------------------------------------------------------------------------------ | |

-- -- | |

-- 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) 2020-2021, 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**(-127), and Duration for example is a 64-bit | |

-- type. This means that a floating-point type with 128 bits of mantissa needs | |

-- to be used, which currently does not exist in any common 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 | |

-- three-tiered approach for 32-bit, 64-bit and 128-bit fixed point types. For | |

-- 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_Fixed_128; use System.Img_Fixed_128; | |

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_Fixed_128; use System.Val_Fixed_128; | |

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; | |

subtype Int128 is Interfaces.Integer_128; use type Int128; | |

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 Aux128 is new | |

Ada.Text_IO.Fixed_Aux (Int128, Scan_Fixed128, Set_Image_Fixed128); | |

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, where type Int64 is OK and where type Int128 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 expression | |

-- 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 | |

OK_Get_128 : constant Boolean := | |

Num'Base'Object_Size <= 128 | |

and then | |

((Num'Small_Numerator = 1 and then Num'Small_Denominator <= 2**127) | |

or else | |

(Num'Small_Denominator = 1 and then Num'Small_Numerator <= 2**127) | |

or else | |

(Num'Small_Numerator <= 2**123 | |

and then Num'Small_Denominator <= 2**123)); | |

-- These conditions are derived from the prerequisites of System.Value_F | |

OK_Put_128 : constant Boolean := | |

Num'Base'Object_Size <= 128 | |

and then | |

((Num'Small_Numerator = 1 and then Num'Small_Denominator <= 2**127) | |

or else | |

(Num'Small_Denominator = 1 and then Num'Small_Numerator <= 2**127) | |

or else | |

(Num'Small_Numerator < Num'Small_Denominator | |

and then Num'Small_Denominator <= 2**123) | |

or else | |

(Num'Small_Denominator < Num'Small_Numerator | |

and then Num'Small_Numerator <= 2**122)); | |

-- These conditions are derived from the prerequisites of System.Image_F | |

E : constant Natural := | |

127 - 64 * Boolean'Pos (OK_Put_64) - 32 * Boolean'Pos (OK_Put_32); | |

-- T'Size - 1 for the selected Int{32,64,128} | |

F0 : constant Natural := 0; | |

F1 : constant Natural := | |

F0 + 38 * Boolean'Pos (2.0**E * Num'Small * 10.0**(-F0) >= 1.0E+38); | |

F2 : constant Natural := | |

F1 + 19 * Boolean'Pos (2.0**E * Num'Small * 10.0**(-F1) >= 1.0E+19); | |

F3 : constant Natural := | |

F2 + 9 * Boolean'Pos (2.0**E * Num'Small * 10.0**(-F2) >= 1.0E+9); | |

F4 : constant Natural := | |

F3 + 5 * Boolean'Pos (2.0**E * Num'Small * 10.0**(-F3) >= 1.0E+5); | |

F5 : constant Natural := | |

F4 + 3 * Boolean'Pos (2.0**E * Num'Small * 10.0**(-F4) >= 1.0E+3); | |

F6 : constant Natural := | |

F5 + 2 * Boolean'Pos (2.0**E * Num'Small * 10.0**(-F5) >= 1.0E+2); | |

F7 : constant Natural := | |

F6 + 1 * Boolean'Pos (2.0**E * Num'Small * 10.0**(-F6) >= 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 + F7; | |

-- Fore value for the fixed point type whose mantissa is Int{32,64,128} 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)); | |

elsif OK_Get_128 then | |

Item := Num'Fixed_Value | |

(Aux128.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)); | |

elsif OK_Get_128 then | |

Item := Num'Fixed_Value | |

(Aux128.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); | |

elsif OK_Put_128 then | |

Aux128.Put (File, Int128'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); | |

elsif OK_Put_128 then | |

Aux128.Puts (To, Int128'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; |