## Crashing Mathematica with HatchShading + Opacity

I attempted to modify a plot for an electric field solution that I had in my old Antenna-Theory notes:
\BE
=
j \omega
\frac{\mu_0 I_{\textrm{eo}} l}{4 \pi r} e^{-j k r}
\lr{ 1 + \cos\theta }
\lr{
-\cos\phi \thetacap
+ \sin\phi \phicap
},

and discovered that you can crash Mathematica (12.1.0.0) by combining PlotStyle with Opacity and HatchShading (new in 12.1).  Here’s a stripped down version of the plot code that demonstrates the crash:

ClearAll[ rcap]
rcap = {Sin[#1] Cos[#2], Sin[#1] Sin[#2], Cos[#1]} & ;

{
ParametricPlot3D[
rcap[t, p]
, {t, 0, π}
, {p, 0, 2 π}
, PlotStyle -> { HatchShading[0.5, Black]}
]
, ParametricPlot3D[
rcap[t, p]
, {t, 0, π}
, {p, 0, 2 π}
, PlotStyle -> {Directive[Opacity[0.5]]}
], ParametricPlot3D[
rcap[t,p]
,{t,0,π}
,{p,0,2 π}
Black]}
]
}

The first two plots, using one, but not both of, Opacity or HatchShading work fine:

In this reproducer, the little dimple at the base has been removed, which was the reason for the Opacity.

I’ve reported the bug to Wolfram, but wonder if they are going to come back to me saying, “Well, don’t do that!”

EDIT: Fixed in Mathematica 12.1.1

## Attack took out my godaddy hosted wordpress blog for most of a day.

Guilty admission: The title of this post is click-baity, as the attack was not likely on my blog, but something colocated on the server that my blog happened to have been hosted on.  In particular, the math, physics, complaining about COBOL, rants, and other random garbage that you’ll find on this blog does not likely warrant a DOS attack.  This isn’t the story of my offending somebody enough to get DOSed, but is just the story of a painful interaction with godaddy customer support.

I used to use a wordpress hosted blog, and eventually decided that I wanted flexibility enough to pay for hosting.  I experimented a bit with amazon hosting, but the variability in price scared me off, and I ended up buying my hosting from godaddy.  I don’t remember anymore what other options I considered, nor why I ended up settling on godaddy’s “managed wordpress” offering, over any others, although low initial cost was a factor.  That hosting has generally been problem free, but their IT support, when there is trouble, has proven to be less than desirable.  Here’s that story in case anybody else is considering using godaddy for their own hosting.

Yesterday, I happened to notice that my blog was completely unresponsive.  I only noticed this because I wanted to make one small change to one of my pages.  All told, to get this resolved, I spent about 3 hrs with their IT support (1/2 last night, and the other 1/2 today).  Ironically, by the time I got to the fifth support professional, the problem resolved itself.  I am glad that I don’t run any sort of business off of this site, as the downtime was at least 16 hours.

My 1.5 hrs on the godaddy IT chat support with Parjeet, Jaspreet, and Shibin was a complete waste of time.  Parjeet (who’s name I am probably butchering, since I didn’t keep a copy of my chat log with him) managed to get the blog restarted.  However, it appears that he also disabled all the plugins at the same time without telling me.  He also didn’t identify the root cause.  Jaspreet insisted that the issue was the content I was hosting, even though that content was not an issue before yesterday.  He gave me various self help options (plugin tuning, …) despite the fact that the blog was performing abysmally even with all plugins disabled, and had been okay prior to the reboot, and despite the fact that even the admin pages were slow, which have nothing to do with the content being served for normal blog page or post content.  He also was not able to identify the root cause, and I insisted on dealing with his manager at that point.  That claimed-manager was Shibin, who was helpful seeming, but was not able to do anything, nor able to find somebody who had access to the server logs to diagnose the issue.  When I gave up for the night, he promised to email me the results of his investigation, but no such email materialized.

The godadday response to an attack is pretty deficient.  If the server that your blog is running on is attacked, they throttle the performance of that server to mitigate the effectiveness of the attack.  The idea is that the attacker will eventually just give up.  That is done apparently done at the server level, and not just for the instance that is under attack.  It seems pretty dumb that godaddy doesn’t migrate the VMs that happen to be unfortunately colocated with attackee onto another physical host.  That’s not a good sign for anybody that wants a service that requires continuous uptime.

