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CDEFTUTORIAL(1) 			     rrdtool				  CDEFTUTORIAL(1)

NAME
       cdeftutorial - Alex van den Bogaerdt's CDEF tutorial

DESCRIPTION
       Intention of this document: to provide some examples of the commonly used parts of
       RRDtool's CDEF language.

       If you think some important feature is not explained properly, and if adding it to this
       document would benefit most users, please do ask me to add it.  I will then try to provide
       an answer in the next release of this tutorial.	No feedback equals no changes! Additions
       to this document are also welcome.  -- Alex van den Bogaerdt <alex@vandenbogaerdt.nl>

   Why this tutorial?
       One of the powerful parts of RRDtool is its ability to do all sorts of calculations on the
       data retrieved from its databases. However, RRDtool's many options and syntax make it
       difficult for the average user to understand. The manuals are good at explaining what
       these options do; however they do not (and should not) explain in detail why they are
       useful. As with my RRDtool tutorial: if you want a simple document in simple language you
       should read this tutorial.  If you are happy with the official documentation, you may find
       this document too simple or even boring. If you do choose to read this tutorial, I also
       expect you to have read and fully understand my other tutorial.

   More reading
       If you have difficulties with the way I try to explain it please read Steve Rader's
       rpntutorial. It may help you understand how this all works.

What are CDEFs?
       When retrieving data from an RRD, you are using a "DEF" to work with that data. Think of
       it as a variable that changes over time (where time is the x-axis). The value of this
       variable is what is found in the database at that particular time and you can't do any
       modifications on it. This is what CDEFs are for: they takes values from DEFs and perform
       calculations on them.

Syntax
	  DEF:var_name_1=some.rrd:ds_name:CF
	  CDEF:var_name_2=RPN_expression

       You first define "var_name_1" to be data collected from data source "ds_name" found in RRD
       "some.rrd" with consolidation function "CF".

       Assume the ifInOctets SNMP counter is saved in mrtg.rrd as the DS "in".	Then the
       following DEF defines a variable for the average of that data source:

	  DEF:inbytes=mrtg.rrd:in:AVERAGE

       Say you want to display bits per second (instead of bytes per second as stored in the
       database.)  You have to define a calculation (hence "CDEF") on variable "inbytes" and use
       that variable (inbits) instead of the original:

	  CDEF:inbits=inbytes,8,*

       This tells RRDtool to multiply inbytes by eight to get inbits. I'll explain later how this
       works. In the graphing or printing functions, you can now use inbits where you would use
       inbytes otherwise.

       Note that the variable name used in the CDEF (inbits) must not be the same as the variable
       named in the DEF (inbytes)!

RPN-expressions
       RPN is short-hand for Reverse Polish Notation. It works as follows.  You put the variables
       or numbers on a stack. You also put operations (things-to-do) on the stack and this stack
       is then processed. The result will be placed on the stack. At the end, there should be
       exactly one number left: the outcome of the series of operations. If there is not exactly
       one number left, RRDtool will complain loudly.

       Above multiplication by eight will look like:

       1.  Start with an empty stack

       2.  Put the content of variable inbytes on the stack

       3.  Put the number eight on the stack

       4.  Put the operation multiply on the stack

       5.  Process the stack

       6.  Retrieve the value from the stack and put it in variable inbits

       We will now do an example with real numbers. Suppose the variable inbytes would have value
       10, the stack would be:

       1.  ||

       2.  |10|

       3.  |10|8|

       4.  |10|8|*|

       5.  |80|

       6.  ||

       Processing the stack (step 5) will retrieve one value from the stack (from the right at
       step 4). This is the operation multiply and this takes two values off the stack as input.
       The result is put back on the stack (the value 80 in this case). For multiplication the
       order doesn't matter, but for other operations like subtraction and division it does.
       Generally speaking you have the following order:

	  y = A - B  -->  y=minus(A,B)	-->  CDEF:y=A,B,-

       This is not very intuitive (at least most people don't think so). For the function f(A,B)
       you reverse the position of "f", but you do not reverse the order of the variables.

