Groups > comp.soft-sys.math.mathematica > #3534

Re: Bug 1+4/10

From	Daniel Lichtblau <danl@wolfram.com>
Newsgroups	comp.soft-sys.math.mathematica
Subject	Re: Bug 1+4/10
Date	2011-07-07 11:35 +0000
Organization	Steven M. Christensen and Associates, Inc and MathTensor, Inc.
Message-ID	<iv45lp$f3e$1@smc.vnet.net> (permalink)
References	<iv1acv$sk7$1@smc.vnet.net>

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On Jul 6, 4:37 am, "slawek" <sla...@host.pl> wrote:
> Let check
>
> In[1]:= 1.4 == 1 + 4/10
> Out[1]= True
>
> In[2]:= a = SetPrecision[1.4, 30]
> Out[2]= 1.39999999999999991118215802999
>
> In[3]:= b = SetPrecision[1 + 4/10, 30]
> Out[3]= 1.40000000000000000000000000000
>
> No comment is needed.
>
> slawek

(1) Approximate numbers in Mathematica are internally stored and
manipulated in a binary base.

(2) Given an approximate number, SetPrecision will pad with binary
zeros if requested to set to a precision that is greater than the
precision of the input.

The result Out[2] shown above is a consequence of these.

In a bit (well, a few bits...) more detail:

In[24]:= bits = RealDigits[1.4,2]

Out[24]//InputForm=
{{1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1,
1, 0,
 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1,
0, 0,
 1, 1, 0}, 1}

In[25]:= morebits = PadRight[bits[[1]], Floor[20*Log[2,10]]]

Out[25]//InputForm=
{1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1,
1, 0,
0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1,
0, 0, 1,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

In[26]:= rational = FromDigits[{morebits, bits[[2]]}, 2]

Out[26]//InputForm= 3152519739159347/2251799813685248

In[27]:= N[rational,20]

Out[27]//InputForm=
1.399999999999999911182158029987476766109466552734375`20.

Daniel Lichtblau
Wolfram Research

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Thread

Bug  1+4/10 "slawek" <slawek@host.pl> - 2011-07-06 09:37 +0000
  Re: Bug  1+4/10 Peter Breitfeld <phbrf@t-online.de> - 2011-07-06 11:06 +0000
    Re: Bug  1+4/10 "slawek" <slawek@host.pl> - 2011-07-07 11:41 +0000
  Re: Bug  1+4/10 "Oleksandr Rasputinov" <oleksandr_rasputinov@hmamail.com> - 2011-07-07 11:27 +0000
    Re: Bug  1+4/10 "slawek" <human@site.pl> - 2011-07-08 08:52 +0000
    Re: Bug  1+4/10 "Oleksandr Rasputinov" <oleksandr_rasputinov@hmamail.com> - 2011-07-09 11:41 +0000
  Re: Bug 1+4/10 Daniel Lichtblau <danl@wolfram.com> - 2011-07-07 11:35 +0000

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