1 ------------------------------------------------------------------------------
3 -- GNAT COMPILER COMPONENTS --
5 -- S Y S T E M . F A T _ G E N --
9 -- Copyright (C) 1992-2006, 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
133 Decompose (Fraction, Arg_Frac, Arg_Exp);
134 return Scaling (Arg_Frac, Exponent);
141 function Copy_Sign (Value, Sign : T) return T is
144 function Is_Negative (V : T) return Boolean;
145 pragma Import (Intrinsic, Is_Negative);
150 if Is_Negative (Sign) then
161 procedure Decompose (XX : T; Frac : out T; Expo : out UI) is
162 X : constant T := T'Machine (XX);
169 -- More useful would be defining Expo to be T'Machine_Emin - 1 or
170 -- T'Machine_Emin - T'Machine_Mantissa, which would preserve
171 -- monotonicity of the exponent function ???
173 -- Check for infinities, transfinites, whatnot
175 elsif X > T'Safe_Last then
177 Expo := T'Machine_Emax + 1;
179 elsif X < T'Safe_First then
181 Expo := T'Machine_Emax + 2; -- how many extra negative values?
184 -- Case of nonzero finite x. Essentially, we just multiply
185 -- by Rad ** (+-2**N) to reduce the range.
191 -- Ax * Rad ** Ex is invariant
195 while Ax >= R_Power (Expbits'Last) loop
196 Ax := Ax * R_Neg_Power (Expbits'Last);
197 Ex := Ex + Log_Power (Expbits'Last);
202 for N in reverse Expbits'First .. Expbits'Last - 1 loop
203 if Ax >= R_Power (N) then
204 Ax := Ax * R_Neg_Power (N);
205 Ex := Ex + Log_Power (N);
219 while Ax < R_Neg_Power (Expbits'Last) loop
220 Ax := Ax * R_Power (Expbits'Last);
221 Ex := Ex - Log_Power (Expbits'Last);
224 -- Rad ** -64 <= Ax < 1
226 for N in reverse Expbits'First .. Expbits'Last - 1 loop
227 if Ax < R_Neg_Power (N) then
228 Ax := Ax * R_Power (N);
229 Ex := Ex - Log_Power (N);
232 -- R_Neg_Power (N) <= Ax < 1
251 function Exponent (X : T) return UI is
255 Decompose (X, X_Frac, X_Exp);
263 function Floor (X : T) return T is
264 XT : constant T := Truncation (X);
279 function Fraction (X : T) return T is
283 Decompose (X, X_Frac, X_Exp);
287 ---------------------
288 -- Gradual_Scaling --
289 ---------------------
291 function Gradual_Scaling (Adjustment : UI) return T is
294 Ex : UI := Adjustment;
297 if Adjustment < T'Machine_Emin - 1 then
298 Y := 2.0 ** T'Machine_Emin;
300 Ex := Ex - T'Machine_Emin;
302 Y := T'Machine (Y / 2.0);
315 return Scaling (1.0, Adjustment);
323 function Leading_Part (X : T; Radix_Digits : UI) return T is
328 if Radix_Digits >= T'Machine_Mantissa then
331 elsif Radix_Digits <= 0 then
332 raise Constraint_Error;
335 L := Exponent (X) - Radix_Digits;
336 Y := Truncation (Scaling (X, -L));
346 -- The trick with Machine is to force the compiler to store the result
347 -- in memory so that we do not have extra precision used. The compiler
348 -- is clever, so we have to outwit its possible optimizations! We do
349 -- this by using an intermediate pragma Volatile location.
351 function Machine (X : T) return T is
353 pragma Volatile (Temp);
359 ----------------------
360 -- Machine_Rounding --
361 ----------------------
363 -- For now, the implementation is identical to that of Rounding, which is
364 -- a permissible behavior, but is not the most efficient possible approach.
366 function Machine_Rounding (X : T) return T is
371 Result := Truncation (abs X);
372 Tail := abs X - Result;
375 Result := Result + 1.0;
384 -- For zero case, make sure sign of zero is preserved
389 end Machine_Rounding;
395 -- We treat Model as identical to Machine. This is true of IEEE and other
396 -- nice floating-point systems, but not necessarily true of all systems.
