1. More important details More fun Part 3
The C++ IF Statement
More important details More fun Part 3
Copyright © Curt Hill

2. Introduction We have several topics we need to master:
Boolean variables and operators
Danger of comparing real numbers
Alternative symbols
Boolean convention
Reversing a Boolean expression
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3. Boolean Variables Recall that bool is a reserved word
It indicates a type that may only have two values: true, false
true and false are constant values
Use whenever only two values are possible: bool ismanager, isfemale, ismember;
Variables of type boolean often start with the word is, because it indicates type
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4. Comparisons Again Comparison operators are not boolean operators
Recall that an integer operator like % takes two integers and produces an integer
A comparison may compare two integers and produce a boolean
A boolean operator does a logical operation on two booleans
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5. Boolean Operators Boolean operators are the AND, OR and NOT
C operators:
&& || !
The single & and | are bit string operators not booleans
AND, OR, and NOT have the same meaning as is commonly used in English
AND/OR have lower precedence than comparisons
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6. C Operator Truth Table P Q P && Q P || Q !P true false
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7. Boolean Comparisons
A sure sign of a novice is to compare a boolean with a truth value: bool b; if(b == true) // or if(b == false) // or if(b != true)
A boolean is already suitable for comparison
Use one of these two: if(b) // or if(!b)
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8. Comparing Real Values
The whole issue of roundoff makes comparisons of real numbers problematic
Consider the following: double d = 1.0, e = 10.0; double f = d/e; … if(f*10 == d) …
On many machines this condition can never be true!
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9. Why not?
Our normal understanding is that they should be equal and the comparison true
We usually think algebraically, that is with infinite precision
The decimal 0.1 is a repeating fraction in binary
It cannot be represented in a finite number of digits
The comparison then becomes something like this: if(1 == )
Where there are digits
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10. You Get Lucky
This kind of comparison is chancy but aided by the ways a Pentium and its successors do arithmetic
These machines always use one more digit of arithmetic
The default mode is to then round that into the right size
That rounding bails us out in certain cases
If roundoff errors get too large even this will not help
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11. So what do we do?
We never compare floats or doubles for equality or inequality!
In general, equality is never true when we want it to be and inequality is always true
We have to be satisfied that the two values are close, even if they are not quite equal
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12. Real Comparisons
Suppose that we want to compare two doubles a and b for equality
Round-off error makes them close but not equal, so use: if(abs(a-b) < )
This is true only if the difference between the two is less than 1E-5
The is the fuzz factor
Needs to be larger than the expected round-off error, but smaller than actual differences
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13. Alternative Names
The C standard allows for some alternatives to some of the symbols
Allows a symbol to have a reserved word:
not for !
not_eq for !=
and for &&
or for ||
Among others
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14. Precedence Again ++ -- (postfix) ++ -- (prefix) + - (unary) casts !
* / %
+ -
< > >= <=
== !=
&& ||
= *= += -= /= %=
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15. Booleans Revisited For about 20 years C did not have a type bool
It had the if, it had comparisons and it even had boolean operators
So what did it do?
It had a convention
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16. The C Boolean Convention
Any type could function as a boolean
If the value was zero it meant false
If the value was not zero it meant true
Thus a character, integer, float could pass for a bool
C++ has maintained this
Java did not
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17. Examples
Given int a = 2, b = 0, c = -5; if(a) // true … if(b) // false … if(c) // true …
All these work and do not generate syntax errors
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18. The tricky one The reason this works: if (a = b)
The value assigned to a is returned as the result
This will be interpreted as false if zero and true otherwise
Allows us to both assign and drive an if at the same time
However, it is usually a mistake, a left out =
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19. Compilers The: if(a = b)… is legal and actually good C/C++
It allows a common mistake
Some compilers give a warning
Like all warnings it may be ignored
Others do not
We should check ours
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20. What do comparison operators do
Whenever a comparison is done a 0/1 is always produced
This is usually cast as a bool but not always int a = b>5; will produce 0 or 1 in a
But no error
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21. The Real Tricky One Suppose that int a = 5, b= 4, c=9;
The comparison: if(a<b<c) will be true
Why?
5<4 => 0 // false
0<9 => 1 // true
Always use (a<b && b<c)
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22. Evaluation of the condition
There are states in the truth table where we do not care about the second operand
TRUE OR TRUE is the same as TRUE OR FALSE
The second operand does not matter
TRUE OR ? is TRUE
Similarly FALSE AND ? is FALSE
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23. Short Circuit Evaluation
The compiler knows this
When ever it knows what the answer will be it stops evaluating
Example: if(a!=0 && b/a>12) should always work
When a == 0 then the compiler knows that FALSE AND ? is FALSE so does not need to evaluate the b/a>12
Avoids the zero division exception
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24. A Problem
Suppose I have a truly ugly condition: if(a+2>5 && b-3<c*2)
I want to do nothing if this is true and several things in a compound statement if it is false
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25. Reversing Conditions
Sometimes we have difficulty with these types of conditions
A complicated condition may be difficult to reverse
There are three solutions:
Negation
Do nothing then
DeMorgan’s Law
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26. Negation One possibility is negating the entire expression
Introduce one more pair of parentheses and insert the negation operator !
Try this: if(!(a+2>5 && b-3<c*2)) {…}
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27. Empty statement An empty statement is just a semicolon
It says “do nothing”
Try this: if(a+2>5 && b-3<c*2) ; // The empty stmt else {…}
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28. DeMorgan’s Laws
Any And may be reversed by negating the conditions and reversing the And to an OR
!(a>b && c<=d) becomes a<=b || c>d
Any Or may be reversed by negating the conditions and reversing the Or to an And
!(a==b || c>=d) becomes a!=b && c<d
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29. DeMorgan’s Solution
Applying this we can solve the problem of the previous if: if(a+2>5 && b-3<c*2)
Try this instead: if(a+2<=5 || b-3>=c*2) {…}
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30. Readability The compiler ignores white space!
People do not ignore white space!
Use indentation to improve the readability of your programs
Indent the statements controlled by an If or any other flow of control statement
The change in left margin is a powerful visual clue to the reader
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31. Example of Readability
Use: if(a>b){ x = a*b; y += 5; }
cin >> s;
Do not: if(a>b){ x = a*b; y += 5;}
cin >> s;
Use: if(a==c){ x = a*b; y += 5;
... else { y *= 2;
Do not: if(a==c){ x = a*b; y += 5;
... else { y *= 2; . . .
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