std::exp,std::expf,std::expl(3)

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

Synopsis
   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.
   The library provides overloads of std::exp for all cv-unqualified floating-point
   types as the type of the parameter.
   (since C++23)
   A) Additional overloads are provided for all integer types, which are (since C++11)
   treated as double.

Parameters
   num - floating-point or integer value

Return value
   If no errors occur, the base-e exponential of num (enum
   ) 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),
     * 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)).

Example
// 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 (\({\small 2^x}\)2^x)
   (C++11) (function)
   (C++11)
   (C++11)
   expm1
   expm1f returns e raised to the given power, minus one (\({\small
   expm1l e^x-1}\)e^x-1)
   (C++11) (function)
   (C++11)
   (C++11)
   log
   logf computes natural (base e) logarithm (\({\small\ln{x}}\)ln(x))
   logl (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