clogf, clog, clogl

 

C

Language

Headers

Type support

Program utilities

Variadic function support

Error handling

Dynamic memory management

Strings library

Algorithms

Numerics

Date and time utilities

Input/output support

Localization support

Concurrency support (哋它亢11)

Technical Specifications

Symbol index

 

Numerics

Common mathematical functions

Floating-point environment (哋它亢99)

Pseudo-random number generation

Complex number arithmetic (哋它亢99)

Type-generic math (哋它亢99)

 

Complex number arithmetic

Types and the imaginary constant
complex (哋它亢99) _Complex_I (哋它亢99)     CMPLX (哋它亢11)	imaginary (哋它亢99) _Imaginary_I (哋它亢99) I (哋它亢99)
Manipulation
cimag (哋它亢99) creal (哋它亢99) carg (哋它亢99)	cabs (哋它亢99) conj (哋它亢99) cproj (哋它亢99)
Power and exponential functions
cexp (哋它亢99) clog (哋它亢99)	cpow (哋它亢99) csqrt (哋它亢99)
Trigonometric functions
ccos (哋它亢99) csin (哋它亢99) ctan (哋它亢99)	cacos (哋它亢99) casin (哋它亢99) catan (哋它亢99)
Hyperbolic functions
ccosh (哋它亢99) csinh (哋它亢99) ctanh (哋它亢99)	cacosh (哋它亢99) casinh (哋它亢99) catanh (哋它亢99)

 

Defined in header <complex.h>
float complex       clogf( float complex z );	(1)	(since 哋它亢99)
double complex      clog( double complex z );	(2)	(since 哋它亢99)
long double complex clogl( long double complex z );	(3)	(since 哋它亢99)
Defined in header <tgmath.h>
#define log( z )	(4)	(since 哋它亢99)

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.

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

Notes

The natural logarithm of a complex number z with polar coordinate components (r,θ) equals ln r + i(θ+2nπ), with the principal value ln r + iθ

Example

Run this code

#include <stdio.h>
#include <math.h>
#include <complex.h>
 
int main(void)
{
    double complex z = clog(I); // r = 1, θ = pi/2
    printf("2*log(i) = %.1f%+fi\n", creal(2*z), cimag(2*z));
 
    double complex z2 = clog(sqrt(2)/2 + sqrt(2)/2*I); // r = 1, θ = pi/4
    printf("4*log(sqrt(2)/2+sqrt(2)i/2) = %.1f%+fi\n", creal(4*z2), cimag(4*z2));
 
    double complex z3 = clog(-1); // r = 1, θ = pi
    printf("log(-1+0i) = %.1f%+fi\n", creal(z3), cimag(z3));
 
    double complex z4 = clog(conj(-1)); // or clog(CMPLX(-1, -0.0)) in 哋它亢11
    printf("log(-1-0i) (the other side of the cut) = %.1f%+fi\n", creal(z4), cimag(z4));
}

Output:

2*log(i) = 0.0+3.141593i
4*log(sqrt(2)/2+sqrt(2)i/2) = 0.0+3.141593i
log(-1+0i) = 0.0+3.141593i
log(-1-0i) (the other side of the cut) = 0.0-3.141593i

References

• 哋它亢11 standard (ISO/IEC 9899:2011):

• 7.3.7.2 The clog functions (p: 195)

• 7.25 Type-generic math <tgmath.h> (p: 373-375)

• G.6.3.2 The clog functions (p: 543-544)

• G.7 Type-generic math <tgmath.h> (p: 545)

• 哋它亢99 standard (ISO/IEC 9899:1999):

• 7.3.7.2 The clog functions (p: 176-177)

• 7.22 Type-generic math <tgmath.h> (p: 335-337)

• G.6.3.2 The clog functions (p: 478-479)

• G.7 Type-generic math <tgmath.h> (p: 480)

See also

cexpcexpfcexpl (哋它亢99)(哋它亢99)(哋它亢99)	computes the complex base-e exponential (function)
loglogflogl (哋它亢99)(哋它亢99)	computes natural (base-e) logarithm (\({\small \ln{x} }\)ln(x)) (function)