Converting your wishes to RPN
       First, get a clear picture of what you want to do. Break down the problem in smaller
       portions until they cannot be split anymore. Then it is rather simple to convert your
       ideas into RPN.

       Suppose you have several RRDs and would like to add up some counters in them. These could
       be, for instance, the counters for every WAN link you are monitoring.

       You have:

	  router1.rrd with link1in link2in
	  router2.rrd with link1in link2in
	  router3.rrd with link1in link2in

       Suppose you would like to add up all these counters, except for link2in inside
       router2.rrd. You need to do:

       (in this example, "router1.rrd:link1in" means the DS link1in inside the RRD router1.rrd)

	  router1.rrd:link1in
	  router1.rrd:link2in
	  router2.rrd:link1in
	  router3.rrd:link1in
	  router3.rrd:link2in
	  --------------------	 +
	  (outcome of the sum)

       As a mathematical function, this could be written:

       "add(router1.rrd:link1in , router1.rrd:link2in , router2.rrd:link1in , router3.rrd:link1in
       , router3.rrd:link2.in)"

       With RRDtool and RPN, first, define the inputs:

	  DEF:a=router1.rrd:link1in:AVERAGE
	  DEF:b=router1.rrd:link2in:AVERAGE
	  DEF:c=router2.rrd:link1in:AVERAGE
	  DEF:d=router3.rrd:link1in:AVERAGE
	  DEF:e=router3.rrd:link2in:AVERAGE

       Now, the mathematical function becomes: "add(a,b,c,d,e)"

       In RPN, there's no operator that sums more than two values so you need to do several
       additions. You add a and b, add c to the result, add d to the result and add e to the
       result.

	  push a:	  a	stack contains the value of a
	  push b and add: b,+	stack contains the result of a+b
	  push c and add: c,+	stack contains the result of a+b+c
	  push d and add: d,+	stack contains the result of a+b+c+d
	  push e and add: e,+	stack contains the result of a+b+c+d+e

       What was calculated here would be written down as:

	  ( ( ( (a+b) + c) + d) + e) >

       This is in RPN:	"CDEF:result=a,b,+,c,+,d,+,e,+"

       This is correct but it can be made more clear to humans. It does not matter if you add a
       to b and then add c to the result or first add b to c and then add a to the result. This
       makes it possible to rewrite the RPN into "CDEF:result=a,b,c,d,e,+,+,+,+" which is
       evaluated differently:

	  push value of variable a on the stack: a
	  push value of variable b on the stack: a b
	  push value of variable c on the stack: a b c
	  push value of variable d on the stack: a b c d
	  push value of variable e on the stack: a b c d e
	  push operator + on the stack: 	 a b c d e +
	  and process it:			 a b c P   (where P == d+e)
	  push operator + on the stack: 	 a b c P +
	  and process it:			 a b Q	   (where Q == c+P)
	  push operator + on the stack: 	 a b Q +
	  and process it:			 a R	   (where R == b+Q)
	  push operator + on the stack: 	 a R +
	  and process it:			 S	   (where S == a+R)

       As you can see the RPN expression "a,b,c,d,e,+,+,+,+,+" will evaluate in
       "((((d+e)+c)+b)+a)" and it has the same outcome as "a,b,+,c,+,d,+,e,+".	This is called
       the commutative law of addition, but you may forget this right away, as long as you
       remember what it means.

       Now look at an expression that contains a multiplication:

       First in normal math: "let result = a+b*c". In this case you can't choose the order
       yourself, you have to start with the multiplication and then add a to it. You may alter
       the position of b and c, you must not alter the position of a and b.

