## Pred to sin some more

I’ve accomplished a good bit of work on Numeric in the last eleven days. Soon after my last post I started work on comparison operators. First I provided Real versions of the numeric comparison operators, all of which delegate to Bridge versions (implemented as Num for now). Then I removed the Num, Num version of the cmp operator, replacing it with a Numeric, Numeric version. Note that despite the presence of Numeric, Numeric cmp, numeric comparisons only work on Real types at the moment.

TimToady++ and I have a theory for supporting comparisons on generic Numeric types, but I have not started to implement it yet. My basic idea is similar to the Bridge idea for Reals. There would be a Numeric method (don’t have a name yet) which converts your generic Numeric type to a list of Real numbers. (Obviously Real numbers would convert to a single Real, Complex would convert to two, etc.) You would then compare the Reals lexicographically. This probably isn’t a mathematically sensible ordering, but it does provide a reasonable ordering that would put Reals in the order you expect and still allow you to sort Complex numbers.

After that I got sqrt working properly in the new system, adding Numeric.sqrt and Real.sqrt, and cleaning up the Num and Complex versions.

Then the big effort (at least in terms of lines of code) was getting the trig functions working properly in the new system. It was just a matter of cloning the approach I’d taken for sin for all the other functions, though there was one bizarre catch. It turned out that several of the trig functions had two different implementations in Complex. When I took away the “multi” from the first implementation, the second one kicked in — and the second one was wrong. Since I didn’t actually realize the second one was there, this lead to about an hour of extreme confusion on my part before I sorted things out.

I finished up with tweaks for ceiling, floor, and log. Then I implemented Numeric versions of postfix i, succ, and pred. These are expressed in terms of simple addition and multiplication, so Numeric’s implementations should work for any reasonably robust Numeric class. I’m guessing it will frequently be worthwhile to still have class-specific versions of succ and pred, both for efficiency and to help ensure that `\$x` and `\$x.pred` usually have the same type.

What’s next? As I mentioned about, generic Numeric comparison code. The rand function — it’s currently listed as Numeric, but it doesn’t take any arguments and returns a Num, so I’m not sure why. srand at least takes a Real, but again, it doesn’t really seem like it fits, IMO. Numeric.roots. Work on more tests. Fixing up the spec a bit. And I may take a look in other math libraries to see if there are obvious functions we are missing.

Thanks to the Perl Foundation and Ian Hague for supporting this work.