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david072 edited this page Feb 3, 2023 · 9 revisions

Documentation

Literals

Literals can be specified using different representations.

3
0xFF
0b110
3.123
.123

Scientific notation

Scientific notation can be used to input big numbers more easily.

1e2
3e5

Objects

funcially supports using objects which encapsulate more complex data structures. Objects always follow the syntax: {<name> <args>}.

The following objects can be used:

Name Syntax
date {date now} / {date <day>.<month>.<year>}1

1: This format can be changed in the settings.

Operators

Basic

Name Operator
Addition +
Subtraction -
Multiplication *
Division /

Extended

Name Operator
Exponentiation ^
Bitwise AND &
Bitwise OR |
Left Shift <<
Right Shift >>
Modulo mod
Taking a percentage of a number of
Unit conversion in

Modifiers

Modifiers are similar to operators, except that they only have one operand.

They change the value of what they were pre- or appended to.

Name Modifier Long form
Percent % n / 100
Bitwise NOT ! (prepended) -
Factorial ! (appended) n * (n - 1) * ... * 1 
20%
!0b101
5!
(50 / 2)%

Operator order

  1. Functions and variables
  2. Groups ("(...)")
  3. Extended operators
  4. Multiplication and division
  5. Addition and subtraction
  6. of and in

Inferred multiplication

The multiplication sign can be left out in the following scenarios:

  • Before variables
  • Before functions
  • Before groups
2pi
2sin(30)
2(3 + 4)
(3 + 4)(1 + 2)

Functions

Standard Functions

Trigonometric functions use parameters in radians and their inverse functions also return values in radians.

To use degrees, simply convert the units:

sin(30°)
asin(.5) in °
Description Function Example
Sine sin sin(1)
Arcsine asin asin(.5)
Cosine cos cos(1)
Arccosine acos acos(.5)
Tangent tan tan(1)
Arctangent atan atan(.5)
Cotangent cot cot(1)
Arccotangent acot acot(.5)
Natural logarithm ln ln(3)
Logarithm log(base, n) log(2, 8)
Square root sqrt sqrt(25)
Cube root cbrt cbrt(1000)
Root root(index, n) root(2, 8)
Absolute value abs abs(-10)
Flooring floor floor(3.5)
Lerping lerp(a, b, t) lerp(0, 50, .5)
Ceiling ceil ceil(20.2)
Clamping clamp(n, start, end) clamp(5, 0, 2)
Map from one range to another map(n, start1, end1, start2, end2) map(5, 0, 10, 20, 100)
Rounding (optional decimal places) round(n) / round(n, <decimal places>) round(5.2) / round(5.123, 2)

Custom functions

Syntax: name(arg1, arg2, ...) := expr

A custom functions is defined with a name, a set of arguments separated by commas and an expression that evaluates to the function's value. In the expression, the names given to the arguments before the definition sign (:=) can be used. As such, this expression cannot be evaluated right away.

If "expr" is empty, the function is removed.

When a function is re-declared (i.e. the function already exists), one of two things happens:

  • If the function being declared is a standard function (e.g. sin), an error occurs, saying that standard functions cannot be overridden.
  • Otherwise, the function's expression and arguments are updated.

The same applies when removing a function.

f(x) := x * 3
f(x, y) := x ^ y
f(x, y) :=

Variables

Constants

Constant Value
pi 3.1415926536
e 2.7182818285
tau 6.2831853072

ans Variable

The ans variable contains the result of the previous calculation. It starts out at 0.

Custom variables

Syntax: name := expr

A custom variable is defined with a name, and an expression that resolves to its value. When the variable is declared, its expression is evaluated and the result (including an optional unit) is stored for future use. Variable do not store formats.

If "expr" is empty, the variable is removed.

When a variable is re-declared (i.e. the variable already exists), one of two things happens:

  • If the variable being declared is a builtin variable (e.g. pi), an error occurs, saying that standard variables cannot be overridden.
  • Otherwise, the variable's value is updated.

The same applies when removing a variable.

x := 4 + 3
pi := 4   => Error: ReservedVariable
x := 20 * 2
x :=

Equality checks

An equals sign ("=") marks this line as an equality check. funcially then returns True or False, depending on whether the two expressions evaluate to the same value (including units).

The equals sign must be at the top level and there can only be one equals sign in a line.

20 + 30 = 25 * 2
20 * 5 = 10

Equation solving

funcially can solve linear equations if there is a question mark (?) in either sides.

  • There can only be one question mark in an equation.
  • The question mark can only be a function argument of custom functions that are themselves linear.

If the question mark is preceded by a variable name, its calculated value will be assigned to the given variable.

30 + ? = 100
? * sin(30) = 1 + 1
20 + x? = 100.5

Units

Units are defined with a name and an optional unit prefix.

Units and unit prefixes are case-sensitive.

Prefix Name Value
n Nano 1e-9
m Milli 1e-3
c Centi 1e-2
d Deci 1e-1
h Hecto 1e2
k Kilo 1e3
M Mega 1e6
G Giga 1e9
T Tera 1e12
P Peta 1e15
E Exa 1e18
Z Zetta 1e21
Y Yotta 1e24

Unit prefixes can be used without a unit and thus act like a modifier (e.g. 3k = 3000).

Numbers with and without units can be mixed, resulting in the unit being carried to the result.
If the line consists only of a literal with a unit, the unit in the result is printed in it's long form. Otherwise, the abbreviated version is used.

Two units can be combined using a / in between.

funcially will automatically convert units to perform operations if needed. In that case, the right hand side's is converted into the left hand side's unit.

10m
10km/h
(10 + 10)km
20 * 2min

Currencies

funcially supports currencies from exchangerate.host, like EUR or USD. These can be used the same way as units. funcially updates the exchange rates on every startup and saves them for when there is no internet connection available.

Converting between representations with "in"

Syntax: <expr> in <decimal/binary/hex>

This is valid everywhere in a line, but only has an effect if it is at the end.

If the left hand side has a unit, the unit's number is converted and the unit is kept.

0xFF in decimal	    => 255 (default)
255 in hex		    => 0xFF
6 in binary	        => 0b110
255km in hex	    => 0xFF Kilometers

Settings

There are some settings, which allow the user to customize funcially to their preferences.

The settings can be accessed via File>Settings in the GUI, or via the set and get commands in the CLI.

set and get commands

Syntax: set <setting> = <value>, get <setting>

A setting is always specified by a "path", delimited by dots.

For both, a question mark behind <setting> may be used to list available settings (e.g. set ? or set date ?).

GUI

Other features:

  • Saving: The input field's text is saved across restarts
  • Syntax highlighting
  • Installation with installers
  • Available on Desktop and Web. The web version can be downloaded to be available offline, and can thus be used on e.g. Android tablets
  • Searching

Comments

Calculations can be annotated using comments. Comments start with # and span the entire rest of the line.

# This is a comment spanning the entire line
3 + 4
sin(30)
20% of 100 # This gives more details about the calculation

Plotting

The GUI supports plotting single argument functions. When declaring a single argument function, a checkbox appears in the output column, allowing the function to be selected to show in the plot. The plot can be brought up via the button in the top right ("🗠 Plot").

If there are multiple re-declarations of a function, each re-declaration can be shown individually.

Shortcuts

"Cmd" is ctrl on Windows and Linux and ⌘ on macOS.

Description Shortcut
Comment/Uncomment selected lines Cmd+Alt+N
Surround selection with parentheses Cmd+B
Copy result of current line Cmd+⇧+C
Format input text Cmd+Alt+L
Search Cmd+F
Go to line Cmd+G
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