Built-in function reference

This page lists every function built into Varlig Calc. Call a function by name, with its arguments in parentheses separated by commas: sqrt(16), round(17.46, 0.05).

• Names ignore case, so SQRT(16) works too.
• The number of arguments is checked. sqrt(4, 9) shows an error rather than ignoring the 9.
• Numbers can keep their thousands separators. A comma followed by three digits groups thousands and a comma followed by a space separates arguments, so max(1,000, 2,000) is 2,000 and sqrt(1,024) is 32.
• Round or convert a function’s answer on the same line, as in sqrt(2) to 4 dp or abs(-5 km) in m.
• Find a name in the table below, then see its section for details and examples.

Many functions also have an English phrase, such as square root of 16; see Word-based mathematics. To write your own, see Your own functions.

All functions

Numbers and counting

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abs(-£45.20) gives £45.20

sign(-5) gives -1

int(7.8) gives 7

sqrt(144 m^2) gives 12 m

cbrt(-27) gives -3

factorial(5) gives 120

gcd(1920, 1080) gives 120

lcm(4, 6) gives 12

clamp(115, 0, 100) gives 100

clamp(£120, £0, £100) gives £100.00

combination(10, 2) gives 45

permutation(8, 3) gives 336

hex(255) gives 0xFF

bin(10) gives 0b1010

A few everyday readings: gcd(1920, 1080) shows that a 1920 × 1080 screen is 16:9 (1920 ÷ 120 by 1080 ÷ 120). combination(10, 2) is the number of different pairs in a group of ten, and permutation(8, 3) the number of ways to fill gold, silver and bronze from eight runners.

clamp keeps money, quantities and durations in their units when the value and both limits measure the same thing, so clamp(£120, £0, £100) caps a refund at £100.00. For factorials and selections, use whole numbers with k no bigger than n. 5! is a shorter way to write factorial(5). For other roots, use the phrase root 3 of 27; there’s no general root(...) function.

Rounding

round, floor and ceil take an optional step to round to:

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round(17.46, 0.05) gives 17.45

ceil(23, 6) gives 24

floor(7.8) gives 7

ceil(23, 6) rounds 23 eggs up to whole boxes of six. The step isn’t a number of decimal places: round(17.456, 2) rounds to the nearest 2 and gives 18, and a hint on round suggests 17.456 to 2 dp instead. For significant figures, write to 3 sf. See Rounding for halves, negative numbers and money.

Trigonometry and angles

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sin(30°) gives 0.5

cosd(60) gives 0.5

tan(45°) gives 1

sin(pi/2) gives 1

asind(0.5) gives 30°

asin(1) gives 1.5707963268 rad

asin(0.5) in degrees gives 30°

atan2(-1, -1) * 180 / pi gives -135

cosh(0) gives 1

sin, cos and tan accept an angle in any angle unit, such as 30° or 30 degrees. To see the result of asin, acos or atan in degrees, add in degrees, as above, or use the degree forms.

atan2 takes the y value first and works out which quadrant the angle is in, so atan2(-1, -1) points down and to the left (−135°), where atan(1) alone can’t tell.

Hyperbolic functions take plain numbers. Inverse functions only accept values in their real range; for example, asin(2) shows Error: imaginary number. For complex results, see Complex numbers.

Logarithms and exponentials

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log(1000) gives 3

log10(1000000) gives 6

log2(1024) gives 10

logbase(81, 3) gives 4

ln(exp(2)) gives 2

exp(0) gives 1

A logarithm needs a positive number: log(0) shows Error: ∞, and log(-100) shows Error: imaginary number. For the complex logarithm, write the number as a complex one, as in ln(-1 + 0i). The base must be positive and not 1. Logarithms, exponentials and hyperbolic functions don’t accept units or money.

Random values

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random number between 1 and 6 gives 4

random(1, 6) gives 2

rand(1, 100) gives 57

random() gives 0.4381930527

rand() gives 0.9102746385

random(0, 1) gives 0.2373052626

• random(a, b) and the phrase random number between a and b give a whole number from a to b, including both ends.
• random() gives a fraction from 0 up to, but not including, 1. random(0, 1) is a special case that does the same.
• rand is another name for random.
• Bounds must be plain whole numbers, lowest first, within the range of 64-bit integers. One argument, more than two, fractions or reversed bounds show an error.
• Varlig can draw a new number whenever the note recalculates. Store a draw in a variable, such as roll = random(1, 6), when later lines should use the same number.

Lists and statistics

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average([12, 18, 9, 21]) gives 15

median([3, 9, 4, 7, 5]) gives 5

sum([£12.50, £8, £4.25]) gives £24.75

max(4, 9, 2) gives 9

stddev([2, 4, 6]) gives 2

sum(k, k, 1, 100) gives 5,050

range(0, 20, 5) gives [0, 5, 10, 15, 20]

sort([3, 1, 2]) gives [1, 2, 3]

slice([10, 20, 30, 40], 1, 3) gives [20, 30]

map(x * 1.2, x, [£10, £25]) gives [£12.00, £30.00]

filter(x > 10, x, [4, 12, 18]) gives [12, 18]

sum (also total), product, average (also mean and avg), median, min, max, count, length, variance and stddev (also stdev) work on a list, and several accept separate arguments too. There’s no percentile function. sum, summation and product with four arguments add or multiply an expression while a counter runs from lo to hi. reverse and unique also take a list. See Lists and statistics for positions in slice, sample and population statistics, and more.

Vectors, matrices and calculus

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dot([1, 2, 3], [4, 5, 6]) gives 32

det([[2, 1], [1, 3]]) gives 5

solve_system([[1, 1], [1, -1]], [10, 2]) gives [6, 4]

solve(x * 1.2 = 60, x, 0, 100) gives 50

differentiate(x^2, x, 3) gives 6

integrate(x^2, x, 0, 3) gives 9

solve_system([[1, 1], [1, -1]], [10, 2]) finds two numbers that add up to 10 and differ by 2. solve(x * 1.2 = 60, x, 0, 100) finds the price before 20% VAT that comes to 60, searching between 0 and 100. For cross, identity, shape, transpose, inverse, trace, rank, eigenvalues, qr, lu and svd, see Vectors and matrices. For derivatives as formulas and the limits of the solver and integrator, see Summation, equation solving and calculus and Advanced mathematics.

Complex numbers

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abs(3 + 4i) gives 5

complex(3, 4) gives 3 + 4i

conj(3 + 4i) gives 3 - 4i

real(3 + 4i) gives 3

imag(3 + 4i) gives 4

arg(z) gives the angle of a complex number in radians. See Complex numbers.

Dates and vehicles

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easter(2030) gives April 21, 2030

tyre_speed(205, 55, 16, 1000 rpm) in km/h gives 119.1103438682 km/h

easter(year) gives Western Easter Sunday for a year, the same date as the phrase Easter 2030. Count days from it directly, as in easter(2030) + 1 day. See Dates. tyre_speed takes the tyre width in millimetres, the aspect ratio as a percentage, the rim size in inches and the wheel’s rotation speed; see Cooking, sound, screens and mechanics.