gcc/ada/s-fatgen.adb

   1 ------------------------------------------------------------------------------
   2 --                                                                          --
   3 --                         GNAT COMPILER COMPONENTS                         --
   4 --                                                                          --
   5 --                       S Y S T E M . F A T _ G E N                        --
   6 --                                                                          --
   7 --                                 B o d y                                  --
   8 --                                                                          --
   9 --          Copyright (C) 1992-2013, 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 --  The implementation here is portable to any IEEE implementation. It does
  33 --  not handle non-binary radix, and also assumes that model numbers and
  34 --  machine numbers are basically identical, which is not true of all possible
  35 --  floating-point implementations. On a non-IEEE machine, this body must be
  36 --  specialized appropriately, or better still, its generic instantiations
  37 --  should be replaced by efficient machine-specific code.
  38
  39 with Ada.Unchecked_Conversion;
  40 with System;
  41 package body System.Fat_Gen is
  42
  43    Float_Radix        : constant T := T (T'Machine_Radix);
  44    Radix_To_M_Minus_1 : constant T := Float_Radix ** (T'Machine_Mantissa - 1);
  45
  46    pragma Assert (T'Machine_Radix = 2);
  47    --  This version does not handle radix 16
  48
  49    --  Constants for Decompose and Scaling
  50
  51    Rad    : constant T := T (T'Machine_Radix);
  52    Invrad : constant T := 1.0 / Rad;
  53
  54    subtype Expbits is Integer range 0 .. 6;
  55    --  2 ** (2 ** 7) might overflow.  How big can radix-16 exponents get?
  56
  57    Log_Power : constant array (Expbits) of Integer := (1, 2, 4, 8, 16, 32, 64);
  58
  59    R_Power : constant array (Expbits) of T :=
  60      (Rad **  1,
  61       Rad **  2,
  62       Rad **  4,
  63       Rad **  8,
  64       Rad ** 16,
  65       Rad ** 32,
  66       Rad ** 64);
  67
  68    R_Neg_Power : constant array (Expbits) of T :=
  69      (Invrad **  1,
  70       Invrad **  2,
  71       Invrad **  4,
  72       Invrad **  8,
  73       Invrad ** 16,
  74       Invrad ** 32,
  75       Invrad ** 64);
  76
  77    -----------------------
  78    -- Local Subprograms --
  79    -----------------------
  80
  81    procedure Decompose (XX : T; Frac : out T; Expo : out UI);
  82    --  Decomposes a floating-point number into fraction and exponent parts.
  83    --  Both results are signed, with Frac having the sign of XX, and UI has
  84    --  the sign of the exponent. The absolute value of Frac is in the range
  85    --  0.0 <= Frac < 1.0. If Frac = 0.0 or -0.0, then Expo is always zero.
  86
  87    function Gradual_Scaling  (Adjustment : UI) return T;
  88    --  Like Scaling with a first argument of 1.0, but returns the smallest
  89    --  denormal rather than zero when the adjustment is smaller than
  90    --  Machine_Emin. Used for Succ and Pred.
  91
  92    --------------
  93    -- Adjacent --
  94    --------------
  95
  96    function Adjacent (X, Towards : T) return T is
  97    begin
  98       if Towards = X then
  99          return X;
 100       elsif Towards > X then
 101          return Succ (X);
 102       else
 103          return Pred (X);
 104       end if;
 105    end Adjacent;
 106
 107    -------------
 108    -- Ceiling --
 109    -------------
 110
 111    function Ceiling (X : T) return T is
 112       XT : constant T := Truncation (X);
 113    begin
 114       if X <= 0.0 then
 115          return XT;
 116       elsif X = XT then
 117          return X;
 118       else
 119          return XT + 1.0;
 120       end if;
 121    end Ceiling;
 122
 123    -------------
 124    -- Compose --
 125    -------------
 126
 127    function Compose (Fraction : T; Exponent : UI) return T is
 128       Arg_Frac : T;
 129       Arg_Exp  : UI;
 130       pragma Unreferenced (Arg_Exp);
 131    begin
 132       Decompose (Fraction, Arg_Frac, Arg_Exp);
 133       return Scaling (Arg_Frac, Exponent);
 134    end Compose;
 135
 136    ---------------
 137    -- Copy_Sign --
 138    ---------------
 139
 140    function Copy_Sign (Value, Sign : T) return T is
 141       Result : T;
 142
 143       function Is_Negative (V : T) return Boolean;
 144       pragma Import (Intrinsic, Is_Negative);
 145
 146    begin
 147       Result := abs Value;
 148
 149       if Is_Negative (Sign) then
 150          return -Result;
 151       else
 152          return Result;
 153       end if;
 154    end Copy_Sign;
 155
 156    ---------------
 157    -- Decompose --
 158    ---------------
 159
 160    procedure Decompose (XX : T; Frac : out T; Expo : out UI) is
 161       X : constant T := T'Machine (XX);
 162
 163    begin
 164       if X = 0.0 then
 165
 166          --  The normalized exponent of zero is zero, see RM A.5.2(15)
