Re: Calculator Accuracy

From	Paul Sture <nospam@sture.ch>
Newsgroups	comp.misc
Subject	Re: Calculator Accuracy
Date	2014-05-10 21:24 +0200
Organization	PostgreSQL and SQLite
Message-ID	<30b24b-a982.ln1@news.chingola.ch> (permalink)
References	<lkfa27$661$1@dont-email.me>

Show all headers | View raw

On 2014-05-08, Gordon Henderson <gordon+usenet@drogon.net> wrote:
> The BASIC is 50 thread, having diverged into floating point issues has
> reminded me of a standard test that wa applied in all the schools where
> I lived to determine if a calculator would be suitable for school use.
>
> Put calculator into degrees mode, enter 45, then push SIN, COS, TAN,
> then the inverses - INV-TAN, INV-COS and INV-SIN - then subtract 45 and
> see what the result is.
>
> With that, you do expect some rounding, but a lot of calculators were
> so far off the mark it was quite incredible.
>
> No-longer having a desktop scientific calculator (that works), I've
> just tried it with gcalctool under my Linux desktop and given up. It's
> a bloody calculator for goodness sake, not something I want to TYPE at!!!
>
> Doing it using my RTB BASIC (standard IEEE 64-bit doubles), I end up
> with -3.606714927e-11.

And we didn't have the IEEE floating point standard before the 1980s.

Lots of good reading in this paper:

"Why do we need a floating-point arithmetic standard?
by W. Kahan, University of California at Berkeley, February 12, 1981

<http://www.cs.berkeley.edu/~wkahan/ieee754status/why-ieee.pdf>

Page 5: a table of the different floating point formats and their 
Over/Underflow Thresholds on different machines

Chapter 11 Programmers vs. Users vs. Computer Salesmen (Page 26) 
gives a good explanation:

"For instance, consider an engineer who has to cope with data and results
to 3 or 4 significant decimals; experience teaches him to calculate with
at least 7 or 6 significant decimals, so he looks for applications
programs and computer systems that will guarantee that much accuracy. The
applications programmers, asked to guarantee the correctness of 7 or 8
significant decimals, demand 14 or 15 from their computer system and its
supporting library. The library programmers play it safe too; they ask for
30. Computer architects obligingly offer 33. The engineer who accepts this
rationale may unknowingly be squandering 3/4 of his system’s data memory
and 9/10 of its speed as well as the opportunity to obtain a satisfactory
system on one chip. I think I have exaggerated the situation here, but
only to emphasize how heavily important decisions will hang upon what
the user and various programmers believe to be practical."

-- 
Paul Sture

The final step of #heartbleed recovery is to call your mother, and advise
her to change her maiden name                                  -- @gojomo

