Re: element-wise exponent operator

[John W. Eaton]

On 2/28/20 1:09 PM, Rik wrote:

> I started trying to understand bug #57671 (Power operator operating on
> complex numbers results in NaN when broadcasting) a week ago.  The problem
> behavior is
>
> ([1;0]*j) .^ [1, 0]
> ans =
>
>     0.0000 + 1.0000i   1.0000 +      0i
>          0 +      0i      NaN -    NaNi
>
> [...]
>
> My first request is for an explanation of the convoluted mapping strategy
> that Octave uses for operators.  There are tons of C++ files in
> libinterp/operators/ which seem to map all of the various combinations of a
> scalar, vector, or matrix object with another scalar, vector, or matrix
> object.

This is a very old part of Octave from before C++ had templates and 
before Octave hadt classes (for dispatching based on type, which could 
also be used for built-in types) or broadcasting.

Since

  scalar .* matrix

behaves differently from

  matrix .* matrix

I decided to have actual scalar types in Octave so that we could write 
operators that did special things for mixed-type operations like the 
above.  Then each operator function could be simpler (no special check 
is needed for scalar-by-matrix operations if matrices are always 
narrowed to scalars by the interpreter before dispatching to specific 
operators.  But you have more operator functions, and when you add in 
complex versions, a LOT more.  But I thought it was worth it to avoid 
wasting memory and time expanding (possibly large) matrices from real to 
complex if we had special operations for mixed types where possible and 
only resort to type conversions when mixed type operations won't work.

To determine which function to call, we have lookup tables for operators 
based on the type of both operands and we may also apply type conversion 
operators.  I agree this is all a bit complicated.  Maybe we can 
simplify some of it.

> And this structure is also echoed in liboctave/operators.

I've been thinking about that a little bit recently while looking at the 
MEX interface.  We have things like Matrix, ComplexMatrix, etc. in 
liboctave and a wrappers for them so they can be octave_value objects 
with a common interface for the interpreter.  Matlab appears to just 
have mxArray that contains various types.  We could do the same by 
moving the array storage directly into an object in the octave_value 
hierarchy, but I thought it would be more convenient for interfacing 
with and writing numerical code if we had separate array types that were 
independent of the Octave interpreter.

> And
> then there are exceptions to this structure such as
> libinterp/corefcn/xpow.cc which slots in to the architecture as it gets
> called from libinterp/operators, but isn't stored there.

The operators directory was originally intended to be a place to store 
the wrapper functions that all had the same signatures (for the table of 
operators in the interpreter) and xpow.cc was for the type-specific 
operations with Matrix, ComplexMatrix, etc. arguments.  It's in 
libinterp instead of liboctave because the return type is octave_value 
because pow operations on two real values can sometimes produce complex.

> Why aren't we
> just mapping the '+' operator to a BLAS call?  Or maybe we are and I don't
> understand how we get there.

Are there BLAS functions for vector addition, subtraction, 
multiplication, or division, or for mixed-type operations?

> For bug #57671, the code which ends up getting called is in xpow.cc case #10.
>
> // -*- 10 -*-
> octave_value
> elem_xpow (const ComplexNDArray& a, const NDArray& b)
> {
>    dim_vector a_dims = a.dims ();
>    dim_vector b_dims = b.dims ();
>
>    if (a_dims != b_dims)
>      {
>        if (! is_valid_bsxfun ("operator .^", a_dims, b_dims))
>          octave::err_nonconformant ("operator .^", a_dims, b_dims);
>
>        return bsxfun_pow (a, b);
>      }
>
>    ComplexNDArray result (a_dims);
>
>    for (octave_idx_type i = 0; i < a.numel (); i++)
>      {
>        octave_quit ();
>        double btmp = b(i);
>        if (xisint (btmp))
>          result(i) = std::pow (a(i), static_cast<int> (btmp));
>        else
>          result(i) = std::pow (a(i), btmp);
>      }
>
>    return result;
> }
>
> For the non-broadcasting case, which works, the key is to note the check
> for an integer power (xisint (btmp)).  If this is found it calls std::pow
> from the C++ library with a different function signature.

Should we be using a wrapper for pow and burying this logic inside a 
template function?

> When
> broadcasting is used it calls bsxfun_pow and this ends up calling code from
> liboctave.  In particular, the individual operation is in
> liboctave/operators/mx-inlines.cc
>
> template <typename R, typename X, typename Y>
> inline void
> mx_inline_pow (size_t n, R *r, const X *x, const Y *y)
> {
>    using std::pow;
>
>    for (size_t i = 0; i < n; i++)
>      r[i] = pow (x[i], y[i]);
> }
>  > This calls std::pow with a function signature of two reals which 
results in
> NaN + NaNi.
>
> At a minimum, all the uses of std::pow in xpow.cc and mx-inlines.cc should
> be checked to see if they need to install a test for an integer and then
> perform the same cast as is done for case 10.

It seems like we should be doing this with a wrapper function for pow to 
get the behavior we want.

There may also be better ways to write the templates for brodcasting.

> Handling Complex values will be a little more difficult.  The function
> signatures available for pow are
>
> template<class T> complex<T> pow (const complex<T>& x, int y);
> template<class T> complex<T> pow (const complex<T>& x, const complex<T>& y);
> template<class T> complex<T> pow (const complex<T>& x, const T& y);
> template<class T> complex<T> pow (const T& x, const complex<T>& y);
>
> There is no signature for pow (complex<real>, complex<int>) which means we
> likely need to check first for whether the exponent can be narrowed to
> real, and then checked subsequently for whether it is an integer.

To do this correctly everywhere would probably be easiest if we provided 
our own Complex class and used it consistently or at least had a wrapper 
function for pow that we used instead of using the ones from 
std::complex directly.

> All of this will be tedious, because there are so many cases, which makes
> one wonder whether the code in xpow.cc can't make better use of templates.

I'm sure it can.  The functions there were originally written long 
before C++ had useful templates.

> Regardless, once fixed we also need to add BIST tests for all the weird
> corner cases.

Yes.

jwe