Re: [gfortran,patch] Fix constant exponentiation with integer exponent

[Toon Moene <toon at moene dot indiv dot nluug dot nl>]

FX Coudert wrote:

> Integer exponentiation
> needs more thinking, and I had to write many cases to get it right every 
> single time (integer exponentiation with negative exponents shouldn't be 
> allowed, let me tell you!)

This is what I wrote about it to the g77-bug mailing list on the 22nd of 
January, 1996:

This all sounds very reasonable, but it is plain wrong.  In Fortran
integers are _signed_ quantities in arithmetic context, so we have
the following 5 x 5 matrix of possibilities for i ** j:

i ** j		j < -1	j = -1	j = 0	j = 1	j > 1

i < -1		0	0	1	i	i**j

i = -1		i**(-j)	-1	1	-1	i**j	

i = 0		Error	Error	1 (!)	0	0

i = 1		1	1	1	1	1

i > 1		0	0	1	i	i**j

based on the truncation rules I think are valid for Fortran.

I hope I didn't make a mistake.  In that case, row 1 and 5 can be
folded, and row 2 can be dumbed down to -1 for j odd and +1 for j
even.  The remaining i**j case can be implemented with the loop as
generated by g77 now (see my previous mail).

Hope this helps,

--
Toon Moene - e-mail: toon@moene.indiv.nluug.nl - phone: +31 346 214290
Saturnushof 14, 3738 XG  Maartensdijk, The Netherlands
At home: http://moene.indiv.nluug.nl/~toon/
Who's working on GNU Fortran: 
http://gcc.gnu.org/ml/gcc/2007-01/msg00059.html