 167
 168          Frac := X;
 169          Expo := 0;
 170
 171       --  Check for infinities, transfinites, whatnot
 172
 173       elsif X > T'Safe_Last then
 174          Frac := Invrad;
 175          Expo := T'Machine_Emax + 1;
 176
 177       elsif X < T'Safe_First then
 178          Frac := -Invrad;
 179          Expo := T'Machine_Emax + 2;    -- how many extra negative values?
 180
 181       else
 182          --  Case of nonzero finite x. Essentially, we just multiply
 183          --  by Rad ** (+-2**N) to reduce the range.
 184
 185          declare
 186             Ax : T  := abs X;
 187             Ex : UI := 0;
 188
 189          --  Ax * Rad ** Ex is invariant
 190
 191          begin
 192             if Ax >= 1.0 then
 193                while Ax >= R_Power (Expbits'Last) loop
 194                   Ax := Ax * R_Neg_Power (Expbits'Last);
 195                   Ex := Ex + Log_Power (Expbits'Last);
 196                end loop;
 197
 198                --  Ax < Rad ** 64
 199
 200                for N in reverse Expbits'First .. Expbits'Last - 1 loop
 201                   if Ax >= R_Power (N) then
 202                      Ax := Ax * R_Neg_Power (N);
 203                      Ex := Ex + Log_Power (N);
 204                   end if;
 205
 206                   --  Ax < R_Power (N)
 207
 208                end loop;
 209
 210                --  1 <= Ax < Rad
 211
 212                Ax := Ax * Invrad;
 213                Ex := Ex + 1;
 214
 215             else
 216                --  0 < ax < 1
 217
 218                while Ax < R_Neg_Power (Expbits'Last) loop
 219                   Ax := Ax * R_Power (Expbits'Last);
 220                   Ex := Ex - Log_Power (Expbits'Last);
 221                end loop;
 222
 223                --  Rad ** -64 <= Ax < 1
 224
 225                for N in reverse Expbits'First .. Expbits'Last - 1 loop
 226                   if Ax < R_Neg_Power (N) then
 227                      Ax := Ax * R_Power (N);
 228                      Ex := Ex - Log_Power (N);
 229                   end if;
 230
 231                   --  R_Neg_Power (N) <= Ax < 1
 232
 233                end loop;
 234             end if;
 235
 236             Frac := (if X > 0.0 then Ax else -Ax);
 237             Expo := Ex;
 238          end;
 239       end if;
 240    end Decompose;
 241
 242    --------------
 243    -- Exponent --
 244    --------------
 245
 246    function Exponent (X : T) return UI is
 247       X_Frac : T;
 248       X_Exp  : UI;
 249       pragma Unreferenced (X_Frac);
 250    begin
 251       Decompose (X, X_Frac, X_Exp);
 252       return X_Exp;
 253    end Exponent;
 254
 255    -----------
 256    -- Floor --
 257    -----------
 258
 259    function Floor (X : T) return T is
 260       XT : constant T := Truncation (X);
 261    begin
 262       if X >= 0.0 then
 263          return XT;
 264       elsif XT = X then
 265          return X;
 266       else
 267          return XT - 1.0;
 268       end if;
 269    end Floor;
 270
 271    --------------
 272    -- Fraction --
 273    --------------
 274
 275    function Fraction (X : T) return T is
 276       X_Frac : T;
 277       X_Exp  : UI;
 278       pragma Unreferenced (X_Exp);
 279    begin
 280       Decompose (X, X_Frac, X_Exp);
 281       return X_Frac;
 282    end Fraction;
 283
 284    ---------------------
 285    -- Gradual_Scaling --
 286    ---------------------
 287
 288    function Gradual_Scaling  (Adjustment : UI) return T is
 289       Y  : T;
 290       Y1 : T;
 291       Ex : UI := Adjustment;
 292
 293    begin
 294       if Adjustment < T'Machine_Emin - 1 then
 295          Y  := 2.0 ** T'Machine_Emin;
 296          Y1 := Y;
 297          Ex := Ex - T'Machine_Emin;
 298          while Ex < 0 loop
 299             Y := T'Machine (Y / 2.0);
 300
 301             if Y = 0.0 then
