Reverse Polish Notation

This is a very easy to program way of entering mathematical expressions into a computer. It comes under other names, too. PostScript is built on this concept.

A complicated function is built of a series of instructions. An instruction can be either

• data, e.g., a number or a parameter. Then it is placed onto the execution stack.
• an operator. The computer takes as many data off the stack as the operator needs, performs the required operation, and places the result onto the stack.

This is all! Now you only have to know that within Grafix the function argument is always called x, and the parameters p0, ..., p19.

• multiply a value by 1000:   x,1000.0,*
• convert degrees Fahrenheit to degrees Celsius:   x,32,-,5,*,9,/
• calculate an exponential, exp(-a x):   x,p0,*,neg,exp
  Here we use a parameter, p0, to hold the value of the coefficient a. Parameters are set with the parameters tag pair.

Note that the operators +, -, *, /, ^ (raising to a power) require 2 operands, whereas neg (change sign), inv (take reciprocal) and all algebraic functions like exp, ln, abs, sin, ... require only 1 operand.