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tclrep/machineparameters - Compute double precision machine parameters.

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.

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

"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

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

*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 © 2008 Michael Baudin <michael.baudin@sourceforge.net>