File : uintp.ads
1 ------------------------------------------------------------------------------
2 -- --
3 -- GNAT COMPILER COMPONENTS --
4 -- --
5 -- U I N T P --
6 -- --
7 -- S p e c --
8 -- --
9 -- Copyright (C) 1992-2015, 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 3, 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. --
17 -- --
18 -- --
19 -- --
20 -- --
21 -- --
22 -- You should have received a copy of the GNU General Public License and --
23 -- a copy of the GCC Runtime Library Exception along with this program; --
24 -- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
25 -- <http://www.gnu.org/licenses/>. --
26 -- --
27 -- GNAT was originally developed by the GNAT team at New York University. --
28 -- Extensive contributions were provided by Ada Core Technologies Inc. --
29 -- --
30 ------------------------------------------------------------------------------
31
32 -- Support for universal integer arithmetic
33
34 -- WARNING: There is a C version of this package. Any changes to this
35 -- source file must be properly reflected in the C header file uintp.h
36
37 with Alloc;
38 with Table;
39 pragma Elaborate_All (Table);
40 with Types; use Types;
41
42 package Uintp is
43
44 -------------------------------------------------
45 -- Basic Types and Constants for Uintp Package --
46 -------------------------------------------------
47
48 type Uint is private;
49 -- The basic universal integer type
50
51 No_Uint : constant Uint;
52 -- A constant value indicating a missing or unset Uint value
53
54 Uint_0 : constant Uint;
55 Uint_1 : constant Uint;
56 Uint_2 : constant Uint;
57 Uint_3 : constant Uint;
58 Uint_4 : constant Uint;
59 Uint_5 : constant Uint;
60 Uint_6 : constant Uint;
61 Uint_7 : constant Uint;
62 Uint_8 : constant Uint;
63 Uint_9 : constant Uint;
64 Uint_10 : constant Uint;
65 Uint_11 : constant Uint;
66 Uint_12 : constant Uint;
67 Uint_13 : constant Uint;
68 Uint_14 : constant Uint;
69 Uint_15 : constant Uint;
70 Uint_16 : constant Uint;
71 Uint_24 : constant Uint;
72 Uint_32 : constant Uint;
73 Uint_63 : constant Uint;
74 Uint_64 : constant Uint;
75 Uint_80 : constant Uint;
76 Uint_128 : constant Uint;
77
78 Uint_Minus_1 : constant Uint;
79 Uint_Minus_2 : constant Uint;
80 Uint_Minus_3 : constant Uint;
81 Uint_Minus_4 : constant Uint;
82 Uint_Minus_5 : constant Uint;
83 Uint_Minus_6 : constant Uint;
84 Uint_Minus_7 : constant Uint;
85 Uint_Minus_8 : constant Uint;
86 Uint_Minus_9 : constant Uint;
87 Uint_Minus_12 : constant Uint;
88 Uint_Minus_36 : constant Uint;
89 Uint_Minus_63 : constant Uint;
90 Uint_Minus_80 : constant Uint;
91 Uint_Minus_128 : constant Uint;
92
93 type UI_Vector is array (Pos range <>) of Int;
94 -- Vector containing the integer values of a Uint value
95
96 -- Note: An earlier version of this package used pointers of arrays of Ints
97 -- (dynamically allocated) for the Uint type. The change leads to a few
98 -- less natural idioms used throughout this code, but eliminates all uses
99 -- of the heap except for the table package itself. For example, Uint
100 -- parameters are often converted to UI_Vectors for internal manipulation.
101 -- This is done by creating the local UI_Vector using the function N_Digits
102 -- on the Uint to find the size needed for the vector, and then calling
103 -- Init_Operand to copy the values out of the table into the vector.
104
105 -----------------
106 -- Subprograms --
107 -----------------
108
109 procedure Initialize;
110 -- Initialize Uint tables. Note that Initialize must not be called if
111 -- Tree_Read is used. Note also that there is no lock routine in this
112 -- unit, these are among the few tables that can be expanded during
113 -- gigi processing.
