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add test for issue #995
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kanigsson committed Jun 30, 2022
1 parent 48b4f54 commit 97c650a
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pragma Style_Checks ("N3aAbcdefhiIklnOprStux");

package body RFLX.RFLX_Arithmetic with
SPARK_Mode
is

function Shift_Left (Value : U64; Amount : Natural) return U64 with
Import,
Convention => Intrinsic,
Global => null;

function Shift_Right (Value : U64; Amount : Natural) return U64 with
Import,
Convention => Intrinsic,
Global => null;

function Shift_Add (V : U64;
Data : U64;
Amount : Natural;
Bits : Natural) return U64
is
pragma Unreferenced (Bits);
begin
return Shift_Left (V, Amount) + Data;
end Shift_Add;

function Right_Shift (V : U64; Amount : Natural; Size : Natural) return U64
is
pragma Unreferenced (Size);
begin
return Shift_Right (V, Amount);
end Right_Shift;

function Left_Shift (V : U64; Amount : Natural; Size : Natural) return U64
is
pragma Unreferenced (Size);
Result : constant U64 := Shift_Left (V, Amount);
begin
return Result;
end Left_Shift;

function Mask_Lower (V : U64; Mask, Bits : Natural) return U64
is
Result : constant U64 := Shift_Left (Shift_Right (V, Mask), Mask);
begin
pragma Assert
(if Bits < U64'Size then Result <= 2 ** Bits - 2 ** Mask
elsif Mask < U64'Size then Result <= U64'Last - 2 ** Mask + 1);
return Result;
end Mask_Lower;

function Mask_Upper (V : U64; Mask : Natural) return U64
is
begin
return V and (2 ** Mask - 1);
end Mask_Upper;

function Add (A : U64; B : U64; Total_Bits, Lower_Bits : Natural) return U64
is
pragma Unreferenced (Total_Bits, Lower_Bits);
begin
return A + B;
end Add;

procedure Lemma_Size (Val : Base_Integer; Size : Positive) is
begin
if Size < Base_Integer'Size then
pragma Assert (Val < 2 ** Size);
pragma Assert (U64 (Val) < 2 ** Size);
pragma Assert (Fits_Into (U64 (Val), Size));
else
pragma Assert (Size = 63);
pragma Assert (Fits_Into (U64 (Val), Size));
end if;
end Lemma_Size;

end RFLX.RFLX_Arithmetic;
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pragma Style_Checks ("N3aAbcdefhiIklnOprStux");

package RFLX.RFLX_Arithmetic with
SPARK_Mode
is

type U64 is mod 2**64 with
Annotate => (GNATprove, No_Wrap_Around);

type Base_Integer is range 0 .. 2 ** 63 - 1;

-- Express that V contains at most Bits non-zero bits, in the least
-- significant part (the rest is zero).
pragma Warnings (Off, "postcondition does not mention function result");
function Fits_Into (V : U64; Bits : Natural) return Boolean
is (if Bits < U64'Size then V < 2 ** Bits)
with Post => True;

function Fits_Into (V : Base_Integer; Bits : Natural) return Boolean
is (if Bits < Base_Integer'Size then V < 2 ** Bits)
with Post => True;

-- Express that V contains (U64'Size - Bits) leading zero bits, then (Bits -
-- Lower) bits of data, then Lower bits of zeros.
-- |- (U64'Size - bits) -|- (Bits-Lower) -|- Lower -|
-- |000000000000000000000|xxxxxxxxxxxxxxxx|000000000|
function Fits_Into_Upper (V : U64; Bits, Lower : Natural) return Boolean
is (if Bits < U64'Size then V <= 2 ** Bits - 2 ** Lower
elsif Lower > 0 and then Lower < U64'Size then V <= U64'Last - 2 ** Lower + 1)
with Pre => Bits <= U64'Size and then Lower <= Bits,
Post => True;
pragma Warnings (On, "postcondition does not mention function result");

-- V is assumed to contain Bits bits of data. Add the Amount bits contained
-- in Data by shifting V to the left and adding Data. The result contains
-- (Bits + Amount) bits of data.
function Shift_Add (V : U64;
Data : U64;
Amount : Natural;
Bits : Natural) return U64
with Pre =>
Bits < U64'Size
and then Amount < U64'Size
and then Fits_Into (V, Bits)
and then U64'Size - Amount >= Bits
and then Fits_Into (Data, Amount),
Post => Fits_Into (Shift_Add'Result, Bits + Amount);

