Raising negative numbers to an inexact integer

Raising negative numbers to an inexact integer

[Mark H Weaver]

Hello all,

I have a local branch which allows Guile to represent non-real complex
numbers with inexact zero imaginary part, such as 1.0+0.0i.  Currently,
Guile automatically converts these numbers into reals.  As pointed out
by Taylor Campbell and others, it is important to distinguish -1.0+0.0i
from -1.0-0.0i in order to handle branch cuts properly.

In one of my pending patches (not yet submitted), I made sure that
any negative number (or -0.0) raised to any inexact power always yields
a non-real complex number.

For example, although (expt -1.0 2) yields 1.0, (expt -1 2.0) yields
1.0+0.0i, which is not `real?' according to the R6RS.  The R6RS requires
that `real?' return #t only if the imaginary part is an _exact_ 0.

Note that operations requiring reals, including the comparison operators
`<', '>', '<=' and '>=' will raise an exception if applied to these
numbers.  However, I made sure that `inexact->exact' would ignore an
inexact zero imaginary part.

I don't expect this to be a problem, since anyone raising a negative
number to an inexact power should expect that the result may not be
real.

What do you think?

      Mark

Re: Raising negative numbers to an inexact integer

[Neil Jerram]

Mark H Weaver <mhw@netris.org> writes:

> Hello all,
>
> I have a local branch which allows Guile to represent non-real complex
> numbers with inexact zero imaginary part, such as 1.0+0.0i.  Currently,
> Guile automatically converts these numbers into reals.  As pointed out
> by Taylor Campbell and others, it is important to distinguish -1.0+0.0i
> from -1.0-0.0i in order to handle branch cuts properly.
>
> In one of my pending patches (not yet submitted), I made sure that
> any negative number (or -0.0) raised to any inexact power always yields
> a non-real complex number.
>
> For example, although (expt -1.0 2) yields 1.0, (expt -1 2.0) yields
> 1.0+0.0i, which is not `real?' according to the R6RS.  The R6RS requires
> that `real?' return #t only if the imaginary part is an _exact_ 0.
>
> Note that operations requiring reals, including the comparison operators
> `<', '>', '<=' and '>=' will raise an exception if applied to these
> numbers.  However, I made sure that `inexact->exact' would ignore an
> inexact zero imaginary part.
>
> I don't expect this to be a problem, since anyone raising a negative
> number to an inexact power should expect that the result may not be
> real.
>
> What do you think?

For what it's worth, that all makes sense to me.  (Speaking as someone
who did a lot of mathematics at university, but hasn't used it seriously
since.)

        Neil

Re: Raising negative numbers to an inexact integer

[Andy Wingo]

On Mon 31 Jan 2011 21:26, Mark H Weaver <mhw@netris.org> writes:

> For example, although (expt -1.0 2) yields 1.0, (expt -1 2.0) yields
> 1.0+0.0i, which is not `real?' according to the R6RS.  The R6RS requires
> that `real?' return #t only if the imaginary part is an _exact_ 0.
>
> Note that operations requiring reals, including the comparison operators
> `<', '>', '<=' and '>=' will raise an exception if applied to these
> numbers.  However, I made sure that `inexact->exact' would ignore an
> inexact zero imaginary part.
>
> I don't expect this to be a problem, since anyone raising a negative
> number to an inexact power should expect that the result may not be
> real.
>
> What do you think?

Sounds sane to me.

Andy
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