| ------------------------------------------------------------------------------ |
| -- -- |
| -- 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) 1992-2021, 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. -- |
| -- -- |
| ------------------------------------------------------------------------------ |
| |
| -- ------------------- |
| -- - 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 algorithms are 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 |
| -- ---------- |
| |
| -- [Wide_[Wide_]]Image attribute (see RM 3.5(27.1/2)) |
| |
| -- 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. |
| |
| -- [Wide_[Wide_]]Value attribute (RM 3.5(39.1/2)) |
| |
| -- 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 64 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 restricted set of acceptable |
| -- fixed point types. |
| |
| -- Implementation Choices |
| -- ---------------------- |
| |
| -- The current implementation in the GNAT runtime uses fixed-precision integer |
| -- arithmetic for fixed point types whose Small is the ratio of two integers |
| -- whose magnitude is bounded relatively to the size of the mantissa, with a |
| -- two-tiered approach for 32-bit and 64-bit fixed point types. For the other |
| -- fixed point types, the implementation uses floating-point arithmetic. |
| |
| -- The exact requirements of the algorithms are analyzed and documented along |
| -- with the implementation in their respective units. |
| |
| 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.Img_LFlt; use System.Img_LFlt; |
| with System.Val_Fixed_32; use System.Val_Fixed_32; |
| with System.Val_Fixed_64; use System.Val_Fixed_64; |
| with System.Val_LFlt; use System.Val_LFlt; |
| |
| package body Ada.Text_IO.Fixed_IO with SPARK_Mode => Off is |
| |
| -- Note: we still use the floating-point I/O routines for types whose small |
| -- is not the ratio of two sufficiently small integers. This will result in |
| -- inaccuracies for fixed point types that require more precision than is |
| -- available in Long_Float. |
| |
| subtype Int32 is Interfaces.Integer_32; use type Int32; |
| subtype Int64 is Interfaces.Integer_64; use type Int64; |
| |
| 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); |
| |
| package Aux_Long_Float is new |
| Ada.Text_IO.Float_Aux (Long_Float, Scan_Long_Float, Set_Image_Long_Float); |
| |
| -- Throughout this generic body, we distinguish between the case where type |
| -- Int32 is OK and where type Int64 is OK. These boolean constants are used |
| -- to test for this, such that only code for the relevant case is included |
| -- in the instance; that's why the computation of their value must be fully |
| -- static (although it is not a static expressions in the RM sense). |
| |
| OK_Get_32 : constant Boolean := |
| Num'Base'Object_Size <= 32 |
| and then |
| ((Num'Small_Numerator = 1 and then Num'Small_Denominator <= 2**31) |
| or else |
| (Num'Small_Denominator = 1 and then Num'Small_Numerator <= 2**31) |
| or else |
| (Num'Small_Numerator <= 2**27 |
| and then Num'Small_Denominator <= 2**27)); |
| -- These conditions are derived from the prerequisites of System.Value_F |
| |
| OK_Put_32 : constant Boolean := |
| Num'Base'Object_Size <= 32 |
| and then |
| ((Num'Small_Numerator = 1 and then Num'Small_Denominator <= 2**31) |
| or else |
| (Num'Small_Denominator = 1 and then Num'Small_Numerator <= 2**31) |
| or else |
| (Num'Small_Numerator < Num'Small_Denominator |
| and then Num'Small_Denominator <= 2**27) |
| or else |
| (Num'Small_Denominator < Num'Small_Numerator |
| and then Num'Small_Numerator <= 2**25)); |
| -- These conditions are derived from the prerequisites of System.Image_F |
| |
| OK_Get_64 : constant Boolean := |
| Num'Base'Object_Size <= 64 |
| and then |
| ((Num'Small_Numerator = 1 and then Num'Small_Denominator <= 2**63) |
| or else |
| (Num'Small_Denominator = 1 and then Num'Small_Numerator <= 2**63) |
| or else |
| (Num'Small_Numerator <= 2**59 |
| and then Num'Small_Denominator <= 2**59)); |
| -- These conditions are derived from the prerequisites of System.Value_F |
| |
| OK_Put_64 : constant Boolean := |
| Num'Base'Object_Size <= 64 |
| and then |
| ((Num'Small_Numerator = 1 and then Num'Small_Denominator <= 2**63) |
| or else |
| (Num'Small_Denominator = 1 and then Num'Small_Numerator <= 2**63) |
| or else |
| (Num'Small_Numerator < Num'Small_Denominator |
| and then Num'Small_Denominator <= 2**59) |
| or else |
| (Num'Small_Denominator < Num'Small_Numerator |
| and then Num'Small_Numerator <= 2**53)); |
| -- These conditions are derived from the prerequisites of System.Image_F |
| |
| E : constant Natural := 63 - 32 * Boolean'Pos (OK_Put_32); |
| -- 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 OK_Get_32 then |
| Item := Num'Fixed_Value |
| (Aux32.Get (File, Width, |
| -Num'Small_Numerator, |
| -Num'Small_Denominator)); |
| elsif OK_Get_64 then |
| Item := Num'Fixed_Value |
| (Aux64.Get (File, Width, |
| -Num'Small_Numerator, |
| -Num'Small_Denominator)); |
| else |
| Aux_Long_Float.Get (File, Long_Float (Item), Width); |
| end if; |
| |
| exception |
| when Constraint_Error => raise Data_Error; |
| end Get; |
| |
| procedure Get |
| (Item : out Num; |
| Width : Field := 0) |
| is |
| begin |
| Get (Current_In, Item, Width); |
| end Get; |
| |
| procedure Get |
| (From : String; |
| Item : out Num; |
| Last : out Positive) |
| is |
| pragma Unsuppress (Range_Check); |
| |
| begin |
| if OK_Get_32 then |
| Item := Num'Fixed_Value |
| (Aux32.Gets (From, Last, |
| -Num'Small_Numerator, |
| -Num'Small_Denominator)); |
| elsif OK_Get_64 then |
| Item := Num'Fixed_Value |
| (Aux64.Gets (From, Last, |
| -Num'Small_Numerator, |
| -Num'Small_Denominator)); |
| else |
| Aux_Long_Float.Gets (From, Long_Float (Item), Last); |
| 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 OK_Put_32 then |
| Aux32.Put (File, Int32'Integer_Value (Item), Fore, Aft, Exp, |
| -Num'Small_Numerator, -Num'Small_Denominator, |
| For0, Num'Aft); |
| elsif OK_Put_64 then |
| Aux64.Put (File, Int64'Integer_Value (Item), Fore, Aft, Exp, |
| -Num'Small_Numerator, -Num'Small_Denominator, |
| For0, Num'Aft); |
| else |
| Aux_Long_Float.Put (File, Long_Float (Item), Fore, Aft, Exp); |
| 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 OK_Put_32 then |
| Aux32.Puts (To, Int32'Integer_Value (Item), Aft, Exp, |
| -Num'Small_Numerator, -Num'Small_Denominator, |
| For0, Num'Aft); |
| elsif OK_Put_64 then |
| Aux64.Puts (To, Int64'Integer_Value (Item), Aft, Exp, |
| -Num'Small_Numerator, -Num'Small_Denominator, |
| For0, Num'Aft); |
| else |
| Aux_Long_Float.Puts (To, Long_Float (Item), Aft, Exp); |
| end if; |
| end Put; |
| |
| end Ada.Text_IO.Fixed_IO; |
