1 ------------------------------------------------------------------------------
3 -- GNAT COMPILER COMPONENTS --
5 -- S Y S T E M . F A T _ G E N --
9 -- Copyright (C) 1992-2007, Free Software Foundation, Inc. --
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, 51 Franklin Street, Fifth Floor, --
20 -- Boston, MA 02110-1301, USA. --
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. --
29 -- GNAT was originally developed by the GNAT team at New York University. --
30 -- Extensive contributions were provided by Ada Core Technologies Inc. --
32 ------------------------------------------------------------------------------
34 -- The implementation here is portable to any IEEE implementation. It does
35 -- not handle non-binary radix, and also assumes that model numbers and
36 -- machine numbers are basically identical, which is not true of all possible
37 -- floating-point implementations. On a non-IEEE machine, this body must be
38 -- specialized appropriately, or better still, its generic instantiations
39 -- should be replaced by efficient machine-specific code.
41 with Ada.Unchecked_Conversion;
43 package body System.Fat_Gen is
45 Float_Radix : constant T := T (T'Machine_Radix);
46 Radix_To_M_Minus_1 : constant T := Float_Radix ** (T'Machine_Mantissa - 1);
48 pragma Assert (T'Machine_Radix = 2);
49 -- This version does not handle radix 16
51 -- Constants for Decompose and Scaling
53 Rad : constant T := T (T'Machine_Radix);
54 Invrad : constant T := 1.0 / Rad;
56 subtype Expbits is Integer range 0 .. 6;
57 -- 2 ** (2 ** 7) might overflow. how big can radix-16 exponents get?
59 Log_Power : constant array (Expbits) of Integer := (1, 2, 4, 8, 16, 32, 64);
61 R_Power : constant array (Expbits) of T :=
70 R_Neg_Power : constant array (Expbits) of T :=
79 -----------------------
80 -- Local Subprograms --
81 -----------------------
83 procedure Decompose (XX : T; Frac : out T; Expo : out UI);
84 -- Decomposes a floating-point number into fraction and exponent parts.
85 -- Both results are signed, with Frac having the sign of XX, and UI has
86 -- the sign of the exponent. The absolute value of Frac is in the range
87 -- 0.0 <= Frac < 1.0. If Frac = 0.0 or -0.0, then Expo is always zero.
89 function Gradual_Scaling (Adjustment : UI) return T;
90 -- Like Scaling with a first argument of 1.0, but returns the smallest
91 -- denormal rather than zero when the adjustment is smaller than
92 -- Machine_Emin. Used for Succ and Pred.
98 function Adjacent (X, Towards : T) return T is
102 elsif Towards > X then
113 function Ceiling (X : T) return T is
114 XT : constant T := Truncation (X);
129 function Compose (Fraction : T; Exponent : UI) return T is
132 pragma Unreferenced (Arg_Exp);
134 Decompose (Fraction, Arg_Frac, Arg_Exp);
135 return Scaling (Arg_Frac, Exponent);
142 function Copy_Sign (Value, Sign : T) return T is
145 function Is_Negative (V : T) return Boolean;
146 pragma Import (Intrinsic, Is_Negative);
151 if Is_Negative (Sign) then
162 procedure Decompose (XX : T; Frac : out T; Expo : out UI) is
163 X : constant T := T'Machine (XX);
170 -- More useful would be defining Expo to be T'Machine_Emin - 1 or
171 -- T'Machine_Emin - T'Machine_Mantissa, which would preserve
172 -- monotonicity of the exponent function ???
174 -- Check for infinities, transfinites, whatnot
176 elsif X > T'Safe_Last then
178 Expo := T'Machine_Emax + 1;
180 elsif X < T'Safe_First then
182 Expo := T'Machine_Emax + 2; -- how many extra negative values?
185 -- Case of nonzero finite x. Essentially, we just multiply
186 -- by Rad ** (+-2**N) to reduce the range.
