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 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.
Pop 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)
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 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.
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,Y
components 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.
ABS
Take the absolute value.
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)
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 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.
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.
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.
Example: VDEF:avg=mydata,AVERAGE
Example: VDEF:first=mydata,FIRST
Example: VDEF:total=mydata,TOTAL
Example: VDEF:perc95=mydata,95,PERCENT
Example: VDEF:slope=mydata,LSLSLOPE
the rrdgraph manpage gives an overview of how rrdtool graph works. the rrdgraph_data manpage describes DEF,CDEF and VDEF in detail. the rrdgraph_rpn manpage describes the RPN language used in the ?DEF statements. the rrdgraph_graph manpage page describes all of the graph and print functions.
Make sure to read the rrdgraph_examples manpage for tips&tricks.
Program by Tobias Oetiker <tobi@oetiker.ch>
This manual page by Alex van den Bogaerdt <alex@ergens.op.het.net>