When I bought godaddy’s hosting initially, I do remember that it was one of the most cost effective options.  The godaddy hosting price went up considerably sometime after the first or second year of initial service, but I haven’t taken the time to figure out how to migrate to something else.  Perhaps amazon is worth looking at again? Basically, I’m allowing myself to be exploited financially a bit because the time cost to figure out how to migrate to other hosting is probably higher than the monetary cost of the blog hosting itself.

The support interaction that I had over the last two days might be enough of a kick in the butt that I’ll take the time to look at other hosting options, and how to do a migration.  One thing that I do recall was nice about amazon was they offered ssh access to the machine.  I only get sftp access on godaddy, which can be a pain in the butt, and is very inflexible.

You might wonder why I even bothered switching from wordpress.com hosting, which was free.  I did that to have the flexibility to install my own non-wordpress.com sanctioned plugins.  For somebody who is crazy enough to blog a lot of mathematics, that was very worthwhile, as I’ve been able to run a customized version of the Mathjax-Latex plugin, which renders very nicely, and allows me to replicate many of the latex macros that I use.  That streamlines my latex-to-wordpress conversion considerably, and has saved me many many hours.  That saving is in comparison to the time that would have been required to blog the same mathematics with the default wordpress.com latex plugin.  Recently, I also installed the Mathematica Toolbox plugin, which looks like it will allow some fun interactivity, much like the original Wolfram CDF plugin had before it became useless and eventually was no longer supported (i.e. it only worked in 32-bit browsers.)  So, I don’t think that I’m going to go back to wordpress.com hosting, but it’s definitely worth some investigation of the options.

## A price increase for Geometric Algebra for Electrical Engineers

As of this week (end of May 2020), I raised the price of the black and white version of my Geometric Algebra book slightly (from $12 to$14.50 USD).  I say slightly, despite the 17% price increase, because the price is still pretty low from an absolute value perspective, as the markup I’d added to the minimum price was fairly small.  This price increase was an experiment in response to a reseller (SuperBookDeals) buying copies at $12 and then reselling them at higher prices. For some reason amazon lists the higher price reseller copies before their own kindle-direct-publishing version, so a buyer had to go out of their way to find the lowest priced version. I wouldn’t care if resellers undercut my list price, and then got a preferential listing from amazon. The fact that this reseller doesn’t play this game with the color version of the book, which has a much higher printing cost (I haven’t changed my price for that, and am still selling it for$40 USD), suggests to me that I’d set the price too low for the black and white version.

If you are interested in a copy of the book, but don’t like the new higher price, please note that the (color) PDF version is still available for free.

I may drop the price back to the original $12 later, but for now I’m going to charge$14.50, and am curious to see how the pricing game plays out.

Note that a temporary side effect of me having changed the price is that SuperBookDeals appears to have dropped their price of one of their listings below $12 (my original price) to clear out their stock. Amazon also appears to be offering a couple copies at the old$12 price, which now lists as a sale price.

## Unexpected COBOL implicit operator distribution!

Another day, another surprise from COBOL.  I was debugging a failure in a set of COBOL programs, and it seemed that the place things started going wrong was a specific IF check, which basically looked like:

The original code was triple incomprehensible, as it:

• Was in German.
• Was in COBOL.
• Was generated by DELTA and was completely disgusting spaghetti code.  A map of the basic blocks would have looked like it was colored by a three year old vigorously scribbling with a crayon.

It turns out that there was a whole pile of error handling code that happened after the IF check, and I correctly guessed that there was something wrong with how our compiler handled the IF statement.

What I didn’t guess was what the actual operator precedence in this IF check was.  Initially, my C programmer trained mind looked at that IF condition, and said “what the hell is that!?”  I then guessed, incorrectly, that it meant:

if ( X != SPACES and X = ZERO)

where X is the array slice expression.  That interpretation did not explain the runtime failure, so I was hoping that I was both wrong about what it meant, but right that there was a compiler bug.

