SYNOPSIS

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

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

Copyright (c) 2008 Michael Baudin <[email protected]>