1------------------------------------------------------------------------------
2--                                                                          --
3--                         GNAT COMPILER COMPONENTS                         --
4--                                                                          --
5--                                U I N T P                                 --
6--                                                                          --
7--                                 S p e c                                  --
8--                                                                          --
9--          Copyright (C) 1992-2003, Free Software Foundation, Inc.         --
10--                                                                          --
11-- GNAT is free software;  you can  redistribute it  and/or modify it under --
12-- terms of the  GNU General Public License as published  by the Free Soft- --
13-- ware  Foundation;  either version 2,  or (at your option) any later ver- --
14-- sion.  GNAT is distributed in the hope that it will be useful, but WITH- --
15-- OUT ANY WARRANTY;  without even the  implied warranty of MERCHANTABILITY --
16-- or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License --
17-- for  more details.  You should have  received  a copy of the GNU General --
18-- Public License  distributed with GNAT;  see file COPYING.  If not, write --
19-- to  the Free Software Foundation,  59 Temple Place - Suite 330,  Boston, --
20-- MA 02111-1307, USA.                                                      --
21--                                                                          --
22-- As a special exception,  if other files  instantiate  generics from this --
23-- unit, or you link  this unit with other files  to produce an executable, --
24-- this  unit  does not  by itself cause  the resulting  executable  to  be --
25-- covered  by the  GNU  General  Public  License.  This exception does not --
26-- however invalidate  any other reasons why  the executable file  might be --
27-- covered by the  GNU Public License.                                      --
28--                                                                          --
29-- GNAT was originally developed  by the GNAT team at  New York University. --
30-- Extensive contributions were provided by Ada Core Technologies Inc.      --
31--                                                                          --
32------------------------------------------------------------------------------
33
34--  Support for universal integer arithmetic
35
36--  WARNING: There is a C version of this package. Any changes to this
37--  source file must be properly reflected in the C header file sinfo.h
38
39with Alloc;
40with Table;
41pragma Elaborate_All (Table);
42with Types; use Types;
43
44package Uintp is
45
46   -------------------------------------------------
47   -- Basic Types and Constants for Uintp Package --
48   -------------------------------------------------
49
50   type Uint is private;
51   --  The basic universal integer type
52
53   No_Uint : constant Uint;
54   --  A constant value indicating a missing or unset Uint value
55
56   Uint_0   : constant Uint;
57   Uint_1   : constant Uint;
58   Uint_2   : constant Uint;
59   Uint_3   : constant Uint;
60   Uint_4   : constant Uint;
61   Uint_5   : constant Uint;
62   Uint_6   : constant Uint;
63   Uint_7   : constant Uint;
64   Uint_8   : constant Uint;
65   Uint_9   : constant Uint;
66   Uint_10  : constant Uint;
67   Uint_12  : constant Uint;
68   Uint_15  : constant Uint;
69   Uint_16  : constant Uint;
70   Uint_24  : constant Uint;
71   Uint_32  : constant Uint;
72   Uint_63  : constant Uint;
73   Uint_64  : constant Uint;
74   Uint_80  : constant Uint;
75   Uint_128 : constant Uint;
76
77   Uint_Minus_1   : constant Uint;
78   Uint_Minus_2   : constant Uint;
79   Uint_Minus_3   : constant Uint;
80   Uint_Minus_4   : constant Uint;
81   Uint_Minus_5   : constant Uint;
82   Uint_Minus_6   : constant Uint;
83   Uint_Minus_7   : constant Uint;
84   Uint_Minus_8   : constant Uint;
85   Uint_Minus_9   : constant Uint;
86   Uint_Minus_12  : constant Uint;
87   Uint_Minus_36  : constant Uint;
88   Uint_Minus_63  : constant Uint;
89   Uint_Minus_80  : constant Uint;
90   Uint_Minus_128 : constant Uint;
91
92   -----------------
93   -- Subprograms --
94   -----------------
95
96   procedure Initialize;
97   --  Initialize Uint tables. Note that Initialize must not be called if
98   --  Tree_Read is used. Note also that there is no lock routine in this
99   --  unit, these are among the few tables that can be expanded during
100   --  gigi processing.
101
102   procedure Tree_Read;
103   --  Initializes internal tables from current tree file using Tree_Read.
104   --  Note that Initialize should not be called if Tree_Read is used.
