------------------------------------------------------------------------------ -- -- -- GNAT RUN-TIME COMPONENTS -- -- -- -- A D A . T E X T _ I O . F I X E D _ I O -- -- -- -- B o d y -- -- -- -- Copyright (C) 1992-2020, 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. -- -- -- ------------------------------------------------------------------------------ -- Fixed point I/O -- --------------- -- The following text documents implementation details of the fixed point -- input/output routines in the GNAT runtime. The first part describes the -- general properties of fixed point types as defined by the Ada standard, -- including the Information Systems Annex. -- Subsequently these are reduced to implementation constraints and the impact -- of these constraints on a few possible approaches to input/output is given. -- Based on this analysis, a specific implementation is selected for use in -- the GNAT runtime. Finally, the chosen algorithm is analyzed numerically in -- order to provide user-level documentation on limits for range and precision -- of fixed point types as well as accuracy of input/output conversions. -- ------------------------------------------- -- - General Properties of Fixed Point Types - -- ------------------------------------------- -- Operations on fixed point types, other than input/output, are not important -- for the purpose of this document. Only the set of values that a fixed point -- type can represent and the input/output operations are significant. -- Values -- ------ -- The set of values of a fixed point type comprise the integral multiples of -- a number called the small of the type. The small can be either a power of -- two, a power of ten or (if the implementation allows) an arbitrary strictly -- positive real value. -- Implementations need to support ordinary fixed point types with a precision -- of at least 24 bits, and (in order to comply with the Information Systems -- Annex) decimal fixed point types with at least 18 digits. For the rest, no -- requirements exist for the minimal small and range that must be supported. -- Operations -- ---------- -- 'Image and 'Wide_Image (see RM 3.5(34)) -- These attributes return a decimal real literal best approximating -- the value (rounded away from zero if halfway between) with a -- single leading character that is either a minus sign or a space, -- one or more digits before the decimal point (with no redundant -- leading zeros), a decimal point, and N digits after the decimal -- point. For a subtype S, the value of N is S'Aft, the smallest -- positive integer such that (10**N)*S'Delta is greater or equal to -- one, see RM 3.5.10(5). -- For an arbitrary small, this means large number arithmetic needs -- to be performed. -- Put (see RM A.10.9(22-26)) -- The requirements for Put add no extra constraints over the image -- attributes, although it would be nice to be able to output more -- than S'Aft digits after the decimal point for values of subtype S. -- 'Value and 'Wide_Value attribute (RM 3.5(40-55)) -- Since the input can be given in any base in the range 2..16, -- accurate conversion to a fixed point number may require -- arbitrary precision arithmetic if there is no limit on the -- magnitude of the small of the fixed point type. -- Get (see RM A.10.9(12-21)) -- The requirements for Get are identical to those of the Value -- attribute. -- ------------------------------ -- - Implementation Constraints - -- ------------------------------ -- The requirements listed above for the input/output operations lead to -- significant complexity, if no constraints are put on supported smalls. -- Implementation Strategies -- ------------------------- -- * Floating point arithmetic -- * Arbitrary-precision integer arithmetic -- * Fixed-precision integer arithmetic -- Although it seems convenient to convert fixed point numbers to floating -- point and then print them, this leads to a number of restrictions. -- The first one is precision. The widest floating-point type generally -- available has 53 bits of mantissa. This means that Fine_Delta cannot -- be less than 2.0**(-53). -- In GNAT, Fine_Delta is 2.0**(-63), and Duration for example is a 64-bit -- type. This means that a floating-point type with 63 bits of mantissa needs -- to be used, which is only generally available on the x86 architecture. It -- would still be possible to use multi-precision floating point to perform -- calculations using longer mantissas, but this is a much harder approach. -- The base conversions needed for input/output of (non-decimal) fixed point -- types can be seen as pairs of integer multiplications and divisions. -- Arbitrary-precision integer arithmetic would be suitable for the job at -- hand, but has the drawback that it is very heavy implementation-wise. -- Especially in embedded systems, where fixed point types are often used, -- it may not be desirable to require large amounts of storage and time -- for fixed I/O operations. -- Fixed-precision integer arithmetic has the advantage of simplicity and -- speed. For the most common fixed point types this would be a perfect -- solution. The downside