114
115 procedure Tree_Read;
116 -- Initializes internal tables from current tree file using the relevant
117 -- Table.Tree_Read routines. Note that Initialize should not be called if
118 -- Tree_Read is used. Tree_Read includes all necessary initialization.
119
120 procedure Tree_Write;
121 -- Writes out internal tables to current tree file using the relevant
122 -- Table.Tree_Write routines.
123
124 function UI_Abs (Right : Uint) return Uint;
125 pragma Inline (UI_Abs);
126 -- Returns abs function of universal integer
127
128 function UI_Add (Left : Uint; Right : Uint) return Uint;
129 function UI_Add (Left : Int; Right : Uint) return Uint;
130 function UI_Add (Left : Uint; Right : Int) return Uint;
131 -- Returns sum of two integer values
132
133 function UI_Decimal_Digits_Hi (U : Uint) return Nat;
134 -- Returns an estimate of the number of decimal digits required to
135 -- represent the absolute value of U. This estimate is correct or high,
136 -- i.e. it never returns a value that is too low. The accuracy of the
137 -- estimate affects only the effectiveness of comparison optimizations
138 -- in Urealp.
139
140 function UI_Decimal_Digits_Lo (U : Uint) return Nat;
141 -- Returns an estimate of the number of decimal digits required to
142 -- represent the absolute value of U. This estimate is correct or low,
143 -- i.e. it never returns a value that is too high. The accuracy of the
144 -- estimate affects only the effectiveness of comparison optimizations
145 -- in Urealp.
146
147 function UI_Div (Left : Uint; Right : Uint) return Uint;
148 function UI_Div (Left : Int; Right : Uint) return Uint;
149 function UI_Div (Left : Uint; Right : Int) return Uint;
150 -- Returns quotient of two integer values. Fatal error if Right = 0
151
152 function UI_Eq (Left : Uint; Right : Uint) return Boolean;
153 function UI_Eq (Left : Int; Right : Uint) return Boolean;
154 function UI_Eq (Left : Uint; Right : Int) return Boolean;
155 pragma Inline (UI_Eq);
156 -- Compares integer values for equality
157
158 function UI_Expon (Left : Uint; Right : Uint) return Uint;
159 function UI_Expon (Left : Int; Right : Uint) return Uint;
160 function UI_Expon (Left : Uint; Right : Int) return Uint;
161 function UI_Expon (Left : Int; Right : Int) return Uint;
162 -- Returns result of exponentiating two integer values.
163 -- Fatal error if Right is negative.
164
165 function UI_GCD (Uin, Vin : Uint) return Uint;
166 -- Computes GCD of input values. Assumes Uin >= Vin >= 0
167
168 function UI_Ge (Left : Uint; Right : Uint) return Boolean;
169 function UI_Ge (Left : Int; Right : Uint) return Boolean;
170 function UI_Ge (Left : Uint; Right : Int) return Boolean;
171 pragma Inline (UI_Ge);
172 -- Compares integer values for greater than or equal
173
174 function UI_Gt (Left : Uint; Right : Uint) return Boolean;
175 function UI_Gt (Left : Int; Right : Uint) return Boolean;
176 function UI_Gt (Left : Uint; Right : Int) return Boolean;
177 pragma Inline (UI_Gt);
178 -- Compares integer values for greater than
179
180 function UI_Is_In_Int_Range (Input : Uint) return Boolean;
181 pragma Inline (UI_Is_In_Int_Range);
182 -- Determines if universal integer is in Int range
183
184 function UI_Le (Left : Uint; Right : Uint) return Boolean;
185 function UI_Le (Left : Int; Right : Uint) return Boolean;
186 function UI_Le (Left : Uint; Right : Int) return Boolean;