105   --  Tree_Read includes all necessary initialization.
106
107   procedure Tree_Write;
108   --  Writes out internal tables to current tree file using Tree_Write.
109
110   function UI_Abs (Right : Uint) return Uint;
111   pragma Inline (UI_Abs);
112   --  Returns abs function of universal integer.
113
114   function UI_Add (Left : Uint; Right : Uint) return Uint;
115   function UI_Add (Left : Int;  Right : Uint) return Uint;
116   function UI_Add (Left : Uint; Right : Int)  return Uint;
117   --  Returns sum of two integer values.
118
119   function UI_Decimal_Digits_Hi (U : Uint) return Nat;
120   --  Returns an estimate of the number of decimal digits required to
121   --  represent the absolute value of U. This estimate is correct or high,
122   --  i.e. it never returns a value that is too low. The accuracy of the
123   --  estimate affects only the effectiveness of comparison optimizations
124   --  in Urealp.
125
126   function UI_Decimal_Digits_Lo (U : Uint) return Nat;
127   --  Returns an estimate of the number of decimal digits required to
128   --  represent the absolute value of U. This estimate is correct or low,
129   --  i.e. it never returns a value that is too high. The accuracy of the
130   --  estimate affects only the effectiveness of comparison optimizations
131   --  in Urealp.
132
133   function UI_Div (Left : Uint; Right : Uint) return Uint;
134   function UI_Div (Left : Int;  Right : Uint) return Uint;
135   function UI_Div (Left : Uint; Right : Int)  return Uint;
136   --  Returns quotient of two integer values. Fatal error if Right = 0
137
138   function UI_Eq (Left : Uint; Right : Uint) return Boolean;
139   function UI_Eq (Left : Int;  Right : Uint) return Boolean;
140   function UI_Eq (Left : Uint; Right : Int)  return Boolean;
141   pragma Inline (UI_Eq);
142   --  Compares integer values for equality.
143
144   function UI_Expon (Left : Uint; Right : Uint) return Uint;
145   function UI_Expon (Left : Int;  Right : Uint) return Uint;
146   function UI_Expon (Left : Uint; Right : Int)  return Uint;
147   function UI_Expon (Left : Int;  Right : Int)  return Uint;
148   --  Returns result of exponentiating two integer values
149   --  Fatal error if Right is negative.
150
151   function UI_GCD (Uin, Vin : Uint) return Uint;
152   --  Computes GCD of input values. Assumes Uin >= Vin >= 0.
153
154   function UI_Ge (Left : Uint; Right : Uint) return Boolean;
155   function UI_Ge (Left : Int;  Right : Uint) return Boolean;
156   function UI_Ge (Left : Uint; Right : Int)  return Boolean;
157   pragma Inline (UI_Ge);
158   --  Compares integer values for greater than or equal.
159
160   function UI_Gt (Left : Uint; Right : Uint) return Boolean;
161   function UI_Gt (Left : Int;  Right : Uint) return Boolean;
162   function UI_Gt (Left : Uint; Right : Int)  return Boolean;
163   pragma Inline (UI_Gt);
164   --  Compares integer values for greater than.
165
166   function UI_Is_In_Int_Range (Input : Uint) return Boolean;
167   pragma Inline (UI_Is_In_Int_Range);
168   --  Determines if universal integer is in Int range.
169
170   function UI_Le (Left : Uint; Right : Uint) return Boolean;
171   function UI_Le (Left : Int;  Right : Uint) return Boolean;
172   function UI_Le (Left : Uint; Right : Int)  return Boolean;
173   pragma Inline (UI_Le);
174   --  Compares integer values for less than or equal.
175
176   function UI_Lt (Left : Uint; Right : Uint) return Boolean;
177   function UI_Lt (Left : Int;  Right : Uint) return Boolean;
178   function UI_Lt (Left : Uint; Right : Int)  return Boolean;
179   --  Compares integer values for less than.
180
181   function UI_Max (Left : Uint; Right : Uint) return Uint;
182   function UI_Max (Left : Int;  Right : Uint) return Uint;
183   function UI_Max (Left : Uint; Right : Int)  return Uint;
184   --  Returns maximum of two integer values
185
186   function UI_Min (Left : Uint; Right : Uint) return Uint;
187   function UI_Min (Left : Int;  Right : Uint) return Uint;
188   function UI_Min (Left : Uint; Right : Int)  return Uint;
189   --  Returns minimum of two integer values.
