559 lines
26 KiB
Ada
559 lines
26 KiB
Ada
------------------------------------------------------------------------------
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-- --
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-- GNAT COMPILER COMPONENTS --
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-- --
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-- U I N T P --
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-- --
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-- S p e c --
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-- --
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-- Copyright (C) 1992-2016, Free Software Foundation, Inc. --
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-- --
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-- GNAT is free software; you can redistribute it and/or modify it under --
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-- terms of the GNU General Public License as published by the Free Soft- --
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-- ware Foundation; either version 3, or (at your option) any later ver- --
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-- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
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-- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
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-- or FITNESS FOR A PARTICULAR PURPOSE. --
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-- --
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-- As a special exception under Section 7 of GPL version 3, you are granted --
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-- additional permissions described in the GCC Runtime Library Exception, --
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-- version 3.1, as published by the Free Software Foundation. --
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-- --
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-- You should have received a copy of the GNU General Public License and --
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-- a copy of the GCC Runtime Library Exception along with this program; --
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-- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
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-- <http://www.gnu.org/licenses/>. --
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-- --
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-- GNAT was originally developed by the GNAT team at New York University. --
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-- Extensive contributions were provided by Ada Core Technologies Inc. --
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-- --
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------------------------------------------------------------------------------
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-- Support for universal integer arithmetic
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-- WARNING: There is a C version of this package. Any changes to this
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-- source file must be properly reflected in the C header file uintp.h
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with Alloc;
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with Table;
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pragma Elaborate_All (Table);
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with Types; use Types;
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package Uintp is
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-------------------------------------------------
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-- Basic Types and Constants for Uintp Package --
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-------------------------------------------------
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type Uint is private;
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-- The basic universal integer type
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No_Uint : constant Uint;
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-- A constant value indicating a missing or unset Uint value
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Uint_0 : constant Uint;
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Uint_1 : constant Uint;
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Uint_2 : constant Uint;
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Uint_3 : constant Uint;
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Uint_4 : constant Uint;
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Uint_5 : constant Uint;
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Uint_6 : constant Uint;
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Uint_7 : constant Uint;
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Uint_8 : constant Uint;
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Uint_9 : constant Uint;
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Uint_10 : constant Uint;
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Uint_11 : constant Uint;
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Uint_12 : constant Uint;
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Uint_13 : constant Uint;
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Uint_14 : constant Uint;
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Uint_15 : constant Uint;
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Uint_16 : constant Uint;
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Uint_24 : constant Uint;
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Uint_32 : constant Uint;
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Uint_63 : constant Uint;
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Uint_64 : constant Uint;
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Uint_80 : constant Uint;
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Uint_128 : constant Uint;
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Uint_Minus_1 : constant Uint;
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Uint_Minus_2 : constant Uint;
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Uint_Minus_3 : constant Uint;
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Uint_Minus_4 : constant Uint;
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Uint_Minus_5 : constant Uint;
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Uint_Minus_6 : constant Uint;
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Uint_Minus_7 : constant Uint;
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Uint_Minus_8 : constant Uint;
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Uint_Minus_9 : constant Uint;
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Uint_Minus_12 : constant Uint;
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Uint_Minus_36 : constant Uint;
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Uint_Minus_63 : constant Uint;
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Uint_Minus_80 : constant Uint;
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Uint_Minus_128 : constant Uint;
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type UI_Vector is array (Pos range <>) of Int;
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-- Vector containing the integer values of a Uint value
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-- Note: An earlier version of this package used pointers of arrays of Ints
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-- (dynamically allocated) for the Uint type. The change leads to a few
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-- less natural idioms used throughout this code, but eliminates all uses
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-- of the heap except for the table package itself. For example, Uint
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-- parameters are often converted to UI_Vectors for internal manipulation.
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-- This is done by creating the local UI_Vector using the function N_Digits
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-- on the Uint to find the size needed for the vector, and then calling
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-- Init_Operand to copy the values out of the table into the vector.
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-----------------
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-- Subprograms --
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-----------------
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procedure Initialize;
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-- Initialize Uint tables. Note that Initialize must not be called if
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-- Tree_Read is used. Note also that there is no lock routine in this
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-- unit, these are among the few tables that can be expanded during
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-- gigi processing.
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procedure Tree_Read;
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-- Initializes internal tables from current tree file using the relevant
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-- Table.Tree_Read routines. Note that Initialize should not be called if
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-- Tree_Read is used. Tree_Read includes all necessary initialization.
