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.
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, NE
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)
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 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,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.
Set Operations
SORT, REV
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.
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
UNKN
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.
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, EXC
Duplicate the top element, remove the top element, exchange the two
top elements.
VARIABLES
These operators work only on
VDEF
statements.
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.
Inf
inite 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
SEE ALSO
././rrdgraph.html
the rrdgraph manpage
gives an overview of how
rrdtool graph
works.
././rrdgraph_data.html
the rrdgraph_data manpage
describes
DEF
,
CDEF
and
VDEF
in detail.
././rrdgraph_rpn.html
the rrdgraph_rpn manpage
describes the
RPN
language used in the
?DEF
statements.
././rrdgraph_graph.html
the rrdgraph_graph manpage
page describes all of the graph and print functions.
Make sure to read
././rrdgraph_examples.html
the rrdgraph_examples manpage
for tips&tricks.
AUTHOR
Program by Tobias Oetiker <
mailto:oetiker@ee.ethz.ch
oetiker@ee.ethz.ch
>
This manual page by Alex van den Bogaerdt <
mailto:alex@ergens.op.het.net
alex@ergens.op.het.net
>