190
191   function UI_Mod (Left : Uint; Right : Uint) return Uint;
192   function UI_Mod (Left : Int;  Right : Uint) return Uint;
193   function UI_Mod (Left : Uint; Right : Int)  return Uint;
194   pragma Inline (UI_Mod);
195   --  Returns mod function of two integer values.
196
197   function UI_Mul (Left : Uint; Right : Uint) return Uint;
198   function UI_Mul (Left : Int;  Right : Uint) return Uint;
199   function UI_Mul (Left : Uint; Right : Int)  return Uint;
200   --  Returns product of two integer values
201
202   function UI_Ne (Left : Uint; Right : Uint) return Boolean;
203   function UI_Ne (Left : Int;  Right : Uint) return Boolean;
204   function UI_Ne (Left : Uint; Right : Int)  return Boolean;
205   pragma Inline (UI_Ne);
206   --  Compares integer values for inequality.
207
208   function UI_Negate (Right : Uint) return Uint;
209   pragma Inline (UI_Negate);
210   --  Returns negative of universal integer.
211
212   function UI_Rem (Left : Uint; Right : Uint) return Uint;
213   function UI_Rem (Left : Int;  Right : Uint) return Uint;
214   function UI_Rem (Left : Uint; Right : Int)  return Uint;
215   --  Returns rem of two integer values.
216
217   function UI_Sub (Left : Uint; Right : Uint) return Uint;
218   function UI_Sub (Left : Int;  Right : Uint) return Uint;
219   function UI_Sub (Left : Uint; Right : Int)  return Uint;
220   pragma Inline (UI_Sub);
221   --  Returns difference of two integer values
222
223   function UI_From_Dint (Input : Dint) return Uint;
224   --  Converts Dint value to universal integer form.
225
226   function UI_From_Int (Input : Int) return Uint;
227   --  Converts Int value to universal integer form.
228
229   function UI_To_Int (Input : Uint) return Int;
230   --  Converts universal integer value to Int. Fatal error
231   --  if value is not in appropriate range.
232
233   function Num_Bits (Input : Uint) return Nat;
234   --  Approximate number of binary bits in given universal integer.
235   --  This function is used for capacity checks, and it can be one
236   --  bit off without affecting its usage.
237
238   ---------------------
239   -- Output Routines --
240   ---------------------
241
242   type UI_Format is (Hex, Decimal, Auto);
243   --  Used to determine whether UI_Image/UI_Write output is in hexadecimal
244   --  or decimal format. Auto, the default setting, lets the routine make
245   --  a decision based on the value.
246
247   UI_Image_Max    : constant := 32;
248   UI_Image_Buffer : String (1 .. UI_Image_Max);
249   UI_Image_Length : Natural;
250   --  Buffer used for UI_Image as described below
251
252   procedure UI_Image (Input : Uint; Format : UI_Format := Auto);
253   --  Places a representation of Uint, consisting of a possible minus sign,
254   --  followed by the value in UI_Image_Buffer. The form of the value is an
255   --  integer literal in either decimal (no base) or hexadecimal (base 16)
256   --  format. If Hex is True on entry, then hex mode is forced, otherwise
257   --  UI_Image makes a guess at which output format is more convenient. The
258   --  value must fit in UI_Image_Buffer. If necessary, the result is an
259   --  approximation of the proper value, using an exponential format. The
260   --  image of No_Uint is output as a single question mark.
261
262   procedure UI_Write (Input : Uint; Format : UI_Format := Auto);
263   --  Writes a representation of Uint, consisting of a possible minus sign,
264   --  followed by the value to the output file. The form of the value is an
265   --  integer literal in either decimal (no base) or hexadecimal (base 16)
266   --  format as appropriate. UI_Format shows which format to use. Auto,
267   --  the default, asks UI_Write to make a guess at which output format
268   --  will be more convenient to read.
269
270   procedure pid (Input : Uint);
271   pragma Export (Ada, pid);
272   --  Writes representation of Uint in decimal with a terminating line
273   --  return. This is intended for use from the debugger.
274
275   procedure pih (Input : Uint);
276   pragma Export (Ada, pih);
277   --  Writes representation of Uint in hex with a terminating line return.
