# FreeBSD Manual Pages

```RRDGRAPH_RPN(1)			    rrdtool		       RRDGRAPH_RPN(1)

NAME
rrdgraph_rpn - About RPN	Math in	rrdtool	graph

SYNOPSIS
RPN expression:=vname|operator|value[,RPN expression]

DESCRIPTION
If you have ever	used a traditional HP calculator you already know RPN.
The idea	behind RPN is that you have a stack and	push your data onto
this stack. Whenever you	execute	an operation, it takes as many ele-
ments from the stack as needed. Pushing is done implicitly, so whenever
you specify a number or a variable, it gets pushed onto the stack auto-
matically.

At the end of the calculation there should be one and only one value
left on the stack.  This	is the outcome of the function and this	is
what is put into	the vname.  For	CDEF instructions, the stack is	pro-
cessed for each data point on the graph.	VDEF instructions work on an
entire data set in one run. Note, that currently	VDEF instructions only
support a limited list of functions.

Example:	"VDEF:maximum=mydata,MAXIMUM"

This will set variable "maximum"	which you now can use in the rest of

Example:	"CDEF:mydatabits=mydata,8,*"

This means:  push variable mydata, push the number 8, execute the oper-
ator *. The operator needs two elements and uses	those to return	one
value.  This value is then stored in mydatabits.	 As you	may have
guessed,	this instruction means nothing more than mydatabits = mydata *
8.  The real power of RPN lies in the fact that it is always clear in
which order to process the input.  For expressions like "a = b +	3 * 5"
you need	to multiply 3 with 5 first before you add b to get a. However,
with parentheses	you could change this order: "a	= (b + 3) * 5".	In
RPN, you	would do "a = b, 3, +, 5, *" without the need for parentheses.

OPERATORS
Boolean operators
LT, LE, GT, GE, EQ, NE

Pop two elements from the stack, compare them for the selected con-
dition and return 1 for true	or 0 for false.	Comparing an unknown
or an infinite value	will always result in 0	(false).

UN, ISINF

Pop one element from	the stack, compare this	to unknown respec-
tively to positive or negative infinity. Returns 1 for true or 0
for false.

IF

Pops	three elements from the	stack.	If the element popped last is
0 (false), the value	popped first is	pushed back onto the stack,
otherwise the value popped second is	pushed back. This does,	in-
deed, mean that any value other than	0 is considered	to be true.

Example: "A,B,C,IF" should be read as "if (A) then (B) else (C)"

Comparing values
MIN,	MAX

Pops	two elements from the stack and	returns	the smaller or larger,
respectively.  Note that infinite is	larger than anything else.  If
one of the input numbers is unknown then the	result of the opera-
tion	will be	unknown	too.

LIMIT

Pops	two elements from the stack and	uses them to define a range.
Then	it pops	another	element	and if it falls	inside the range, it
is pushed back. If not, an unknown is pushed.

The range defined includes the two boundaries (so: a	number equal
to one of the boundaries will be pushed back). If any of the	three
numbers involved is either unknown or infinite this function	will
always return an unknown

Example: "CDEF:a=alpha,0,100,LIMIT" will return unknown if alpha is
lower than 0	or if it is higher than	100.

Arithmetics
+, -, *, /, %

SIN,	COS, LOG, EXP, SQRT

Sine	and cosine (input in radians), log and exp (natural loga-
rithm), square root.

ATAN

ATAN2

Arctangent of y,x components	(output	in radians).  This pops	one
element from	the stack, the x (cosine) component, and then a	sec-
ond,	which is the y (sine) component.  It then pushes the arctan-
gent	of their ratio,	resolving the ambiguity	between	quadrants.

Example: "CDEF:angle=Y,X,ATAN2,RAD2DEG" will	convert	"X,Y" compo-
nents into an angle in degrees.

FLOOR, CEIL

Round down or up to the nearest integer.

ABS

Take	the absolute value.

Set Operations
SORT, REV

Pop one element from	the stack.  This is the	count of items to be
sorted (or reversed).  The top count	of the remaining elements are
then	sorted (or reversed) in	place on the stack.

Example: "CDEF:x=v1,v2,v3,v4,v5,v6,6,SORT,POP,5,REV,POP,+,+,+,4,/"
will	compute	the average of the values v1 to	v6 after removing the
smallest and	largest.

AVG

Pop one element (count) from	the stack. Now pop count elements and
build the average, ignoring all UNKNOWN values in the process.

Example: "CDEF:x=a,b,c,d,4,AVG"

TREND

Create a "sliding window" average of	another	data series.

