Learning style reminder

Transcription

1 Learning style reminder Please answer honestly: Have you written from scratch at least two short programs with each of these? if switch case while do while for rand() and srand()

2 Learning style reminder If you answered NO, please set aside a couple of hours this weekend for writing C code. If necessary, take another look at the file How to learn programming (webpage)

3 Chapter 6: Functions

4 Introduction Basic idea: By using functions, a large task is broken down into smaller ones, a.k.a. modularity. Why this is important/necessary: Keep the code small enough to understand it. Develop and test portions of the code separately, maybe even multiple programmers. Reusability: develop a program based upon what others have already done. Do not have to start from scratch.

5 Function Definitions return_type function_name(argument declaration) { Example: statements int addition(int a, int b) { int s; s = a + b; return s; int main() { int sum; sum = addition(3, 4); printf("sum = %d\n", sum); return 0;

6 The return type can be any valid type specifier. The return statement can be used to return a value from the called function to the calling function as in return expression; If necessary, the expression will be converted to the return type of the function. However, if the expression cannot be converted to the return type of the function according to the built-in C conversion rules, it is a syntax error. Example: int func(void){ double d; d = 4.6; return d; // Automatic type conversion, returns 4

7 If the return type is not void, a return statement is necessary at the end of the function in C99. A calling function can freely ignore the return value. Example: int func(int i){ return i+1; // the same as return (i+1); int main() { int j; j = func(4); func(5); return 0; // ignore the return value

8 If the return type is void, the return statement is optional. However, no expression should follow return, otherwise, it is a syntax error. Example: void func(int i){ if(i == 3){ printf("i is equal to 3 \n"); return i; else if(i > 3){ // ERROR: return int printf("i is not equal to 3 \n"); return; // OK i = -1; // return not necessary since return type is void int main(){ func(2); return 0;

9 The data type of an actual argument of the calling function can be different from that of the formal argument of the called function as long as they are compatible. The value of an actual argument will be converted to the data type of its formal definition according to the built-in data conversion rules implicitly at the function interface stage. Example: int func1(int i) { // argument type is int return 2*i; int main(){ func1(5); // OK func1(5.0); // OK, 5.0 converted to 5 return 0;

10 Sample Problem: The system in Figure1 (a) consists of a single body with mass m moving on a horizontal surface. An external force p acts on the body. The coefficient of kinetic friction between body and horizontal surface is. The freebody diagram for the system is shown in Figure1 (b). Figure1: The system diagram and FBD of a sample problem

11 Program 1: Use a function to calculate the external force. #include <stdio.h> #define M_G 9.81 double force(double t) { double p; p = 4*(t-3)+20; return p; int main() { double a, mu, m, p, t; mu = 0.2; m = 5.0; t = 2.0; p = force(t); a = (p-mu*m*m_g)/m; printf("acceleration a = %f (m/s^2)\n", a); return 0; Output: Acceleration a = (m/s^2)

12 #include <stdio.h> #define M_G 9.81 Program 2: Use functions that: have multiple arguments call other functions double force(double t) { double p; p = 4*(t-3)+20; return p; double accel(double t, double mu, double m) { double a, p; p = force(t); a = (p-mu*m*m_g)/m; return a; void main() { double a, mu, m, t; mu = 0.2; m = 5; t = 2; a = accel(t, mu, m); printf("acceleration a = %f\n (m/s^2)", a);

13 The types of the arguments and returned value need not be related in any way double force(int i, float f, long long LL ) {......

14 6.2 Function Prototypes Basic idea: abstraction, modularity and the black box: double accel(double t, double mu, double m) { double a, p; p = force(t); a = (p-mu*m*m_g)/m; return a; double t double mu double m Black box double accel

15 A function prototype: Declares only the interface of that function: return type types of all parameters Shouldn t this read the names and types? Parameter names must appear in function definitions, but they are optional in function prototypes. The following two function prototypes are the same: double accel(double, double, double); double accel(double t, double mu, double m);

16 A function prototype: Contains no function definition. Like the function definition itself, it cannot be inside the body of another function. Can be declared before or after its function definition, but widespread programming style is to have it before Actually, we ll be even more strict than this: Either put the entire function definition before main(), in which case do not use a prototype, or Put the prototype before main() and the definition after main().

