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 | | From: | Krishna Myneni | | Subject: | FMOD in Forth | | Date: | Fri, 21 Jan 2005 21:43:30 -0800 |
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 | [I tried to reply to Anton's original message, but it was apparently
deleted from my newsgroup server. It is copied below, and belongs as
part of the FMOD in Forth thread].
Anton Ertl wrote:
> Krishna Myneni writes:
>
>> After re-reading DPANS94, Floating Point Extensions,
>> I find there is no equivalent of the C library function
>> fmod() which returns the remainder (fractional part) of
>> the result of dividing two fp numbers. Needing this, I
>> had to resort to the clumsy and inefficient source level
>> definition
>
>
>> : FMOD ( f1 f2 -- f | remainder of f1/f2 )
>> FOVER FOVER F/ F>D D>F F* F- ;
>
>
> It divides flags?-) Floats are indicated by an r prefix.
>
Ok. This is an overdue reply. As some of you already know,
we have had two new additions to our family: our twin
daughters. So I've had my hands full, literally, day and night.
[Mother and daughters are doing fine]. Well, onto the reply.
stack notation: f to represent a floating pt number.
I don't believe I'm the first to use this notation. In
fact I probably picked it up from my days working with
LMI Forth.
> This is an explicitly round-towards-zero-symmetric operation, whereas
> MOD in Forth does not define division rounding and FM/MOD is
> explicitly floored. Maybe it should be called FREM in analogy with
> SM/REM (OTOH, there is the C name fmod() as precedent). OTOH, there
> is a C function drem(), which works with round-to-nearest division.
>
IMO, the Forth FMOD should mimick the C fmod() function. I haven't
actually tested the C fmod() to see what the division rounding is,
but I suspect it is truncation towards zero, as provided by F>D
in my Forth definition.
> Is there any reason why you find the round-to-0 variant preferable
> over the other two?
>
Yes. Round to nearest or flooring is not as useful, because when
working with positive real numbers for the two arguments, we would
like a positive modulus, rather than a negative one. As an example,
suppose we want to take the fp modulus of 270e and 360e. If we round
270e/360e to the nearest integer, rather than truncate towards zero, we
would get a rounded quotient of 1e, rather than 0e. Then FMOD would
return -90e rather than 270e. The latter is consistent with what we
expect from a modulus function (and consistent with MOD, e.g. 270 360 MOD).
>> FMOD is particularly useful for calculations involving
>> angles, which are quite common.
>
>
> Hmm, a round-towards-zero 2pi FMOD produces results between 2pi and
> -2pi, whereas a round-to-nearest 2pi FMOD produces results between pi
> and -pi, and a floored 2pi FMOD produces results between 2pi and 0.
>
Results in the range 0 to 2pi or 0 to -2pi are preferred, because they
are easy to visualize in terms of a phase angle for a wave. When one
visualizes a vector spinning on the unit circle in a counterclockwise
fashion, it is easier to think of the angle as changing continuously
from 0 to 2pi, rather than suffering a discontinuity in sign at pi.This
is standard in the physical sciences, although mathematically it is
equivalent to using the range -pi to pi.
> - anton
> --
> M. Anton Ertl http://www.complang.tuwien.ac.at/anton/home.html
> comp.lang.forth FAQs: http://www.complang.tuwien.ac.at/forth/faq/toc.html
>
Krishna
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