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## DESCRIPTION

```       This tutorial should help you get to grips with rrdtool
RPN expressions as seen in CDEF arguments of rrdtool
graph.

```

```       The LT, LE, GT, GE and EQ RPN logic operators are not as
tricky as they appear.  These operators act on the two
values on the stack preceding them (to the left).  Read
these two values on the stack from left to right inserting
the operator in the middle.  If the resulting statement is
true, the replace the three values from the stack with
"1".  If the statement if false, replace the three values
with "0".

For example think about "2,1,GT".  This RPN expression
could be read as "is two greater than one?"  The answer to
that question is "true".  So the three values should be
replaced with "1".  Thus the RPN expression 2,1,GT evalu­
ates to 1.

Now also consider "2,1,LE".  This RPN expression could be
read as "is two less than or equal to one?".   The natural
response is "no" and thus the RPN expression 2,1,LE evalu­
ates to 0.

```

```       The IF RPN logic operator can be straightforward also.
The key to reading IF operators is to understand that the
condition part of the traditional "if X than Y else Z"
notation has *already* been evaluated.  So the IF operator
acts on only one value on the stack: the third value to
the left of the IF value.  The second value to the left of
the IF corresponds to the true ("Y") branch.  And the
first value to the left of the IF corresponds to the false
("Z") branch.  Read the RPN expression "X,Y,Z,IF" from
left to right like so: "if X then Y else Z".

For example, consider "1,10,100,IF".  It looks bizzare to
me.  But when I read "if 1 then 10 else 100" it's crystal
clear: 1 is true so the answer is 10.  Note that only zero
is false; all other values are true.  "2,20,200,IF" ("if 2
then 20 else 200") evaluates to 20.  And "0,1,2,IF" ("if 0
then 1 else 2) evaluates to 2.

Notice that none of the above examples really simulate the
whole "if X then Y else Z" statement.  This is because
computer programmers read this statement as "if Some Con­
dition then Y else Z".  So it's important to be able to
read IF operators along with the LT, LE, GT, GE and EQ
operators.
sake, it's useful to write this set of operations as:

1) 1,2,3,+,+    eval is 2,3,+ = 5    result is 1,5,+
2) 1,5,+        eval is 1,5,+ = 6    result is 6
3) 6

Let's use that notation to conviently solve some complex
RPN expressions with multiple logic operators:

1) 20,10,GT,10,20,IF  eval is 20,10,GT = 1     result is 1,10,20,IF

read the eval as pop "20 is greater than 10" so push 1

2) 1,10,20,IF         eval is 1,10,20,IF = 10  result is 10

read pop "if 1 then 10 else 20" so push 10.  Only 10 is
left so 10 is the answer.

Let's read a complex RPN expression that also has the tra­
ditional multiplication operator:

1) 128,8,*,7000,GT,7000,128,8,*,IF  eval 128,8,*       result is 1024
2) 1024,7000,GT,7000,128,8,*,IF     eval 1024,7000,GT  result is 0
3) 0,128,8,*,IF                     eval 128,8,*       result is 1024
4) 0,7000,1024,IF                                      result is 1024

Now let's go back to the first example of multiple logic
operators but replace the value 20 with the variable
"input":

1) input,10,GT,10,input,IF  eval is input,10,GT  result is A

Read eval as "if input > 10 then true" and replace
"input,10,GT" with "A:

2) A,10,input,IF            eval is A,10,input,IF

read "if A then 10 else input".  Now replace A it's ver­
bose description and--voila!--you have a easily readable
description of the expression:

if input > 10 then 10 else input

Lastly, let's to back the first most complex example and
replace the value 128 with "input":

1) input,8,*,7000,GT,7000,input,8,*,IF  eval input,8,*     result is A

where A is "input * 8"

2) A,7000,GT,7000,input,8,*,IF          eval is A,7000,GT  result is B

Exercise 1:

Compute "3,2,*,1,+ and "3,2,1,+,*" by hand.  Rewrite them
in traditional notation.  Explain why they have different

3*2+1 = 7 and 3*(2+1) = 9.  These expressions have
different answers because the altering of the plus and
times operators alter the order of their evaluation.

Exercise 2:

One may be tempted to shorten the expression

input,8,*,56000,GT,56000,input,*,8,IF

by removing the redundant use of "input,8,*" like so:

input,56000,GT,56000,input,IF,8,*

Use tradition notation to show these expressions are not
the same.  Write an expression that's equivalent to the
first expression but uses the LE and DIV operators.

if (input <= 56000/8 ) { input*8 } else { 56000 }
input,56000,8,DIV,LT,input,8,*,56000,IF

Exercise 3:

Briefly explain why traditional mathematic notation
requires the use of parentheses.  Explain why RPN notation
does not require the use of parentheses.

Traditional mathematic expressions are evaluated by
doing multiplication and division first, then addition and
subtraction.  Perentences are used to force the evaluation of
addition before multiplication (etc).  RPN does not require
parentheses because the ordering of objects on the stack
can force the evaluation of addition before multiplication.

Exercise 4:

Explain why it is desirable for the RRDtool developers to
notation.

```

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