Usage: CDEF:smoothed=x,1800,TREND

This	will create a half-hour	(1800 second) sliding window average
of x.  The average is essentially computed as shown here:

+---!---!---!---!---!---!---!---!--->
now
delay	    t0
<--------------->
delay	t1
<--------------->
delay	    t2
<--------------->

Value at sample	(t0) will be the average between (t0-delay) and	(t0)
Value at sample	(t1) will be the average between (t1-delay) and	(t1)
Value at sample	(t2) will be the average between (t2-delay) and	(t2)

Special values
UNKN

Pushes an unknown value on the stack

INF,	NEGINF

Pushes a positive or	negative infinite value	on the stack. When
such	a value	is graphed, it appears at the top or bottom of the
graph, no matter what the actual value on the y-axis	is.

PREV

Pushes an unknown value if this is the first	value of a data	set or
otherwise the result	of this	CDEF at	the previous time step.	This
allows you to do calculations across	the data.  This	function can-
not be used in VDEF instructions.

PREV(vname)

Pushes an unknown value if this is the first	value of a data	set or
otherwise the result	of the vname variable at the previous time
step. This allows you to do calculations across the data. This
function cannot be used in VDEF instructions.

COUNT

Pushes the number 1 if this is the first value of the data set, the
number 2 if it is the second, and so	on. This special value allows
you to make calculations based on the position of the value within
the data set. This function cannot be used in VDEF instructions.

Time
Time	inside RRDtool is measured in seconds since the	epoch. The
epoch is defined to be "Thu Jan 1 00:00:00 UTC 1970".

NOW

Pushes the current time on the stack.

TIME

Pushes the time the currently processed value was taken at onto the
stack.

LTIME

Takes the time as defined by	TIME, applies the time zone offset
valid at that time including	daylight saving	time if	your OS	sup-
ports it, and pushes	the result on the stack.  There	is an elabo-
rate	example	in the examples	section	below on how to	use this.

Processing the stack directly
DUP,	POP, EXC

Duplicate the top element, remove the top element, exchange the two
top elements.

VARIABLES
These operators work only on VDEF statements. Note that currently ONLY
these work for VDEF.

MAXIMUM,	MINIMUM, AVERAGE
Return the corresponding value, MAXIMUM and MINIMUM also return the
first occurrence of that value in the time component.

Example: "VDEF:avg=mydata,AVERAGE"

LAST, FIRST
Return the last/first value including its time.  The	time for FIRST
is actually the start of the	corresponding interval,	whereas	LAST
returns the end of the corresponding	interval.

Example: "VDEF:first=mydata,FIRST"

TOTAL
Returns the rate from each defined time slot	multiplied with	the
when	you have logged	bytes per second. The time component returns
the number of seconds.

Example: "VDEF:total=mydata,TOTAL"

PERCENT
This	should follow a	DEF or CDEF vname. The vname is	popped,	an-
other number	is popped which	is a certain percentage	(0..100). The
data	set is then sorted and the value returned is chosen such that
percentage percent of the values is lower or	equal than the result.
Unknown values are considered lower than any	finite number for this
purpose so if this operator returns an unknown you have quite a lot
of them in your data.  Infinite numbers are lesser, or more,	than
the finite numbers and are always more than the Unknown numbers.
(NaN	< -INF < finite	values < INF)

Example: "VDEF:perc95=mydata,95,PERCENT"

LSLSLOPE, LSLINT, LSLCORREL
Return the parameters for a Least Squares Line (y = mx +b) which
approximate the provided dataset.  LSLSLOPE is the slope (m)	of the
line	related	to the COUNT position of the data.  LSLINT is the
y-intercept (b), which happens also to be the first data point on
the graph. LSLCORREL	is the Correlation Coefficient (also know as
Pearson's Product Moment Correlation	Coefficient).  It will range
from	0 to +/-1 and represents the quality of	fit for	the approxima-
tion.

Example: "VDEF:slope=mydata,LSLSLOPE"

rrdgraph	gives an overview of how rrdtool graph works.  rrdgraph_data
describes DEF,CDEF and VDEF in detail.  rrdgraph_rpn describes the RPN
language	used in	the ?DEF statements.  rrdgraph_graph page describes
all of the graph	and print functions.

Make sure to read rrdgraph_examples for tips&tricks.

AUTHOR
Program by Tobias Oetiker <tobi@oetiker.ch>

This manual page	by Alex	van den	Bogaerdt <alex@ergens.op.het.net>

1.2.30				  2009-01-19		       RRDGRAPH_RPN(1)
```

NAME | SYNOPSIS | DESCRIPTION | OPERATORS | VARIABLES | SEE ALSO | AUTHOR

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