Silico formulae support a number of builtin functions with extended functionality.

# Mathematical Functions

## abs(x)

Return the absolute value of a number

abs(5) => 5

abs(-5) => 5

## ceil(x)

Round a number upwards (towards infinity)

ceil(5) => 5

ceil(5.1) => 6

ceil(-5.9) => -5

## exp(x)

Return the natural exponential of a number

exp(0) => 0

exp(1) => 2.718..

## floor(x)

Round a number downwards (towards negative infinity)

floor(5) => 5

floor(5.1) => 5

floor(-5.9) => -6

## sqrt(x)

Take the square root of a number

sqrt(4) => 2

sqrt(16) => 4

## div(x, y, z = 0)

Divide x by y. In the case where y is zero, return the fallback value z, defaulting to 0.

## frac(x)

Return the fractional part of a number.

frac(5.5) => 0.5

frac(-5.5) => -0.5

## int(x)

Return the integral part of a number. This can also be thought of as rounding towards 0. Note that `frac(x) + int(x)`

will always equal x.

int(5.5) => 5

int(-5.5) => -5

## ln(x)

Return the natural logarithm of a number.

ln(1) => 0

ln(2) => 0.6931..

ln(exp(3)) => 3

## log(x, base = 10)

Return the logarithm of a number, with an arbitrary base. Defaults to the logarithm of base 10.

log(100) => 2

log(8, 2) => 3

## bound(x, min, max)

Return a number, bounded to be between min and max.

bound(0.5, 1, 2) => 1

bound(1.5, 1, 2) => 1.5

bound(2.5, 1, 2) => 2

## power(x, n)

Raise a number to the nth power. Supports fractional powers.

power(4, 2) => 16

## root(x, n = 2)

Find the nth root of a number, defaulting to the 2nd root (or sqrt).

root(4) => 2

root(27, 3) => 3

## sign(x)

Return the sign of a number, in the form of -1 for negative, and 1 for non-negative.

sign(-5) => -1

sign(0) => 1

sign(16) => 1

## round(x, places = 0)

Round a number towards the nearest integer. In the case of equal distance, rounds away from 0.

round(4.4) => 4

round(4.6) => 5

round(4.5) => 5

round(-4.5) => -5

If places is provided, rounds to the given number of decimal places, otherwise following the same rules.

round(4.4, 1) => 4.4

round(4.35, 1) => 4.4

## round2(x, places = 0)

Round a number using convergent rounding, or bankers' rounding. In the case of equal distance, rounds to the even number.

round2(4.5) => 4

round2(5.5) => 6

As with round, can be provided with a places argument to round to a certain number of decimal places.

round2(4.65, 1) => 4.6

round2(4.75, 1) => 4.8

# Aggregation Functions

All aggregation functions take any number of arguments, and return a single result.

## min(x, y, ...), max(x, y, ...)

Return the minimum or maximum value of all arguments. If no arguments are provided, return 0.

min(4, 5) => 4

min(8, 7, -2, 4) => -2

min() => 0

max(4, 5) => 5

min(8, 7, -2, 4) => 8

max() => 0

# Window Functions

Window functions compute a value from their argument across time periods.

## moving_avg(x, periods)

Return the simple moving average of the given expression x, across the given number of time periods.

## exp_moving_avg(x, factor)

Return the exponential moving average of a given expression x, with the provided decay factor.

## delay(x, periods, fallback = 0)

Return the value of the expression x the given number of time periods in the past. If the provided time offset would be 0 or point to before the start time of the model, return the fallback value. Note that delay can be used to break circular dependencies, as with a variable X depending on Y, Y can reference a delayed value of X safely.

There is an optional mode (in Project Settings > Advanced) that changes the behaviour of delay, such that in the case a fallback is not provided, the behaviour is to instead return the oldest value of x known, which could be its current value. In this mode, if a fallback is not provided, then the delay function will not break circular dependencies, as a delay ordinarily would.

# Time-Varying Functions

## ramp(x, start_time)

Return a value increasing by x each time period, starting at the given start_time, which will default to the start of the model if not provided.

## pulse(x, start_time, interval = 0)

Return a value that pulses at given times. If start_time is not provided, it will default to the start of the model. If interval is not provided, then the function will pulse only once (at start_time), otherwise after start_time the function will return the value x every interval time periods.

## step(x, start_time)

Return a value that is 0 before start_time, and x at start_time or after. If a start_time is not provided, it defaults to the start of the model, and so will always return the value of x.

# Random Number Functions

Silico provides a number of builtin functions for sampling from random number distributions. All of these functions uses a seeded pseudorandom number generator, and so will return the same sampled distributions. Each call to a pseudo-random function is however independently seeded, and so will not affect the results from other functions. Functionality for controlling the PRNG seeds will be coming in a future release.

## random(max = 1)

Return a number sampled uniformly between 0 and max. Equivalent to rand_uniform(0, max).

## rand_bernoulli(p = 0.5)

Return a sample from the Bernoulli distribution with default probability 0.5, i.e. an even chance between returning 0 or 1.

## rand_binomial(n, p = 0.5)

Return a sample from the Binomial distribution with n trials and probability p.

## rand_discrete(min = 0, max = 1)

Return a sample from the Discrete uniform distribution between given min and max bounds.

## rand_uniform(min = 0, max = 1)

Return a sample from the Continuous uniform distribution between given min and max bounds.

## rand_exp(lambda = 1)

Return a sample from the Exponential distribution with given lambda.

## rand_exp_percentile(lambda = 1, percentile = 0.5)

Return the quantile function result for the Exponential distribution at the given percentile.

## rand_gaussian(mean = 0, std_dev = 1)

Return a sample from the Gaussian distribution with given mean and standard deviation.

## rand_gaussian_percentile(mean = 0, std_dev = 1, percentile = 0.5)

Return the quantile function result for the Gaussian distribution at the given percentile.

## rand_pareto(xm = 1, alpha = 1.16)

Return a sample from the Pareto distribution with given xm and alpha.

## rand_poisson(lambda = 1)

Return a sample from the Poisson distribution with given lambda.

## rand_poisson_percentile(lambda = 1, percentile = 0.5)

Return the quantile function result for the Poisson distribution at the given percentile.

## rand_poisson_binomial(p1, p2, p3..)

Return a sample from the Poisson binomial distribution with given p values.

## rand_student(dof = 1)

Return a sample from the Student's t-distribution with given degrees of freedom.

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