17 #include <stdio.h> #define M_G 9.81 Program 3: Using function prototypes. double force(double t); double accel(double, double, double); void main() { double a, mu, m, t; mu = 0.2; m = 5.0; t = 2.0; a = accel(t, mu, m); printf("acceleration a = %f (m/s^2)\n", a); double force(double t) { double p; p = 4*(t-3)+20; return p; double accel(double t, double mu, double m) { double a, p; p = force(t); a = (p-mu*m*m_g)/m; return a;

18 Function prototype: no arguments In C, declaring a function without arguments may result in ambiguity, b/c the compiler does not check the calls to make sure they have no arguments, e.g. int foo(); void main(){... foo(42);... { //no compilation error! Solution: use void int foo( void );

19 Function prototype: no arguments In C++, explicitly specifying that a function requires no arguments is the same as declaring a function with an empty argument declaration list. Therefore, the following two statements are identical: int foo(); int foo( void );

20 We have covered sections 6.1 and 6.2 Solve the following end-of-chapter problems in notebook for next time: 2 5 6a

21 6.3 Calling functions by value or by reference Call by value the variables used as parameters are copied, then the copies are passed to the function If the parameters are changed inside the function, the change does not propagate to the original variables Call by reference the variables addresses are passed to the function If the parameters are changed inside the function, the change affects the original variables In C, the default is by value.

22 What s wrong with these functions? void increment (int x){ x++; void swap(int x, int y) { int temp; temp = x; x = y; y = temp;

23 Solution: call by reference void swap(int *x, int *y) { int temp;... *temp = *x; *x = *y; *y = *temp; swap (&a, &b); //call it like this

24 Extra-credit: rewrite to call by ref. and show how the main program will call it void increment (int x){ x++;

25 Another example: scanf("%d", &counter); Why not scanf("%d", counter);

26 6.4 Standard C Header Files and Libraries Header files contain function prototypes for performing operations that are related to one another. For example, math.h contains extern double sin(double x); extern double exp(double x); for the mathematical functions sin(x) and e x. The type qualifier extern means that the functions are defined outside of the header file (in a library or other module). Header files may also include macros and type definitions required by some of the functions, e.g. FLT _EPSILON in float.h INT_MIN and INT_MAX in limits.h typedef unsigned int size_t; in types.h

27 Each C compiler has its own header files for the standard C libraries C:\Program Files\Microsoft Visual Studio.NET 2003\Vc7\include

28 Some Standard C Header Files File limits.h float.h math.h stdbool.h stdio.h stdlib.h time.h Description Define several macros that expand to various limits and parameters of the standard integer types. Define several macros that expand to various limits and parameters of the standard floating-point types. Declare two types and several functions and define several macros for general mathematical operations. Define macros for boolean operations Declare types, macros, and functions for standard input and output. Declare several types, macros, and functions for general utility, such as conversion of numbers to text and text to numbers, memory allocation, and generation of random numbers. Define macros and declare sever types and functions for manipulating time and date.

29 A few snippets from math.h

30 6.5 Math functions and Type Generic functions A type generic function is a built-in system function that is polymorphic: Several versions of the TG function exist, that can handle various types of argument (e.g. float, double, complex) When the TG function such as sin(x) is called, the compiler chooses that version of sin() that matches the type of the argument x. To use type generic mathematical functions in C99, the header file tgmath.h shall be included instead of math.h TG math functions are not supported in MSVS.

31 Standard C functions Reference manuals with detailed description for each function in the standard C libraries are available on many websites, e.g. Use either website above to find the functions: sin() time()

32 6.6 Example: A Mathematical Formula with a Single Variable Calculate the function sinc(x) = sin(x)/x from -10 <= x <= 10 with a step size 5. Cardinal sine Generate data points (x, y) for x in the range x0 <= x <= xf with step size xstep linearly. The number of points should be n = (xf x0)/xstep + 1; Each data point can be calculated in a for loop: for(i = 0; i <n; i++) { x = x0 + i*xstep; y = f(x);

33 /* File: sinc.c */ #include <stdio.h> /* for printf() */ #include <math.h> /* for sin() and fabs() */ #include <float.h> /* for FLT_EPSILON */ Output: x sinc(x) double sinc(double x) { double retval; if(fabs(x) < FLT_EPSILON) retval = 1.0; else retval = sin(x)/x; return retval; int main() { double x, x0, xf, xstep, result; int i, n; Explain this! printf(" x sinc(x)\n"); printf(" \n"); x0 = -10.0; /* initial value */ xf = 10.0; /* final value */ xstep = 5.0; /* step size */ n = (xf - x0)/xstep + 1; /* num of points */ for(i = 0; i < n; i++) { x = x0 + i*xstep; /* value x */ result = sinc(x); printf("%8.4f %8.4f\n", x, result); return 0;

34 C x for Engineers and Scientists: An Interpretive Approach Example: A Mathematical Formula with Multiple Variables Calculate the function f 2 ( x, y) sin( x x 2 2 y y 2 2 ) for x from -10 <= x <= 10 with a step size 10 and y from -10 <= y <= 10 with a step size of 10.