It turns out that in COBOL the implicit operator for the second part of the IF statement is  ‘NOT =’.  i.e. the NOT= distributes over the AND, so this IF actually meant:

if ( X != SPACES and X != ZERO)

In the original program, that IF condition actually makes sense.  After some reflection, I see there is some sense to this distribution, but it certainly wasn’t intuitive after programming C and C++ for 27 years. I’d argue that the root cause of the confusion is COBOL itself. A real programming language would use a temporary variable for the really long array slice expression, which would obliterate the need for counter-intuitive operator distribution requirements. Imagine something like:

  VAR X = PAYLOAD-DATA(PAYLOAD-START(TALLY): PAYLOAD-END(TALLY))

IF (X NOT = SPACES) AND (X NOT = LOW-VALUE)
NEXT SENTENCE ELSE GO TO CHECK-IT-DONE.


(Incidentally LOW-VALUE means binary-zero, not a ‘0’ character that has a 0xF0 value in EBCDIC).

COBOL is made especially incomprehensible since you can’t declare an in-line temporary in COBOL.  If you want one, you have to go thousands of lines up in the code to the WORKING-STORAGE section, and put a variable in there somewhere.  Such a variable is global to the whole program, and you have to search to determine it’s usage scope.  You probably also need a really long name for it because of namespace collision with all the other global variables.  Basically, you are better off not using any helper variables, unless you want to pay an explicit cost in overall code complexity.

In my test program that illustrated the compiler bug, I made other COBOL errors. I blame the fact that I was using gross GOTO ridden code like the original. Here was my program:

Because I misinterpreted the NOT= distribution, I thought this should produce:

000000001: !(not space and low-value.)
000000002: !(not space and low-value.)
000000003: !(not space and low-value.)
000000003: not space and low-value.


Once the subtle compiler bug was fixed, the actual SYSOUT from the program was:

000000001: not space and low-value.
000000001: !(not space and low-value.)
000000002: !(not space and low-value.)
000000003: !(not space and low-value.)


See how both the TRUE and FALSE basic blocks executed in my code. That didn’t occur in the original code, because it used an additional dummy EXIT paragraph to end the PERFORM range, and had a GOTO out of the first paragraph.

There is more modern COBOL syntax that can avoid this GOTO hell, but I hadn’t used it, as I kept the reproducer somewhat like the original code.

## My collection of Peeter Joot physics paperbacks

I ordered a copy of my old PHY456 Quantum Mechanics II notes for myself, and it arrived today!  Here it is with it’s buddies (Grad QM and QFT):

With the shipping cost from the US to Canada (because I’m now paying for amazon prime anyways) it’s actually cheaper for me to get a regular copy than to order an author proof, so this time I have no “not for resale” banding.

