std::exp,st...f,std::expl(3)

💖 std::exp, std::expf, std::expl 💖

Okay bestie, this is the std::exp,st...f,std::expl(3) page from the C++ Standard Libary (their spelling, not mine 💅). It’s all about the exponential function, and yes, it’s giving math-girlie main character energy. ✨

🎀 NAME 🎀

std::exp,std::expf,std::expl - std::exp,std::expf,std::expl

🌸 Synopsis 🌸

So the original synopsis is a little feral with the line wraps, but every signature, label, and version tag is right here, bestie. 🫶

Defined in header <cmath>

float       exp ( float num );

double      exp ( double num );                            (until C++23)

long double exp ( long double num );
/* floating-point-type */                                  (since C++23)
            exp ( /* floating-point-type */ num );         (constexpr since C++26)

float       expf( float num );                     (1) (2) (since C++11)
                                                             (constexpr since C++26)
long double expl( long double num );                   (3) (since C++11)
                                                             (constexpr since C++26)

Additional overloads (since C++11)
Defined in header <cmath>
template< class Integer >                              (A) (constexpr since C++26)
double      exp ( Integer num );

1-3) Computes e (Euler's number, 2.7182818...) raised to the given power num. 🧚

Since C++23, the library provides overloads of std::exp for all cv-unqualified floating-point types as the type of the parameter. ✨

A) Additional overloads are provided for all integer types, which are treated as double. (since C++11) 💖

🍓 Parameters 🍓

• num — floating-point or integer value.

🔥 Return value 🔥

If no errors occur, the base-e exponential of num (that’s e^num, periodt) is returned. 🌈

If a range error occurs due to overflow, +HUGE_VAL, +HUGE_VALF, or +HUGE_VALL is returned. 😭

If a range error occurs due to underflow, the correct result (after rounding) is returned. 💅

💀 Error handling 💀

Errors are reported as specified in math_errhandling. 🫶

If the implementation supports IEEE floating-point arithmetic (IEC 60559), then:

• If the argument is ±0, 1 is returned.
• If the argument is -∞, +0 is returned.
• If the argument is +∞, +∞ is returned.
• If the argument is NaN, NaN is returned.

🦋 Notes 🦋

For IEEE-compatible type double, overflow is guaranteed if 709.8 < num, and underflow is guaranteed if num < -708.4. 🔥

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::exp(num) has the same effect as std::exp(static_cast<double>(num)). 👑

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🌈 Example 🌈

// Run this code — yes bestie, run it. 🏃‍♀️💨

// Run this code

#include <cerrno>
#include <cfenv>
#include <cmath>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <numbers>

// #pragma STDC FENV_ACCESS ON

consteval double approx_e()
{
    long double e{1.0};
    for (auto fac{1ull}, n{1llu}; n != 18; ++n, fac *= n)
        e += 1.0 / fac;
    return e;
}

int main()
{
    std::cout << std::setprecision(16)
              << "exp(1) = e¹ = " << std::exp(1) << '\n'
              << "numbers::e  = " << std::numbers::e << '\n'
              << "approx_e    = " << approx_e() << '\n'
              << "FV of $100, continuously compounded at 3% for 1 year = "
              << std::setprecision(6) << 100 * std::exp(0.03) << '\n';

    // special values
    std::cout << "exp(-0) = " << std::exp(-0.0) << '\n'
              << "exp(-Inf) = " << std::exp(-INFINITY) << '\n';

    // error handling
    errno = 0;
    std::feclearexcept(FE_ALL_EXCEPT);

    std::cout << "exp(710) = " << std::exp(710) << '\n';

    if (errno == ERANGE)
        std::cout << "    errno == ERANGE: " << std::strerror(errno) << '\n';
    if (std::fetestexcept(FE_OVERFLOW))
        std::cout << "    FE_OVERFLOW raised\n";
}

✨ Possible output ✨

exp(1) = e¹ = 2.718281828459045
numbers::e  = 2.718281828459045
approx_e    = 2.718281828459045
FV of $100, continuously compounded at 3% for 1 year = 103.045
exp(-0) = 1
exp(-Inf) = 0
exp(710) = inf
    errno == ERANGE: Numerical result out of range
    FE_OVERFLOW raised

👑 See also 👑

• exp2, exp2f, exp2l — returns 2 raised to the given power (2^x); (function); (C++11) (C++11) (C++11).
• expm1, expm1f, expm1l — returns e raised to the given power, minus one (e^x-1); (function); (C++11) (C++11) (C++11).
• log, logf, logl — computes natural (base e) logarithm (ln(x)); (function); (C++11) (C++11).
• exp(std::complex) — complex base e exponential; (function template).
• exp(std::valarray) — applies the function std::exp to each element of valarray; (function template).
• C documentation for exp.

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Source/version/date tea: http://cppreference.com, version 2024.06.10, page std::exp,st...f,std::expl(3) — byeee bestie, go exponentiate something iconic 💜🫶💅