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MathGroup Archive 2004

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Re: bug in IntegerPart ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47813] Re: bug in IntegerPart ?
  • From: Jon Harrop <jdh30 at cam.ac.uk>
  • Date: Tue, 27 Apr 2004 04:48:07 -0400 (EDT)
  • Organization: University of Cambridge
  • References: <c6g015$4lk$1@smc.vnet.net> <c6ibta$6i2$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

AC wrote:
> Your 'explanation' makes no sense whatsoever. Mathematica's binary
> representations of 1.65-1.3 and 0.35 are the same.

No, they are not.

> That can be seen by
> comparing
>   BaseForm[1.65 - 1.3, 2]
> with
>   BaseForm[0.35,2]

BaseForm[...] gives you fewer digits than RealDigit[...], so it isn't giving
you enough of them...

> The problem occurs because Mathematica changes, what is apparently
> intended as an exact number, 1.65-1.3 (=0.35) to 0.34999999999999987
> but leaves 0.35 unchanged.
[SNIP]
> I admit to be utterly confused by that loss of accuracy and precision.

Are you asking why:

Table[N[165/100, i] - N[13/10, i] === N[35/100, i], {i, 100}]

Exhibits a sudden change in the treatment of numbers when machine precision
is exceeded?

> Additionally, a completely legitimate expression
> 2^^BaseForm[0.35`, 2]
> produces a syntax error message.

Then it is not a legitimate expression. ;-)

Mathematica does perform some naughtinesses with floating-point arithmetic.
Plus[...] is still "orderless" (commutative), even though it shouldn't be
for this arithmetic, e.g. a+b-a == b is not true in general.

Cheers,
Jon.


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