---
name: "clogl"
section: "3"
platform: "freebsd"
package: "base"
version: "16.0-CURRENT-20261027-61c70dc16a79"
release: "FreeBSD 16.0-CURRENT (2026-10-27)"
platforms: ["linux", "freebsd"]
url: "https://new.carta.tech/clog/3"
---

# clogl(3)

complex natural logarithm functions

Part of [clog(3)](/clog/3.md).

## NAME

**clog**, **clogf** and **clogl** – complex natural logarithm functions

## 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

The **clog**(), **clogf**(), and **clogl**() functions compute the complex natural logarithm of *z*. with a branch cut along the negative real axis .

## RETURN VALUES

The **clog**() function returns the complex natural logarithm value, in the range of a strip mathematically unbounded along the real axis and in the interval \[-I\*  , +I\*  \] along the imaginary axis. The function satisfies the relationship: **clog**(**conj**(*z*, *Fc*) = **conj**(**clog**(*z*, *Fc*).

| | | |
| --- | --- | --- |
| **Argument** | **Return** **value** | **Comment** |
| -0 + I\*0 | - + I\* | Divide-by-zero exception |
|  |  | raised |
| +0 + I\*0 | - + I\*0 | Divide by zero exception |
|  |  | raised |
| x + I\* | + + I\*/2 | For finite x |
| x + I\* | + I\* | Optionally raises invalid |
|  |  | floating-point exception |
|  |  | for finite x |
| - + I\*y | + + I\* | For finite positive-signed y |
| + + I\*y | + + I\*0 | For finite positive-signed y |
| - + I\* | + + I\*3/4 |
| + + I\* | + + I\*/4 |
| + I\* | + + I\* |
| + I\*y | + I\* | Optionally raises invalid |
|  |  | floating-point exception |
|  |  | for finite y |
| + I\* | + + I\* |
| + I\* | + I\* |

## SEE ALSO

[complex(3)](/complex/3.md), [log(3)](/log/3.md), [math(3)](/math/3.md)

## STANDARDS

The **clog**(), **cexpf**(), and **clogl**() functions conform to ISO/IEC 9899:1999 (“ISO C99”).