192 -- Ax * Rad ** Ex is invariant
196 while Ax >= R_Power (Expbits'Last) loop
197 Ax := Ax * R_Neg_Power (Expbits'Last);
198 Ex := Ex + Log_Power (Expbits'Last);
203 for N in reverse Expbits'First .. Expbits'Last - 1 loop
204 if Ax >= R_Power (N) then
205 Ax := Ax * R_Neg_Power (N);
206 Ex := Ex + Log_Power (N);
220 while Ax < R_Neg_Power (Expbits'Last) loop
221 Ax := Ax * R_Power (Expbits'Last);
222 Ex := Ex - Log_Power (Expbits'Last);
225 -- Rad ** -64 <= Ax < 1
227 for N in reverse Expbits'First .. Expbits'Last - 1 loop
228 if Ax < R_Neg_Power (N) then
229 Ax := Ax * R_Power (N);
230 Ex := Ex - Log_Power (N);
233 -- R_Neg_Power (N) <= Ax < 1
252 function Exponent (X : T) return UI is
255 pragma Unreferenced (X_Frac);
257 Decompose (X, X_Frac, X_Exp);
265 function Floor (X : T) return T is
266 XT : constant T := Truncation (X);
281 function Fraction (X : T) return T is
284 pragma Unreferenced (X_Exp);
286 Decompose (X, X_Frac, X_Exp);
290 ---------------------
291 -- Gradual_Scaling --
292 ---------------------
294 function Gradual_Scaling (Adjustment : UI) return T is
297 Ex : UI := Adjustment;
300 if Adjustment < T'Machine_Emin - 1 then
301 Y := 2.0 ** T'Machine_Emin;
303 Ex := Ex - T'Machine_Emin;
305 Y := T'Machine (Y / 2.0);
318 return Scaling (1.0, Adjustment);
326 function Leading_Part (X : T; Radix_Digits : UI) return T is
331 if Radix_Digits >= T'Machine_Mantissa then
334 elsif Radix_Digits <= 0 then
335 raise Constraint_Error;
338 L := Exponent (X) - Radix_Digits;
339 Y := Truncation (Scaling (X, -L));
349 -- The trick with Machine is to force the compiler to store the result
350 -- in memory so that we do not have extra precision used. The compiler
351 -- is clever, so we have to outwit its possible optimizations! We do
352 -- this by using an intermediate pragma Volatile location.
354 function Machine (X : T) return T is
356 pragma Volatile (Temp);
362 ----------------------
363 -- Machine_Rounding --
364 ----------------------
366 -- For now, the implementation is identical to that of Rounding, which is
367 -- a permissible behavior, but is not the most efficient possible approach.
369 function Machine_Rounding (X : T) return T is
374 Result := Truncation (abs X);
375 Tail := abs X - Result;
378 Result := Result + 1.0;
387 -- For zero case, make sure sign of zero is preserved
392 end Machine_Rounding;
398 -- We treat Model as identical to Machine. This is true of IEEE and other
399 -- nice floating-point systems, but not necessarily true of all systems.
401 function Model (X : T) return T is
410 -- Subtract from the given number a number equivalent to the value of its
411 -- least significant bit. Given that the most significant bit represents
412 -- a value of 1.0 * radix ** (exp - 1), the value we want is obtained by
413 -- shifting this by (mantissa-1) bits to the right, i.e. decreasing the
414 -- exponent by that amount.
416 -- Zero has to be treated specially, since its exponent is zero
418 function Pred (X : T) return T is
427 Decompose (X, X_Frac, X_Exp);
429 -- A special case, if the number we had was a positive power of
430 -- two, then we want to subtract half of what we would otherwise
431 -- subtract, since the exponent is going to be reduced.
433 -- Note that X_Frac has the same sign as X, so if X_Frac is 0.5,
434 -- then we know that we have a positive number (and hence a
435 -- positive power of 2).
