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Re: bug in IntegerPart ?

• To: mathgroup at smc.vnet.net
• Subject: [mg47850] Re: bug in IntegerPart ?
• From: ancow65 at yahoo.com (AC)
• Date: Wed, 28 Apr 2004 06:56:52 -0400 (EDT)
• References: <c6l8dj$isr$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Bill Rowe <readnewsciv at earthlink.net> wrote in message news:<c6l8dj$isr$1 at smc.vnet.net>...
> On 4/26/04 at 2:41 AM, ancow65 at yahoo.com (AC) wrote:
> 
> >"DrBob" <drbob at bigfoot.com> wrote in message
> >news:<c6g015$4lk$1 at smc.vnet.net>...
> >>There's NO reason to be puzzled. 1.65 and 1.3 can't be represented
> >>exactly in binary, so of course their difference may not be exact,
> >>either. Hence the division problems have different numerators.
> >
> >Your 'explanation' makes no sense whatsoever. Mathematica's binary
> >representations of 1.65-1.3 and 0.35 are the same. That can be seen
> >by comparing BaseForm[1.65 - 1.3, 2] with BaseForm[0.35,2]
> 
> BaseForm isn't doing what you think and will not show the difference. BaseForm controls only the display of a number. By default Mathematica displays a number to 6 significant digits. Both 1.65 - 1.3 and .35 are the same to 6 significant digits. Consequently, these will display the same when using BaseForm.
> 
> To see the difference use RealDigits or FullForm. Both of these clearly show the difference between 1.65 - 1.3 and .35.

The decimal numbers (1.65 - 1.3) and .35 are identical. The way
Mathematica performs subtraction makes them different.

> 
> >(n = 2^^0.010110011001100110011 )
> > => 0.350000
> 
> Right, here you've inputed a number accurate to 6 significant digits. So, Mathematica displays 6 significant digits

When I type 0.35, Mathematica assumes the machine precision. 

Precision[0.35]
=> MachinePrecision

% // N 
=> 15.9546

Isn't that natural to expect similar for binary numbers?

> 
> > Notice the unussual display of trailing zeros. 
> 
> No, not unusual. Exactly as it should be. If I input 6 significant digits as
> 
> .35`6, I expect Mathematica to display 6 significant digits with the default settings.

And, I guess, you don't see any problems with these three inputs 
 0.350000000000
 N[0.350000000000, 6]
 0.35`2
producing the same output 0.35.


> 
> >Additionally, a completely legitimate expression
> >2^^BaseForm[0.35`, 2]
> >produces a syntax error message.
> 
> The expression 2^^BaseForm[0.35, 2] isn't a legitimate expression. BaseForm puts a wrapper on the expression to control display. That is Head at BaseForm[0.35, 2] is BaseForm, not a sequence of binary digits. 

BaseForm[0.35, 2] might be wrong as argument for 2^^#& but still it is
not a syntax error. Would you agree that the following expression
(which also generates a syntax error) is legitimate?

  fun := 2^^# & 

What about this syntax error?
  x=1;
  2^^x

In better design 2^^BaseForm[0.35, 2] should return 0.35` or at
minimum unchanged expression.

AC

• Follow-Ups:
  • Re: Re: bug in IntegerPart ?
    • From: Daniel Lichtblau <danl@wolfram.com>