------------------------------------------------------------------------------ -- -- -- GNAT COMPILER COMPONENTS -- -- -- -- U I N T P -- -- -- -- S p e c -- -- -- -- -- -- Copyright (C) 1992-2002, 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 2, 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. See the GNU General Public License -- -- for more details. You should have received a copy of the GNU General -- -- Public License distributed with GNAT; see file COPYING. If not, write -- -- to the Free Software Foundation, 59 Temple Place - Suite 330, Boston, -- -- MA 02111-1307, USA. -- -- -- -- As a special exception, if other files instantiate generics from this -- -- unit, or you link this unit with other files to produce an executable, -- -- this unit does not by itself cause the resulting executable to be -- -- covered by the GNU General Public License. This exception does not -- -- however invalidate any other reasons why the executable file might be -- -- covered by the GNU Public License. -- -- -- -- GNAT was originally developed by the GNAT team at New York University. -- -- Extensive contributions were provided by Ada Core Technologies Inc. -- -- -- ------------------------------------------------------------------------------ -- Support for universal integer arithmetic -- WARNING: There is a C version of this package. Any changes to this -- source file must be properly reflected in the C header file sinfo.h with Alloc; with Table; pragma Elaborate_All (Table); with Types; use Types; package Uintp is ------------------------------------------------- -- Basic Types and Constants for Uintp Package -- ------------------------------------------------- type Uint is private; -- The basic universal integer type No_Uint : constant Uint; -- A constant value indicating a missing or unset Uint value Uint_0 : constant Uint; Uint_1 : constant Uint; Uint_2 : constant Uint; Uint_3 : constant Uint; Uint_4 : constant Uint; Uint_5 : constant Uint; Uint_6 : constant Uint; Uint_7 : constant Uint; Uint_8 : constant Uint; Uint_9 : constant Uint; Uint_10 : constant Uint; Uint_12 : constant Uint; Uint_15 : constant Uint; Uint_16 : constant Uint; Uint_24 : constant Uint; Uint_32 : constant Uint; Uint_63 : constant Uint; Uint_64 : constant Uint; Uint_128 : constant Uint; Uint_Minus_1 : constant Uint; Uint_Minus_2 : constant Uint; Uint_Minus_3 : constant Uint; Uint_Minus_4 : constant Uint; Uint_Minus_5 : constant Uint; Uint_Minus_6 : constant Uint; Uint_Minus_7 : constant Uint; Uint_Minus_8 : constant Uint; Uint_Minus_9 : constant Uint; Uint_Minus_12 : constant Uint; Uint_Minus_128 : constant Uint; ----------------- -- Subprograms -- ----------------- procedure Initialize; -- Initialize Uint tables. Note that Initialize must not be called if -- Tree_Read is used. Note also that there is no lock routine in this -- unit, these are among the few tables that can be expanded during -- gigi processing. procedure Tree_Read; -- Initializes internal tables from current tree file using Tree_Read. -- Note that Initialize should not be called if Tree_Read is used. -- Tree_Read includes all necessary initialization. procedure Tree_Write; -- Writes out internal tables to current tree file using Tree_Write. function UI_Abs (Right : Uint) return Uint; pragma Inline (UI_Abs); -- Returns abs function of universal integer. function UI_Add (Left : Uint; Right : Uint) return Uint; function UI_Add (Left : Int; Right : Uint) return Uint; function UI_Add (Left : Uint; Right : Int) return Uint; -- Returns sum of two integer values. function UI_Decimal_Digits_Hi (U : Uint) return Nat; -- Returns an estimate of the number of decimal digits required to -- represent the absolute value of U. This estimate is correct or high, -- i.e. it never returns a value that is too low. The accuracy of the -- estimate affects only the effectiveness of comparison optimizations -- in Urealp. function UI_Decimal_Digits_Lo (U : Uint) return Nat; -- Returns an estimate of the number of decimal digits required to -- represent the absolute value of U. This estimate is correct or low, -- i.e. it never returns a value that is too high. The accuracy of the -- estimate affects only the effectiveness of comparison optimizations -- in Urealp. function UI_Div (Left : Uint; Right : Uint) return Uint; function UI_Div (Left : Int; Right : Uint) return Uint; function UI_Div (Left : Uint; Right : Int) return Uint; -- Returns quotient of two integer values. Fatal error if Right = 0 function UI_Eq (Left : Uint; Right : Uint) return Boolean; function UI_Eq (Left : Int; Right : Uint) return Boolean; function