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wcalc(1) General Commands Manual wcalc(1) NAME wcalc - a natural-expression command-line calculator SYNOPSIS wcalc [ options ] [ expression ... ] DESCRIPTION wcalc is a command-line calculator designed to accept all valid mathemati- cal expressions. It supports all standard mathematical operations, paren- thesis, brackets, trigonometric functions, hyperbolic trig functions, logs, and boolean operators. wcalc accepts input in a variety of manners. If no mathematical expression is given at the commandline, it will evaluate the contents of an environ- ment variable named wcalc_input if one exists. If that variable is not set, wcalc will try to read input from standard input (i.e. piped input). If there is no input from that, wcalc enters "interactive" mode. Interactive mode has more features. While in interactive mode, detailed information about commands, functions, symbols, and variables can be obtained by executing: \explain thing-to-ex- plain OPTIONS -H or --help Prints a help usage message to standard output, then exits. -E Specifies that numerical output should be in scientific notation. -EE Specifies that numerical output should NOT be in scientific notation. -PXXX Sets the "precision", or the number of decimal places displayed, to be XXX. This setting only affects output, not internal representations. If the precision is set to -1, the number of decimal places displayed will depend on the value. Precision is set to autoadjust (-1) by default. Example: wcalc -P6 -v or --version Prints the version number and exits. -d or -dec or --decimal Results are printed in decimal (base 10). This option is the default, and does not have a default prefix to indicate that numbers are in base 10. -h or -hex or --hexadecimal Results are printed in hexadecimal (base 16). Numbers printed in hexa- decimal have a prefix of 0x unless the -p or --prefixes option is used. -o or -oct or --octal Results are printed in octal (base 8). Numbers printed in octal have a prefix of 0 unless the -p or --prefixes option is used. -b or -bin or --binary Results are printed in binary (base 2). Numbers printed in binary have a prefix of 0b unless the -p or --prefixes option is used. -p or --prefixes Toggles printing prefixes for hexadecimal, octal, and binary forms. -l or --lenient Makes the parser assume that uninitialized variables have a value of zero. -r or --radians Toggles whether trigonometric functions assume input (and output) is in radians. By default, trigonometric functions assume input is in de- grees. -q or --quiet Toggles whether the equals sign will be printed before the results. -c or --conservative Toggles accuracy guards. Because of the way floating point numbers are stored in computers, some numbers cannot be represented exactly (such as 0.1). Because of this, calculating with those numbers can produce results that are not exactly correct, but are different from the cor- rect answer by a very small value (smaller than the floating point value can represent accurately). For example, the calculation of 1-.9-.1 can return an extremely small number that is not zero but is less than what can be represented accurately, and thus for all intents and purposes, it is 0. The accuracy guard feature will round numbers to zero if they are less than the representable accuracy of the floating point number. However, sometimes numbers that small or smaller need to be displayed, and thus the accuracy guard should be turned off. Alter- natively, the number of internal bits could be increased, which makes it possible to represent numbers with more accuracy. -u or --units [type] Prints units used for conversions; parameter type can be: lengths, ar- eas, volumes, masses, speeds, powers, forces, accelerations, tempera- tures, angles, or pressures. If the parameter is not supplied, all units are printed. --remember Toggles whether or not expressions that produce errors are remembered in the history. Does not affect command-line math. --round= { none | simple | sig_fig } Wcalc can attempt to warn you when numbers have been rounded in the output display. It has two methods of keeping track---either by using significant figures (sig_fig), or by a simple digit-counting algorithm. Rounding in the command-line version is denoted by a tilde before the equals sign (~=). Rounding in the GUI version is denoted by changing the text color to red. In some cases, Wcalc may think that the number has been rounded even if it shouldn't have been necessary (this is be- cause of the way floating point numbers are represented internally). --dsep=X Sets the decimal separator character to be X. --tsep=X Sets the thousands separator character to be X. --idsep=X Sets the input-only decimal separator character to be X. --itsep=X Sets the input-only thousands separator character to be X. --bitsXXXX