187 pragma Inline (UI_Le);
188 -- Compares integer values for less than or equal
189
190 function UI_Lt (Left : Uint; Right : Uint) return Boolean;
191 function UI_Lt (Left : Int; Right : Uint) return Boolean;
192 function UI_Lt (Left : Uint; Right : Int) return Boolean;
193 -- Compares integer values for less than
194
195 function UI_Max (Left : Uint; Right : Uint) return Uint;
196 function UI_Max (Left : Int; Right : Uint) return Uint;
197 function UI_Max (Left : Uint; Right : Int) return Uint;
198 -- Returns maximum of two integer values
199
200 function UI_Min (Left : Uint; Right : Uint) return Uint;
201 function UI_Min (Left : Int; Right : Uint) return Uint;
202 function UI_Min (Left : Uint; Right : Int) return Uint;
203 -- Returns minimum of two integer values
204
205 function UI_Mod (Left : Uint; Right : Uint) return Uint;
206 function UI_Mod (Left : Int; Right : Uint) return Uint;
207 function UI_Mod (Left : Uint; Right : Int) return Uint;
208 pragma Inline (UI_Mod);
209 -- Returns mod function of two integer values
210
211 function UI_Mul (Left : Uint; Right : Uint) return Uint;
212 function UI_Mul (Left : Int; Right : Uint) return Uint;
213 function UI_Mul (Left : Uint; Right : Int) return Uint;
214 -- Returns product of two integer values
215
216 function UI_Ne (Left : Uint; Right : Uint) return Boolean;
217 function UI_Ne (Left : Int; Right : Uint) return Boolean;
218 function UI_Ne (Left : Uint; Right : Int) return Boolean;
219 pragma Inline (UI_Ne);
220 -- Compares integer values for inequality
221
222 function UI_Negate (Right : Uint) return Uint;
223 pragma Inline (UI_Negate);
224 -- Returns negative of universal integer
225
226 function UI_Rem (Left : Uint; Right : Uint) return Uint;
227 function UI_Rem (Left : Int; Right : Uint) return Uint;
228 function UI_Rem (Left : Uint; Right : Int) return Uint;
229 -- Returns rem of two integer values
230
231 function UI_Sub (Left : Uint; Right : Uint) return Uint;
232 function UI_Sub (Left : Int; Right : Uint) return Uint;
233 function UI_Sub (Left : Uint; Right : Int) return Uint;
234 pragma Inline (UI_Sub);
235 -- Returns difference of two integer values
236
237 function UI_Modular_Exponentiation
238 (B : Uint;
239 E : Uint;
240 Modulo : Uint) return Uint;
241 -- Efficiently compute (B ** E) rem Modulo
242
243 function UI_Modular_Inverse (N : Uint; Modulo : Uint) return Uint;
244 -- Compute the multiplicative inverse of N in modular arithmetics with the
245 -- given Modulo (uses Euclid's algorithm). Note: the call is considered
246 -- to be erroneous (and the behavior is undefined) if n is not invertible.
247
248 function UI_From_Int (Input : Int) return Uint;
249 -- Converts Int value to universal integer form
250
251 function UI_From_CC (Input : Char_Code) return Uint;
252 -- Converts Char_Code value to universal integer form
253
254 function UI_To_Int (Input : Uint) return Int;
255 -- Converts universal integer value to Int. Fatal error if value is not in
256 -- appropriate range.
257
258 function UI_To_CC (Input : Uint) return Char_Code;
259 -- Converts universal integer value to Char_Code. Fatal error if value is
260 -- not in Char_Code range.
261
262 function Num_Bits (Input : Uint) return Nat;
263 -- Approximate number of binary bits in given universal integer. This
264 -- function is used for capacity checks, and it can be one bit off
265 -- without affecting its usage.
