Presentation is loading. Please wait.

Presentation is loading. Please wait.

CSE1222: Lecture 4The Ohio State University1. Mathematical Functions (1)  The math library file cmath Yes, this is a file with definitions for common.

Published byArlene Cain Modified over 8 years ago

Similar presentations

Presentation on theme: "CSE1222: Lecture 4The Ohio State University1. Mathematical Functions (1)  The math library file cmath Yes, this is a file with definitions for common."— Presentation transcript:

1 CSE1222: Lecture 4The Ohio State University1

2 Mathematical Functions (1)  The math library file cmath Yes, this is a file with definitions for common and often used mathematical functions including: sine, cosine, log, and square root Provided by our C++ geniuses (Be thankful!)  Using the math library Include the following at the top of your program #include CSE1222: Lecture 4The Ohio State University2

3 Mathematical Functions (1)  How do you use or invoke a function in math? Specify … Its name Input parameters Retrieve its … Output or answer  Remember y = f(x) from math? f is the name x is the input parameter y will hold the output  A function has three parts: Name, input, and output CSE1222: Lecture 4The Ohio State University3

4 Mathematical Functions (1)  The cmath library defines a function called sqrt … What do you think it does? Function names are descriptive Function names must be spelled exactly how they are defined in their defining library (cmath here, so don’t guess! Look it up) You must provide exactly how many input parameters a function is defined to take A function can output at most one answer only  The square root function : Spelled sqrt Requires exactly one input parameter (a number) Outputs the square root of the input parameter  Question: Where does the output or answer go??? CSE1222: Lecture 4The Ohio State University4

5 Mathematical Functions (2)  This function invocation: double a = 81; double b = sqrt(a); Takes the value of the variable a as a single input parameter Executes the computation for a square root “Outputs” its answer in the assignment statement Rule (Memorize this!): The output value of a function invocation will relace the syntax of the function call in your program during program execution  During execution of this code the second line will execute in the following way: double b = sqrt(a); <---- Before execution double b = sqrt(81); <---- Evaluates the input parameter double b = 9.0; <---- This line uses the rule above CSE1222: Lecture 4The Ohio State University5

6 Mathematical Functions (2)  Is this program snippet nonsensical … Why or why not? double a = 81; sqrt(a); Is there a syntax error, i.e. will it compile? - No syntax error! But, avoid invoking a function in this way if it outputs a value. You are throwing away the output!  Is there a syntax error? Is it nonsensical? double a = 81; cout << sqrt(a); No syntax error! If a function invocation outputs a value, then ensure that the syntax of the function call is used with other code that performs useful work  This statement would output 11 cout << sqrt(121.0) << endl; CSE1222: Lecture 4The Ohio State University6

7 Mathematical Functions (2)  Is there a syntax error? double a = 81; double b = sqrt(a); double c = sqrt(sqrt(a)) * b;  No syntax error! A function can be used like a variable of the same data type  Remember our rule regarding the output of a function invocation How is it used here to evaluate the third line?  Here, a is 81, b is 9, and c is 27. Why? The sqrt function is called three separate times in this code snippet Which function is invoked first, which is invoked second, and then which is invoked third? CSE1222: Lecture 4The Ohio State University7

8 Mathematical Functions (3)  What does the cmath library function pow do? Computes a b, where a and b are two numbers Its name tries to tell you what operation the function performs for you  How many input parameters does this function require? We need a base and an exponent, so two input parameters  Does this function output a single answer or no answer? It must return the value for a b, so one answer  For example cout << pow(3.0, 4.0); would output 81 which is 3 to the 4 th power. Notice the two input parameters in the parenthesis (comma separated). The base must come BEFORE the power! CSE1222: Lecture 4The Ohio State University8

9 Mathematical Functions (4)  Arguments passed into any function can be a constant, variable, or an expression that evaluates to the appropriate data type  For Example, double j = 2.0; cout << sqrt(j * 32.0); //outputs 8 Remember, the sqrt function requires exactly one argument CSE1222: Lecture 4The Ohio State University9

10 Mathematical Functions (5)  Functions can themselves be part of an expression double x = 10; cout << 5 * pow( (x - 3), 2.0 ); //output? Remember our rule regarding function output and where it goes? Remember, the pow function requires exactly two arguments CSE1222: Lecture 4The Ohio State University10

