1------------------------------------------------------------------------------ 2-- -- 3-- GNAT COMPILER COMPONENTS -- 4-- -- 5-- U I N T P -- 6-- -- 7-- S p e c -- 8-- -- 9-- Copyright (C) 1992-2019, 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-- As a special exception under Section 7 of GPL version 3, you are granted -- 19-- additional permissions described in the GCC Runtime Library Exception, -- 20-- version 3.1, as published by the Free Software Foundation. -- 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 37with Alloc; 38with Table; 39pragma Elaborate_All (Table); 40with Types; use Types; 41 42package 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 generic 252 type In_T is range <>; 253 function UI_From_Integral (Input : In_T) return Uint; 254 -- Likewise, but converts from any integer type. 255 -- Must not be applied to biased types (instantiation will provide 256 -- a warning if actual is a biased type). 257 258 function UI_From_CC (Input : Char_Code) return Uint; 259 -- Converts Char_Code value to universal integer form 260 261 function UI_To_Int (Input : Uint) return Int; 262 -- Converts universal integer value to Int. Constraint_Error if value is 263 -- not in appropriate range. 264 265 function UI_To_CC (Input : Uint) return Char_Code; 266 -- Converts universal integer value to Char_Code. Constraint_Error if value 267 -- is not in Char_Code range. 268 269 function Num_Bits (Input : Uint) return Nat; 270 -- Approximate number of binary bits in given universal integer. This 271 -- function is used for capacity checks, and it can be one bit off 272 -- without affecting its usage. 273 274 function Vector_To_Uint 275 (In_Vec : UI_Vector; 276 Negative : Boolean) return Uint; 277 -- Functions that calculate values in UI_Vectors, call this function to 278 -- create and return the Uint value. In_Vec contains the multiple precision 279 -- (Base) representation of a non-negative value. Leading zeroes are 280 -- permitted. Negative is set if the desired result is the negative of the 281 -- given value. The result will be either the appropriate directly 282 -- represented value, or a table entry in the proper canonical format is 283 -- created and returned. 284 -- 285 -- Note that Init_Operand puts a signed value in the result vector, but 286 -- Vector_To_Uint is always presented with a non-negative value. The 287 -- processing of signs is something that is done by the caller before 288 -- calling Vector_To_Uint. 289 290 --------------------- 291 -- Output Routines -- 292 --------------------- 293 294 type UI_Format is (Hex, Decimal, Auto); 295 -- Used to determine whether UI_Image/UI_Write output is in hexadecimal 296 -- or decimal format. Auto, the default setting, lets the routine make a 297 -- decision based on the value. 298 299 UI_Image_Max : constant := 48; -- Enough for a 128-bit number 300 UI_Image_Buffer : String (1 .. UI_Image_Max); 301 UI_Image_Length : Natural; 302 -- Buffer used for UI_Image as described below 303 304 procedure UI_Image (Input : Uint; Format : UI_Format := Auto); 305 -- Places a representation of Uint, consisting of a possible minus sign, 306 -- followed by the value in UI_Image_Buffer. The form of the value is an 307 -- integer literal in either decimal (no base) or hexadecimal (base 16) 308 -- format. If Hex is True on entry, then hex mode is forced, otherwise 309 -- UI_Image makes a guess at which output format is more convenient. The 310 -- value must fit in UI_Image_Buffer. The actual length of the result is 311 -- returned in UI_Image_Length. If necessary to meet this requirement, the 312 -- result is an approximation of the proper value, using an exponential 313 -- format. The image of No_Uint is output as a single question mark. 314 315 function UI_Image (Input : Uint; Format : UI_Format := Auto) return String; 316 -- Functional form, in which the result is returned as a string. This call 317 -- also leaves the result in UI_Image_Buffer/Length as described above. 