Numerical Library

Numerical Library#

Standard math functions are provided by the C++ numerics library which are accessed through the <cmath> header.

This provides math functions like \(\sin(x)\)

Important

Trigonometric functions like \(\sin(x)\) expect their arguments to be in radians.

For raising numbers to a power, e.g., \(x**y\), we use the std::pow() function. This differs a bit from some languages which have an operator for exponentiation, like x**y.

Sine of angle in degrees#

Here’s an example of:

  • initializing an angle in degrees

  • converting the angle to radians

  • computing the sine of the angle in radians

Listing 10 sine.cpp#
#include <cmath>
#include <iostream>
#include <numbers>

int main() {

    double angle_degrees{60.0};
    double angle_radians = angle_degrees * std::numbers::pi / 180.0;
    double sine_angle = std::sin(angle_radians);

    std::cout << sine_angle << std::endl;

}

Powers#

Listing 11 power.cpp#
#include <cmath>
#include <iostream>

int main() {

    double x{2.0};

    // compute x**3
    std::cout << "x**3 = " << std::pow(x, 3.0) << std::endl;
    std::cout << std::endl;

    // compute x**0.5
    std::cout << "x**0.5 = " << std::pow(x, 0.5) << std::endl;
    std::cout << "       = " << std::sqrt(x) << std::endl;
    std::cout << std::endl;

    // compute x**(1./3.)
    std::cout << "x**(1./3.) = " << std::pow(x, 1.0 / 3.0) << std::endl;
    std::cout << "           = " << std::cbrt(x) << std::endl;
    std::cout << std::endl;

}

Exponential and logs#

Important

std::log() is the natural logarithm. For common logarithm (base-10), use std:log10().

Listing 12 exp_log.cpp#
#include <cmath>
#include <iostream>

int main() {

    double x{123456.789};

    double ln_x = std::log(x);
    double log10_x = std::log10(x);

    std::cout << "ln(x)    = " << ln_x << std::endl;
    std::cout << "log10(x) = " << log10_x << std::endl;
    std::cout << std::endl;

    // notice that we use { } here to "scope" this
    // meaning that x_recovered is not defined outside
    // of this block.

    {
        double x_recovered = std::exp(ln_x);

        std::cout << "exp(ln(x)) = " << x_recovered << std::endl;
        std::cout << "difference = " << x - x_recovered << std::endl;

        std::cout << std::endl;
    }

    {
        double x_recovered = std::pow(10.0, log10_x);

        std::cout << "10**log10(x) = " << x_recovered << std::endl;
        std::cout << "difference = " << x - x_recovered << std::endl;

        std::cout << std::endl;
    }
}

Absolute value#

Caution

You may see some examples on the internet that add the line

using namespace std;

and then access functions without the std:: namespace.

This can be dangerous, since you might not get the function you intend from the C++ standard library.

This can be especially dangerous with std:abs().

Listing 13 absolute.cpp#
#include <cmath>
#include <iostream>

int main() {

    double x{-1.234};

    std::cout << "std::abs(x) = " << std::abs(x) << std::endl;
    std::cout << "abs(x) = " << abs(x) << std::endl;

}
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