 302                return Y1;
 303             end if;
 304
 305             Ex := Ex + 1;
 306             Y1 := Y;
 307          end loop;
 308
 309          return Y1;
 310
 311       else
 312          return Scaling (1.0, Adjustment);
 313       end if;
 314    end Gradual_Scaling;
 315
 316    ------------------
 317    -- Leading_Part --
 318    ------------------
 319
 320    function Leading_Part (X : T; Radix_Digits : UI) return T is
 321       L    : UI;
 322       Y, Z : T;
 323
 324    begin
 325       if Radix_Digits >= T'Machine_Mantissa then
 326          return X;
 327
 328       elsif Radix_Digits <= 0 then
 329          raise Constraint_Error;
 330
 331       else
 332          L := Exponent (X) - Radix_Digits;
 333          Y := Truncation (Scaling (X, -L));
 334          Z := Scaling (Y, L);
 335          return Z;
 336       end if;
 337    end Leading_Part;
 338
 339    -------------
 340    -- Machine --
 341    -------------
 342
 343    --  The trick with Machine is to force the compiler to store the result
 344    --  in memory so that we do not have extra precision used. The compiler
 345    --  is clever, so we have to outwit its possible optimizations. We do
 346    --  this by using an intermediate pragma Volatile location.
 347
 348    function Machine (X : T) return T is
 349       Temp : T;
 350       pragma Volatile (Temp);
 351    begin
 352       Temp := X;
 353       return Temp;
 354    end Machine;
 355
 356    ----------------------
 357    -- Machine_Rounding --
 358    ----------------------
 359
 360    --  For now, the implementation is identical to that of Rounding, which is
 361    --  a permissible behavior, but is not the most efficient possible approach.
 362
 363    function Machine_Rounding (X : T) return T is
 364       Result : T;
 365       Tail   : T;
 366
 367    begin
 368       Result := Truncation (abs X);
 369       Tail   := abs X - Result;
 370
 371       if Tail >= 0.5  then
 372          Result := Result + 1.0;
 373       end if;
 374
 375       if X > 0.0 then
 376          return Result;
 377
 378       elsif X < 0.0 then
 379          return -Result;
 380
 381       --  For zero case, make sure sign of zero is preserved
 382
 383       else
 384          return X;
 385       end if;
 386    end Machine_Rounding;
 387
 388    -----------
 389    -- Model --
 390    -----------
 391
 392    --  We treat Model as identical to Machine. This is true of IEEE and other
 393    --  nice floating-point systems, but not necessarily true of all systems.
 394
 395    function Model (X : T) return T is
 396    begin
 397       return Machine (X);
 398    end Model;
 399
 400    ----------
 401    -- Pred --
 402    ----------
 403
 404    --  Subtract from the given number a number equivalent to the value of its
 405    --  least significant bit. Given that the most significant bit represents
 406    --  a value of 1.0 * radix ** (exp - 1), the value we want is obtained by
 407    --  shifting this by (mantissa-1) bits to the right, i.e. decreasing the
 408    --  exponent by that amount.
 409
 410    --  Zero has to be treated specially, since its exponent is zero
 411
 412    function Pred (X : T) return T is
 413       X_Frac : T;
 414       X_Exp  : UI;
 415
 416    begin
 417       if X = 0.0 then
 418          return -Succ (X);
 419
 420       else
 421          Decompose (X, X_Frac, X_Exp);
 422
 423          --  A special case, if the number we had was a positive power of
 424          --  two, then we want to subtract half of what we would otherwise
 425          --  subtract, since the exponent is going to be reduced.
 426
 427          --  Note that X_Frac has the same sign as X, so if X_Frac is 0.5,
 428          --  then we know that we have a positive number (and hence a
 429          --  positive power of 2).
