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RRDGRAPH_RPN(1)			    rrdtool		       RRDGRAPH_RPN(1)

       rrdgraph_rpn - About RPN	Math in	rrdtool	graph

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

       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-

       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
       your RRD	script.

       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.

       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).


	   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.


	   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.


	   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.

	   +, -, *, /, %

	   Add,	subtract, multiply, divide, modulo


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


	   Arctangent (output in radians).


	   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.


	   Round down or up to the nearest integer.


	   Convert angle in degrees to radians,	or radians to degrees.


	   Take	the absolute value.

       Set Operations

	   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.


	   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"


	   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:

				  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

	   Pushes an unknown value on the stack


	   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.


	   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.


	   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.


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


	   Pushes the current time on the stack.


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


	   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

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

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

	   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"

	   Returns the rate from each defined time slot	multiplied with	the
	   step	size.  This can, for instance, return total bytes transfered
	   when	you have logged	bytes per second. The time component returns
	   the number of seconds.

	   Example: "VDEF:total=mydata,TOTAL"

	   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"

	   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-

	   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.

       Program by Tobias Oetiker <>

       This manual page	by Alex	van den	Bogaerdt <>

1.2.30				  2009-01-19		       RRDGRAPH_RPN(1)


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