clogf, clog, clogl

 

C

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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(C11)

Technical Specifications

Symbol index

 

Numerics

Common mathematical functions

Floating-point environment(C99)

Pseudo-random number generation

Complex number arithmetic(C99)

Type-generic math(C99)

Bit manipulation(C23)

Checked integer arithmetic(C23)

 

Complex number arithmetic

Types and the imaginary constant
complex (C99) _Complex_I (C99)     CMPLX (C11)	imaginary (C99) _Imaginary_I (C99) I (C99)
Manipulation
cimag (C99) creal (C99) carg (C99)	cabs (C99) conj (C99) cproj (C99)
Power and exponential functions
cexp (C99) clog (C99)	cpow (C99) csqrt (C99)
Trigonometric functions
ccos (C99) csin (C99) ctan (C99)	cacos (C99) casin (C99) catan (C99)
Hyperbolic functions
ccosh (C99) csinh (C99) ctanh (C99)	cacosh (C99) casinh (C99) catanh (C99)

 

Defined in header <complex.h>
floatcomplex       clogf(floatcomplex z );	(1)	(since C99)
doublecomplex      clog(doublecomplex z );	(2)	(since C99)
longdoublecomplex clogl(longdoublecomplex z );	(3)	(since C99)
Defined in header <tgmath.h>
#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 longdoublecomplex, clogl is called. if z has type doublecomplex, clog is called, if z has type floatcomplex, 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){doublecomplex z = clog(I);// r = 1, θ = pi/2printf("2*log(i) = %.1f%+fi\n", creal(2*z), cimag(2*z));   doublecomplex z2 = clog(sqrt(2)/2+sqrt(2)/2*I);// r = 1, θ = pi/4printf("4*log(sqrt(2)/2+sqrt(2)i/2) = %.1f%+fi\n", creal(4*z2), cimag(4*z2));   doublecomplex z3 = clog(-1);// r = 1, θ = piprintf("log(-1+0i) = %.1f%+fi\n", creal(z3), cimag(z3));   doublecomplex z4 = clog(conj(-1));// or clog(CMPLX(-1, -0.0)) in C11printf("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

• C11 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)

• C99 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 (C99)(C99)(C99)	computes the complex base-e exponential (function)
loglogflogl (C99)(C99)	computes natural (base-e) logarithm (\({\small \ln{x} }\)ln(x)) (function)
C++ documentation for log