11 Common Math Functions FunctionReturned ValueData Type of Returned Value abs(a) Absolute value of a Data type of a pow(b,e) Value of b raised to the e th power float or double Data type of b sqrt(a) Square root of a double sin(a) Sine of a in radians double cos(a) Cosine of a in radians double tan(a) Tangent of a in radians double log(a) Natural log of a double log10(a) Common log (base 10) of a double exp(a)e raised to the a th power double CSE1222: Lecture 4The Ohio State University11

12 Example: sqrt() #include using namespace std; int main() { double x(0.0), y(0.0); double dist(0.0); cout << "Enter x, y: "; cin >> x >> y; dist = sqrt(x * x + y * y); cout << "Distance of (" << x << "," << y << ") to (0,0) = " << dist << endl; return 0; } // What are we computing here (in plain english)? // Compile and execute after class! CSE1222: Lecture 4The Ohio State University12

13 > distance.exe Enter x, y: 3 4 Distance of (3,4) to (0,0) = 5 > distance.exe Enter x, y: 5 8 Distance of (5,8) to (0,0) = 9.43398 CSE1222: Lecture 4The Ohio State University13 … cout << "Enter x, y: "; cin >> x >> y; dist = sqrt(x * x + y * y); cout << "Distance of (" << x << "," << y << ") to (0,0) = " << dist << endl; …

14 Example 2: sqrt() #include #include // math function library using namespace std; int main () { double height(0), time(0.0); cout << "Enter height (feet): "; cin >> height; time = sqrt(2.0 * height / 32.2); cout << "It will take " << time << " seconds to fall " << height << " feet. " << endl; return 0; } // What are we computing here (in plain english)? CSE1222: Lecture 4The Ohio State University14

15 > gravity.exe Enter height: 100 It will take 2.49222 seconds to fall 100 feet. > gravity.exe Enter height (feet): 500 It will take 5.57278 seconds to fall 500 feet. CSE1222: Lecture 4The Ohio State University15 … cout << "Enter height (feet): "; cin >> height; time = sqrt(2.0 * height / 32.2); cout << "It will take " << time << " seconds to fall " << height << " feet. " << endl; …

16 Example: log() #include using namespace std; int main() { double rate(0.0), years(0.0); cout << "Enter annual interest rate (percentage): "; cin >> rate; years = log(2.0) / log(1 + (rate / 100.0)); cout << "Your money will double in " << years << " years." << endl; return 0; } // What are we computing here (in plain english)? CSE1222: Lecture 4The Ohio State University16

17 > interest.exe Enter annual interest rate (percentage): 7 Your money will double in 10.2448 years. > interest.exe Enter annual interest rate (percentage): 2 Your money will double in 35.0028 years. CSE1222: Lecture 4The Ohio State University17 … cout << "Enter annual interest rate (percentage): "; cin >> rate; years = log(2.0) / log(1 + (rate / 100.0)); cout << "Your money will double in " << years << " years." << endl; …

18 Trigonometric Math Functions  Read your documentation on functions!  Trigonometric math functions (such as sin, cos, and tan ) require input parameters to be in radians CSE1222: Lecture 4The Ohio State University18

19 Example: sin(), cos() #include using namespace std; int main() { double angle(0.0), x(0.0), y(0.0); cout << "Enter rotation angle (radians): "; cin >> angle; x = cos(angle); y = sin(angle); cout << "Point (1,0) rotates to point" << "(" << x << "," << y << ")" << endl; return 0; } // What are we computing here (in plain english)? CSE1222: Lecture 4The Ohio State University19

20 > rotate_radians.exe Enter rotation angle (radians): 1.57 Point (1,0) rotates to point (0.000796327,1) > rotate_radians.exe Enter rotation angle (radians): 0.78 Point (1,0) rotates to point (0.710914,0.703279) CSE1222: Lecture 4The Ohio State University20 … cout << "Enter rotation angle (radians): "; cin >> angle; x = cos(angle); y = sin(angle); cout << "Point (1,0) rotates to point" << "(" << x << "," << y << ")" << endl; …

21 Common Math Constants  Besides functions, the cmath library file also defines some commonly used math constants  Use these like variables Though, being “constants” you cannot assign a new value to them ConstantValue M_PI π, 3.14159… M_E e, the base of natural logarithms M_LOG2E Base-2 logarithm of e M_LOG10E Base-10 logarithm of e M_LN2 Natural log of 2 M_LN10 Natural log of 10 CSE1222: Lecture 4The Ohio State University21

