File : s-imgrea.adb
------------------------------------------------------------------------------
-- --
-- GNAT RUN-TIME COMPONENTS --
-- --
-- S Y S T E M . I M G _ R E A L --
-- --
-- B o d y --
-- --
-- Copyright (C) 1992-2011, 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. --
-- --
-- --
-- --
-- --
-- --
-- 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.Img_LLU; use System.Img_LLU;
with System.Img_Uns; use System.Img_Uns;
with System.Powten_Table; use System.Powten_Table;
with System.Unsigned_Types; use System.Unsigned_Types;
with System.Float_Control;
package body System.Img_Real is
-- The following defines the maximum number of digits that we can convert
-- accurately. This is limited by the precision of Long_Long_Float, and
-- also by the number of digits we can hold in Long_Long_Unsigned, which
-- is the integer type we use as an intermediate for the result.
-- We assume that in practice, the limitation will come from the digits
-- value, rather than the integer value. This is true for typical IEEE
-- implementations, and at worst, the only loss is for some precision
-- in very high precision floating-point output.
-- Note that in the following, the "-2" accounts for the sign and one
-- extra digits, since we need the maximum number of 9's that can be
-- supported, e.g. for the normal 64 bit case, Long_Long_Integer'Width
-- is 21, since the maximum value (approx 1.6 * 10**19) has 20 digits,
-- but the maximum number of 9's that can be supported is 19.
Maxdigs : constant :=
Natural'Min
(Long_Long_Unsigned'Width - 2, Long_Long_Float'Digits);
Unsdigs : constant := Unsigned'Width - 2;
-- Number of digits that can be converted using type Unsigned
-- See above for the explanation of the -2.
Maxscaling : constant := 5000;
-- Max decimal scaling required during conversion of floating-point
-- numbers to decimal. This is used to defend against infinite
-- looping in the conversion, as can be caused by erroneous executions.
-- The largest exponent used on any current system is 2**16383, which
-- is approximately 10**4932, and the highest number of decimal digits
-- is about 35 for 128-bit floating-point formats, so 5000 leaves
-- enough room for scaling such values
function Is_Negative (V : Long_Long_Float) return Boolean;
pragma Import (Intrinsic, Is_Negative);
--------------------------
-- Image_Floating_Point --
--------------------------
procedure Image_Floating_Point
(V : Long_Long_Float;
S : in out String;
P : out Natural;
Digs : Natural)
is
pragma Assert (S'First = 1);
begin
-- Decide whether a blank should be prepended before the call to
-- Set_Image_Real. We generate a blank for positive values, and
-- also for positive zeroes. For negative zeroes, we generate a
-- space only if Signed_Zeroes is True (the RM only permits the
-- output of -0.0 on targets where this is the case). We can of
-- course still see a -0.0 on a target where Signed_Zeroes is
-- False (since this attribute refers to the proper handling of
-- negative zeroes, not to their existence).
if not Is_Negative (V)
or else (not Long_Long_Float'Signed_Zeros and then V = -0.0)
then
S (1) := ' ';
P := 1;
else
P := 0;
end if;
Set_Image_Real (V, S, P, 1, Digs - 1, 3);
end Image_Floating_Point;
--------------------------------
-- Image_Ordinary_Fixed_Point --
--------------------------------
procedure Image_Ordinary_Fixed_Point
(V : Long_Long_Float;
S : in out String;
P : out Natural;
Aft : Natural)
is
pragma Assert (S'First = 1);
begin
-- Output space at start if non-negative
if V >= 0.0 then
S (1) := ' ';
P := 1;
else
P := 0;
end if;
Set_Image_Real (V, S, P, 1, Aft, 0);
end Image_Ordinary_Fixed_Point;
--------------------
-- Set_Image_Real --
--------------------
procedure Set_Image_Real
(V : Long_Long_Float;
S : out String;
P : in out Natural;
Fore : Natural;
Aft : Natural;
Exp : Natural)
is
NFrac : constant Natural := Natural'Max (Aft, 1);
Sign : Character;
X : aliased Long_Long_Float;
-- This is declared aliased because the expansion of X'Valid passes
-- X by access and JGNAT requires all access parameters to be aliased.
-- The Valid attribute probably needs to be handled via a different
-- expansion for JGNAT, and this use of aliased should be removed
-- once Valid is handled properly. ???
