left-right (up-down) parsing may lead to over/underflow of prod

[Rolf Fabian]

I consider the following 'feature' as a
major drawback of Octave because
it infringes the expected commutativity
and associativity while building products.

Parsing products from left to right (for vectors)
or up-to-down (columnwise product of matrices)
may lead to avoidable over /underflow if
some involved factors are extraordinarily
large and/or small

:> computer, version
i686-pc-msdosmsvc
ans = 3.0.0

EXAMPLE 1 (prod of a vector)
:> x1 = [1e150, 1e160, 1e150, 1e160, 1e-310, 1e-310]
It is obvious that the correct product of x is equal to 1,
but Octave either overflows if the product is
evaluated from left-to-right:
:> prod (x)
ans = Inf

or underflows (without any warning)
if the product is evaluated from right-to-left
:> prod  (fliplr (x))
ans = 0

Thus simply rearranging the order of factors changes
Octave's result of the product from 'Inf' to '0', which
is unexpected because  generally a product should
not depend on the ordering of its factors.

Expected correct answer is returned by
:> prod_via_sum_of_logs = exp (sum (log (x)))
ans =  1

Similar artefacts occur if input to prod is a matrix like:
:> y = [1e300, 1e-200; 1e300, 1e-200; 1e-200, 1e300; 1e-200, 1e300]

:> prod(y)
ans =
   Inf     0

:> prod (flipud (y))
ans =
     0   Inf

The correct result can again be obtained via sums of logarithms:
:> prod_via_sum_of_logs  = exp (sum (log (y)))
ans =
   1.0000e+200   1.0000e+200

Of course, some spurious complex noise might appear if some factors
are negative while using sums of logarithms, but this can be adjusted
easily.

In order to avoid similar artefacts as outlined above I propose to implement
the 'prod' function via (column) sums of logarithms of factors.

Rolf


-----
Rolf Fabian
<r dot fabian at jacobs-university dot de>

-- 
View this message in context: 
http://www.nabble.com/left-right-%28up-down%29-parsing-may-lead-to-over-underflow-of-prod-tp16823819p16823819.html
Sent from the Octave - Maintainers mailing list archive at Nabble.com.