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Showing content from https://en.cppreference.com/w/cpp/language/../error/error_code/../../../cpp/numeric/math/log1p.html below:

std::log1p, std::log1pf, std::log1pl - cppreference.com

(1) float       log1p ( float num );

double      log1p ( double num );

long double log1p ( long double num ); (until C++23)

/*floating-point-type*/
            log1p ( /*floating-point-type*/ num );

(since C++23)
(constexpr since C++26)

float       log1pf( float num );

(2) (since C++11)
(constexpr since C++26)

long double log1pl( long double num );

(3) (since C++11)
(constexpr since C++26) template< /*math-floating-point*/ V >

constexpr /*deduced-simd-t*/<V>

            log1p ( const V& v_num ); (S) (since C++26)

template< class Integer >
double      log1p ( Integer num );

(A) (constexpr since C++26) 1-3)

Computes the

natural (base-e) logarithm

of

1 + num

. This function is more precise than the expression

std::log(1 + num)

if

num

is close to zero.

The library provides overloads of std::log1p 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) [edit] Parameters num - floating-point or integer value [edit] Return value

If no errors occur ln(1+num) is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a pole error 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.

[edit] Error handling

Errors are reported as specified in math_errhandling.

Domain error occurs if num is less than -1.

Pole error may occur if num is -1.

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

[edit] 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.

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::log1p(num) has the same effect as std::log1p(static_cast<double>(num)).

[edit] Example 
#include <cerrno>
#include <cfenv>
#include <cmath>
#include <cstring>
#include <iostream>
// #pragma STDC FENV_ACCESS ON
 
int main()
{
    std::cout << "log1p(0) = " << log1p(0) << '\n'
              << "Interest earned in 2 days on $100, compounded daily at 1%\n"
              << "    on a 30/360 calendar = "
              << 100 * expm1(2 * log1p(0.01 / 360)) << '\n'
              << "log(1+1e-16) = " << std::log(1 + 1e-16)
              << ", but log1p(1e-16) = " << std::log1p(1e-16) << '\n';
 
    // special values
    std::cout << "log1p(-0) = " << std::log1p(-0.0) << '\n'
              << "log1p(+Inf) = " << std::log1p(INFINITY) << '\n';
 
    // error handling
    errno = 0;
    std::feclearexcept(FE_ALL_EXCEPT);
 
    std::cout << "log1p(-1) = " << std::log1p(-1) << '\n';
 
    if (errno == ERANGE)
        std::cout << "    errno == ERANGE: " << std::strerror(errno) << '\n';
    if (std::fetestexcept(FE_DIVBYZERO))
        std::cout << "    FE_DIVBYZERO raised\n";
}

Possible output:

log1p(0) = 0
Interest earned in 2 days on $100, compounded daily at 1%
    on a 30/360 calendar = 0.00555563
log(1+1e-16) = 0, but log1p(1e-16) = 1e-16
log1p(-0) = -0
log1p(+Inf) = inf
log1p(-1) = -inf
    errno == ERANGE: Result too large
    FE_DIVBYZERO raised
[edit] See also computes natural (base e) logarithm (\({\small\ln{x}}\)ln(x))
(function) [edit] computes common (base 10) logarithm (\({\small\log_{10}{x}}\)log10(x))
(function) [edit] base 2 logarithm of the given number (\({\small\log_{2}{x}}\)log2(x))
(function) [edit] returns e raised to the given power, minus 1 (\({\small e^x-1}\)ex-1)
(function) [edit]

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