1 ------------------------------------------------------------------------------
3 -- GNAT COMPILER COMPONENTS --
5 -- S Y S T E M . F A T _ G E N --
9 -- Copyright (C) 1992-2003 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, 59 Temple Place - Suite 330, Boston, --
20 -- MA 02111-1307, 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
86 function Gradual_Scaling (Adjustment : UI) return T;
87 -- Like Scaling with a first argument of 1.0, but returns the smallest
88 -- denormal rather than zero when the adjustment is smaller than
89 -- Machine_Emin. Used for Succ and Pred.
95 function Adjacent (X, Towards : T) return T is
100 elsif Towards > X then
112 function Ceiling (X : T) return T is
113 XT : constant T := Truncation (X);
131 function Compose (Fraction : T; Exponent : UI) return T is
136 Decompose (Fraction, Arg_Frac, Arg_Exp);
137 return Scaling (Arg_Frac, Exponent);
144 function Copy_Sign (Value, Sign : T) return T is
147 function Is_Negative (V : T) return Boolean;
148 pragma Import (Intrinsic, Is_Negative);
153 if Is_Negative (Sign) then
164 procedure Decompose (XX : T; Frac : out T; Expo : out UI) is
165 X : constant T := T'Machine (XX);
172 -- More useful would be defining Expo to be T'Machine_Emin - 1 or
173 -- T'Machine_Emin - T'Machine_Mantissa, which would preserve
174 -- monotonicity of the exponent function ???
176 -- Check for infinities, transfinites, whatnot.
178 elsif X > T'Safe_Last then
180 Expo := T'Machine_Emax + 1;
182 elsif X < T'Safe_First then
184 Expo := T'Machine_Emax + 2; -- how many extra negative values?
187 -- Case of nonzero finite x. Essentially, we just multiply
188 -- by Rad ** (+-2**N) to reduce the range.
194 -- Ax * Rad ** Ex is invariant.
198 while Ax >= R_Power (Expbits'Last) loop
199 Ax := Ax * R_Neg_Power (Expbits'Last);
200 Ex := Ex + Log_Power (Expbits'Last);
205 for N in reverse Expbits'First .. Expbits'Last - 1 loop
206 if Ax >= R_Power (N) then
207 Ax := Ax * R_Neg_Power (N);
208 Ex := Ex + Log_Power (N);
222 while Ax < R_Neg_Power (Expbits'Last) loop
223 Ax := Ax * R_Power (Expbits'Last);
224 Ex := Ex - Log_Power (Expbits'Last);
227 -- Rad ** -64 <= Ax < 1
229 for N in reverse Expbits'First .. Expbits'Last - 1 loop
230 if Ax < R_Neg_Power (N) then
231 Ax := Ax * R_Power (N);
232 Ex := Ex - Log_Power (N);
235 -- R_Neg_Power (N) <= Ax < 1
254 function Exponent (X : T) return UI is
259 Decompose (X, X_Frac, X_Exp);
267 function Floor (X : T) return T is
268 XT : constant T := Truncation (X);
286 function Fraction (X : T) return T is
291 Decompose (X, X_Frac, X_Exp);
295 ---------------------
296 -- Gradual_Scaling --
297 ---------------------
299 function Gradual_Scaling (Adjustment : UI) return T is
302 Ex : UI := Adjustment;
305 if Adjustment < T'Machine_Emin then
306 Y := 2.0 ** T'Machine_Emin;
308 Ex := Ex - T'Machine_Emin;
311 Y := T'Machine (Y / 2.0);
324 return Scaling (1.0, Adjustment);
332 function Leading_Part (X : T; Radix_Digits : UI) return T is
337 if Radix_Digits >= T'Machine_Mantissa then
341 L := Exponent (X) - Radix_Digits;
342 Y := Truncation (Scaling (X, -L));
353 -- The trick with Machine is to force the compiler to store the result
354 -- in memory so that we do not have extra precision used. The compiler
355 -- is clever, so we have to outwit its possible optimizations! We do
356 -- this by using an intermediate pragma Volatile location.
358 function Machine (X : T) return T is
360 pragma Volatile (Temp);
371 -- We treat Model as identical to Machine. This is true of IEEE and other
372 -- nice floating-point systems, but not necessarily true of all systems.
374 function Model (X : T) return T is
383 -- Subtract from the given number a number equivalent to the value of its
384 -- least significant bit. Given that the most significant bit represents
385 -- a value of 1.0 * radix ** (exp - 1), the value we want is obtained by
386 -- shifting this by (mantissa-1) bits to the right, i.e. decreasing the
387 -- exponent by that amount.
389 -- Zero has to be treated specially, since its exponent is zero
391 function Pred (X : T) return T is
400 Decompose (X, X_Frac, X_Exp);
402 -- A special case, if the number we had was a positive power of
403 -- two, then we want to subtract half of what we would otherwise
404 -- subtract, since the exponent is going to be reduced.