Scale : Integer;
Expon : Integer;
Field_Max : constant := 255;
-- This should be the same value as Ada.[Wide_]Text_IO.Field'Last.
-- It is not worth dragging in Ada.Text_IO to pick up this value,
-- since it really should never be necessary to change it!
Digs : String (1 .. 2 * Field_Max + 16);
-- Array used to hold digits of converted integer value. This is a
-- large enough buffer to accommodate ludicrous values of Fore and Aft.
Ndigs : Natural;
-- Number of digits stored in Digs (and also subscript of last digit)
procedure Adjust_Scale (S : Natural);
-- Adjusts the value in X by multiplying or dividing by a power of
-- ten so that it is in the range 10**(S-1) <= X < 10**S. Includes
-- adding 0.5 to round the result, readjusting if the rounding causes
-- the result to wander out of the range. Scale is adjusted to reflect
-- the power of ten used to divide the result (i.e. one is added to
-- the scale value for each division by 10.0, or one is subtracted
-- for each multiplication by 10.0).
procedure Convert_Integer;
-- Takes the value in X, outputs integer digits into Digs. On return,
-- Ndigs is set to the number of digits stored. The digits are stored
-- in Digs (1 .. Ndigs),
procedure Set (C : Character);
-- Sets character C in output buffer
procedure Set_Blanks_And_Sign (N : Integer);
-- Sets leading blanks and minus sign if needed. N is the number of
-- positions to be filled (a minus sign is output even if N is zero
-- or negative, but for a positive value, if N is non-positive, then
-- the call has no effect).
procedure Set_Digs (S, E : Natural);
-- Set digits S through E from Digs buffer. No effect if S > E
procedure Set_Special_Fill (N : Natural);
-- After outputting +Inf, -Inf or NaN, this routine fills out the
-- rest of the field with * characters. The argument is the number
-- of characters output so far (either 3 or 4)
procedure Set_Zeros (N : Integer);
-- Set N zeros, no effect if N is negative
pragma Inline (Set);
pragma Inline (Set_Digs);
pragma Inline (Set_Zeros);
------------------
-- Adjust_Scale --
------------------
procedure Adjust_Scale (S : Natural) is
Lo : Natural;
Hi : Natural;
Mid : Natural;
XP : Long_Long_Float;
begin
-- Cases where scaling up is required
if X < Powten (S - 1) then
-- What we are looking for is a power of ten to multiply X by
-- so that the result lies within the required range.
loop
XP := X * Powten (Maxpow);
exit when XP >= Powten (S - 1) or else Scale < -Maxscaling;
X := XP;
Scale := Scale - Maxpow;
end loop;
-- The following exception is only raised in case of erroneous
-- execution, where a number was considered valid but still
-- fails to scale up. One situation where this can happen is
-- when a system which is supposed to be IEEE-compliant, but
-- has been reconfigured to flush denormals to zero.
if Scale < -Maxscaling then
raise Constraint_Error;
end if;
-- Here we know that we must multiply by at least 10**1 and that
-- 10**Maxpow takes us too far: binary search to find right one.
-- Because of roundoff errors, it is possible for the value
-- of XP to be just outside of the interval when Lo >= Hi. In
-- that case we adjust explicitly by a factor of 10. This
-- can only happen with a value that is very close to an
-- exact power of 10.
Lo := 1;
Hi := Maxpow;
loop
Mid := (Lo + Hi) / 2;
XP := X * Powten (Mid);
if XP < Powten (S - 1) then
if Lo >= Hi then
Mid := Mid + 1;
XP := XP * 10.0;
exit;
else
Lo := Mid + 1;
end if;
elsif XP >= Powten (S) then
if Lo >= Hi then
Mid := Mid - 1;
XP := XP / 10.0;
exit;
else
Hi := Mid - 1;
end if;
else
exit;
end if;
end loop;
X := XP;
Scale := Scale - Mid;
-- Cases where scaling down is required
elsif X >= Powten (S) then
-- What we are looking for is a power of ten to divide X by
-- so that the result lies within the required range.
loop
XP := X / Powten (Maxpow);
exit when XP < Powten (S) or else Scale > Maxscaling;
X := XP;
Scale := Scale + Maxpow;
end loop;
-- The following exception is only raised in case of erroneous
-- execution, where a number was considered valid but still
-- fails to scale up. One situation where this can happen is
-- when a system which is supposed to be IEEE-compliant, but
-- has been reconfigured to flush denormals to zero.
if Scale > Maxscaling then
raise Constraint_Error;
end if;
-- Here we know that we must divide by at least 10**1 and that
-- 10**Maxpow takes us too far, binary search to find right one.