This little stack of Quantum notes weighs in at about 1050 pages, and makes a rather impressive pile.  There’s a lot of info there, for the bargain price of either free or about $30 USD, depending on whether you want a PDF or print copy of this set. Of course, most people want neither, and get all their quantum mechanics through osmosis from the engineering of the microchips and electronics in their phones and computers. I have to admit that it’s a fun ego boost to see your name in print. In order to maximize the ego boost, you can use my strategy and do large scale vanity press, making a multiple volume set for yourself. Here’s my whole collection, which includes the bulk of my course notes, plus my little book: Based on the height of the stack, I’d guess this is about 3000 pages total, the product of about 10 years of study and work. Making these all available for free to anybody in PDF form surely cripples my potential physical copy sales volume, but that doesn’t matter too much since I’ve set the price so low that I only get a token payment for each copy anyways. Based on linear extrapolation of my sales so far, I’ll recoup my tuition costs (not counting the opportunity cost of working part time while I took the courses) after another 65 years of royalties. ## Does this COBOL level-88 IF check make any sense? May 21, 2020 COBOL 2 comments , I find COBOL level-88 declarations a bit confusing, which isn’t made any easier by usage that is probably wrong. Here’s an example from code that I was trying to step through in the debugger (anonymized):  WORKING-STORAGE SECTION. 01 data. 10 function-type PIC X(01). 88 option-a VALUE '1'. 88 option-b VALUE '2'. 88 option-c VALUE '3'. 88 option-d VALUE '4'.  With the use like so:  IF option-a AND option-b AND option-c NEXT SENTENCE ELSE GO TO meaningless-label-2.  It’s my understanding that this is essentially equivalent to:  IF function-type = '1' AND function-type = '2' AND function-type = '3' NEXT SENTENCE ELSE GO TO meaningless-label-2.  Do I misunderstand the level-88 variables should be used, or is this just a plain old impossible-to-be-true if check? Putting this into a little sample program, confirms that we hit the ELSE:  IDENTIFICATION DIVISION. PROGRAM-ID. TESTPROG. ENVIRONMENT DIVISION. CONFIGURATION SECTION. DATA DIVISION. WORKING-STORAGE SECTION. 01 data. 10 function-type PIC X(01). 88 option-a VALUE '1'. 88 option-b VALUE '2'. 88 option-c VALUE '3'. 88 option-d VALUE '4'. PROCEDURE DIVISION. move '1' to function-type perform meaningless-label-1 thru meaningless-label-6 goback . meaningless-label-1. * IF function-type = '1' AND function-type = '2' AND * function-type = '3' IF option-a AND option-b AND option-c NEXT SENTENCE ELSE GO TO meaningless-label-2. display 'IF was true.' goto meaningless-label-6 . meaningless-label-2. display 'IF was not true.' . meaningless-label-6. EXIT .  I get SYSOUT of: IF was not true.  as I expected. If these were level-88 variables each “belonging” to a different variable, such as:  IDENTIFICATION DIVISION. PROGRAM-ID. TESTPROG. ENVIRONMENT DIVISION. CONFIGURATION SECTION. DATA DIVISION. WORKING-STORAGE SECTION. 01 data. 10 blah PIC X(01). 88 blah-option-a VALUE '1'. 88 blah-option-b VALUE '2'. 10 foo PIC X(01). 88 foo-option-a VALUE '1'. 88 foo-option-b VALUE '2'. 88 foo-option-c VALUE '3'. 10 bar PIC X(01). 88 bar-option-c VALUE '3'. 88 bar-option-d VALUE '4'. PROCEDURE DIVISION. move '1' to blah move '2' to foo move '3' to bar perform meaningless-label-1 thru meaningless-label-6 goback . meaningless-label-1. IF blah-option-a AND foo-option-b AND bar-option-c NEXT SENTENCE ELSE GO TO meaningless-label-2. display 'IF was true.' goto meaningless-label-6 . meaningless-label-2. display 'IF was not true.' . meaningless-label-6. EXIT .  This has the ‘IF was true’ SYSOUT. Perhaps the original coder meant to use OR instead of AND? ## COBOL spaghetti code: EXIT does nothing! I was staring down COBOL code of the following form:  LOOP-COUNTER-INCREMENT. ADD 1 TO J. LOOP-PREDICATE-CHECK. IF J GREATER 10 GO TO MYSTERIOUS-LABEL-1. IF ARRAY-1 (J) NOT = ZERO NEXT SENTENCE ELSE GO TO MYSTERIOUS-LABEL-1. IF ARRAY-2 (J) = MYSTERIOUS-MAGIC-NUMBER-CONSTANT NEXT SENTENCE ELSE GO TO COUNTER-INCREMENT-SPAGGETTIFI. * ...MORE STUFF... GO TO MYSTERIOUS-LABEL-3. COUNTER-INCREMENT-SPAGGETTIFI. GO TO LOOP-COUNTER-INCREMENT. MYSTERIOUS-LABEL-1. EXIT. MYSTERIOUS-LABEL-2. EXIT. MYSTERIOUS-LABEL-3. EXIT.  