22 degrees2radians.cpp #include #include // cmath contains definitions of math constants using namespace std; int main() { double degrees(0.0), radians(0.0); cout << "Enter angle in degrees: "; cin >> degrees; radians = (degrees * M_PI) / 180.0; // Convert degrees to radians cout << "Angle in radians = " << radians << endl; return 0; } // What are we computing here (in plain english)? CSE1222: Lecture 4The Ohio State University22

23 rotate_degrees.cpp #include #include // cmath contains definitions of math constants using namespace std; int main() { double degrees(0.0), radians(0.0), x(0.0), y(0.0); cout << "Enter rotation angle (degrees): "; cin >> degrees; radians = (degrees * M_PI) / 180.0; x = cos(radians); y = sin(radians); cout << "Point (1,0) rotates to point (" << x << "," << y << ")" << endl; return 0; } // What are we computing here (in plain english)? CSE1222: Lecture 4The Ohio State University23

24 > rotate_degrees.exe Enter rotation angle (degrees): 90 Point (1,0) rotates to point (6.12323e-17,1) > rotate_degrees.exe Enter rotation angle (degrees): 45 Point (1,0) rotates to point (0.707107,0.707107) CSE1222: Lecture 4The Ohio State University24 … cout << "Enter rotation angle (degrees): "; cin >> degrees; radians = (degrees * M_PI) / 180.0; x = cos(radians); y = sin(radians); cout << "Point (1,0) rotates to point" << "(" << x << "," << y << ")" << endl; …

25 log_2.cpp #include #include // cmath contains definitions of math constants using namespace std; int main() { double x(0.0), y(0.0); cout << "Enter number: "; cin >> x; y = log(x) / M_LN2; cout << "log_e(" << x << ") = " << log(x) << endl; cout << "log_2(" << x << ") = " << y << endl; return 0; } // What are we computing here (in plain english)? CSE1222: Lecture 4The Ohio State University25

26 Arguments to Math Functions  Input parameters (i.e., arguments) to math functions should have type double  For example, double x(3.6), y(0.3), z(0.0); z = sin(1.2); z = sqrt(x); z = log(3.2 * x); z = pow(x / 0.5, 1.2 * y); CSE1222: Lecture 4The Ohio State University26

27 logError.cpp... int main() { int value(0); cout << "Enter value: "; cin >> value; // log(value) generates a compiler error cout << "At 10% interest, it will take " << log(value)/log(1.1) << " years for a $1 investment to be worth $" << value << "." << endl; return 0; } CSE1222: Lecture 4The Ohio State University27

28 > g++ logError.cpp –o logError.exe Compiling logError.cpp into logError.exe. logError.cpp: In function 'int main()': logError.cpp:16: call of overloaded 'log(int&)' is ambiguous /usr/include/iso/math_iso.h:52: candidates are: double log(double) /usr/local/include/g++-v3/bits/std_cmath.h:333: long double std::log(long double) /usr/local/include/g++-v3/bits/std_cmath.h:323: float std::log(float) CSE1222: Lecture 4The Ohio State University28 … 15. // log(value) generates a compiler error 16. cout << "At 10% interest, it will take " << log(value) / log(1.1) 17. << " years for a $1 investment to be worth $" << value << "." << 18. endl; … // What is the problem here? What is the data type for variable “value”?

29 logExample.cpp... int main() { int value(0); double x(0.0); cout << "Enter value: "; cin >> value; x = value; // implicit conversion to double cout << "At 10% interest, it will take " << log(x)/log(1.1) << " years for a $1 investment to be worth $" << value << "." << endl; return 0; } // Will this do the trick? CSE1222: Lecture 4The Ohio State University29

30 > logExample.cpp Enter value: 10 At 10% interest, it will take 24.1589 years for a $1 investment to be worth $10. > CSE1222: Lecture 4The Ohio State University30 … double x(0.0);... x = value;// implicit conversion to double cout << "At 10% interest, it will take " << log(x)/log(1.1) << " years for a $1 investment to be worth $" << value << "." << endl; …

31 CSE1222: Lecture 4The Ohio State University31

32 Modulus Operator: %  In math a mod b is the remainder after integer a is divided by integer b  You can think of this operator as a function: 1) name (%), two operands (two integer input parameters), one output (an integer)  In C++ a mod b is written as: a % b  Examples: 25 % 3 = ? 137 % 10 = ? 2751 % 2 = ? CSE1222: Lecture 4The Ohio State University32

