std::expm1,...std::expm1l(3)

📦 version 2024.07.05, in nixpkgs unstable, opensuse-leap 16.0

std::expm1,...std::expm1l(3) 💅✨

okay so this is the manual page for the std::expm1 family, and the manual name up top is C++ Standard Libary (yes, “Libary” — we are not fixing it, we are respecting the typo’s main character energy 🫶). Bestie, it’s giving tiny-argument math safety with a whole lot of floating-point drama.

NAME 🎀

std::expm1, std::expm1f, std::expm1l — literally the page says std::expm1,std::expm1f,std::expm1l - std::expm1,std::expm1f,std::expm1l, which is the manual-page equivalent of introducing the girlies by saying the girlies’ names twice 💖.

Synopsis 📚

Defined in header <cmath>
float       expm1 ( float num );

double      expm1 ( double num );                            (until C++23)

long double expm1 ( long double num );
/* floating-point-type */                                    (since C++23)
                expm1 ( /* floating-point-type */ num );
 (constexpr since C++26)
float       expm1f( float num );                     (1) (2) (since C++11)
                                                                 (constexpr since C++26)
long double expm1l( 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      expm1 ( Integer num );

1-3) compute the e (Euler’s number, 2.7182818...) raised to the given power num, minus 1.0. This function is more accurate than the expression std::exp(num) - 1.0 if num is close to zero. Tiny num girlies, this one’s for you ✨.

The library provides overloads of std::expm1 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 treated as double. (since C++11)

Parameters 🌸

num — floating-point or integer value

Return value 💫

If no errors occur, you get e^num - 1 returned — the page’s math rendering coughs up enum -1, and honestly, math rendering said what it said 😭.

If a range error due to overflow occurs, +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, it is returned, unmodified.
If the argument is -∞, -1 is returned.
If the argument is +∞, +∞ is returned.
If the argument is NaN, NaN is returned.

Notes 🧚

The functions std::expm1 and std::log1p are useful for financial calculations, for example, when calculating small daily interest rates: (1+x)^n - 1 can be expressed as std::expm1(n * std::log1p(x)). These functions also simplify writing accurate inverse hyperbolic functions. Money math and inverse-hyperbolic math in the same function? Obsessed, actually 💸.

For IEEE-compatible type double, overflow is guaranteed if 709.8 < num.

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::expm1(num) has the same effect as std::expm1(static_cast<double>(num)).

Example 🍓

// Run this code

#include <cerrno>
#include <cfenv>
#include <cmath>
#include <cstring>
#include <iostream>
// #pragma STDC FENV_ACCESS ON

int main()
{
    std::cout << "expm1(1) = " << std::expm1(1) << '\n'
              << "Interest earned in 2 days on $100, compounded daily at 1%\n"
              << "    on a 30/360 calendar = "
              << 100 * std::expm1(2 * std::log1p(0.01 / 360)) << '\n'
              << "exp(1e-16)-1 = " << std::exp(1e-16) - 1
              << ", but expm1(1e-16) = " << std::expm1(1e-16) << '\n';

    // special values
    std::cout << "expm1(-0) = " << std::expm1(-0.0) << '\n'
              << "expm1(-Inf) = " << std::expm1(-INFINITY) << '\n';

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

    std::cout << "expm1(710) = " << std::expm1(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 🌈

expm1(1) = 1.71828
Interest earned in 2 days on $100, compounded daily at 1%
    on a 30/360 calendar = 0.00555563
exp(1e-16)-1 = 0, but expm1(1e-16) = 1e-16
expm1(-0) = -0
expm1(-Inf) = -1
expm1(710) = inf
    errno == ERANGE: Result too large
    FE_OVERFLOW raised

std::expm1,...std::expm1l(3)