398 function Model (X : T) return T is
407 -- Subtract from the given number a number equivalent to the value of its
408 -- least significant bit. Given that the most significant bit represents
409 -- a value of 1.0 * radix ** (exp - 1), the value we want is obtained by
410 -- shifting this by (mantissa-1) bits to the right, i.e. decreasing the
411 -- exponent by that amount.
413 -- Zero has to be treated specially, since its exponent is zero
415 function Pred (X : T) return T is
424 Decompose (X, X_Frac, X_Exp);
426 -- A special case, if the number we had was a positive power of
427 -- two, then we want to subtract half of what we would otherwise
428 -- subtract, since the exponent is going to be reduced.
430 -- Note that X_Frac has the same sign as X, so if X_Frac is 0.5,
431 -- then we know that we have a positive number (and hence a
432 -- positive power of 2).
435 return X - Gradual_Scaling (X_Exp - T'Machine_Mantissa - 1);
437 -- Otherwise the exponent is unchanged
440 return X - Gradual_Scaling (X_Exp - T'Machine_Mantissa);
449 function Remainder (X, Y : T) return T is
465 raise Constraint_Error;
481 P_Exp := Exponent (P);
484 Decompose (Arg, Arg_Frac, Arg_Exp);
485 Decompose (P, P_Frac, P_Exp);
487 P := Compose (P_Frac, Arg_Exp);
488 K := Arg_Exp - P_Exp;
492 for Cnt in reverse 0 .. K loop
493 if IEEE_Rem >= P then
495 IEEE_Rem := IEEE_Rem - P;
504 -- That completes the calculation of modulus remainder. The final
505 -- step is get the IEEE remainder. Here we need to compare Rem with
506 -- (abs Y) / 2. We must be careful of unrepresentable Y/2 value
507 -- caused by subnormal numbers
518 if A > B or else (A = B and then not P_Even) then
519 IEEE_Rem := IEEE_Rem - abs Y;
522 return Sign_X * IEEE_Rem;
529 function Rounding (X : T) return T is
534 Result := Truncation (abs X);
535 Tail := abs X - Result;
538 Result := Result + 1.0;
547 -- For zero case, make sure sign of zero is preserved
558 -- Return x * rad ** adjustment quickly,
559 -- or quietly underflow to zero, or overflow naturally.
561 function Scaling (X : T; Adjustment : UI) return T is
563 if X = 0.0 or else Adjustment = 0 then
567 -- Nonzero x. essentially, just multiply repeatedly by Rad ** (+-2**n)
571 Ex : UI := Adjustment;
573 -- Y * Rad ** Ex is invariant
577 while Ex <= -Log_Power (Expbits'Last) loop
578 Y := Y * R_Neg_Power (Expbits'Last);
579 Ex := Ex + Log_Power (Expbits'Last);
584 for N in reverse Expbits'First .. Expbits'Last - 1 loop
585 if Ex <= -Log_Power (N) then
586 Y := Y * R_Neg_Power (N);
587 Ex := Ex + Log_Power (N);
590 -- -Log_Power (N) < Ex <= 0
598 while Ex >= Log_Power (Expbits'Last) loop
599 Y := Y * R_Power (Expbits'Last);
600 Ex := Ex - Log_Power (Expbits'Last);
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);
611 -- 0 <= Ex < Log_Power (N)
626 -- Similar computation to that of Pred: find value of least significant
627 -- bit of given number, and add. Zero has to be treated specially since
628 -- the exponent can be zero, and also we want the smallest denormal if
629 -- denormals are supported.
631 function Succ (X : T) return T is
638 X1 := 2.0 ** T'Machine_Emin;
640 -- Following loop generates smallest denormal
643 X2 := T'Machine (X1 / 2.0);
651 Decompose (X, X_Frac, X_Exp);
653 -- A special case, if the number we had was a negative power of
654 -- two, then we want to add half of what we would otherwise add,
655 -- since the exponent is going to be reduced.