438 return X - Gradual_Scaling (X_Exp - T'Machine_Mantissa - 1);
440 -- Otherwise the exponent is unchanged
443 return X - Gradual_Scaling (X_Exp - T'Machine_Mantissa);
452 function Remainder (X, Y : T) return T is
466 pragma Unreferenced (Arg_Frac);
470 raise Constraint_Error;
486 P_Exp := Exponent (P);
489 Decompose (Arg, Arg_Frac, Arg_Exp);
490 Decompose (P, P_Frac, P_Exp);
492 P := Compose (P_Frac, Arg_Exp);
493 K := Arg_Exp - P_Exp;
497 for Cnt in reverse 0 .. K loop
498 if IEEE_Rem >= P then
500 IEEE_Rem := IEEE_Rem - P;
509 -- That completes the calculation of modulus remainder. The final
510 -- step is get the IEEE remainder. Here we need to compare Rem with
511 -- (abs Y) / 2. We must be careful of unrepresentable Y/2 value
512 -- caused by subnormal numbers
523 if A > B or else (A = B and then not P_Even) then
524 IEEE_Rem := IEEE_Rem - abs Y;
527 return Sign_X * IEEE_Rem;
534 function Rounding (X : T) return T is
539 Result := Truncation (abs X);
540 Tail := abs X - Result;
543 Result := Result + 1.0;
552 -- For zero case, make sure sign of zero is preserved
563 -- Return x * rad ** adjustment quickly,
564 -- or quietly underflow to zero, or overflow naturally.
566 function Scaling (X : T; Adjustment : UI) return T is
568 if X = 0.0 or else Adjustment = 0 then
572 -- Nonzero x. essentially, just multiply repeatedly by Rad ** (+-2**n)
576 Ex : UI := Adjustment;
578 -- Y * Rad ** Ex is invariant
582 while Ex <= -Log_Power (Expbits'Last) loop
583 Y := Y * R_Neg_Power (Expbits'Last);
584 Ex := Ex + Log_Power (Expbits'Last);
589 for N in reverse Expbits'First .. Expbits'Last - 1 loop
590 if Ex <= -Log_Power (N) then
591 Y := Y * R_Neg_Power (N);
592 Ex := Ex + Log_Power (N);
595 -- -Log_Power (N) < Ex <= 0
603 while Ex >= Log_Power (Expbits'Last) loop
604 Y := Y * R_Power (Expbits'Last);
605 Ex := Ex - Log_Power (Expbits'Last);
610 for N in reverse Expbits'First .. Expbits'Last - 1 loop
611 if Ex >= Log_Power (N) then
612 Y := Y * R_Power (N);
613 Ex := Ex - Log_Power (N);
616 -- 0 <= Ex < Log_Power (N)
631 -- Similar computation to that of Pred: find value of least significant
632 -- bit of given number, and add. Zero has to be treated specially since
633 -- the exponent can be zero, and also we want the smallest denormal if
634 -- denormals are supported.
636 function Succ (X : T) return T is
643 X1 := 2.0 ** T'Machine_Emin;
645 -- Following loop generates smallest denormal
648 X2 := T'Machine (X1 / 2.0);
656 Decompose (X, X_Frac, X_Exp);
658 -- A special case, if the number we had was a negative power of
659 -- two, then we want to add half of what we would otherwise add,
660 -- since the exponent is going to be reduced.
662 -- Note that X_Frac has the same sign as X, so if X_Frac is -0.5,
663 -- then we know that we have a ngeative number (and hence a
664 -- negative power of 2).