Sets the number of bits of memory that will be used to internally rep- resent numbers to be XXXX. The default is 1024. Set higher if you need to work with extremely large or extremely small numbers, set lower if you want to use less memory. --ints Toggles whether long integers will be abbreviated or not. This con- flicts with engineering notation for large numbers, but not for deci- mals. --verbose Toggles verbose mode, which displays the expression to be calculated before calculating it. --defaults Prevents reading the .wcalcrc file. -C or --color Toggles the use of color in the commandline output. USER-DEFINED VARIABLES Variables are supported and may be assigned using the = operator. To assign a variable use the form: foo = anylegalexpression Thereafter, that variable name is the same as the literal value it repre- sents. Expressions can be stored in variables like this: foo = 'anylegalexpression' Expressions stored this way will be interpreted at evaluation time, rather than assignment-time. Note that these cannot be recursive. All variables may also be stored with a description of what they are. This description is added in the form of a quoted string after the assignment, like this: foo = 'anylegalexpression' 'description' ACTIVE VARIABLES Active variables are designed to give a functionality similar to user-de- fined functions. They are variables that rather than representing a value, represent an expression that is evaluated whenever the variable is evalu- ated. This expression may contain other variable names. For example, after the following sequence of commands: foo=5 bar='foo+4' The variable bar will evaluate to 9, or four more than whatever foo evalu- ates to be. These can be stacked, like so: baz='sin(bar)+foo' In this case, baz will evaluate to be 5.15643, or the sin of whatever foo+4 is plus whatever foo is. To demonstrate the utility of these active variables, here are two func- tions written by Stephen M. Lawson. The first computes the weekday of a given day (dy) in a given month (mo) in a given year (yr). The value it re- turns is in the range of 1 to 7, where 1 is Sunday, 2 is Monday, 3 is Tues- day, and so forth. weekday='(((floor((yr - floor(0.6 + 1 / mo)) / 400) - floor((yr - floor(0.6 + 1 / mo)) / 100) + floor((5 * (yr - floor(0.6 + 1 / mo))) / 4) + floor(13 * (mo + 12 * floor(0.6 + 1 / mo) + 1) / 5)) - (7 * floor((floor((yr - floor(0.6 + 1 / mo)) / 400) - floor((yr - floor(0.6 + 1 / mo)) / 100) + floor((5 * (yr - floor(0.6 + 1 / mo))) / 4) + floor(13 * (mo + 12 * floor(0.6 + 1 / mo) + 1) / 5)) / 7)) + 1) + 5 + dy) % 7 + 1' The second function computes what day Easter will be for a given year (yr) and returns an offset from March 31st. For example, for the year 2005, it returns -4, which means March 27th. Because of leap-year problems, this only works from the year 1900 to 2099, but is a good demonstration never- theless. easter='((19 * (yr - 19 * floor(yr / 19)) + 24) - floor((19 * (yr - 19 * floor(yr / 19)) + 24) / 30) * 30) + ((2 * (yr - 4 * floor(yr / 4)) + 4 * (yr - 7 * floor(yr / 7)) + 6 * ((19 * (yr - 19 * floor(yr / 19)) + 24) - floor((19 * (yr - 19 * floor(yr / 19)) + 24) / 30) * 30) + 5) - floor((2 * (yr - 4 * floor(yr / 4)) + 4 * (yr - 7 * floor(yr / 7)) + 6 * ((19 * (yr - 19 * floor(yr / 19)) + 24) - floor((19 * (yr - 19 * floor(yr / 19)) + 24) / 30) * 30) + 5) / 7) * 7) - 9' BUILT-IN SYMBOLS There are two basic kinds of built-in symbols in wcalc: functions and con- stants. FUNCTIONS The functions supported in wcalc are almost all self-explanatory. Here are the basic descriptions. sin cos tan cot The standard trigonometric functions asin acos atan acot or arcsin arccos arctan arccot or sin^-1 cos^-1 tan^-1 cot^-1 The standard arc- trigonometric functions. sinh cosh tanh coth The standard hyperbolic trigonometric functions. asinh acosh atanh acoth or arcsinh arccosh arctanh arccoth or sinh^-1 cosh^-1 tanh^-1 coth^-1 The standard arc- hyperbolic trigonometric functions. log ln logtwo Log-base-ten, log-base-e and log-base-two, respectively. Remember, you can also construct log-base-X of number Y by computing log(Y)/log(X). round Returns the integral value nearest to the argument according to the typical rounding rules. abs Returns the absolute value of the argument. ceil ceiling floor Returns the ceiling or floor of the argument. sqrt cbrt The square and cube root functions. rand Returns a random number between 0 and the number given. irand Returns a random integer between 0 and the number given. fact Returns the factorial of a number. Gamma Returns the value of the Gamma function at that value. lnGamma Returns the value of the log Gamma function at that value. zeta Returns the value of the Riemann zeta function at that value. sinc Returns the sinc function (for sinus cardinalis) of the input, also known as the interpolation function, filtering