I had to get some guru help understanding what this was about (thanks Roger!). I didn’t understand why somebody would code a GOTO LABEL, when the the code at that LABEL just did an EXIT. If my intuition could be trusted, I would have assumed that this code was equivalent to the much simpler:  LOOP-COUNTER-INCREMENT. ADD 1 TO J. LOOP-PREDICATE-CHECK. IF J GREATER 10 EXIT. IF ARRAY-1 (J) NOT = ZERO NEXT SENTENCE ELSE EXIT. IF ARRAY-2 (J) = MYSTERIOUS-MAGIC-NUMBER-CONSTANT NEXT SENTENCE ELSE GO TO LOOP-COUNTER-INCREMENT. * ...MORE STUFF... EXIT.  It turns out that intuition is not much use when looking at COBOL code. In this case, that intuition failure is because EXIT doesn’t actually do anything. It is not like a return, which is what I assumed, but is just something that you can put in a paragraph at the end of the section so that the code can exit the section (or at the end of a sequence of paragraphs invoked by PERFORM THRU, so that the code can return to the caller.) The EXIT in such a paragraph is just a comment, and you could use an empty paragraph to do the same thing. In my transformation of the code the EXIT would do nothing, and execution would just fall through to the next sentence! Some of the transformations I made are valid. In particular, the spaghettification-indirection used to increment the loop counter, by using a goto to goto the target location instead of straight there, has no reason to exist. The code in question was an edited version of a program that was generated by a 4GL language (DELTA), so some of the apparent stupidity can be blamed on the code generator. I also assume DELTA can also be blamed for the multiple EXIT paragraphs, when it would seem more natural to just have one per section. This code also uses EXIT after other paragraph labels too. The first paragraph in the following serving of horror has such an example:  PERFORM TRANSFER-CHECK THRU TRANSFER-CHECK-EXIT. [snip] TRANSFER-CHECK. EXIT. MEANINGLESS-LABEL-1. IF [A COMPOUND PREDICATE CHECK] NEXT SENTENCE ELSE GO TO MEANINGLESS-LABEL-2. [SNIP] PERFORM [MORE STUFF] GO TO MEANINGLESS-LABEL-100. MEANINGLESS-LABEL-2. [STUFF] GO TO MEANINGLESS-LABEL-4. MEANINGLESS-LABEL-3. [increment loop counter, and fall through] MEANINGLESS-LABEL-4. [loop body] ... MEANINGLESS-LABEL-50. GO TO MEANINGLESS-LABEL-3. [SNIP] ... MEANINGLESS-LABEL-99. EXIT. MEANINGLESS-LABEL-100. EXIT. TRANSFER-CHECK-EXIT. EXIT.  Nothing ever branches to MEANINGLESS-LABEL-1 directly, so why even have that there? Using my new found knowledge that EXIT doesn’t do anything, I’m pretty sure that you could just write:  PERFORM TRANSFER-CHECK THRU TRANSFER-CHECK-EXIT. [snip] TRANSFER-CHECK. IF [A COMPOUND PREDICATE CHECK]  Is there some subtle reason that this first no-op paragraph was added? My guess is that the programmer was either being paid per line of code, or the code generator is to blame. I’m not certain about the flow-control in the TRUE evaluation above. My intuition about the THRU use above is that if we have a GOTO that bypasses one of the paragraphs, then all the preceding paragraphs are counted as taken (i.e. if you get to the final paragraph in the THRU evaluation, no matter how you get there, then you are done.) I’ll have to do an experiment to determine if that’s actually the case. ## My old Quantum II notes are now available on amazon PHY456, Quantum Mechanics II was one of the first few courses that I did as part of my non-degree upper year physics program. That was a self directed study part time program, where I took most of interesting seeming fourth year undergrad physics courses at UofT. I was never really pleased with how my QMII notes came out, and unlike some of my other notes compilations, I never made a version available on amazon, instead just had the PDF available for free on my Quantum Mechanics page. That page also outlines how to get a copy of the latex sources for the notes (for the curious, or for the zealous reader who wants to submit merge requests with corrections.) Well, over the last month or so, I’ve gradually cleaned up these QMII notes enough that they are “print-ready” (no equations overflowing into the “gutter”, …) , and have gone ahead and made it available on amazon, for$10 USD.  Like my other class notes “books”, this is published using amazon’s print on demand service.  In the likely event that nobody will order a copy, there is no upfront requirement for me to order a minimal sized print run, and then be stuck with a whole bunch of copies that I can’t give away.

