Floating-point number representation on various platforms

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Floating-point number representation on various platforms

Tom Verhoeff
While writing a paper (several years ago) about the traps of using
floating-point numbers, I prepared a unit FloatView to "play" with
the internal representation according to the IEEE Std, including
to print it in various formats.

Initially, I made this work for the Linux/i386 platform only.  Later,
I tweaked it for Mac OS X (different byte order).  It supports only the
IEEE Std Single and Double format (not Extended).

I would like to make this unit available, but hesitate, because of
its platform dependence (and currently limited platform support).

Question 1: Is there an interest in such a unit?

Question 2: Any suggestions as to how to make it more platform independent,
or how to support multiple platforms in an easy way?

Looking forward to some feedback,

        Tom Verhoeff
--
E-MAIL: T.Verhoeff @ TUE.NL     | Fac. of Math. & Computing Science
PHONE:  +31 40 247 41 25        | Eindhoven University of Technology
FAX:    +31 40 247 54 04        | PO Box 513, NL-5600 MB Eindhoven
http://www.win.tue.nl/~wstomv/  | The Netherlands
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Re: Floating-point number representation on various platforms

Jonas Maebe-2

On 05 Feb 2006, at 13:32, Tom Verhoeff wrote:

> Question 2: Any suggestions as to how to make it more platform  
> independent,
> or how to support multiple platforms in an easy way?

The only differences are little/big endian. So if it works on PPC and  
I386, you have support for all platforms. Just use {$ifdef  
FPC_LITTLE_ENDIAN}


Jonas
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Re: Floating-point number representation on various platforms

Tom Verhoeff
On Sun, Feb 05, 2006 at 01:39:25PM +0100, Jonas Maebe wrote:

>
> On 05 Feb 2006, at 13:32, Tom Verhoeff wrote:
>
> >Question 2: Any suggestions as to how to make it more platform  
> >independent,
> >or how to support multiple platforms in an easy way?
>
> The only differences are little/big endian. So if it works on PPC and  
> I386, you have support for all platforms. Just use {$ifdef  
> FPC_LITTLE_ENDIAN}

[This is about IEEE floating-point numbers]

Two further questions.

Which platforms use which endian?  (Of course, I could just experiment,
or maybe even read the FPC source, but asking is simpler. :-)

When I looked at my code again, it seems to me that the change that I made
to support both PPC and I386 is not endian-related, but I may be wrong,
or it may be more complicated.

So, here are some pieces of the code, it uses a variant array to
access the bits of the IEEE floating-point numbers in Single and Double:
-----
interface

const
  SignIndexSingle =    31; { position of sign bit in single format }
  ExpSizeSingle   =     8; { size of exponent field in single format }
  MaxExpSingle    =   255;
  ExpBiasSingle   =   127;
  EminSingle      = 1 - ExpBiasSingle;
  EmaxSingle      = MaxExpSingle - 1 - ExpBiasSingle;
  FracSizeSingle  =    23; { size of fraction field in single format }

type
  BitIndexSingle = 0 .. SignIndexSingle;
  ConvertSingle = record
    case Boolean of
      False: ( d: Single )
    ; True : ( s: set of BitIndexSingle )  { i in s == bit i = 1 }
    end;

procedure WriteBitsSingle ( const x: Single );
procedure WriteBinarySingle ( const x: Single );
function PowerOf2Single ( const x: Single; n: Integer ): Single;

const
  SignIndexDouble =    63; { position of sign bit in double format }
  ExpSizeDouble   =    11; { size of exponent field in double format }
  MaxExpDouble    =  2047;
  ExpBiasDouble   =  1023;
  EminDouble      = 1 - ExpBiasDouble;
  EmaxDouble      = MaxExpSingle - 1 - ExpBiasDouble;
  FracSizeDouble  =    52; { size of fraction field in double format }

type
  BitIndexDouble = 0 .. SignIndexDouble;
  ConvertDouble = record
    case Boolean of
      False: ( d: Double )
    ; True : ( s: set of BitIndexDouble )  { i in s == bit i = 1 }
    end;

procedure WriteBitsDouble ( const x: Double );
procedure WriteBinaryDouble ( const x: Double );
procedure FlipBitDouble ( var x: Double; i: BitIndexDouble );
function PowerOf2Double ( const x: Double; n: Integer ): Double;
-----

It turns out that my code for the Single type works on both PPC
and I386 without change.  However for Double, I had to write e.g.

-----
procedure WriteBitsDouble ( const x: Double );
  var c: ConvertDouble; i, i_: BitIndexDouble;
  begin
    with c do begin
      d := x

    ; for i := SignIndexDouble downto 0 do begin
{$IFDEF CPUPOWERPC}
        i_ := (i + 32) mod 64
{$ENDIF}
{$IFDEF CPUI386}
        i_ := i
{$ENDIF}
      ; if i_ in s then write ( '1' )
        else write ( '0' )
      ; if i in [ SignIndexDouble, SignIndexDouble - ExpSizeDouble ] then
          write ( ' ' )
      end { for i }

    end { with c }
  end; { WriteBitsDouble }
-----

That is, the lower and upper 32 bits (4 bytes) got swapped.

Maybe this is the case because both the 64-bit set and the Double
get allocated differently depending on endianess?

Can someone enlighten me?

Thanks,

        Tom
--
E-MAIL: T.Verhoeff @ TUE.NL     | Fac. of Math. & Computing Science
PHONE:  +31 40 247 41 25        | Eindhoven University of Technology
FAX:    +31 40 247 54 04        | PO Box 513, NL-5600 MB Eindhoven
http://www.win.tue.nl/~wstomv/  | The Netherlands
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Re: Floating-point number representation on various platforms

Tom Verhoeff
On Sat, Feb 18, 2006 at 09:43:31AM +0100, Tom Verhoeff wrote:
>
> So, here are some pieces of the code, it uses a variant array to
> access the bits of the IEEE floating-point numbers in Single and Double:

That should be 'record' insteady of 'array', of course.

        Tom
--
E-MAIL: T.Verhoeff @ TUE.NL     | Fac. of Math. & Computing Science
PHONE:  +31 40 247 41 25        | Eindhoven University of Technology
FAX:    +31 40 247 54 04        | PO Box 513, NL-5600 MB Eindhoven
http://www.win.tue.nl/~wstomv/  | The Netherlands
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