Quoting Mike Bilow to Brian Converse in a message dated 12/14

MB>  BC> One would hope that an optimizing compiler manages to reduce 
MB>  BC> the log. form to the power form. Exp, log, and (I think) power 
MB>  BC> are intrinsic Intel FPU functions, but are all done using a 
MB>  BC> microcoded series and interpolation approach. Using the log 
MB>  BC> form not only incurs more function calls, but also cascades 
MB>  BC> errors in precision. One strives to avoid cascaded operations 
MB>  BC> unless needed.
MB> 
MB> Yes, there are direct FPU instructions for all of these 
MB> things.

Well, not exactly!  You do them all using the FPU, but it requires 
combining rudimentary operations like raising 2 to a power, taking the
logarithm of a nuumber to the base 2, etc.  Take a look at Richard
Startz's book (8087 Applications and Programming for the IBM PC and
Other PCs).  The newer 80287, 80387, 80486 all have essentially the same
FP instructions, and none directly do the log, exponential or power
functions. 

MB> This is becoming clear to me.  As you may have guessed by 
MB> now, I don't know very much about Pascal.  I answered the 
MB> question from a mathematical point of view, never thinking 
MB> that some modern language would be unable to implement 
                                       ^^^^^^^^^^^^^^^^^^^ 
MB> exponentiation directly.

It's just not included in the library with most Pascal compilers, just
as it wasn't included with C in the old days.  It's easy enough to add
the feature in a Pascal unit, just as it's added in a library for C. 

I know there are things C can do that Pascal can't, but adding functions
is no harder in Pascal than in C...

Patrick

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