 430
 431          if X_Frac = 0.5 then
 432             return X - Gradual_Scaling (X_Exp - T'Machine_Mantissa - 1);
 433
 434          --  Otherwise the exponent is unchanged
 435
 436          else
 437             return X - Gradual_Scaling (X_Exp - T'Machine_Mantissa);
 438          end if;
 439       end if;
 440    end Pred;
 441
 442    ---------------
 443    -- Remainder --
 444    ---------------
 445
 446    function Remainder (X, Y : T) return T is
 447       A        : T;
 448       B        : T;
 449       Arg      : T;
 450       P        : T;
 451       P_Frac   : T;
 452       Sign_X   : T;
 453       IEEE_Rem : T;
 454       Arg_Exp  : UI;
 455       P_Exp    : UI;
 456       K        : UI;
 457       P_Even   : Boolean;
 458
 459       Arg_Frac : T;
 460       pragma Unreferenced (Arg_Frac);
 461
 462    begin
 463       if Y = 0.0 then
 464          raise Constraint_Error;
 465       end if;
 466
 467       if X > 0.0 then
 468          Sign_X :=  1.0;
 469          Arg := X;
 470       else
 471          Sign_X := -1.0;
 472          Arg := -X;
 473       end if;
 474
 475       P := abs Y;
 476
 477       if Arg < P then
 478          P_Even := True;
 479          IEEE_Rem := Arg;
 480          P_Exp := Exponent (P);
 481
 482       else
 483          Decompose (Arg, Arg_Frac, Arg_Exp);
 484          Decompose (P,   P_Frac,   P_Exp);
 485
 486          P := Compose (P_Frac, Arg_Exp);
 487          K := Arg_Exp - P_Exp;
 488          P_Even := True;
 489          IEEE_Rem := Arg;
 490
 491          for Cnt in reverse 0 .. K loop
 492             if IEEE_Rem >= P then
 493                P_Even := False;
 494                IEEE_Rem := IEEE_Rem - P;
 495             else
 496                P_Even := True;
 497             end if;
 498
 499             P := P * 0.5;
 500          end loop;
 501       end if;
 502
 503       --  That completes the calculation of modulus remainder. The final
 504       --  step is get the IEEE remainder. Here we need to compare Rem with
 505       --  (abs Y) / 2. We must be careful of unrepresentable Y/2 value
 506       --  caused by subnormal numbers
 507
 508       if P_Exp >= 0 then
 509          A := IEEE_Rem;
 510          B := abs Y * 0.5;
 511
 512       else
 513          A := IEEE_Rem * 2.0;
 514          B := abs Y;
 515       end if;
 516
 517       if A > B or else (A = B and then not P_Even) then
 518          IEEE_Rem := IEEE_Rem - abs Y;
 519       end if;
 520
 521       return Sign_X * IEEE_Rem;
 522    end Remainder;
 523
 524    --------------
 525    -- Rounding --
 526    --------------
 527
 528    function Rounding (X : T) return T is
 529       Result : T;
 530       Tail   : T;
 531
 532    begin
 533       Result := Truncation (abs X);
 534       Tail   := abs X - Result;
 535
 536       if Tail >= 0.5  then
 537          Result := Result + 1.0;
 538       end if;
 539
 540       if X > 0.0 then
 541          return Result;
 542
 543       elsif X < 0.0 then
 544          return -Result;
 545
 546       --  For zero case, make sure sign of zero is preserved
 547
 548       else
 549          return X;
 550       end if;
 551    end Rounding;
 552
 553    -------------
 554    -- Scaling --
 555    -------------
 556
 557    --  Return x * rad ** adjustment quickly, or quietly underflow to zero,
 558    --  or overflow naturally.
