From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: X-Spam-Checker-Version: SpamAssassin 3.4.2 (2018-09-13) on inbox.vuxu.org X-Spam-Level: X-Spam-Status: No, score=-0.8 required=5.0 tests=DKIM_SIGNED,DKIM_VALID, DKIM_VALID_AU,FREEMAIL_FORGED_FROMDOMAIN,FREEMAIL_FROM, HEADER_FROM_DIFFERENT_DOMAINS,HTML_MESSAGE,MAILING_LIST_MULTI, RCVD_IN_DNSWL_NONE autolearn=ham autolearn_force=no version=3.4.2 Received: from minnie.tuhs.org (minnie.tuhs.org [45.79.103.53]) by inbox.vuxu.org (OpenSMTPD) with ESMTP id f9dc9216 for ; Sat, 19 Oct 2019 18:34:11 +0000 (UTC) Received: by minnie.tuhs.org (Postfix, from userid 112) id 8AC4393D80; Sun, 20 Oct 2019 04:34:10 +1000 (AEST) Received: from minnie.tuhs.org (localhost [127.0.0.1]) by minnie.tuhs.org (Postfix) with ESMTP id 7F0FA93D2D; Sun, 20 Oct 2019 04:33:38 +1000 (AEST) Authentication-Results: minnie.tuhs.org; dkim=pass (2048-bit key; unprotected) header.d=gmail.com header.i=@gmail.com header.b="kNScsf+F"; dkim-atps=neutral Received: by minnie.tuhs.org (Postfix, from userid 112) id D608993D2D; Sun, 20 Oct 2019 04:33:35 +1000 (AEST) Received: from mail-ed1-f48.google.com (mail-ed1-f48.google.com [209.85.208.48]) by minnie.tuhs.org (Postfix) with ESMTPS id 1C09493D1B for ; Sun, 20 Oct 2019 04:33:35 +1000 (AEST) Received: by mail-ed1-f48.google.com with SMTP id j8so7026743eds.1 for ; Sat, 19 Oct 2019 11:33:35 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025; h=mime-version:references:in-reply-to:from:date:message-id:subject:to :cc; bh=MIXtPpVlJKRxA9iIndZe+UzfNkBVcIUDyF1KV2wmnhU=; b=kNScsf+FlZHEk3Lo5vg/j3klFe4ZTcMaRtQK+PwH6PdEyponWXKVd+5Gz9+f+LaPK5 5/Fd8V9dGi53cYaXR0gcJ+wmaKuSPUTWdA+6migGj88oAHYmxnlI47297j8FtEYsD9Pt 7GyTkHVZBn379OXODfvJhhh0/g5kOfQy5EQMAlWOLPP2IHlHa73jcZMKSVXs/46/aHr/ dVOdaGDLVgBPJZ6QTUeY/MmS8S28cQkNCL3jUvhUymp5On1LyZXiKh3OFZPcxVE4JqpY gfvGrKZlMIIPLtPKguGq+65CbonEgOjKsUeh2jVRZ3ivQLjqFIKa7tckXwoRtvXTyA/3 O/nw== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:mime-version:references:in-reply-to:from:date :message-id:subject:to:cc; bh=MIXtPpVlJKRxA9iIndZe+UzfNkBVcIUDyF1KV2wmnhU=; b=Xc6Md9g9BEuAgS6LRO7zQEMDkL/ALRk5goOcJc0yd+wkCIBQdiFf21KbWLYK+884hE 19gN6UNTIMovuDBETq5/XHCfGeAuKOM/5S3eU52u0+SKBDcU0bqFWucG9OmWkNPvCrVY qYW91Tgeit1O5Wid63cwkoUcmeWYPPSFFWaxNl32yRRZeOnavaJiamFdFNlT72U1rwWy 3S1du/WcbWmzbXOMoR+ySZCbyKTfrdONhD20s46qTDNZRYlzgdK6Ujro9oR0R6xsPma8 bZNoEfU4FnE8MR7eKo7Oj3Q/g5gXUaU6xAYQwOg8O4xvOmQZ2n9yn/QMDG1m6abfvHTK +23w== X-Gm-Message-State: APjAAAWarwTNC2LwVllpQAgLAtdLhlNk4LRdRJuJ190LXtsTvqelAeYB oJfiwswa+DChgunZeqPQ207T6WNc4Gdiz5XljUg= X-Google-Smtp-Source: APXvYqxSXtzXCw8Kb/9yHJFwaotY3h7En+0fnsPD65ToIMBgIMFwcwCiAJN9VUABApxt0rTmqouGpy3gNehUONmazJw= X-Received: by 2002:a17:906:6451:: with SMTP id l17mr14431164ejn.114.1571510013391; Sat, 19 Oct 2019 11:33:33 -0700 (PDT) MIME-Version: 1.0 References: <201910191440.x9JEe8PB035921@tahoe.cs.Dartmouth.EDU> In-Reply-To: <201910191440.x9JEe8PB035921@tahoe.cs.Dartmouth.EDU> From: Abhinav Rajagopalan Date: Sun, 20 Oct 2019 00:02:56 +0530 Message-ID: To: Doug McIlroy Content-Type: multipart/alternative; boundary="0000000000001bf9a6059547b068" Subject: Re: [TUHS] Space Travel, was New: The Earliest UNIX Code X-BeenThere: tuhs@minnie.tuhs.org X-Mailman-Version: 2.1.26 Precedence: list List-Id: The Unix Heritage Society mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Cc: tuhs@tuhs.org Errors-To: tuhs-bounces@minnie.tuhs.org Sender: "TUHS" --0000000000001bf9a6059547b068 Content-Type: text/plain; charset="UTF-8" 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 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 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 --0000000000001bf9a6059547b068 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
Forgive me for both hijacking this= thread, and to address my amateurish gnawing concern, but how was it be po= ssible to write differential/integral equations at an assembly/machine leve= l 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, especial= ly the floating=C2=A0point=C2=A0math being done. Surmising from some person= al experience that writing mathematical programs is hard even now, although= there exist certain functional paradigms, and specialised environments suc= h as MATLAB or Mathematica. The complexity=C2=A0seems to remain the same if= not more now, due to the vast oodles of data to handle stemming from the= =C2=A0nature of the world.

Were they loaded as just words as any other instruction or were there s= eparate=C2=A0coprocessors that did the number=C2=A0crunching? I'm guess= ing Fortran-ish kind of implementations were done, but the hardware level c= omputation itself I just can't process.

It just blows my mind now thinking backwards in terms= of those monster=C2=A0machines being loaded with trails of paper tape inst= ructions to play Space Travel. Being born in the late 90's doesn't = help me too.
<= br>
Also, on a= related note, don't know if you've watched the=C2=A0interview=C2=A0of Ken done by Brian at the V= intage Comptuer Federation 2019, there might be a few surprises lurking aro= und the middle of that when they discuss pipes and grep.=C2=A0

Thank you!
<= br>
On Sat,= Oct 19, 2019 at 8:11 PM Doug McIlroy <doug@cs.dartmouth.edu> wrote:
I wa= s 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)=3Df(t)+f'(t)dt.
Dick saw that the formula did not conserve
energy and found an alternative that did.


--
=

Abhinav Rajagopalan


=
--0000000000001bf9a6059547b068--