Converting Pascal Real's to Numeric

[wgcs]

I've been trying to adapt faq184-1932 Float64ToNum to work with the 48 bit Pascal Real data type.

So far, I've been unsuccessful...

Here's a description of the difference:

http://info.borland.com/techpubs/delphi/delphi5/oplg/memory.html

Here's my code so far:

LPARAMETERS Float48 AS STRING

* Pascal Real:
***  S MMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM EEEEEEEE
*    1 2345678 90123456 78901234 56789012 34567890 12345678
*               1          2          3          4

* 64 bit float:
*!*        S XXXXXXX XXXX MMMM MMMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM
*!*        0 0000000 0000 0000 00000000 00000000 00000000 00000000 00000000 00000000
*!*        1 2345678 9012 3456 78901234
*!*                   1           2         3

LOCAL SIGN AS INTEGER
LOCAL Bias AS INTEGER
LOCAL Exponent AS INTEGER
LOCAL I AS INTEGER
LOCAL x AS STRING
LOCAL Mantissa AS NUMBER
LOCAL OldDecimals AS INTEGER
LOCAL oldFixed AS STRING
IF LEN(Float48) < 6
  RETURN 0
ENDIF
*OldDecimals=SET(&quot;Decimals&quot;)
*SET DECIMALS TO 20
oldFixed=SET(&quot;Fixed&quot;)
SET FIXED OFF
Mantissa = 1
SIGN     = 0
Bias     = 129 && 64bit bias: 1023
Exponent = 0
Float48  = LEFT(Float48,6)

SIGN=IIF(BITTEST(ASC(LEFT(Float48,1)),7),-1,1)

FOR I=48 TO 41 STEP -1
  Exponent=Exponent+IIF(BITTEST(ASC(SUBSTR(Float48,INT((I-1)/8)+1,1)),7-MOD((I-1),8)),1,0) * (2^(47-I))
*  Exponent=Exponent+IIF(BITTEST(ASC(SUBSTR(Float64,INT((I-1)/8)+1,1)),7-MOD((I-1),8)),1,0)*(2^(12-I))
NEXT
Exponent=Exponent-bias

FOR I=2 TO 40
  AA=INT((I-1)/8)+1
  BB=7-MOD((I-1),8)
  B=IIF(BITTEST(ASC(SUBSTR(Float48,INT((I-1)/8)+1,1)),7-MOD((I-1),8)),1,0)
  Mantissa=Mantissa+IIF(BITTEST(ASC( SUBSTR(Float48,INT((I-1)/8)+1,1)), 7-MOD((I-1),8)),1,0) * (1/(2^(I-1)))
*  Mantissa=Mantissa+IIF(BITTEST(ASC(SUBSTR(Float64,INT((I-1)/8)+1,1)),7-MOD((I-1),8)),1,0)*(1/(2^(I-12)))
NEXT
SET FIXED &oldFixed
RETURN SIGN*(Mantissa)*(2^Exponent)
ENDFUNC

Any help would be appreciated!

 

[wgcs]

BTW: Here are some sample Real's to test with (generated by a Borland Pascal v7 program):

Literal value = ASCII char values representing a Pascal Real

1   = 129 0 0 0 0 0 
2   = 130 0 0 0 0 0 
10  = 132 0 0 0 0 32 
20  = 133 0 0 0 0 32 
100 = 135 0 0 0 0 72 
200 = 136 0 0 0 0 72 
0.1 = 125 205 204 204 204 76 
0.01= 122 113  61  10 215 35 
1.1 = 129 205 204 204 204 12

 

[wgcs]

Ok, I got it: It took me a while to realize that, finally, my conversion was correct, but that pascal was writing the real to the file 'backwards' (ie byte #6 comes first).