 559
 560    function Scaling (X : T; Adjustment : UI) return T is
 561    begin
 562       if X = 0.0 or else Adjustment = 0 then
 563          return X;
 564       end if;
 565
 566       --  Nonzero x essentially, just multiply repeatedly by Rad ** (+-2**n)
 567
 568       declare
 569          Y  : T  := X;
 570          Ex : UI := Adjustment;
 571
 572       --  Y * Rad ** Ex is invariant
 573
 574       begin
 575          if Ex < 0 then
 576             while Ex <= -Log_Power (Expbits'Last) loop
 577                Y := Y * R_Neg_Power (Expbits'Last);
 578                Ex := Ex + Log_Power (Expbits'Last);
 579             end loop;
 580
 581             --  -64 < Ex <= 0
 582
 583             for N in reverse Expbits'First .. Expbits'Last - 1 loop
 584                if Ex <= -Log_Power (N) then
 585                   Y := Y * R_Neg_Power (N);
 586                   Ex := Ex + Log_Power (N);
 587                end if;
 588
 589                --  -Log_Power (N) < Ex <= 0
 590
 591             end loop;
 592
 593             --  Ex = 0
 594
 595          else
 596             --  Ex >= 0
 597
 598             while Ex >= Log_Power (Expbits'Last) loop
 599                Y := Y * R_Power (Expbits'Last);
 600                Ex := Ex - Log_Power (Expbits'Last);
 601             end loop;
 602
 603             --  0 <= Ex < 64
 604
 605             for N in reverse Expbits'First .. Expbits'Last - 1 loop
 606                if Ex >= Log_Power (N) then
 607                   Y := Y * R_Power (N);
 608                   Ex := Ex - Log_Power (N);
 609                end if;
 610
 611                --  0 <= Ex < Log_Power (N)
 612
 613             end loop;
 614
 615             --  Ex = 0
 616
 617          end if;
 618
 619          return Y;
 620       end;
 621    end Scaling;
 622
 623    ----------
 624    -- Succ --
 625    ----------
 626
 627    --  Similar computation to that of Pred: find value of least significant
 628    --  bit of given number, and add. Zero has to be treated specially since
 629    --  the exponent can be zero, and also we want the smallest denormal if
 630    --  denormals are supported.
 631
 632    function Succ (X : T) return T is
 633       X_Frac : T;
 634       X_Exp  : UI;
 635       X1, X2 : T;
 636
 637    begin
 638       if X = 0.0 then
 639          X1 := 2.0 ** T'Machine_Emin;
 640
 641          --  Following loop generates smallest denormal
 642
 643          loop
 644             X2 := T'Machine (X1 / 2.0);
 645             exit when X2 = 0.0;
 646             X1 := X2;
 647          end loop;
 648
 649          return X1;
 650
 651       else
 652          Decompose (X, X_Frac, X_Exp);
 653
 654          --  A special case, if the number we had was a negative power of two,
 655          --  then we want to add half of what we would otherwise add, since the
 656          --  exponent is going to be reduced.
 657
 658          --  Note that X_Frac has the same sign as X, so if X_Frac is -0.5,
 659          --  then we know that we have a negative number (and hence a negative
 660          --  power of 2).
 661
 662          if X_Frac = -0.5 then
 663             return X + Gradual_Scaling (X_Exp - T'Machine_Mantissa - 1);
 664
 665          --  Otherwise the exponent is unchanged
 666
 667          else
 668             return X + Gradual_Scaling (X_Exp - T'Machine_Mantissa);
 669          end if;
 670       end if;
 671    end Succ;
 672
 673    ----------------
 674    -- Truncation --
 675    ----------------
 676
 677    --  The basic approach is to compute
 678
 679    --    T'Machine (RM1 + N) - RM1
 680
 681    --  where N >= 0.0 and RM1 = radix ** (mantissa - 1)
 682
 683    --  This works provided that the intermediate result (RM1 + N) does not
 684    --  have extra precision (which is why we call Machine). When we compute
 685    --  RM1 + N, the exponent of N will be normalized and the mantissa shifted
 686    --  shifted appropriately so the lower order bits, which cannot contribute
 687    --  to the integer part of N, fall off on the right. When we subtract RM1
 688    --  again, the significant bits of N are shifted to the left, and what we
 689    --  have is an integer, because only the first e bits are different from
 690    --  zero (assuming binary radix here).
