------------------------------------------------------------------------------ -- -- -- GNAT COMPILER COMPONENTS -- -- -- -- S Y S T E M . A R I T H _ D O U B L E -- -- -- -- S p e c -- -- -- -- Copyright (C) 1992-2023, 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 -- -- . -- -- -- -- GNAT was originally developed by the GNAT team at New York University. -- -- Extensive contributions were provided by Ada Core Technologies Inc. -- -- -- ------------------------------------------------------------------------------ -- This package provides software routines for doing arithmetic on "double" -- signed integer values in cases where either overflow checking is required, -- or intermediate results are longer than the result type. with Ada.Numerics.Big_Numbers.Big_Integers_Ghost; generic type Double_Int is range <>; type Double_Uns is mod <>; type Single_Uns is mod <>; with function Shift_Left (A : Double_Uns; B : Natural) return Double_Uns is <>; with function Shift_Right (A : Double_Uns; B : Natural) return Double_Uns is <>; with function Shift_Left (A : Single_Uns; B : Natural) return Single_Uns is <>; package System.Arith_Double with Pure, SPARK_Mode is -- 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); package BI_Ghost renames Ada.Numerics.Big_Numbers.Big_Integers_Ghost; subtype Big_Integer is BI_Ghost.Big_Integer with Ghost; subtype Big_Natural is BI_Ghost.Big_Natural with Ghost; subtype Big_Positive is BI_Ghost.Big_Positive with Ghost; use type BI_Ghost.Big_Integer; package Signed_Conversion is new BI_Ghost.Signed_Conversions (Int => Double_Int); function Big (Arg : Double_Int) return Big_Integer is (Signed_Conversion.To_Big_Integer (Arg)) with Ghost, Annotate => (GNATprove, Inline_For_Proof); package Unsigned_Conversion is new BI_Ghost.Unsigned_Conversions (Int => Double_Uns); function Big (Arg : Double_Uns) return Big_Integer is (Unsigned_Conversion.To_Big_Integer (Arg)) with Ghost, Annotate => (GNATprove, Inline_For_Proof); function In_Double_Int_Range (Arg : Big_Integer) return Boolean is (BI_Ghost.In_Range (Arg, Big (Double_Int'First), Big (Double_Int'Last))) with Ghost, Annotate => (GNATprove, Inline_For_Proof); function Add_With_Ovflo_Check (X, Y : Double_Int) return Double_Int with Pre => In_Double_Int_Range (Big (X) + Big (Y)), Post => Add_With_Ovflo_Check'Result = X + Y; -- Raises Constraint_Error if sum of operands overflows Double_Int, -- otherwise returns the signed integer sum. function Subtract_With_Ovflo_Check (X, Y : Double_Int) return Double_Int with Pre => In_Double_Int_Range (Big (X) - Big (Y)), Post => Subtract_With_Ovflo_Check'Result = X - Y; -- Raises Constraint_Error if difference of operands overflows Double_Int, -- otherwise returns the signed integer difference. function Multiply_With_Ovflo_Check (X, Y : Double_Int) return Double_Int with Pre => In_Double_Int_Range (Big (X) * Big (Y)), Post => Multiply_With_Ovflo_Check'Result = X * Y; pragma Convention (C, Multiply_With_Ovflo_Check); -- Raises Constraint_Error if product of operands overflows Double_Int, -- otherwise returns the signed integer product. Gigi may also call this -- routine directly. function Same_Sign (X, Y : Big_Integer) return Boolean is (X = Big (Double_Int'(0)) or else Y = Big (Double_Int'(0)) or else (X < Big (Double_Int'(0))) = (Y < Big (Double_Int'(0)))) with Ghost; function Round_Quotient (X, Y, Q, R : Big_Integer) return Big_Integer is (if abs R > (abs Y - Big (Double_Int'(1))) / Big (Double_Int'(2)) then (if Same_Sign (X, Y) then Q + Big (Double_Int'(1)) else Q - Big (Double_Int'(1))) else Q) with Ghost, Pre => Y /= 0 and then Q = X / Y and then R = X rem Y; procedure Scaled_Divide (X, Y, Z : Double_Int; Q, R : out Double_Int; Round : Boolean) with Pre => Z /= 0 and then In_Double_Int_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 Double_Int. 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. procedure Double_Divide (X, Y, Z : Double_Int; Q, R : out Double_Int; Round : Boolean) with Pre => Y /= 0 and then Z /= 0 and then In_Double_Int_Range (if Round then Round_Quotient (Big (X), Big (Y) * Big (Z), Big (X) / (Big (Y) * Big (Z)), Big (X) rem (Big (Y) * Big (Z))) else Big (X) / (Big (Y) * Big (Z))), Post => Big (R) = Big (X) rem (Big (Y) * 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 X / (Y * Z), storing the quotient in Q and -- the remainder in R. Constraint_Error is raised if Y or Z is zero, -- or if the quotient does not fit in Double_Int. 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_Double;