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# std::log1p

From cppreference.com
< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
float log1p( float arg ); | (1) | (since C++11)
double log1p( double arg ); | (2) | (since C++11)
long double log1p( long double arg ); | (3) | (since C++11)
double log1p( Integral arg ); | (4) | (since C++11)

1-3) Computes the natural (base e) logarithm of 1+arg. This function is more precise than the expression std::log(1+arg) if `arg` is close to zero.
4) A set of overloads or a function template accepting an argument of any integral type. Equivalent to 2) (the argument is cast to double).

### [edit] Parameters

arg | - | value of floating-point or Integral type

### [edit] Return value

If no errors occur ln(1+arg) 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 `arg` is less than -1.

Pole error may occur if `arg` is -1.

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

- If the argument is ±0, it is returned unmodified
- If the argument is -1, -∞ is returned and FE_DIVBYZERO is raised.
- If the argument is less than -1, NaN is returned and FE_INVALID is raised.
- If the argument is +∞, +∞ is returned
- If the argument is NaN, NaN is returned

### [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.

### [edit] Example

Run this code

    #include <iostream>
    #include <cfenv>
    #include <cmath>
    #include <cerrno>
    #include <cstring>
    #pragma STDC FENV_ACCESS ON
    int main()
    {
        std::cout << "log1p(0) = " << log1p(0) << '\n'
                  << "Interest earned in 2 days on 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)
                  << " 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 on $100, compounded daily at 1%
     on a 30/360 calendar = 0.00555563
    log(1+1e-16) = 0 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

log | computes natural (base e) logarithm (to base e) (ln(x)) (function) [edit]
log10 | computes common (base 10) logarithm (log10(x)) (function) [edit]
log2 (C++11) | base 2 logarithm of the given number (log2(x)) (function) [edit]
expm1 (C++11) | returns e raised to the given power, minus one (ex-1) (function) [edit]
C documentation for log1p

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