318 319 procedure UI_Write (Input : Uint; Format : UI_Format := Auto); 320 -- Writes a representation of Uint, consisting of a possible minus sign, 321 -- followed by the value to the output file. The form of the value is an 322 -- integer literal in either decimal (no base) or hexadecimal (base 16) 323 -- format as appropriate. UI_Format shows which format to use. Auto, the 324 -- default, asks UI_Write to make a guess at which output format will be 325 -- more convenient to read. 326 327 procedure pid (Input : Uint); 328 pragma Export (Ada, pid); 329 -- Writes representation of Uint in decimal with a terminating line 330 -- return. This is intended for use from the debugger. 331 332 procedure pih (Input : Uint); 333 pragma Export (Ada, pih); 334 -- Writes representation of Uint in hex with a terminating line return. 335 -- This is intended for use from the debugger. 336 337 ------------------------ 338 -- Operator Renamings -- 339 ------------------------ 340 341 function "+" (Left : Uint; Right : Uint) return Uint renames UI_Add; 342 function "+" (Left : Int; Right : Uint) return Uint renames UI_Add; 343 function "+" (Left : Uint; Right : Int) return Uint renames UI_Add; 344 345 function "/" (Left : Uint; Right : Uint) return Uint renames UI_Div; 346 function "/" (Left : Int; Right : Uint) return Uint renames UI_Div; 347 function "/" (Left : Uint; Right : Int) return Uint renames UI_Div; 348 349 function "*" (Left : Uint; Right : Uint) return Uint renames UI_Mul; 350 function "*" (Left : Int; Right : Uint) return Uint renames UI_Mul; 351 function "*" (Left : Uint; Right : Int) return Uint renames UI_Mul; 352 353 function "-" (Left : Uint; Right : Uint) return Uint renames UI_Sub; 354 function "-" (Left : Int; Right : Uint) return Uint renames UI_Sub; 355 function "-" (Left : Uint; Right : Int) return Uint renames UI_Sub; 356 357 function "**" (Left : Uint; Right : Uint) return Uint renames UI_Expon; 358 function "**" (Left : Uint; Right : Int) return Uint renames UI_Expon; 359 function "**" (Left : Int; Right : Uint) return Uint renames UI_Expon; 360 function "**" (Left : Int; Right : Int) return Uint renames UI_Expon; 361 362 function "abs" (Real : Uint) return Uint renames UI_Abs; 363 364 function "mod" (Left : Uint; Right : Uint) return Uint renames UI_Mod; 365 function "mod" (Left : Int; Right : Uint) return Uint renames UI_Mod; 366 function "mod" (Left : Uint; Right : Int) return Uint renames UI_Mod; 367 368 function "rem" (Left : Uint; Right : Uint) return Uint renames UI_Rem; 369 function "rem" (Left : Int; Right : Uint) return Uint renames UI_Rem; 370 function "rem" (Left : Uint; Right : Int) return Uint renames UI_Rem; 371 372 function "-" (Real : Uint) return Uint renames UI_Negate; 373 374 function "=" (Left : Uint; Right : Uint) return Boolean renames UI_Eq; 375 function "=" (Left : Int; Right : Uint) return Boolean renames UI_Eq; 376 function "=" (Left : Uint; Right : Int) return Boolean renames UI_Eq; 377 378 function ">=" (Left : Uint; Right : Uint) return Boolean renames UI_Ge; 379 function ">=" (Left : Int; Right : Uint) return Boolean renames UI_Ge; 380 function ">=" (Left : Uint; Right : Int) return Boolean renames UI_Ge; 381 382 function ">" (Left : Uint; Right : Uint) return Boolean renames UI_Gt; 383 function ">" (Left : Int; Right : Uint) return Boolean renames UI_Gt; 384 function ">" (Left : Uint; Right : Int) return Boolean renames UI_Gt; 385 386 function "<=" (Left : Uint; Right : Uint) return Boolean renames UI_Le; 387 function "<=" (Left : Int; Right : Uint) return Boolean renames UI_Le; 388 function "<=" (Left : Uint; Right : Int) return Boolean renames UI_Le; 389 390 function "<" (Left : Uint; Right : Uint) return Boolean renames UI_Lt; 391 function "<" (Left : Int; Right : Uint) return Boolean renames UI_Lt; 392 function "<" (Left : Uint; Right : Int) return Boolean renames UI_Lt; 393 394 ----------------------------- 395 -- Mark/Release Processing -- 396 ----------------------------- 