There are still lots of defects in this set of notes.  In particular, I seem to have never written up my problem set solutions in latex, and subsequently lost those solutions.  There’s also lots of redundant material, as I reworked a few of the derivations multiple times, and never went back and purged the crud.  That said, they are available as-is, now in paper form, as well as a free PDF.

I’ll share the preface, and the contents below.

## Preface.

These are my personal lecture notes for the Fall 2011, University of Toronto Quantum mechanics II course (PHY456H1F), taught by Prof. John E Sipe.

The official description of this course was:

“Quantum dynamics in Heisenberg and Schrodinger Pictures; WKB approximation; Variational Method; Time-Independent Perturbation Theory; Spin; Addition of Angular Momentum; Time-Dependent Perturbation Theory; Scattering.”

This document contains a few things

• My lecture notes.
• Notes from reading of the text \citep{desai2009quantum}. This may include observations, notes on what seem like errors, and some solved problems.
• Different ways of tackling some of the assigned problems than the solution sets.
• Some personal notes exploring details that were not clear to me from the lectures.
• Some worked problems.

There were three main themes in this course, my notes for which can be found in

• Approximate methods and perturbation,
• Spin, angular momentum, and two particle systems, and
• Scattering theory.

Unlike some of my other course notes compilations, this one is short and contains few worked problems. It appears that I did most of my problem sets on paper and subsequently lost my solutions. There are also some major defects in these notes:

• There are plenty of places where things weren’t clear, and there are still comments to followup on those issues to understand them.
• There is redundant content, from back to back lectures on materials that included review of the previous lecture notes.
• A lot of the stuff in the appendix (mostly personal notes and musings) should be merged into the appropriate lecture note chapters. Some work along those lines has been started, but that work was very preliminary.
• I reworked some ideas from the original lecture notes to make sense of them (in particular, adiabatic approximation theory), but then didn’t go back and consolidate all the different notes for the topic into a single coherent unit.
• There were Mathematica notebooks for some of the topics with issues that I never did figure out.
• Lots of typos, bad spelling, and horrendous grammar.
• The indexing is very spotty.

Hopefully, despite these and other defects, these notes may be of some value to other students of Quantum Mechanics.

I’d like to thank Professor Sipe for teaching this course. I learned a lot and it provided a great foundation for additional study.

## Phy456 (QM II) Contents:

• Document Version
• Dedication
• Preface
• Contents
• List of Figures
• 1 Approximate methods.
• 1.1 Approximate methods for finding energy eigenvalues and eigenkets.
• 1.2 Variational principle.
• 2 Perturbation methods.
• 2.1 States and wave functions.
• 2.2 Excited states.
• 2.3 Problems.
• 3 Time independent perturbation.
• 3.1 Time independent perturbation.
• 3.2 Issues concerning degeneracy.
• 3.3 Examples.
• 4 Time dependent perturbation.
• 4.1 Review of dynamics.
• 4.2 Interaction picture.
• 4.3 Justifying the Taylor expansion above (not class notes).
• 4.4 Recap: Interaction picture.
• 4.5 Time dependent perturbation theory.
• 4.6 Perturbation expansion.
• 4.7 Time dependent perturbation.
• 4.8 Sudden perturbations.
• 4.10 Adiabatic perturbation theory (cont.)
• 4.11 Examples.
• 5 Fermi’s golden rule.
• 5.1 Recap. Where we got to on Fermi’s golden rule.
• 5.2 Fermi’s Golden rule.
• 5.3 Problems.
• 6 WKB Method.
• 6.1 WKB (Wentzel-Kramers-Brillouin) Method.
• 6.2 Turning points..
• 6.3 Examples.
• 7 Composite systems.
• 7.1 Hilbert Spaces.
• 7.2 Operators.
• 7.3 Generalizations.
• 7.4 Recalling the Stern-Gerlach system from PHY354.
• 8 Spin and Spinors.
• 8.1 Generators.
• 8.2 Generalizations.
• 8.3 Multiple wavefunction spaces.
• 9 Two state kets and Pauli matrices.
• 9.1 Representation of kets.
• 9.2 Representation of two state kets.
• 9.3 Pauli spin matrices.
• 10 Rotation operator in spin space.
• 10.1 Formal Taylor series expansion.
• 10.2 Spin dynamics.
• 10.3 The hydrogen atom with spin.
• 11 Two spins, angular momentum, and Clebsch-Gordon.
• 11.1 Two spins.
• 11.2 More on two spin systems.
• 11.3 Recap: table of two spin angular momenta.
• 11.4 Tensor operators.
• 12 Rotations of operators and spherical tensors.
• 12.1 Setup.
• 12.2 Infinitesimal rotations.
• 12.3 A problem.
• 12.4 How do we extract these buried simplicities?
• 12.5 Motivating spherical tensors.
• 12.6 Spherical tensors (cont.)
• 13 Scattering theory.
• 13.1 Setup.
• 13.2 1D QM scattering. No potential wave packet time evolution.
• 13.3 A Gaussian wave packet.
• 13.4 With a potential.
• 13.5 Considering the time independent case temporarily.
• 13.6 Recap.
• 14 3D Scattering.
• 14.1 Setup.
• 14.2 Seeking a post scattering solution away from the potential.
• 14.3 The radial equation and its solution.
• 14.4 Limits of spherical Bessel and Neumann functions.
• 14.5 Back to our problem.
• 14.6 Scattering geometry and nomenclature.
• 14.7 Appendix.
• 14.8 Verifying the solution to the spherical Bessel equation.
• 14.9 Scattering cross sections.
• 15 Born approximation.
• A Harmonic oscillator Review.
• A.1 Problems.
• B Simple entanglement example.
• C Problem set 4, problem 2 notes.
• E 2nd order adiabatically Hamiltonian.
• F Degeneracy and diagonalization.
• F.1 Motivation.
• F.2 A four state Hamiltonian.
• F.3 Generalizing slightly.
• G Review of approximation results.
• G.1 Motivation.
• G.2 Variational method.
• G.3 Time independent perturbation.
• G.4 Degeneracy.
• G.5 Interaction picture.
• G.6 Time dependent perturbation.
• G.7 Sudden perturbations.
• G.9 WKB.
• H Clebsh-Gordan zero coefficients.
• H.1 Motivation.
• H.2 Recap on notation.
• H.3 The $$J_z$$ action.
• I One more adiabatic perturbation derivation.
• I.1 Motivation.
• I.2 Build up.
• I.4 Summary.
• J Time dependent perturbation revisited.
• K Second form of adiabatic approximation.
• L Verifying the Helmholtz Green’s function.
• M Mathematica notebooks.
• Index
• Bibliography