657 -- Note that X_Frac has the same sign as X, so if X_Frac is -0.5,
658 -- then we know that we have a ngeative number (and hence a
659 -- negative power of 2).
661 if X_Frac = -0.5 then
662 return X + Gradual_Scaling (X_Exp - T'Machine_Mantissa - 1);
664 -- Otherwise the exponent is unchanged
667 return X + Gradual_Scaling (X_Exp - T'Machine_Mantissa);
676 -- The basic approach is to compute
678 -- T'Machine (RM1 + N) - RM1
680 -- where N >= 0.0 and RM1 = radix ** (mantissa - 1)
682 -- This works provided that the intermediate result (RM1 + N) does not
683 -- have extra precision (which is why we call Machine). When we compute
684 -- RM1 + N, the exponent of N will be normalized and the mantissa shifted
685 -- shifted appropriately so the lower order bits, which cannot contribute
686 -- to the integer part of N, fall off on the right. When we subtract RM1
687 -- again, the significant bits of N are shifted to the left, and what we
688 -- have is an integer, because only the first e bits are different from
689 -- zero (assuming binary radix here).
691 function Truncation (X : T) return T is
697 if Result >= Radix_To_M_Minus_1 then
701 Result := Machine (Radix_To_M_Minus_1 + Result) - Radix_To_M_Minus_1;
703 if Result > abs X then
704 Result := Result - 1.0;
713 -- For zero case, make sure sign of zero is preserved
721 -----------------------
722 -- Unbiased_Rounding --
723 -----------------------
725 function Unbiased_Rounding (X : T) return T is
726 Abs_X : constant T := abs X;
731 Result := Truncation (Abs_X);
732 Tail := Abs_X - Result;
735 Result := Result + 1.0;
737 elsif Tail = 0.5 then
738 Result := 2.0 * Truncation ((Result / 2.0) + 0.5);
747 -- For zero case, make sure sign of zero is preserved
752 end Unbiased_Rounding;
758 -- Note: this routine does not work for VAX float. We compensate for this
759 -- in Exp_Attr by using the Valid functions in Vax_Float_Operations rather
760 -- than the corresponding instantiation of this function.
762 function Valid (X : not null access T) return Boolean is
764 IEEE_Emin : constant Integer := T'Machine_Emin - 1;
765 IEEE_Emax : constant Integer := T'Machine_Emax - 1;
767 IEEE_Bias : constant Integer := -(IEEE_Emin - 1);
769 subtype IEEE_Exponent_Range is
770 Integer range IEEE_Emin - 1 .. IEEE_Emax + 1;
772 -- The implementation of this floating point attribute uses a
773 -- representation type Float_Rep that allows direct access to the
774 -- exponent and mantissa parts of a floating point number.
776 -- The Float_Rep type is an array of Float_Word elements. This
777 -- representation is chosen to make it possible to size the type based
778 -- on a generic parameter. Since the array size is known at compile
779 -- time, efficient code can still be generated. The size of Float_Word
780 -- elements should be large enough to allow accessing the exponent in
781 -- one read, but small enough so that all floating point object sizes
782 -- are a multiple of the Float_Word'Size.
784 -- The following conditions must be met for all possible
785 -- instantiations of the attributes package:
787 -- - T'Size is an integral multiple of Float_Word'Size
789 -- - The exponent and sign are completely contained in a single
790 -- component of Float_Rep, named Most_Significant_Word (MSW).
792 -- - The sign occupies the most significant bit of the MSW and the
793 -- exponent is in the following bits. Unused bits (if any) are in
794 -- the least significant part.
796 type Float_Word is mod 2**Positive'Min (System.Word_Size, 32);
797 type Rep_Index is range 0 .. 7;
799 Rep_Words : constant Positive :=
800 (T'Size + Float_Word'Size - 1) / Float_Word'Size;
801 Rep_Last : constant Rep_Index := Rep_Index'Min
802 (Rep_Index (Rep_Words - 1), (T'Mantissa + 16) / Float_Word'Size);
803 -- Determine the number of Float_Words needed for representing the
804 -- entire floating-point value. Do not take into account excessive
805 -- padding, as occurs on IA-64 where 80 bits floats get padded to 128
806 -- bits. In general, the exponent field cannot be larger than 15 bits,
807 -- even for 128-bit floating-poin t types, so the final format size
808 -- won't be larger than T'Mantissa + 16.
