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Old 2020-02-23, 13:16   #23
Romulan Interpreter
LaurV's Avatar
Jun 2011

5×23×73 Posts

Originally Posted by jwaltos View Post
...where I had to purchase a math co-processor emulator.
(my stressing)

Well, I don't think you ever bought one of those. That usually means a software component (a library, like gwnum), and not a piece of hardware. The piece of hardware, is just "math co-processor". Or maybe you indeed bought a library, I remember the coprocessor cards were so bloody expensive, like the GPUs are now, but more, and some guy I know had two computers (one 8086 and one 8088) connected together on parallel cable, and he told me at the time he is using one to compute something for the other, because buying I don't know which extension would be more expensive. I didn't understand at the time, but maybe you did exactly that.

Anyhow, it doesn't matter now... In the old times, the CPUs either had a math co-processor or don't.

All CPUs can/could do integer calculations like additions and subtractions, shifts, rotations and complements, if they had an ALU (not all had one!).

If the ALU was complex enough to contain a hardware multiplier, which is a different king of monster, then the CPUs could multiply integers in their range, fast, and (sometimes) divide too, keeping the integer quotient result and the modular reminder. Otherwise, they still could multiply and divide integers, but much slower (because, of course, any multiplication is a repetitive addition, and you can get rid of most of the additions by keeping partial results, in binary this is the "shift and add" method).

Having a multiplier on chip already took like 80% of the silicon or so, in spite that such toy could only handle integer numbers, so introducing more silicon to take care about the fractional numbers too, was a luxury. In fact, fractions, up to some precision, are just integers, multiplied with some negative power of the base, and the most of the manufacturers even didn't think to use silicon space space to make place for such nonsense.

At the time when the good old 8086 started to catch the PC market, this was the situation, and it remained so, for a while.

Unfortunately, or for us, prime hunters, I would say, fortunately, many numerical algorithms, and many physical processes, etc, couldn't care less about integers, these are just curious things only some crazy people who hunt mersenne primes care about. The rest of the Universe does not give a dime, the nature thinks fractional.

When they made 8086 they knew about it, but they preferred to have a cheap CPU to hit the market, nobody would have bought a CPU which was 3 times more expensive, but have features you would never use unless you were some researcher in atomic physics.

And they sold the math coprocessor separate, called 8087. This persisted for a while, but pushed by the competition, eventually they put all in one chip. Luckily for us, otherwise, no AVX2 today...

Last fiddled with by LaurV on 2020-02-23 at 13:29
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