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 &lt;doug(a)cs.dartmouth.edu&gt; wrote: -- Abhinav Rajagopalan

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&gt; 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 &lt;doug(a)cs.dartmouth.edu&gt; > 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 > > >

s there a authentic space travel release available in C for Linux?

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.

From there to emulating floating-point instead is not a huge leap.

Not to mention, if you start using log/alog tables, and/or sin/cos/tan tables, and interpolation, you can quickly ramp up computation speed for simple games that have a small matrix of coordinates.

Star Wars on a GT-40, which Andrew Hume (formerly UNSW, who is now at Bell last I heard) reverse-engineered to support three players, not two.

Does that still exist?

Am I the only one who remembers the Defectium (as we called it)? Intel denied the the problem until their noses got rubbed into it, after which they instructed Sales to refuse replacements for any chip that failed after using a demo program that demonstrated said defect, claiming that it would hardly ever happen.

Err, would you fly on an aircraft designed by Defectiums? Or cross a bridge, etc?