Lo := 1;
Hi := Maxpow;
loop
Mid := (Lo + Hi) / 2;
XP := X / Powten (Mid);
if XP < Powten (S - 1) then
if Lo >= Hi then
XP := XP * 10.0;
Mid := Mid - 1;
exit;
else
Hi := Mid - 1;
end if;
elsif XP >= Powten (S) then
if Lo >= Hi then
XP := XP / 10.0;
Mid := Mid + 1;
exit;
else
Lo := Mid + 1;
end if;
else
exit;
end if;
end loop;
X := XP;
Scale := Scale + Mid;
-- Here we are already scaled right
else
null;
end if;
-- Round, readjusting scale if needed. Note that if a readjustment
-- occurs, then it is never necessary to round again, because there
-- is no possibility of such a second rounding causing a change.
X := X + 0.5;
if X >= Powten (S) then
X := X / 10.0;
Scale := Scale + 1;
end if;
end Adjust_Scale;
---------------------
-- Convert_Integer --
---------------------
procedure Convert_Integer is
begin
-- Use Unsigned routine if possible, since on many machines it will
-- be significantly more efficient than the Long_Long_Unsigned one.
if X < Powten (Unsdigs) then
Ndigs := 0;
Set_Image_Unsigned
(Unsigned (Long_Long_Float'Truncation (X)),
Digs, Ndigs);
-- But if we want more digits than fit in Unsigned, we have to use
-- the Long_Long_Unsigned routine after all.
else
Ndigs := 0;
Set_Image_Long_Long_Unsigned
(Long_Long_Unsigned (Long_Long_Float'Truncation (X)),
Digs, Ndigs);
end if;
end Convert_Integer;
---------
-- Set --
---------
procedure Set (C : Character) is
begin
P := P + 1;
S (P) := C;
end Set;
-------------------------
-- Set_Blanks_And_Sign --
-------------------------
procedure Set_Blanks_And_Sign (N : Integer) is
begin
if Sign = '-' then
for J in 1 .. N - 1 loop
Set (' ');
end loop;
Set ('-');
else
for J in 1 .. N loop
Set (' ');
end loop;
end if;
end Set_Blanks_And_Sign;
--------------
-- Set_Digs --
--------------
procedure Set_Digs (S, E : Natural) is
begin
for J in S .. E loop
Set (Digs (J));
end loop;
end Set_Digs;
----------------------
-- Set_Special_Fill --
----------------------
procedure Set_Special_Fill (N : Natural) is
F : Natural;
begin
F := Fore + 1 + Aft - N;
if Exp /= 0 then
F := F + Exp + 1;
end if;
for J in 1 .. F loop
Set ('*');
end loop;
end Set_Special_Fill;
---------------
-- Set_Zeros --
---------------
procedure Set_Zeros (N : Integer) is
begin
for J in 1 .. N loop
Set ('0');
end loop;
end Set_Zeros;
-- Start of processing for Set_Image_Real
begin
-- We call the floating-point processor reset routine so that we can
-- be sure the floating-point processor is properly set for conversion
-- calls. This is notably need on Windows, where calls to the operating
-- system randomly reset the processor into 64-bit mode.
System.Float_Control.Reset;
Scale := 0;
-- Deal with invalid values first,
if not V'Valid then
-- Note that we're taking our chances here, as V might be
-- an invalid bit pattern resulting from erroneous execution
-- (caused by using uninitialized variables for example).
-- No matter what, we'll at least get reasonable behaviour,
-- converting to infinity or some other value, or causing an
-- exception to be raised is fine.
-- If the following test succeeds, then we definitely have
-- an infinite value, so we print Inf.
if V > Long_Long_Float'Last then
Set ('+');
Set ('I');
Set ('n');
Set ('f');
Set_Special_Fill (4);
-- In all other cases we print NaN
elsif V < Long_Long_Float'First then
Set ('-');
Set ('I');
Set ('n');
Set ('f');
Set_Special_Fill (4);
else
Set ('N');
Set ('a');
Set ('N');
Set_Special_Fill (3);
end if;
return;
end if;
-- Positive values
if V > 0.0 then
X := V;
Sign := '+';
-- Negative values
elsif V < 0.0 then
X := -V;
Sign := '-';
-- Zero values
elsif V = 0.0 then
if Long_Long_Float'Signed_Zeros and then Is_Negative (V) then
Sign := '-';
else
Sign := '+';
end if;
Set_Blanks_And_Sign (Fore - 1);
Set ('0');
Set ('.');
Set_Zeros (NFrac);
if Exp /= 0 then
Set ('E');
Set ('+');
Set_Zeros (Natural'Max (1, Exp - 1));
end if;
return;
else
-- It should not be possible for a NaN to end up here.
