Comments, documentation.

  * README.md: Comment cards count when calculating jumps. Added note
      on check_for_prime.ae.
  * check_for_prime.ae: Improved commenting. Updated branches to
      match.

Author: simonjwright

README.md

@@ -31,17 +31,17 @@ The Ada emulator is written using [Ada2012][], and uses the
 [GNU Multiple Precision Arithmetic library][], via the
 [GMP binding in GNATCOLL][].
 
-If you have the [FSF GCC 6.1.0 binary for OS X][] a suitable library
-is provided. Otherwise, GMP and GNATCOLL are reasonably
-straightforward to build.
+If you have one of the [FSF GCC binaries for OS X][] (6.1 or later), a
+suitable library is provided. Otherwise, GMP and GNATCOLL are
+reasonably straightforward to build.
 
 [Ada2012]: http://www.ada-auth.org/standards/rm12_w_tc1/html/RM-TOC.html
 
 [GNU Multiple Precision Arithmetic library]: https://gmplib.org
 
 [GMP binding in GNATCOLL]: https://github.com/AdaCore/gnatcoll/blob/master/src/gmp/gnatcoll-gmp-integers.ads
 
-[FSF GCC 6.1.0 binary for OS X]: https://sourceforge.net/projects/gnuada/files/GNAT_GCC%20Mac%20OS%20X/6.1.0/
+[FSF GCC binaries for OS X]: https://sourceforge.net/projects/gnuada/files/GNAT_GCC%20Mac%20OS%20X/
 
 ## Running
 
@@ -65,7 +65,7 @@ transferring the value on the source to the destination as the source
 digits were rotated back to zeros.
 
 If `-z` is given, overwriting will be allowed; otherwise, an error
-will be reported ane exceution will halt.
+will be reported and execution will halt.
 
 [this paper]: http://rclab.de/rclab/_media/analyticalengine/aal_noteg_glaschick_v1.2.pdf
 
@@ -94,14 +94,21 @@ These card types have not been implemented (yet):
     * Card Library Inclusion Requests
     * Decimal Place Expansion Cards
 
-As a minor change, lower case can be used: `n001 42` is
-acceptable (it stores 42 into column 1).
-
 As in the [Fourmilab Java implementation][], multiplication can be
 indicated by `*` or `×`, division by `/` or `÷`.
 
 [Fourmilab Java implementation]: https://www.fourmilab.ch/babbage/cards.html
 
+When counting for Combinatorial Cards (conditional and unconditional
+jumps), remember that comment cards (cards starting with a period or
+white space) need to be included!
+
+### Changes
+
+  * As a minor change, lower case can be used: `n001 42` is acceptable
+  (it stores 42 into column 1).
+  * Text after the required content is ignored, so comments can be included: `n001 42 the answer` is acceptable.
+
 ## Examples
 
 The file `bernouilli.ae` is an implementation of the Lovelace design
@@ -126,12 +133,15 @@ might have hoped for. To deal with this, all real values are scaled by
 For more on this, see the notes on _Stepping Up and Down Cards_ in the
 [Fourmilab Java implementation][].
 
+[Sketch of the Analytical Engine]: https://www.fourmilab.ch/babbage/sketch.html
+
 The file `bernouilli5.ae` adds another "iteration" to the above
 program; the previously computed B7 is stored on column 24, and
 operations 13 to 23 are repeated once more (now using column 24 as
 input at operation 21).
 
-[Sketch of the Analytical Engine]: https://www.fourmilab.ch/babbage/sketch.html
+The file `check_for_prime.ae` determines whether a number is
+prime. It's set to check 203 (AAL's 203rd birthday was in 2018).
 
 ## Performance
 

check_for_prime.ae

@@ -6,20 +6,63 @@ N001 203 the number to be checked
 N000 0   constant 0 - actually the default
 N002 1   constant 1
 N003 2   constant 2
+N004 3   starting test divisor
 
-N004 3   starting test value
+. column 10 is used as a scratch register; it must be zero before
+. storing into it, so always load using Z10
 
 A write in columns
 
-/        main loop: divide target by test value
+. if target number is < 4, it's prime
++        add 1 to 3, makes 4
+L004
+L002
+S010
+-        subtract 4 from target number
+L001
+Z010     leave column 10 zero
+CF?1     skip if sign changed (target < 4)
+CF+9     continue
+A write numbers as ##9
++        report the target is prime
+L001
+L000
+P
+A write annotation  is prime
+A write new line
+H
+
+. if target number is divisible by 2, it isn't prime
+/
+L001
+L003
+S010     store remainder
+-        check for zero
+Z010     load remainder, leaving column 10 zeroed
+L002     subtract 1
+CF?1     skip to print/halt if sign changed (i.e. was zero)
+CF+8     continue to check next divisor
+A write numbers as ##9
++        print the target number
+L001
+L000
+P
+A write annotation  is divisible by 2
+A write new line
+H
+
+. main loop
+/        divide target by test value
 L001
 L004
 S010     store remainder (column 10 must be zero previously)
 -        check for zero
 Z010     load remainder, leaving column 10 zeroed
 L002     subtract 1
 CF?1     skip to print/halt if sign changed (i.e. was zero)
-CF+13    continue to check next divisor
+CF+15    continue to check next divisor
+
+. divisor found!
 A write numbers as ##9
 +        print the target number
 L001
@@ -33,6 +76,7 @@ L000
 P
 A write new line
 H
+
 +        check next possible factor
 Z004     load current candidate, clear store
 L003     add 2
@@ -45,7 +89,9 @@ S010
 L001     load target
 Z010     load (candidate squared), leaving column 10 zeroed
 CF?1     skip if sign changed (i.e. no divisor found)
-CB+35    back to main loop
+CB+39    back to main loop
+
+. no divisor found!
 A write numbers as ##9
 +        report the target is prime
 L001