       You have to take this in consideration when converting this expression into RPN. Read it
       as: "Add the outcome of b*c to a" and then it is easy to write the RPN expression:
       "result=a,b,c,*,+" Another expression that would return the same: "result=b,c,*,a,+"

       In normal math, you may encounter something like "a*(b+c)" and this can also be converted
       into RPN. The parenthesis just tell you to first add b and c, and then multiply a with the
       result. Again, now it is easy to write it in RPN: "result=a,b,c,+,*". Note that this is
       very similar to one of the expressions in the previous paragraph, only the multiplication
       and the addition changed places.

       When you have problems with RPN or when RRDtool is complaining, it's usually a good thing
       to write down the stack on a piece of paper and see what happens. Have the manual ready
       and pretend to be RRDtool.  Just do all the math by hand to see what happens, I'm sure
       this will solve most, if not all, problems you encounter.

Some special numbers
   The unknown value
       Sometimes collecting your data will fail. This can be very common, especially when
       querying over busy links. RRDtool can be configured to allow for one (or even more)
       unknown value(s) and calculate the missing update. You can, for instance, query your
       device every minute. This is creating one so called PDP or primary data point per minute.
       If you defined your RRD to contain an RRA that stores 5-minute values, you need five of
       those PDPs to create one CDP (consolidated data point).	These PDPs can become unknown in
       two cases:

       1.  The updates are too far apart. This is tuned using the "heartbeat" setting.

       2.  The update was set to unknown on purpose by inserting no value (using the template
	   option) or by using "U" as the value to insert.

       When a CDP is calculated, another mechanism determines if this CDP is valid or not. If
       there are too many PDPs unknown, the CDP is unknown as well.  This is determined by the
       xff factor. Please note that one unknown counter update can result in two unknown PDPs! If
       you only allow for one unknown PDP per CDP, this makes the CDP go unknown!

       Suppose the counter increments with one per second and you retrieve it every minute:

	  counter value    resulting rate
	  10'000
	  10'060	    1; (10'060-10'000)/60 == 1
	  10'120	    1; (10'120-10'060)/60 == 1
	  unknown	    unknown; you don't know the last value
	  10'240	    unknown; you don't know the previous value
	  10'300	    1; (10'300-10'240)/60 == 1

       If the CDP was to be calculated from the last five updates, it would get two unknown PDPs
       and three known PDPs. If xff would have been set to 0.5 which by the way is a commonly
       used factor, the CDP would have a known value of 1. If xff would have been set to 0.2 then
       the resulting CDP would be unknown.

       You have to decide the proper values for heartbeat, number of PDPs per CDP and the xff
       factor. As you can see from the previous text they define the behavior of your RRA.

   Working with unknown data in your database
       As you have read in the previous chapter, entries in an RRA can be set to the unknown
       value. If you do calculations with this type of value, the result has to be unknown too.
       This means that an expression such as "result=a,b,+" will be unknown if either a or b is
       unknown.  It would be wrong to just ignore the unknown value and return the value of the
       other parameter. By doing so, you would assume "unknown" means "zero" and this is not
       true.

       There has been a case where somebody was collecting data for over a year.  A new piece of
       equipment was installed, a new RRD was created and the scripts were changed to add a
       counter from the old database and a counter from the new database. The result was
       disappointing, a large part of the statistics seemed to have vanished mysteriously ...
       They of course didn't, values from the old database (known values) were added to values
       from the new database (unknown values) and the result was unknown.

       In this case, it is fairly reasonable to use a CDEF that alters unknown data into zero.
       The counters of the device were unknown (after all, it wasn't installed yet!) but you know
       that the data rate through the device had to be zero (because of the same reason: it was
       not installed).

       There are some examples below that make this change.

   Infinity
       Infinite data is another form of a special number. It cannot be graphed because by
       definition you would never reach the infinite value. You can think of positive and
       negative infinity depending on the position relative to zero.

