wcalc(1)wcalc(1)NAMEwcalc - a natural-expression command-line calculator
SYNOPSISwcalc [ options ] [ expression ... ]
DESCRIPTIONwcalc is a command-line calculator designed to accept all valid mathe‐
matical expressions. It supports all standard mathematical operations,
parenthesis, brackets, trigonometric functions, hyperbolic trig func‐
tions, logs, and boolean operators.
wcalc accepts input in a variety of manners. If no mathematical expres‐
sion 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 "interac‐
tive" mode. Interactive mode has more features.
While in interactive mode, detailed information about commands, func‐
tions, 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 nota‐
tion.
-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.
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 num‐
bers 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 fea‐
ture will round numbers to zero if they are less than the repre‐
sentable 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 repre‐
sent numbers with more accuracy.
-u or --units [type]
Prints units used for conversions; parameter type can be: lengths,
areas, volumes, masses, speeds, powers, forces, accelerations, tem‐
peratures, angles, or pressures. If the parameter is not supplied,
all units are printed.
--remember
Toggles whether or not expressions that produce errors are remem‐
bered 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 con‐
flicts with engineering notation for large numbers, but not for
decimals.
--verbose
Toggles verbose mode, which displays the expression to be calcu‐
lated 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 rep‐
resents. 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 prob‐
lems, this only works from the year 1900 to 2099, but is a good demon‐
stration 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/con‐
stants, 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 num‐
ber 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
represent 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
operations.
@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 repre‐
sentations. 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 num‐
bers 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 accu‐
rately). 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 pur‐
poses, 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.
\open filename.txt
Loads file filename.txt.
\save filename.txt
Saves the current session and variable list to a file, file‐
name.txt.
\bitsXXXX
Sets the number of bits of precision that will be used to inter‐
nally 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 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,
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.
\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 assign‐
ment. 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). Equiva‐
lent 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 dis‐
played in engineering notation or not.
use_radians
Either true ("yes" or "true") or false (anything else). Equiva‐
lent 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). Equiva‐
lent to the \prefixes command. Specifies whether base prefixes
(e.g. 0x for hexadecimal numbers) are used when displaying out‐
put.
save_errors
Either true ("yes" or "true") or false (anything else). Equiva‐
lent 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). Equiva‐
lent 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 approxi‐
mation of the inputs).
print_integers
Either true ("yes" or "true") or false (anything else). Equiva‐
lent to the \ints command. Specifies whether whole integers will
be printed un-abbreviated or not. This conflicts with engineer‐
ing notation for large integers, but not for decimals.
print_delimiters
Either true ("yes" or "true") or false (anything else). Equiva‐
lent 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 com‐
mand.
c_style_mod
Either true ("yes" or "true") or false (anything else). Equiva‐
lent 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). Equiva‐
lent 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
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.
COPYRIGHTwcalc 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)
