Logic Operations

Optimizing logic is more of a speed issue than a size issue. Logic takes time for the calculator to interpret and thus requires optimization to be fast.

Because the calculator treats every nonzero value as true and zero as false, you don't need a comparison if a variable's value is nonzero. Instead, you can just put the variable by itself.

```
:If C≠0
can be
:If C
```

Instead of comparing a variable to zero, use the not( logical operator. Because not( returns the opposite value of the variable, true will become false and false will become true.

```
:While A=0
can be
:While not(A
```

When making expressions that combine the and and or operators where the and operator comes first, you don't need to include parentheses around the and operator. The and operator has a higher precedence than or, so it is evaluated first. This can become complicated with complex expressions, so you might want to leave some of the parentheses for clarity.

```
:If (A=1 and B=2) or (A=2 and B=1)
can be
:If A=1 and B=2 or A=2 and B=1
```

If you are comparing two unary expressions (expressions with no comparison operator) with the and operator, you don't need the and operator. For and to be true, both values must be nonzero. So, multiplying them will produce the same effect because if either one of the values is zero, the product of both values will also be zero.

```
:If A and B
can be
:If AB
```

A similar technique can be applied to expressions with comparison operators, except some restrictions are required.

With unary expressions, to test if A and B is true you multiply them. With equations, you can multiply the left sides of each together and you can do the same for the right sides. However, a value being 0 could return a different result than anticipated, so it is best to use this technique when the values are not 0. Also, this technique does not work when there are multiple values of A and C that multiply to get B times D. For instance, if A equals four, C equals 12, B equals six, and D equals eight, then this optimization will not work because A and B are not equal but A*C equals B*D.

```
:If A=B and C=D
can sometimes be
:If AC=BD
```

As and is similar to multiplying, the or operator is similar to addition. Adding two values together yields a non-zero result if one of the conditions is true. When you are comparing equations using the or operator, you can add the two together (This is usually not used for unary expressions because the plus and or symbols are both one-byte tokens). For this, the only restriction is that all values must have the same sign (or be 0), or you can circumvent this by using abs(. This is necessary because if two variables have the same value except one is negative, this expression could return false.

```
:If A=B or C=D
can sometimes be
:If A+C=B+D
```

The most unused logical operator is xor (exclusive or). The xor operator is useful when comparing two expressions and checking if one but not both are true. In fact, xor is specifically designed for this purpose.

```
:If A=2 and B≠2 or A≠2 and B=2
can be
:If A=2 xor B=2
```

Many times a compound expression can be shortened by combining expressions that have the same meaning or replacing expressions that can be written another way. Think about what the expression means and then think about how to make a shorter equivalent expression. There are many ways of writing an expression, so there are usually ways to rewrite it.

```
:If A>B or A<B
can be
:If A≠B
```

If you have the not( operator around an expression, you can usually change the logical operator to the math opposite. This allows you to remove the not( operator.

```
:If not(B=C and A=D
can be
:If B≠C or A≠D
```

DeMorgan's Law can be used for expressions in which the not( operator is around two separate unary expressions joined by the and or or operators. It allows you to remove the second not( operator and then change the and to or and vice versa.

```
:If not(A) and not(B
can be
:If not(A or B
```

Min( is useful when you are comparing one variable or value to several other variables to see if they are all equal to the variable or value. To use min you just create an expression with the min function and put the common variable or value inside it followed by an equal sign and a left curly brace. You then list out the variables that you are comparing the variable or value to, separating each one with a comma.

```
:If A=10 and B=10 and C=10
can be
:If min(10={A,B,C
```

Max( is useful when you are comparing one variable or value to several other variables to see if at least one is equal to the variable or value. You do the same thing as the min function, just replacing min with max.

```
:If A=10 or B=10 or C=10
can be
:If max(10={A,B,C
```

You can put a comparison operator inside the min or max functions to compare when several values or variables are equal to one variable and several values or variables are equal to another variable. This works especially well with three or more variables.

```
:If A=X and B=U or A=Y and B=V
can be
:If max(A={X,Y} and B={U,V
```

Abs( is useful when you are comparing a variable to two even or odd values using the or operator. You subtract the smaller value from the larger value, divide the result by two, and then put it on the left side of the equal sign. Next, you subtract the number on the left of the equal sign from the larger value, and then subtract that from the variable being tested inside the abs( command. Lastly, you place the resulting equation on the right of the equal sign.

In other words:

```
:If A=45 or A=105
can be
:If 30=abs(A-75
```

X=n1 or X=n2 should become abs(n1-mean({n1,n2}))=abs(X-mean({n1,n2})) (simplified) if n1 and n2 are positive integers and n1+n2 is even. If there are three terms, then see if you can simplify two of them according to this rule. If you can't, then a string of or's will be faster than the max(X={n1,n2,… approach. If there are four terms or more, then use max().

<< Math Operations |
Table of Contents |
Conditionals >> |