| ------------------------------------------------------------------------------ |
| -- -- |
| -- GNAT COMPILER COMPONENTS -- |
| -- -- |
| -- S Y S T E M . A R I T H _ 3 2 -- |
| -- -- |
| -- S p e c -- |
| -- -- |
| -- Copyright (C) 2020-2022, Free Software Foundation, Inc. -- |
| -- -- |
| -- GNAT is free software; you can redistribute it and/or modify it under -- |
| -- terms of the GNU General Public License as published by the Free Soft- -- |
| -- ware Foundation; either version 3, or (at your option) any later ver- -- |
| -- sion. GNAT is distributed in the hope that it will be useful, but WITH- -- |
| -- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY -- |
| -- or FITNESS FOR A PARTICULAR PURPOSE. -- |
| -- -- |
| -- As a special exception under Section 7 of GPL version 3, you are granted -- |
| -- additional permissions described in the GCC Runtime Library Exception, -- |
| -- version 3.1, as published by the Free Software Foundation. -- |
| -- -- |
| -- You should have received a copy of the GNU General Public License and -- |
| -- a copy of the GCC Runtime Library Exception along with this program; -- |
| -- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see -- |
| -- <http://www.gnu.org/licenses/>. -- |
| -- -- |
| -- GNAT was originally developed by the GNAT team at New York University. -- |
| -- Extensive contributions were provided by Ada Core Technologies Inc. -- |
| -- -- |
| ------------------------------------------------------------------------------ |
| |
| -- This unit provides software routines for doing arithmetic on 32-bit |
| -- signed integer values in cases where either overflow checking is |
| -- required, or intermediate results are longer than 32 bits. |
| |
| -- Preconditions in this unit are meant for analysis only, not for run-time |
| -- checking, so that the expected exceptions are raised. This is enforced |
| -- by setting the corresponding assertion policy to Ignore. Postconditions |
| -- and contract cases should not be executed at runtime as well, in order |
| -- not to slow down the execution of these functions. |
| |
| pragma Assertion_Policy (Pre => Ignore, |
| Post => Ignore, |
| Contract_Cases => Ignore, |
| Ghost => Ignore); |
| |
| with Interfaces; |
| with Ada.Numerics.Big_Numbers.Big_Integers_Ghost; |
| |
| package System.Arith_32 |
| with Pure, SPARK_Mode |
| is |
| use type Ada.Numerics.Big_Numbers.Big_Integers_Ghost.Big_Integer; |
| use type Interfaces.Integer_32; |
| |
| subtype Int32 is Interfaces.Integer_32; |
| |
| subtype Big_Integer is |
| Ada.Numerics.Big_Numbers.Big_Integers_Ghost.Big_Integer |
| with Ghost; |
| |
| package Signed_Conversion is new |
| Ada.Numerics.Big_Numbers.Big_Integers_Ghost.Signed_Conversions |
| (Int => Int32); |
| |
| function Big (Arg : Int32) return Big_Integer is |
| (Signed_Conversion.To_Big_Integer (Arg)) |
| with Ghost; |
| |
| function In_Int32_Range (Arg : Big_Integer) return Boolean is |
| (Ada.Numerics.Big_Numbers.Big_Integers_Ghost.In_Range |
| (Arg, Big (Int32'First), Big (Int32'Last))) |
| with Ghost; |
| |
| function Same_Sign (X, Y : Big_Integer) return Boolean is |
| (X = Big (Int32'(0)) |
| or else Y = Big (Int32'(0)) |
| or else (X < Big (Int32'(0))) = (Y < Big (Int32'(0)))) |
| with Ghost; |
| |
| function Round_Quotient (X, Y, Q, R : Big_Integer) return Big_Integer is |
| (if abs R > (abs Y - Big (Int32'(1))) / Big (Int32'(2)) then |
| (if Same_Sign (X, Y) then Q + Big (Int32'(1)) |
| else Q - Big (Int32'(1))) |
| else |
| Q) |
| with |
| Ghost, |
| Pre => Y /= 0 and then Q = X / Y and then R = X rem Y; |
| |
| procedure Scaled_Divide32 |
| (X, Y, Z : Int32; |
| Q, R : out Int32; |
| Round : Boolean) |
| with |
| Pre => Z /= 0 |
| and then In_Int32_Range |
| (if Round then Round_Quotient (Big (X) * Big (Y), Big (Z), |
| Big (X) * Big (Y) / Big (Z), |
| Big (X) * Big (Y) rem Big (Z)) |
| else Big (X) * Big (Y) / Big (Z)), |
| Post => Big (R) = Big (X) * Big (Y) rem Big (Z) |
| and then |
| (if Round then |
| Big (Q) = Round_Quotient (Big (X) * Big (Y), Big (Z), |
| Big (X) * Big (Y) / Big (Z), Big (R)) |
| else |
| Big (Q) = Big (X) * Big (Y) / Big (Z)); |
| -- Performs the division of (X * Y) / Z, storing the quotient in Q |
| -- and the remainder in R. Constraint_Error is raised if Z is zero, |
| -- or if the quotient does not fit in 32 bits. Round indicates if |
| -- the result should be rounded. If Round is False, then Q, R are |
| -- the normal quotient and remainder from a truncating division. |
| -- If Round is True, then Q is the rounded quotient. The remainder |
| -- R is not affected by the setting of the Round flag. |
| |
| end System.Arith_32; |
