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How equations are evaluated:
Calculations are performed from left-to-right until the end of the equation is reached. As the equation is parsed, each
token's value is pushed onto a stack until an operator is found. When an operator is found, the previous 2 values are
popped from the stack and are used to perform the operation (the first item popped is the SECOND operand). The
result of the operation is then pushed onto the stack. This repeats until the end of the equation is reached. An
equation is valid only if there is exactly ONE item left in the stack when the end of the equation is reached.
Example of how an equation is evaluated:
Equation: a8 a5 a6 + * a4 -
Input Operation Stack Comment
a8 Push value a8
a5 Push value a5
a8
a6 Push value a6
a5
a8
+ Add (a5+a6)
a8
Pop a6 and a5, add them, push result to stack
* Multiply a8*(a5+a6) Pop (a5+a6) and a8, multiply them, push result to stack
a4 Push value a4
a8*(a5+a6)
- Subtract a8*(a5+a6) - a4 Pop a4 and a8*(a5+a6), subtract them, push result to stack
In this example, after the subtraction there is only ONE item left in the stack (which is the result of all of the
previous computations), mak ing this a valid equation.
Equation: d1 d2 + d3 * r1 =
Input Operation Stack Comment
d1 Push value d1
d2 Push value d2
d1
+ OR (d1+d2) Pop d1 and d2, OR them, push result to stack
d3 Push value d3
(d1+d2)
* AND (d1+d2)*d3 Pop (d1+d2) and d3, AND them, push result to stack
r1 Push value r1
(d1+d2)*d3
= Assign Value r1=(d1+d2)*d3 Pop (d1+d2)*d3 and r1and assign value to r1
In this example, after the assignment, there is only ONE item left in the stack (which is the result of all of the
previous computations), mak ing this a valid equation.