33 Expression Types  An expression consists of constants, variables, and function invocations that output single values and evaluates to a single answer For example, 5 * pow( (x - 3), 2.0 )  An expression that contains only integer operands is an integer expression  An expression that contains only floating point operands is a floating-point expression CSE1222: Lecture 4The Ohio State University33

34 Mixing Expression Types  A mixed-mode expression has both floating-point and integer data types  The rules governing the data type of the result are: 1. If both operands are integers, the result is an integer 2. If one operand is a floating-point number, then the result is a double CSE1222: Lecture 4The Ohio State University34

35 Mixed Mode Expressions int a(3); double x(3.5), y(5), z(0.0); z = 3.0 * 25; z = a * x; z = a * y; What about: z = x + (a / 2); CSE1222: Lecture 4The Ohio State University35

36 Exercises int a(3), b(2); double y(5), z(0.0); After each operation, what is z? z = (y + a) / b; z = (y * a) / b; z = y * (a / b); z = (y / b) * (a / b); z = (a + b) / (b * y); CSE1222: Lecture 4The Ohio State University36

37 logError.cpp... int main() { int value(0); cout << "Enter value: "; cin >> value; // log(value) generates a compiler error cout << "At 10% interest, it will take " << log(value)/log(1.1) << " years for a $1 investment to be worth $" << value << "." << endl; return 0; } CSE1222: Lecture 4The Ohio State University37

38 logExample2.cpp... int main() { int value(0); cout << "Enter value: "; cin >> value; // Mixed mode expression "value * 1.0" returns double. cout << "At 10% interest, it will take " << log(value * 1.0)/log(1.1) << " years for a $1 investment to be worth $" << value << "." << endl; return 0; } CSE1222: Lecture 4The Ohio State University38

39 CSE1222: Lecture 4The Ohio State University39

40 Evaluate  What does this express evaluate to? 1 + 3 * 6 – 4 / 2 = ??? Try it out on a sheet of paper CSE1222: Lecture 4The Ohio State University40

41 Evaluate  What does this express evaluate to? 20 – 16 / 2 + 2 * 3 = ???  What if we insert parenthesis in different places?  (((20 – 16) /2) +2) * 3 = 12  ((20 – 16) / (2 + 2)) * 3 = 3  20 – ((16/2) + (2*3)) = -4 CSE1222: Lecture 4The Ohio State University41

42 Operator Precedence and Associativity  The minus sign is overloaded Used as a binary operator for subtraction Used as a unary operator to negate the sign  How do you know which one you are using? int a = b – c;<---- Is this negation? int a = - c; <---- Is this negation?  Depends on the context, operator precedence, and associativity rules CSE1222: Lecture 4The Ohio State University42

43 Operator Precedence and Associativity  Expressions are evaluated from left to right  If there is an ambiguity, then operator precedence determines which operators is evaluated first PrecedenceAssociativity () Unary - * / %Left to right + -Left to right CSE1222: Lecture 4The Ohio State University43

44 arithmetic3.cpp // Precedence of arithmetic operators #include using namespace std; int main() { cout << "-3+5*2 = " << -3+5*2 << endl << endl; // Is this? cout << "((-3)+5)*2 = " << ((-3)+5)*2 << endl; cout << "(-(3+5))*2 = " << (-(3+5))*2 << endl; cout << "(-3)+(5*2) = " << (-3)+(5*2) << endl; cout << "-(3+(5*2)) = " << -(3+(5*2)) << endl; return 0; } CSE1222: Lecture 4The Ohio State University44

45 Math in C++ Review  Use #include for math functions  Common math functions: abs(a), pow(b,e), sqrt(a), sin(a), cos(a), tan(a), log(a), log10(a), exp(a)  Common math constants: M_PI, M_E, M_LN2, M_LN10 CSE1222: Lecture 4The Ohio State University45

46 Math in C++ Review  Arguments to functions should always be double  Mixed mode operations: (3.0 + 5) or (3.0 * 5) have type double;  Operator precedence: Multiplication and division before addition and subtraction CSE1222: Lecture 4The Ohio State University46

Download ppt "CSE1222: Lecture 4The Ohio State University1. Mathematical Functions (1)  The math library file cmath Yes, this is a file with definitions for common."

