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tclrep/machineparameters(n) 1.0 "tclrep"
Name
tclrep/machineparameters  Compute double precision machine parameters.
Synopsis
 package require snit
 package require math::machineparameters 0.1
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) = 2.6.2419generic 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 : 1.11022302463e16 Beta : 2 Rounding : proper Mantissa : 53 Maximum exponent : 1024 Minimum exponent : 1021 Overflow threshold : 8.98846567431e+307 Underflow threshold : 2.22507385851e308
That compares well with the results produced by Lapack 3.1.1 :
Epsilon = 1.11022302462515654E016 Safe minimum = 2.22507385850720138E308 Base = 2.0000000000000000 Precision = 2.22044604925031308E016 Number of digits in mantissa = 53.000000000000000 Rounding mode = 1.00000000000000000 Minimum exponent = 1021.0000000000000 Underflow threshold = 2.22507385850720138E308 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 FloatingPoint 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.
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 floatingpoint 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.
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. Please also report any ideas for enhancements you may have for either package and/or documentation.
Copyright
Copyright © 2008 Michael Baudin <michael.baudin@sourceforge.net>