double expint ( double num );
/* 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)template< class Integer >
double expint ( Integer num );
Computes the
Exponential integralof
num.
The library provides overloads ofstd::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.
[edit] Parameters num - floating-point or integer value [edit] Return valueIf no errors occur, value of the exponential integral of
num, that is
-∫â, is returned.
[edit] Error handlingErrors may be reported as specified in math_errhandling.
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)).
[edit] Example#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: 'â' 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 << "â " : std::cout << "â´ " << *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 â ⬠666.505 â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â â´ 1.89512[edit] External links
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