Table of Contents

Name

wcalc - a natural-expression command-line calculator

Synopsis

wcalc [ options ] [ expression ... ]

Description

wcalc is a command-line calculator designed to accept all valid mathematical expressions. It supports all standard mathematical operations, parenthesis, brackets, trigonometric functions, hyperbolic trig functions, logs, and boolean operators.

wcalc accepts input in a variety of manners. I it will evaluate If no mathematical expression is given at the commandline, it will evaluate the contents of an environment 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.

Within wcalc, detailed information about commands, functions, symbols, and variables can be obtained by executing: \explain thing-to-explain

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 hexadecimal 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 degrees.
-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 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 increased, which makes it possible to represent numbers with more accuracy.
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 because 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 represent 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 conflicts with engineering notation for large numbers, but not for decimals.

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 represents. 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-defined functions. They are variables that rather than representing a value, represent an expression that is evaluated whenever the variable is evaluated. 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 evaluates 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 functions 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 returns is in the range of 1 to 7, where 1 is Sunday, 2 is Monday, 3 is Tuesday, 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 nevertheless.

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 constants.

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 monotonically 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:
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245869974724822361502823407955151120558811684656967313093357387193011055974127397801166600823447367841524950037348489795545416453901986117572722731871388422643588974212021713194956805142308399313566247553371620129340026051601856684677033122428187855479365508702723110143458240736806341798963338923286460351089772720817919599675133363110147505797173662675795471777702814318804385560929672479177350549251018537674006123614790110383192502897923367993783619310166679013187969315172579438604030363957033826325935372151289640167976948453904619615481368332936937026831888367580239969088932697527811653282224950410336573385944190516446146423694037380609059088222036945727944116946240616684848934170304346480406820774078369140625

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 represent the constants hardcoded into wcalc:

e
The logarithm constant:
2.718281828459045235360287471352662497757247093699959574966
gamma
Euler’s Constant: 0.57721566490153286060651209008240243104215933593992359880576723488486772677766467093694706329174674951463144724980708248096050401448654283622417399764492353625350033374293733773767394279259525824709491600873520394816567
K
Catalan Constant: 0.91596559417721901505460351493238411077414937428167213426649811962176301977625476947935651292611510624857442261919619957903589880332585905943159473748115840699533202877331946051903872747816408786590902
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

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 representations. 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 scientific notation, and choosing to do scientific notation when convenient. 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 calculations.
\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 increased, which makes it possible to represent numbers with more accuracy.
\p or \picky or \l or \lenient
Toggles variable parsing rules. When wcalc is "picky" it will complain 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 remembered 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 default, 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 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 because of the way floating point numbers are represented 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.
\openXXXXX
Loads file XXXXX.
\saveXXXXX
Saves the history and variable list to a file, XXXXX.
\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 conflicts with engineering notation for large numbers, but not for decimals.
\prefs or \preferences
Displays the current preference settings.
\convert unit1 unit1
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, constant, function, or command.
\verbose
Verbose mode displays the expression to be calculated before calculating it.
\del or \delim or \delimiters
Display delimiters in numerical output.
\cmod
Toggle between C-style modulus operation and a more flexible method.

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 including 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 command, where -1 means "auto" and anything else specifies the number of decimal places. This does not affect the behind-the-scenes precision.
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 \engineering command. Specifies whether answers will be displayed in engineering 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 contain 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 attempt to eliminate numbers too small to be accurate (hopefully, these are only errors created by the binary approximation of the inputs).
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 notation 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. Equivalent 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. Equivalent to the \dsep command. Specifies what the decimal delimiter is.
input_thousands_delimiter
Uses the next character after the equals sign as its value. Equivalent 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. Equivalent 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

Preload

Wcalc uses a file, ~/.wcalc_preload, to store persistent information between instances. Typically, this is used to store variables that are frequently defined. This file can be edited by hand with a standard text editor. There is also a command within wcalc (\store) to append a variable definition to the end of this file. Any variable defined in this file is defined and available for use in any subsequent invocation of wcalc.

Copyright

wcalc is Copyright (C) 2000-2007 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.


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