NAME

std::expint,std::expintf,std::expintl - std::expint,std::expintf,std::expintl

Synopsis

Defined in header <cmath>
double expint( double arg );

float expint( float arg );
long double expint( long double arg ); (1) (since C++17)
float expintf( float arg );

long double expintl( long double arg );
double expint( IntegralType arg ); (2) (since C++17)

1) Computes the exponential integral of arg.
2) A set of overloads or a function template accepting an argument of any integral
type. Equivalent to (1) after casting the argument to double.

Parameters

arg - value of a floating-point or Integral type

Return value

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

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

Example

// Run this code

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

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((Height > 0) && (BarWidth > 0) && (Padding >= 0) && (Offset >= 0));
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(*cbegin(s)) V; V e : s)
qr.push_back(std::div(std::lerp(V(0), Height*8, (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.