Re: Q: division vs multiplication

In article 95-04-003,
Mr Tomas Hulek <t.hulek@imperial.ac.uk> wrote:
>It is presumably well known that on many hardware platform floating point
>division is slower than floating point multiplication.


[example deleted]


>My question is: does this also apply to division by constants that are powers
>of 2? For real-world compilers (C,C++ let's say) and machines, is there any
>benefit in using
>
>r = 0.5*(a+b);
>
>rather than
>
>r = (a+b)/2.0;
>
>???


An obvious way to simplify the operation would be to decrement the exponent
of the floating-point value (a+b) by one. No compiler I know does so, as it
would not work in all cases. First of all, it would be wrong for the value
0.0. Furthermore, it would be wrong for denormalized numbers in the IEEE
standard. One could check for these cases, but it is questionable whether the
resulting code pattern would be faster than the division.


In general, compilers tend to not rewrite floating-point operations too much,
as slight changes in ordering or other modifications could change rounding
errors or the exception behavior of the code.




Marc-Michael Brandis
Institute for Computer Systems
ETH-Zentrum (Swiss Federal Institute of Technology)
CH-8092 Zurich, Switzerland
email: brandis@inf.ethz.ch
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