Thread

Calculator Accuracy Gordon Henderson <gordon+usenet@drogon.net> - 2014-05-08 07:00 +0000
  Re: Calculator Accuracy David Hume <David.Hume@example.com> - 2014-05-08 08:39 +0100
  Re: Calculator Accuracy Andy Burns <usenet.feb2014@adslpipe.co.uk> - 2014-05-08 09:14 +0100
    Re: Calculator Accuracy Andy Burns <usenet.feb2014@adslpipe.co.uk> - 2014-05-12 19:02 +0100
  Re: Calculator Accuracy "BartC" <bc@freeuk.com> - 2014-05-08 09:43 +0100
    Re: Calculator Accuracy Tim Streater <timstreater@greenbee.net> - 2014-05-08 09:53 +0100
      Re: Calculator Accuracy "BartC" <bc@freeuk.com> - 2014-05-08 10:22 +0100
        Re: Calculator Accuracy David Hume <David.Hume@example.com> - 2014-05-08 12:17 +0100
          Re: Calculator Accuracy RS Wood <rsw@therandymon.com> - 2014-05-08 14:09 +0000
            Re: Calculator Accuracy David Hume <David.Hume@example.com> - 2014-05-08 16:04 +0100
            Re: Calculator Accuracy Rich <rich@example.com> - 2014-05-08 16:49 +0000
              Re: Calculator Accuracy Rich <rich@example.com> - 2014-05-09 00:03 +0000
            Re: Calculator Accuracy Rich <rich@example.com> - 2014-05-09 00:10 +0000
              Re: Calculator Accuracy RS Wood <rsw@therandymon.com> - 2014-05-09 21:32 +0000
                Re: Calculator Accuracy Rich <rich@example.com> - 2014-05-10 03:30 +0000
            Re: Calculator Accuracy "G. Paul Ziemba" <paul+usenet@w6yx.stanford.edu> - 2014-05-09 03:43 +0000
    Re: Calculator Accuracy David Hume <David.Hume@example.com> - 2014-05-08 10:55 +0100
      Re: Calculator Accuracy "BartC" <bc@freeuk.com> - 2014-05-08 11:23 +0100
      Re: Calculator Accuracy Hils <hils@saynotospam.net> - 2014-05-08 12:09 +0100
        Re: Calculator Accuracy Hils <hils@saynotospam.net> - 2014-05-08 23:02 +0100
          Re: Calculator Accuracy Marc Auslander <marcslists@gmail.NOSPAM.com> - 2014-05-08 19:51 -0400
            Re: Calculator Accuracy Will Honea <whonea@whonea.net> - 2014-05-08 18:19 -0600
        Re: Calculator Accuracy Eric Pozharski <whynot@pozharski.name> - 2014-05-09 15:19 +0300
          Re: Calculator Accuracy David Hume <David.Hume@example.com> - 2014-05-09 19:06 +0100
            Re: Calculator Accuracy Eric Pozharski <whynot@pozharski.name> - 2014-05-10 08:38 +0300
              Re: Calculator Accuracy Eric Pozharski <whynot@pozharski.name> - 2014-05-12 09:30 +0300
          Re: Calculator Accuracy David Hume <David.Hume@example.com> - 2014-05-10 00:00 +0100
      Re: Calculator Accuracy Rich <rich@example.com> - 2014-05-08 11:40 +0000
  Re: Calculator Accuracy Rich <rich@example.com> - 2014-05-08 11:32 +0000
  Re: Calculator Accuracy Anssi Saari <as@sci.fi> - 2014-05-08 20:20 +0300
    Re: Calculator Accuracy Gordon Henderson <gordon+usenet@drogon.net> - 2014-05-08 17:40 +0000
      Re: Calculator Accuracy David Hume <David.Hume@example.com> - 2014-05-09 08:43 +0100
        Re: Calculator Accuracy Rich <rich@example.com> - 2014-05-09 10:42 +0000
        Re: Calculator Accuracy Whiskers <catwheezel@operamail.com> - 2014-05-09 21:56 +0100
      Re: Calculator Accuracy Geoff Clare <geoff@clare.See-My-Signature.invalid> - 2014-05-12 13:50 +0100
  Re: Calculator Accuracy Caecilius <nospam@spamless.invalid> - 2014-05-08 19:34 +0100
  Re: Calculator Accuracy Caecilius <nospam@spamless.invalid> - 2014-05-08 19:38 +0100
    Re: Calculator Accuracy Hils <hils@saynotospam.net> - 2014-05-08 22:06 +0100
  Re: Calculator Accuracy Paul Sture <nospam@sture.ch> - 2014-05-10 21:24 +0200
  Re: Calculator Accuracy Lewis <g.kreme@gmail.com.dontsendmecopies> - 2014-05-11 16:22 +0000
    Re: Calculator Accuracy Will Honea <whonea@whonea.net> - 2014-05-11 15:41 -0600
      Re: Calculator Accuracy Tim Streater <timstreater@greenbee.net> - 2014-05-11 23:02 +0100
  Re: Calculator Accuracy David Harmon <source@netcom.com> - 2014-05-12 18:20 -0700
  Re: Calculator Accuracy Yeechang Lee <ylee@pobox.com> - 2014-07-25 20:26 -0700

csiph-web