NAME¶

std::log1p,std::log1pf,std::log1pl - std::log1p,std::log1pf,std::log1pl

Synopsis¶

Defined in header <cmath>
float log1p ( float arg ); (1) (since C++11)
float log1pf( float arg );
double log1p ( double arg ); (2) (since C++11)
long double log1p ( long double arg ); (3) (since C++11)
long double log1pl( long double arg );
double log1p ( IntegralType 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).

Parameters¶

arg - value of floating-point or Integral type

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.

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

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.

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

See also¶

log
logf computes natural (base e) logarithm (\({\small \ln{x} }\)ln(x))
logl (function)
(C++11)
(C++11)
log10
log10f computes common (base 10) logarithm (\({\small \log_{10}{x} }\)log[10](x))
log10l (function)
(C++11)
(C++11)
log2
log2f
log2l base 2 logarithm of the given number (\({\small \log_{2}{x} }\)log[2](x))
(C++11) (function)
(C++11)
(C++11)
expm1
expm1f
expm1l returns e raised to the given power, minus one (\({\small e^x-1}\)e^x-1)
(C++11) (function)
(C++11)
(C++11)