# std::expint, std::expintf, std::expintl

From cppreference.com
< cpp‎ | numeric‎ | special functions

Defined in header `<cmath>` |  |
| (1) |
float expint ( float num ); double expint ( double num ); long double expint ( long double num ); |  | (since C++17) (until C++23)
/* floating-point-type */ expint( /* floating-point-type */ num ); |  | (since C++23)
float expintf( float num ); | (2) | (since C++17)
long double expintl( long double num ); | (3) | (since C++17)
Additional overloads |  |
Defined in header `<cmath>` |  |
template< class Integer > double expint ( Integer num ); | (A) | (since C++17)

1-3) Computes the Exponential integral of num. The library provides overloads of `std::expint` for all cv-unqualified floating-point types as the type of the parameter num. (since C++23)
A) Additional overloads are provided for all integer types, which are treated as double.

### Parameters

num | - | floating-point or integer value

### Return value

If no errors occur, value of the exponential integral of num, that is -∫∞
-num

e-t
t

dt, is returned.

### Error handling

Errors may be reported as specified in math_errhandling.

- If the argument is NaN, NaN is returned and domain error is not reported.
- If the argument is ±0, -∞ is returned.

### Notes

Implementations that do not support C++17, but support ISO 29124:2010, provide this function if `__STDCPP_MATH_SPEC_FUNCS__` is defined by the implementation to a value at least 201003L and if the user defines `__STDCPP_WANT_MATH_SPEC_FUNCS__` before including any standard library headers.

Implementations that do not support ISO 29124:2010 but support TR 19768:2007 (TR1), provide this function in the header `tr1/cmath` and namespace `std::tr1`.

An implementation of this function is also available in boost.math

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::expint(num) has the same effect as std::expint(static_cast<double>(num)).

### Example

Run this code

    #include <algorithm>
    #include <cmath>
    #include <iostream>
    #include <vector>

    template<int Height = 5, int BarWidth = 1, int Padding = 1, int Offset = 0, class Seq>
    void draw_vbars(Seq&& s, const bool DrawMinMax = true)
    {
        static_assert(0 < Height and 0 < BarWidth and 0 <= Padding and 0 <= Offset);

        auto cout_n = [](auto&& v, int n = 1)
        {
            while (n-- > 0)
                std::cout << v;
        };

        const auto [min, max] = std::minmax_element(std::cbegin(s), std::cend(s));

        std::vector<std::div_t> qr;
        for (typedef decltype(*std::cbegin(s)) V; V e : s)
            qr.push_back(std::div(std::lerp(V(0), 8 * Height,
                                            (e - *min) / (*max - *min)), 8));

        for (auto h {Height}; h-- > 0; cout_n('\n'))
        {
            cout_n(' ', Offset);

            for (auto dv : qr)
            {
                const auto q {dv.quot}, r {dv.rem};
                unsigned char d[] {0xe2, 0x96, 0x88, 0}; // Full Block: '█'
                q < h ? d[0] = ' ', d[1] = 0 : q == h ? d[2] -= (7 - r) : 0;
                cout_n(d, BarWidth), cout_n(' ', Padding);
            }

            if (DrawMinMax && Height > 1)
                Height - 1 == h ? std::cout << "┬ " << *max:
                              h ? std::cout << "│ "
                                : std::cout << "┴ " << *min;
        }
    }

    int main()
    {
        std::cout << "Ei(0) = " << std::expint(0) << '\n'
                  << "Ei(1) = " << std::expint(1) << '\n'
                  << "Gompertz constant = " << -std::exp(1) * std::expint(-1) << '\n';

        std::vector<float> v;
        for (float x{1.f}; x < 8.8f; x += 0.3565f)
            v.push_back(std::expint(x));
        draw_vbars<9, 1, 1>(v);
    }

Output:

    Ei(0) = -inf
    Ei(1) = 1.89512
    Gompertz constant = 0.596347
                                              █ ┬ 666.505
                                              █ │
                                            ▆ █ │
                                            █ █ │
                                          █ █ █ │
                                        ▆ █ █ █ │
                                    ▁ ▆ █ █ █ █ │
                                ▂ ▅ █ █ █ █ █ █ │
    ▁ ▁ ▁ ▁ ▁ ▁ ▁ ▂ ▂ ▃ ▃ ▄ ▆ ▇ █ █ █ █ █ █ █ █ ┴ 1.89512

### External links

Weisstein, Eric W. "Exponential Integral." From MathWorld — A Wolfram Web Resource.

Retrieved from "https://en.cppreference.com/mwiki/index.php?title=cpp/numeric/special_functions/expint&oldid=151243"