4. Functions - TUM · Functions 1Call-by-reference vs. Call-by-valueconst ModiﬁerFunctions...

Functions 1 Call-by-reference vs. Call-by-value const Modifier Functions 2 Recursion

4. Functions

March 10, 2010

4. Functions

Einfuhrung in die Programmierung—Introduction to C/C++, Tobias Weinzierl page 1 of 40

http://www5.in.tum.de/wiki/index.php/Dr._rer._nat._Tobias_Weinzierl


Outline

• Recapitulation

• Functions Part 1—What is aProcedure?

• Call-by-value and Call-by-reference

• Functions Part 2—The Details

• Recursion

• An Example: gcd (greatest commondivisor)

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Recapitulation

• What is the difference between = and ==?

• What is a strict boolean expression?

• Why should an if-statement always be followed by a {?

• What is a scope?

• What is the meaning of a while-loop?

• What does a while-loop look like?

• Can we modify a parameter within a while-loop?

• What happens if a single integer is argument/guard of a while-loop?

• What is dangerous if we declare two integer variables in one row:

i n t a , b=10;

• What is the difference of the compiler and the linker?

• What is the difference of a declaration and the definition?

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—4.1. Functions 1—

What do these two sayings have in common?

Common saying: Good things come in small packages.

Common saying: Never reinvent the wheel.

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Code Dublication

i n t main ( ) {double pr iceOfMouta inBike = 1200.0;double exchangeRateJanuary = 1.4272; / / Januarydouble exchangeRateFebruary = 1.3686; / / Februarydouble exchangeRateMarch = 1 ,3569; / / March/∗∗ We always have to pay 60% of t o t a l cost∗ t h i s month .∗ /

double f i r s tPayment = 0 .60 ;double t o t a l C o s t ;

t o t a l C o s t = ( f i r s tPayment∗pr iceOfMouta inBike )∗exchangeRateJanuary+ ( (1 .0+ f i r s tPayment )∗ pr iceOfMouta inBike )∗ exchangeRateFebruary ;

s td : : cout << ” p r i ce o f January : ” << t o t a l C o s t << std : : endl ;

t o t a l C o s t = ( f i r s tPayment∗pr iceOfMouta inBike )∗ exchangeRateFebruary+ ( (1 .0+ f i r s tPayment )∗ pr iceOfMouta inBike )∗ exchangeRateMarch ;

s td : : cout << ” p r i ce o f February : ” << t o t a l C o s t << s td : : endl ;}

There is two bugs in this code!

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Code Dublication

• Duplicated code is difficult to maintain, to fix, and to extend.

vo id main ( ) {code pa r t Acode pa r t A

}

• Long code is difficult to read and to understand (Spaghetti code).

vo id main ( ) {code doing one th i ngcode doing something d i f f e r e n t

}

• Duplicated code is a loss of development time.

vo id main ( ) {code implementing Gauss quadrature

}

vo id main ( ) {another implementing Gauss quadrature

}

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Functions

vo id compute (double pr ice , double f i rs tPayment , double rateA , double rateB

) {double t o t a l C o s t =

( f i r s tPayment∗p r i ce )∗ rateA+ ((1.0− f i r s tPayment )∗ p r i ce ) ∗ rateB ;

s td : : cout << t o t a l C o s t << s td : : endl ;}

i n t main ( ) {double p r i ce = 1200.0;double january = 1.4272; / / Januarydouble february = 1.3686; / / Februarydouble march = 1 ,3569; / / Marchdouble f i r s tPayment = 0 .60 ;

s td : : cout << ” January : ” ;compute (

pr ice , f i rs tPayment , january , feb ruary) ;s td : : cout << ” February : ” ;compute (

pr ice , f i rs tPayment , february , march) ;

}4. Functions




vo id foo ( i n t a ) {a += 20;s td : : cout << a ;

}

. . .foo ( 3 9 ) ;i n t b=20;foo ( b ) ;foo ( b+10) ;

• C/C++ mechanism: Function or procedure.

• A function is a helper/assistant of the whole program.

i n t a0 = 39; / / foo (39)a0 += 20;s td : : cout << a0 ;i n t b=20;i n t a1 = b ; / / foo ( b )a1 += 20;s td : : cout << a1 ;i n t a2 = b+10; / / foo ( b+10). . .

