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Binary Fixed Point calculations with Ruby
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= fixedpnt

== DESCRIPTION

Binary Fixed Point calculations with Ruby.

fixedpnt allows simulating binary fixed point calculations done in hardware.

If you want to know what fixed point numbers are, you can read this: 
http://en.wikipedia.org/wiki/Fixed-point_arithmetic

There is another library from Phil Tomson which serves the same purpose
but with different properties:
http://rubyforge.org/projects/fixedpt/

For _decimal_ fixed point calculations there is at least the library
from Karl Brodowsky:
http://rubyforge.org/projects/long-decimal/


== FEATURES/PROBLEMS:

GOALS: 
* Simulating fixed point calculations done in hardware
* Relatively fast (pure Ruby, for I don't know C...) 
* The fixed point format of the result of an expression shall be the same as
  with Matlab. Example: Lets x and y each be 4 bits long with the binary point
  at one place from right. With z = x * y, z will have a length of 8 bits 
  with the binary point at two places from right.

IT HAS: 
* tracking (at the very end you can read the min and max value a variable was assigned to)
* "Inheritance" of fixed-point format ("right" format will be calculated automatically);
* Overflow check;

IT HAS _NOT_: 
* OVERFLOW: NO overflow handler; instead: raises error;
* NO COERCE;
* Syntax _not_ Matlab-compatible; 
* no rounding; 
* SIGNED only.
* As of now, NO DIVISION (I did not need it)

KNOWN ISSUES:
* Exception raising on overflow isn't well done.


== SYNOPSIS:

EXAMPLE USAGE:
  require 'fixedpnt'
  include FixedPntModule
  $fixedpnt_track_min_max = true
  
  a = fp(64, 8) 
  b = fp(64, 8) 
  c = fp
  
  10000.times do |i| 
    a.assign( i )
    b.assign( 2.2 * i ) 
    if  i > 5000 
      c.is a - b 
    else 
      c.is a + b 
    end 
  end    
  
  puts "a.abs_min_max = "  + a.abs_min_max.inspect  #=> [0.0, 99999.0]
  puts "b.abs_min_max = "  + b.abs_min_max.inspect  #=> [0.0, 219997.796875] 
  puts "c.abs_min_max = "  + c.abs_min_max.inspect  #=> [-119998.796875, 160000.0]
  puts "c.format = " + c.format.inspect   #=> [65, 57, 8]
  p required_fp_format(0.001, 220000)     #=> [30, 10]


GENERAL USAGE: 

CREATION:
FixedPnt.new(total_bits=nil, frac_width=nil, value=nil)

fp1 = FixedPnt.new(32,16, 1.234)
  * Sets fixed-point format to:
  ** total number of bits, including sign = 32; 
  ** number of fractional bits = 16; 
   (Total number of bits may be smaller than number of fractional bits.)
  * Sets value to 1.234; 
fp1 = FixedPnt.new(32,16)
  * Sets fixed-point format;
  * Value is assigned later;
fp1 = FixedPnt.new()
  * Fixed-point format and value are assigned later;
  * Usefull for format-"inheritance"
  * Usefull for min-max-tracking

SHORTCUT to FixedPnt.new(...):
  include FixedPntModule
  fp(...)

ASSIGNMENT ( # # #  IMPORTANT !! # # # )

"fp1 = ...": 
   Use this in rare cases only! 
   ("=": Assignment of variable name to object.) 

instead, use (for speed and tracking):

"fp2.is(fp1)":
   Sets value (and format) of fp2 to equal fp1. 
   fp2 and fp1 must have same format, OR: 
   fp2's format is automatically taken from fp1
   ("inherited"), OR raises error if formats are different.
"fp3.is(fp1 + fp2"): 
   fp3 and "fp1 + fp2" must have same format, OR: 
   fp3's format is automatically taken from "fp1 + fp2" 
   ("inherited"), OR raises error if formats are different.
 "fp1.assign( a_float)" or "fp1.assign( an_integer )":
    Assignes value to fp1. 
"fp2.fit(fp1)":
  Use this to reformat ("resize") fp1. 

MEMORIZE:
"is": left and right side are FixedPnt, formats are equal or automtically set;
"fit": left and right side are FixedPnt, formats are unequal;
"assign": left is FixedPnt, right is Numeric;
    
MIN-MAX-TRACKING:
  Stores min and max value ever assigned to this fixed-point instance.
  Tracking can be disabled by setting:
    $fixedpnt_track_min_max = false ;


== REQUIREMENTS:

* Ruby 1.8.7 or higher

(I used it with Ruby 1.8.7 and 1.9.3.)


== INSTALL:

* gem install fixedpnt

== LICENSE:

(The MIT License)

Copyright (c) 2013 Axel Friedrich and contributors (see the CONTRIBUTORS file)

Permission is hereby granted, free of charge, to any person obtaining
a copy of this software and associated documentation files (the
'Software'), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:

The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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