Formula

This block performs a freely entered calculation on its inputs. Instead of chaining several arithmetic and comparison blocks, the calculation is simply written down as text, for example (E1+E2)/2 or if E1>20 then E2 else E3.

The formula is edited using the button next to the "Formula" parameter. The editor checks the entry as you type and points out where something is wrong; only a valid formula can be applied.

The block works exclusively with the values currently present at its inputs. It remembers nothing, has no loops and accesses nothing else. If more is required, the Lua script is the right tool.

Inputs
TR	Trigger	Starts the calculation when the calculation mode is set to "Only on trigger". The calculation runs on the rising edge, that is when the value changes from 0 to any value other than 0. In the other modes this input has no effect and may be left unconnected.
E1 ... E8	Input 1 to 8	The values the formula works with. These are exactly the names used in the formula. The "Number of inputs" parameter determines how many inputs the block has. An unconnected input supplies 0.
Outputs
AW	Result	The result of the formula.
AB	Result as bit	1 as long as the result is not 0, otherwise 0. Handy for formulas that test a condition, because comparisons always return 1 or 0.
FE	Error	1 as long as the formula cannot be calculated - either because it contains an error or because the calculation does not work out, for example a division by zero. Otherwise 0.
Parameters
	Formula	The button opens the editor in which the calculation is entered. The permitted notation is described below.
	Number of inputs	How many value inputs the block gets, 1 to 8. The formula may only use inputs that actually exist.
	Calculation	When the calculation runs: On input change - as soon as an input value changes. This is the normal case. Only on trigger - only on the rising edge at input TR. Useful when several inputs arrive one after another and the calculation should only run on a complete set of values. Cyclic - at the interval set under "Cycle time", regardless of whether anything has changed.
	Cycle time	Interval between two calculations in seconds. Only shown when the calculation mode is set to "Cyclic".
	Decimal places	How many decimal places the result is rounded to. -1 means the result is not rounded at all.
	On error	What output AW shows while no calculation is possible: Hold last value - the last valid result stays in place. Output 0 - the output goes to 0. Output FE reports the error in either case.
How a formula is written
	Inputs	In the formula the input values are called E1 to E8 - exactly as they are labelled on the block. The trigger input TR is not used in the formula.
	Upper and lower case	Does not matter. E1, e1, IF and if are all equivalent.
	Numbers	Always with a decimal point: 0.5, not 0,5. In a formula the comma separates the values of a function.
	Spaces	May be used freely. E1+E2 and E1 + E2 are the same. Line breaks are allowed as well, so long formulas can be laid out clearly.
	True and false	There are no separate truth values. A comparison returns 1 when it applies and 0 when it does not. Conversely, any value other than 0 counts as true in a condition.
Arithmetic
Symbol	Meaning	Example with E1 = 20 and E2 = 8
+	Addition	E1 + E2 gives 28
-	Subtraction	E1 - E2 gives 12
*	Multiplication	*E1 E2** gives 160
/	Division	E1 / E2 gives 2.5
%	Remainder of a division	E1 % E2 gives 4, because 20 divided by 8 goes twice and leaves 4
-	Sign	-E1 gives -20
( )	Brackets	Without brackets, multiplication comes before addition: *E1 + E2 2 gives 36, whereas (E1 + E2) * 2** gives 56
Comparisons
Symbol	Meaning	Example with E1 = 20 and E2 = 8
<	less than	E1 < E2 gives 0
<=	less than or equal	E1 <= E2 gives 0
>	greater than	E1 > E2 gives 1
>=	greater than or equal	E1 >= E2 gives 1
==	equal	E1 == E2 gives 0. Note: two equals signs, a single one is reported as an error
!=	not equal	E1 != E2 gives 1
Logic
Symbol	Meaning	Example with E1 = 1 and E2 = 0
and &&	and - both must apply	E1 and E2 gives 0
or \|\|	or - either one is enough	E1 or E2 gives 1
not !	not - inverts	not E1 gives 0, not E2 gives 1
Functions
Function	Meaning	Example
min(a,b)	the smaller of the two values	min(E1,E2) with E1 = 18 and E2 = 21 gives 18
max(a,b)	the larger of the two values	max(E1,E2) with E1 = 18 and E2 = 21 gives 21
abs(x)	absolute value, the value without its sign	abs(E1-E2) with E1 = 18 and E2 = 21 gives 3
round(x)	round to the nearest whole number	round(E1) with E1 = 21.6 gives 22
floor(x)	round down to the next whole number	floor(E1) with E1 = 21.6 gives 21
