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Re: Fixed-point arithmetic library

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On 02/23/2012 02:03 PM, Gene Wirchenko wrote:
> On Thu, 23 Feb 2012 21:16:04 +0000, Tom Anderson
> <twic@urchin.earth.li>  wrote:
>
>> On Wed, 22 Feb 2012, Gene Wirchenko wrote:
>
> [snip]
>
>>>      I have been working with fixed-point arithmetic in JavaScript so
>>> that I can add dollar amounts exactly.  Maybe OP has something similar
>>> in mind, though with the number of digits of precision that he wants
>>> before the decimal point, I hope it is not currency-related.
>>
>> It is currency-related. What's wrong with that?
>
>       You are dealing with monstrously-large numbers.  National debts
> or something similar?
>
>       If you only needed up to fifteen [decimal] digits of precision total, you
> could use IEEE 754 64-bit floating point format and store integers.
> They will be stored exactly.  IEEE 754 is the only number format that
> JavaScript exposes for variable types (though it does use 32-bit
> integers internally on some operations).
>
>       I had to experiment with this, but I got it working.
>
>       Looking up further, according to Wikipedia, there is a 128-bit
> format that has 34.02 [decimal] digits of precision.  If your target language
> has this format as one of its number types, you could store integers
> in such variables.  You did state that you need 30 [decimal] digits of
> precision, so this would fit.  This would be a cheap, fairly simple
> solution.

Are you taking into account the precision of intermediate results?

If you multiply to 30-digit values you need 60 digits of precision to 
represent the calculation.

This is a good time to recommend that everyone read "What Every Computer 
Scientist Should Know About Floating Point Arithmetic", by David Goldberg.

-- 
Lew
Honi soit qui mal y pense.
http://upload.wikimedia.org/wikipedia/commons/c/cf/Friz.jpg

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Fixed-point arithmetic library Tom Anderson <twic@urchin.earth.li> - 2012-02-22 21:39 +0000
  Re: Fixed-point arithmetic library Jan Burse <janburse@fastmail.fm> - 2012-02-22 22:59 +0100
    Re: Fixed-point arithmetic library Tom Anderson <twic@urchin.earth.li> - 2012-02-23 21:15 +0000
      Re: Fixed-point arithmetic library markspace <-@.> - 2012-02-23 13:53 -0800
      Re: Fixed-point arithmetic library Robert Klemme <shortcutter@googlemail.com> - 2012-02-23 23:21 +0100
      Re: Fixed-point arithmetic library Jan Burse <janburse@fastmail.fm> - 2012-02-24 00:02 +0100
  Re: Fixed-point arithmetic library Robert Klemme <shortcutter@googlemail.com> - 2012-02-22 23:13 +0100
    Re: Fixed-point arithmetic library Gene Wirchenko <genew@ocis.net> - 2012-02-22 14:59 -0800
      Re: Fixed-point arithmetic library Martin Gregorie <martin@address-in-sig.invalid> - 2012-02-23 01:05 +0000
        Re: Fixed-point arithmetic library Tom Anderson <twic@urchin.earth.li> - 2012-02-23 21:21 +0000
          Re: Fixed-point arithmetic library Gene Wirchenko <genew@ocis.net> - 2012-02-23 13:49 -0800
      Re: Fixed-point arithmetic library Tom Anderson <twic@urchin.earth.li> - 2012-02-23 21:16 +0000
        Re: Fixed-point arithmetic library Gene Wirchenko <genew@ocis.net> - 2012-02-23 14:03 -0800
          Re: Fixed-point arithmetic library Lew <noone@lewscanon.com> - 2012-02-23 14:42 -0800
            Re: Fixed-point arithmetic library Gene Wirchenko <genew@ocis.net> - 2012-02-23 15:08 -0800
        Re: Fixed-point arithmetic library Martin Gregorie <martin@address-in-sig.invalid> - 2012-02-23 23:05 +0000
    Re: Fixed-point arithmetic library glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2012-02-27 00:59 +0000
      Re: Fixed-point arithmetic library Arne Vajhøj <arne@vajhoej.dk> - 2012-02-26 20:50 -0500
        Re: Fixed-point arithmetic library Robert Klemme <shortcutter@googlemail.com> - 2012-02-27 07:32 +0100
          Re: Fixed-point arithmetic library Jan Burse <janburse@fastmail.fm> - 2012-02-27 13:46 +0100
  Re: Fixed-point arithmetic library Roedy Green <see_website@mindprod.com.invalid> - 2012-02-24 16:26 -0800

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