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fpc/rtl/inc/real2str.inc
Jonas Maebe d9c608a373 + $maxfpuregisters 0 for i386 in systemh (to avoid requiring too much 
empty FPU registers for sysstem routines
  * fixed bug in str_real when using ❌0
  * str_real now doesn't call exp() anymore at runtime, so it should
    require less free FPU registers now (and be slightly faster)
2000-03-26 11:36:28 +00:00

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{
$Id$
This file is part of the Free Pascal run time library.
Copyright (c) 1999-2000 by Michael Van Canneyt,
member of the Free Pascal development team
See the file COPYING.FPC, included in this distribution,
for details about the copyright.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
**********************************************************************}
type
{ See symdefh.inc tfloattyp }
treal_type = (rt_s32real,rt_s64real,rt_s80real,rt_c64bit,rt_f16bit,rt_f32bit);
{ corresponding to single double extended fixed comp for i386 }
Procedure str_real (len,f : longint; d : ValReal; real_type :treal_type; var s : string);
{$ifdef SUPPORT_EXTENDED}
type
TSplitExtended = packed record
case byte of
0: (bytes: Array[0..9] of byte);
1: (words: Array[0..4] of word);
2: (cards: Array[0..1] of cardinal; w: word);
end;
const
maxDigits = 17;
{$else}
{$ifdef SUPPORT_DOUBLE}
type
TSplitDouble = packed record
case byte of
0: (bytes: Array[0..7] of byte);
1: (words: Array[0..3] of word);
2: (cards: Array[0..1] of cardinal);
end;
const
maxDigits = 14;
{$else}
{$ifdef SUPPORT_SINGLE}
type
TSplitSingle = packed record
case byte of
0: (bytes: Array[0..3] of byte);
1: (words: Array[0..1] of word);
2: (cards: Array[0..0] of cardinal);
end;
const
maxDigits = 9;
{$endif SUPPORT_SINGLE}
{$endif SUPPORT_DOUBLE}
{$endif SUPPORT_EXTENDED}
type
{ the value in the last position is used for rounding }
TIntPartStack = array[1..maxDigits+1] of valReal;
var
roundCorr, corrVal: valReal;
intPart, spos, endpos, fracCount: longint;
correct, currprec: longint;
temp : string;
power : string[10];
sign : boolean;
dot : byte;
mantZero, expMaximal: boolean;
procedure RoundStr(var s: string; lastPos: byte);
var carry: longint;
begin
carry := 1;
repeat
s[lastPos] := chr(ord(s[lastPos])+carry);
carry := 0;
if s[lastPos] > '9' then
begin
s[lastPos] := '0';
carry := 1;
end;
dec(lastPos);
until carry = 0;
end;
procedure getIntPart(d: extended);
var
intPartStack: TIntPartStack;
stackPtr, endStackPtr, digits: longint;
overflow: boolean;
begin
{ position in the stack (gets increased before first write) }
stackPtr := 0;
{ number of digits processed }
digits := 0;
{ did we wrap around in the stack? Necessary to know whether we should round }
overflow :=false;
{ generate a list consisting of d, d/10, d/100, ... until d < 1.0 }
while d > 1.0-roundCorr do
begin
inc(stackPtr);
inc(digits);
if stackPtr > maxDigits+1 then
begin
stackPtr := 1;
overflow := true;
end;
intPartStack[stackPtr] := d;
d := d / 10.0;
end;
{ if no integer part, exit }
if digits = 0 then
exit;
endStackPtr := stackPtr+1;
if endStackPtr > maxDigits + 1 then
endStackPtr := 1;
{ now, all digits are calculated using trunc(d*10^(-n)-int(d*10^(-n-1))*10) }
corrVal := 0.0;
{ the power of 10 with which the resulting string has to be "multiplied" }
{ if the decimal point is placed after the first significant digit }
correct := digits-1;
repeat
if (currprec > 0) then
begin
intPart:= trunc(intPartStack[stackPtr]-corrVal);
dec(currPrec);
inc(spos);
temp[spos] := chr(intPart+ord('0'));
if temp[spos] > '9' then
begin
temp[spos] := chr(ord(temp[spos])-10);
roundStr(temp,spos-1);
end;
end;
corrVal := int(intPartStack[stackPtr]) * 10.0;
dec(stackPtr);
if stackPtr = 0 then
stackPtr := maxDigits+1;
until (overflow and (stackPtr = endStackPtr)) or
(not overflow and (stackPtr = maxDigits+1)) or (currPrec = 0);
{ round if we didn't use all available digits yet and if the }
{ remainder is > 5 }
if overflow and
(trunc(intPartStack[stackPtr]-corrVal) > 5.0 - roundCorr) then
roundStr(temp,spos);
end;
var maxlen : longint; { Maximal length of string for float }
minlen : longint; { Minimal length of string for float }
explen : longint; { Length of exponent, including E and sign.