ceil(x)	round up to the next whole number	ceil(E1) with E1 = 21.2 gives 22
sqrt(x)	square root	sqrt(E1) with E1 = 16 gives 4. A negative value sets output FE
pow(a,b)	a to the power of b	pow(E1,2) with E1 = 3 gives 9
limit(x,lo,hi)	restrict a value to a range	limit(E1,0,100) gives 100 for E1 = 137, 0 for E1 = -5 and 42 for E1 = 42
pi	the number pi, 3.14159...	*pipow(E1,2)** with E1 = 2 gives 12.566
Conditions
	Structure	if condition then value else value If the condition applies, the value after then is used, otherwise the one after else. The else part must always be given - the block has to output a value in every case.
	Simple example	if E1 > 20 then 1 else 0 Gives 1 as soon as E1 rises above 20, otherwise 0.
	Several stages	if E1 > 30 then 3 else if E1 > 20 then 2 else 1 Gives 3 above 30, 2 between 20 and 30 and 1 otherwise. Conditions can be nested as deeply as required.
	Only the applicable branch is calculated	if E2 == 0 then 0 else E1 / E2 If E2 equals 0, the part after else is not calculated at all. This is a clean way to protect a division without output FE reacting.
Practical examples
Task	Formula	Explanation
Average of two sensors	(E1+E2)/2	E1 and E2 are the two room sensors. The brackets matter - without them only E2 would be halved.
Temperature difference without a sign	abs(E1-E2)	Always returns the positive distance between flow and return, no matter which value is larger.
Restrict a setpoint	limit(E1,18,26)	Forces the setpoint entered through the visualisation into a sensible range.
Convert a control value to per cent	*limit(E110,0,100)**	Turns a value from 0 to 10 into a percentage from 0 to 100. The limit catches outliers.
Release only when two conditions apply	E1 > 200 and E2 < 25	Gives 1 when the brightness is above 200 and the temperature is below 25 - otherwise 0. Output AB can be used directly as a release signal.
Switch between two setpoints	if E3 then E1 else E2	E3 is the operating state: when it is set, the comfort setpoint E1 applies, otherwise the setback setpoint E2.
Fill level in per cent	*limit((E1-E2)/(E3-E2)100,0,100)**	E1 is the measured value, E2 the value when empty and E3 the value when full. The result is restricted to 0 to 100.
Protect a division	if E2 == 0 then 0 else E1/E2	Prevents output FE from reacting when the divisor is temporarily 0.
Messages in the editor
For every error the editor names the position where it occurs and highlights it in the text. Only a formula without errors can be applied with OK.
Message	Example	The correct way
The formula is empty	(no text)	E1
This character does not belong in a formula	E1 $ E2	*E1 E2**
Unknown name	value(E1)	abs(E1) - only the functions listed above are allowed
This input does not exist	E1 + E3 with two inputs	Raise the "Number of inputs" parameter to 3 or write E1 + E2
A value is missing here	E1 +	E1 + E2
A bracket is missing or superfluous	(E1+E2	(E1+E2)
The function expects a different number of values	min(E1)	min(E1,E2)
"then" is missing after the condition	if E1 2	if E1 then 2 else 0
"else" is missing for "then"	if E1 then 2	if E1 then 2 else 0
There is something after the formula	E1 E2	E1 + E2 - the operator is missing here
The formula is too extensive	very long formulas	Formulas with hundreds of calculation steps are too extensive. Split the calculation across several formula blocks
Errors during operation
Some errors only appear during the calculation because they depend on the input values. In these cases output FE goes to 1 and output AW behaves as set by the "On error" parameter. As soon as the calculation succeeds again, FE returns to 0 by itself.
Cause	Example	Remedy
Division by zero	E1 / E2 with E2 = 0	if E2 == 0 then 0 else E1/E2
Remainder of a division by zero	E1 % E2 with E2 = 0	if E2 == 0 then 0 else E1%E2
Square root of a negative number	sqrt(E1) with E1 = -4	sqrt(abs(E1)) or if E1 < 0 then 0 else sqrt(E1)
Result too large	pow(E1,E2)	With very large values the result can no longer be represented. Check the value range of the inputs and restrict the result with limit
Limitations
The formula works exclusively with the values currently present at the inputs. It remembers nothing from one calculation to the next, has no loops and accesses neither addresses nor the time of day. Where that is needed, the Lua script is the right tool - that is what it is made for.

Formula

Inputs

Outputs

Parameters

How a formula is written

Arithmetic

Comparisons

Logic

Functions

Conditions

Practical examples

Messages in the editor

Errors during operation

Limitations