406 if X_Frac = 0.5 and then X > 0.0 then
407 return X - Gradual_Scaling (X_Exp - T'Machine_Mantissa - 1);
409 -- Otherwise the exponent stays the same
412 return X - Gradual_Scaling (X_Exp - T'Machine_Mantissa);
421 function Remainder (X, Y : T) return T is
449 P_Exp := Exponent (P);
452 Decompose (Arg, Arg_Frac, Arg_Exp);
453 Decompose (P, P_Frac, P_Exp);
455 P := Compose (P_Frac, Arg_Exp);
456 K := Arg_Exp - P_Exp;
460 for Cnt in reverse 0 .. K loop
461 if IEEE_Rem >= P then
463 IEEE_Rem := IEEE_Rem - P;
472 -- That completes the calculation of modulus remainder. The final
473 -- step is get the IEEE remainder. Here we need to compare Rem with
474 -- (abs Y) / 2. We must be careful of unrepresentable Y/2 value
475 -- caused by subnormal numbers
486 if A > B or else (A = B and then not P_Even) then
487 IEEE_Rem := IEEE_Rem - abs Y;
490 return Sign_X * IEEE_Rem;
498 function Rounding (X : T) return T is
503 Result := Truncation (abs X);
504 Tail := abs X - Result;
507 Result := Result + 1.0;
516 -- For zero case, make sure sign of zero is preserved
528 -- Return x * rad ** adjustment quickly,
529 -- or quietly underflow to zero, or overflow naturally.
531 function Scaling (X : T; Adjustment : UI) return T is
533 if X = 0.0 or else Adjustment = 0 then
537 -- Nonzero x. essentially, just multiply repeatedly by Rad ** (+-2**n).
541 Ex : UI := Adjustment;
543 -- Y * Rad ** Ex is invariant
547 while Ex <= -Log_Power (Expbits'Last) loop
548 Y := Y * R_Neg_Power (Expbits'Last);
549 Ex := Ex + Log_Power (Expbits'Last);
554 for N in reverse Expbits'First .. Expbits'Last - 1 loop
555 if Ex <= -Log_Power (N) then
556 Y := Y * R_Neg_Power (N);
557 Ex := Ex + Log_Power (N);
560 -- -Log_Power (N) < Ex <= 0
568 while Ex >= Log_Power (Expbits'Last) loop
569 Y := Y * R_Power (Expbits'Last);
570 Ex := Ex - Log_Power (Expbits'Last);
575 for N in reverse Expbits'First .. Expbits'Last - 1 loop
576 if Ex >= Log_Power (N) then
577 Y := Y * R_Power (N);
578 Ex := Ex - Log_Power (N);
581 -- 0 <= Ex < Log_Power (N)
594 -- Similar computation to that of Pred: find value of least significant
595 -- bit of given number, and add. Zero has to be treated specially since
596 -- the exponent can be zero, and also we want the smallest denormal if
597 -- denormals are supported.
599 function Succ (X : T) return T is
606 X1 := 2.0 ** T'Machine_Emin;
608 -- Following loop generates smallest denormal
611 X2 := T'Machine (X1 / 2.0);
619 Decompose (X, X_Frac, X_Exp);
621 -- A special case, if the number we had was a negative power of
622 -- two, then we want to add half of what we would otherwise add,
623 -- since the exponent is going to be reduced.
625 if X_Frac = 0.5 and then X < 0.0 then
626 return X + Gradual_Scaling (X_Exp - T'Machine_Mantissa - 1);
628 -- Otherwise the exponent stays the same
631 return X + Gradual_Scaling (X_Exp - T'Machine_Mantissa);
640 -- The basic approach is to compute
642 -- T'Machine (RM1 + N) - RM1.
644 -- where N >= 0.0 and RM1 = radix ** (mantissa - 1)
646 -- This works provided that the intermediate result (RM1 + N) does not
647 -- have extra precision (which is why we call Machine). When we compute
648 -- RM1 + N, the exponent of N will be normalized and the mantissa shifted
649 -- shifted appropriately so the lower order bits, which cannot contribute
650 -- to the integer part of N, fall off on the right. When we subtract RM1
651 -- again, the significant bits of N are shifted to the left, and what we
652 -- have is an integer, because only the first e bits are different from
653 -- zero (assuming binary radix here).
655 function Truncation (X : T) return T is
661 if Result >= Radix_To_M_Minus_1 then
665 Result := Machine (Radix_To_M_Minus_1 + Result) - Radix_To_M_Minus_1;
667 if Result > abs X then
668 Result := Result - 1.0;
677 -- For zero case, make sure sign of zero is preserved
686 -----------------------
687 -- Unbiased_Rounding --
688 -----------------------
690 function Unbiased_Rounding (X : T) return T is
691 Abs_X : constant T := abs X;
696 Result := Truncation (Abs_X);
697 Tail := Abs_X - Result;
700 Result := Result + 1.0;
702 elsif Tail = 0.5 then
703 Result := 2.0 * Truncation ((Result / 2.0) + 0.5);
712 -- For zero case, make sure sign of zero is preserved
718 end Unbiased_Rounding;
724 function Valid (X : access T) return Boolean is
726 IEEE_Emin : constant Integer := T'Machine_Emin - 1;
727 IEEE_Emax : constant Integer := T'Machine_Emax - 1;
729 IEEE_Bias : constant Integer := -(IEEE_Emin - 1);
731 subtype IEEE_Exponent_Range is
732 Integer range IEEE_Emin - 1 .. IEEE_Emax + 1;
734 -- The implementation of this floating point attribute uses
735 -- a representation type Float_Rep that allows direct access to
736 -- the exponent and mantissa parts of a floating point number.