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Functions and Scopes

vo id foo ( i n t a ) {a += 20;s td : : cout << a ;b += 1;

}

vo id bar ( i n t b ) {foo ( b ) ;foo ( b+10) ;foo ( b+20) ;

}

What happens here?

• Functions define a scope due to the brackets { } (basis block).

• Variables of other scopes are not defined within the function.

• Code above consequently does not work.

4. Functions




Functions and Scopes


}


}

What happens here?• Functions define a scope due to the brackets { } (basis block).

• Variables of other scopes are not defined within the function.

• Code above consequently does not work.

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Global Variables

i n t b ;


}


}

• C/C++ allows programmer to define (global variables).

• Good practice: avoid them due to side effects.

• Now, code does work.

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Functions and the Program Counter

Memory

PC

21:22; foo1 // first operation of foo23; foo224; foo325; 26;27; foo() // call of foo28: foo()

void foo() { foo1; foo2; foo3; } ... foo(); // call foo foo();

• Function call modifies program counter.

• Computer remembers where to jump back.

• Function code is only stored once in memory.

• Not only the program counter is “remembered”, but all the variables.

4. Functions




The Call-Stack

vo id foo ( ) {i n t a = 20;/ / do something wi th a

/ / a now equals 50;}

vo id bar ( ) {i n t a = 30;foo ( ) ;

}

• Function call modifies program counter.

• Computer remembers where to jump back.

• Function code is only stored once in memory.

• Not only the program counter is “remembered”, but all the variables.

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The Return Statements

i n t increment ( i n t a ) {a = a+1;r e t u r n a ;

}

vo id bar ( ) {i n t a = 30;i n t b = increment ( a ) ;s td : : cout << b ;

}

• Functions can return a value due to the return command.

• Returned type has to equal the type of the function.

• If a function doesn’t return a value, the function’s type is void.

• Consequently, void is a new primitive datatype.

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What is the main Function?

i n t main ( ) {/ / do something

}

vo id bar ( ) {/ / do something

}

double foo ( ) {/ / do something

}

• Any program is a collection of functions. They have to have unique signatures(names).

• At startup, the computer has to know where to set the program counter to.

• It always sets it to the main function.

• The main function returns 0 if it has been successful (error code). This is a UNIXconvention.

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Functions—Some Best Practices

i n t main ( ) {/ / do something

}

vo id bar ( ) {/ / do something

}

double foo ( ) {/ / do something

}

• One purpose, one function. Any function should concentrate solely on one job.

• One page, one function. With a less, one should be able to see the completefunction.

• A function without documentation does not exist.

• Functions should have meaningful names (verbs).

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—4.2. Call-by-reference vs. Call-by-value—

The Call-Stack and Variables

vo id foo ( ) {i n t a = 20;/ / do something wi th a

/ / a now equals 50;}

vo id bar ( ) {i n t a = 30;i n t b = 20;foo ( ) ;

}

• Computer encounters function call (foo()).• It stores away all variables and remembers where it has been called from.• It resets the program counter.• As soon as the function terminates, it jumps back to the place of invocation, and• it restores all variables.• This way, a function cannot modify an “outer” variable.

4. Functions




Call-by-value

vo id foo ( i n t x ) {/ / do something wi th x/ / x now equals 50;

}

vo id bar ( ) {i n t a = 30;i n t b = 20;foo ( a ) ;

}

• Computer encounters function call (foo()) with argument a.

• It stores away all variables and remembers where it has been called from.

• Furthermore, it creates a copy of a.

• It resets the program counter.

• . . .

• This way, a function cannot modify an “outer” variable.

4. Functions




Call-by-value

• In C/C++, parameters (arguments) are passed call-by-value.

• Functions work on copies of the original variables.

• The original variables are saved away on the call stack.

• As soon as the operation terminates, the old variable values are restored.

4. Functions




The Return Statement and Call-by-value

i n t foo ( i n t x ) {x = x∗2;r e t u r n x ;

}

vo id bar ( ) {i n t a = 30;i n t b = foo ( a ) ;

a = foo ( a ) ;}

The return statement takes the value of the function’s copy and writes it to the left-handside of the function invocation.

4. Functions




Call-by-reference

i n t foo ( i n t & x ) {x = x∗2;r e t u r n x ;

}


}

• The & operator is the reference operator.

