[TUHS] Space Travel, was New: The Earliest UNIX Code

[Clem Cole]

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 at 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 at 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.
>>
>> > 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.
>>
>
>
> --
>
> Abhinav Rajagopalan
>
>
>
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