666 if X_Frac = -0.5 then
667 return X + Gradual_Scaling (X_Exp - T'Machine_Mantissa - 1);
669 -- Otherwise the exponent is unchanged
672 return X + Gradual_Scaling (X_Exp - T'Machine_Mantissa);
681 -- The basic approach is to compute
683 -- T'Machine (RM1 + N) - RM1
685 -- where N >= 0.0 and RM1 = radix ** (mantissa - 1)
687 -- This works provided that the intermediate result (RM1 + N) does not
688 -- have extra precision (which is why we call Machine). When we compute
689 -- RM1 + N, the exponent of N will be normalized and the mantissa shifted
690 -- shifted appropriately so the lower order bits, which cannot contribute
691 -- to the integer part of N, fall off on the right. When we subtract RM1
692 -- again, the significant bits of N are shifted to the left, and what we
693 -- have is an integer, because only the first e bits are different from
694 -- zero (assuming binary radix here).
696 function Truncation (X : T) return T is
702 if Result >= Radix_To_M_Minus_1 then
706 Result := Machine (Radix_To_M_Minus_1 + Result) - Radix_To_M_Minus_1;
708 if Result > abs X then
709 Result := Result - 1.0;
718 -- For zero case, make sure sign of zero is preserved
726 -----------------------
727 -- Unbiased_Rounding --
728 -----------------------
730 function Unbiased_Rounding (X : T) return T is
731 Abs_X : constant T := abs X;
736 Result := Truncation (Abs_X);
737 Tail := Abs_X - Result;
740 Result := Result + 1.0;
742 elsif Tail = 0.5 then
743 Result := 2.0 * Truncation ((Result / 2.0) + 0.5);
752 -- For zero case, make sure sign of zero is preserved
757 end Unbiased_Rounding;
763 -- Note: this routine does not work for VAX float. We compensate for this
764 -- in Exp_Attr by using the Valid functions in Vax_Float_Operations rather
765 -- than the corresponding instantiation of this function.
767 function Valid (X : not null access T) return Boolean is
769 IEEE_Emin : constant Integer := T'Machine_Emin - 1;
770 IEEE_Emax : constant Integer := T'Machine_Emax - 1;
772 IEEE_Bias : constant Integer := -(IEEE_Emin - 1);
774 subtype IEEE_Exponent_Range is
775 Integer range IEEE_Emin - 1 .. IEEE_Emax + 1;
777 -- The implementation of this floating point attribute uses a
778 -- representation type Float_Rep that allows direct access to the
779 -- exponent and mantissa parts of a floating point number.
781 -- The Float_Rep type is an array of Float_Word elements. This
782 -- representation is chosen to make it possible to size the type based
783 -- on a generic parameter. Since the array size is known at compile
784 -- time, efficient code can still be generated. The size of Float_Word
785 -- elements should be large enough to allow accessing the exponent in
786 -- one read, but small enough so that all floating point object sizes
787 -- are a multiple of the Float_Word'Size.
789 -- The following conditions must be met for all possible
790 -- instantiations of the attributes package:
792 -- - T'Size is an integral multiple of Float_Word'Size
794 -- - The exponent and sign are completely contained in a single
795 -- component of Float_Rep, named Most_Significant_Word (MSW).
797 -- - The sign occupies the most significant bit of the MSW and the
798 -- exponent is in the following bits. Unused bits (if any) are in
799 -- the least significant part.
801 type Float_Word is mod 2**Positive'Min (System.Word_Size, 32);
802 type Rep_Index is range 0 .. 7;
804 Rep_Words : constant Positive :=
805 (T'Size + Float_Word'Size - 1) / Float_Word'Size;
806 Rep_Last : constant Rep_Index := Rep_Index'Min
807 (Rep_Index (Rep_Words - 1), (T'Mantissa + 16) / Float_Word'Size);
808 -- Determine the number of Float_Words needed for representing the
809 -- entire floating-point value. Do not take into account excessive
810 -- padding, as occurs on IA-64 where 80 bits floats get padded to 128
811 -- bits. In general, the exponent field cannot be larger than 15 bits,
812 -- even for 128-bit floating-poin t types, so the final format size
813 -- won't be larger than T'Mantissa + 16.