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procedure Tree_Write;
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-- Writes out internal tables to current tree file using the relevant
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-- Table.Tree_Write routines.
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function UI_Abs (Right : Uint) return Uint;
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pragma Inline (UI_Abs);
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-- Returns abs function of universal integer
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function UI_Add (Left : Uint; Right : Uint) return Uint;
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function UI_Add (Left : Int; Right : Uint) return Uint;
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function UI_Add (Left : Uint; Right : Int) return Uint;
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-- Returns sum of two integer values
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function UI_Decimal_Digits_Hi (U : Uint) return Nat;
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-- Returns an estimate of the number of decimal digits required to
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-- represent the absolute value of U. This estimate is correct or high,
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-- i.e. it never returns a value that is too low. The accuracy of the
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-- estimate affects only the effectiveness of comparison optimizations
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-- in Urealp.
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function UI_Decimal_Digits_Lo (U : Uint) return Nat;
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-- Returns an estimate of the number of decimal digits required to
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-- represent the absolute value of U. This estimate is correct or low,
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-- i.e. it never returns a value that is too high. The accuracy of the
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-- estimate affects only the effectiveness of comparison optimizations
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-- in Urealp.
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function UI_Div (Left : Uint; Right : Uint) return Uint;
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function UI_Div (Left : Int; Right : Uint) return Uint;
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function UI_Div (Left : Uint; Right : Int) return Uint;
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-- Returns quotient of two integer values. Fatal error if Right = 0
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function UI_Eq (Left : Uint; Right : Uint) return Boolean;
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function UI_Eq (Left : Int; Right : Uint) return Boolean;
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function UI_Eq (Left : Uint; Right : Int) return Boolean;
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pragma Inline (UI_Eq);
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-- Compares integer values for equality
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function UI_Expon (Left : Uint; Right : Uint) return Uint;
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function UI_Expon (Left : Int; Right : Uint) return Uint;
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function UI_Expon (Left : Uint; Right : Int) return Uint;
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function UI_Expon (Left : Int; Right : Int) return Uint;
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-- Returns result of exponentiating two integer values.
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-- Fatal error if Right is negative.
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function UI_GCD (Uin, Vin : Uint) return Uint;
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-- Computes GCD of input values. Assumes Uin >= Vin >= 0
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function UI_Ge (Left : Uint; Right : Uint) return Boolean;
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function UI_Ge (Left : Int; Right : Uint) return Boolean;
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function UI_Ge (Left : Uint; Right : Int) return Boolean;
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pragma Inline (UI_Ge);
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-- Compares integer values for greater than or equal
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function UI_Gt (Left : Uint; Right : Uint) return Boolean;
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function UI_Gt (Left : Int; Right : Uint) return Boolean;
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function UI_Gt (Left : Uint; Right : Int) return Boolean;
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pragma Inline (UI_Gt);
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-- Compares integer values for greater than
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function UI_Is_In_Int_Range (Input : Uint) return Boolean;
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pragma Inline (UI_Is_In_Int_Range);
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-- Determines if universal integer is in Int range
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function UI_Le (Left : Uint; Right : Uint) return Boolean;
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function UI_Le (Left : Int; Right : Uint) return Boolean;
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function UI_Le (Left : Uint; Right : Int) return Boolean;
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pragma Inline (UI_Le);
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-- Compares integer values for less than or equal
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function UI_Lt (Left : Uint; Right : Uint) return Boolean;
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function UI_Lt (Left : Int; Right : Uint) return Boolean;
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function UI_Lt (Left : Uint; Right : Int) return Boolean;
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-- Compares integer values for less than
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function UI_Max (Left : Uint; Right : Uint) return Uint;
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function UI_Max (Left : Int; Right : Uint) return Uint;
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function UI_Max (Left : Uint; Right : Int) return Uint;
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-- Returns maximum of two integer values
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function UI_Min (Left : Uint; Right : Uint) return Uint;
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function UI_Min (Left : Int; Right : Uint) return Uint;
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function UI_Min (Left : Uint; Right : Int) return Uint;
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-- Returns minimum of two integer values
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function UI_Mod (Left : Uint; Right : Uint) return Uint;
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function UI_Mod (Left : Int; Right : Uint) return Uint;
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function UI_Mod (Left : Uint; Right : Int) return Uint;
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pragma Inline (UI_Mod);
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-- Returns mod function of two integer values
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function UI_Mul (Left : Uint; Right : Uint) return Uint;
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function UI_Mul (Left : Int; Right : Uint) return Uint;
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function UI_Mul (Left : Uint; Right : Int) return Uint;
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-- Returns product of two integer values
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function UI_Ne (Left : Uint; Right : Uint) return Boolean;