278   --  This is intended for use from the debugger.
279
280   ------------------------
281   -- Operator Renamings --
282   ------------------------
283
284   function "+" (Left : Uint; Right : Uint) return Uint renames UI_Add;
285   function "+" (Left : Int;  Right : Uint) return Uint renames UI_Add;
286   function "+" (Left : Uint; Right : Int)  return Uint renames UI_Add;
287
288   function "/" (Left : Uint; Right : Uint) return Uint renames UI_Div;
289   function "/" (Left : Int;  Right : Uint) return Uint renames UI_Div;
290   function "/" (Left : Uint; Right : Int)  return Uint renames UI_Div;
291
292   function "*" (Left : Uint; Right : Uint) return Uint renames UI_Mul;
293   function "*" (Left : Int;  Right : Uint) return Uint renames UI_Mul;
294   function "*" (Left : Uint; Right : Int)  return Uint renames UI_Mul;
295
296   function "-" (Left : Uint; Right : Uint) return Uint renames UI_Sub;
297   function "-" (Left : Int;  Right : Uint) return Uint renames UI_Sub;
298   function "-" (Left : Uint; Right : Int)  return Uint renames UI_Sub;
299
300   function "**"  (Left : Uint; Right : Uint) return Uint renames UI_Expon;
301   function "**"  (Left : Uint; Right : Int)  return Uint renames UI_Expon;
302   function "**"  (Left : Int;  Right : Uint) return Uint renames UI_Expon;
303   function "**"  (Left : Int;  Right : Int)  return Uint renames UI_Expon;
304
305   function "abs" (Real : Uint) return Uint renames UI_Abs;
306
307   function "mod" (Left : Uint; Right : Uint) return Uint renames UI_Mod;
308   function "mod" (Left : Int;  Right : Uint) return Uint renames UI_Mod;
309   function "mod" (Left : Uint; Right : Int)  return Uint renames UI_Mod;
310
311   function "rem" (Left : Uint; Right : Uint) return Uint renames UI_Rem;
312   function "rem" (Left : Int;  Right : Uint) return Uint renames UI_Rem;
313   function "rem" (Left : Uint; Right : Int)  return Uint renames UI_Rem;
314
315   function "-"   (Real : Uint) return Uint renames UI_Negate;
316
317   function "="   (Left : Uint; Right : Uint) return Boolean renames UI_Eq;
318   function "="   (Left : Int;  Right : Uint) return Boolean renames UI_Eq;
319   function "="   (Left : Uint; Right : Int)  return Boolean renames UI_Eq;
320
321   function ">="  (Left : Uint; Right : Uint) return Boolean renames UI_Ge;
322   function ">="  (Left : Int;  Right : Uint) return Boolean renames UI_Ge;
323   function ">="  (Left : Uint; Right : Int)  return Boolean renames UI_Ge;
324
325   function ">"   (Left : Uint; Right : Uint) return Boolean renames UI_Gt;
326   function ">"   (Left : Int;  Right : Uint) return Boolean renames UI_Gt;
327   function ">"   (Left : Uint; Right : Int)  return Boolean renames UI_Gt;
328
329   function "<="  (Left : Uint; Right : Uint) return Boolean renames UI_Le;
330   function "<="  (Left : Int;  Right : Uint) return Boolean renames UI_Le;
331   function "<="  (Left : Uint; Right : Int)  return Boolean renames UI_Le;
332
333   function "<"   (Left : Uint; Right : Uint) return Boolean renames UI_Lt;
334   function "<"   (Left : Int;  Right : Uint) return Boolean renames UI_Lt;
335   function "<"   (Left : Uint; Right : Int)  return Boolean renames UI_Lt;
336
337   -----------------------------
338   -- Mark/Release Processing --
339   -----------------------------
340
341   --  The space used by Uint data is not automatically reclaimed. However,
342   --  a mark-release regime is implemented which allows storage to be
343   --  released back to a previously noted mark. This is used for example
344   --  when doing comparisons, where only intermediate results get stored
345   --  that do not need to be saved for future use.