816 array (Rep_Index range 0 .. Rep_Index (Rep_Words - 1)) of Float_Word;
818 pragma Suppress_Initialization (Float_Rep);
819 -- This pragma supresses the generation of an initialization procedure
820 -- for type Float_Rep when operating in Initialize/Normalize_Scalars
821 -- mode. This is not just a matter of efficiency, but of functionality,
822 -- since Valid has a pragma Inline_Always, which is not permitted if
823 -- there are nested subprograms present.
825 Most_Significant_Word : constant Rep_Index :=
826 Rep_Last * Standard'Default_Bit_Order;
827 -- Finding the location of the Exponent_Word is a bit tricky. In general
828 -- we assume Word_Order = Bit_Order. This expression needs to be refined
831 Exponent_Factor : constant Float_Word :=
832 2**(Float_Word'Size - 1) /
833 Float_Word (IEEE_Emax - IEEE_Emin + 3) *
834 Boolean'Pos (Most_Significant_Word /= 2) +
835 Boolean'Pos (Most_Significant_Word = 2);
836 -- Factor that the extracted exponent needs to be divided by to be in
837 -- range 0 .. IEEE_Emax - IEEE_Emin + 2. Special kludge: Exponent_Factor
838 -- is 1 for x86/IA64 double extended as GCC adds unused bits to the
841 Exponent_Mask : constant Float_Word :=
842 Float_Word (IEEE_Emax - IEEE_Emin + 2) *
844 -- Value needed to mask out the exponent field. This assumes that the
845 -- range IEEE_Emin - 1 .. IEEE_Emax + contains 2**N values, for some N
848 function To_Float is new Ada.Unchecked_Conversion (Float_Rep, T);
850 type Float_Access is access all T;
851 function To_Address is
852 new Ada.Unchecked_Conversion (Float_Access, System.Address);
854 XA : constant System.Address := To_Address (Float_Access (X));
857 pragma Import (Ada, R);
858 for R'Address use XA;
859 -- R is a view of the input floating-point parameter. Note that we
860 -- must avoid copying the actual bits of this parameter in float
861 -- form (since it may be a signalling NaN.
863 E : constant IEEE_Exponent_Range :=
864 Integer ((R (Most_Significant_Word) and Exponent_Mask) /
867 -- Mask/Shift T to only get bits from the exponent. Then convert biased
868 -- value to integer value.
871 -- Float_Rep representation of significant of X.all
876 -- All denormalized numbers are valid, so only invalid numbers are
877 -- overflows and NaN's, both with exponent = Emax + 1.
879 return E /= IEEE_Emax + 1;
883 -- All denormalized numbers except 0.0 are invalid
885 -- Set exponent of X to zero, so we end up with the significand, which
886 -- definitely is a valid number and can be converted back to a float.
889 SR (Most_Significant_Word) :=
890 (SR (Most_Significant_Word)
891 and not Exponent_Mask) + Float_Word (IEEE_Bias) * Exponent_Factor;
893 return (E in IEEE_Emin .. IEEE_Emax) or else
894 ((E = IEEE_Emin - 1) and then abs To_Float (SR) = 1.0);
897 ---------------------
898 -- Unaligned_Valid --
899 ---------------------
901 function Unaligned_Valid (A : System.Address) return Boolean is
902 subtype FS is String (1 .. T'Size / Character'Size);
903 type FSP is access FS;
905 function To_FSP is new Ada.Unchecked_Conversion (Address, FSP);
910 -- Note that we have to be sure that we do not load the value into a
911 -- floating-point register, since a signalling NaN may cause a trap.
912 -- The following assignment is what does the actual alignment, since
913 -- we know that the target Local_T is aligned.
915 To_FSP (Local_T'Address).all := To_FSP (A).all;
917 -- Now that we have an aligned value, we can use the normal aligned
918 -- version of Valid to obtain the required result.
920 return Valid (Local_T'Access);