       RRDtool is capable of representing (-not- graphing!) infinity by stopping at its current
       maximum (for positive infinity) or minimum (for negative infinity) without knowing this
       maximum (minimum).

       Infinity in RRDtool is mostly used to draw an AREA without knowing its vertical
       dimensions. You can think of it as drawing an AREA with an infinite height and displaying
       only the part that is visible in the current graph. This is probably a good way to
       approximate infinity and it sure allows for some neat tricks. See below for examples.

   Working with unknown data and infinity
       Sometimes you would like to discard unknown data and pretend it is zero (or any other
       value for that matter) and sometimes you would like to pretend that known data is unknown
       (to discard known-to-be-wrong data).  This is why CDEFs have support for unknown data.
       There are also examples available that show unknown data by using infinity.

Some examples
   Example: using a recently created RRD
       You are keeping statistics on your router for over a year now. Recently you installed an
       extra router and you would like to show the combined throughput for these two devices.

       If you just add up the counters from router.rrd and router2.rrd, you will add known data
       (from router.rrd) to unknown data (from router2.rrd) for the bigger part of your stats.
       You could solve this in a few ways:

       o   While creating the new database, fill it with zeros from the start to now.  You have
	   to make the database start at or before the least recent time in the other database.

       o   Alternatively, you could use CDEF and alter unknown data to zero.

       Both methods have their pros and cons. The first method is troublesome and if you want to
       do that you have to figure it out yourself. It is not possible to create a database filled
       with zeros, you have to put them in manually. Implementing the second method is described
       next:

       What we want is: "if the value is unknown, replace it with zero". This could be written in
       pseudo-code as:	if (value is unknown) then (zero) else (value). When reading the rrdgraph
       manual you notice the "UN" function that returns zero or one. You also notice the "IF"
       function that takes zero or one as input.

       First look at the "IF" function. It takes three values from the stack, the first value is
       the decision point, the second value is returned to the stack if the evaluation is "true"
       and if not, the third value is returned to the stack. We want the "UN" function to decide
       what happens so we combine those two functions in one CDEF.

       Lets write down the two possible paths for the "IF" function:

	  if true  return a
	  if false return b

       In RPN:	"result=x,a,b,IF" where "x" is either true or false.

       Now we have to fill in "x", this should be the "(value is unknown)" part and this is in
       RPN:  "result=value,UN"

       We now combine them: "result=value,UN,a,b,IF" and when we fill in the appropriate things
       for "a" and "b" we're finished:

       "CDEF:result=value,UN,0,value,IF"

       You may want to read Steve Rader's RPN guide if you have difficulties with the way I
       explained this last example.

       If you want to check this RPN expression, just mimic RRDtool behavior:

	  For any known value, the expression evaluates as follows:
	  CDEF:result=value,UN,0,value,IF  (value,UN) is not true so it becomes 0
	  CDEF:result=0,0,value,IF	   "IF" will return the 3rd value
	  CDEF:result=value		   The known value is returned

	  For the unknown value, this happens:
	  CDEF:result=value,UN,0,value,IF  (value,UN) is true so it becomes 1
	  CDEF:result=1,0,value,IF	   "IF" sees 1 and returns the 2nd value
	  CDEF:result=0 		   Zero is returned

       Of course, if you would like to see another value instead of zero, you can use that other
       value.

       Eventually, when all unknown data is removed from the RRD, you may want to remove this
       rule so that unknown data is properly displayed.

   Example: better handling of unknown data, by using time
       The above example has one drawback. If you do log unknown data in your database after
       installing your new equipment, it will also be translated into zero and therefore you
       won't see that there was a problem. This is not good and what you really want to do is:

       o   If there is unknown data, look at the time that this sample was taken.

       o   If the unknown value is before time xxx, make it zero.

       o   If it is after time xxx, leave it as unknown data.