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function UI_Ne (Left : Int; Right : Uint) return Boolean;
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function UI_Ne (Left : Uint; Right : Int) return Boolean;
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pragma Inline (UI_Ne);
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-- Compares integer values for inequality
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function UI_Negate (Right : Uint) return Uint;
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pragma Inline (UI_Negate);
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-- Returns negative of universal integer
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function UI_Rem (Left : Uint; Right : Uint) return Uint;
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function UI_Rem (Left : Int; Right : Uint) return Uint;
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function UI_Rem (Left : Uint; Right : Int) return Uint;
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-- Returns rem of two integer values
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function UI_Sub (Left : Uint; Right : Uint) return Uint;
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function UI_Sub (Left : Int; Right : Uint) return Uint;
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function UI_Sub (Left : Uint; Right : Int) return Uint;
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pragma Inline (UI_Sub);
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-- Returns difference of two integer values
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function UI_Modular_Exponentiation
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(B : Uint;
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E : Uint;
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Modulo : Uint) return Uint;
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-- Efficiently compute (B ** E) rem Modulo
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function UI_Modular_Inverse (N : Uint; Modulo : Uint) return Uint;
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-- Compute the multiplicative inverse of N in modular arithmetics with the
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-- given Modulo (uses Euclid's algorithm). Note: the call is considered
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-- to be erroneous (and the behavior is undefined) if n is not invertible.
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function UI_From_Int (Input : Int) return Uint;
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-- Converts Int value to universal integer form
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function UI_From_CC (Input : Char_Code) return Uint;
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-- Converts Char_Code value to universal integer form
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function UI_To_Int (Input : Uint) return Int;
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-- Converts universal integer value to Int. Constraint_Error if value is
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-- not in appropriate range.
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function UI_To_CC (Input : Uint) return Char_Code;
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-- Converts universal integer value to Char_Code. Constraint_Error if value
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-- is not in Char_Code range.
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function Num_Bits (Input : Uint) return Nat;
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-- Approximate number of binary bits in given universal integer. This
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-- function is used for capacity checks, and it can be one bit off
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-- without affecting its usage.
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function Vector_To_Uint
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(In_Vec : UI_Vector;
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Negative : Boolean) return Uint;
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-- Functions that calculate values in UI_Vectors, call this function to
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-- create and return the Uint value. In_Vec contains the multiple precision
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-- (Base) representation of a non-negative value. Leading zeroes are
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-- permitted. Negative is set if the desired result is the negative of the
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-- given value. The result will be either the appropriate directly
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-- represented value, or a table entry in the proper canonical format is
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-- created and returned.
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--
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-- Note that Init_Operand puts a signed value in the result vector, but
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-- Vector_To_Uint is always presented with a non-negative value. The
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-- processing of signs is something that is done by the caller before
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-- calling Vector_To_Uint.
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---------------------
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-- Output Routines --
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---------------------
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type UI_Format is (Hex, Decimal, Auto);
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-- Used to determine whether UI_Image/UI_Write output is in hexadecimal
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-- or decimal format. Auto, the default setting, lets the routine make a
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-- decision based on the value.
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UI_Image_Max : constant := 48; -- Enough for a 128-bit number
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UI_Image_Buffer : String (1 .. UI_Image_Max);
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UI_Image_Length : Natural;
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-- Buffer used for UI_Image as described below
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procedure UI_Image (Input : Uint; Format : UI_Format := Auto);
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-- Places a representation of Uint, consisting of a possible minus sign,
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-- followed by the value in UI_Image_Buffer. The form of the value is an
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-- integer literal in either decimal (no base) or hexadecimal (base 16)
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-- format. If Hex is True on entry, then hex mode is forced, otherwise
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-- UI_Image makes a guess at which output format is more convenient. The
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-- value must fit in UI_Image_Buffer. The actual length of the result is
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-- returned in UI_Image_Length. If necessary to meet this requirement, the
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-- result is an approximation of the proper value, using an exponential
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-- format. The image of No_Uint is output as a single question mark.
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function UI_Image (Input : Uint; Format : UI_Format := Auto) return String;
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-- Functional form, in which the result is returned as a string. This call
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-- also leaves the result in UI_Image_Buffer/Length as described above.