UI_Eq (Left : Uint; Right : Int) return Boolean; pragma Inline (UI_Eq); -- Compares integer values for equality. function UI_Expon (Left : Uint; Right : Uint) return Uint; function UI_Expon (Left : Int; Right : Uint) return Uint; function UI_Expon (Left : Uint; Right : Int) return Uint; function UI_Expon (Left : Int; Right : Int) return Uint; -- Returns result of exponentiating two integer values -- Fatal error if Right is negative. function UI_GCD (Uin, Vin : Uint) return Uint; -- Computes GCD of input values. Assumes Uin >= Vin >= 0. function UI_Ge (Left : Uint; Right : Uint) return Boolean; function UI_Ge (Left : Int; Right : Uint) return Boolean; function UI_Ge (Left : Uint; Right : Int) return Boolean; pragma Inline (UI_Ge); -- Compares integer values for greater than or equal. function UI_Gt (Left : Uint; Right : Uint) return Boolean; function UI_Gt (Left : Int; Right : Uint) return Boolean; function UI_Gt (Left : Uint; Right : Int) return Boolean; pragma Inline (UI_Gt); -- Compares integer values for greater than. function UI_Is_In_Int_Range (Input : Uint) return Boolean; pragma Inline (UI_Is_In_Int_Range); -- Determines if universal integer is in Int range. function UI_Le (Left : Uint; Right : Uint) return Boolean; function UI_Le (Left : Int; Right : Uint) return Boolean; function UI_Le (Left : Uint; Right : Int) return Boolean; pragma Inline (UI_Le); -- Compares integer values for less than or equal. function UI_Lt (Left : Uint; Right : Uint) return Boolean; function UI_Lt (Left : Int; Right : Uint) return Boolean; function UI_Lt (Left : Uint; Right : Int) return Boolean; -- Compares integer values for less than. function UI_Max (Left : Uint; Right : Uint) return Uint; function UI_Max (Left : Int; Right : Uint) return Uint; function UI_Max (Left : Uint; Right : Int) return Uint; -- Returns maximum of two integer values function UI_Min (Left : Uint; Right : Uint) return Uint; function UI_Min (Left : Int; Right : Uint) return Uint; function UI_Min (Left : Uint; Right : Int) return Uint; -- Returns minimum of two integer values. function UI_Mod (Left : Uint; Right : Uint) return Uint; function UI_Mod (Left : Int; Right : Uint) return Uint; function UI_Mod (Left : Uint; Right : Int) return Uint; pragma Inline (UI_Mod); -- Returns mod function of two integer values. function UI_Mul (Left : Uint; Right : Uint) return Uint; function UI_Mul (Left : Int; Right : Uint) return Uint; function UI_Mul (Left : Uint; Right : Int) return Uint; -- Returns product of two integer values function UI_Ne (Left : Uint; Right : Uint) return Boolean; function UI_Ne (Left : Int; Right : Uint) return Boolean; function UI_Ne (Left : Uint; Right : Int) return Boolean; pragma Inline (UI_Ne); -- Compares integer values for inequality. function UI_Negate (Right : Uint) return Uint; pragma Inline (UI_Negate); -- Returns negative of universal integer. function UI_Rem (Left : Uint; Right : Uint) return Uint; function UI_Rem (Left : Int; Right : Uint) return Uint; function UI_Rem (Left : Uint; Right : Int) return Uint; -- Returns rem of two integer values. function UI_Sub (Left : Uint; Right : Uint) return Uint; function UI_Sub (Left : Int; Right : Uint) return Uint; function UI_Sub (Left : Uint; Right : Int) return Uint; pragma Inline (UI_Sub); -- Returns difference of two integer values function UI_From_Dint (Input : Dint) return Uint; -- Converts Dint value to universal integer form. function UI_From_Int (Input : Int) return Uint; -- Converts Int value to universal integer form. function UI_To_Int (Input : Uint) return Int; -- Converts universal integer value to Int. Fatal error -- if value is not in appropriate range. function Num_Bits (Input : Uint) return Nat; -- Approximate number of binary bits in given universal integer. -- This function is used for capacity checks, and it can be one -- bit off without affecting its usage. --------------------- -- Output Routines -- --------------------- type UI_Format is (Hex, Decimal, Auto); -- Used to determine whether UI_Image/UI_Write output is in hexadecimal -- or decimal format. Auto, the default setting, lets the routine make -- a decision based on the value. UI_Image_Max : constant := 32; UI_Image_Buffer : String (1 .. UI_Image_Max); UI_Image_Length : Natural; -- Buffer used for UI_Image as described below procedure UI_Image (Input : Uint; Format : UI_Format := Auto); -- Places a representation of Uint, consisting of a possible minus sign, -- followed by the value in UI_Image_Buffer. The form of the value is an -- integer literal in either decimal (no base) or hexadecimal (base 16) -- format. If