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From: mitchalsup@aol.com (MitchAlsup1)
Newsgroups: comp.arch
Subject: Re: Instruction Tracing
Date: Sat, 10 Aug 2024 19:54:50 +0000
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References: <2024Aug10.121802@mips.complang.tuwien.ac.at> <memo.20240810204133.20940T@jgd.cix.co.uk>
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On Sat, 10 Aug 2024 19:41:00 +0000, John Dallman wrote:

> In article <2024Aug10.121802@mips.complang.tuwien.ac.at>,
> anton@mips.complang.tuwien.ac.at (Anton Ertl) wrote:
>
>> IIRC IA-64 has no FP division.
>
> You recall correctly. It has an "approximation to reciprocal"
> instruction,
> which gives you about 8 bits of precision, and then requires the
> compiler
> to generate Newton-Raphson sequences. Intel's manual, 2010 edition, says
> this is advantageous because users can generate only the precision they
> need. Writing Itanium assembler for customised precision? Not many
> people
> would have wanted to do that in 2001, let alone 2010.
>
> In, I think, 1996, my employers had visitors from Intel trying to
> persuade us to adopt their C/C++ compiler for IA-32. They had been able
> to speed up one of our competitors' code by a factor of two, and hoped
> to
> do the same for us.
>
> They failed. We already had that factor of two, which was "ordinary
> compiler optimisation." That competitor had some rather odd coding
> standards at the time, which meant most compilers failed if asked to
> optimise their code. Someone from Intel had stayed at their site for
> most
> of a year, reporting the bugs and getting them fixed until Intel's
> compiler could optimise the code.
>
> While visiting us, Intel asked what may have been a significant question
> about the mixture of floating-point arithmetic instructions we used. We
> didn't have precise figures, but were sure that we used at least as many
> square roots as divides. IA-64 does square roots like divides, with a
> starter approximation and Newton-Raphson sequences. Slowly, because the
> N-R instructions all depend on the previous instruction, and can't be
> run in parallel.

Newton-Raphson has 2 dependent multiplies in a dependent loop.
Goldschmidt is a rearrangement of N-R such that the multiplies are
independent with loop-to-loop dependencies. The way IA-64 did
them it was 8 cycles per loop. Had they been done in function
unit sequencing, instead, the loop would have only been 4 cycles.
Converting to Goldschmidt it would have only been 2.

Goldschmidt does not correct for arithmetic anomalies, whereas
N-R does. Thus IEEE accurate Goldschmidt iterators use N-R as
their last iteration.
>
> John