| ------------------------------------------------------------------------------ |
| -- -- |
| -- GNAT COMPILER COMPONENTS -- |
| -- -- |
| -- S Y S T E M . V A L _ R E A L -- |
| -- -- |
| -- B o d y -- |
| -- -- |
| -- Copyright (C) 1992-2021, 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 -- |
| -- <http://www.gnu.org/licenses/>. -- |
| -- -- |
| -- 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 |
| |
| Need_Extra : constant Boolean := Num'Machine_Mantissa > Uns'Size - 4; |
| -- If the mantissa of the floating-point type is almost as large as the |
| -- unsigned type, we do not have enough space for an extra digit in the |
| -- unsigned type so we handle the extra digit separately, at the cost of |
| -- a bit more work in Integer_to_Real. |
| |
| Precision_Limit : constant Uns := |
| (if Need_Extra then 2**Num'Machine_Mantissa - 1 else 2**Uns'Size - 1); |
| -- If we handle the extra digit separately, we use the precision of the |
| -- floating-point type so that the conversion is exact. |
| |
| package Impl is new Value_R (Uns, Precision_Limit, Round => Need_Extra); |
| |
| 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 => 38, 11 => 37, |
| 12 => 35, 13 => 34, 14 => 33, 15 => 32, 16 => 31); |
| |
| Maxexp64 : constant array (Base_T) of Positive := |
| (2 => 1023, 3 => 646, 4 => 511, 5 => 441, 6 => 396, |
| 7 => 364, 8 => 341, 9 => 323, 10 => 308, 11 => 296, |
| 12 => 285, 13 => 276, 14 => 268, 15 => 262, 16 => 255); |
| |
| Maxexp80 : constant array (Base_T) of Positive := |
| (2 => 16383, 3 => 10337, 4 => 8191, 5 => 7056, 6 => 6338, |
| 7 => 5836, 8 => 5461, 9 => 5168, 10 => 4932, 11 => 4736, |
| 12 => 4570, 13 => 4427, 14 => 4303, 15 => 4193, 16 => 4095); |
| |
| 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 Integer_to_Real |
| (Str : String; |
| Val : Uns; |
| Base : Unsigned; |
| Scale : Integer; |
| Extra : Unsigned; |
| Minus : Boolean) return Num; |
| -- Convert the real value from integer to real representation |
| |
| function Large_Powten (Exp : Natural) return Double_T; |
| -- Return 10.0**Exp as a double number, where Exp > Maxpow |
| |
| --------------------- |
| -- Integer_to_Real -- |
| --------------------- |
| |
| function Integer_to_Real |
| (Str : String; |
| Val : Uns; |
| Base : Unsigned; |
| Scale : Integer; |
| Extra : Unsigned; |
| 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 |
| |
| R_Val : Num; |
| D_Val : Double_T; |
| S : Integer := Scale; |
| |
| 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; |
| |
| -- Take into account the extra digit, i.e. do the two computations |
| |
| -- (1) R_Val := R_Val * Num (B) + Num (Extra) |
| -- (2) S := S - 1 |
| |
| -- In the first, the three operands are exact, so using an FMA would |
| -- be ideal, but we are most likely running on the x87 FPU, hence we |
| -- may not have one. That is why we turn the multiplication into an |
| -- iterated addition with exact error handling, so that we can do a |
| -- single rounding at the end. |
| |
| if Need_Extra and then Extra > 0 then |
| declare |
| B : Unsigned := Base; |
| Acc : Num := 0.0; |
| Err : Num := 0.0; |
| Fac : Num := Num (Val); |
| DS : Double_T; |
| |
| begin |
| loop |
| -- If B is odd, add one factor. Note that the accumulator is |
| -- never larger than the factor at this point (it is in fact |
| -- never larger than the factor minus the initial value). |
| |
| if B rem 2 /= 0 then |
| if Acc = 0.0 then |
| Acc := Fac; |
| else |
| DS := Double_Real.Quick_Two_Sum (Fac, Acc); |
| Acc := DS.Hi; |
| Err := Err + DS.Lo; |
| end if; |
| exit when B = 1; |
| end if; |
| |
| -- Now B is (morally) even, halve it and double the factor, |
| -- which is always an exact operation. |
| |
| B := B / 2; |
| Fac := Fac * 2.0; |
| end loop; |
| |
