Dotdown™ · functions

Functions

Write a function name, an open bracket, its values separated by commas, and a close bracket. Inside the brackets you can put any formula.

A function name only counts when a bracket follows it, so a variable can still be called mean or slope. Functions are calculated exactly, like the rest of Dotdown™. They can sit inside bigger formulas: sqrt(a) + 1, pow(1 + r, years) × start.

Numbers

Function	Gives	Example
`sqrt(x)`	Square root. A negative number cannot be calculated.	sqrt(16) → 4
`abs(x)`	Drops the minus sign.	abs(0 − 7) → 7
`pow(x, n)`	x to the power n. A whole n is exact and can be negative. A fraction (0.5, 1 ÷ 3) needs x above zero.	pow(1.05, 10) → 1.62889… pow(8, 1 ÷ 3) → 2
`min(a, b)`	The smaller of two.	min(3, 8) → 3
`max(a, b)`	The larger of two.	max(3, 8) → 8
`mod(a, b)`	The remainder of a ÷ b, with the sign of b, like Excel.	mod(10, 3) → 1 mod(-3, 2) → 1
`floor(x)`	Down to a whole number.	floor(-2.5) → -3
`ceil(x)`	Up to a whole number.	ceil(2.1) → 3
`factorial(n)`	n × (n−1) × … × 1. n is a whole number from 0 to 1000.	factorial(5) → 120
`choose(n, k)`	Ways to pick k out of n, order ignored.	choose(5, 2) → 10

Growth, logs and angles

Function	Gives	Example
`exp(x)`	e to the power x.	exp(1) → 2.71828…
`ln(x)`	Natural log. x must be above zero.	ln(2) → 0.69314…
`log(x)`	Log base 10. x must be above zero.	log(1000) → 3
`pi()`	π. The brackets stay empty.	pi() → 3.14159…
`sin(x)`	Sine. x is in radians.	sin(pi() ÷ 6) → 0.5
`cos(x)`	Cosine. x is in radians.	cos(pi()) → -1
`tan(x)`	Tangent. x is in radians.	tan(pi() ÷ 4) → 1

These are worked out to about 30 digits, which is far more than a result shows, and sin(pi()) comes out as exactly 0. Angles are in radians: multiply degrees by pi() ÷ 180.

Lists

List functions take a .list variable, which the customer fills with comma-separated numbers. The value must be that one variable, not a formula. See Inputs.

Function	Gives	For example
`sum(list)`	Add them up.	70, 85, 90 → 245
`count(list)`	How many numbers.	70, 85, 90 → 3
`product(list)`	Multiply them together.	2, 3, 4 → 24
`lowest(list)`	The smallest number.	9, 4, 6 → 4
`highest(list)`	The largest number.	9, 4, 6 → 9
`mean(list)`	The average.	70, 85, 90 → 81.66…
`median(list)`	The middle value, or the average of the middle two.	70, 85, 90 → 85
`variance(list)`	Spread, over exactly these numbers (divides by n).	2, 4, 6 → 2.66…
`stddev(list)`	Square root of the variance.	2, 4, 6 → 1.63…
`percentile(list, p)`	The value at p percent, p from 0 to 100, between neighbours like Excel’s PERCENTILE.INC.	p = 50 gives the median
`zscore(x, list)`	How many standard deviations x is from the list’s mean.	zscore(95, scores)
`sumproduct(list1, list2)`	Multiply two equal-length lists item by item, then add up. A weighted sum, a dot product.	1, 2, 3 and 4, 5, 6 → 32
`slope(xs, ys)`	The slope of the best-fit straight line through paired lists (least squares, like Excel’s SLOPE).	1, 2, 3 and 3, 5, 7 → 2
`intercept(xs, ys)`	Where that line sits at x = 0 (like Excel’s INTERCEPT).	1, 2, 3 and 3, 5, 7 → 1
`correlation(list1, list2)`	How closely two equal-length lists move together, from -1 to 1.	correlation(hours, marks)

.list scores: Test scores
.r1 Average: mean(scores)
.r2 Marks given: count(scores)

A trend line

.list months: Month number
.list sales: Sales (RM)
.input next: Month to predict positive
.r1 Growth per month (RM): slope(months, sales)
.r2 Predicted sales (RM): intercept(months, sales) + r1 × next

Chance (normal distribution)

For bell-curve questions: where a score ranks, or what cutoff leaves 5% above. sd is the standard deviation and must be above zero.

Function	Gives	Example
`normdist(x, mean, sd)`	The chance a normally spread value is at or below x.	normdist(70, 50, 10) → 0.97725
`norminv(p, mean, sd)`	The reverse: the x that a value stays below with chance p (p between 0 and 1).	norminv(0.975, 0, 1) → 1.95996…

.input score: Your score
.input average: Average score
.input sd: Spread (standard deviation) positive
.r1 Share of people at or below you: normdist(score, average, sd) × 100

Answers beyond 10 standard deviations from the mean are rounded to 0 or 1, and norminv refuses a p that close to 0 or 1.

Money

Function	Gives
`pmt(rate, periods, loan)`	The payment each period to pay off a loan.
`fv(rate, periods, payment)`	What regular payments grow to.
`pv(rate, periods, payment)`	What regular payments are worth today.

The rate is per period. For a yearly rate paid monthly, divide by 12 (and by 100 for a percent), and make the periods months: years × 12.
Signs follow Excel. Money you pay out is negative, so pmt on a positive loan is negative. Wrap it in abs(), or write 0 − pmt(…), for a plain positive payment. For fv and pv put the payment in as a negative (0 − monthly) to get a positive result.
Periods must be a whole number of at least 1 for pmt. A rate of 0 works (the loan is split evenly). Payments are at the end of each period.

Loan payment

.input loan: Loan (RM) positive
.input rate: Yearly interest (%) positive
.input years: Years positive
.r1 Monthly payment (RM): abs(pmt(rate ÷ 100 ÷ 12, years × 12, loan))

Savings

.input monthly: Saved each month (RM) positive
.input years: Years positive
.r1 After the years (RM): fv(0.04 ÷ 12, years × 12, 0 − monthly)

Present value

.r1 Worth today (RM): pv(0.05, 10, 0 − 1000)
// 1000 a year for 10 years, at 5%, is worth 7721.73 today

Not in Dotdown yet

Dotdown™ does numbers and true / false only. There are no dates, no text, no lookups like VLOOKUP, no cell ranges like A1:B10, no matrices, no loops, and no multi-variable regression or other distributions. Use a constant for a fixed table of numbers, and a module to pick from it.

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