------------------------------------------------------------------------------
--                                                                          --
--                         GNAT COMPILER COMPONENTS                         --
--                                                                          --
--                     S Y S T E M . A R I T H _ 1 2 8                      --
--                                                                          --
--                                 S p e c                                  --
--                                                                          --
--            Copyright (C) 2020-2024, 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 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;