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procedure UI_Write (Input : Uint; Format : UI_Format := Auto);
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-- Writes a representation of Uint, consisting of a possible minus sign,
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-- followed by the value to the output file. The form of the value is an
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-- integer literal in either decimal (no base) or hexadecimal (base 16)
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-- format as appropriate. UI_Format shows which format to use. Auto, the
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-- default, asks UI_Write to make a guess at which output format will be
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-- more convenient to read.
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procedure pid (Input : Uint);
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pragma Export (Ada, pid);
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-- Writes representation of Uint in decimal with a terminating line
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-- return. This is intended for use from the debugger.
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procedure pih (Input : Uint);
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pragma Export (Ada, pih);
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-- Writes representation of Uint in hex with a terminating line return.
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-- This is intended for use from the debugger.
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------------------------
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-- Operator Renamings --
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------------------------
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function "+" (Left : Uint; Right : Uint) return Uint renames UI_Add;
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function "+" (Left : Int; Right : Uint) return Uint renames UI_Add;
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function "+" (Left : Uint; Right : Int) return Uint renames UI_Add;
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function "/" (Left : Uint; Right : Uint) return Uint renames UI_Div;
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function "/" (Left : Int; Right : Uint) return Uint renames UI_Div;
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function "/" (Left : Uint; Right : Int) return Uint renames UI_Div;
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function "*" (Left : Uint; Right : Uint) return Uint renames UI_Mul;
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function "*" (Left : Int; Right : Uint) return Uint renames UI_Mul;
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function "*" (Left : Uint; Right : Int) return Uint renames UI_Mul;
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function "-" (Left : Uint; Right : Uint) return Uint renames UI_Sub;
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function "-" (Left : Int; Right : Uint) return Uint renames UI_Sub;
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function "-" (Left : Uint; Right : Int) return Uint renames UI_Sub;
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function "**" (Left : Uint; Right : Uint) return Uint renames UI_Expon;
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function "**" (Left : Uint; Right : Int) return Uint renames UI_Expon;
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function "**" (Left : Int; Right : Uint) return Uint renames UI_Expon;
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function "**" (Left : Int; Right : Int) return Uint renames UI_Expon;
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function "abs" (Real : Uint) return Uint renames UI_Abs;
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function "mod" (Left : Uint; Right : Uint) return Uint renames UI_Mod;
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function "mod" (Left : Int; Right : Uint) return Uint renames UI_Mod;
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function "mod" (Left : Uint; Right : Int) return Uint renames UI_Mod;
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function "rem" (Left : Uint; Right : Uint) return Uint renames UI_Rem;
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function "rem" (Left : Int; Right : Uint) return Uint renames UI_Rem;
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function "rem" (Left : Uint; Right : Int) return Uint renames UI_Rem;
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function "-" (Real : Uint) return Uint renames UI_Negate;
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function "=" (Left : Uint; Right : Uint) return Boolean renames UI_Eq;
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function "=" (Left : Int; Right : Uint) return Boolean renames UI_Eq;
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function "=" (Left : Uint; Right : Int) return Boolean renames UI_Eq;
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function ">=" (Left : Uint; Right : Uint) return Boolean renames UI_Ge;
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function ">=" (Left : Int; Right : Uint) return Boolean renames UI_Ge;
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function ">=" (Left : Uint; Right : Int) return Boolean renames UI_Ge;
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function ">" (Left : Uint; Right : Uint) return Boolean renames UI_Gt;
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function ">" (Left : Int; Right : Uint) return Boolean renames UI_Gt;
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function ">" (Left : Uint; Right : Int) return Boolean renames UI_Gt;
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function "<=" (Left : Uint; Right : Uint) return Boolean renames UI_Le;
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function "<=" (Left : Int; Right : Uint) return Boolean renames UI_Le;
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function "<=" (Left : Uint; Right : Int) return Boolean renames UI_Le;
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function "<" (Left : Uint; Right : Uint) return Boolean renames UI_Lt;
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function "<" (Left : Int; Right : Uint) return Boolean renames UI_Lt;
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function "<" (Left : Uint; Right : Int) return Boolean renames UI_Lt;
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-----------------------------
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-- Mark/Release Processing --
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-----------------------------
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-- The space used by Uint data is not automatically reclaimed. However, a
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-- mark-release regime is implemented which allows storage to be released
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-- back to a previously noted mark. This is used for example when doing
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-- comparisons, where only intermediate results get stored that do not
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-- need to be saved for future use.
