C++ Math (cmath)

C++ has two places for mathematics: std::max and std::min in the algorithm header, and the functions of the cmath header (square roots, powers, rounding and trigonometry).

max and min

#include <algorithm>
#include <iostream>

int main() {
    std::cout << std::max(7, 12) << "\n";
    std::cout << std::min(7, 12) << "\n";
    std::cout << std::max({4, 19, 8, 11}) << "\n";   // several values in braces
    return 0;
}

12
7
19

Both values must have the same type: std::max(3, 4.5) does not compile; write std::max(3.0, 4.5).

cmath

#include <cmath>
#include <cstdlib>
#include <iostream>

int main() {
    std::cout << std::sqrt(64) << "\n";
    std::cout << std::pow(2, 10) << "\n";
    std::cout << std::abs(-4.5) << "\n";
    std::cout << std::round(4.5) << " " << std::floor(4.8) << " " << std::ceil(4.2) << "\n";
    std::cout << std::hypot(3, 4) << "\n";
    return 0;
}

8
1024
4.5
5 4 5
5

Angles in radians

The trigonometric functions use radians. C++20 gives the exact value of pi as std::numbers::pi in the numbers header:

#include <cmath>
#include <cstdlib>
#include <iomanip>
#include <iostream>
#include <numbers>

int main() {
    double degrees = 30;
    double radians = degrees * std::numbers::pi / 180;
    std::cout << std::fixed << std::setprecision(2);
    std::cout << "sin(30) = " << std::sin(radians) << "\n";
    std::cout << "cos(60) = " << std::cos(60 * std::numbers::pi / 180) << "\n";
    return 0;
}

sin(30) = 0.50
cos(60) = 0.50

Decimals are approximate

A double stores most decimal fractions approximately: 0.1 + 0.2 is very slightly more than 0.3. Never test decimals with ==; check that the difference is tiny: std::abs(a - b) < 1e-9.

#include <cmath>
#include <cstdlib>
#include <iostream>

int main() {
    double a = 0.1 + 0.2;
    std::cout << std::boolalpha;
    std::cout << (a == 0.3) << "\n";
    std::cout << (std::abs(a - 0.3) < 1e-9) << "\n";
    return 0;
}

false
true

Integer and decimal versions

std::abs works for both whole numbers and decimals: the integer versions are declared in cstdlib, the decimal ones in cmath, which is why the examples include both. The functions of cmath return double, so std::pow(2, 10) is the decimal 1024.0; for an exact integer power of small numbers, a loop or a bit shift (1 << 10) is better. Store the result of std::round in an int with static_cast<int>(std::round(x)).

Practice exercises

1. Compute the area of a circle with radius 5 using std::numbers::pi.
2. Read a number and print its square root, or a message if it is negative.
3. Compute 1000 at 7% interest for 10 years: 1000 × 1.07 to the power 10.