How to determine that 2.0 == (float) 2 in a front-end.

[Erik Schnetter]

Robert Dewar wrote:
> 
> x**6.0 can be rendered as x**6 (which is y=x*x, z=y*y, z=z*y).         
> 
> Note that this is liikely less accurate than calling a well written 
> pow routine.
> 
> Note that for example x*x*x*x is generally more accurate than x**2**2

Why is that?  Naively, I would think that x*x*x*x (evaluated left to right) 
has 3 multiplications in a row, while (x**2)**2 has only two.  So, from an 
error propagation point of view, the latter should be more accurate.

Wrt your first statement: I assume that a "well written pow routine" would 
calculate that as or similar to exp(6.0 * log(x)).  This surely involves many 
more floating point operations.  Is it really more accurate?  [Checking 
glibc...  Moving on to to http://oss.software.ibm.com/mathlib/...]  Okay, it 
seems to be.  I'm impressed.

-erik

-- 
Erik Schnetter <schnetter@uni-tuebingen.de>
Web: http://www.tat.physik.uni-tuebingen.de/~schnette/