346
347   type Save_Mark is private;
348
349   function Mark return Save_Mark;
350   --  Note mark point for future release
351
352   procedure Release (M : Save_Mark);
353   --  Release storage allocated since mark was noted
354
355   procedure Release_And_Save (M : Save_Mark; UI : in out Uint);
356   --  Like Release, except that the given Uint value (which is typically
357   --  among the data being released) is recopied after the release, so
358   --  that it is the most recent item, and UI is updated to point to
359   --  its copied location.
360
361   procedure Release_And_Save (M : Save_Mark; UI1, UI2 : in out Uint);
362   --  Like Release, except that the given Uint values (which are typically
363   --  among the data being released) are recopied after the release, so
364   --  that they are the most recent items, and UI1 and UI2 are updated if
365   --  necessary to point to the copied locations. This routine is careful
366   --  to do things in the right order, so that the values do not clobber
367   --  one another.
368
369   -----------------------------------
370   -- Representation of Uint Values --
371   -----------------------------------
372
373private
374
375   type Uint is new Int range Uint_Low_Bound .. Uint_High_Bound;
376   for Uint'Size use 32;
377
378   No_Uint : constant Uint := Uint (Uint_Low_Bound);
379
380   --  Uint values are represented as multiple precision integers stored in
381   --  a multi-digit format using Base as the base. This value is chosen so
382   --  that the product Base*Base is within the range of allowed Int values.
383
384   --  Base is defined to allow efficient execution of the primitive
385   --  operations (a0, b0, c0) defined in the section "The Classical
386   --  Algorithms" (sec. 4.3.1) of Donald Knuth's "The Art of Computer
387   --  Programming", Vol. 2. These algorithms are used in this package.
388
389   Base_Bits : constant := 15;
390   --  Number of bits in base value
391
392   Base : constant Int := 2 ** Base_Bits;
393
394   --  Values in the range -(Base+1) .. maxdirect are encoded directly as
395   --  Uint values by adding a bias value. The value of maxdirect is chosen
396   --  so that a directly represented number always fits in two digits when
397   --  represented in base format.
398
399   Min_Direct : constant Int := -(Base - 1);
400   Max_Direct : constant Int := (Base - 1) * (Base - 1);
401
402   --  The following values define the bias used to store Uint values which
403   --  are in this range, as well as the biased values for the first and
404   --  last values in this range. We use a new derived type for these
405   --  constants to avoid accidental use of Uint arithmetic on these
406   --  values, which is never correct.
407
408   type Ctrl is range Int'First .. Int'Last;
409
410   Uint_Direct_Bias  : constant Ctrl := Ctrl (Uint_Low_Bound) + Ctrl (Base);
411   Uint_Direct_First : constant Ctrl := Uint_Direct_Bias + Ctrl (Min_Direct);
412   Uint_Direct_Last  : constant Ctrl := Uint_Direct_Bias + Ctrl (Max_Direct);
413
414   Uint_0   : constant Uint := Uint (Uint_Direct_Bias);
415   Uint_1   : constant Uint := Uint (Uint_Direct_Bias + 1);
416   Uint_2   : constant Uint := Uint (Uint_Direct_Bias + 2);
417   Uint_3   : constant Uint := Uint (Uint_Direct_Bias + 3);
418   Uint_4   : constant Uint := Uint (Uint_Direct_Bias + 4);
419   Uint_5   : constant Uint := Uint (Uint_Direct_Bias + 5);
420   Uint_6   : constant Uint := Uint (Uint_Direct_Bias + 6);
421   Uint_7   : constant Uint := Uint (Uint_Direct_Bias + 7);
422   Uint_8   : constant Uint := Uint (Uint_Direct_Bias + 8);
423   Uint_9   : constant Uint := Uint (Uint_Direct_Bias + 9);
424   Uint_10  : constant Uint := Uint (Uint_Direct_Bias + 10);
425   Uint_12  : constant Uint := Uint (Uint_Direct_Bias + 12);
426   Uint_15  : constant Uint := Uint (Uint_Direct_Bias + 15);
427   Uint_16  : constant Uint := Uint (Uint_Direct_Bias + 16);
428   Uint_24  : constant Uint := Uint (Uint_Direct_Bias + 24);
429   Uint_32  : constant Uint := Uint (Uint_Direct_Bias + 32);
430   Uint_63  : constant Uint := Uint (Uint_Direct_Bias + 63);