• It tells C/C++ to pass the argument with call-by-reference semantics.

• Then, C/C++ does not create a copy, but the operation works on the originalvariable.

4. Functions




i n t foo ( i n t & x ) {x = x∗2;r e t u r n x ;

}


a = foo ( a ) ;}

• The & operator is the reference operator.

• It tells C/C++ to pass the argument with call-by-reference semantics.

• Then, C/C++ does not create a copy, but the operation works on the originalvariable.

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Exercise: Swap Two Variables

vo id main ( ) {i n t a = 3 ;i n t b = 4;/ / in terchange a and ba = b ;b = a ;s td : : cout << a << std : : endl ;s td : : cout << b << std : : endl ;

}

• Fix the code above.

• Extract the swap functionality in afunction of its own.

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Efficient Codes

• Copy-by-value is save as it forbids side-effects. Whenever possible, usecopy-by-value (default).

• Copy-by-reference is faster.

Question: Can we write fast and save code?

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Const References

vo id foo ( i n t a , i n t b ) {. . .

}

vo id bar ( i n t & a , i n t & b ) {. . .

}

vo id e f f i c i e n t F o o ( const i n t & a , const i n t & b ) {. . .

}

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—4.3. const Modifier—

—an Excursus

In C++, we can mark any argument to be a const argument, i.e. the function is notallowed to modify it.

vo id foo ( const i n t a ) {. . .

}

• const allows compiler to optimise code aggressively.

• const allows you to write bug-safe code (user cannot modify a variable byaccident).

• const closes the performance gap between C/C++ and Fortran.

4. Functions




Please, Use Const

• Remember the 80 : 20 rule—you never know the performance properties.

• Remember that it might help others and you to produce less bugs.

• Remeber the implications.

vo id foo ( i n t & a ) {. . .

}

vo id bar ( i n t a ) { / / t h i s f u n c t i o n i s very slow and has to be tunedfoo ( a ) ;/ / cont inue c a l c u l a t i o n s

}

. . .foo ( 1 0 ) ; / / t h i s does not work , ins tead we have to w r i t ei n t tmp = 10;foo ( tmp ) ;

We cannot optimise bar, as foo does not have a const signature.

The last example is an aritificial one, but we will encounter similar problems soon.

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—4.4. Functions 2—

The Signature of a Function

i n t foo ( )i n t bar ( )i n t foo ( i n t a )i n t foo ( double x )i n t foo ( i n t a , const double& b , double x )

A function is unique• due to its name, and

• due to the number of arguments, and

• due to the type of the arguments, and

• due to the const modifiers of its arguments, and

• due to a const modifier (not addressed yet).

Everything besides the name defines the signature. The name and the signature makethe function unique. The return value however does not come into play. Some definitionmake the const modifier not part of the signature.

4. Functions




Overloading

i n t foo ( )i n t foo ( i n t a ) {}i n t foo ( double a ) {}

. . .

foo ( ) ;foo ( 3 . 4 ) ;foo ( 4 ) ;

To overload a function means to offer it with different signatures. C/C++ thenautomatically tries to find the right signature. However, be aware of automatic typeconversions.

4. Functions




Automatic Type Conversion

i n t foo ( )i n t foo ( i n t a ) {}i n t foo ( double a ) {}

. . .

i n t a = 10;double b = a ;foo ( a ) ;foo ( b ) ;foo ( a / 3 . 0 ) ;

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Priority

i n t foo ( )i n t foo ( i n t a ) {}i n t foo ( double a ) {}i n t bar ( i n t a , i n t b ) {}i n t bar ( double a , double b ) {}. . .

i n t a = 10;double b = a ;foo ( a ) ;foo ( b ) ;foo ( a / 3 . 0 ) ;bar ( a , 3 ) ;bar ( b , 3 ) ;bar ( a , 3 . 0 ) ;

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Rules for Overloading

• If the arguments match exactly without type conversion, use this definition.

• If there is no exact match but a match due to automatic type conversion, C/C++uses this definition.

• If there’s a const and a non-const argument, C/C++ uses the const variant (not forall compilers).

