Defined in header `<cmath>` | ||
---|---|---|

float log1p ( float arg ); float log1pf( float arg ); | (1) | (since C++11) |

double log1p ( double arg ); | (2) | (since C++11) |

long double log1p ( long double arg ); long double log1pl( long double arg ); | (3) | (since C++11) |

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`

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

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.

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

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.

#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

(C++11)(C++11) | computes natural (base e) logarithm (ln(x)) (function) |

(C++11)(C++11) | computes common (base 10) logarithm (log_{10}(x)) (function) |

(C++11)(C++11)(C++11) | base 2 logarithm of the given number (log_{2}(x)) (function) |

(C++11)(C++11)(C++11) | returns e raised to the given power, minus one (e^{x}-1) (function) |

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