Arithmetic

Here are the normal math operators that work on integers and floating point numbers:

+ (add)
- (subtract; or a negative number, e.g. int x = -5)
* (multiply)

Here are somewhat-unique math operators that work with integers:

/ (quotient: 13 / 5 is 2 because 5 goes into 13 two times)
% (remainder: 13 % 5 is 3 because the remainder of 5/13 is 2)

Note that / works as you would expect with floating point numbers (e.g. 1.2 / 5.6 is about 0.214).

Precedence works the same as you would expect: * / % happen before + - so (5 + 6 % 4 - (3 + 4) / 2) equals 4 as you would expect. You can use parentheses to clarify the math.

Arithmetic shorthand

You can use the following shorthand for changing the values of variables. The shorthand form is shown, then the equivalent form is described in comments.

double a = 0.0;
int x = 0;
x++;            // same as: x = x + 1;
++x;            // same as: x = x + 1;
x--;            // same as: x = x - 1;
--x;            // same as: x = x - 1;
x += 2;         // same as: x = x + 2;
x -= 2;         // same as: x = x - 2;
x *= 2;         // same as: x = x * 2;
x /= 2;         // same as: x = x / 2;
x %= 2;         // same as: x = x % 2;
    
a += 2.0;       // same as: a = a + 2.0;
// etc.

What’s the difference between x++ and ++x (or x-- and --x)? An assignment expression actually has a value. So x = 5 turns into the value 5 (and changes x to equal 5). That makes the following possible: y = x = 5, which sets y equal to the value x = 5, which is the value 5.

The difference is that x++ gives back the old value of x (but also increments x), while ++x increments x then gives its value. So if x is 5, and we have y = x++ then y is 5 and x is 6. On the other hand, if we have y = ++x then y is 6 and x is 6.

Boolean operators

Variables of type bool have the following special operators:

bool p = true;
bool q = false;
bool r;
r = !p;        // "!" means "not" or "opposite", so r == false
r = p || q;    // "||" means "or", so r == true
r = p && q;    // "&&" means "and", so r == false
r = q || (!p)  // r == false

Mathy example

This example shows use of several mathematical functions and operators.

// math example
#include <iostream>
#include <cmath>
using namespace std;

int main()
{
    cout << "The reciprocal of 10 is " << 1.0/10.0 << endl;
    cout << "The square root of 10 is " << sqrt(10.0) << endl;
    cout << "e^(10.0) = " << exp(10.0) << endl;
    cout << "The reciprocal of 15 is " << 1.0/15.0 << endl;
    cout << "The square root of 15 is " << sqrt(15.0) << endl;
    cout << "e^(15.0) = " << exp(15.0) << endl;

    return 0; // exit program
}

Here is the example again, but this time with a variable x:

#include <iostream>
#include <cmath>
using namespace std;

int main()
{
    double x;
       
    x = 10.0;

    cout << "The reciprocal of 10 is " << 1.0/x << endl;
    cout << "The square root of 10 is " << sqrt(x) << endl;
    cout << "e^(" << x << ") = " << exp(x) << endl;

    x = 15.0;

    cout << "The reciprocal of 15 is " << 1.0/x << endl;
    cout << "The square root of 15 is " << sqrt(x) << endl;
    cout << "e^(" << x << ") = " << exp(x) << endl;

    return 0; // exit program
}

In these examples, various useful math functions were used. Here is a larger list. These all come from cmath (which must be “included”).

pow(a, b) – raise a to the power b; a and b should have type double
exp(a) – raise Euler’s number e to the power a (a double)
log(a) – find the natural logarithm of a (a double)
log10(a) – find the “base 10” logarithm of a
sqrt(a) – find the square root of a (a double)
sin(a) – the result of sine(a) (a is a double, in radians)
cos(a), tan(a) – obvious
acos(a), asin(a) – the arc cosine/sine of a; answer is in radians (a is a double, as is the answer)

Conversion example

This code converts teaspoons to other units of measurement.

#include <iostream>
using namespace std;

int main()
{
    int teaspoons;

    cout << "Please enter the number of teaspoons: ";
    cin >> teaspoons;

    int gallons = teaspoons/(3*16*2*8);
    teaspoons -= gallons*(3*16*2*8);
    int pints = teaspoons/(3*16*2);
    teaspoons -= pints*(3*16*2);
    int cups = teaspoons/(16*3);
    teaspoons -= cups*(16*3);
    int tablespoons = teaspoons/3;
    teaspoons -= tablespoons*3;

    cout << "Number of gallons: " << gallons << endl;
    cout << "Number of pints: " << pints << endl;
    cout << "Number of cups: " << cups << endl;
    cout << "Number of tablespoons: " << tablespoons << endl;
    cout << "Number of teaspoons: " << teaspoons << endl;

    return 0;
}

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