397 398 -- The space used by Uint data is not automatically reclaimed. However, a 399 -- mark-release regime is implemented which allows storage to be released 400 -- back to a previously noted mark. This is used for example when doing 401 -- comparisons, where only intermediate results get stored that do not 402 -- need to be saved for future use. 403 404 type Save_Mark is private; 405 406 function Mark return Save_Mark; 407 -- Note mark point for future release 408 409 procedure Release (M : Save_Mark); 410 -- Release storage allocated since mark was noted 411 412 procedure Release_And_Save (M : Save_Mark; UI : in out Uint); 413 -- Like Release, except that the given Uint value (which is typically among 414 -- the data being released) is recopied after the release, so that it is 415 -- the most recent item, and UI is updated to point to its copied location. 416 417 procedure Release_And_Save (M : Save_Mark; UI1, UI2 : in out Uint); 418 -- Like Release, except that the given Uint values (which are typically 419 -- among the data being released) are recopied after the release, so that 420 -- they are the most recent items, and UI1 and UI2 are updated if necessary 421 -- to point to the copied locations. This routine is careful to do things 422 -- in the right order, so that the values do not clobber one another. 423 424 ----------------------------------- 425 -- Representation of Uint Values -- 426 ----------------------------------- 427 428private 429 430 type Uint is new Int range Uint_Low_Bound .. Uint_High_Bound; 431 for Uint'Size use 32; 432 433 No_Uint : constant Uint := Uint (Uint_Low_Bound); 434 435 -- Uint values are represented as multiple precision integers stored in 436 -- a multi-digit format using Base as the base. This value is chosen so 437 -- that the product Base*Base is within the range of allowed Int values. 438 439 -- Base is defined to allow efficient execution of the primitive operations 440 -- (a0, b0, c0) defined in the section "The Classical Algorithms" 441 -- (sec. 4.3.1) of Donald Knuth's "The Art of Computer Programming", 442 -- Vol. 2. These algorithms are used in this package. In particular, 443 -- the product of two single digits in this base fits in a 32-bit integer. 444 445 Base_Bits : constant := 15; 446 -- Number of bits in base value 447 448 Base : constant Int := 2**Base_Bits; 449 450 -- Values in the range -(Base-1) .. Max_Direct are encoded directly as 451 -- Uint values by adding a bias value. The value of Max_Direct is chosen 452 -- so that a directly represented number always fits in two digits when 453 -- represented in base format. 454 455 Min_Direct : constant Int := -(Base - 1); 456 Max_Direct : constant Int := (Base - 1) * (Base - 1); 457 458 -- The following values define the bias used to store Uint values which 459 -- are in this range, as well as the biased values for the first and last 460 -- values in this range. We use a new derived type for these constants to 461 -- avoid accidental use of Uint arithmetic on these values, which is never 462 -- correct. 463 464 type Ctrl is new Int; 465 466 Uint_Direct_Bias : constant Ctrl := Ctrl (Uint_Low_Bound) + Ctrl (Base); 467 Uint_Direct_First : constant Ctrl := Uint_Direct_Bias + Ctrl (Min_Direct); 468 Uint_Direct_Last : constant Ctrl := Uint_Direct_Bias + Ctrl (Max_Direct); 469 470 Uint_0 : constant Uint := Uint (Uint_Direct_Bias + 0); 471 Uint_1 : constant Uint := Uint (Uint_Direct_Bias + 1); 472 Uint_2 : constant Uint := Uint (Uint_Direct_Bias + 2); 473 Uint_3 : constant Uint := Uint (Uint_Direct_Bias + 3); 474 Uint_4 : constant Uint := Uint (Uint_Direct_Bias + 4); 475 Uint_5 : constant Uint := Uint (Uint_Direct_Bias + 5); 476 Uint_6 : constant Uint := Uint (Uint_Direct_Bias + 6); 477 Uint_7 : constant Uint := Uint (Uint_Direct_Bias + 7); 478 Uint_8 : constant Uint := Uint (Uint_Direct_Bias + 8); 479 Uint_9 : constant Uint := Uint (Uint_Direct_Bias + 9); 480 Uint_10 : constant Uint := Uint (Uint_Direct_Bias + 