Re: Issues with rounding

There's a huge body of literature out there on BIGNUM algorithms including issues of
rounding.

A good start would be

http://en.wikipedia.org/wiki/Bignum

There is a classic joke about El Camino Real being known as El Camino Bignum. The story
is retold in

http://en.wikipedia.org/wiki/El_Camino_Real_(California)
joe


On Sat, 03 Mar 2007 11:05:44 -0600, "Doug Harrison [MVP]" <dsh@xxxxxxxx> wrote:

On 2 Mar 2007 12:10:09 -0800, "chris.dannemiller@xxxxxxxxx"
<chris.dannemiller@xxxxxxxxx> wrote:

Since the user is entering the data "18.05" I was wondering if there
was a way to round the string before I convert it to a float.

Certainly you can round the string representation. Start by converting the
string to mantissa and exponent, i.e. M = "1805" and E = 1. There is still
an implied decimal point so the number is really 1.805 x 10^1, but it's
easier to work on the string if you remove it. Now you need to determine
the position of the rounding digit. That's given by R = E+1+N, where N is
the number of decimal places you're rounding to. Now if M[R] == '5', work
backwards through the string until you reach something besides a '9' or
fall off the front of the string. If you reach a non-'9', increment it. If
you fall off the front, make the string "1" and increment the exponent.
Actually, if you store a '0' in the front of your buffer, then you can
always increment the digit at the cursor position once you stop the
backwards iteration. Then you truncate the string and reconstruct the
number for passing to a function like strtod. On the other hand, if M[R] <
'5', then truncate the string right there. Anyway, that's a sketch of an
algorithm. You'll have to be careful to avoid buffer overruns and
underruns, of course, and no doubt there are edge cases you'll need to
handle. Please note that once you convert "18.1" to FP, it may still be an
approximation; that is, you might end up with 18.100000000000001 or
something like that.

It seems
a trivial to approach it for decade based rounding 0.1, 0.01 ect. But
not trivial for other rounding criteria such as 0.25, 0.0625 ect.

The general formula is to divide by the rounding factor, add .5, truncate
to integer, and multiply by the factor. The idea is to treat the rounding
factor as a counting unit and convert the number to be rounded to the
nearest whole number multiple of this unit. Of course, all this
multiplication and division is subject to round-off error. I don't know how
you'd do it on the string representation.
Joseph M. Newcomer [MVP]
email: newcomer@xxxxxxxxxxxx
Web: http://www.flounder.com
MVP Tips: http://www.flounder.com/mvp_tips.htm
.

Relevant Pages

  • Re: Why (0.09+0.01-0.1) is not equal to 0.09+0.01-0.1 ?
    ... The binary to decimal conversion gives full accuracy by default, but also includes rounding algorithms since users will seldom care about hundreds of figures. ... Function D2BAs String ... the work involved in avoiding lost precision due to type conversion ... ' D2Dis sufficient to uniquely determine the binary representation of x ...
    (microsoft.public.excel)
  • Re: Why (0.09+0.01-0.1) is not equal to 0.09+0.01-0.1 ?
    ... > gives full accuracy by default, but also includes rounding algorithms ... > partitioned mantissa by without risk of overflow ... > Function D2BAs String ... the work involved in avoiding lost precision due to type ...
    (microsoft.public.excel)
  • Re: Decimal rounding function
    ... I'm searching for cheap, quick and easy rounding function in C, but (there ... double round (double number, unsigned decimalPlaces) { ... Rounding a floating-point to a specified number of decimal places is ... useful only if you're producing a string representation of the number. ...
    (comp.lang.c)
  • Re: ANN: FPOUT v2.0
    ... REPRESENT for negative string lengths? ... to be the number of significant digits. ... "Rounding" and "significant ... No ambiguity there. ...
    (comp.lang.forth)
  • Re: Round off
    ... rounding to two decimal places which necessarily gives a String. ... The OP asked about rounding a number to 2 decimals - not about converting it ... Number 3.5 is a multiple of ... FAQ 4.6 can be correspondingly changed. ...
    (comp.lang.javascript)
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