[doc] Comments & Readme

.gitignore

@@ -5,3 +5,4 @@
 src/*.o
 tests/*.o
 testrunner
+cheapgmp

README.md

@@ -1,78 +1,38 @@
 # Purpose
 
-Prove I'm not an idiot.
+This was a résumé test question given to someone else, who had brought
+it to the August 7th, 2015 Beer && Coding, in the hopes that we would
+help him solve it.  We were not successful, although I did get pretty
+far on my own with a solution written in Scheme.
 
-As an exercise, I decided to do this homework in C++.  As I haven't
-written any C++ in 15 years, this was... entertaining.
+The problem stated was:
 
-# Task #1
+    Given a number (assume base 10) less than 10,000, write a program in
+    C++ that will reverse the digits of that number, calculate the
+    original number to the power of the new number, and print it out.
+    You may not use Boost, GMP, or any library other than that provide
+    by the C++ Standard Library.
 
-   Write a function which computes the some [sic] of q, q^2, q^3, … q^n,
-   where "^" denotes power or exponent.  For example, the sum of
-   2,4,8,16 is 30.  What is the complexity?
+I don't know C++.  I haven't ever written C++ profesionally, and I
+haven't actually *looked* at C++ since 1999 or so.  As a professional,
+I'm aware of what's going on in the zeitgeist, and at my job at Spiral
+Genetics I interacted with two very talented C++ developers a lot, so I
+was aware of things like the emerging C++ Standard Library and RAII and
+so forth.  I didn't know what they *meant*, but I had heard them.  I've
+also been aware of the emerging standards in C++11 and C++14, mostly
+thanks to Slashdot, Lobsters, and their ilk (don't read the comments,
+don't **ever** read the comments), so I'd *heard* about auto_ptr and
+C++11 lambdas and the like.
 
-The complexity is linear.  This is a basic sigma function, once you know
-the underlying formula, production is simple.  The requirements for the
-code (that you determine both the base of your exponent collection, and
-know how many you want) are difficult to discern from a simple reading
-of the instructions.  
+It took about an hour of googling to get up to speed on things like
+namespaces, containers, for_each, lambdas, and the like.  I really like
+the new unique\_ptr construction.  That's very nice.
 
-If I'd allowed myself to use boost(), I've written this using the
-accumulate() function, but I'd have to figure out how to create a range
-iterator.
+My basic solution degrades to 4th-grade mathematics: Break the
+multiplicand up into a list of single digits, multiply each digit
+with the multiplier, then redistribute the values up the tens, hundreds,
+etc. etc.  This solution is not particularly fast or space-efficient,
+but it has the virtue of being comprehensible by any ten-year-old.
 
 
-# Task #2
-
-   Write a function GetMax(Node list), which finds the maximum integer
-   value in the list
-
-In order to make this at all interesting, I set myself the task of
-learning how to create function templates, which we didn't have back in
-1999.  It turned out to be relatively straightforward, although the
-"typename" declarator in the template before std::list<t>::iterator is a
-bit of cargo-cult I got from compiler's warnings; I really need to go
-back and read some of Alexandrescu's books, especially since I got them
-all for free after spotting a typo in one back in 1997 or so.  
-
-I've provided a Makefile and unit tests using the Aeryn C++ Test
-Framework.  It was a framework chosen at random from a list I found
-after searching for "C++ Test Frameworks," I can't comment on its
-quality, but it did the job.  It looked familiar enough compared to
-JUnit or Mocha.
-
-# Commentary
-
-It's been a long time since I wrote C++.  The syntactical noise of C++
-annoys me a bit since I've started writing in "An elegant language for a
-more civilized time," and I'm so far out of experience with it that the
-modern paradigm of Resource Allocation Is Initialization and all of the
-wonderful new toys like auto, unique_ptr, lambdas and the like would
-take me a month or two to catch up.
-
-If I'd written this in Javascript they'd have been one-liners:
-
-    exponentialSum = (base, count) => 
-        _.reduce(_.range(1, count + 1), ((m, v) => return m + Math.pow(base, v)), 0);
-
-    largestValue = _.max;
-
-or:
-
-    largestValue = (list) => Math.max.apply(Math, list);
-
-I'm pretty sure that the functions I wrote have simple equivalents in
-some library somewhere.  Boost seems to have just about everything.
-
-The Makefile is just something I pulled out of an old project and
-cleaned up for the purposes of this exercise.
-
-Total time spent: Approximately 75 minutes.
-
-# Addenda
-
-The [sic] in the original task description is a bit of a snark.  That
-and the instruction to "Please use of of [sic] Java/C++/C#/Javascript"
-ought to be professionally embarrassing to someone seeking viable,
-self-respecting candidates.
 

src/cheapgmp.cpp

@@ -4,21 +4,34 @@ using namespace std;
 
 namespace cheapgmp {
   namespace {
-    void multiply(gmrep &in, ulong by) {
+
+    /* Given a list representing a decimal number as a multiplicand,
+       multiply each digit by a multiplier, leaving in its place the
+       remainder modulo 10 of the result, and using result diviso 10
+       as a carryover to the 10^(n+1) slot */
+
+    void multiply(gmrep &multiplicand, ulong multiplier) {
       gmrep res(new lmrep());
       ulong rem = 0;
-      for_each(in->rbegin(), in->rend(), [&rem, by](ulong &i) { 
-          ulong t = (i * by) + rem ; 
+      for_each(multiplicand->rbegin(), multiplicand->rend(), [&rem, by](ulong &i) { 
+          ulong t = (i * multiplier) + rem ; 
           i = t % 10 ; 
           rem = t / 10; 
         });
 
+      /* When out of list elements, drain the result diviso 10 until
+         the new result is complete */
+      
       while(rem > 0) {
         in->push_front(rem % 10);
         rem = rem / 10;
       }
     }
 
+    /* Given an integer, return a std::list<int> in which each node
+       represents a decimal placement, i.e the end() is the ones,
+       end().prev() is the tens, etc. */
+    
     gmrep makerep(const ulong in) {
       gmrep res(new lmrep());
       if (in == 0) {
@@ -35,6 +48,9 @@ namespace cheapgmp {
     }
   }
 
+  /* Perform the operation multiple times, to produce an exponential
+     result */
+  
   gmrep makepower(const ulong base, const ulong power) {
     if (power == 0) {
       return makerep(base == 0 ? 0 : 1);