 691
 692    function Truncation (X : T) return T is
 693       Result : T;
 694
 695    begin
 696       Result := abs X;
 697
 698       if Result >= Radix_To_M_Minus_1 then
 699          return Machine (X);
 700
 701       else
 702          Result := Machine (Radix_To_M_Minus_1 + Result) - Radix_To_M_Minus_1;
 703
 704          if Result > abs X  then
 705             Result := Result - 1.0;
 706          end if;
 707
 708          if X > 0.0 then
 709             return  Result;
 710
 711          elsif X < 0.0 then
 712             return -Result;
 713
 714          --  For zero case, make sure sign of zero is preserved
 715
 716          else
 717             return X;
 718          end if;
 719       end if;
 720    end Truncation;
 721
 722    -----------------------
 723    -- Unbiased_Rounding --
 724    -----------------------
 725
 726    function Unbiased_Rounding (X : T) return T is
 727       Abs_X  : constant T := abs X;
 728       Result : T;
 729       Tail   : T;
 730
 731    begin
 732       Result := Truncation (Abs_X);
 733       Tail   := Abs_X - Result;
 734
 735       if Tail > 0.5  then
 736          Result := Result + 1.0;
 737
 738       elsif Tail = 0.5 then
 739          Result := 2.0 * Truncation ((Result / 2.0) + 0.5);
 740       end if;
 741
 742       if X > 0.0 then
 743          return Result;
 744
 745       elsif X < 0.0 then
 746          return -Result;
 747
 748       --  For zero case, make sure sign of zero is preserved
 749
 750       else
 751          return X;
 752       end if;
 753    end Unbiased_Rounding;
 754
 755    -----------
 756    -- Valid --
 757    -----------
 758
 759    --  Note: this routine does not work for VAX float. We compensate for this
 760    --  in Exp_Attr by using the Valid functions in Vax_Float_Operations rather
 761    --  than the corresponding instantiation of this function.
 762
 763    function Valid (X : not null access T) return Boolean is
 764
 765       IEEE_Emin : constant Integer := T'Machine_Emin - 1;
 766       IEEE_Emax : constant Integer := T'Machine_Emax - 1;
 767
 768       IEEE_Bias : constant Integer := -(IEEE_Emin - 1);
 769
 770       subtype IEEE_Exponent_Range is
 771         Integer range IEEE_Emin - 1 .. IEEE_Emax + 1;
 772
 773       --  The implementation of this floating point attribute uses a
 774       --  representation type Float_Rep that allows direct access to the
 775       --  exponent and mantissa parts of a floating point number.
 776
 777       --  The Float_Rep type is an array of Float_Word elements. This
 778       --  representation is chosen to make it possible to size the type based
 779       --  on a generic parameter. Since the array size is known at compile
 780       --  time, efficient code can still be generated. The size of Float_Word
 781       --  elements should be large enough to allow accessing the exponent in
 782       --  one read, but small enough so that all floating point object sizes
 783       --  are a multiple of the Float_Word'Size.
 784
 785       --  The following conditions must be met for all possible instantiations
 786       --  of the attributes package:
 787
 788       --    - T'Size is an integral multiple of Float_Word'Size
 789
 790       --    - The exponent and sign are completely contained in a single
 791       --      component of Float_Rep, named Most_Significant_Word (MSW).
 792
 793       --    - The sign occupies the most significant bit of the MSW and the
 794       --      exponent is in the following bits. Unused bits (if any) are in
 795       --      the least significant part.
 796
 797       type Float_Word is mod 2**Positive'Min (System.Word_Size, 32);
 798       type Rep_Index is range 0 .. 7;
 799
 800       Rep_Words : constant Positive :=
 801                     (T'Size + Float_Word'Size - 1) / Float_Word'Size;
 802       Rep_Last  : constant Rep_Index :=
 803                     Rep_Index'Min
 804                       (Rep_Index (Rep_Words - 1),
 805                        (T'Mantissa + 16) / Float_Word'Size);
 806       --  Determine the number of Float_Words needed for representing the
 807       --  entire floating-point value. Do not take into account excessive
 808       --  padding, as occurs on IA-64 where 80 bits floats get padded to 128
 809       --  bits. In general, the exponent field cannot be larger than 15 bits,
 810       --  even for 128-bit floating-point types, so the final format size
 811       --  won't be larger than T'Mantissa + 16.
 812
 813       type Float_Rep is
 814          array (Rep_Index range 0 .. Rep_Index (Rep_Words - 1)) of Float_Word;
 815
 816       pragma Suppress_Initialization (Float_Rep);
 817       --  This pragma suppresses the generation of an initialization procedure
 818       --  for type Float_Rep when operating in Initialize/Normalize_Scalars
 819       --  mode. This is not just a matter of efficiency, but of functionality,
 820       --  since Valid has a pragma Inline_Always, which is not permitted if
 821       --  there are nested subprograms present.