Hex is True on entry, then hex mode is forced, otherwise -- UI_Image makes a guess at which output format is more convenient. The -- value must fit in UI_Image_Buffer. If necessary, the result is an -- approximation of the proper value, using an exponential format. The -- image of No_Uint is output as a single question mark. procedure UI_Write (Input : Uint; Format : UI_Format := Auto); -- Writes a representation of Uint, consisting of a possible minus sign, -- followed by the value to the output file. The form of the value is an -- integer literal in either decimal (no base) or hexadecimal (base 16) -- format as appropriate. UI_Format shows which format to use. Auto, -- the default, asks UI_Write to make a guess at which output format -- will be more convenient to read. procedure pid (Input : Uint); pragma Export (Ada, pid); -- Writes representation of Uint in decimal with a terminating line -- return. This is intended for use from the debugger. procedure pih (Input : Uint); pragma Export (Ada, pih); -- Writes representation of Uint in hex with a terminating line return. -- This is intended for use from the debugger. ------------------------ -- Operator Renamings -- ------------------------ function "+" (Left : Uint; Right : Uint) return Uint renames UI_Add; function "+" (Left : Int; Right : Uint) return Uint renames UI_Add; function "+" (Left : Uint; Right : Int) return Uint renames UI_Add; function "/" (Left : Uint; Right : Uint) return Uint renames UI_Div; function "/" (Left : Int; Right : Uint) return Uint renames UI_Div; function "/" (Left : Uint; Right : Int) return Uint renames UI_Div; function "*" (Left : Uint; Right : Uint) return Uint renames UI_Mul; function "*" (Left : Int; Right : Uint) return Uint renames UI_Mul; function "*" (Left : Uint; Right : Int) return Uint renames UI_Mul; function "-" (Left : Uint; Right : Uint) return Uint renames UI_Sub; function "-" (Left : Int; Right : Uint) return Uint renames UI_Sub; function "-" (Left : Uint; Right : Int) return Uint renames UI_Sub; function "**" (Left : Uint; Right : Uint) return Uint renames UI_Expon; function "**" (Left : Uint; Right : Int) return Uint renames UI_Expon; function "**" (Left : Int; Right : Uint) return Uint renames UI_Expon; function "**" (Left : Int; Right : Int) return Uint renames UI_Expon; function "abs" (Real : Uint) return Uint renames UI_Abs; function "mod" (Left : Uint; Right : Uint) return Uint renames UI_Mod; function "mod" (Left : Int; Right : Uint) return Uint renames UI_Mod; function "mod" (Left : Uint; Right : Int) return Uint renames UI_Mod; function "rem" (Left : Uint; Right : Uint) return Uint renames UI_Rem; function "rem" (Left : Int; Right : Uint) return Uint renames UI_Rem; function "rem" (Left : Uint; Right : Int) return Uint renames UI_Rem; function "-" (Real : Uint) return Uint renames UI_Negate; function "=" (Left : Uint; Right : Uint) return Boolean renames UI_Eq; function "=" (Left : Int; Right : Uint) return Boolean renames UI_Eq; function "=" (Left : Uint; Right : Int) return Boolean renames UI_Eq; function ">=" (Left : Uint; Right : Uint) return Boolean renames UI_Ge; function ">=" (Left : Int; Right : Uint) return Boolean renames UI_Ge; function ">=" (Left : Uint; Right : Int) return Boolean renames UI_Ge; function ">" (Left : Uint; Right : Uint) return Boolean renames UI_Gt; function ">" (Left : Int; Right : Uint) return Boolean renames UI_Gt; function ">" (Left : Uint; Right : Int) return Boolean renames UI_Gt; function "<=" (Left : Uint; Right : Uint) return Boolean renames UI_Le; function "<=" (Left : Int; Right : Uint) return Boolean renames UI_Le; function "<=" (Left : Uint; Right : Int) return Boolean renames UI_Le; function "<" (Left : Uint; Right : Uint) return Boolean renames UI_Lt; function "<" (Left : Int; Right : Uint) return Boolean renames UI_Lt; function "<" (Left : Uint; Right : Int) return Boolean renames UI_Lt; ----------------------------- -- Mark/Release Processing -- ----------------------------- -- The space used by Uint data is not automatically reclaimed. However, -- a mark-release regime is implemented which allows storage to be -- released back to a previously noted mark. This is used for example -- when doing comparisons, where only intermediate results get stored -- that do not need to be saved for future use. type Save_Mark is private; function Mark return Save_Mark; -- Note mark point for future release procedure Release (M : Save_Mark); -- Release storage allocated since mark was noted procedure Release_And_Save (M : Save_Mark; UI : in out Uint); -- Like Release, except that the given