Page 216 - Introduction to Microcontrollers Architecture, Programming, and Interfacing of The Motorola 68HC12

7,3 From Formulas to Subroutine Calls 193

Figure 7.11. Stack Movement when Evaluating (8)

PUSH X
PUSH K2
PUSH Y
BSR FPMUL
BSR FPADD
PUSH U (10)
BSR SIN
PUSH W
BSR FPADD
BSR FPDIV
PULL Z
How does one write a program segment to evaluate formula or expression (8)? The
method comes from the work of the Polish logician Jan Lucasiewicz, who investigated
ways of writing expressions without using parentheses. With his technique, referred to as
Polish notation, one would write (8) as

Notice that when reading (11) from left to right, each variable name generates a PUSH in
(10) and each operation generates a subroutine call. Going between (10) and (11) is easy.
We soon show a simple algorithm to write a segment for any expression.
The way to display a formula by parsing it into its basic operations uses a binary
tree as we will use again in §10.4. Moreover, the technique to write a program segment