Besides, the automatic type conversion, also take care of return type conversion:

double foo ( i n t a ) {r e t u r n a / 3 ;

}

. . .foo ( 4 . 0 ) ; / / we l l , t h i s does not workfoo ( 4 ) ;

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Default Arguments

vo id foo ( i n t a =3) ;vo id bar ( ) ;vo id bar ( i n t b =3) ; / / not al lowedvo id tee1 ( i n t c , double d = 2 . 0 ) ;vo id tee2 ( i n t c=2 , double d ) ; / / not al lowedvo id tee3 ( i n t c=2 , double d = 4 . 0 ) ;

. . .foo ( ) ;foo ( 7 ) ;tee3 ( ) ;tee1 ( 1 ) ;tee1 ( 1 , 4 . 0 ) ;

• C/C++ support default arguments.

• They may not interfere with overloaded functions.

• They may not be followed by arguments without default arguments.

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Return Statements

double foo ( double a , double h ) {i f ( h==0) {

r e t u r n 0 . 0 ;}i f ( a==0)

r e t u r n ; / / e r r o r/ / do something compl icated wi th a and hr e t u r n a ;

}

vo id foo ( double a , double h ) {. . .r e t u r n 1 ; / / e r r o r

}

• A return statements makes the application leave the current function.

• A return statement accepts one argument: the return value (if it is not a voidfunction).

• A return statement may be everywhere in the function. However, multiple returnstatements often are considered to be bad style.

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—4.5. Recursion—

A Simple Game

vo id foo (i n t l e f t , i n t r i g h t , i n t t

) {/ / value o f v a r i a b l e si n t b = l e f t + r i g h t ;/ / value o f v a r i a b l e sb /= 2 ;/ / value o f v a r i a b l e si f ( b<t ) {

foo ( b , r i g h t , t ) ;/ / value o f v a r i a b l e s

}i f ( b>t ) {

foo ( l e f t , b , t ) ;/ / value o f v a r i a b l e s

}}

. . .foo (−12 ,40 ,7);

4. Functions




Recursion—Principles

vo id foo1 ( i n t a ) {i f ( a==0) {

r e t u r n ;}. . .foo1 ( a−1);

}

• Functions may call themselves (recursion).• Each function call has its own copy of all the variables.• This may not terminate, so we have to be careful. So code a proper termination

criterion.• The underlying pattern often is referred to divide and conquer (which is not a

Roman saying!).• Recursion is a very powerful tool (matrix block algorithms, multiscale basis

systems, adaptive mesh refinement, e.g.)—a tool many programmers however donot understand.

4. Functions




Greatest Common Divisor

• Write a recursive function gcd(int a,

int b) which computes the greatestcommon divisor.

• Test it for a=50,b=54.

• Make it plot the trace.

• Idea:

• a%b = 0⇒ b is the gcd.• Otherwise

gcd(a, b)← gcd(b, a%b).

4. Functions




Types of Recursion—Linear vs. Non-linear Recursion

/ / F inonacc i implementat ion 1vo id foo ( i n t a ) {

i f ( a==0) {r e t u r n ;

}. . .foo1 ( a−1);. . .

}

/ / F inonacc i implementat ion 2vo id bar ( i n t a ) {

i f ( a==0) {r e t u r n ;

}. . .bar ( a−1);bar ( a−2);. . .

}

4. Functions




Types of Recursion—(Linear) Tail Recursion

/ / F inonacc i implementat ion 1vo id foo ( i n t a ) {

i f ( a==0) {r e t u r n ;

}. . .foo1 ( a−1);

}

vo id bar ( i n t a ) {whi le ( . . . ) {

i f ( a==0) {r e t u r n ;

}. . .

}}

Theorem: You can rewrite every tail recursion into a loop.

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Tail Recursion in Action

i n t foo ( i n t a ) {i f ( a <= 1) {

r e t u r n 1 ;}r e t u r n a ∗ foo ( a−1);

}

• What is the semantics of foo(int)?

• Rewrite foo(int) without recursion.

• Which variant might perform faster?

4. Functions




Indirekt Recursion (Kaskadische Rekursion

vo id foo ( i n t a ) {i f ( . . . ) {

foo ( a−4);}bar ( a−1);foo ( a−1);. . .

}

vo id bar ( i n t a ) {. . .foo ( a−1);. . .

}

• Is foo a recursive function?• Is foo a tail recursion?• Is foo linear?• Is bar a recursive function?• Is bar a tail recursion?• Is bar linear?

4. Functions



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