function or the first spherical Bessel function, is the product of a sine function and a mo- notonically decreasing function. CONSTANTS Wcalc supports a lot of constants. Some are special (like pi), and some are simply mathematical or physical constants that have been hardcoded in. The physics constants are taken from http://physics.nist.gov/constants, and should all be in predictable SI units. The value of pi is special, as it is calculated to however many bits of precision have been specified with the \bits command. The default number of bits is 1024, or a value of: 3.14159265358979323846264338327950288419716939937 5105820974944592307816406286208998628034825342117 0679821480865132823066470938446095505822317253594 0812848111745028410270193852110555964462294895493 0381964428810975665933446128475648233786783165271 2019091456485669234603486104543266482133936072602 4914127372458699747248223615028234079551511205588 1168465696731309335738719301105597412739780116660 0823447367841524950037348489795545416453901986117 5727227318713884226435889742120217131949568051423 0839931356624755337162012934002605160185668467703 3122428187855479365508702723110143458240736806341 7989633389232864603510897727208179195996751333631 1014750579717366267579547177770281431880438556092 9672479177350549251018537674006123614790110383192 5028979233679937836193101666790131879693151725794 3860403036395703382632593537215128964016797694845 3904619615481368332936937026831888367580239969088 9326975278116532822249504103365733859441905164461 4642369403738060905908822203694572794411694624061 6684848934170304346480406820774078369140625 Similarly, all values that rely on the value of pi, like mu0, have the same level of precision. Here is a complete list of the symbols used to repre- sent the constants hardcoded into wcalc: e The logarithm constant: 2.718281828459045235360287471352662497757247093699959574966 gamma Euler's Constant: 0.5772156649015328606065120900824024310421 593359399235988057672348848677267776646709369470632917467495 146314472498070824809605040144865428362241739976449235362535 0033374293733773767394279259525824709491600873520394816567 K Catalan Constant: 0.9159655941772190150546035149323841107741 493742816721342664981196217630197762547694793565129261151062 485744226191961995790358988033258590594315947374811584069953 3202877331946051903872747816408786590902 g Acceleration due to gravity: 9.80665 m/s/s Cc Coulomb's Constant: 8987551787.37 Universal Constants Z0 or Zzero Impedance of Vacuum: 376.730313461 ohms epsilon0 or epsilonzero Permittivity of Free Space: 8.854187817e-12 F/m mu0 or muzero Permeability of Free Space calculated as 4*pi*10^-7. G Gravitational Constant: 6.67259e-11 h Planck Constant: 6.6260755e-34 c Speed of Light: 299792458 Electromagnetic Constants muB Bohr Magneton: 5.78838174943e-11 J/T muN Nuclear Magneton: 3.15245123824e-14 J/T G0 Conductance Quantum: 7.748091733e-5 S ec Elementary Charge: 1.60217653e-19 Kj Josephson Constant: 483597.879e9 Hz/V Rk Von Klitzing Constant: 25812.807449 omega Atomic and Nuclear Constants Malpha Alpha Particle Mass: 6.6446565e-27 kg a0 Bohr Radius: 5.291772108e-11 m Md Deuteron Mass: 3.34358335e-27 kg Me Electron Mass: 9.1093897e-31 kg re Electron Radius: 2.817940325e-15 m eV Electron Volt: 1.602177250e-12 J Gf Fermi Coupling Constant: 1.16638e-5 GeV^-2 alpha Fine Structure Constant: 7.29735253327e-3 eh Hartree Energy: 4.35974417e-18 J Mh Helion Mass: 5.00641214e-27 kg Mmu Muon Mass: 1.88353140e-28 kg Mn Neutron Mass: 1.67492728e-27 kg Mp Proton Mass: 1.67262171e-27 kg Rinf Rydberg Constant: 10973731.568525 1/m Mt Tau Mass: 3.16777e-27 kg Physio-Chemical Constants u Atomic Mass Constant: 1.66053886e-27 kg Na or NA Avogadro's Constant: 6.0221367e23 k Boltzmann Constant: 1.3806505e-23 F Faraday Constant: 96485.3383 C/mol c1 First Radiation Constant: 3.74177138e-16 W m^2 n0 or nzero Loschmidt Constant: 2.6867773e25 m^-3 R Molar Gas Constant: 8.314472 Vm or NAk Molar Volume of Ideal Gas: 22.413996e-3 (m^3)/mol c2 Second Radiation Constant: 1.4387752e-2 m K sigma Stefan-Boltzmann Constant: 5.670400e-8 b Wien Displacement Law Constant: 2.8977686e-3 m K Random Constants random A Random Value irandom A Random Integer SPECIAL SYMBOLS There are some special symbols that wcalc accept as input for compound op- erations. @Inf@ Symbol that represents Infinity @NaN@ Symbol that represents "Not a Number" COMMANDS There are several commands that are supported in wcalc. \pXXX Sets the "precision", or the number of decimal places displayed, to be XXX. This setting only affects output, not internal representa- tions. If the precision is set to -1, the number of decimal places displayed will depend on the value. The default is -1. \e or \eng or \engineering Rotates between always using scientific notation, never using scien- tific notation, and choosing to do scientific notation when