-- Either the 'Valid test has failed, or we have some form
-- of erroneous execution. Raise Constraint_Error instead of
-- attempting to go ahead printing the value.
raise Constraint_Error;
end if;
-- X and Sign are set here, and X is known to be a valid,
-- non-zero floating-point number.
-- Case of non-zero value with Exp = 0
if Exp = 0 then
-- First step is to multiply by 10 ** Nfrac to get an integer
-- value to be output, an then add 0.5 to round the result.
declare
NF : Natural := NFrac;
begin
loop
-- If we are larger than Powten (Maxdigs) now, then
-- we have too many significant digits, and we have
-- not even finished multiplying by NFrac (NF shows
-- the number of unaccounted-for digits).
if X >= Powten (Maxdigs) then
-- In this situation, we only to generate a reasonable
-- number of significant digits, and then zeroes after.
-- So first we rescale to get:
-- 10 ** (Maxdigs - 1) <= X < 10 ** Maxdigs
-- and then convert the resulting integer
Adjust_Scale (Maxdigs);
Convert_Integer;
-- If that caused rescaling, then add zeros to the end
-- of the number to account for this scaling. Also add
-- zeroes to account for the undone multiplications
for J in 1 .. Scale + NF loop
Ndigs := Ndigs + 1;
Digs (Ndigs) := '0';
end loop;
exit;
-- If multiplication is complete, then convert the resulting
-- integer after rounding (note that X is non-negative)
elsif NF = 0 then
X := X + 0.5;
Convert_Integer;
exit;
-- Otherwise we can go ahead with the multiplication. If it
-- can be done in one step, then do it in one step.
elsif NF < Maxpow then
X := X * Powten (NF);
NF := 0;
-- If it cannot be done in one step, then do partial scaling
else
X := X * Powten (Maxpow);
NF := NF - Maxpow;
end if;
end loop;
end;
-- If number of available digits is less or equal to NFrac,
-- then we need an extra zero before the decimal point.
if Ndigs <= NFrac then
Set_Blanks_And_Sign (Fore - 1);
Set ('0');
Set ('.');
Set_Zeros (NFrac - Ndigs);
Set_Digs (1, Ndigs);
-- Normal case with some digits before the decimal point
else
Set_Blanks_And_Sign (Fore - (Ndigs - NFrac));
Set_Digs (1, Ndigs - NFrac);
Set ('.');
Set_Digs (Ndigs - NFrac + 1, Ndigs);
end if;
-- Case of non-zero value with non-zero Exp value
else
-- If NFrac is less than Maxdigs, then all the fraction digits are
-- significant, so we can scale the resulting integer accordingly.
if NFrac < Maxdigs then
Adjust_Scale (NFrac + 1);
Convert_Integer;
-- Otherwise, we get the maximum number of digits available
else
Adjust_Scale (Maxdigs);
Convert_Integer;
for J in 1 .. NFrac - Maxdigs + 1 loop
Ndigs := Ndigs + 1;
Digs (Ndigs) := '0';
Scale := Scale - 1;
end loop;
end if;
Set_Blanks_And_Sign (Fore - 1);
Set (Digs (1));
Set ('.');
Set_Digs (2, Ndigs);
-- The exponent is the scaling factor adjusted for the digits
-- that we output after the decimal point, since these were
-- included in the scaled digits that we output.
Expon := Scale + NFrac;
Set ('E');
Ndigs := 0;
if Expon >= 0 then
Set ('+');
Set_Image_Unsigned (Unsigned (Expon), Digs, Ndigs);
else
Set ('-');
Set_Image_Unsigned (Unsigned (-Expon), Digs, Ndigs);
end if;
Set_Zeros (Exp - Ndigs - 1);
Set_Digs (1, Ndigs);
end if;
end Set_Image_Real;
end System.Img_Real;