68k Was: Re: Math Error?

[William Squires <wsquires at satx dot rr dot com>]

IIRC, the 68040 uP from Motorola (now Freescale) had an extended  
format, too... at least for the "real" 68040 (not the LC040).
On Jul 28, 2006, at 12:45 PM, Joseph wrote:

> If I recall correctly the intel chip has an "extended precision"  
> format that
> uses 80 bits when doing calculation.  These are used during calculation
> regardless of the original floating point format.  So if the values in  
> the
> calculation are single precision (one's compliment 24 bit mantissa  
> with an 8
> bit exponent) the full 80 bits are used as 'guard bits' to increase the
> precision of the calculation.  Of course the result is then truncated  
> to
> single precision.  In High Level Assembly (Randall Hyde's interesting  
> fusion
> of assembly and high level language constructs) you can declare an 80  
> bit
> value.
>
> ~joe
>
> -----Original Message-----
> From: realbasic-nug-bounces at lists dot realsoftware dot com
> [mailto:realbasic-nug-bounces at lists dot realsoftware dot com] On Behalf Of  
> Peter K.
> Stys
> Sent: Friday, July 28, 2006 11:36 AM
> To: REALbasic NUG
> Subject: Re: Re: Math Error?
> Actually we're both right and wrong:
>
> In[55]:=RealDigits[0.036,2,100]
>
> Out[55]={{1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,1,0,1 
> ,0,0,
> 1,1,1,1,
>      
> 1,1,0,1,1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 
> ,
>     0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},-4}
>
> Shows that 0.036 can be represented exactly in binary, but requires 51
> significant digits (if I counted correctly to the last 1).  So with a
> 64 bit double, it probably just missed the # of digits in the mantissa
> to represent 0.036 exactly.
> Nuf time wasted on this, just a curiosity.
>
> P.
>
> --
> ----------------------------------------------------------------------- 
> -----
> ---
> Peter K. Stys, MD
> Professor of Medicine(Neurology), Senior Scientist
> Ottawa Health Research Institute, Div. of Neuroscience
> Ottawa Hospital / University of Ottawa
> Ontario, CANADA
> tel:    (613)761-5444
> fax:    (613)761-5330
> http://www.ohri.ca/profiles/stys.asp
> realsoftware.com/listarchives/lists.html>
>
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William H Squires Jr
4400 Horizon Hill #4006
San Antonio, TX 78229
wsquires at satx dot rr dot com dot nospam <- remove the .nospam

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