------------------------------------------------------------------------------ -- -- -- GNAT COMPILER COMPONENTS -- -- -- -- S Y S T E M . A R I T H _ 6 4 -- -- -- -- S p e c -- -- -- -- Copyright (C) 1992-2025, 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 64-bit -- signed integer values in cases where either overflow checking is -- required, or intermediate results are longer than 64 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_64 with Pure, SPARK_Mode is use type Ada.Numerics.Big_Numbers.Big_Integers_Ghost.Big_Integer; use type Interfaces.Integer_64; subtype Int64 is Interfaces.Integer_64; 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 => Int64); function Big (Arg : Int64) return Big_Integer is (Signed_Conversion.To_Big_Integer (Arg)) with Ghost; function In_Int64_Range (Arg : Big_Integer) return Boolean is (Ada.Numerics.Big_Numbers.Big_Integers_Ghost.In_Range (Arg, Big (Int64'First), Big (Int64'Last))) with Ghost; function Add_With_Ovflo_Check64 (X, Y : Int64) return Int64 with Pre => In_Int64_Range (Big (X) + Big (Y)), Post => Add_With_Ovflo_Check64'Result = X + Y; -- Raises Constraint_Error if sum of operands overflows 64 bits, -- otherwise returns the 64-bit signed integer sum. -- -- The sum of ``X`` and ``Y`` is first computed using wrap-around -- semantics. -- -- If the sign of ``X`` and ``Y`` are opposed, no overflow is possible and -- the result is correct. -- -- Otherwise, ``X`` and ``Y`` have the same sign; if the sign of the result -- is not identical to ``X`` (or ``Y``), then an overflow occurred and -- the exception *Constraint_Error* is raised; otherwise the result is -- correct. function Subtract_With_Ovflo_Check64 (X, Y : Int64) return Int64 with Pre => In_Int64_Range (Big (X) - Big (Y)), Post => Subtract_With_Ovflo_Check64'Result = X - Y; -- Raises Constraint_Error if difference of operands overflows 64 -- bits, otherwise returns the 64-bit signed integer difference. -- -- The logic of the implementation is reversed from *Add_With_Ovflo_Check*: -- if ``X`` and ``Y`` have the same sign, no overflow is checked, otherwise -- a sign of the result is compared with the sign of ``X`` to check for -- overflow. function Multiply_With_Ovflo_Check64 (X, Y : Int64) return Int64 with Pre => In_Int64_Range (Big (X) * Big (Y)), Post => Multiply_With_Ovflo_Check64'Result = X * Y; pragma Export (C, Multiply_With_Ovflo_Check64, "__gnat_mulv64"); -- Raises Constraint_Error if product of operands overflows 64 -- bits, otherwise returns the 64-bit signed integer product. -- The code generator may also generate direct calls to this routine. -- -- The multiplication is done using pencil and paper algorithm using base -- 2**32. The multiplication is done on unsigned values, then the correct -- signed value is returned. Overflow check is performed by looking at -- higher digits. function Same_Sign (X, Y : Big_Integer) return Boolean is (X = Big (Int64'(0)) or else Y = Big (Int64'(0)) or else (X < Big (Int64'(0))) = (Y < Big (Int64'(0)))) with Ghost; function Round_Quotient (X, Y, Q, R : Big_Integer) return Big_Integer with Ghost, Pre => Y /= 0 and then Q = X / Y and then R = X rem Y, Post => Round_Quotient'Result = (if abs R > (abs Y - Big (Int64'(1))) / Big (Int64'(2)) then (if Same_Sign (X, Y) then Q + Big (Int64'(1)) else Q - Big (Int64'(1))) else Q); procedure Scaled_Divide64 (X, Y, Z : Int64; Q, R : out Int64; Round : Boolean) with Pre => Z /= 0 and then In_Int64_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 64-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. -- -- The multiplication is done using pencil and paper algorithm using base -- 2**32. The multiplication is done on unsigned values. The result is a -- 128 bit value. -- -- The overflow is detected on the intermediate value. -- -- If Z is a 32 bit value, the division is done using pencil and paper -- algorithm. -- -- Otherwise, the division is performed using the algorithm D from section -- 4.3.1 of "The Art of Computer Programming Vol. 2" [TACP2]. Rounding is -- applied on the result. -- -- Finally, the sign is applied to the result and returned. procedure Scaled_Divide (X, Y, Z : Int64; Q, R : out Int64; Round : Boolean) renames Scaled_Divide64; -- Renamed procedure to preserve compatibility with earlier versions procedure Double_Divide64 (X, Y, Z : Int64; Q, R : out Int64; Round : Boolean) with Pre => Y /= 0 and then Z /= 0 and then In_Int64_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 64-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. -- -- Division by 0 is first detected. -- -- The intermediate value ``Y`` * ``Z`` is then computed on 128 bits. The -- multiplication is done on unsigned values. -- -- If the high 64 bits of the intermediate value is not 0, then 0 is -- returned. The overflow case of the largest negative number divided by -- -1 is detected here. -- -- 64-bit division is then performed, the result is rounded, its sign is -- corrected, and then returned. procedure Double_Divide (X, Y, Z : Int64; Q, R : out Int64; Round : Boolean) renames Double_Divide64; -- Renamed procedure to preserve compatibility with earlier versions end System.Arith_64;