266
267 function Vector_To_Uint
268 (In_Vec : UI_Vector;
269 Negative : Boolean) return Uint;
270 -- Functions that calculate values in UI_Vectors, call this function to
271 -- create and return the Uint value. In_Vec contains the multiple precision
272 -- (Base) representation of a non-negative value. Leading zeroes are
273 -- permitted. Negative is set if the desired result is the negative of the
274 -- given value. The result will be either the appropriate directly
275 -- represented value, or a table entry in the proper canonical format is
276 -- created and returned.
277 --
278 -- Note that Init_Operand puts a signed value in the result vector, but
279 -- Vector_To_Uint is always presented with a non-negative value. The
280 -- processing of signs is something that is done by the caller before
281 -- calling Vector_To_Uint.
282
283 ---------------------
284 -- Output Routines --
285 ---------------------
286
287 type UI_Format is (Hex, Decimal, Auto);
288 -- Used to determine whether UI_Image/UI_Write output is in hexadecimal
289 -- or decimal format. Auto, the default setting, lets the routine make a
290 -- decision based on the value.
291
292 UI_Image_Max : constant := 48; -- Enough for a 128-bit number
293 UI_Image_Buffer : String (1 .. UI_Image_Max);
294 UI_Image_Length : Natural;
295 -- Buffer used for UI_Image as described below
296
297 procedure UI_Image (Input : Uint; Format : UI_Format := Auto);
298 -- Places a representation of Uint, consisting of a possible minus sign,
299 -- followed by the value in UI_Image_Buffer. The form of the value is an
300 -- integer literal in either decimal (no base) or hexadecimal (base 16)
301 -- format. If Hex is True on entry, then hex mode is forced, otherwise
302 -- UI_Image makes a guess at which output format is more convenient. The
303 -- value must fit in UI_Image_Buffer. The actual length of the result is
304 -- returned in UI_Image_Length. If necessary to meet this requirement, the
305 -- result is an approximation of the proper value, using an exponential
306 -- format. The image of No_Uint is output as a single question mark.
307
308 function UI_Image (Input : Uint; Format : UI_Format := Auto) return String;
309 -- Functional form, in which the result is returned as a string. This call
310 -- also leaves the result in UI_Image_Buffer/Length as described above.
311
312 procedure UI_Write (Input : Uint; Format : UI_Format := Auto);
313 -- Writes a representation of Uint, consisting of a possible minus sign,
314 -- followed by the value to the output file. The form of the value is an
315 -- integer literal in either decimal (no base) or hexadecimal (base 16)
316 -- format as appropriate. UI_Format shows which format to use. Auto, the
317 -- default, asks UI_Write to make a guess at which output format will be
318 -- more convenient to read.
319
320 procedure pid (Input : Uint);
321 pragma Export (Ada, pid);
322 -- Writes representation of Uint in decimal with a terminating line
323 -- return. This is intended for use from the debugger.
324
325 procedure pih (Input : Uint);
326 pragma Export (Ada, pih);
327 -- Writes representation of Uint in hex with a terminating line return.
328 -- This is intended for use from the debugger.
