machineparameters.3tcl

Langue: en

Version: 1.0 (ubuntu - 24/10/10)

Section: 3 (Bibliothèques de fonctions)

Sommaire

NAME

tclrep/machineparameters - Compute double precision machine parameters.

SYNOPSIS

package require snit

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

machineparameters create objectname ?options...?
The command creates a new machineparameters object and returns the fully qualified name of the object command as its result.
-verbose verbose
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

objectname configure ?options...?
The command configure the options of the object objectname. The options are the same as the static method create.
objectname cget opt
Returns the value of the option which name is opt. The options are the same as the method create and configure.
objectname destroy
Destroys the object objectname.
objectname compute
Computes the machine parameters.
objectname get key
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
objectname tostring
Return a report for machine parameters.
objectname print
Print machine parameters on standard output.
 Copyright (c) 2008 Michael Baudin <michael.baudin@sourceforge.net>