       This is doable: you can compare the time that the sample was taken to some known time.
       Assuming you started to monitor your device on Friday September 17, 1999, 00:35:57 MET
       DST. Translate this time in seconds since 1970-01-01 and it becomes 937'521'357. If you
       process unknown values that were received after this time, you want to leave them unknown
       and if they were "received" before this time, you want to translate them into zero (so you
       can effectively ignore them while adding them to your other routers counters).

       Translating Friday September 17, 1999, 00:35:57 MET DST into 937'521'357 can be done by,
       for instance, using gnu date:

	  date -d "19990917 00:35:57" +%s

       You could also dump the database and see where the data starts to be known. There are
       several other ways of doing this, just pick one.

       Now we have to create the magic that allows us to process unknown values different
       depending on the time that the sample was taken.  This is a three step process:

       1.  If the timestamp of the value is after 937'521'357, leave it as is.

       2.  If the value is a known value, leave it as is.

       3.  Change the unknown value into zero.

       Lets look at part one:

	   if (true) return the original value

       We rewrite this:

	   if (true) return "a"
	   if (false) return "b"

       We need to calculate true or false from step 1. There is a function available that returns
       the timestamp for the current sample. It is called, how surprisingly, "TIME". This time
       has to be compared to a constant number, we need "GT". The output of "GT" is true or false
       and this is good input to "IF". We want "if (time > 937521357) then (return a) else
       (return b)".

       This process was already described thoroughly in the previous chapter so lets do it quick:

	  if (x) then a else b
	     where x represents "time>937521357"
	     where a represents the original value
	     where b represents the outcome of the previous example

	  time>937521357       --> TIME,937521357,GT

	  if (x) then a else b --> x,a,b,IF
	  substitute x	       --> TIME,937521357,GT,a,b,IF
	  substitute a	       --> TIME,937521357,GT,value,b,IF
	  substitute b	       --> TIME,937521357,GT,value,value,UN,0,value,IF,IF

       We end up with: "CDEF:result=TIME,937521357,GT,value,value,UN,0,value,IF,IF"

       This looks very complex, however, as you can see, it was not too hard to come up with.

   Example: Pretending weird data isn't there
       Suppose you have a problem that shows up as huge spikes in your graph.  You know this
       happens and why, so you decide to work around the problem.  Perhaps you're using your
       network to do a backup at night and by doing so you get almost 10mb/s while the rest of
       your network activity does not produce numbers higher than 100kb/s.

       There are two options:

       1.  If the number exceeds 100kb/s it is wrong and you want it masked out by changing it
	   into unknown.

       2.  You don't want the graph to show more than 100kb/s.

       Pseudo code: if (number > 100) then unknown else number or Pseudo code: if (number > 100)
       then 100 else number.

       The second "problem" may also be solved by using the rigid option of RRDtool graph,
       however this has not the same result. In this example you can end up with a graph that
       does autoscaling. Also, if you use the numbers to display maxima they will be set to
       100kb/s.

       We use "IF" and "GT" again. "if (x) then (y) else (z)" is written down as
       "CDEF:result=x,y,z,IF"; now fill in x, y and z.	For x you fill in "number greater than
       100kb/s" becoming "number,100000,GT" (kilo is 1'000 and b/s is what we measure!).  The "z"
       part is "number" in both cases and the "y" part is either "UNKN" for unknown or "100000"
       for 100kb/s.

       The two CDEF expressions would be:

	   CDEF:result=number,100000,GT,UNKN,number,IF
	   CDEF:result=number,100000,GT,100000,number,IF

   Example: working on a certain time span
       If you want a graph that spans a few weeks, but would only want to see some routers' data
       for one week, you need to "hide" the rest of the time frame. Don't ask me when this would
       be useful, it's just here for the example :)

       We need to compare the time stamp to a begin date and an end date.  Comparing isn't
       difficult:

	       TIME,begintime,GE
	       TIME,endtime,LE

       These two parts of the CDEF produce either 0 for false or 1 for true.  We can now check if
       they are both 0 (or 1) using a few IF statements but, as Wataru Satoh pointed out, we can
       use the "*" or "+" functions as logical AND and logical OR.

