF5638A9429@sourceware.org> (raw) https://gcc.gnu.org/g:ee22e1aa71b30a699d051ca9aa65ddf342a2635b commit r12-6462-gee22e1aa71b30a699d051ca9aa65ddf342a2635b Author: Yannick Moy <moy@adacore.com> Date: Wed Jan 5 14:36:13 2022 +0000 [Ada] Adapt proof of System.Arith_Double gcc/ada/ * libgnat/s-aridou.adb (Double_Divide): Adjust proof of lemma Prove_Signs, call lemma for commutation of Big and multiplication. (Multiply_With_Ovflo_Check): Adjust postcondition of Prove_Pos_Int. (Scaled_Divide): Explicit commutation in the proof of lemma Prove_Multiplication, add new lemma Prove_Shift_Progress for congruence property that is not proved in a larger context, add assertions at the end of the loop to state loop invariant properties. Diff: --- gcc/ada/libgnat/s-aridou.adb | 43 ++++++++++++++++++++++++++++++++++--------- 1 file changed, 34 insertions(+), 9 deletions(-) diff --git a/gcc/ada/libgnat/s-aridou.adb b/gcc/ada/libgnat/s-aridou.adb index df4faf1d646..0fefb6bd945 100644 --- a/gcc/ada/libgnat/s-aridou.adb +++ b/gcc/ada/libgnat/s-aridou.adb @@ -868,11 +868,14 @@ is if (X >= 0) = Den_Pos then pragma Assert (Quot >= 0); pragma Assert (Big_Q >= 0); + pragma Assert (Q >= 0); pragma Assert (Big (Q) = Big_Q); else pragma Assert ((X >= 0) /= (Big (Y) * Big (Z) >= 0)); pragma Assert (Quot <= 0); pragma Assert (Big_Q <= 0); + pragma Assert (if X >= 0 then R >= 0); + pragma Assert (if X < 0 then R <= 0); pragma Assert (Big (R) = Big_R); end if; end Prove_Signs; @@ -893,6 +896,7 @@ is else Big_Q := Quot; end if; + Lemma_Abs_Mult_Commutation (Big (Y), Big (Z)); Lemma_Mult_Decomposition (Mult, Yu, Zu, Yhi, Ylo, Zhi, Zlo); -- Compute Y * Z. Note that if the result overflows Double_Uns, then @@ -1417,7 +1421,8 @@ is Pre => In_Double_Int_Range (Big (X) * Big (Y)) and then Mult = Big (T2) and then ((X >= 0 and then Y >= 0) or else (X < 0 and then Y < 0)), - Post => To_Pos_Int (T2) = X * Y; + Post => In_Double_Int_Range (Big (T2)) + and then To_Pos_Int (T2) = X * Y; procedure Prove_Result_Too_Large with @@ -1925,6 +1930,10 @@ is Lemma_Hi_Lo (T1, Hi (T1), S3); Lemma_Hi_Lo (T2, Hi (T2), Lo (T2)); Lemma_Hi_Lo (T3, Hi (T3), S2); + Lemma_Mult_Commutation (Double_Uns (Q), Double_Uns (Lo (Zu)), T1); + Lemma_Mult_Commutation (Double_Uns (Q), Double_Uns (Hi (Zu)), T2); + pragma Assert (Big (Double_Uns (Q)) * Big (Zu) = + Big_2xxSingle * Big (T2) + Big (T1)); pragma Assert (Big (Double_Uns (Q)) * Big (Zu) = Big_2xxSingle * Big_2xxSingle * Big (Double_Uns (Hi (T2))) + Big_2xxSingle * Big_2xxSingle * Big (Double_Uns (Hi (T3))) @@ -2321,6 +2330,21 @@ is Post => Shift / 2 = 2 ** (Log_Single_Size - (Inter + 1)) and then (Shift = 2 or (Shift / 2) mod 2 = 0); + procedure Prove_Shift_Progress + with + Ghost, + Pre => Shift <= Single_Size / 2 + and then Shift_Prev = 2 * Shift + and then Mask_Prev = + Shift_Left (Single_Uns'Last, Single_Size - Shift_Prev) + and then Mask = + Shift_Left (Single_Uns'Last, + Single_Size - Shift_Prev + Shift), + Post => Mask_Prev = + Shift_Left (Single_Uns'Last, Single_Size - 2 * Shift) + and then Mask = + Shift_Left (Single_Uns'Last, Single_Size - Shift); + procedure Prove_Shifting with Ghost, @@ -2333,17 +2357,13 @@ is and then (Hi (Zu_Prev) and Mask_Prev and not Mask) /= 0, Post => (Hi (Zu) and Mask) /= 0; - ----------------- - -- Prove_Power -- - ----------------- + ----------------------------- + -- Local lemma null bodies -- + ----------------------------- procedure Prove_Power is null; - - -------------------- - -- Prove_Shifting -- - -------------------- - procedure Prove_Shifting is null; + procedure Prove_Shift_Progress is null; begin Prove_Power; @@ -2357,6 +2377,7 @@ is Lemma_Double_Shift (Single_Uns'Last, Single_Size - Shift_Prev, Shift); + Prove_Shift_Progress; if (Hi (Zu) and Mask) = 0 then Zu := Shift_Left (Zu, Shift); @@ -2378,9 +2399,13 @@ is Scale := Scale + Shift; + pragma Assert (Zu = Shift_Left (abs Z, Scale)); pragma Assert (Big (Zu) = Big (Double_Uns'(abs Z)) * Big_2xx (Scale)); end if; + + pragma Assert + (Big (Zu) = Big (Double_Uns'(abs Z)) * Big_2xx (Scale)); end; end loop;
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