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------------------------------------------------------------------------------
-- --
-- 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) 2020-2022, 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;
|
