std::log1p
| 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) |
arg is close to zero.Contents |
[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
#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
| computes natural (base e) logarithm (to base e) (ln(x)) (function) | |
| computes common (base 10) logarithm (log10(x)) (function) | |
| (C++11) |
base 2 logarithm of the given number (log2(x)) (function) |
| (C++11) |
returns e raised to the given power, minus one (ex-1) (function) |
| C documentation for log1p
| |