conve- nient. Can also take an argument that is one of always, never, and automatic to choose a mode directly. \help or ? Displays a help screen. \prefs Prints out the current preference settings. \li or \list or \listvars Prints out the currently defined variables. \r or \radians Toggles between using and not using radians for trigonometric calcu- lations. \cons or \conservative Toggles accuracy guards. Because of the way floating point numbers are stored in computers, some numbers cannot be represented exactly (such as 0.1). Because of this, calculating with those numbers can produce results that are not exactly correct, but are different from the correct answer by a very small value (smaller than the floating point value can represent accurately). For example, the calculation of 1-.9-.1 can return an extremely small number that is not zero but is less than what can be represented accurately, and thus for all intents and purposes, it is 0. The accuracy guard feature will round numbers to zero if they are less than the representable accuracy of the floating point number. However, sometimes numbers that small or smaller need to be displayed, and thus the accuracy guard should be turned off. Alternatively, the number of internal bits could be in- creased, which makes it possible to represent numbers with more ac- curacy. \p or \picky or \l or \lenient Toggles variable parsing rules. When wcalc is "picky" it will com- plain if you use undefined variables. If it is "lenient", wcalc will assume a value of 0 for undefined variables. \re or \remember or \remember_errors Toggles whether or not expressions that produce errors are remem- bered in the history. \pre or \prefix or \prefixes Toggles the display of prefixes for hexadecimal, octal, and binary output. \b or \bin or \binary Results are printed in binary (base 2). Numbers printed in binary have a prefix of 0b unless the \prefixes command is used. \d or \dec or \decimal Results are printed in decimal (base 10). This option is the de- fault, and does not have a default prefix to indicate that numbers are in base 10. \h or \x or \hex or \hexadecimal Results are printed in hexadecimal (base 16). Numbers printed in hexadecimal have a prefix of 0x unless the \prefixes command is used. \o or \oct or \octal Results are printed in octal (base 8). Numbers printed in octal have a prefix of 0 unless the \prefixes command is used. \round none|simple|sig_fig Wcalc can attempt to warn you when numbers have been rounded in the output display. It has two methods of keeping track---either by us- ing significant figures (sig_fig), or by a simple digit-counting al- gorithm. Rounding in the command-line version is denoted by a tilde before the equals sign (~=). Rounding in the GUI version is denoted by changing the text color to red. In some cases, Wcalc may think that the number has been rounded even if it shouldn't have been nec- essary (this is because of the way floating point numbers are repre- sented internally). \dsepX Sets the decimal separator character to be X. \tsepX Sets the thousands-place separator character to be X. \idsepX Sets the input-only decimal separator character to be X. \itsepX Sets the input-only thousands-place separator character to be X. \hlimitX Sets the limit (X) on the length of the history. \open filename.txt Loads file filename.txt. \save filename.txt Saves the current session and variable list to a file, filename.txt. \bitsXXXX Sets the number of bits of precision that will be used to internally represent numbers to be XXXX. The default is 1024. Set higher if you need more precision, set lower if you want to use less memory. \ints Toggles whether long integers will be abbreviated or not. This con- flicts with engineering notation for large numbers, but not for dec- imals. \prefs or \preferences Displays the current preference settings. \convert unit1 unit2 Converts the previous answer from unit1 to unit2. \store variablename Saves the specified variable in the preload file, ~/.wcalc_preload \explain object Explains the specified object. The object can be a variable, con- stant, function, or command. \verbose Verbose mode displays the expression to be calculated before calcu- lating it. \del or \delim or \delimiters Display delimiters in numerical output. \cmod Toggle between C-style modulus operation and a more flexible method. \color Toggles the use of color in the commandline output. PREFERENCES Preferences and settings can be retained between invocations of wcalc by storing them in the file ~/.wcalcrc The format of the file is that each line is either blank or an assignment. Comments are ignored, and are defined as anything to the right of and in- cluding a hash mark (#). Assignments are of the form: key=value The possible keys are: precision A number defining the display precision. Equivalent to the \P com- mand, where -1 means "auto" and anything else specifies the number of decimal places. This does not affect the behind-the-scenes preci- sion. show_equals Either true ("yes" or "true") or false (anything else). Equivalent to the --quiet argument. Specifies whether answers will begin with an equals sign or not. engineering Either "always", "never", or "automatic". Equivalent to the \engi- neering command. Specifies whether answers will be displayed in en- gineering notation or not. use_radians Either true ("yes" or "true") or false (anything else). Equivalent to the \radians command. Specifies whether trigonometric functions accept input in radians or degrees. print_prefixes Either true ("yes" or "true") or false (anything else). Equivalent to the \prefixes command. Specifies whether base prefixes (e.g. 0x for hexadecimal numbers) are used when displaying output. save_errors Either true ("yes" or "true") or false (anything else). Equivalent to the \remember_errors command. Specifies whether lines that con- tain a syntax error are added to the history or not. precision_guard Either true ("yes" or "true") or false (anything else). Equivalent to the \conservative command. Specifies whether the display will at- tempt to eliminate numbers too small to be accurate (hopefully, these are only errors created by the binary approximation of the in- puts). print_integers Either true ("yes" or "true") or false (anything else). Equivalent to the \ints command. Specifies whether whole integers will be printed un-abbreviated or not. This conflicts with engineering nota- tion for large integers, but not for decimals. print_delimiters Either true ("yes" or "true") or false (anything else). Equivalent to the \delimiters command. Specifies whether delimiters will be added to output when displaying. thousands_delimiter Uses the next character after the equals sign as its value. Equiva- lent to the \tsep command. Specifies what the thousands delimiter is, and can affect output if print_delimiters is enabled. decimal_delimiter Uses the next character after the equals sign as its value. Equiva- lent to the \dsep command. Specifies what the decimal delimiter is. input_thousands_delimiter Uses the next character after the equals sign as its value. Equiva- lent to the \itsep command. Specifies what the input-only thousands delimiter is, and cannot affect output. input_decimal_delimiter Uses the next character after the equals sign as its value. Equiva- lent to the \idsep command. Specifies what the input-only decimal delimiter is, and cannot affect output. history_limit Either "no", for no limit, or a number. Equivalent to the \hlimit command. output_format Either decimal, octal, binary, hex, or hexadecimal. rounding_indication Either no, simple, or sig_fig. Equivalent to the \rounding command. c_style_mod Either true ("yes" or "true") or false (anything else). Equivalent to the \cmod command. Specifies whether the modulo operator (%) will behave as it does in the C programming language, or whether it will use a more flexible method. This only affects modulo operations where negative numbers are involved. As an example, with c_style_mod set to true (the default): -340 % 60 == -40; 340 % -60 == 40; -340 % -60 == -40 However, with c_style_mod set to false: -340 % 60 == -40; 340 % -60 == -20; -340 % -60 == 20 color Either true ("yes" or "true") or false (anything else). Equivalent to the \color command. Specifies whether the commandline interface will use color in its output or not. colors[XXX] This is used to specify the color of specific interface elements in the commandline interface. Valid colors are: (bold)black (bold)red (bold)green (bold)yellow (bold)blue (bold)magenta (bold)cyan (bold)white The XXX must be one of the following values: conversion_category conversion_unit prompt approx_answer exact_answer err_location err_text pref_name pref_val pref_cmd status var_name var_desc subvar_name explanation PRELOAD Wcalc uses a file, ~/.wcalc_preload, to store persistent information be- tween instances. Typically, this is used to store variables that are fre- quently defined. This file can be edited by hand with a standard text edi- tor. There is also a command within wcalc (\store) to append a variable de- finition to the end of this file. Any variable defined in this file is de- fined and available for use in any subsequent invocation of wcalc. COPYRIGHT wcalc is Copyright (C) 2000-2014 Kyle Wheeler. It is distributed under the GPL, version 2, or (at your option) any later version.. SUGGESTIONS AND BUG REPORTS Any bugs found should be reported to Kyle Wheeler at kyle-wcalc@memoryhole.net. wcalc(1)
NAME | SYNOPSIS | DESCRIPTION | USER-DEFINED VARIABLES | BUILT-IN SYMBOLS | SPECIAL SYMBOLS | COMMANDS | PREFERENCES | PRELOAD | COPYRIGHT | SUGGESTIONS AND BUG REPORTS
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