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type Save_Mark is private;
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function Mark return Save_Mark;
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-- Note mark point for future release
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procedure Release (M : Save_Mark);
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-- Release storage allocated since mark was noted
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procedure Release_And_Save (M : Save_Mark; UI : in out Uint);
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-- Like Release, except that the given Uint value (which is typically among
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-- the data being released) is recopied after the release, so that it is
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-- the most recent item, and UI is updated to point to its copied location.
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procedure Release_And_Save (M : Save_Mark; UI1, UI2 : in out Uint);
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-- Like Release, except that the given Uint values (which are typically
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-- among the data being released) are recopied after the release, so that
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-- they are the most recent items, and UI1 and UI2 are updated if necessary
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-- to point to the copied locations. This routine is careful to do things
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-- in the right order, so that the values do not clobber one another.
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-----------------------------------
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-- Representation of Uint Values --
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-----------------------------------
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private
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type Uint is new Int range Uint_Low_Bound .. Uint_High_Bound;
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for Uint'Size use 32;
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No_Uint : constant Uint := Uint (Uint_Low_Bound);
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-- Uint values are represented as multiple precision integers stored in
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-- a multi-digit format using Base as the base. This value is chosen so
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-- that the product Base*Base is within the range of allowed Int values.
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-- Base is defined to allow efficient execution of the primitive operations
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-- (a0, b0, c0) defined in the section "The Classical Algorithms"
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-- (sec. 4.3.1) of Donald Knuth's "The Art of Computer Programming",
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-- Vol. 2. These algorithms are used in this package. In particular,
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-- the product of two single digits in this base fits in a 32-bit integer.
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Base_Bits : constant := 15;
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-- Number of bits in base value
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Base : constant Int := 2 ** Base_Bits;
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-- Values in the range -(Base-1) .. Max_Direct are encoded directly as
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-- Uint values by adding a bias value. The value of Max_Direct is chosen
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-- so that a directly represented number always fits in two digits when
|
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-- represented in base format.
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Min_Direct : constant Int := -(Base - 1);
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Max_Direct : constant Int := (Base - 1) * (Base - 1);
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-- The following values define the bias used to store Uint values which
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-- are in this range, as well as the biased values for the first and last
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-- values in this range. We use a new derived type for these constants to
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-- avoid accidental use of Uint arithmetic on these values, which is never
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-- correct.
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type Ctrl is range Int'First .. Int'Last;
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Uint_Direct_Bias : constant Ctrl := Ctrl (Uint_Low_Bound) + Ctrl (Base);
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Uint_Direct_First : constant Ctrl := Uint_Direct_Bias + Ctrl (Min_Direct);
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Uint_Direct_Last : constant Ctrl := Uint_Direct_Bias + Ctrl (Max_Direct);
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Uint_0 : constant Uint := Uint (Uint_Direct_Bias);
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Uint_1 : constant Uint := Uint (Uint_Direct_Bias + 1);
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Uint_2 : constant Uint := Uint (Uint_Direct_Bias + 2);
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Uint_3 : constant Uint := Uint (Uint_Direct_Bias + 3);