however may be a too limited set of acceptable -- fixed point types. with Interfaces; with Ada.Text_IO.Fixed_Aux; with Ada.Text_IO.Float_Aux; with System.Img_Fixed_32; use System.Img_Fixed_32; with System.Img_Fixed_64; use System.Img_Fixed_64; with System.Val_Fixed_32; use System.Val_Fixed_32; with System.Val_Fixed_64; use System.Val_Fixed_64; package body Ada.Text_IO.Fixed_IO is -- Note: we still use the floating-point I/O routines for types whose small -- is not a sufficiently small integer or the reciprocal thereof. This will -- result in inaccuracies for fixed point types that require more precision -- than is available in Long_Long_Float. subtype Int32 is Interfaces.Integer_32; subtype Int64 is Interfaces.Integer_64; package Aux32 is new Ada.Text_IO.Fixed_Aux (Int32, Scan_Fixed32, Set_Image_Fixed32); package Aux64 is new Ada.Text_IO.Fixed_Aux (Int64, Scan_Fixed64, Set_Image_Fixed64); Exact : constant Boolean := (Float'Floor (Num'Small) = Float'Ceiling (Num'Small) or else Float'Floor (1.0 / Num'Small) = Float'Ceiling (1.0 / Num'Small)) and then Num'Small >= 2.0**(-63) and then Num'Small <= 2.0**63; -- True if the exact algorithm implemented in Fixed_Aux can be used. The -- condition is a Small which is either an integer or the reciprocal of an -- integer with the appropriate magnitude. Need_64 : constant Boolean := Num'Object_Size > 32 or else Num'Small > 2.0**31 or else Num'Small < 2.0**(-31); -- Throughout this generic body, we distinguish between the case where type -- Int32 is acceptable and where type Int64 is needed. This Boolean is used -- to test for these cases and since it is a constant, only code for the -- relevant case will be included in the instance. E : constant Natural := 31 + 32 * Boolean'Pos (Need_64); -- T'Size - 1 for the selected Int{32,64} F0 : constant Natural := 0; F1 : constant Natural := F0 + 18 * Boolean'Pos (2.0**E * Num'Small * 10.0**(-F0) >= 1.0E+18); F2 : constant Natural := F1 + 9 * Boolean'Pos (2.0**E * Num'Small * 10.0**(-F1) >= 1.0E+9); F3 : constant Natural := F2 + 5 * Boolean'Pos (2.0**E * Num'Small * 10.0**(-F2) >= 1.0E+5); F4 : constant Natural := F3 + 3 * Boolean'Pos (2.0**E * Num'Small * 10.0**(-F3) >= 1.0E+3); F5 : constant Natural := F4 + 2 * Boolean'Pos (2.0**E * Num'Small * 10.0**(-F4) >= 1.0E+2); F6 : constant Natural := F5 + 1 * Boolean'Pos (2.0**E * Num'Small * 10.0**(-F5) >= 1.0E+1); -- Binary search for the number of digits - 1 before the decimal point of -- the product 2.0**E * Num'Small. For0 : constant Natural := 2 + F6; -- Fore value for the fixed point type whose mantissa is Int{32,64} and -- whose small is Num'Small. --------- -- Get -- --------- procedure Get (File : File_Type; Item : out Num; Width : Field := 0) is pragma Unsuppress (Range_Check); begin if not Exact then Float_Aux.Get (File, Long_Long_Float (Item), Width); elsif Need_64 then Item := Num'Fixed_Value (Aux64.Get (File, Width, Int64 (-Float'Ceiling (Num'Small)), Int64 (-Float'Ceiling (1.0 / Num'Small)))); else Item := Num'Fixed_Value (Aux32.Get (File, Width, Int32 (-Float'Ceiling (Num'Small)), Int32 (-Float'Ceiling (1.0 / Num'Small)))); end if; exception when Constraint_Error => raise Data_Error; end Get; procedure Get (Item : out Num; Width : Field := 0) is begin Get (Current_Input, Item, Width); end Get; procedure Get (From : String; Item : out Num; Last : out Positive) is pragma Unsuppress (Range_Check); begin if not Exact then Float_Aux.Gets (From, Long_Long_Float (Item), Last); elsif Need_64 then Item := Num'Fixed_Value (Aux64.Gets (From, Last, Int64 (-Float'Ceiling (Num'Small)), Int64 (-Float'Ceiling (1.0 / Num'Small)))); else Item := Num'Fixed_Value (Aux32.Gets (From, Last, Int32 (-Float'Ceiling (Num'Small)), Int32 (-Float'Ceiling (1.0 / Num'Small)))); end if; exception when Constraint_Error => raise Data_Error; end Get; --------- -- Put -- --------- procedure Put (File : File_Type; Item : Num; Fore : Field := Default_Fore; Aft : Field := Default_Aft; Exp : Field := Default_Exp) is begin if not Exact then Float_Aux.Put (File, Long_Long_Float (Item), Fore, Aft, Exp); elsif Need_64 then Aux64.Put (File, Int64'Integer_Value (Item), Fore, Aft, Exp, Int64 (-Float'Ceiling (Num'Small)), Int64 (-Float'Ceiling (1.0 / Num'Small)), For0, Num'Aft); else Aux32.Put (File, Int32'Integer_Value (Item), Fore, Aft, Exp, Int32 (-Float'Ceiling (Num'Small)), Int32 (-Float'Ceiling (1.0 / Num'Small)), For0, Num'Aft); end if; end Put; procedure Put (Item : Num; Fore : Field := Default_Fore; Aft : Field := Default_Aft; Exp : Field := Default_Exp) is begin Put (Current_Out, Item, Fore, Aft, Exp); end Put; procedure Put (To : out String; Item : Num; Aft : Field := Default_Aft; Exp : Field := Default_Exp) is begin if not Exact then Float_Aux.Puts (To, Long_Long_Float (Item), Aft, Exp); elsif Need_64 then Aux64.Puts (To, Int64'Integer_Value (Item), Aft, Exp, Int64 (-Float'Ceiling (Num'Small)), Int64 (-Float'Ceiling (1.0 / Num'Small)), For0, Num'Aft); else Aux32.Puts (To, Int32'Integer_Value (Item), Aft, Exp, Int32 (-Float'Ceiling (Num'Small)), Int32 (-Float'Ceiling (1.0 / Num'Small)), For0, Num'Aft); end if; end Put; end Ada.Text_IO.Fixed_IO;