------------------------------------------------------------------------------ -- -- -- GNAT COMPILER COMPONENTS -- -- -- -- S Y S T E M . A R I T H _ 1 2 8 -- -- -- -- S p e c -- -- -- -- Copyright (C) 2020-2023, 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 unit provides software routines for doing arithmetic on 128-bit -- signed integer values in cases where either overflow checking is -- required, or intermediate results are longer than 128 bits. pragma Restrictions (No_Elaboration_Code); -- Allow direct call from gigi generated code -- 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 Ada.Numerics.Big_Numbers.Big_Integers_Ghost; with Interfaces; package System.Arith_128 with Pure, SPARK_Mode is use type Ada.Numerics.Big_Numbers.Big_Integers_Ghost.Big_Integer; use type Interfaces.Integer_128; subtype Int128 is Interfaces.Integer_128; 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 => Int128); function Big (Arg : Int128) return Big_Integer is (Signed_Conversion.To_Big_Integer (Arg)) with Ghost; function In_Int128_Range (Arg : Big_Integer) return Boolean is (Ada.Numerics.Big_Numbers.Big_Integers_Ghost.In_Range (Arg, Big (Int128'First), Big (Int128'Last))) with Ghost; function Add_With_Ovflo_Check128 (X, Y : Int128) return Int128 with Pre => In_Int128_Range (Big (X) + Big (Y)), Post => Add_With_Ovflo_Check128'Result = X + Y; -- Raises Constraint_Error if sum of operands overflows 128 bits, -- otherwise returns the 128-bit signed integer sum. function Subtract_With_Ovflo_Check128 (X, Y : Int128) return Int128 with Pre => In_Int128_Range (Big (X) - Big (Y)), Post => Subtract_With_Ovflo_Check128'Result = X - Y; -- Raises Constraint_Error if difference of operands overflows 128 -- bits, otherwise returns the 128-bit signed integer difference. function Multiply_With_Ovflo_Check128 (X, Y : Int128) return Int128 with Pre => In_Int128_Range (Big (X) * Big (Y)), Post => Multiply_With_Ovflo_Check128'Result = X * Y; pragma Export (C, Multiply_With_Ovflo_Check128, "__gnat_mulv128"); -- Raises Constraint_Error if product of operands overflows 128 -- bits, otherwise returns the 128-bit signed integer product. -- Gigi may also call this routine directly. function Same_Sign (X, Y : Big_Integer) return Boolean is (X = Big (Int128'(0)) or else Y = Big (Int128'(0)) or else (X < Big (Int128'(0))) = (Y < Big (Int128'(0)))) with Ghost; function Round_Quotient (X, Y, Q, R : Big_Integer) return Big_Integer is (if abs R > (abs Y - Big (Int128'(1))) / Big (Int128'(2)) then (if Same_Sign (X, Y) then Q + Big (Int128'(1)) else Q - Big (Int128'(1))) else Q) with Ghost, Pre => Y /= 0 and then Q = X / Y and then R = X rem Y; procedure Scaled_Divide128 (X, Y, Z : Int128; Q, R : out Int128; Round : Boolean) with Pre => Z /= 0 and then In_Int128_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 128 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. procedure Double_Divide128 (X, Y, Z : Int128; Q, R : out Int128; Round : Boolean) with Pre => Y /= 0 and then Z /= 0 and then In_Int128_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 128 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_128;