------------------------------------------------------------------------------ -- -- -- GNAT COMPILER COMPONENTS -- -- -- -- S Y S T E M . V A L _ R E A L -- -- -- -- B o d y -- -- -- -- Copyright (C) 1992-2024, Free Software Foundation, Inc. -- -- -- -- GNAT is free software; you can redistribute it and/or modify it under -- -- terms of the GNU General Public License as published by the Free Soft- -- -- ware Foundation; either version 3, or (at your option) any later ver- -- -- sion. GNAT is distributed in the hope that it will be useful, but WITH- -- -- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY -- -- or FITNESS FOR A PARTICULAR PURPOSE. -- -- -- -- As a special exception under Section 7 of GPL version 3, you are granted -- -- additional permissions described in the GCC Runtime Library Exception, -- -- version 3.1, as published by the Free Software Foundation. -- -- -- -- You should have received a copy of the GNU General Public License and -- -- a copy of the GCC Runtime Library Exception along with this program; -- -- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see -- -- . -- -- -- -- GNAT was originally developed by the GNAT team at New York University. -- -- Extensive contributions were provided by Ada Core Technologies Inc. -- -- -- ------------------------------------------------------------------------------ with System.Double_Real; with System.Float_Control; with System.Unsigned_Types; use System.Unsigned_Types; with System.Val_Util; use System.Val_Util; with System.Value_R; pragma Warnings (Off, "non-static constant in preelaborated unit"); -- Every constant is static given our instantiation model package body System.Val_Real is pragma Assert (Num'Machine_Mantissa <= Uns'Size); -- We need an unsigned type large enough to represent the mantissa Is_Large_Type : constant Boolean := Num'Machine_Mantissa >= 53; -- True if the floating-point type is at least IEEE Double Precision_Limit : constant Uns := 2**Num'Machine_Mantissa - 1; -- See below for the rationale package Impl is new Value_R (Uns, 2, Precision_Limit, Round => False); subtype Base_T is Unsigned range 2 .. 16; -- The following tables compute the maximum exponent of the base that can -- fit in the given floating-point format, that is to say the element at -- index N is the largest K such that N**K <= Num'Last. Maxexp32 : constant array (Base_T) of Positive := [2 => 127, 3 => 80, 4 => 63, 5 => 55, 6 => 49, 7 => 45, 8 => 42, 9 => 40, 10 => 55, 11 => 37, 12 => 35, 13 => 34, 14 => 33, 15 => 32, 16 => 31]; -- The actual value for 10 is 38 but we also use scaling for 10 Maxexp64 : constant array (Base_T) of Positive := [2 => 1023, 3 => 646, 4 => 511, 5 => 441, 6 => 396, 7 => 364, 8 => 341, 9 => 323, 10 => 441, 11 => 296, 12 => 285, 13 => 276, 14 => 268, 15 => 262, 16 => 255]; -- The actual value for 10 is 308 but we also use scaling for 10 Maxexp80 : constant array (Base_T) of Positive := [2 => 16383, 3 => 10337, 4 => 8191, 5 => 7056, 6 => 6338, 7 => 5836, 8 => 5461, 9 => 5168, 10 => 7056, 11 => 4736, 12 => 4570, 13 => 4427, 14 => 4303, 15 => 4193, 16 => 4095]; -- The actual value for 10 is 4932 but we also use scaling for 10 package Double_Real is new System.Double_Real (Num); use type Double_Real.Double_T; subtype Double_T is Double_Real.Double_T; -- The double floating-point type function Exact_Log2 (N : Unsigned) return Positive is (case N is when 2 => 1, when 4 => 2, when 8 => 3, when 16 => 4, when others => raise Program_Error); -- Return the exponent of a power of 2 function Integer_to_Real (Str : String; Val : Impl.Value_Array; Base : Unsigned; Scale : Impl.Scale_Array; Minus : Boolean) return Num; -- Convert the real value from integer to real representation function Large_Powfive (Exp : Natural) return Double_T; -- Return 5.0**Exp as a double number, where Exp > Maxpow function Large_Powfive (Exp : Natural; S : out Natural) return Double_T; -- Return Num'Scaling (5.0**Exp, -S) as a double number where Exp > Maxexp --------------------- -- Integer_to_Real -- --------------------- function Integer_to_Real (Str : String; Val : Impl.Value_Array; Base : Unsigned; Scale : Impl.Scale_Array; Minus : Boolean) return Num is pragma Assert (Base in 2 .. 