-> Errr ... perhaps I meant `long integers'.  Nevertheless, the  
-> programme is impressively fast - and superbly annotated.... 
  
The DEFLNG A-Z at the beginning makes the variables default to "long" 
(32-bit) integers, unless their names carry suffixes such as "$"
or "#" 
to indicate some other type. In fact, there is only one variable that 
isn't a long integer, Z#, which is shorthand for SQR(2) + 1. 
  
I did produce a version, a week or so ago, in which I used DEFDBL 
instead of DEFLNG, and changed all the integer operations to 
floating-point ones. It could handle values of A up to 2^27 (more than 
130 *million*), and the values of B and C were sometimes 16 decimal 
digits long! It was fun in a way, but catastrophically slow. 
Floating-point arithmetic is *far* slower than integer arithmetic. I 
stashed it away on my disk, and didn't take it any further. The integer 
version does everything I can imagine anyone wanting it to do, and much 
more neatly and quickly. 
  
Here's an example of how clumsy it got. The upper loop-limit for the 
FOR D... loop in the Odd case can be calculated to be the next-lower 
*odd* integer to SQR(S/Z#), where S is A/2. In integer arithmetic, I 
can write it as: 
  
J = INT(SQR(S / Z#)) - 1 OR 1 
  
In floating-point arithmetic, I had to do something like: 
  
T# = SQR(S / Z#) 
U = 2 * INT(T# / 2) 
IF T# - U > 1 THEN J = U + 1 ELSE J = U - 1 
  
Three lines to replace one! 
  
                             dow 
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