# clogf, clog, clogl

< c‎ | numeric‎ | complex

C
 Language Standard Library Type support Dynamic memory management Error handling Program utilities Date and time utilities Strings library Algorithms Numerics Input/output support Localization support Thread support (C11) Atomic operations (C11)

Complex number arithmetic
Types and the imaginary constant
Manipulation
Power and exponential functions
 cexp clog
Trigonometric functions
Hyperbolic functions

 Defined in header `` float complex       clogf( float complex z ); (1) (since C99) double complex      clog( double complex z ); (2) (since C99) long double complex clogl( long double complex z ); (3) (since C99) Defined in header `` #define log( z ) (4) (since C99)
1-3) Computes the complex natural (base-e) logarithm of `z` with branch cut along the negative real axis.
4) Type-generic macro: If `z` has type long double complex, `clogl` is called. if `z` has type double complex, `clog` is called, if `z` has type float complex, `clogf` is called. If `z` is real or integer, then the macro invokes the corresponding real function (logf, log, logl). If `z` is imaginary, the corresponding complex number version is called.

## Contents

### Parameters

 z - complex argument

### Return value

If no errors occur, the complex natural logarithm of `z` is returned, in the range of a strip in the interval [−iπ, +iπ] along the imaginary axis and mathematically unbounded along the real axis.

### Error handling and special values

Errors are reported consistent with math_errhandling

If the implementation supports IEEE floating-point arithmetic,

• The function is continuous onto the branch cut taking into account the sign of imaginary part
• clog(conj(z)) == conj(clog(z))
• If `z` is `-0+0i`, the result is `-∞+πi` and FE_DIVBYZERO is raised
• If `z` is `+0+0i`, the result is `-∞+0i` and FE_DIVBYZERO is raised
• If `z` is `x+∞i` (for any finite x), the result is `+∞+πi/2`
• If `z` is `x+NaNi` (for any finite x), the result is `NaN+NaNi` and FE_INVALID may be raised
• If `z` is `-∞+yi` (for any finite positive y), the result is `-∞+πi`
• If `z` is `+∞+yi` (for any finite positive y), the result is `-∞+0i`
• If `z` is `-∞+∞i`, the result is `+∞+3πi/4`
• If `z` is `+∞+∞i`, the result is `+∞+πi/4`
• If `z` is `±∞+NaNi`, the result is `+∞+NaNi`
• If `z` is `NaN+yi` (for any finite y), the result is `NaN+NaNi` and FE_INVALID may be raised
• If `z` is `NaN+∞i`, the result is `+∞+NaNi`
• If `z` is `NaN+NaNi`, the result is `NaN+NaNi`