Difference between revisions of "cpp/numeric/special functions/expint"
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{{cpp/title|expint|expintf|expintl}} | {{cpp/title|expint|expintf|expintl}} | ||
− | {{cpp/numeric/ | + | {{cpp/numeric/special_functions/navbar}} |
{{dcl begin}} | {{dcl begin}} | ||
− | {{dcl |num=1| | + | {{dcl header|cmath}} |
− | + | {{dcl rev multi|num=1|since1=c++17|dcl1= | |
− | + | float expint ( float num ); | |
− | long double expint( long double | + | double expint ( double num ); |
− | + | long double expint ( long double num ); | |
− | + | |since2=c++23|dcl2= | |
+ | /* floating-point-type */ expint( /* floating-point-type */ num ); | ||
}} | }} | ||
− | {{dcl |num=2|since=c++17| | + | {{dcl|num=2|since=c++17| |
− | double expint( | + | float expintf( float num ); |
+ | }} | ||
+ | {{dcl|num=3|since=c++17| | ||
+ | long double expintl( long double num ); | ||
+ | }} | ||
+ | {{dcl h|[[#Notes|Additional overloads]]}} | ||
+ | {{dcl header|cmath}} | ||
+ | {{dcl|num=A|since=c++17| | ||
+ | template< class Integer > | ||
+ | double expint ( Integer num ); | ||
}} | }} | ||
{{dcl end}} | {{dcl end}} | ||
− | @1@ Computes the | + | @1-3@ Computes the {{enwiki|Exponential integral}} of {{c|num}}.{{rev inl|since=c++23| The library provides overloads of {{tt|std::expint}} for all cv-unqualified floating-point types as the type of the parameter {{c|num}}.}} |
− | + | @A@ Additional overloads are provided for all integer types, which are treated as {{c/core|double}}. | |
===Parameters=== | ===Parameters=== | ||
{{par begin}} | {{par begin}} | ||
− | {{par | | + | {{par|num|floating-point or integer value}} |
{{par end}} | {{par end}} | ||
===Return value=== | ===Return value=== | ||
− | If no errors occur, value of the exponential integral of {{ | + | If no errors occur, value of the exponential integral of {{c|num}}, that is {{math|-{{minteg|-num|∞|{{mfrac|{{mexp|-t}}|t}}d''t''}}}}, is returned. |
===Error handling=== | ===Error handling=== | ||
− | Errors may be reported as specified in | + | Errors may be reported as specified in {{lc|math_errhandling}}. |
− | + | * If the argument is NaN, NaN is returned and domain error is not reported. | |
− | * If the argument is NaN, NaN is returned and domain error is not reported | + | * If the argument is ±0, -∞ is returned. |
− | * If the argument is ±0, -∞ is returned | + | |
===Notes=== | ===Notes=== | ||
− | {{cpp/numeric/ | + | {{cpp/numeric/special functions/older impl note}} |
− | An implementation of this function is also [ | + | An implementation of this function is also [https://www.boost.org/doc/libs/release/libs/math/doc/html/math_toolkit/expint/expint_i.html available in boost.math]. |
+ | |||
+ | {{cpp/numeric/special functions/additional integer overload note|expint}} | ||
===Example=== | ===Example=== | ||
− | {{example|code= | + | {{example |
+ | |code= | ||
+ | #include <algorithm> | ||
#include <cmath> | #include <cmath> | ||
#include <iostream> | #include <iostream> | ||
+ | #include <vector> | ||
+ | |||
+ | {{cpp/numeric/draw_vbars}} | ||
+ | |||
int main() | int main() | ||
{ | { | ||
std::cout << "Ei(0) = " << std::expint(0) << '\n' | std::cout << "Ei(0) = " << std::expint(0) << '\n' | ||
<< "Ei(1) = " << std::expint(1) << '\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= | |output= | ||
Ei(0) = -inf | Ei(0) = -inf | ||
Ei(1) = 1.89512 | Ei(1) = 1.89512 | ||
− | + | Gompertz constant = 0.596347 | |
+ | █ ┬ 666.505 | ||
+ | █ │ | ||
+ | ▆ █ │ | ||
+ | █ █ │ | ||
+ | █ █ █ │ | ||
+ | ▆ █ █ █ │ | ||
+ | ▁ ▆ █ █ █ █ │ | ||
+ | ▂ ▅ █ █ █ █ █ █ │ | ||
+ | ▁ ▁ ▁ ▁ ▁ ▁ ▁ ▂ ▂ ▃ ▃ ▄ ▆ ▇ █ █ █ █ █ █ █ █ ┴ 1.89512 | ||
}} | }} | ||
===External links=== | ===External links=== | ||
− | [ | + | {{eli|[https://mathworld.wolfram.com/ExponentialIntegral.html Weisstein, Eric W. "Exponential Integral."] From MathWorld — A Wolfram Web Resource.}} |
− | + | {{langlinks|de|es|fr|it|ja|pt|ru|zh}} | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + |
Latest revision as of 23:38, 16 October 2023
Defined in header <cmath>
|
||
(1) | ||
float expint ( float num ); double expint ( 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) |
Defined in header <cmath>
|
||
template< class Integer > double expint ( Integer num ); |
(A) | (since C++17) |
std::expint
for all cv-unqualified floating-point types as the type of the parameter num.(since C++23)Contents |
[edit] Parameters
num | - | floating-point or integer value |
[edit] Return value
If no errors occur, value of the exponential integral of num, that is -∫∞-nume-t |
t |
[edit] 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.
[edit] 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)).
[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: '█' 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
[edit] External links
Weisstein, Eric W. "Exponential Integral." From MathWorld — A Wolfram Web Resource. |