-- Wrapper of Shift_Right that expresses the operation in terms of
-- Fits_Into.
function Right_Shift (V : U64; Amount : Natural; Size : Natural) return U64 with
Pre =>
Size <= U64'Size
and then Fits_Into (V, Size)
and then Amount <= Size
and then Size - Amount < U64'Size,
Post => Fits_Into (Right_Shift'Result, Size - Amount);

-- Wrapper of Shift_Left that expresses the operation in terms of
-- Fits_Into/Fits_Into_Upper.
function Left_Shift (V : U64; Amount : Natural; Size : Natural) return U64 with
Pre =>
Size < U64'Size
and then Amount < U64'Size
and then Fits_Into (V, Size)
and then Size + Amount < U64'Size,
Post => Fits_Into_Upper (Left_Shift'Result, Size + Amount, Amount);

-- V is assumed to have Bits bits of data. Set the lower bits of V to zero.
function Mask_Lower (V : U64; Mask, Bits : Natural) return U64
with Pre => Bits <= U64'Size and then Fits_Into (V, Bits) and then Mask <= Bits and then Mask >= 1,
Post => Fits_Into_Upper (Mask_Lower'Result, Bits, Mask);

-- Set the upper bits of V to zero.
function Mask_Upper (V : U64; Mask : Natural) return U64
with Pre => Mask < U64'Size,
Post => Fits_Into (Mask_Upper'Result, Mask);

-- Add A and B in the special case where A only uses the upper bits and B
-- only the lower bits.
function Add (A : U64; B : U64; Total_Bits, Lower_Bits : Natural) return U64
with Pre =>
Total_Bits <= U64'Size
and then Lower_Bits <= Total_Bits
and then (if Total_Bits = U64'Size then Lower_Bits /= U64'Size)
and then Fits_Into_Upper (A, Total_Bits, Lower_Bits)
and then Fits_Into (B, Lower_Bits),
Post => Add'Result = A + B and Fits_Into (Add'Result, Total_Bits),
Global => null;

procedure Lemma_Size (Val : Base_Integer; Size : Positive)
with Ghost,
Pre => Size in 1 .. 63 and then Fits_Into (Val, Size),
Post => Fits_Into (U64 (Val), Size);

end RFLX.RFLX_Arithmetic;
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pragma Style_Checks ("N3aAbcdefhiIklnOprStux");

with RFLX.RFLX_Arithmetic;

package RFLX.RFLX_Builtin_Types.Conversions with
SPARK_Mode
is

pragma Annotate (GNATprove, Always_Return, Conversions);

function Valid_Boolean (Val : RFLX.RFLX_Arithmetic.U64) return Boolean is
(case Val is
when 0 | 1 =>
True,
when others =>
False);

function To_U64 (Enum : Boolean) return RFLX.RFLX_Arithmetic.U64 is
(case Enum is
when False =>
0,
when True =>
1);

function To_Actual (Val : RFLX.RFLX_Arithmetic.U64) return Boolean is
(case Val is
when 0 =>
False,
when 1 =>
True,
when others =>
False)
with
Pre =>
Valid_Boolean (Val);

function Valid_Boolean (Val : RFLX.RFLX_Arithmetic.Base_Integer) return Boolean is
(case Val is
when 0 | 1 =>
True,
when others =>
False);

function To_Base_Integer (Enum : Boolean) return RFLX.RFLX_Arithmetic.Base_Integer is
(case Enum is
when False =>
0,
when True =>
1);

function To_Actual (Val : RFLX.RFLX_Arithmetic.Base_Integer) return Boolean is
(case Val is
when 0 =>
False,
when 1 =>
True,
when others =>
False)
with
Pre =>
Valid_Boolean (Val);

end RFLX.RFLX_Builtin_Types.Conversions;
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pragma Style_Checks ("N3aAbcdefhiIklnOprStux");

package RFLX.RFLX_Builtin_Types with
SPARK_Mode
is

type Length is new Natural;

type Index is new Length range 1 .. Length'Last;

type Byte is mod 2**8;

type Bytes is array (Index range <>) of Byte;

type Bytes_Ptr is access Bytes;

type Bit_Length is range 0 .. Length'Last * 8;

type Boolean_Base is mod 2;

end RFLX.RFLX_Builtin_Types;
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