Must be strictly larger than 2 }
const
maxexp = 1e+35; { Maximum value for decimal expressions }
minexp = 1e-35; { Minimum value for decimal expressions }
zero = '0000000000000000000000000000000000000000';
begin
case real_type of
rt_s32real :
begin
maxlen:=16;
minlen:=8;
explen:=4;
{ correction used with comparing to avoid rounding/precision errors }
roundCorr := (1/exp((16-4-3)*ln(10)));
end;
rt_s64real :
begin
{ if the maximum suppported type is double, we can print out one digit }
{ less, because otherwise we can't round properly and 1e-400 becomes }
{ 0.99999999999e-400 (JM) }
{$ifdef support_extended}
maxlen:=23;
{ correction used with comparing to avoid rounding/precision errors }
roundCorr := (1/exp((23-5-3)*ln(10)));
{$else support_extended}
{$ifdef support_double}
maxlen := 22;
{ correction used with comparing to avoid rounding/precision errors }
roundCorr := (1/exp((22-4-3)*ln(10)));
{$endif support_double}
{$endif support_extended}
minlen:=9;
explen:=5;
end;
rt_s80real :
begin
maxlen:=26;
minlen:=10;
explen:=6;
{ correction used with comparing to avoid rounding/precision errors }
roundCorr := (1/exp((26-6-3)*ln(10)));
end;
rt_c64bit :
begin
maxlen:=22;
minlen:=9;
{ according to TP (was 5) (FK) }
explen:=6;
{ correction used with comparing to avoid rounding/precision errors }
roundCorr := (1/exp((22-6-3)*ln(10)));
end;
rt_f16bit :
begin
maxlen:=16;
minlen:=8;
explen:=4;
{ correction used with comparing to avoid rounding/precision errors }
roundCorr := (1/exp((16-4-3)*ln(10)));
end;
rt_f32bit :
begin
maxlen:=16;
minlen:=8;
explen:=4;
{ correction used with comparing to avoid rounding/precision errors }
roundCorr := (1/exp((16-4-3)*ln(10)));
end;
end;
{ check parameters }
{ default value for length is -32767 }
if len=-32767 then
len:=maxlen;
{ determine sign. before precision, needs 2 less calls to abs() }
{$ifndef big_endian}
{$ifdef SUPPORT_EXTENDED}
{ extended, format (MSB): 1 Sign bit, 15 bit exponent, 64 bit mantissa }
sign := (TSplitExtended(d).w and $8000) <> 0;
expMaximal := (TSplitExtended(d).w and $7fff) = 32767;
mantZero := (TSplitExtended(d).cards[0] = 0) and
(TSplitExtended(d).cards[1] = 0);
{$else SUPPORT_EXTENDED}
{$ifdef SUPPORT_DOUBLE}
{ double, format (MSB): 1 Sign bit, 11 bit exponent, 52 bit mantissa }
sign := ((TSplitDouble(d).cards[1] shr 20) and $800) <> 0;
expMaximal := ((TSplitDouble(d).cards[1] shr 20) and $7ff) = 2047;
mantZero := (TSplitDouble(d).cards[1] and $fffff = 0) and
(TSplitDouble(d).cards[0] = 0);
{$else SUPPORT_DOUBLE}
{$ifdef SUPPORT_SINGLE}
{ single, format (MSB): 1 Sign bit, 8 bit exponent, 23 bit mantissa }
sign := ((TSplitSingle(d).words[1] shr 7) and $100) <> 0;
expMaximal := ((TSplitSingle(d).words[1] shr 7) and $ff) = 255;
mantZero := (TSplitSingle(d).cards[0] and $7fffff = 0);
{$else SUPPORT_SINGLE}
{$error No big endian floating type supported yet in real2str}
{$endif SUPPORT_SINGLE}
{$endif SUPPORT_DOUBLE}
{$endif SUPPORT_EXTENDED}
{$else big_endian}
{$error sign/NaN/Inf not yet supported for big endian CPU's in str_real}
{$endif big_endian}
if expMaximal then
if mantZero then
if sign then
temp := '-Inf'
else temp := 'Inf'
else temp := 'NaN'
else
begin
{ d:=abs(d); this converts d to double so we loose precision }
{ for the same reason I converted d:=frac(d) to d:=d-int(d); (PM) }
if sign then
d:=-d;
{ determine precision : maximal precision is : }
currPrec := maxlen-explen-2;
{ this is also the maximal number of decimals !!}
if f>currprec then
f:=currprec;
{ when doing a fixed-point, we need less characters.}
if (f<0) {or ((d<>0) and ((d>maxexp) and (d>minexp)))} then
begin
{ determine maximal number of decimals }
if (len>=0) and (len<minlen) then
len:=minlen;
if (len>0) and (len<maxlen) then
currprec:=len-explen-2;
end;
{ leading zero, may be necessary for things like str(9.999:0:2) to }
{ be able to insert an extra character at the start of the string }
temp := ' 0';
{ position in the temporary output string }
spos := 2;
{ get the integer part }
correct := 0;
GetIntPart(d);
{ now process the fractional part }
d := frac(d);
{ if we have to round earlier than the amount of available precision, }
{ only calculate digits up to that point }
if (f >= 0) and (currPrec > f) then
currPrec := f;
