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Re: Fixed-point arithmetic library

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Robert Klemme schrieb:
> On 27.02.2012 02:50, Arne Vajhøj wrote:
>> On 2/26/2012 7:59 PM, glen herrmannsfeldt wrote:
>>> Robert Klemme<shortcutter@googlemail.com> wrote:
>>>
>>> (snip)
>>>>> I would quite like to represent some numbers in fixed point,
>>>>> and do arithmetic with them.
>>>
>>>> Fixed point math is susceptible to precision issues which can
>>>> be more severe than those of float and double: 0.01 * 0.2 -> 0.00
>>>
>>> In PL/I, if you multiply, you get the appropriate number if digits
>>> after the radix point.
>>>
>>> FIXED DECIMAL(3,2) times FIXED DECIMAL(2,1) generates a
>>> product of FIXED DECIMAL(5,3). If you force it to throw away
>>> low order digits, then, yes you can lose precision.
>>
>> That is rather similar to how BigDecimal works.
>
> And that is not exactly how FP arithmetic is described in Wikipedia:
>
> "For simplicity, fixed-point multiply procedures use the same result
> format as the operands. This has the effect of keeping the middle bits;
> the I-number of least significant integer bits, and the Q-number of most
> significant fractional bits. Fractional bits lost below this value
> represent a precision loss which is common in fractional multiplication.
> If any integer bits are lost, however, the value will be radically
> inaccurate."
>
> It boils down to how fixed "fixed" is. In my understanding decimal
> places are fixed throughout the whole calculation which is not what BD
> does (obviously to avoid precision loss).
>
> Kind regards
>
> robert
>

In this respect fixnums and limited precission floating point
numbers are not that different. Take a single precission
floating point number from Java:

    float a, b;

The above has 23-bit mantissa, which amounts to ~8 decimal
digits. If you multiply two numbers you don't get ~16
decimal digits, it is also rounded to ~8 decimals.

The difference between fixnums and floating point numbers
is only, that fixnums have no exponent. The exponent
floating points extends the range but not the precision.

For fixnums you have to be a little bit more careful
with the range. Adapt your choice of fixnums to the
expected range of your application.

BigDecimals are not fixnums per-se. They are also
floating point, but precision can be arbirary high. So
they are not limited precision floating points.

Bye

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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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