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[comment {-*- tclrep -*- doctools manpage}]
[manpage_begin math::machineparameters n 0.2]
[copyright {2008 Michael Baudin <michael.baudin@sourceforge.net>}]
[moddesc tclrep]
[require Tcl "8.5 9"]
[require snit]
[require math::machineparameters 0.2]
[titledesc {Compute double precision machine parameters.}]
[description]
The [emph math::machineparameters] package
is the Tcl equivalent of the DLAMCH LAPACK function.
In floating point systems, a floating point number is represented
by
[example {
x = +/- d1 d2 ... dt basis^e
}]
where digits satisfy
[example {
0 <= di <= basis - 1, i = 1, t
}]
with the convention :
[list_begin itemized]
[item] t is the size of the mantissa
[item] basis is the basis (the "radix")
[list_end]
[para]
The [method compute] method computes all machine parameters.
Then, the [method get] method can be used to get each
parameter.
The [method print] method prints a report on standard output.
[section EXAMPLE]
In the following example, one compute the parameters of a desktop
under Linux with the following Tcl 8.4.19 properties :
[example {
% 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.
[example {
set pp [machineparameters create %AUTO%]
$pp compute
$pp print
$pp destroy
}]
This prints out :
[example {
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 :
[example {
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.
[example {
set pp [machineparameters create %AUTO%]
$pp compute
set eps [$pp get -epsilon]
$pp destroy
}]
[section REFERENCES]
[list_begin itemized]
[item] "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
[item] "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
[list_end]
[section {CLASS API}]
[list_begin definitions]
[call [cmd machineparameters] create [arg objectname] [opt [arg options]...]]
The command creates a new machineparameters object and returns the fully
qualified name of the object command as its result.
[list_begin options]
[opt_def -verbose [arg verbose]]
Set this option to 1 to enable verbose logging.
This option is mainly for debug purposes.
The default value of [arg verbose] is 0.
[list_end]
[list_end]
[section {OBJECT API}]
[list_begin definitions]
[call [arg objectname] [method configure] [opt [arg options]...]]
The command configure the options of the object [arg objectname]. The options
are the same as the static method [method create].
[call [arg objectname] [method cget] [arg opt]]
Returns the value of the option which name is [arg opt]. The options
are the same as the method [method create] and [method configure].
[call [arg objectname] [method destroy]]
Destroys the object [arg objectname].
[call [arg objectname] [method compute]]
Computes the machine parameters.
[call [arg objectname] [method get] [arg key]]
Returns the value corresponding with given key.
The following is the list of available keys.
[list_begin itemized]
[item] -epsilon : smallest value so that 1+epsilon>1 is false
[item] -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".
[item] -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...
[item] -mantissa : the number of bits in the mantissa
[item] -exponentmax : the largest positive exponent before overflow occurs
[item] -exponentmin : the largest negative exponent before (gradual) underflow occurs
[item] -vmax : largest positive value before overflow occurs
[item] -vmin : largest negative value before (gradual) underflow occurs
[list_end]
[call [arg objectname] [method tostring]]
Return a report for machine parameters.
[call [arg objectname] [method print]]
Print machine parameters on standard output.
[list_end]
[vset CATEGORY math]
[include ../common-text/feedback.inc]
[manpage_end]
|