431   Uint_64  : constant Uint := Uint (Uint_Direct_Bias + 64);
432   Uint_80  : constant Uint := Uint (Uint_Direct_Bias + 80);
433   Uint_128 : constant Uint := Uint (Uint_Direct_Bias + 128);
434
435   Uint_Minus_1   : constant Uint := Uint (Uint_Direct_Bias - 1);
436   Uint_Minus_2   : constant Uint := Uint (Uint_Direct_Bias - 2);
437   Uint_Minus_3   : constant Uint := Uint (Uint_Direct_Bias - 3);
438   Uint_Minus_4   : constant Uint := Uint (Uint_Direct_Bias - 4);
439   Uint_Minus_5   : constant Uint := Uint (Uint_Direct_Bias - 5);
440   Uint_Minus_6   : constant Uint := Uint (Uint_Direct_Bias - 6);
441   Uint_Minus_7   : constant Uint := Uint (Uint_Direct_Bias - 7);
442   Uint_Minus_8   : constant Uint := Uint (Uint_Direct_Bias - 8);
443   Uint_Minus_9   : constant Uint := Uint (Uint_Direct_Bias - 9);
444   Uint_Minus_12  : constant Uint := Uint (Uint_Direct_Bias - 12);
445   Uint_Minus_36  : constant Uint := Uint (Uint_Direct_Bias - 36);
446   Uint_Minus_63  : constant Uint := Uint (Uint_Direct_Bias - 63);
447   Uint_Minus_80  : constant Uint := Uint (Uint_Direct_Bias - 80);
448   Uint_Minus_128 : constant Uint := Uint (Uint_Direct_Bias - 128);
449
450   type Save_Mark is record
451      Save_Uint   : Uint;
452      Save_Udigit : Int;
453   end record;
454
455   --  Values outside the range that is represented directly are stored
456   --  using two tables. The secondary table Udigits contains sequences of
457   --  Int values consisting of the digits of the number in a radix Base
458   --  system. The digits are stored from most significant to least
459   --  significant with the first digit only carrying the sign.
460
461   --  There is one entry in the primary Uints table for each distinct Uint
462   --  value. This table entry contains the length (number of digits) and
463   --  a starting offset of the value in the Udigits table.
464
465   Uint_First_Entry : constant Uint := Uint (Uint_Table_Start);
466
467   --  Some subprograms defined in this package manipulate the Udigits
468   --  table directly, while for others it is more convenient to work with
469   --  locally defined arrays of the digits of the Universal Integers.
470   --  The type UI_Vector is defined for this purpose and some internal
471   --  subprograms used for converting from one to the other are defined.
472
473   type UI_Vector is array (Pos range <>) of Int;
474   --  Vector containing the integer values of a Uint value
475
476   --  Note: An earlier version of this package used pointers of arrays
477   --  of Ints (dynamically allocated) for the Uint type. The change
478   --  leads to a few less natural idioms used throughout this code, but
479   --  eliminates all uses of the heap except for the table package itself.
480   --  For example, Uint parameters are often converted to UI_Vectors for
481   --  internal manipulation. This is done by creating the local UI_Vector
482   --  using the function N_Digits on the Uint to find the size needed for
483   --  the vector, and then calling Init_Operand to copy the values out
484   --  of the table into the vector.
485
486   type Uint_Entry is record
487      Length : Pos;
488      --  Length of entry in Udigits table in digits (i.e. in words)
489
490      Loc : Int;
491      --  Starting location in Udigits table of this Uint value
492   end record;
493
494   package Uints is new Table.Table (
495     Table_Component_Type => Uint_Entry,
496     Table_Index_Type     => Uint,
497     Table_Low_Bound      => Uint_First_Entry,
498     Table_Initial        => Alloc.Uints_Initial,
499     Table_Increment      => Alloc.Uints_Increment,
500     Table_Name           => "Uints");
501
502   package Udigits is new Table.Table (
503     Table_Component_Type => Int,
504     Table_Index_Type     => Int,
505     Table_Low_Bound      => 0,
506     Table_Initial        => Alloc.Udigits_Initial,
507     Table_Increment      => Alloc.Udigits_Increment,
508     Table_Name           => "Udigits");
509
510   --  Note: the reason these tables are defined here in the private part of
511   --  the spec, rather than in the body, is that they are refrerenced
512   --  directly by gigi.
513
514end Uintp;
515