So, here's the working code:

* info from: [URL unfurl="true"]http://docs.sun.com/db/doc/801-5055/6hvhckkeh?a=view[/URL]
*            [URL unfurl="true"]http://info.borland.com/techpubs/delphi/delphi5/oplg/memory.html[/URL]
*            [URL unfurl="true"]http://www.tek-tips.com/faqs.cfm?spid=184&sfid=1932[/URL]
*              faq184-1932
* A 6-byte (48-bit) Real48 number is divided into three fields:
*
*   1 bit: Sign
*  39 bits: f (mantissa)
*   8 bits: e (exponent)
*  If 0 < e <= 255, the value v of the number is given by 
*     v = (-1)^s * 2^(e-129) * (1.f ) 
*  If e = 0, then v = 0. 

LPARAMETERS Float48 AS STRING

* Pascal Real:
***  S MMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM EEEEEEEE
*    1 2345678 90123456 78901234 56789012 34567890 12345678
*               1          2          3          4

* 64 bit float:
*!*        S XXXXXXX XXXX MMMM MMMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM
*!*        0 0000000 0000 0000 00000000 00000000 00000000 00000000 00000000 00000000
*!*        1 2345678 9012 3456 78901234
*!*                   1           2         3

LOCAL SIGN AS INTEGER
LOCAL Bias AS INTEGER
LOCAL Exponent AS INTEGER
LOCAL I AS INTEGER
LOCAL x AS STRING
LOCAL Mantissa AS NUMBER
LOCAL OldDecimals AS INTEGER
LOCAL oldFixed AS STRING
IF LEN(Float48) < 6
  RETURN 0
ENDIF
*OldDecimals=SET(&quot;Decimals&quot;)
*SET DECIMALS TO 20
oldFixed=SET(&quot;Fixed&quot;)
SET FIXED OFF
Mantissa = 1
SIGN     = 0
Bias     = 129 && 64bit bias: 1023
Exponent = 0
Float48  = LEFT(Float48,6)

SIGN=IIF( BITTEST(ASC(Float48),7), -1, 1)

FOR I=48 TO 41 STEP -1
*FOR I=12 TO 2 STEP -1
  AA = INT((I-1)/8)+1  && Find the appropriate Byte to look in
  BB = 7-MOD((I-1),8)  && Find the appropriate bit in that byte
  B = BITTEST(ASC(SUBSTR(Float48,AA,1)),BB)      && Find out if that bit is set
  
  Exponent=Exponent+IIF( B, 2^(48-I), 0) 
                        
*  Exponent=Exponent+IIF(BITTEST(ASC(SUBSTR(Float64,INT((I-1)/8)+1,1)),7-MOD((I-1),8)),1,0)*(2^(12-I))
NEXT
Exponent=Exponent-bias

FOR I=2 TO 40
*FOR I=13 TO 64
  AA = INT((I-1)/8)+1  && Find the appropriate Byte to look in
  BB = 7-MOD((I-1),8)  && Find the appropriate bit in that byte
  B = BITTEST(ASC(SUBSTR(Float48,AA,1)),BB)      && Find out if that bit is set
  Mantissa = Mantissa + IIF( B, 1/(2^(I-1)), 0 ) && If set, add to the total Mantissa
  
*  Mantissa=Mantissa+IIF(BITTEST(ASC(SUBSTR(Float64,INT((I-1)/8)+1,1)),7-MOD((I-1),8)),1,0)*(1/(2^(I-12)))
NEXT
SET FIXED &oldFixed
RETURN SIGN*(Mantissa)*(2^Exponent)
ENDFUNC

 

[DSummZZZ]

Glad we could help you out.


-Dave S.-

Even more Fox stuff at:

http://www.davesummers.net/foxprolinks.htm

 

[wgcs]

The FAQ (I don't know who wrote it... user name: 738262) was invaluable... but it was really frustrating when the info from converting the char's to the pieces of the Float just didn't make sense! I think I now have a handle on the math behind it, and everything just came clear when I realized the Real numbers were stored in reverse-byte-order.

Sometimes you just need a wall to bounce Ideas off of....