clogf, clog, clogl

[edit] Parameters

[edit] 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.

[edit] 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

[edit] 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

[edit] Example

#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));
}

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

[edit] References

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