20 Oct
2019
20 Oct
'19
1:19 a.m.
Abhinav -- it is still done today. For Intel's MKL we must have a team of
programmers that specialize in writing math at the lowest levels. DEC,
CDC, Cray, IBM did the same thing back in the day. Check out: Intel Math
Kernel Library (*a.k.a.* MKL) <https://software.intel.com/en-us/mkl>.
On Sat, Oct 19, 2019 at 2:34 PM Abhinav Rajagopalan <
abhinavrajagopalan(a)gmail.com> wrote:
Forgive me for both hijacking this thread, and to
address my amateurish
gnawing concern, but how was it be possible to write differential/integral
equations at an assembly/machine level at the time, especially in machines
such as the PDP-7 and such which had IIRC just 16 instructions and operated
on the basis of mere words, especially the floating point math being done.
Surmising from some personal experience that writing mathematical programs
is hard even now, although there exist certain functional paradigms, and
specialised environments such as MATLAB or Mathematica. The
complexity seems to remain the same if not more now, due to the vast oodles
of data to handle stemming from the nature of the world.
Were they loaded as just words as any other instruction or were there
separate coprocessors that did the number crunching? I'm guessing
Fortran-ish kind of implementations were done, but the hardware level
computation itself I just can't process.
It just blows my mind now thinking backwards in terms of those
monster machines being loaded with trails of paper tape instructions to
play Space Travel. Being born in the late 90's doesn't help me too.
Also, on a related note, don't know if you've watched the interview
<https://youtu.be/EY6q5dv_B-o> of Ken done by Brian at the Vintage
Comptuer Federation 2019, there might be a few surprises lurking around the
middle of that when they discuss pipes and grep.
Thank you!
On Sat, Oct 19, 2019 at 8:11 PM Doug McIlroy <doug(a)cs.dartmouth.edu>
wrote:
I was about to add a footnote to history about
how the broad interests and collegiality of
Bell Labs staff made Space Travel work, when
I saw that Ken beat me to telling how he got
help from another Turing Award winner.
--
Abhinav Rajagopalan
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.
If I remember correctly, the cause of Ken's
difficulty was not roundoff error. It
was discretization error in the integration
formula--probably f(t+dt)=f(t)+f'(t)dt.
Dick saw that the formula did not conserve
energy and found an alternative that did.