| -- Add Extra to the error, which are both small integers |
| |
| D_Val := Double_Real.Quick_Two_Sum (Acc, Err + Num (Extra)); |
| |
| S := S - 1; |
| end; |
| |
| -- Or else, if the Extra digit is zero, do the exact conversion |
| |
| elsif Need_Extra then |
| D_Val := Double_Real.To_Double (Num (Val)); |
| |
| -- Otherwise, the value contains more bits than the mantissa so do the |
| -- conversion in two steps. |
| |
| else |
| declare |
| Mask : constant Uns := 2**(Uns'Size - Num'Machine_Mantissa) - 1; |
| Hi : constant Uns := Val and not Mask; |
| Lo : constant Uns := Val and Mask; |
| |
| begin |
| if Hi = 0 then |
| D_Val := Double_Real.To_Double (Num (Lo)); |
| else |
| D_Val := Double_Real.Quick_Two_Sum (Num (Hi), Num (Lo)); |
| end if; |
| end; |
| end if; |
| |
| -- Compute the final value by applying the scaling, if any |
| |
| if Val = 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 => |
| R_Val := Num'Scaling (Double_Real.To_Single (D_Val), S); |
| |
| when 4 => |
| if Integer'First / 2 <= S and then S <= Integer'Last / 2 then |
| S := S * 2; |
| end if; |
| |
| R_Val := Num'Scaling (Double_Real.To_Single (D_Val), S); |
| |
| when 8 => |
| if Integer'First / 3 <= S and then S <= Integer'Last / 3 then |
| S := S * 3; |
| end if; |
| |
| R_Val := Num'Scaling (Double_Real.To_Single (D_Val), S); |
| |
| when 16 => |
| if Integer'First / 4 <= S and then S <= Integer'Last / 4 then |
| S := S * 4; |
| end if; |
| |
| R_Val := Num'Scaling (Double_Real.To_Single (D_Val), S); |
| |
| -- If the base is 10, use a double implementation for the sake |
| -- of accuracy, to be removed when exponentiation is improved. |
| |
| -- 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 10 => |
| declare |
| Powten : constant array (0 .. Maxpow) of Double_T; |
| pragma Import (Ada, Powten); |
| for Powten'Address use Powten_Address; |
| |
| begin |
| if S > 0 then |
| if S <= Maxpow then |
| D_Val := D_Val * Powten (S); |
| else |
| D_Val := D_Val * Large_Powten (S); |
| end if; |
| |
| else |
| if S < -Maxexp then |
| D_Val := D_Val / Large_Powten (Maxexp); |
| S := S + Maxexp; |
| end if; |
| |
| if S >= -Maxpow then |
| D_Val := D_Val / Powten (-S); |
| else |
| D_Val := D_Val / Large_Powten (-S); |
| end if; |
| end if; |
| |
| R_Val := Double_Real.To_Single (D_Val); |
| 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_Powten -- |
| ------------------ |
| |
| function Large_Powten (Exp : Natural) return Double_T is |
| Powten : constant array (0 .. Maxpow) of Double_T; |
| pragma Import (Ada, Powten); |
| for Powten'Address use Powten_Address; |
| |
| R : Double_T; |
| E : Natural; |
| |
| begin |
| pragma Assert (Exp > Maxpow); |
| |
| R := Powten (Maxpow); |
| E := Exp - Maxpow; |
| |
| while E > Maxpow loop |
| R := R * Powten (Maxpow); |
| E := E - Maxpow; |
| end loop; |
| |
| R := R * Powten (E); |
| |
| return R; |
| end Large_Powten; |
| |
| --------------- |
| -- Scan_Real -- |
| --------------- |
| |
| function Scan_Real |
| (Str : String; |
| Ptr : not null access Integer; |
| Max : Integer) return Num |
| is |
| Base : Unsigned; |
| Scale : Integer; |
| Extra : Unsigned; |
| Minus : Boolean; |
| Val : Uns; |
| |
| begin |
| Val := Impl.Scan_Raw_Real (Str, Ptr, Max, Base, Scale, Extra, Minus); |
| |
| return Integer_to_Real (Str, Val, Base, Scale, Extra, Minus); |
| end Scan_Real; |
| |
| ---------------- |
| -- Value_Real -- |
| ---------------- |
| |
| function Value_Real (Str : String) return Num is |
| Base : Unsigned; |
| Scale : Integer; |
| Extra : Unsigned; |
| Minus : Boolean; |
| Val : Uns; |
| |
| begin |
| Val := Impl.Value_Raw_Real (Str, Base, Scale, Extra, Minus); |
| |
| return Integer_to_Real (Str, Val, Base, Scale, Extra, Minus); |
| end Value_Real; |
| |
| end System.Val_Real; |
