Groups > comp.soft-sys.math.mathematica > #3468

Numerical accuracy/precision - this is a bug or a feature?

From	"slawek" <slawek@host.pl>
Newsgroups	comp.soft-sys.math.mathematica
Subject	Numerical accuracy/precision - this is a bug or a feature?
Date	2011-07-04 10:47 +0000
Organization	Steven M. Christensen and Associates, Inc and MathTensor, Inc.
Message-ID	<ius5op$2g7$1@smc.vnet.net> (permalink)

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Let Mathematica (6.x, 7.x) compute quite a simple product

In[1]:= N[N[2.0, 20] * N[Sqrt[2] , 20], 20]

Out[1]= 2.82843

This is a bug.

Why?

Now we analyze it in details:

1. N[2.0,20] should give 2 with accuracy/precision/whatsever about 20 
decimal digits, i.e. 2.00000000000000000000

2. Sqrt[2] should give... Sqrt[2]

3. N[Sqrt[2]] should give 1.4142135623730950488 (this is copy-paste from 
Mathematica output to N[Sqrt[2]] )

4. The product 2.00000000000000000000 * 1.4142135623730950488 is 
2.8284271247461900976 (again copy-paste)

5. BUT THE RESULT OF  N[2.0, 20] * N[Sqrt[2] , 20]  "truncated to 20 digits" 
is Out[1]= 2.82843

Where are missing digits?!

slawek

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Numerical accuracy/precision - this is a bug or a feature? "slawek" <slawek@host.pl> - 2011-07-04 10:47 +0000
  Re: Numerical accuracy/precision - this is a bug or a feature? "Kevin J. McCann" <kjm@KevinMcCann.com> - 2011-07-04 11:14 +0000
    Re: Numerical accuracy/precision - this is a bug or a feature? "slawek" <slawek@host.pl> - 2011-07-05 09:17 +0000
      Re: Numerical accuracy/precision - this is a bug or a feature? "Kevin J. McCann" <Kevin.McCann@umbc.edu> - 2011-07-06 09:35 +0000
        Re: Numerical accuracy/precision - this is a bug or a feature? "slawek" <slawek@host.pl> - 2011-07-07 11:40 +0000
      Re: Numerical accuracy/precision - this is a bug or a feature? Daniel Lichtblau <danl@wolfram.com> - 2011-07-07 11:34 +0000
    Re: Numerical accuracy/precision - this is a bug or a feature? "Oleksandr Rasputinov" <oleksandr_rasputinov@hmamail.com> - 2011-07-06 09:39 +0000
      Re: Numerical accuracy/precision - this is a bug or a feature? Richard Fateman <fateman@cs.berkeley.edu> - 2011-07-07 11:33 +0000
    Re: Numerical accuracy/precision - this is a bug or a feature? Noqsi <noqsiaerospace@gmail.com> - 2011-07-08 08:51 +0000
      Re: Numerical accuracy/precision - this is a bug or a feature? "slawek" <slawek@host.pl> - 2011-07-12 11:01 +0000
    Re: Numerical accuracy/precision - this is a bug or a feature? "Oleksandr Rasputinov" <oleksandr_rasputinov@hmamail.com> - 2011-07-08 09:04 +0000
      Re: Numerical accuracy/precision - this is a bug or a feature? Richard Fateman <fateman@cs.berkeley.edu> - 2011-07-09 11:34 +0000
      Re: Numerical accuracy/precision - this is a bug or a feature? "slawek" <slawek@host.pl> - 2011-07-12 11:02 +0000
    Re: Numerical accuracy/precision - this is a bug or a feature? "Oleksandr Rasputinov" <oleksandr_rasputinov@hmamail.com> - 2011-07-09 11:37 +0000
      Re: Numerical accuracy/precision - this is a bug or a feature? Noqsi <noqsiaerospace@gmail.com> - 2011-07-13 07:11 +0000
        Re: Numerical accuracy/precision - this is a bug or a feature? Richard Fateman <fateman@cs.berkeley.edu> - 2011-07-14 09:23 +0000
        Re: Numerical accuracy/precision - this is a bug or a feature? Andrzej Kozlowski <akoz@mimuw.edu.pl> - 2011-07-15 01:19 +0000
        Re: Numerical accuracy/precision - this is a bug or a feature? "W. Craig Carter" <ccarter@mit.edu> - 2011-07-15 01:25 +0000
        Re: Numerical accuracy/precision - this is a bug or a feature? Andrzej Kozlowski <akoz@mimuw.edu.pl> - 2011-07-15 08:12 +0000
        Re: Numerical accuracy/precision - this is a bug or a feature? Andrzej Kozlowski <akoz@mimuw.edu.pl> - 2011-07-16 09:45 +0000
        Re: Numerical accuracy/precision - this is a bug or a feature? Andrzej Kozlowski <akoz@mimuw.edu.pl> - 2011-07-16 09:40 +0000
    Re: Numerical accuracy/precision - this is a bug or a feature? Noqsi <noqsiaerospace@gmail.com> - 2011-07-13 07:12 +0000
    Re: Numerical accuracy/precision - this is a bug or a feature? Noqsi <noqsiaerospace@gmail.com> - 2011-07-15 01:23 +0000
      Re: Numerical accuracy/precision - this is a bug or a feature? Richard Fateman <fateman@cs.berkeley.edu> - 2011-07-15 08:10 +0000
    Re: Numerical accuracy/precision - this is a bug or a feature? Noqsi <noqsiaerospace@gmail.com> - 2011-07-16 09:41 +0000
      Re: Numerical accuracy/precision - this is a bug or a feature? Richard Fateman <fateman@cs.berkeley.edu> - 2011-07-17 10:02 +0000
        Re: Numerical accuracy/precision - this is a bug or a feature? "slawek" <slawek@host.pl> - 2011-07-18 10:14 +0000
      Re: Numerical accuracy/precision - this is a bug or a feature? Andrzej Kozlowski <akoz@mimuw.edu.pl> - 2011-07-18 10:17 +0000
        Re: Numerical accuracy/precision - this is a bug or a feature? Richard Fateman <fateman@cs.berkeley.edu> - 2011-07-19 10:55 +0000
  Re: Numerical accuracy/precision - this is a bug or a feature? "Kevin J. McCann" <kjm@KevinMcCann.com> - 2011-07-04 11:18 +0000
    Re: Numerical accuracy/precision - this is a bug or a feature? Richard Fateman <fateman@cs.berkeley.edu> - 2011-07-05 09:15 +0000
      Re: Numerical accuracy/precision - this is a bug or a feature? "slawek" <slawek@host.pl> - 2011-07-06 09:34 +0000
      Re: Numerical accuracy/precision - this is a bug or a feature? Daniel Lichtblau <danl@wolfram.com> - 2011-07-07 11:35 +0000
        Re: Numerical accuracy/precision - this is a bug or a feature? Richard Fateman <fateman@cs.berkeley.edu> - 2011-07-08 08:53 +0000

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