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Uint_4 : constant Uint := Uint (Uint_Direct_Bias + 4);
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Uint_5 : constant Uint := Uint (Uint_Direct_Bias + 5);
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Uint_6 : constant Uint := Uint (Uint_Direct_Bias + 6);
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Uint_7 : constant Uint := Uint (Uint_Direct_Bias + 7);
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Uint_8 : constant Uint := Uint (Uint_Direct_Bias + 8);
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Uint_9 : constant Uint := Uint (Uint_Direct_Bias + 9);
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Uint_10 : constant Uint := Uint (Uint_Direct_Bias + 10);
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Uint_11 : constant Uint := Uint (Uint_Direct_Bias + 11);
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Uint_12 : constant Uint := Uint (Uint_Direct_Bias + 12);
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|
Uint_13 : constant Uint := Uint (Uint_Direct_Bias + 13);
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|
Uint_14 : constant Uint := Uint (Uint_Direct_Bias + 14);
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|
Uint_15 : constant Uint := Uint (Uint_Direct_Bias + 15);
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|
Uint_16 : constant Uint := Uint (Uint_Direct_Bias + 16);
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|
Uint_24 : constant Uint := Uint (Uint_Direct_Bias + 24);
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|
Uint_32 : constant Uint := Uint (Uint_Direct_Bias + 32);
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|
Uint_63 : constant Uint := Uint (Uint_Direct_Bias + 63);
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|
Uint_64 : constant Uint := Uint (Uint_Direct_Bias + 64);
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|
Uint_80 : constant Uint := Uint (Uint_Direct_Bias + 80);
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|
Uint_128 : constant Uint := Uint (Uint_Direct_Bias + 128);
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|
|
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Uint_Minus_1 : constant Uint := Uint (Uint_Direct_Bias - 1);
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|
Uint_Minus_2 : constant Uint := Uint (Uint_Direct_Bias - 2);
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|
Uint_Minus_3 : constant Uint := Uint (Uint_Direct_Bias - 3);
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|
Uint_Minus_4 : constant Uint := Uint (Uint_Direct_Bias - 4);
|
|
Uint_Minus_5 : constant Uint := Uint (Uint_Direct_Bias - 5);
|
|
Uint_Minus_6 : constant Uint := Uint (Uint_Direct_Bias - 6);
|
|
Uint_Minus_7 : constant Uint := Uint (Uint_Direct_Bias - 7);
|
|
Uint_Minus_8 : constant Uint := Uint (Uint_Direct_Bias - 8);
|
|
Uint_Minus_9 : constant Uint := Uint (Uint_Direct_Bias - 9);
|
|
Uint_Minus_12 : constant Uint := Uint (Uint_Direct_Bias - 12);
|
|
Uint_Minus_36 : constant Uint := Uint (Uint_Direct_Bias - 36);
|
|
Uint_Minus_63 : constant Uint := Uint (Uint_Direct_Bias - 63);
|
|
Uint_Minus_80 : constant Uint := Uint (Uint_Direct_Bias - 80);
|
|
Uint_Minus_128 : constant Uint := Uint (Uint_Direct_Bias - 128);
|
|
|
|
Uint_Max_Simple_Mul : constant := Uint_Direct_Bias + 2 ** 15;
|
|
-- If two values are directly represented and less than or equal to this
|
|
-- value, then we know the product fits in a 32-bit integer. This allows
|
|
-- UI_Mul to efficiently compute the product in this case.
|
|
|
|
type Save_Mark is record
|
|
Save_Uint : Uint;
|
|
Save_Udigit : Int;
|
|
end record;
|
|
|
|
-- Values outside the range that is represented directly are stored using
|
|
-- two tables. The secondary table Udigits contains sequences of Int values
|
|
-- consisting of the digits of the number in a radix Base system. The
|
|
-- digits are stored from most significant to least significant with the
|
|
-- first digit only carrying the sign.
|
|
|
|
-- There is one entry in the primary Uints table for each distinct Uint
|
|
-- value. This table entry contains the length (number of digits) and
|
|
-- a starting offset of the value in the Udigits table.
|
|
|
|
Uint_First_Entry : constant Uint := Uint (Uint_Table_Start);
|
|
|
|
-- Some subprograms defined in this package manipulate the Udigits table
|
|
-- directly, while for others it is more convenient to work with locally
|
|
-- defined arrays of the digits of the Universal Integers. The type
|
|
-- UI_Vector is defined for this purpose and some internal subprograms
|
|
-- used for converting from one to the other are defined.
|
|
|
|
type Uint_Entry is record
|
|
Length : Pos;
|
|
-- Length of entry in Udigits table in digits (i.e. in words)
|
|
|
|
Loc : Int;
|
|
-- Starting location in Udigits table of this Uint value
|
|
end record;
|
|
|
|
package Uints is new Table.Table (
|
|
Table_Component_Type => Uint_Entry,
|
|
Table_Index_Type => Uint'Base,
|
|
Table_Low_Bound => Uint_First_Entry,
|
|
Table_Initial => Alloc.Uints_Initial,
|
|
Table_Increment => Alloc.Uints_Increment,
|
|
Table_Name => "Uints");
|
|
|
|
package Udigits is new Table.Table (
|
|
Table_Component_Type => Int,
|
|
Table_Index_Type => Int,
|
|
Table_Low_Bound => 0,
|
|
Table_Initial => Alloc.Udigits_Initial,
|
|
Table_Increment => Alloc.Udigits_Increment,
|
|
Table_Name => "Udigits");
|
|
|
|
-- Note: the reason these tables are defined here in the private part of
|
|
-- the spec, rather than in the body, is that they are referenced directly
|
|
-- by gigi.
|
|
|
|
end Uintp;
|