Defined in header `<math.h>` | ||
---|---|---|

float log1pf( float arg ); | (1) | (since C99) |

double log1p( double arg ); | (2) | (since C99) |

long double log1pl( long double arg ); | (3) | (since C99) |

Defined in header `<tgmath.h>` | ||

#define log1p( arg ) | (4) | (since C99) |

1-3) Computes the natural (base

`e`

) logarithm of `1+arg`

. This function is more precise than the expression `log(1+arg)`

if `arg`

is close to zero.
4) Type-generic macro: If

`arg`

has type `long double`

, `log1pl`

is called. Otherwise, if `arg`

has integer type or the type `double`

, `log1p`

is called. Otherwise, `log1pf`

is called.arg | - | floating point 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.

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 `expm1`

and `log1p`

are useful for financial calculations, for example, when calculating small daily interest rates: (1+x)n

-1 can be expressed as `expm1(n * log1p(x))`

. These functions also simplify writing accurate inverse hyperbolic functions.

#include <stdio.h> #include <math.h> #include <float.h> #include <errno.h> #include <fenv.h> #pragma STDC FENV_ACCESS ON int main(void) { printf("log1p(0) = %f\n", log1p(0)); printf("Interest earned in 2 days on $100, compounded daily at 1%%\n" " on a 30/360 calendar = %f\n", 100*expm1(2*log1p(0.01/360))); printf("log(1+1e-16) = %g, but log1p(1e-16) = %g\n", log(1+1e-16), log1p(1e-16)); // special values printf("log1p(-0) = %f\n", log1p(-0.0)); printf("log1p(+Inf) = %f\n", log1p(INFINITY)); //error handling errno = 0; feclearexcept(FE_ALL_EXCEPT); printf("log1p(-1) = %f\n", log1p(-1)); if(errno == ERANGE) perror(" errno == ERANGE"); if(fetestexcept(FE_DIVBYZERO)) puts(" FE_DIVBYZERO raised"); }

Possible output:

log1p(0) = 0.000000 Interest earned in 2 days on $100, compounded daily at 1% on a 30/360 calendar = 0.005556 log(1+1e-16) = 0, but log1p(1e-16) = 1e-16 log1p(-0) = -0.000000 log1p(+Inf) = Inf log1p(-1) = -Inf errno == ERANGE: Result too large FE_DIVBYZERO raised

- C11 standard (ISO/IEC 9899:2011):
- 7.12.6.9 The log1p functions (p: 245)
- 7.25 Type-generic math <tgmath.h> (p: 373-375)
- F.10.3.9 The log1p functions (p: 522)
- C99 standard (ISO/IEC 9899:1999):
- 7.12.6.9 The log1p functions (p: 226)
- 7.22 Type-generic math <tgmath.h> (p: 335-337)
- F.9.3.9 The log1p functions (p: 459)

(C99)(C99) | computes natural (base-e) logarithm (\({\small \ln{x} }\)ln(x)) (function) |

(C99)(C99) | computes common (base-10) logarithm (\({\small \log_{10}{x} }\)log_{10}(x)) (function) |

(C99)(C99)(C99) | computes base-2 logarithm (\({\small \log_{2}{x} }\)log_{2}(x)) (function) |

(C99)(C99)(C99) | computes e raised to the given power, minus one (\({\small e^x-1}\)e^{x}-1) (function) |

C++ documentation for `log1p` |

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