Precision of reals through writeln/readln in Delphi

Question

My clients application exports and imports quite a few variables of type real through a text file using writeln and readln. I've tried to increase the width of the fields written so the code looks like:

writeln(file, exportRealvalue:30); //using excess width of field
....
readln(file, importRealvalue);

When I export and then import and export again and compare the files I get a difference in the last two digits, e.g (might be off on the actual number of digits here but you get it):

-1.23456789012E-0002
-1.23456789034E-0002

This actually makes a difference in the app so the client wants to know what I can do about it. Now I'm not sure it's only the write/read that does it but I thought I'd throw a quick question out there before I dive into the hey stack again. Do I need to go binary on this?

This is not an app dealing with currency or something, I just write and read the values to/from file. I know floating points are a bit strange sometimes and I thought one of the routines (writeln/readln) may have some funny business going on.

Answer 1

When using floating point types, you should be aware of the precision limitations on the specified types. A 4 byte IEEE-754 type, for instance, has only about 7.5 significant digits of precision. An eight byte IEEE-754 type has roughly double the number of significant digits. Apparently, the delphi real type has a precision that lies around 11 significant digits. The result of this is that any extra digits of formatting that you specify are likely to be noise that can result in conversions between base 10 formatted values and base 2 floating point values.

Answer 2

You might try switching to extended for greater precision. As was pointed out though, floating point numbers only have so many significant digits of precision, so it is still possible to display more digits then are accurately stored, which could result in the behavior you specified.

From the Delphi help:

Fundamental Win32 real types

                                            | Significant | Size in 
Type     | Range                            | digits      | bytes
---------+----------------------------------+-------------+----------
Real     | -5.0 x 10^–324 .. 1.7 x 10^308   | 15–16       |   8  
Real48   | -2.9 x 10^–39 .. 1.7 x 10^38     | 11-12       |   6   
Single   | -1.5 x 10^–45 .. 3.4 x 10^38     |  7-8        |   4   
Double   | -5.0 x 10^–324 .. 1.7 x 10^308   | 15-16       |   8   
Extended | -3.6 x 10^–4951 .. 1.1 x 10^4932 | 10-20       |  10   
Comp     | -2^63+1 .. 2^63–1                | 10-20       |   8   
Currency | -922337203685477.5808..          |             | 
                    922337203685477.5807    | 10-20       |   8   

Note: The six-byte Real48 type was called Real in earlier versions of Object Pascal. If you are recompiling code that uses the older, six-byte Real type in Delphi, you may want to change it to Real48. You can also use the {$REALCOMPATIBILITY ON} compiler directive to turn Real back into the six-byte type. The following remarks apply to fundamental real types.

• Real48 is maintained for backward compatibility. Since its storage format is not native to the Intel processor architecture, it results in slower performance than other floating-point types.
• Extended offers greater precision than other real types but is less portable. Be careful using Extended if you are creating data files to share across platforms.

Notice that the range is greater then the significant digits. So you can have a number larger then can be accurately stored. I would recommend rounding to the significant digits to prevent that from happening.

Answer 3

First of all I would try to see if I could get any help from using Str with different arguments or increasing the precision of the types in your app. (Have you tried using Extended?)

As a last resort, (Warning! Workaround!!) I'd try saving the customer's string representation along with the binary representation in a sorted list. Before writing back a floating point value I'd see if there already is a matching value in the table, whose string representation is already known and can be used instead. In order to make get this lookup quick, you can sort it on the numeric value and use binary search for finding the best match.

Answer 4

If you want to specify the precision of a real with a WriteLn, use the following:

WriteLn(RealVar:12:3);

It outputs the value Realvar with at least 12 positions and a precision of 3.

Answer 5

Depending on how much processing you need to do, an alternative could be to keep the numbers in BCD format to retain original accuracy.

Answer 6

It's hard to answer this without knowing what type your ExportRealValue and ImportRealValue are. As others have mentioned, the real types all have different precisions.

It's worth noting, contrary to some thought, extended is not always higher precision. Extended is 10-20 significant figures where double is 15-16. As you are having trouble around the tenth sig fig perhaps you are using extended already.

To get more control over the reading and writing you can convert the numbers to and from strings yourself and write them to a file stream. At least that way you don't have to worry if readln and writeln are up to no good behind your back.