[Rd] Power (^) 10x slower in R since version 1.7.1... What next?

[Philippe Grosjean]

OK, I have made a little search about this "problem" that apparently occurs
only on Windows platform... (but I am sure most of you are already aware of
it): the slow down is due to the adoption of a different algorithm for pow
in mingw 3.x. This is motivated by some other changes in mingw. Here is a
quote of Danny Smith that did this change:

>When mingw changed default FPU settings from 53-bit mantissa
>to 64 bit mantisa, the dll-provided pow function no longer
>returned integral values when both operands were integral.  Now, I don't
>think that is a requiremnet of the standard but every other pow
>implementation I looked at did that. So I changed to a well-tested
>pow function (from the Cepehes math library) that did.  As you found out
>it is expensive.

>I have written another pow function that use exp2 and log2 library
functions
>rather than the polynomial expansion used by Cephes package.  It seems to
be
>accurarte enough (except when the result of pow is near 1.0 (eg,
pow(1.00001, 0.99999))
>and is as fast as the msvcrt.dll version.  I still need to tweak for cass
>near range boundaries.

>The other alternative is to write a wrapper for the wrapper for the dll
pow,
>to fix up the special cases when both args are integral.  That doesn't add
to
>much overhead.

>Danny

Since pow is much, much slower in mingw 3.x than in mingw 2.x, other people
started to search for a solution. I found this interesting enough:
http://www.willus.com/mingw/ (look at "Some Fast Math Functions" at the end
of the page).

Thus here, there are two possibilities: to match the standards and provide
full-proof math functions, like it is done in current mingw (and in R,
consequently)... but sacrificing speed. Or, to rely to online assembler that
uses Pentium or Athlon fast calculation potentials (but with less checking
of errors) like Willus proposes.

I think at this point, it should be the user's choice. So, R should propose
both and should allow to switch from one to the other easily. Any
suggestion? (one idea: make a fastmath package that would provide faster,
but less error-proof ^, exp(), cos(), sin(),... functions). Unfortunately, I
am not fluent enough in C and assembler to do it myself.

Best,

Philippe Grosjean

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