329
330 ------------------------
331 -- Operator Renamings --
332 ------------------------
333
334 function "+" (Left : Uint; Right : Uint) return Uint renames UI_Add;
335 function "+" (Left : Int; Right : Uint) return Uint renames UI_Add;
336 function "+" (Left : Uint; Right : Int) return Uint renames UI_Add;
337
338 function "/" (Left : Uint; Right : Uint) return Uint renames UI_Div;
339 function "/" (Left : Int; Right : Uint) return Uint renames UI_Div;
340 function "/" (Left : Uint; Right : Int) return Uint renames UI_Div;
341
342 function "*" (Left : Uint; Right : Uint) return Uint renames UI_Mul;
343 function "*" (Left : Int; Right : Uint) return Uint renames UI_Mul;
344 function "*" (Left : Uint; Right : Int) return Uint renames UI_Mul;
345
346 function "-" (Left : Uint; Right : Uint) return Uint renames UI_Sub;
347 function "-" (Left : Int; Right : Uint) return Uint renames UI_Sub;
348 function "-" (Left : Uint; Right : Int) return Uint renames UI_Sub;
349
350 function "**" (Left : Uint; Right : Uint) return Uint renames UI_Expon;
351 function "**" (Left : Uint; Right : Int) return Uint renames UI_Expon;
352 function "**" (Left : Int; Right : Uint) return Uint renames UI_Expon;
353 function "**" (Left : Int; Right : Int) return Uint renames UI_Expon;
354
355 function "abs" (Real : Uint) return Uint renames UI_Abs;
356
357 function "mod" (Left : Uint; Right : Uint) return Uint renames UI_Mod;
358 function "mod" (Left : Int; Right : Uint) return Uint renames UI_Mod;
359 function "mod" (Left : Uint; Right : Int) return Uint renames UI_Mod;
360
361 function "rem" (Left : Uint; Right : Uint) return Uint renames UI_Rem;
362 function "rem" (Left : Int; Right : Uint) return Uint renames UI_Rem;
363 function "rem" (Left : Uint; Right : Int) return Uint renames UI_Rem;
364
365 function "-" (Real : Uint) return Uint renames UI_Negate;
366
367 function "=" (Left : Uint; Right : Uint) return Boolean renames UI_Eq;
368 function "=" (Left : Int; Right : Uint) return Boolean renames UI_Eq;
369 function "=" (Left : Uint; Right : Int) return Boolean renames UI_Eq;
370
371 function ">=" (Left : Uint; Right : Uint) return Boolean renames UI_Ge;
372 function ">=" (Left : Int; Right : Uint) return Boolean renames UI_Ge;
373 function ">=" (Left : Uint; Right : Int) return Boolean renames UI_Ge;
374
375 function ">" (Left : Uint; Right : Uint) return Boolean renames UI_Gt;
376 function ">" (Left : Int; Right : Uint) return Boolean renames UI_Gt;
377 function ">" (Left : Uint; Right : Int) return Boolean renames UI_Gt;
378
379 function "<=" (Left : Uint; Right : Uint) return Boolean renames UI_Le;
380 function "<=" (Left : Int; Right : Uint) return Boolean renames UI_Le;
381 function "<=" (Left : Uint; Right : Int) return Boolean renames UI_Le;
382
383 function "<" (Left : Uint; Right : Uint) return Boolean renames UI_Lt;
384 function "<" (Left : Int; Right : Uint) return Boolean renames UI_Lt;
385 function "<" (Left : Uint; Right : Int) return Boolean renames UI_Lt;
386
387 -----------------------------
388 -- Mark/Release Processing --
389 -----------------------------
390
391 -- The space used by Uint data is not automatically reclaimed. However, a
392 -- mark-release regime is implemented which allows storage to be released
393 -- back to a previously noted mark. This is used for example when doing
394 -- comparisons, where only intermediate results get stored that do not
395 -- need to be saved for future use.
396
397 type Save_Mark is private;
398
399 function Mark return Save_Mark;
400 -- Note mark point for future release
401
402 procedure Release (M : Save_Mark);
403 -- Release storage allocated since mark was noted
404
405 procedure Release_And_Save (M : Save_Mark; UI : in out Uint);
406 -- Like Release, except that the given Uint value (which is typically among
407 -- the data being released) is recopied after the release, so that it is
408 -- the most recent item, and UI is updated to point to its copied location.
409
410 procedure Release_And_Save (M : Save_Mark; UI1, UI2 : in out Uint);
411 -- Like Release, except that the given Uint values (which are typically
412 -- among the data being released) are recopied after the release, so that
413 -- they are the most recent items, and UI1 and UI2 are updated if necessary
414 -- to point to the copied locations. This routine is careful to do things
415 -- in the right order, so that the values do not clobber one another.
