How good was Woz's FP code?

Question

I just came across this amazing 1976 article by Woz. In it he describes a relatively complete floating-point system for the 6502 with a 32-bit format (similar to earlier MS code).

I understand the code, mostly, but I am curious about its performance. I know that a lot of it runs through FMUL and thus one would expect that newer designs using unwound loops and/or self-modifying code would improve on that.

But given the constraints of the time, mostly memory and a desire to be read-only (for some machines anyway), has this code been greatly improved upon?

I have poked about a bit for benchmarks comparing this code to MS's version, but have not found anything applicable - the Rugg/Feldmann would do it but the only numbers I see are for MS BASIC vs. Integer, so Woz's FP code is not being run in either case.

Answer 1

Steve Wozniak wrote most of his software to be compact rather than fast, reflecting the constraints of affordable memory hardware of his time. That often resulted in contortions that made it run considerably slower than a speed-optimised implementation, such as the extensive reuse of the FMUL subroutine mentioned.

Home micros sold before 1980 typically came with 8K or 16K of ROM in total, which had to support all the features of both BASIC and native user programs. The early Apple machines were no exception.

FP routines written for a less space-constrained machine, such as the BBC Micro which often had 48K of ROM from the factory (16K MOS, 16K BASIC, 16K DFS), could be considerably faster due to the use of more specialised routines and more speed-optimised coding techniques that took up more space. The BBC Master capitalised on a 128K "MegaROM" (named because 128KB = 1 megabit) and the more capable 65C02 to further accelerate the FP and graphics routines.

It's hard to directly compare Woz FP and BBC Micro FP because they operate to different precisions - 4 and 5 bytes respectively - so the BBC Micro has to do more work to complete its calculations. Nevertheless, a Mandelbrot-based benchmark on different BASICs ported to a common (relatively fast) machine shows that the BBC implementation was still faster:

ehBasic: 172 seconds
Applesoft: 161 seconds
BBC Basic 1-3: 124 seconds
BBC Basic 4: 96 seconds

In the above table, ehBasic is effectively an expanded version of MS BASIC implementing a 5-byte FP format. BBC Basic 4 is the Master version using 65C02 instructions.