---
name: "log1p"
section: "3"
platform: "linux"
package: "man-pages"
version: "6.19-1"
release: "Arch Linux 2026-11-01"
platforms: ["linux", "freebsd"]
url: "https://new.carta.tech/log1p"
---

# log1p(3)

logarithm of 1 plus argument

## NAME

log1p, log1pf, log1pl -  logarithm of 1 plus argument

## LIBRARY

Math library (*libm*, *-lm*)

## SYNOPSIS

```
#include <math.h>
```

**double log1p(double** *x***);** **float log1pf(float** *x***);** **long double log1pl(long double** *x***);**

Feature Test Macro Requirements for glibc (see [**feature\_test\_macros**(7)](/feature_test_macros/7.md)):

```
log1p():
    _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
        || _XOPEN_SOURCE >= 500
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
```

**log1pf**(), **log1pl**():

```
    _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
```

## DESCRIPTION

These functions return a value equivalent to

```
log(1 + x)
```

The result is computed in a way that is accurate even if the value of *x* is near zero.

## RETURN VALUE

On success, these functions return the natural logarithm of *(1 + x)*.

If *x* is a NaN, a NaN is returned.

If *x* is positive infinity, positive infinity is returned.

If *x* is -1, a pole error occurs, and the functions return -**HUGE\_VAL**, -**HUGE\_VALF**, or -**HUGE\_VALL**, respectively.

If *x* is less than -1 (including negative infinity), a domain error occurs, and a NaN (not a number) is returned.

## ERRORS

See [**math\_error**(7)](/math_error/7.md) for information on how to determine whether an error has occurred when calling these functions.

The following errors can occur:

- Domain error: *x* is less than -1.

  *errno* is set to **EDOM** (but see BUGS). An invalid floating-point exception (**FE\_INVALID**) is raised.

- Pole error: *x* is -1.

  *errno* is set to **ERANGE** (but see BUGS). A divide-by-zero floating-point exception (**FE\_DIVBYZERO**) is raised.

## ATTRIBUTES

For an explanation of the terms used in this section, see [**attributes**(7)](/attributes/7.md).

| | | |
| --- | --- | --- |
| **Interface** | **Attribute** | **Value** |
| **log1p**(), **log1pf**(), **log1pl**() | Thread safety | MT-Safe |

## STANDARDS

C11, POSIX.1-2008.

## HISTORY

C99, POSIX.1-2001.

## BUGS

Before glibc 2.22, the glibc implementation did not set *errno* to **EDOM** when a domain error occurred.

Before glibc 2.22, the glibc implementation did not set *errno* to **ERANGE** when a range error occurred.

## SEE ALSO

[**exp**(3)](/exp/3.md), [**expm1**(3)](/expm1/3.md), [**log**(3)](/log/3.md)