       For "*", the result will be zero (false) if either one of the two operators is zero.  For
       "+", the result will only be false (0) when two false (0) operators will be added.
       Warning: *any* number not equal to 0 will be considered "true". This means that, for
       instance, "-1,1,+" (which should be "true or true") will become FALSE ...  In other words,
       use "+" only if you know for sure that you have positive numbers (or zero) only.

       Let's compile the complete CDEF:

	       DEF:ds0=router1.rrd:AVERAGE
	       CDEF:ds0modified=TIME,begintime,GT,TIME,endtime,LE,*,ds0,UNKN,IF

       This will return the value of ds0 if both comparisons return true. You could also do it
       the other way around:

	       DEF:ds0=router1.rrd:AVERAGE
	       CDEF:ds0modified=TIME,begintime,LT,TIME,endtime,GT,+,UNKN,ds0,IF

       This will return an UNKNOWN if either comparison returns true.

   Example: You suspect to have problems and want to see unknown data.
       Suppose you add up the number of active users on several terminal servers.  If one of them
       doesn't give an answer (or an incorrect one) you get "NaN" in the database ("Not a
       Number") and NaN is evaluated as Unknown.

       In this case, you would like to be alerted to it and the sum of the remaining values is of
       no value to you.

       It would be something like:

	   DEF:users1=location1.rrd:onlineTS1:LAST
	   DEF:users2=location1.rrd:onlineTS2:LAST
	   DEF:users3=location2.rrd:onlineTS1:LAST
	   DEF:users4=location2.rrd:onlineTS2:LAST
	   CDEF:allusers=users1,users2,users3,users4,+,+,+

       If you now plot allusers, unknown data in one of users1..users4 will show up as a gap in
       your graph. You want to modify this to show a bright red line, not a gap.

       Define an extra CDEF that is unknown if all is okay and is infinite if there is an unknown
       value:

	   CDEF:wrongdata=allusers,UN,INF,UNKN,IF

       "allusers,UN" will evaluate to either true or false, it is the (x) part of the "IF"
       function and it checks if allusers is unknown.  The (y) part of the "IF" function is set
       to "INF" (which means infinity) and the (z) part of the function returns "UNKN".

       The logic is: if (allusers == unknown) then return INF else return UNKN.

       You can now use AREA to display this "wrongdata" in bright red. If it is unknown (because
       allusers is known) then the red AREA won't show up.  If the value is INF (because allusers
       is unknown) then the red AREA will be filled in on the graph at that particular time.

	  AREA:allusers#0000FF:combined user count
	  AREA:wrongdata#FF0000:unknown data

   Same example useful with STACKed data:
       If you use stack in the previous example (as I would do) then you don't add up the values.
       Therefore, there is no relationship between the four values and you don't get a single
       value to test.  Suppose users3 would be unknown at one point in time: users1 is plotted,
       users2 is stacked on top of users1, users3 is unknown and therefore nothing happens,
       users4 is stacked on top of users2.  Add the extra CDEFs anyway and use them to overlay
       the "normal" graph:

	  DEF:users1=location1.rrd:onlineTS1:LAST
	  DEF:users2=location1.rrd:onlineTS2:LAST
	  DEF:users3=location2.rrd:onlineTS1:LAST
	  DEF:users4=location2.rrd:onlineTS2:LAST
	  CDEF:allusers=users1,users2,users3,users4,+,+,+
	  CDEF:wrongdata=allusers,UN,INF,UNKN,IF
	  AREA:users1#0000FF:users at ts1
	  STACK:users2#00FF00:users at ts2
	  STACK:users3#00FFFF:users at ts3
	  STACK:users4#FFFF00:users at ts4
	  AREA:wrongdata#FF0000:unknown data

       If there is unknown data in one of users1..users4, the "wrongdata" AREA will be drawn and
       because it starts at the X-axis and has infinite height it will effectively overwrite the
       STACKed parts.

