---
name: "clog"
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/clog/3"
---

# clog(3)

natural logarithm of a complex number

## NAME

clog, clogf, clogl - natural logarithm of a complex number

## LIBRARY

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

## SYNOPSIS

```
#include <complex.h>
```

**double complex clog(double complex** *z***);** **float complex clogf(float complex** *z***);** **long double complex clogl(long double complex** *z***);**

## DESCRIPTION

These functions calculate the complex natural logarithm of *z*, with a branch cut along the negative real axis.

The logarithm **clog**() is the inverse function of the exponential [**cexp**(3)](/cexp/3.md). Thus, if *y = clog(z)*, then *z = cexp(y)*. The imaginary part of *y* is chosen in the interval \[-pi,pi\].

One has:

```
clog(z) = log(cabs(z)) + I * carg(z)
```

Note that *z* close to zero will cause an overflow.

## ATTRIBUTES

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

| | | |
| --- | --- | --- |
| **Interface** | **Attribute** | **Value** |
| **clog**(), **clogf**(), **clogl**() | Thread safety | MT-Safe |

## STANDARDS

C11, POSIX.1-2008.

## HISTORY

glibc 2.1. C99, POSIX.1-2001.

## SEE ALSO

[**cabs**(3)](/cabs/3.md), [**cexp**(3)](/cexp/3.md), [**clog10**(3)](/clog10/3.md), [**clog2**(3)](/clog2/3.md), [**complex**(7)](/complex/7.md)