416
417 -----------------------------------
418 -- Representation of Uint Values --
419 -----------------------------------
420
421 private
422
423 type Uint is new Int range Uint_Low_Bound .. Uint_High_Bound;
424 for Uint'Size use 32;
425
426 No_Uint : constant Uint := Uint (Uint_Low_Bound);
427
428 -- Uint values are represented as multiple precision integers stored in
429 -- a multi-digit format using Base as the base. This value is chosen so
430 -- that the product Base*Base is within the range of allowed Int values.
431
432 -- Base is defined to allow efficient execution of the primitive operations
433 -- (a0, b0, c0) defined in the section "The Classical Algorithms"
434 -- (sec. 4.3.1) of Donald Knuth's "The Art of Computer Programming",
435 -- Vol. 2. These algorithms are used in this package. In particular,
436 -- the product of two single digits in this base fits in a 32-bit integer.
437
438 Base_Bits : constant := 15;
439 -- Number of bits in base value
440
441 Base : constant Int := 2 ** Base_Bits;
442
443 -- Values in the range -(Base-1) .. Max_Direct are encoded directly as
444 -- Uint values by adding a bias value. The value of Max_Direct is chosen
445 -- so that a directly represented number always fits in two digits when
446 -- represented in base format.
447
448 Min_Direct : constant Int := -(Base - 1);
449 Max_Direct : constant Int := (Base - 1) * (Base - 1);
450
451 -- The following values define the bias used to store Uint values which
452 -- are in this range, as well as the biased values for the first and last
453 -- values in this range. We use a new derived type for these constants to
454 -- avoid accidental use of Uint arithmetic on these values, which is never
455 -- correct.
456
457 type Ctrl is range Int'First .. Int'Last;
458
459 Uint_Direct_Bias : constant Ctrl := Ctrl (Uint_Low_Bound) + Ctrl (Base);
460 Uint_Direct_First : constant Ctrl := Uint_Direct_Bias + Ctrl (Min_Direct);
461 Uint_Direct_Last : constant Ctrl := Uint_Direct_Bias + Ctrl (Max_Direct);
462
463 Uint_0 : constant Uint := Uint (Uint_Direct_Bias);
464 Uint_1 : constant Uint := Uint (Uint_Direct_Bias + 1);
465 Uint_2 : constant Uint := Uint (Uint_Direct_Bias + 2);
466 Uint_3 : constant Uint := Uint (Uint_Direct_Bias + 3);
467 Uint_4 : constant Uint := Uint (Uint_Direct_Bias + 4);
468 Uint_5 : constant Uint := Uint (Uint_Direct_Bias + 5);
469 Uint_6 : constant Uint := Uint (Uint_Direct_Bias + 6);
470 Uint_7 : constant Uint := Uint (Uint_Direct_Bias + 7);
471 Uint_8 : constant Uint := Uint (Uint_Direct_Bias + 8);
472 Uint_9 : constant Uint := Uint (Uint_Direct_Bias + 9);
473 Uint_10 : constant Uint := Uint (Uint_Direct_Bias + 10);
474 Uint_11 : constant Uint := Uint (Uint_Direct_Bias + 11);
475 Uint_12 : constant Uint := Uint (Uint_Direct_Bias + 12);
476 Uint_13 : constant Uint := Uint (Uint_Direct_Bias + 13);
477 Uint_14 : constant Uint := Uint (Uint_Direct_Bias + 14);
478 Uint_15 : constant Uint := Uint (Uint_Direct_Bias + 15);
479 Uint_16 : constant Uint := Uint (Uint_Direct_Bias + 16);
480 Uint_24 : constant Uint := Uint (Uint_Direct_Bias + 24);
481 Uint_32 : constant Uint := Uint (Uint_Direct_Bias + 32);
482 Uint_63 : constant Uint := Uint (Uint_Direct_Bias + 63);
483 Uint_64 : constant Uint := Uint (Uint_Direct_Bias + 64);
484 Uint_80 : constant Uint := Uint (Uint_Direct_Bias + 80);
