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 elements from the stack as needed. Pushing is done
implicitly, so whenever you specify a number or a variable, it gets
pushed onto the stack automatically.
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 processed 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 operator 
+. 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, NEPop two elements from the stack, compare them for the selected condition
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 respectively
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, 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, MAXPops 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 operation 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 +, -, *, /, %Add, subtract, multiply, divide, modulo
SIN, COS, LOG, EXP, SQRT
Sine and cosine (input in radians), log and exp (natural logarithm),
square root.
ATAN
Arctangent (output in radians).
ATAN2
Arctangent of y,x components (output in radians).
This pops one element from the stack, the x (cosine) component, and then
a second, which is the y (sine) component.
It then pushes the arctangent of their ratio, resolving the ambiguity between
quadrants.
Example: CDEF:angle=Y,X,ATAN2,RAD2DEG will convert X,Ycomponents into an angle in degrees.
FLOOR, CEIL
Round down or up to the nearest integer.
DEG2RAD, RAD2DEG
Convert angle in degrees to radians, or radians to degrees.
Set Operations SORT, REVPop 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.
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 UNKNPushes 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 cannot 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 supports
it, and pushes the result on the stack.  There is an elaborate example
in the examples section below on how to use this.
Processing the stack directly DUP, POP, EXCDuplicate 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
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
PERCENT 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
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 approximation.
Example: VDEF:slope=mydata,LSLSLOPE
SEE ALSO 
././rrdgraph.htmlthe rrdgraph manpage  gives an overview of how rrdtool graph works.
././rrdgraph_data.htmlthe rrdgraph_data manpage  describes DEF,CDEF and VDEF in detail.
././rrdgraph_rpn.htmlthe rrdgraph_rpn manpage  describes the RPN language used in the ?DEF statements.
././rrdgraph_graph.htmlthe rrdgraph_graph manpage  page describes all of the graph and print functions.
Make sure to read ././rrdgraph_examples.htmlthe rrdgraph_examples manpage  for tips&tricks.
AUTHOR 
Program by Tobias Oetiker < mailto:oetiker@ee.ethz.choetiker@ee.ethz.ch >
This manual page by Alex van den Bogaerdt < mailto:alex@ergens.op.het.netalex@ergens.op.het.net >
