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RRDGRAPH_RPN(1) 		    rrdtool		       RRDGRAPH_RPN(1)

       rrdgraph_rpn - About RPN Math in rrdtool graph

       RPN expression:=vnameoperatorvalue[,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,
	   indeed, 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.

       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,
	   another 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
	   Pearsons 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 

1.2.15				  2006-07-14		       RRDGRAPH_RPN(1)

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