10); 481 Uint_11 : constant Uint := Uint (Uint_Direct_Bias + 11); 482 Uint_12 : constant Uint := Uint (Uint_Direct_Bias + 12); 483 Uint_13 : constant Uint := Uint (Uint_Direct_Bias + 13); 484 Uint_14 : constant Uint := Uint (Uint_Direct_Bias + 14); 485 Uint_15 : constant Uint := Uint (Uint_Direct_Bias + 15); 486 Uint_16 : constant Uint := Uint (Uint_Direct_Bias + 16); 487 Uint_24 : constant Uint := Uint (Uint_Direct_Bias + 24); 488 Uint_32 : constant Uint := Uint (Uint_Direct_Bias + 32); 489 Uint_63 : constant Uint := Uint (Uint_Direct_Bias + 63); 490 Uint_64 : constant Uint := Uint (Uint_Direct_Bias + 64); 491 Uint_80 : constant Uint := Uint (Uint_Direct_Bias + 80); 492 Uint_128 : constant Uint := Uint (Uint_Direct_Bias + 128); 493 494 Uint_Minus_1 : constant Uint := Uint (Uint_Direct_Bias - 1); 495 Uint_Minus_2 : constant Uint := Uint (Uint_Direct_Bias - 2); 496 Uint_Minus_3 : constant Uint := Uint (Uint_Direct_Bias - 3); 497 Uint_Minus_4 : constant Uint := Uint (Uint_Direct_Bias - 4); 498 Uint_Minus_5 : constant Uint := Uint (Uint_Direct_Bias - 5); 499 Uint_Minus_6 : constant Uint := Uint (Uint_Direct_Bias - 6); 500 Uint_Minus_7 : constant Uint := Uint (Uint_Direct_Bias - 7); 501 Uint_Minus_8 : constant Uint := Uint (Uint_Direct_Bias - 8); 502 Uint_Minus_9 : constant Uint := Uint (Uint_Direct_Bias - 9); 503 Uint_Minus_12 : constant Uint := Uint (Uint_Direct_Bias - 12); 504 Uint_Minus_36 : constant Uint := Uint (Uint_Direct_Bias - 36); 505 Uint_Minus_63 : constant Uint := Uint (Uint_Direct_Bias - 63); 506 Uint_Minus_80 : constant Uint := Uint (Uint_Direct_Bias - 80); 507 Uint_Minus_128 : constant Uint := Uint (Uint_Direct_Bias - 128); 508 509 Uint_Max_Simple_Mul : constant := Uint_Direct_Bias + 2**15; 510 -- If two values are directly represented and less than or equal to this 511 -- value, then we know the product fits in a 32-bit integer. This allows 512 -- UI_Mul to efficiently compute the product in this case. 513 514 type Save_Mark is record 515 Save_Uint : Uint; 516 Save_Udigit : Int; 517 end record; 518 519 -- Values outside the range that is represented directly are stored using 520 -- two tables. The secondary table Udigits contains sequences of Int values 521 -- consisting of the digits of the number in a radix Base system. The 522 -- digits are stored from most significant to least significant with the 523 -- first digit only carrying the sign. 524 525 -- There is one entry in the primary Uints table for each distinct Uint 526 -- value. This table entry contains the length (number of digits) and 527 -- a starting offset of the value in the Udigits table. 528 529 Uint_First_Entry : constant Uint := Uint (Uint_Table_Start); 530 531 -- Some subprograms defined in this package manipulate the Udigits table 532 -- directly, while for others it is more convenient to work with locally 533 -- defined arrays of the digits of the Universal Integers. The type 534 -- UI_Vector is defined for this purpose and some internal subprograms 535 -- used for converting from one to the other are defined. 536 537 type Uint_Entry is record 538 Length : Pos; 539 -- Length of entry in Udigits table in digits (i.e. in words) 540 541 Loc : Int; 542 -- Starting location in Udigits table of this Uint value 543 end record; 544 545 package Uints is new Table.Table ( 546 Table_Component_Type => Uint_Entry, 547 Table_Index_Type => Uint'Base, 548 Table_Low_Bound => Uint_First_Entry, 549 Table_Initial => Alloc.Uints_Initial, 550 Table_Increment => Alloc.Uints_Increment, 551 Table_Name => "Uints"); 552 553 package Udigits is new Table.Table ( 554 Table_Component_Type => Int, 555 Table_Index_Type => Int, 556 Table_Low_Bound => 0, 557 Table_Initial => Alloc.Udigits_Initial, 558 Table_Increment => Alloc.Udigits_Increment, 559 Table_Name => "Udigits"); 560 561 -- Note: the reason these tables are defined here in the private part of 562 -- the spec, rather than in the body, is that they are referenced directly 563 -- by gigi. 564 565end Uintp; 566