 822
 823       Most_Significant_Word : constant Rep_Index :=
 824                                 Rep_Last * Standard'Default_Bit_Order;
 825       --  Finding the location of the Exponent_Word is a bit tricky. In general
 826       --  we assume Word_Order = Bit_Order. This expression needs to be refined
 827       --  for VMS.
 828
 829       Exponent_Factor : constant Float_Word :=
 830                           2**(Float_Word'Size - 1) /
 831                             Float_Word (IEEE_Emax - IEEE_Emin + 3) *
 832                               Boolean'Pos (Most_Significant_Word /= 2) +
 833                                 Boolean'Pos (Most_Significant_Word = 2);
 834       --  Factor that the extracted exponent needs to be divided by to be in
 835       --  range 0 .. IEEE_Emax - IEEE_Emin + 2. Special kludge: Exponent_Factor
 836       --  is 1 for x86/IA64 double extended as GCC adds unused bits to the
 837       --  type.
 838
 839       Exponent_Mask : constant Float_Word :=
 840                         Float_Word (IEEE_Emax - IEEE_Emin + 2) *
 841                           Exponent_Factor;
 842       --  Value needed to mask out the exponent field. This assumes that the
 843       --  range IEEE_Emin - 1 .. IEEE_Emax + contains 2**N values, for some N
 844       --  in Natural.
 845
 846       function To_Float is new Ada.Unchecked_Conversion (Float_Rep, T);
 847
 848       type Float_Access is access all T;
 849       function To_Address is
 850          new Ada.Unchecked_Conversion (Float_Access, System.Address);
 851
 852       XA : constant System.Address := To_Address (Float_Access (X));
 853
 854       R : Float_Rep;
 855       pragma Import (Ada, R);
 856       for R'Address use XA;
 857       --  R is a view of the input floating-point parameter. Note that we
 858       --  must avoid copying the actual bits of this parameter in float
 859       --  form (since it may be a signalling NaN.
 860
 861       E  : constant IEEE_Exponent_Range :=
 862              Integer ((R (Most_Significant_Word) and Exponent_Mask) /
 863                                                         Exponent_Factor)
 864                - IEEE_Bias;
 865       --  Mask/Shift T to only get bits from the exponent. Then convert biased
 866       --  value to integer value.
 867
 868       SR : Float_Rep;
 869       --  Float_Rep representation of significant of X.all
 870
 871    begin
 872       if T'Denorm then
 873
 874          --  All denormalized numbers are valid, so the only invalid numbers
 875          --  are overflows and NaNs, both with exponent = Emax + 1.
 876
 877          return E /= IEEE_Emax + 1;
 878
 879       end if;
 880
 881       --  All denormalized numbers except 0.0 are invalid
 882
 883       --  Set exponent of X to zero, so we end up with the significand, which
 884       --  definitely is a valid number and can be converted back to a float.
 885
 886       SR := R;
 887       SR (Most_Significant_Word) :=
 888            (SR (Most_Significant_Word)
 889              and not Exponent_Mask) + Float_Word (IEEE_Bias) * Exponent_Factor;
 890
 891       return (E in IEEE_Emin .. IEEE_Emax) or else
 892          ((E = IEEE_Emin - 1) and then abs To_Float (SR) = 1.0);
 893    end Valid;
 894
 895    ---------------------
 896    -- Unaligned_Valid --
 897    ---------------------
 898
 899    function Unaligned_Valid (A : System.Address) return Boolean is
 900       subtype FS is String (1 .. T'Size / Character'Size);
 901       type FSP is access FS;
 902
 903       function To_FSP is new Ada.Unchecked_Conversion (Address, FSP);
 904
 905       Local_T : aliased T;
 906
 907    begin
 908       --  Note that we have to be sure that we do not load the value into a
 909       --  floating-point register, since a signalling NaN may cause a trap.
 910       --  The following assignment is what does the actual alignment, since
 911       --  we know that the target Local_T is aligned.
 912
 913       To_FSP (Local_T'Address).all := To_FSP (A).all;
 914
 915       --  Now that we have an aligned value, we can use the normal aligned
 916       --  version of Valid to obtain the required result.
 917
 918       return Valid (Local_T'Access);
 919    end Unaligned_Valid;
 920
 921 end System.Fat_Gen;