# Manual Pages  — CLOG

### 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* π , +I* π ] along the imaginary axis. The function satisfies the relationship: clog(conj(z)) = conj(clog(z)).

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