From: Arthur Krewat <krewat@kilonet.net>
To: tuhs@minnie.tuhs.org
Subject: Re: [TUHS] Space Travel, was New: The Earliest UNIX Code
Date: Fri, 18 Oct 2019 19:20:35 -0400 [thread overview]
Message-ID: <9053c41b-e306-8547-50fd-207e0bfb49af@kilonet.net> (raw)
In-Reply-To: <CAG=a+rgS8iJKnd85wv5kt8JfgZNkOR0u47FySMXYvD+jsOKEZA@mail.gmail.com>
On 10/18/2019 6:04 PM, Ken Thompson via TUHS wrote:
> while writing "space travel,"
> i could not get the space ship integration
> around a planet to keep from either gaining or
> losing energy due to floating point errors.
> i asked dick hamming if he could help. after
> a couple hours, he came back with a formula.
> i tried it and it worked perfectly. it was some
> weird simple double integration that self
> corrected for fp round off. as near as i can
> ascertain, the formula was never published
> and no one i have asked (including me) has
> been able to recreate it.
>
>
This reminds me of an experiment I performed comparing speeds of x86
assembler, and C, when I first started working in it. The experiment was
to generate a 3D cube wireframe, and rotate it about any (or all three)
of it's axes, moving it X degrees at a time. Simple vector math, really.
Included perspective, so that the back-end of the wireframe cube would
look smaller than the front side.
I had been an assembler snob, having started in MACRO-10 on a KA10
PDP-10 in 9th grade. I always assumed assembler would be faster for
anything, given the right amount of optimization. The assembler side of
the experiment, I did the CGA graphics directly. I think in the C
version, I used the built-in library that came with it. I no longer have
the source for the C version, but I do, for the assembler version. I
didn't have an 8087 floating point accelerator, so I wrote my assembler
example to use two 16-bit words of integers, combining them for a 31-bit
integer value with sign.
Timing 1000 rotations, the assembler version took X amount of time. The
C version took X*1.5
Now mind you, the C version used real floating point, and a software
floating point library with no hardware accelerator. At that point, I
realized C was the way to go. It had passed my experiment with flying
colors. The C compiler, I believe, was from Computer Innovations,
Copyright (c)1981,82,83,84,85
The reason this is similar to Ken's statement above: In the assembler
version, the cube would deform quite a bit before the run would finish.
A 31-bit integer didn't accurately reflect the result of the math. Over
time, that slight inaccuracy really added up. The accuracy of the C
version using floats was spot on. So while I basically cheated for the
assembler version, causing the deformation of the cube over time, the C
version was 100% accurate even though it was slower.
I wonder, is there something inherently different between PDP-11/7
floats and Intel's leading to the inaccuracy Ken mentions? Was the
PDP-11 (or the -7) floating point that much different than IEEE-754 ?
art k.
next prev parent reply other threads:[~2019-10-18 23:21 UTC|newest]
Thread overview: 26+ messages / expand[flat|nested] mbox.gz Atom feed top
2019-10-18 11:52 Doug McIlroy
2019-10-18 18:36 ` Steffen Nurpmeso
2019-10-18 20:19 ` SPC
2019-10-18 22:04 ` Ken Thompson via TUHS
2019-10-18 23:20 ` Arthur Krewat [this message]
2019-10-19 0:57 ` G. Branden Robinson
2019-10-19 1:11 ` Arthur Krewat
2019-10-29 2:18 ` Lawrence Stewart
2019-10-26 15:10 ` Lars Brinkhoff
-- strict thread matches above, loose matches on Subject: below --
2019-10-19 14:40 Doug McIlroy
2019-10-19 18:32 ` Abhinav Rajagopalan
2019-10-19 18:44 ` Abhinav Rajagopalan
2019-10-19 19:19 ` Clem Cole
2019-10-19 19:50 ` Henry Bent
2019-10-19 20:24 ` Arthur Krewat
2019-10-19 13:13 Doug McIlroy
2019-10-17 19:21 [TUHS] New: The Earliest UNIX Code - From the Collection of the Software History Center, Computer History Museum Lyle Bickley
2019-10-17 20:44 ` [TUHS] Space Travel, was New: The Earliest UNIX Code Warren Toomey
2019-10-17 22:39 ` Warner Losh
2019-10-17 22:51 ` Warren Toomey
2019-10-18 5:59 ` Lars Brinkhoff
2019-10-18 9:30 ` SPC
2019-10-18 17:36 ` Nemo
2019-10-18 3:01 ` Warren Toomey
2019-10-18 5:07 ` Lars Brinkhoff
2019-10-18 5:10 ` Lars Brinkhoff
2019-10-18 13:37 ` Warner Losh
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