Uint value (which is typically -- among the data being released) is recopied after the release, so -- that it is the most recent item, and UI is updated to point to -- its copied location. procedure Release_And_Save (M : Save_Mark; UI1, UI2 : in out Uint); -- Like Release, except that the given Uint values (which are typically -- among the data being released) are recopied after the release, so -- that they are the most recent items, and UI1 and UI2 are updated if -- necessary to point to the copied locations. This routine is careful -- to do things in the right order, so that the values do not clobber -- one another. ----------------------------------- -- Representation of Uint Values -- ----------------------------------- private type Uint is new Int range Uint_Low_Bound .. Uint_High_Bound; for Uint'Size use 32; No_Uint : constant Uint := Uint (Uint_Low_Bound); -- Uint values are represented as multiple precision integers stored in -- a multi-digit format using Base as the base. This value is chosen so -- that the product Base*Base is within the range of allowed Int values. -- Base is defined to allow efficient execution of the primitive -- operations (a0, b0, c0) defined in the section "The Classical -- Algorithms" (sec. 4.3.1) of Donald Knuth's "The Art of Computer -- Programming", Vol. 2. These algorithms are used in this package. Base_Bits : constant := 15; -- Number of bits in base value Base : constant Int := 2 ** Base_Bits; -- Values in the range -(Base+1) .. maxdirect are encoded directly as -- Uint values by adding a bias value. The value of maxdirect is chosen -- so that a directly represented number always fits in two digits when -- represented in base format. Min_Direct : constant Int := -(Base - 1); Max_Direct : constant Int := (Base - 1) * (Base - 1); -- The following values define the bias used to store Uint values which -- are in this range, as well as the biased values for the first and -- last values in this range. We use a new derived type for these -- constants to avoid accidental use of Uint arithmetic on these -- values, which is never correct. type Ctrl is range Int'First .. Int'Last; Uint_Direct_Bias : constant Ctrl := Ctrl (Uint_Low_Bound) + Ctrl (Base); Uint_Direct_First : constant Ctrl := Uint_Direct_Bias + Ctrl (Min_Direct); Uint_Direct_Last : constant Ctrl := Uint_Direct_Bias + Ctrl (Max_Direct); Uint_0 : constant Uint := Uint (Uint_Direct_Bias); Uint_1 : constant Uint := Uint (Uint_Direct_Bias + 1); Uint_2 : constant Uint := Uint (Uint_Direct_Bias + 2); Uint_3 : constant Uint := Uint (Uint_Direct_Bias + 3); Uint_4 : constant Uint := Uint (Uint_Direct_Bias + 4); Uint_5 : constant Uint := Uint (Uint_Direct_Bias + 5); Uint_6 : constant Uint := Uint (Uint_Direct_Bias + 6); Uint_7 : constant Uint := Uint (Uint_Direct_Bias + 7); Uint_8 : constant Uint := Uint (Uint_Direct_Bias + 8); Uint_9 : constant Uint := Uint (Uint_Direct_Bias + 9); Uint_10 : constant Uint := Uint (Uint_Direct_Bias + 10); Uint_12 : constant Uint := Uint (Uint_Direct_Bias + 12); Uint_15 : constant Uint := Uint (Uint_Direct_Bias + 15); Uint_16 : constant Uint := Uint (Uint_Direct_Bias + 16); Uint_24 : constant Uint := Uint (Uint_Direct_Bias + 24); Uint_32 : constant Uint := Uint (Uint_Direct_Bias + 32); Uint_63 : constant Uint := Uint (Uint_Direct_Bias + 63); Uint_64 : constant Uint := Uint (Uint_Direct_Bias + 64); Uint_128 : constant Uint := Uint (Uint_Direct_Bias + 128); Uint_Minus_1 : constant Uint := Uint (Uint_Direct_Bias - 1); Uint_Minus_2 : constant Uint := Uint (Uint_Direct_Bias - 2); Uint_Minus_3 : constant Uint := Uint (Uint_Direct_Bias - 3); 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_128 : constant Uint := Uint (Uint_Direct_Bias - 128); 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 UI_Vector is array (Pos range <>) of Int; -- Vector containing the integer values of a Uint value -- Note: An earlier version of this package used pointers of arrays -- of Ints (dynamically allocated) for the Uint type. The change -- leads to a few less natural idioms used throughout this code, but -- eliminates all uses of the heap except for the table package itself. -- For example, Uint parameters are often converted to UI_Vectors for -- internal manipulation. This is done by creating the local UI_Vector -- using the function N_Digits on the Uint to find the size needed for -- the vector, and then calling Init_Operand to copy the values out -- of the table into the vector. 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, 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 refrerenced -- directly by gigi. end Uintp;