738 -- The Float_Rep type is an array of Float_Word elements. This
739 -- representation is chosen to make it possible to size the
740 -- type based on a generic parameter. Since the array size is
741 -- known at compile-time, efficient code can still be generated.
742 -- The size of Float_Word elements should be large enough to allow
743 -- accessing the exponent in one read, but small enough so that all
744 -- floating point object sizes are a multiple of the Float_Word'Size.
746 -- The following conditions must be met for all possible
747 -- instantiations of the attributes package:
749 -- - T'Size is an integral multiple of Float_Word'Size
751 -- - The exponent and sign are completely contained in a single
752 -- component of Float_Rep, named Most_Significant_Word (MSW).
754 -- - The sign occupies the most significant bit of the MSW
755 -- and the exponent is in the following bits.
756 -- Unused bits (if any) are in the least significant part.
758 type Float_Word is mod 2**Positive'Min (System.Word_Size, 32);
759 type Rep_Index is range 0 .. 7;
761 Rep_Last : constant Rep_Index := (T'Size - 1) / Float_Word'Size;
763 type Float_Rep is array (Rep_Index range 0 .. Rep_Last) of Float_Word;
765 pragma Suppress_Initialization (Float_Rep);
766 -- This pragma supresses the generation of an initialization procedure
767 -- for type Float_Rep when operating in Initialize/Normalize_Scalars
768 -- mode. This is not just a matter of efficiency, but of functionality,
769 -- since Valid has a pragma Inline_Always, which is not permitted if
770 -- there are nested subprograms present.
772 Most_Significant_Word : constant Rep_Index :=
773 Rep_Last * Standard'Default_Bit_Order;
774 -- Finding the location of the Exponent_Word is a bit tricky.
775 -- In general we assume Word_Order = Bit_Order.
776 -- This expression needs to be refined for VMS.
778 Exponent_Factor : constant Float_Word :=
779 2**(Float_Word'Size - 1) /
780 Float_Word (IEEE_Emax - IEEE_Emin + 3) *
781 Boolean'Pos (T'Size /= 96) +
782 Boolean'Pos (T'Size = 96);
783 -- Factor that the extracted exponent needs to be divided by
784 -- to be in range 0 .. IEEE_Emax - IEEE_Emin + 2.
785 -- Special kludge: Exponent_Factor is 0 for x86 double extended
786 -- as GCC adds 16 unused bits to the type.
788 Exponent_Mask : constant Float_Word :=
789 Float_Word (IEEE_Emax - IEEE_Emin + 2) *
791 -- Value needed to mask out the exponent field.
792 -- This assumes that the range IEEE_Emin - 1 .. IEEE_Emax + 1
793 -- contains 2**N values, for some N in Natural.
795 function To_Float is new Ada.Unchecked_Conversion (Float_Rep, T);
797 type Float_Access is access all T;
798 function To_Address is
799 new Ada.Unchecked_Conversion (Float_Access, System.Address);
801 XA : constant System.Address := To_Address (Float_Access (X));
804 pragma Import (Ada, R);
805 for R'Address use XA;
806 -- R is a view of the input floating-point parameter. Note that we
807 -- must avoid copying the actual bits of this parameter in float
808 -- form (since it may be a signalling NaN.
810 E : constant IEEE_Exponent_Range :=
811 Integer ((R (Most_Significant_Word) and Exponent_Mask) /
814 -- Mask/Shift T to only get bits from the exponent
815 -- Then convert biased value to integer value.
818 -- Float_Rep representation of significant of X.all
823 -- All denormalized numbers are valid, so only invalid numbers
824 -- are overflows and NaN's, both with exponent = Emax + 1.
826 return E /= IEEE_Emax + 1;
830 -- All denormalized numbers except 0.0 are invalid
832 -- Set exponent of X to zero, so we end up with the significand, which
833 -- definitely is a valid number and can be converted back to a float.
836 SR (Most_Significant_Word) :=
837 (SR (Most_Significant_Word)
838 and not Exponent_Mask) + Float_Word (IEEE_Bias) * Exponent_Factor;
840 return (E in IEEE_Emin .. IEEE_Emax) or else
841 ((E = IEEE_Emin - 1) and then abs To_Float (SR) = 1.0);
844 ---------------------
845 -- Unaligned_Valid --
846 ---------------------
848 function Unaligned_Valid (A : System.Address) return Boolean is
849 subtype FS is String (1 .. T'Size / Character'Size);
850 type FSP is access FS;
852 function To_FSP is new Ada.Unchecked_Conversion (Address, FSP);
857 To_FSP (Local_T'Address).all := To_FSP (A).all;
858 return Valid (Local_T'Access);