485 Uint_128 : constant Uint := Uint (Uint_Direct_Bias + 128);
486
487 Uint_Minus_1 : constant Uint := Uint (Uint_Direct_Bias - 1);
488 Uint_Minus_2 : constant Uint := Uint (Uint_Direct_Bias - 2);
489 Uint_Minus_3 : constant Uint := Uint (Uint_Direct_Bias - 3);
490 Uint_Minus_4 : constant Uint := Uint (Uint_Direct_Bias - 4);
491 Uint_Minus_5 : constant Uint := Uint (Uint_Direct_Bias - 5);
492 Uint_Minus_6 : constant Uint := Uint (Uint_Direct_Bias - 6);
493 Uint_Minus_7 : constant Uint := Uint (Uint_Direct_Bias - 7);
494 Uint_Minus_8 : constant Uint := Uint (Uint_Direct_Bias - 8);
495 Uint_Minus_9 : constant Uint := Uint (Uint_Direct_Bias - 9);
496 Uint_Minus_12 : constant Uint := Uint (Uint_Direct_Bias - 12);
497 Uint_Minus_36 : constant Uint := Uint (Uint_Direct_Bias - 36);
498 Uint_Minus_63 : constant Uint := Uint (Uint_Direct_Bias - 63);
499 Uint_Minus_80 : constant Uint := Uint (Uint_Direct_Bias - 80);
500 Uint_Minus_128 : constant Uint := Uint (Uint_Direct_Bias - 128);
501
502 Uint_Max_Simple_Mul : constant := Uint_Direct_Bias + 2 ** 15;
503 -- If two values are directly represented and less than or equal to this
504 -- value, then we know the product fits in a 32-bit integer. This allows
505 -- UI_Mul to efficiently compute the product in this case.
506
507 type Save_Mark is record
508 Save_Uint : Uint;
509 Save_Udigit : Int;
510 end record;
511
512 -- Values outside the range that is represented directly are stored using
513 -- two tables. The secondary table Udigits contains sequences of Int values
514 -- consisting of the digits of the number in a radix Base system. The
515 -- digits are stored from most significant to least significant with the
516 -- first digit only carrying the sign.
517
518 -- There is one entry in the primary Uints table for each distinct Uint
519 -- value. This table entry contains the length (number of digits) and
520 -- a starting offset of the value in the Udigits table.
521
522 Uint_First_Entry : constant Uint := Uint (Uint_Table_Start);
523
524 -- Some subprograms defined in this package manipulate the Udigits table
525 -- directly, while for others it is more convenient to work with locally
526 -- defined arrays of the digits of the Universal Integers. The type
527 -- UI_Vector is defined for this purpose and some internal subprograms
528 -- used for converting from one to the other are defined.
529
530 type Uint_Entry is record
531 Length : Pos;
532 -- Length of entry in Udigits table in digits (i.e. in words)
533
534 Loc : Int;
535 -- Starting location in Udigits table of this Uint value
536 end record;
537
538 package Uints is new Table.Table (
539 Table_Component_Type => Uint_Entry,
540 Table_Index_Type => Uint'Base,
541 Table_Low_Bound => Uint_First_Entry,
542 Table_Initial => Alloc.Uints_Initial,
543 Table_Increment => Alloc.Uints_Increment,
544 Table_Name => "Uints");
545
546 package Udigits is new Table.Table (
547 Table_Component_Type => Int,
548 Table_Index_Type => Int,
549 Table_Low_Bound => 0,
550 Table_Initial => Alloc.Udigits_Initial,
551 Table_Increment => Alloc.Udigits_Increment,
552 Table_Name => "Udigits");
553
554 -- Note: the reason these tables are defined here in the private part of
555 -- the spec, rather than in the body, is that they are referenced directly
556 -- by gigi.
557
558 end Uintp;