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The instruction you refer to is for evaluating polynomials, not solving them, so I’m a bit confused by your claims. It is pretty common to evaluate polynomials

The instruction you refer to is for evaluating polynomials, not solving them, so I’m a bit confused by your claims. It is pretty common to evaluate polynomials as part of solving them (if you’re aiming for numeric solutions), but solving tends to also require: - some kind of root finding (note that methods like Newton–Raphson don’t work when zeros have multiplicity) - dividing polynomials by (X - a) after finding one root to find the next root

PopePompus 2y ago
The POLY instruction was the CISCiest of the VAX instructions. One machine instruction could evaluate a polynomial. I think it could even handle the situation where fetching one of the coefficients caused a page fault. If you knew the VAX instruction set well, writing code in VAX assembly was almost as easy as using a higher level language.
- dan-robertson 2y ago
  Was the instruction really much more complex than eg some byte-string comparison instruction? For string comparison you’re doing a simpler operation at each step, and the accumulation is much simpler, but maybe you have short-circuiting too. POLY corresponds to the following C, I think: float poly(int d, float x, float *c) { c+=d; float y = *c; while(d--) y = *c-- + y * x; return y; } I also don’t see why you consider this to be the CISCiest instruction from an architecture that includes a substring-search instruction, a vaguely printf-like instruction with its own mini instruction set for the pattern strings it takes, and an instruction to do polynomial division in the ring of polynomials over F_2 (ok this is just CRC)
shagie 2y ago
It's me recalling a story from... '93 or there abouts. My memory about the specifics of it might have suffered a bit over three decades. I do recall that it was something to do with polynomials. It was also something that was fun to port. http://neilrieck.net/docs/openvms_notes_alpha_diary.html http://neilrieck.net/docs/openvms_notes_alpha_diary.html

PopePompus 2y ago

The POLY instruction was the CISCiest of the VAX instructions. One machine instruction could evaluate a polynomial. I think it could even handle the situation where fetching one of the coefficients caused a page fault. If you knew the VAX instruction set well, writing code in VAX assembly was almost as easy as using a higher level language.

dan-robertson 2y ago
Was the instruction really much more complex than eg some byte-string comparison instruction? For string comparison you’re doing a simpler operation at each step, and the accumulation is much simpler, but maybe you have short-circuiting too. POLY corresponds to the following C, I think: float poly(int d, float x, float *c) { c+=d; float y = *c; while(d--) y = *c-- + y * x; return y; } I also don’t see why you consider this to be the CISCiest instruction from an architecture that includes a substring-search instruction, a vaguely printf-like instruction with its own mini instruction set for the pattern strings it takes, and an instruction to do polynomial division in the ring of polynomials over F_2 (ok this is just CRC)

shagie 2y ago

It's me recalling a story from... '93 or there abouts. My memory about the specifics of it might have suffered a bit over three decades. I do recall that it was something to do with polynomials. It was also something that was fun to port. http://neilrieck.net/docs/openvms_notes_alpha_diary.html http://neilrieck.net/docs/openvms_notes_alpha_diary.html