Similar presentations

Functions. COMP104 Functions / Slide 2 Introduction to Functions * A complex problem is often easier to solve by dividing it into several smaller parts,

Functions. COMP104 Functions / Slide 2 Introduction to Functions * A complex problem is often easier to solve by dividing it into several smaller parts,
Computer Programming w/ Eng. Applications

Computer Programming w/ Eng. Applications
Chapter 3: Expressions and Interactivity. Outline cin object Mathematical expressions Type Conversion and Some coding styles.

Chapter 3: Expressions and Interactivity. Outline cin object Mathematical expressions Type Conversion and Some coding styles.
BBS514 Structured Programming (Yapısal Programlama)1 Functions and Structured Programming.

BBS514 Structured Programming (Yapısal Programlama)1 Functions and Structured Programming.
CSE202: Lecture 2The Ohio State University1 Variables and C++ Data Types.

CSE202: Lecture 2The Ohio State University1 Variables and C++ Data Types.
1 Lecture 6 Chapter 3 Numeric Types, Expressions, and Output Dale/Weems/Headington.

1 Lecture 6 Chapter 3 Numeric Types, Expressions, and Output Dale/Weems/Headington.
Computer Science 1620 Arithmetic. C++ Math we have seen how to use numbers in our program to represent data however, we can also manipulate this data.

Computer Science 1620 Arithmetic. C++ Math we have seen how to use numbers in our program to represent data however, we can also manipulate this data.
Copyright © 2012 Pearson Education, Inc. Chapter 3: Expressions and Interactivity.

Copyright © 2012 Pearson Education, Inc. Chapter 3: Expressions and Interactivity.
1 Fundamental Data types Overview l Primitive Data Types l Variable declaration l Arithmetical Operations l Expressions l Assignment statement l Increment.

1 Fundamental Data types Overview l Primitive Data Types l Variable declaration l Arithmetical Operations l Expressions l Assignment statement l Increment.
1 9/20/06CS150 Introduction to Computer Science 1 Review: Exam 1.

1 9/20/06CS150 Introduction to Computer Science 1 Review: Exam 1.
1 9/08/06CS150 Introduction to Computer Science 1 Arithmetic Operators.

1 9/08/06CS150 Introduction to Computer Science 1 Arithmetic Operators.
CS180 Recitation 3. Lecture: Overflow byte b; b = 127; b += 1; System.out.println(b is + b); b is -128 byte b; b = 128; //will not compile! b went out.

CS180 Recitation 3. Lecture: Overflow byte b; b = 127; b += 1; System.out.println("b is" + b); b is -128 byte b; b = 128; //will not compile! b went out.
1 Chapter 3 Topics Constants of Type int and float l Evaluating Arithmetic Expressions l Implicit Type Coercion and Explicit Type Conversion l Calling.

1 Chapter 3 Topics Constants of Type int and float l Evaluating Arithmetic Expressions l Implicit Type Coercion and Explicit Type Conversion l Calling.
ICS 103 Lab 2-Arithmetic Expressions. Lab Objectives Learn different arithmetic operators Learn different arithmetic operators Learn how to use arithmetic.

ICS 103 Lab 2-Arithmetic Expressions. Lab Objectives Learn different arithmetic operators Learn different arithmetic operators Learn how to use arithmetic.
Copyright © 2015, 2012, 2009 Pearson Education, Inc., Publishing as Addison-Wesley All rights reserved. Chapter 3: Expressions and Interactivity.

Copyright © 2015, 2012, 2009 Pearson Education, Inc., Publishing as Addison-Wesley All rights reserved. Chapter 3: Expressions and Interactivity.
CSE202: Lecture 10AThe Ohio State University1 Numerical Error.

CSE202: Lecture 10AThe Ohio State University1 Numerical Error.
Topic 2A – Library Functions and Casting. CISC 105 – Topic 2A Functions A function is a piece of code which performs a specific task. When a function.

Topic 2A – Library Functions and Casting. CISC 105 – Topic 2A Functions A function is a piece of code which performs a specific task. When a function.
1 Data types, operations, and expressions Continued l Overview l Assignment statement l Increment and Decrement operators l Short hand operators l The.

1 Data types, operations, and expressions Continued l Overview l Assignment statement l Increment and Decrement operators l Short hand operators l The.
Data Types, Expressions and Functions (part I)

Data Types, Expressions and Functions (part I)
What is a variable?  A variable holds data in memory so the program may use that data, or store results.  Variables have a data type. int, boolean, char,

What is a variable?  A variable holds data in memory so the program may use that data, or store results.  Variables have a data type. int, boolean, char,

Similar presentations

Ads by Google