16); pragma Assert (Num'Machine_Radix = 2); pragma Unsuppress (Range_Check); Maxexp : constant Positive := (if Num'Size = 32 then Maxexp32 (Base) elsif Num'Size = 64 then Maxexp64 (Base) elsif Num'Machine_Mantissa = 64 then Maxexp80 (Base) else raise Program_Error); -- Maximum exponent of the base that can fit in Num D_Val : Double_T; R_Val : Num; S : Integer; begin -- We call the floating-point processor reset routine so we can be sure -- that the x87 FPU is properly set for conversions. This is especially -- needed on Windows, where calls to the operating system randomly reset -- the processor into 64-bit mode. if Num'Machine_Mantissa = 64 then System.Float_Control.Reset; end if; -- First convert the integer mantissa into a double real. The conversion -- of each part is exact, given the precision limit we used above. Then, -- if the contribution of the low part might be nonnull, scale the high -- part appropriately and add the low part to the result. if Val (2) = 0 then D_Val := Double_Real.To_Double (Num (Val (1))); S := Scale (1); else declare V1 : constant Num := Num (Val (1)); V2 : constant Num := Num (Val (2)); DS : Positive; begin DS := Scale (1) - Scale (2); case Base is -- If the base is a power of two, we use the efficient Scaling -- attribute up to an amount worth a double mantissa. when 2 | 4 | 8 | 16 => declare L : constant Positive := Exact_Log2 (Base); begin if DS <= 2 * Num'Machine_Mantissa / L then DS := DS * L; D_Val := Double_Real.Quick_Two_Sum (Num'Scaling (V1, DS), V2); S := Scale (2); else D_Val := Double_Real.To_Double (V1); S := Scale (1); end if; end; -- If the base is 10, we also scale up to an amount worth a -- double mantissa. when 10 => declare Powfive : constant array (0 .. Maxpow) of Double_T; pragma Import (Ada, Powfive); for Powfive'Address use Powfive_Address; begin if DS <= Maxpow then D_Val := Powfive (DS) * Num'Scaling (V1, DS) + V2; S := Scale (2); else D_Val := Double_Real.To_Double (V1); S := Scale (1); end if; end; -- Inaccurate implementation for other bases when others => D_Val := Double_Real.To_Double (V1); S := Scale (1); end case; end; end if; -- Compute the final value by applying the scaling, if any if (Val (1) = 0 and then Val (2) = 0) or else S = 0 then R_Val := Double_Real.To_Single (D_Val); else case Base is -- If the base is a power of two, we use the efficient Scaling -- attribute with an overflow check, if it is not 2, to catch -- ludicrous exponents that would result in an infinity or zero. when 2 | 4 | 8 | 16 => declare L : constant Positive := Exact_Log2 (Base); begin if Integer'First / L <= S and then S <= Integer'Last / L then S := S * L; end if; R_Val := Num'Scaling (Double_Real.To_Single (D_Val), S); end; -- If the base is 10, we use a double implementation for the sake -- of accuracy combining powers of 5 and scaling attribute. Using -- this combination is better than using powers of 10 only because -- the Large_Powfive function may overflow only if the final value -- will also either overflow or underflow, thus making it possible -- to use a single division for the case of negative powers of 10. when 10 => declare Powfive : constant array (0 .. Maxpow) of Double_T; pragma Import (Ada, Powfive); for Powfive'Address use Powfive_Address; RS : Natural; begin if S > 0 then if S <= Maxpow then D_Val := D_Val * Powfive (S); else D_Val := D_Val * Large_Powfive (S); end if; else if S >= -Maxpow then D_Val := D_Val / Powfive (-S); -- For small types, typically IEEE Single, the trick -- described above does not fully work. elsif not Is_Large_Type and then S < -Maxexp then D_Val := D_Val / Large_Powfive (-S, RS); S := S - RS; else D_Val := D_Val / Large_Powfive (-S); end if; end if; R_Val := Num'Scaling (Double_Real.To_Single (D_Val), S); end; -- Implementation for other bases with exponentiation -- When the exponent is positive, we can do the computation -- directly because, if the exponentiation overflows, then -- the final value overflows as well. But when the exponent -- is negative, we may need to do it in two steps to avoid -- an artificial underflow. when others => declare B : constant Num := Num (Base); begin R_Val := Double_Real.To_Single (D_Val); if S > 0 then R_Val := R_Val * B ** S; else if S < -Maxexp then R_Val := R_Val / B ** Maxexp; S := S + Maxexp; end if; R_Val := R_Val / B ** (-S); end if; end; end case; end if; -- Finally deal with initial minus sign, note that this processing is -- done even if Uval is zero, so that -0.0 is correctly interpreted. return (if Minus then -R_Val else R_Val); exception when Constraint_Error => Bad_Value (Str); end Integer_to_Real; ------------------- -- Large_Powfive -- ------------------- function Large_Powfive (Exp : Natural) return Double_T is Powfive : constant array (0 .. Maxpow) of Double_T; pragma Import (Ada, Powfive); for Powfive'Address use Powfive_Address; Powfive_100 : constant Double_T; pragma Import (Ada, Powfive_100); for Powfive_100'Address use Powfive_100_Address; Powfive_200 : constant Double_T; pragma Import (Ada, Powfive_200); for Powfive_200'Address use Powfive_200_Address; Powfive_300 : constant Double_T; pragma Import (Ada, Powfive_300); for Powfive_300'Address use Powfive_300_Address; R : Double_T; E : Natural; begin pragma Assert (Exp > Maxpow); if Is_Large_Type and then Exp >= 300 then R := Powfive_300; E := Exp - 300; elsif Is_Large_Type and then Exp >= 200 then R := Powfive_200; E := Exp - 200; elsif Is_Large_Type and then Exp >= 100 then R := Powfive_100; E := Exp - 100; else R := Powfive (Maxpow); E := Exp - Maxpow; end if; while E > Maxpow loop R := R * Powfive (Maxpow); E := E - Maxpow; end loop; R := R * Powfive (E); return R; end Large_Powfive; function Large_Powfive (Exp : Natural; S : out Natural) return Double_T is Maxexp : constant Positive := (if Num'Size = 32 then Maxexp32 (5) elsif Num'Size = 64 then Maxexp64 (5) elsif Num'Machine_Mantissa = 64 then Maxexp80 (5) else raise Program_Error); -- Maximum exponent of 5 that can fit in Num Powfive : constant array (0 .. Maxpow) of Double_T; pragma Import (Ada, Powfive); for Powfive'Address use Powfive_Address; R : Double_T; E : Natural; begin pragma Assert (Exp > Maxexp); pragma Warnings (Off, "-gnatw.a"); pragma Assert (not Is_Large_Type); pragma Warnings (On, "-gnatw.a"); R := Powfive (Maxpow); E := Exp - Maxpow; -- If the exponent is not too large, then scale down the result so that -- its final value does not overflow but, if it's too large, then do not -- bother doing it since overflow is just fine. The scaling factor is -3 -- for every power of 5 above the maximum, in other words division by 8. if Exp - Maxexp <= Maxpow then S := 3 * (Exp - Maxexp); R.Hi := Num'Scaling (R.Hi, -S); R.Lo := Num'Scaling (R.Lo, -S); else S := 0; end if; while E > Maxpow loop R := R * Powfive (Maxpow); E := E - Maxpow; end loop; R := R * Powfive (E); return R; end Large_Powfive; --------------- -- Scan_Real -- --------------- function Scan_Real (Str : String; Ptr : not null access Integer; Max : Integer) return Num is Base : Unsigned; Scale : Impl.Scale_Array; Extra : Unsigned; Minus : Boolean; Val : Impl.Value_Array; begin Val := Impl.Scan_Raw_Real (Str, Ptr, Max, Base, Scale, Extra, Minus); return Integer_to_Real (Str, Val, Base, Scale, Minus); end Scan_Real; ---------------- -- Value_Real -- ---------------- function Value_Real (Str : String) return Num is Base : Unsigned; Scale : Impl.Scale_Array; Extra : Unsigned; Minus : Boolean; Val : Impl.Value_Array; begin Val := Impl.Value_Raw_Real (Str, Base, Scale, Extra, Minus); return Integer_to_Real (Str, Val, Base, Scale, Minus); end Value_Real; end System.Val_Real;