------------------------------------------------------------------------------ | |

-- -- | |

-- GNAT COMPILER COMPONENTS -- | |

-- -- | |

-- S Y S T E M . A R I T H _ 1 2 8 -- | |

-- -- | |

-- 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 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; |