{ if integer part was zero, go to the first significant digit of the }
{ fractional part }
{ make sure we don't get an endless loop if d = 0 }
if (spos = 2) and (d <> 0.0) then
begin
{ take rounding errors into account }
while d < 0.1-roundCorr do
begin
d := d * 10.0;
dec(correct);
{ adjust the precision depending on how many digits we }
{ already "processed" by multiplying by 10, but only if }
{ the amount of precision is specified }
if f >= 0 then
dec(currPrec);
end;
dec(correct);
end;
{ current length of the output string in endPos }
endPos := spos;
{ always calculate at least 1 fractional digit for rounding }
if (currPrec >= 0) then
begin
corrVal := 0.5;
for fracCount := 1 to currPrec do
corrVal := corrVal / 10.0;
if d >= corrVal then
d := d + corrVal;
if int(d) = 1 then
begin
roundStr(temp,spos);
d := frac(d);
end;
{ calculate the necessary fractional digits }
for fracCount := 1 to currPrec do
begin
d := frac(d) * 10.0;
inc(spos);
temp[spos] := chr(trunc(d)+ord('0'));
if temp[spos] > '9' then
{ possible because trunc and the "*10.0" aren't exact :( }
begin
temp[spos] := chr(ord(temp[spos]) - 10);
roundStr(temp,spos-1);
end;
end;
{ new length of string }
endPos := spos;
end;
setLength(temp,endPos);
{ delete leading zero if we didn't need it while rounding at the }
{ string level }
if temp[2] = '0' then
delete(temp,2,1)
{ the rounding caused an overflow to the next power of 10 }
else inc(correct);
if sign then
temp[1] := '-';
if (f<0) or (correct>(round(ln(maxexp)/ln(10)))) then
begin
insert ('.',temp,3);
str(abs(correct),power);
if length(power)<explen-2 then
power:=copy(zero,1,explen-2-length(power))+power;
if correct<0 then
power:='-'+power
else
power:='+'+power;
temp:=temp+'E'+power;
end
else
begin
if not sign then
begin
delete(temp,1,1);
dot := 2
end
else
dot := 3;
{ set zeroes and dot }
if correct>=0 then
begin
if length(temp)<correct+dot+f-1 then
temp:=temp+copy(zero,1,correct+dot+f-length(temp));
insert ('.',temp,correct+dot);
end
else
begin
correct:=abs(correct);
insert(copy(zero,1,correct),temp,dot-1);
insert ('.',temp,dot);
end;
{ correct length to fit precision }
if f>0 then
setlength(temp,pos('.',temp)+f)
else
setLength(temp,pos('.',temp)-1);
end;
end;
if length(temp)<len then
s:=space(len-length(temp))+temp
else s:=temp;
end;
{
$Log$
Revision 1.30 2000-03-26 11:36:28 jonas
+ $maxfpuregisters 0 for i386 in systemh (to avoid requiring too much
empty FPU registers for sysstem routines
* fixed bug in str_real when using :x:0
* str_real now doesn't call exp() anymore at runtime, so it should
require less free FPU registers now (and be slightly faster)
Revision 1.29 2000/03/21 12:00:30 jonas
* fixed more bugs due to inexact nature of FPU
Revision 1.28 2000/03/17 20:20:33 jonas
* fixed rounding bugs with certain formatting parameters in str_real
* fixed tbs0218 so it compares both results only until max precision
Revision 1.27 2000/03/05 09:41:05 jonas
* fixed rounding problem when writing out single/double type vars
Revision 1.26 2000/03/02 07:35:57 jonas
* sign was not written in some cases
Revision 1.25 2000/02/27 14:41:25 peter
* removed warnings/notes
Revision 1.24 2000/02/26 18:53:11 jonas
* fix for lost precision because sometimes the correction value was
larger than the number to be corrected
* incompatibility with TP's output fixed
Revision 1.23 2000/02/26 15:49:40 jonas
+ new str_real which is completely TP compatible regarding output
format and which should have no rounding errors anymore
Revision 1.22 2000/02/09 16:59:31 peter
* truncated log
Revision 1.21 2000/02/09 12:17:51 peter
* moved halt to system.inc
* syslinux doesn't use direct asm anymore
Revision 1.20 2000/01/17 13:00:51 jonas
+ support for NaN's, cleaner support for Inf
Revision 1.19 2000/01/07 16:41:36 daniel
* copyright 2000
Revision 1.18 1999/11/28 23:57:23 pierre
* Infinite loop for infinite value problem fixed
Revision 1.17 1999/11/03 09:54:24 peter
* another fix for precision
Revision 1.16 1999/11/03 00:55:09 pierre
* problem of last commit for large d values corrected
Revision 1.15 1999/11/02 15:05:53 peter
* better precisio by dividing only once with a calculated longint
instead of multiple times by 10
Revision 1.14 1999/08/03 21:58:44 peter
* small speed improvements
}
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