--- name: "machineparameters" section: "3tcl" platform: "linux" package: "tcllib" version: "2.0+dfsg-4" release: "Debian 13 (Trixie)" platforms: ["linux"] url: "https://new.carta.tech/machineparameters" --- # machineparameters(3tcl) Compute double precision machine parameters. ``` ``` ## NAME math::machineparameters - Compute double precision machine parameters. ## SYNOPSIS package require **Tcl 8.5 9** package require **snit** package require **math::machineparameters 0.2** **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) = 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. ## 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* \[http://core.tcl.tk/tcllib/reportlist\]. Please also report any ideas for enhancements you may have for either package and/or documentation. When proposing code changes, please provide *unified diffs*, i.e the output of **diff -u**. Note further that *attachments* are strongly preferred over inlined patches. Attachments can be made by going to the **Edit** form of the ticket immediately after its creation, and then using the left-most button in the secondary navigation bar. ## COPYRIGHT ``` Copyright (c) 2008 Michael Baudin ```