From: martin.vahi@...1.com
Date: 2014-11-13T07:01:27+00:00
Subject: [ruby-core:66249] [ruby-trunk - Feature #9528] mathn.rb library

Issue #9528 has been updated by Martin Vahi.


I wasn't aware of the existence of the gamma function before reading Your comment. I guess I got a bit smarter due to Your comment. Thank You for that. :-)

According to some sources, including the

    http://mathworld.wolfram.com/GammaFunction.html

it seems to me that the gamma function is an approximation. I think that a clean solution for functions that are based on approximations should always have a maximum error size as a second argument. For example,

    sin(x)    
    
is actually calculated through series and is never absolutely correct. Therefore the

    sin(x)
    cos(x)
    gamma(x)
    etc...

should be

    sin(x,absolute_value_of_max_error=<some default value>)
    cos(x,absolute_value_of_max_error=<some default value>)
    gamma(x,absolute_value_of_max_error=<some default value>)
    etc...

The IEEE_754

    https://en.wikipedia.org/wiki/IEEE_floating_point

determines some "default" error "size" through its rounding. Due to the exponent mechanism of the IEEE_754, the same property that gives

    fd_big=(9**99).to_f
    puts "No difference detected." if fd_big == (fd_big+1.to_f)

there is no single minimum approximation-result-changing value for the error size. Therefore, to find a clean solution for the proper implementation of the gamma/sin/cos/etc. function(s), further work has to be done and that's probably going to be pretty complex and time consuming. However, it is a fact that the current Math.gamma(x) implementation is flawed, because it gives IEEE_754 "infinity" for Math.gamma(10000). That probably limits cryptography related experiments.

The good news is that it seems (at least to me) that dependency wise factorial of integers is very general. Even some forms of the gamma(x) formulae depend on factorials of integers. That's why it seems to me that the proposed 

    Fixnum.factorial
    Bignum.factorial
    
do not clutter the stdlib. That is to say, as of my current comment, I stick with my initial proposal.

Well, one way or the other, I still thank You all for Your answers and efforts. :-)



----------------------------------------
Feature #9528: mathn.rb library
https://bugs.ruby-lang.org/issues/9528#change-49928

* Author: Umair Amjad
* Status: Open
* Priority: Normal
* Assignee: Zachary Scott
* Category: lib
* Target version: current: 2.2.0
----------------------------------------
I want to add factorial method mathn.rb file as feature of Math module.

---Files--------------------------------
the_code.rb (7.49 KB)
run_demo.bash (591 Bytes)


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