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math::machineparameters(n) tclrep math::machineparameters(n) 





NAME


math::machineparameters - Compute double precision machine
    parameters.






SYNOPSIS


package require Tcl 8.4


package require snit 


package require math::machineparameters 0.1


machineparameters create objectname
    ?options...?


objectname configure ?options...?


objectname cget opt


objectname destroy


objectname compute


objectname get key


objectname tostring


objectname print










DESCRIPTION


The math::machineparameters package is the Tcl equivalent
    of the DLAMCH LAPACK function. In floating point systems, a floating point
    number is represented by




x = +/- d1 d2 ... dt basis^e




where digits satisfy



0 <= di <= basis - 1, i = 1, t




with the convention :

    
  
  • t is the size of the mantissa
    • 
  
  • basis is the basis (the "radix")
    • 



The compute method computes all machine parameters. Then,
    the get method can be used to get each parameter. The print
    method prints a report on standard output.






EXAMPLE


In the following example, one compute the parameters of a desktop
    under Linux with the following Tcl 8.4.19 properties :




% parray tcl_platform
tcl_platform(byteOrder) = littleEndian
tcl_platform(machine)   = i686
tcl_platform(os)        = Linux
tcl_platform(osVersion) = 2.6.24-19-generic
tcl_platform(platform)  = unix
tcl_platform(tip,268)   = 1
tcl_platform(tip,280)   = 1
tcl_platform(user)      = <username>
tcl_platform(wordSize)  = 4




The following example creates a machineparameters object, computes the
  properties and displays it.





     set pp [machineparameters create %AUTO%]


     $pp compute


     $pp print


     $pp destroy




This prints out :





     Machine parameters


     Epsilon : 1.11022302463e-16


     Beta : 2


     Rounding : proper


     Mantissa : 53


     Maximum exponent : 1024


     Minimum exponent : -1021


     Overflow threshold : 8.98846567431e+307


     Underflow threshold : 2.22507385851e-308




That compares well with the results produced by Lapack 3.1.1 :





     Epsilon                      =   1.11022302462515654E-016


     Safe minimum                 =   2.22507385850720138E-308


     Base                         =    2.0000000000000000


     Precision                    =   2.22044604925031308E-016


     Number of digits in mantissa =    53.000000000000000


     Rounding mode                =   1.00000000000000000


     Minimum exponent             =   -1021.0000000000000


     Underflow threshold          =   2.22507385850720138E-308


     Largest exponent             =    1024.0000000000000


     Overflow threshold           =   1.79769313486231571E+308


     Reciprocal of safe minimum   =   4.49423283715578977E+307




The following example creates a machineparameters object, computes the
  properties and gets the epsilon for the machine.





     set pp [machineparameters create %AUTO%]


     $pp compute


     set eps [$pp get -epsilon]


     $pp destroy









REFERENCES


    
  
  • "Algorithms to Reveal Properties of Floating-Point Arithmetic",
      Michael A. Malcolm, Stanford University, Communications of the ACM, Volume
      15 , Issue 11 (November 1972), Pages: 949 - 951
    • 
  
  • "More on Algorithms that Reveal Properties of Floating, Point
      Arithmetic Units", W. Morven Gentleman, University of Waterloo, Scott
      B. Marovich, Purdue University, Communications of the ACM, Volume 17 ,
      Issue 5 (May 1974), Pages: 276 - 277
    • 







CLASS API



  

  
The command creates a new machineparameters object and returns the fully
      qualified name of the object command as its result.







  

  
Set this option to 1 to enable verbose logging. This option is mainly for
      debug purposes. The default value of verbose is 0.










OBJECT API



  

  
The command configure the options of the object objectname. The
      options are the same as the static method create.

  

  
Returns the value of the option which name is opt. The options are
      the same as the method create and configure.

  

  
Destroys the object objectname.

  

  
Computes the machine parameters.

  

  
Returns the value corresponding with given key. The following is the list
      of available keys.






    
  
  • -epsilon : smallest value so that 1+epsilon>1 is false
    • 
  
  • -rounding : The rounding mode used on the machine. The rounding occurs
      when more than t digits would be required to represent the number. Two
      modes can be determined with the current system : "chop" means
      than only t digits are kept, no matter the value of the number
      "proper" means that another rounding mode is used, be it
      "round to nearest", "round up", "round
      down".
    • 
  
  • -basis : the basis of the floating-point representation. The basis is
      usually 2, i.e. binary representation (for example IEEE 754 machines), but
      some machines (like HP calculators for example) uses 10, or 16,
    etc...
    • 
  
  • -mantissa : the number of bits in the mantissa
    • 
  
  • -exponentmax : the largest positive exponent before overflow occurs
    • 
  
  • -exponentmin : the largest negative exponent before (gradual) underflow
      occurs
    • 
  
  • -vmax : largest positive value before overflow occurs
    • 
  
  • -vmin : largest negative value before (gradual) underflow occurs
    • 






  

  
Return a report for machine parameters.

  

  
Print machine parameters on standard output.








BUGS, IDEAS, FEEDBACK


This document, and the package it describes, will undoubtedly
    contain bugs and other problems. Please report such in the category
    math of the Tcllib Trackers
    [http://core.tcl.tk/tcllib/reportlist]. Please also report any ideas for
    enhancements you may have for either package and/or documentation.


When proposing code changes, please provide unified diffs,
    i.e the output of diff -u.


Note further that attachments are strongly preferred over
    inlined patches. Attachments can be made by going to the Edit form of
    the ticket immediately after its creation, and then using the left-most
    button in the secondary navigation bar.






COPYRIGHT


Copyright (c) 2008 Michael Baudin <michael.baudin@sourceforge.net>








  

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