811 array (Rep_Index range 0 .. Rep_Index (Rep_Words - 1)) of Float_Word;
813 pragma Suppress_Initialization (Float_Rep);
814 -- This pragma supresses the generation of an initialization procedure
815 -- for type Float_Rep when operating in Initialize/Normalize_Scalars
816 -- mode. This is not just a matter of efficiency, but of functionality,
817 -- since Valid has a pragma Inline_Always, which is not permitted if
818 -- there are nested subprograms present.
820 Most_Significant_Word : constant Rep_Index :=
821 Rep_Last * Standard'Default_Bit_Order;
822 -- Finding the location of the Exponent_Word is a bit tricky. In general
823 -- we assume Word_Order = Bit_Order. This expression needs to be refined
826 Exponent_Factor : constant Float_Word :=
827 2**(Float_Word'Size - 1) /
828 Float_Word (IEEE_Emax - IEEE_Emin + 3) *
829 Boolean'Pos (Most_Significant_Word /= 2) +
830 Boolean'Pos (Most_Significant_Word = 2);
831 -- Factor that the extracted exponent needs to be divided by to be in
832 -- range 0 .. IEEE_Emax - IEEE_Emin + 2. Special kludge: Exponent_Factor
833 -- is 1 for x86/IA64 double extended as GCC adds unused bits to the
836 Exponent_Mask : constant Float_Word :=
837 Float_Word (IEEE_Emax - IEEE_Emin + 2) *
839 -- Value needed to mask out the exponent field. This assumes that the
840 -- range IEEE_Emin - 1 .. IEEE_Emax + contains 2**N values, for some N
843 function To_Float is new Ada.Unchecked_Conversion (Float_Rep, T);
845 type Float_Access is access all T;
846 function To_Address is
847 new Ada.Unchecked_Conversion (Float_Access, System.Address);
849 XA : constant System.Address := To_Address (Float_Access (X));
852 pragma Import (Ada, R);
853 for R'Address use XA;
854 -- R is a view of the input floating-point parameter. Note that we
855 -- must avoid copying the actual bits of this parameter in float
856 -- form (since it may be a signalling NaN.
858 E : constant IEEE_Exponent_Range :=
859 Integer ((R (Most_Significant_Word) and Exponent_Mask) /
862 -- Mask/Shift T to only get bits from the exponent. Then convert biased
863 -- value to integer value.
866 -- Float_Rep representation of significant of X.all
871 -- All denormalized numbers are valid, so only invalid numbers are
872 -- overflows and NaN's, both with exponent = Emax + 1.
874 return E /= IEEE_Emax + 1;
878 -- All denormalized numbers except 0.0 are invalid
880 -- Set exponent of X to zero, so we end up with the significand, which
881 -- definitely is a valid number and can be converted back to a float.
884 SR (Most_Significant_Word) :=
885 (SR (Most_Significant_Word)
886 and not Exponent_Mask) + Float_Word (IEEE_Bias) * Exponent_Factor;
888 return (E in IEEE_Emin .. IEEE_Emax) or else
889 ((E = IEEE_Emin - 1) and then abs To_Float (SR) = 1.0);
892 ---------------------
893 -- Unaligned_Valid --
894 ---------------------
896 function Unaligned_Valid (A : System.Address) return Boolean is
897 subtype FS is String (1 .. T'Size / Character'Size);
898 type FSP is access FS;
900 function To_FSP is new Ada.Unchecked_Conversion (Address, FSP);
905 -- Note that we have to be sure that we do not load the value into a
906 -- floating-point register, since a signalling NaN may cause a trap.
907 -- The following assignment is what does the actual alignment, since
908 -- we know that the target Local_T is aligned.
910 To_FSP (Local_T'Address).all := To_FSP (A).all;
912 -- Now that we have an aligned value, we can use the normal aligned
913 -- version of Valid to obtain the required result.
915 return Valid (Local_T'Access);