Well, there's a very simple fix for the problem we're seeing here. Here's
the definition of the remainder function, from vz.c (you don't have to read
the whole thing!)
ZF2(jtzrem){D a,b,d;Z q;
if(ZEZ(u))R v;
ZASSERT(!ZINF(v),EVNAN);
if(INF(u.re)&&!u.im&&!v.im){
if(u.re==inf )R 0<=v.re?v:u;
if(u.re==infm)R 0>=v.re?v:u;
}
ZASSERT(!ZINF(u),EVNONCE);
d=u.re*u.re+u.im*u.im;
a=u.re*v.re+u.im*v.im; q.re=tfloor(0.5+a/d);
b=u.re*v.im-u.im*v.re; q.im=tfloor(0.5+b/d);
R zminus(v,ztymes(u,q));
}
The offending code here is the "0.5+" when q.re and q.im are evaluated. q
should be the "integer division" of u by v, so that v - u*q (the last line)
will give us the remainder.
I'm looking into how this affects antibase just to check that I don't mess
anything up there. However, I think that barring backwards compatibility
issues, this is definitely a fix that needs to be made.
Marshall
On Sun, Jan 22, 2012 at 2:36 PM, Marshall Lochbaum <mwlochb...@gmail.com>wrote:
> That isn't what complex | does, or what it should do, I think. However, it
> is a consistent extension of "mod" to the complex numbers--we are just
> using a different subgroup of the complex numbers to mod out by.
> Note, however, that this approach adapts poorly to complex left arguments.
> It still works, by subtracting (real) integer multiples of x from y, but
> the resultant range is a weird bar in the complex plane.
> As you noted, it's easy to define your version in terms of real | .
>
> Marshall
>
>
> On Sun, Jan 22, 2012 at 2:27 PM, Bo Jacoby <bojac...@yahoo.dk> wrote:
>
>> I wanted to take 'mod' of the real part and leave the imaginary part
>> untouched.
>> f=:(|9&o.)+j.&(11&o.)&]
>> 7 f 73j73+i.6
>> 3j73 4j73 5j73 6j73 0j73 1j73
>> Perhaps this is not done by a complex '|' ?
>>
>>
>>
>>
>> >________________________________
>> > Fra: Marshall Lochbaum <mwlochb...@gmail.com>
>> >Til: Programming forum <programming@jsoftware.com>
>> >Sendt: 19:50 søndag den 22. januar 2012
>> >Emne: Re: [Jprogramming] 5|0 1 2 3 4 is not equal to 5|0 1 2 3 4 j.0
>> >
>> >It would be possible to change complex mod without changing floor. Floor
>> is
>> >consistent on reals and complex numbers, while complex mod is not, so it
>> >doesn't necessarily need to be fixed.
>> >
>> >The problem with complex mod is that for left argument b it that it
>> ensures
>> >that the result is in the box defined by corners -:(j./~ _0.5 0.5)*b .
>> That
>> >means that it subtracts the closest Gaussian integer multiple of b from
>> the
>> >right argument. This is inconsistent with mod for the reals, which
>> >subtracts the floor under division by b.
>> >
>> >Marshall
>> >
>> >On Sun, Jan 22, 2012 at 1:28 PM, Henry Rich <henryhr...@nc.rr.com>
>> wrote:
>> >
>> >> Well, I know complex floor was something Gene McDonnell was proud of,
>> >> and I expect it's embedded in some applications. You'll need to
>> produce
>> >> a compelling argument for changing it.
>> >>
>> >> Henry Rich
>> >>
>> >> On 1/22/2012 12:38 PM, Marshall Lochbaum wrote:
>> >> > I'm pretty sure I understand the definition, but I still don't get
>> the
>> >> > rationale. Under my scheme the "obvious" complex floor would be (-
>> 1&|),
>> >> > which also has the properties of convexity, translatability, and
>> >> > compatibility listed in the dictionary.
>> >> >
>> >> > Marshall
>> >> >
>> >> > On Sun, Jan 22, 2012 at 12:08 PM, Henry Rich<henryhr...@nc.rr.com>
>> >> wrote:
>> >> >
>> >> >> As Don said, make sure you understand complex floor before you start
>> >> >> coding.
>> >> >>
>> >> >> Henry Rich
>> >> >>
>> >> >> On 1/22/2012 11:38 AM, Marshall Lochbaum wrote:
>> >> >>> The theory of moduli is based on the quotient group of the
>> integers by
>> >> a
>> >> >>> subgroup. For instance, the integers (mod 2) are produced by
>> taking all
>> >> >> the
>> >> >>> integers and identifying all the ones that are even, as well as
>> all the
>> >> >>> ones that are odd. Then we get a two-element group which we can
>> preform
>> >> >>> addition on: even+even=even, even+odd=odd, etc.
>> >> >>>
>> >> >>> To reduce a number in a particular modulus, we need to find a
>> canonical
>> >> >>> representation for that number. For positive numbers n the choice
>> is
>> >> >> fairly
>> >> >>> simple: n|l gives the l' such that 0<=l'<n. In the complex plane, a
>> >> >> number
>> >> >>> generates a grid by taking its product with the Gaussian integers;
>> try
>> >> >>> 'dot; pensize 2' plot , 1j2 * j./~i:10
>> >> >>> to see what I mean. Then what we want is a canonical form for what
>> >> >> happens
>> >> >>> when we identify all those points together. We're allowed to
>> "shift" by
>> >> >> any
>> >> >>> Gaussian integer times the modulus.
>> >> >>>
>> >> >>> Based on this, I think a good way to calculate the modulus is to
>> get
>> >> the
>> >> >>> number into the square that lies counterclockwise of the modulus
>> >> number.
>> >> >>> Practically, this means we decompose a complex number y into (a
>> j.b)*x,
>> >> >> and
>> >> >>> then return (1|a)j.(1|b) .
>> >> >>>
>> >> >>> I'll see if I can get around to editing this. I have a working
>> copy of
>> >> >> the
>> >> >>> source, but I haven't made sense of it entirely.
>> >> >>>
>> >> >>> Marshall
>> >> >>>
>> >> >>> On Sun, Jan 22, 2012 at 10:45 AM, Raul Miller<
>> rauldmil...@gmail.com>
>> >> >> wrote:
>> >> >>>
>> >> >>>> Yes, this is a bug.
>> >> >>>>
>> >> >>>> Someone should fix it.
>> >> >>>>
>> >> >>>> J is open source. (Though distributed sources do not compile for
>> me,
>> >> >>>> and I keep getting sidetracked when I investigate forks that might
>> >> >>>> compile.)
>> >> >>>>
>> >> >>>> --
>> >> >>>> Raul
>> >> >>>>
>> ----------------------------------------------------------------------
>> >> >>>> For information about J forums see
>> >> http://www.jsoftware.com/forums.htm
>> >> >>>>
>> >> >>>
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>> >> >
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