35 /* File: sinr.c */ #include <stdio.h> #include <math.h> double sinr(double x, double y) { double retval, r; r = sqrt(x*x + y*y); retval = sin(r)/r; return retval; int main() { double x, x0, xf, xstep, y, y0, yf, ystep, result; int i, j, nx, ny; printf(" x y sinr(x,y)\n"); printf(" \n"); x0 = -10.0; xf = 10.0; xstep = 10.0; nx = (xf - x0)/xstep + 1; /* num of points for x */

36 y0 = -10.0; yf = 10.0; ystep = 10.0; ny = (yf - y0)/ystep + 1; /* num of points for y */ for(i = 0; i < nx; i++) { x = x0 + i*xstep; /* calculate value for x */ for(j = 0; j <ny; j++) { y = y0 + j*ystep; /* calculate value for y */ result = sinr(x, y); printf("%10.4f %10.4f %8.4f\n", x, y, result);

37 y0 = -10.0; yf = 10.0; ystep = 10.0; ny = (yf - y0)/ystep + 1; /* num of points for y */ for(i = 0; i < nx; i++) { x = x0 + i*xstep; /* caclulate value for x */ for(j = 0; j <ny; j++) { y = y0 + j*ystep; /* calculate value for y */ result = sinr(x, y); printf("%10.4f %10.4f %8.4f\n", x, y, result); Output: sin(0)/0 is NaN x y sinr(x,y) NaN

38 SKIP for now 6.7 Plotting Functions

39 Local variables in functions double force(double t) { double p; p = 4*(t-3)+20; return p; int main() { double a, mu, m, p, t; mu = 0.2; m = 5.0; t = 2.0; p = force(t); a = (p-mu*m*m_g)/m; printf("acceleration a = %f (m/s^2)\n", a); return 0;

40 We have covered sections 6.3, 6.4, 6.5, 6.6 Solve the following end-of-chapter problems in notebook for next time: 3 4 6b

41 6.8 Recursive Functions Functions in C may be used recursively: a function calls itself! Each function call will have a new set of local variables. Recursive functions usually contain conditional statements, such as if-else, to allow exit of the function and return control to the calling function. A function may also call itself indirectly.

42 Example: Calculating the factorial iteratively, using a function with a for-loop. #include <stdio.h> unsigned int factorial(int n); int main() { int i; for(i=0; i<=5; i++) printf("%d! = %d\n", i, factorial(i)); return 0; unsigned int factorial(int n) { unsigned int i, f; Output: 0! = 1 1! = 1 2! = 2 3! = 6 4! = 24 5! = 120 for(i=1, f=1; i<=n; i++) { f *= i; return f;

43 Example: Calculating the factorial recursively using a function that calls itself: #include <stdio.h> unsigned int factorial(int n); int main() { int i; for(i=0; i<=5; i++) printf("%d! = %u\n", i, factorial(i)); return 0; unsigned int factorial(int n) { if(n == 0) { // n == 1 also works return 1; else { return n*factorial(n-1); Output: 0! = 1 1! = 1 2! = 2 3! = 6 4! = 24 5! = 120

44 Another example of recursion Problem 16/219 the Fibonacci numbers

45

46 6.10 Finding Roots of Equations Using Bisection Method

47 The bisection method Read and understand: Program 6.17 (pseudocode) Program 6.18 (iterative solution) Not in text: recursive implementation of bisection!

48 Recursion detail: storage classes static variables are initialized only once, no matter how many times the block (function) in which they are defined is called during execution! In C, the default storage class is auto but it s almost never written! More details in Ch.8.

49 6.9 func Double underscore on each side! In C99 it is a static, constant string Use this in Visual Studio (uppercase!). It s a macro (#define)

50 SKIP 6.11, 6.12, 6.13 End of chapter problems: 6 b, c 7 b, c a Homework for Ch.6 Due Friday, Oct Hint: First enter the original program 6.18 in Visual Studio and make sure it works. Only then modify it! Extra-credit: Re-write program 6.18 using a recursive function