## Reverse engineering a horrible COBOL structure initialization

The COBOL code that I was looking at used a magic value 999, and I couldn’t see where it could be coming from.  After considerable head scratching, I managed to figure out that all the array structure instantiations in the code are initialized using strings.  That seems to be the origin of the magic (standalone) 999’s scattered through the code.

To share the horror, here is an (anonymized) example of the offending array structure initialization

where I added in the block comment that points out each of the interesting regions of the initialization strings.

Here’s what’s going on.  We have a global variable array (effectively unnamed) that has three fields:

• two-characters (numeric only)
• dummy-structure-name, containing a 3 character field and a pad.
• nine-more-characters

If you add up all the characters in this data structure we have: 2 + 1 + 4 * (3 + 1) + 9 = 28, so this array initialization is effectively done by aliasing the array elements with the memory containing a char[7][28].

My eyes are burning!

As far as I can tell, COBOL has no notion of a structure type, you just have instances of structures everywhere (they are probably called something different — a level 01 declaration, or something like that).  A lot of the PL/I code I’ve seen is also like that, although in PL/I you can declare your structure types if you want to.

The display’s above make use of the fact that COBOL variables don’t have to use all the high level qualifiers (unless there is ambiguity).  My SYSOUT shows that, sure enough, the (5) element of the array (COBOL arrays are one’s counted) has the values I expected:

1 22 2 999 3 1/2 4 5 6 SF

Basically, the horrendous initialization above, is as if you if declared your structure as:

struct arrayname
{
char numeric2[2];
char filler1[1];
struct
{
char threemore[3];
char filler2[1];

char ninemore[9];
};


and then initialized it with:

char globalmemory[7][28] = {
// n2       f    x    x    x    y    x    x    x    y    x    x    x    y    x    x    x    y    'K', 'l', 'a', 's', 's', 'e', ' ', ' ', ' '},
{ '0', '1', ' ', ' ', ' ', '0', ' ', ' ', ' ', '0', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', 'K', 'l', 'a', 's', 's', 'e', ' ', ' ', ' '},
{ '0', '2', ' ', ' ', ' ', '0', ' ', ' ', ' ', '0', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', 'K', 'l', 'a', 's', 's', 'e', ' ', ' ', ' '},
{ '1', '3', ' ', '9', '9', '9', ' ', '9', '9', '9', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', 'K', 'l', 'a', 's', 's', 'e', ' ', ' ', ' '},
{ '2', '1', ' ', '9', '9', '9', ' ', '1', '/', '2', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', 'S', 'F', ' ', ' ', ' ', ' ', ' ', ' ', ' '},
{ '2', '2', ' ', '9', '9', '9', ' ', '1', '/', '2', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', 'S', 'F', ' ', ' ', ' ', ' ', ' ', ' ', ' '},
{ '2', '3', ' ', '1', '/', '2', ' ', '1', '/', '2', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', 'S', 'F', ' ', ' ', ' ', ' ', ' ', ' ', ' '},
{ '3', '1', ' ', ' ', ' ', '1', ' ', ' ', ' ', '1', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', 'S', 'F', ' ', ' ', ' ', ' ', ' ', ' ', ' '},
};

struct arrayname * p = (struct arrayname*)globalmemory;


and then and then printed:

   printf( "1 %.2s\n", p[4].numeric2 );
printf( "6 %.9s\n", p[4].ninemore );


Of course, the use of fixed length strings without a null terminator wouldn’t ever be done in C, so a more natural equivalent (assuming one doesn’t care about the specific memory equivalence of the two representations, and can tolerate null terminators instead of spaces) would just be something like:

struct arrayname
{
char numeric2[3];
struct
{
char threemore[4];

char ninemore[9];
};

struct arrayname g[7] = {
{ "01", {"  0", "  0", "   ", "   "}, "Klasse  " },
{ "02", {"  0", "  0", "   ", "   "}, "Klasse  " },
{ "13", {"999", "999", "   ", "   "}, "Klasse  " },
{ "21", {"999", "1/2", "   ", "   "}, "SF      " },
{ "22", {"999", "1/2", "   ", "   "}, "SF      " },
{ "23", {"1/2", "1/2", "   ", "   "}, "SF      " },
{ "31", {"  1", "  1", "   ", "   "}, "SF      " }
};


You could argue that the COBOL way isn’t so bad once you’ve seen the pattern, and is only cosmetically different from the natural C analogue. That is, if you ignore the fact that there is no separation of fields in the initializer strings, and that you have to name a whole bunch of dummy initializer objects and fill characters, and the fact that any semblance of typing is completely obliterated.

The code in question is also complete spaghetti, with GOTO all over the place.  Perhaps COBOL versions after COBOL77, which is what I assume I’m looking at, added loops and better initialization syntax?

## Computing “offsetof” in COBOL

May 15, 2020 Mainframe 1 comment , , , , ,

I couldn’t find a way to compute something like C offsetof in COBOL code.  What I could manage to figure out how to do is compare addresses of a runtime instantiation of the structure, effectively doing this indirectly.  Here’s the ugly mess that I cooked up:

I couldn’t figure out the right syntax to do a single compute statement that was just the difference of addresses, as I got numeric/pointer compare errors from the compiler, no matter what I tried.  I think that ‘USAGE IS POINTER’ may be required on my variables, but that would still require a temporary.  I’m probably either doing this the hard way, or there is no easy way in COBOL.

This program was run with the following simple JCL

//TESTPROG JOB //A EXEC PGM=TESTPROG //SYSOUT DD SYSOUT=* //STEPLIB DD DSN=COBRC.NATIVE.TESTPROG, // DISP=SHR

and produced the following SYSOUT

address of TESTPROG-STRUCT = 0016800264 offsetof(ARRAY-NAME,RUECK-BKL) = 0000000002 offsetof(ARRAY-NAME,RUECK-BS) = 0000000004 offsetof(ARRAY-NAME,RUECK-SF) = 0000000007 sizeof(ARRAY-NAME(1)) = 0000000019

Looking at that output, we can conclude the following:

• PIC S9(3) COMP-3 is effectively horrible eye-burning syntax for a “short”
• There is no alignment padding between fields, nor end of array-member padding to force natural alignment of the next array element, should the structure start have been aligned.

I knew the latter, but wasn’t sure what size the first field was, and thought that trying to figure it out with COBOL code would be a good learning exercise.