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Showing content from http://en.cppreference.com/w/c/numeric/math/../../io/../error/../numeric/math/../complex/clog.html below:

clogf, clog, clogl - cppreference.com

#define log( z )

1-3) Computes the complex natural (base-e) logarithm of z with branch cut along the negative real axis.

Type-generic macro: If

has type

,

is called. if

has type

,

is called, if

has type

,

is called. If

is real or integer, then the macro invokes the corresponding real function (

,

,

). If

is imaginary, the corresponding complex number version is called.

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.

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

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

#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 C11
    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

• 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)

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