Arbitrary Precision Floating Point (APFP)
by Dennis Darland  pal at dennisdarland dot com
dennisdarland.com
Comments welcome
 Initially developed as procedures in Icon then reworked as classes & overloaded operators in Unicon.

Reworked much more elegantly in Ruby. Mostly because of greatly increased
knowledge of problem from having done it before. Also conciseness of Ruby.
 2/25/2015 added ruby on rails calculators
 3/1/2015 Setup and ran aptst.rb
Found I had to change some "require" statements to "require_relative".
 Then reworked totally the error handling in Apfp.rb
Added error_flag to class  always initialized to false/
Added function to report error  or if method is given value that had error previously.
Added function to set error and then call function reporting it.
All errors seem to be because of domain errors.
The check is not catching all cases  because of "fuzziness" of comparisons  (or some may be missing)  doesn't always catch very close cases.
I think I already have functions that can do tests  but I will have to examine each case carefully.
 Then I will have to make the rails code use this error handling also.
 It is past 5:00am (3/1/2015) so I am done for the night  as was on a roll, I did not want to quit  I will sleep better.
 Worked till 4:00am (3/2/2015) then again in afternoon  uploaded new versions realcalc0004.zip, compcalc0004.zip, and also batch test aptst0004.zip
Also text files of batch tests below
 Need to redo demos  but too tired  will wait until I am fresher.
Demos of Complex Number Calculator (version 0006 on 3/5/2015) with everything that was wrong fixed as far as I know
I can thing of improvements  such as red error messages
 Complex Number Calculator 6 Demo 1 simple imaginary values
 Complex Number Calculator 6 Demo 2 simple complex arithmetic
 Complex Number Calculator 6 Demo 3 trig functions (some had trouble before  now work)
 Complex Number Calculator 6 Demo 4 trig, inverse trig, hyperbolic, and inverse hyperbolic functions of complex values
 Complex Number Calculator 6 Demo 5 some log and exponentiation
 Complex Number Calculator 6 Demo 6 misc functions
 Complex Number Calculator 6 Demo 7 calculating with lower precision
Original Demos of Complex Number Calculator  I'm not used to doing this as you can tell.
 Complex Number Calculator Demo 1  The values were at least approximate  compared with Maple  but I later discovered I used wrong version of library
 Complex Number Calculator Demo 2  with correct library  the problem had been noticed with asin
 Complex Number Calculator Demo 3  add, subtract, multiply divide
 Complex Number Calculator Demo 4  trig  worked until 5 minute video time limit ran out on tan of pi/2 which failed
 Complex Number Calculator Demo 5  trig  tan pi/2 failing
 Complex Number Calculator Demo 6  trig  tan pi/4 worked but arctan of result failed
 Complex Number Calculator Demo 7  trig and arctrig of 0.1
 Complex Number Calculator Demo 8  trig and arctrig of complex value (0.1 + 0.2i)
 Complex Number Calculator Demo 9  hyperbolic and archyperbolic of complex values  also log and exp (0.3 + 0.2i)
 Complex Number Calculator Demo 10  other functions
 Complex Number Calculator Demo 11  entering using scientific notation
 Complex Number Calculator Demo 12  entering data less accurately known
For Comparison to Maple
 Values for comparison from Maple 18 for Demo 1
 Values for comparison from Maple 18 for Demo 2
 Values for comparison from Maple 18 for Demo 3
 Values for comparison from Maple 18 for Demos 4 to 10
I compared all the cases where APFP returned numeric answers for demos 210 and the answers were very accurate.
Demo 1 was using a wrong library and arcsin was off & threw off subsequent answers in that demo.
It appeared that deviations were on the order of magnitude of the estimated error but I would have to rely on an automated test to determine that conclusively.
There were execution errors on tan(pi/2), and arctan(1)
3/2/2015 Extensive Batch Tests
The Ruby Program to generate a Ruby program to generate a Maple test program
The generated Ruby program to generate a Maple test program
The generated Maple test program
Test Results  Just all functions
Test Results EXCEPTIONS  all functions
Ap.rb
ApConfig.rb
Apc.rb
Apfp.rb
Real.rb
3/3/2015 Extensive Batch Tests of IMPROVED library
The Ruby Program to generate a Ruby program to generate a Maple test program
The generated Ruby program to generate a Maple test program
The generated Maple test program
Test Results  Just all functions
Test Results EXCEPTIONS  all functions
Ap.rb
ApConfig.rb
Apc.rb
Apfp.rb
Real.rb
2/26/2015  Fixed a couple bugs in installation procedure and updated README for Installing above.
Later discovered that version on rapfp library I grabbed for rails  switched to one which I ran tests below on.
Had noticed error in asin which was correct in this version.
Doing more testing while working also on more demos.
Use realcalc0003.zip and compcalc00031.zip
 2/3/2010 Start development of regression test for APFP (Ruby program to generate a Ruby Program to generate a Maple Program
to compare answers.
 2/5/2010 Test program for APFP almost finished.
 2/6/2010 Test program basically finished  tests ran OK on sin, cos and tan.
 2/7/2010 Tested all functions  fixed some problems  log, log10 and sqrt not as accurate as desired.
sinh and tanh also had one problem.
 2/8/2010 Enhanced information in Exception file and added time info. Maple took about 16 minutes clock time  but I didn't find a function for that.
 2/13/2010 Struggling with how to compute logarithms  I see what is wrong  but not how to fix it.
 2/13/2010 Fixed problems with logarithms and other less difficult problems. Links to programs and results below.
Maple produces results almost immediately if screen output is suppressed by using ":" instead of ";"
 2/15/2010 Correction to calculation of percentage
 Samples:
The Ruby Program to generate a Ruby program to generate a Maple test program
The generated Ruby program to generate a Maple test program
The generated Maple test program
Test Results  Just all functions
Test Results EXCEPTIONS  all functions
Ap.rb
ApConfig.rb
Apc.rb
Apfp.rb
Real.rb

NOTE about purpose of Apfp. I am trying to write an arbitrary precision floating point with a capability of
tracking the possible error in values calculated from possible error in input or through rounding error. It is very slow,
but its purpose is not speed. It is mainly an experiment to see how errors may propagate in calculations. In fact, in the
tests above I am calculating to only 16 digits. But in practical applications I doubt if inputs are often known to this
accuracy. Larger input errors can be specified as +/error in literals. I think some improvements in both speed and accuracy
are still possible  but it will never be very fast.
 Worked on Documentation: (via simple sample program)
Sample program with comments
Results are in: (I haven't checked all of them closely  I did check the comparison operators and made some improvements
The tests above were also updated.
Results from sample program.
Generated rdoc files (documentation)
 Sourceforge Project Apfp page APFP PAGE
Dennis J. Darland