Re: unary mapper system redesigned + a few questions

[John W. Eaton]

On 17-Nov-2009, Jaroslav Hajek wrote:

| No. Quoting the C++ standard:
| 
|        template<class T> complex<T> log(const complex<T>& x);
|   Notes: the branch cuts are along the negative real axis.
| 
|   Returns: the complex natural (base e) logarithm of x, in the range of a
| strip mathematically unbounded
|      along the real axis and in the interval [-i times pi, i times pi ]
| along the imaginary axis. When x is a
|      negative real number, imag(log(x)) is pi.
| 
| ..end of story.

Sorry, but I don't see why

  (0, -1) / (large representable number)

should be considered to have a complex imaginary part yet

  (0, -1) / inf

should not.

| > If you throw away the negative zero imaginary part before it even gets
| > to the log function, then there is no way to fix this problem.
| >
| 
| Surely there is; just do
| 
| y = complex (0, -1 ./ x)
| 
| instead. "complex" skips the narrowing.

I don't see any practical way to do this for every computation which
might result in an underflow on the negative side of zero.

jwe