The C IF Statement More important details More

Introduction • We have several topics we need to master: – Boolean variables and

Boolean Variables • Recall that bool is a reserved word • It indicates a

Comparisons Again • Comparison operators are not boolean operators • Recall that an integer

Boolean Operators • Boolean operators are the AND, OR and NOT • C operators:

C Operator Truth Table P Q P && Q P || Q !P true

Boolean Comparisons • A sure sign of a novice is to compare a boolean

Comparing Real Values • The whole issue of roundoff makes comparisons of real numbers

Why not? • Our normal understanding is that they should be equal and the

You Get Lucky • This kind of comparison is chancy but aided by the

So what do we do? • We never compare floats or doubles for equality

Real Comparisons • Suppose that we want to compare two doubles a and b

Alternative Names • The C++ 2011 standard allows for some alternatives to some of

Precedence Again • • • ++ -- (postfix) ++ -- (prefix) + - (unary)

Booleans Revisited • For about 20 years C did not have a type bool

The C Boolean Convention • • Any type could function as a boolean If

Examples • Given int a = 2, b = 0, c = -5; if(a)

The tricky one • The reason this works: if (a = b) • The

Compilers • The: if(a = b)… is legal and actually good C/C++ • It

What do comparison operators do • Whenever a comparison is done a 0/1 is

The Real Tricky One • Suppose that int a = 5, b= 4, c=9;

Evaluation of the condition • There are states in the truth table where we

Short Circuit Evaluation • The compiler knows this • When ever it knows what

Impact • Not evaluating the second half of a condition usually does not matter

A Problem • Suppose I have a truly ugly condition: if(a+2>5 && b-3<c*2) •

Reversing Conditions • Sometimes we have difficulty with these types of conditions • A

Negation • One possibility is negating the entire expression • Introduce one more pair

Empty statement • An empty statement is just a semicolon • It says “do

De. Morgan’s Laws • Any And may be reversed by negating the conditions and

De. Morgan’s Solution • Applying this we can solve the problem of the previous

Readability • The compiler ignores white space! • People do not ignore white space!

Example of Readability Use: if(a>b){ x = a*b; y += 5; } cin >>

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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 Copyright © 2004 -2017 Curt Hill

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 Copyright © 2004 -2017 Curt Hill

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 Copyright © 2004 -2017 Curt Hill

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 Copyright © 2004 -2017 Curt Hill

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) Copyright © 2004 -2017 Curt Hill

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! Copyright © 2004 -2017 Curt Hill

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 == 0. 9999) • Where there are 7 -14 9 digits Copyright © 2004 -2017 Curt Hill

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 Copyright © 2004 -2017 Curt Hill

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 Copyright © 2004 -2017 Curt Hill

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) < 0. 00001) • This is true only if the difference between the two is less than 1 E-5 • The 0. 00001 is the fuzz factor – Needs to be larger than the expected round -off error, but smaller than actual differences Copyright © 2004 -2017 Curt Hill

Alternative Names • The C++ 2011 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 Copyright © 2004 -2017 Curt Hill

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 Copyright © 2004 -2017 Curt Hill

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 Copyright © 2004 -2017 Curt Hill

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 = Copyright © 2004 -2017 Curt Hill

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 Copyright © 2004 -2017 Curt Hill

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 Copyright © 2004 -2017 Curt Hill

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) Copyright © 2004 -2017 Curt Hill

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 Copyright © 2004 -2017 Curt Hill

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 Copyright © 2004 -2017 Curt Hill

Impact • Not evaluating the second half of a condition usually does not matter • Usually but not always • Consider: if(a>b && ++c < d) – When the a>b is false there is no reason to do anything with the secondition – Thus the c variable is not incremented – Some function calls may have side effects as well Copyright © 2004 -2017 Curt Hill

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 Copyright © 2004 -2017 Curt Hill

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 – De. Morgan’s Law Copyright © 2004 -2017 Curt Hill

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)) {…} Copyright © 2004 -2017 Curt Hill

De. Morgan’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 Copyright © 2004 -2017 Curt Hill

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 Copyright © 2004 -2017 Curt Hill

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; . . . Copyright © 2004 -2017 Curt Hill