       You could combine the two CDEF lines into one (we don't use "allusers") if you like.  But
       there are good reasons for writing two CDEFS:

       o   It improves the readability of the script.

       o   It can be used inside GPRINT to display the total number of users.

       If you choose to combine them, you can substitute the "allusers" in the second CDEF with
       the part after the equal sign from the first line:

	  CDEF:wrongdata=users1,users2,users3,users4,+,+,+,UN,INF,UNKN,IF

       If you do so, you won't be able to use these next GPRINTs:

	  COMMENT:"Total number of users seen"
	  GPRINT:allusers:MAX:"Maximum: %6.0lf"
	  GPRINT:allusers:MIN:"Minimum: %6.0lf"
	  GPRINT:allusers:AVERAGE:"Average: %6.0lf"
	  GPRINT:allusers:LAST:"Current: %6.0lf\n"

The examples from the RRD graph manual page
   Degrees Celsius vs. Degrees Fahrenheit
       To convert Celsius into Fahrenheit use the formula F=9/5*C+32

	  rrdtool graph demo.png --title="Demo Graph" \
	     DEF:cel=demo.rrd:exhaust:AVERAGE \
	     CDEF:far=9,5,/,cel,*,32,+ \
	     LINE2:cel#00a000:"D. Celsius" \
	     LINE2:far#ff0000:"D. Fahrenheit\c"

       This example gets the DS called "exhaust" from database "demo.rrd" and puts the values in
       variable "cel". The CDEF used is evaluated as follows:

	  CDEF:far=9,5,/,cel,*,32,+
	  1. push 9, push 5
	  2. push function "divide" and process it
	     the stack now contains 9/5
	  3. push variable "cel"
	  4. push function "multiply" and process it
	     the stack now contains 9/5*cel
	  5. push 32
	  6. push function "plus" and process it
	     the stack contains now the temperature in Fahrenheit

   Changing unknown into zero
	  rrdtool graph demo.png --title="Demo Graph" \
	     DEF:idat1=interface1.rrd:ds0:AVERAGE \
	     DEF:idat2=interface2.rrd:ds0:AVERAGE \
	     DEF:odat1=interface1.rrd:ds1:AVERAGE \
	     DEF:odat2=interface2.rrd:ds1:AVERAGE \
	     CDEF:agginput=idat1,UN,0,idat1,IF,idat2,UN,0,idat2,IF,+,8,* \
	     CDEF:aggoutput=odat1,UN,0,odat1,IF,odat2,UN,0,odat2,IF,+,8,* \
	     AREA:agginput#00cc00:Input Aggregate \
	     LINE1:aggoutput#0000FF:Output Aggregate

       These two CDEFs are built from several functions. It helps to split them when viewing what
       they do. Starting with the first CDEF we would get:

	idat1,UN --> a
	0	 --> b
	idat1	 --> c
	if (a) then (b) else (c)

       The result is therefore "0" if it is true that "idat1" equals "UN".  If not, the original
       value of "idat1" is put back on the stack.  Lets call this answer "d". The process is
       repeated for the next five items on the stack, it is done the same and will return answer
       "h". The resulting stack is therefore "d,h".  The expression has been simplified to
       "d,h,+,8,*" and it will now be easy to see that we add "d" and "h", and multiply the
       result with eight.

       The end result is that we have added "idat1" and "idat2" and in the process we effectively
       ignored unknown values. The result is multiplied by eight, most likely to convert bytes/s
       to bits/s.

