clogf, clog, clogl - cppreference.com (original) (raw)

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

1. 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

• 1 Parameters
• 2 Return value
• 3 Error handling and special values
• 4 Notes
• 5 Example
• 6 References
• 7 See also

[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("2log(i) = %.1f%+fi\n", creal(2z), cimag(2z));   double complex z2 = clog(sqrt(2)/2 + sqrt(2)/2I); // r = 1, θ = pi/4 printf("4log(sqrt(2)/2+sqrt(2)i/2) = %.1f%+fi\n", creal(4z2), 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:

2log(i) = 0.0+3.141593i 4log(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

• 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)

[edit] See also