   Infinity demo
	  rrdtool graph example.png --title="INF demo" \
	     DEF:val1=some.rrd:ds0:AVERAGE \
	     DEF:val2=some.rrd:ds1:AVERAGE \
	     DEF:val3=some.rrd:ds2:AVERAGE \
	     DEF:val4=other.rrd:ds0:AVERAGE \
	     CDEF:background=val4,POP,TIME,7200,%,3600,LE,INF,UNKN,IF \
	     CDEF:wipeout=val1,val2,val3,val4,+,+,+,UN,INF,UNKN,IF \
	     AREA:background#F0F0F0 \
	     AREA:val1#0000FF:Value1 \
	     STACK:val2#00C000:Value2 \
	     STACK:val3#FFFF00:Value3 \
	     STACK:val4#FFC000:Value4 \
	     AREA:whipeout#FF0000:Unknown

       This demo demonstrates two ways to use infinity. It is a bit tricky to see what happens in
       the "background" CDEF.

	  "val4,POP,TIME,7200,%,3600,LE,INF,UNKN,IF"

       This RPN takes the value of "val4" as input and then immediately removes it from the stack
       using "POP". The stack is now empty but as a side effect we now know the time that this
       sample was taken.  This time is put on the stack by the "TIME" function.

       "TIME,7200,%" takes the modulo of time and 7'200 (which is two hours).  The resulting
       value on the stack will be a number in the range from 0 to 7199.

       For people who don't know the modulo function: it is the remainder after an integer
       division. If you divide 16 by 3, the answer would be 5 and the remainder would be 1. So,
       "16,3,%" returns 1.

       We have the result of "TIME,7200,%" on the stack, lets call this "a". The start of the RPN
       has become "a,3600,LE" and this checks if "a" is less or equal than "3600". It is true
       half of the time.  We now have to process the rest of the RPN and this is only a simple
       "IF" function that returns either "INF" or "UNKN" depending on the time. This is returned
       to variable "background".

       The second CDEF has been discussed earlier in this document so we won't do that here.

       Now you can draw the different layers. Start with the background that is either unknown
       (nothing to see) or infinite (the whole positive part of the graph gets filled).

       Next you draw the data on top of this background, it will overlay the background. Suppose
       one of val1..val4 would be unknown, in that case you end up with only three bars stacked
       on top of each other.  You don't want to see this because the data is only valid when all
       four variables are valid. This is why you use the second CDEF, it will overlay the data
       with an AREA so the data cannot be seen anymore.

       If your data can also have negative values you also need to overwrite the other half of
       your graph. This can be done in a relatively simple way: what you need is the "wipeout"
       variable and place a negative sign before it:  "CDEF:wipeout2=wipeout,-1,*"

   Filtering data
       You may do some complex data filtering:

	 MEDIAN FILTER: filters shot noise

	   DEF:var=database.rrd:traffic:AVERAGE
	   CDEF:prev1=PREV(var)
	   CDEF:prev2=PREV(prev1)
	   CDEF:prev3=PREV(prev2)
	   CDEF:median=prev1,prev2,prev3,+,+,3,/
	   LINE3:median#000077:filtered
	   LINE1:prev2#007700:'raw data'

	 DERIVATE:

	   DEF:var=database.rrd:traffic:AVERAGE
	   CDEF:prev1=PREV(var)
	   CDEF:time=var,POP,TIME
	   CDEF:prevtime=PREV(time)
	   CDEF:derivate=var,prev1,-,time,prevtime,-,/
	   LINE3:derivate#000077:derivate
	   LINE1:var#007700:'raw data'

Out of ideas for now
       This document was created from questions asked by either myself or by other people on the
       RRDtool mailing list. Please let me know if you find errors in it or if you have trouble
       understanding it. If you think there should be an addition, mail me:
       <alex@vandenbogaerdt.nl>

       Remember: No feedback equals no changes!

SEE ALSO
       The RRDtool manpages

AUTHOR
       Alex van den Bogaerdt <alex@vandenbogaerdt.nl>

1.4.8					    2013-05-23				  CDEFTUTORIAL(1)
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