clogf, clog, clogl
From cppreference.com
| Defined in header <complex.h>
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| (1) | (since C99) | |
| (2) | (since C99) | |
| (3) | (since C99) | |
| Defined in header <tgmath.h>
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| #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 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
zis-0+0i, the result is-∞+πiand FE_DIVBYZERO is raised - If
zis+0+0i, the result is-∞+0iand FE_DIVBYZERO is raised - If
zisx+∞i(for any finite x), the result is+∞+πi/2 - If
zisx+NaNi(for any finite x), the result isNaN+NaNiand FE_INVALID may be raised - If
zis-∞+yi(for any finite positive y), the result is+∞+πi - If
zis+∞+yi(for any finite positive y), the result is+∞+0i - If
zis-∞+∞i, the result is+∞+3πi/4 - If
zis+∞+∞i, the result is+∞+πi/4 - If
zis±∞+NaNi, the result is+∞+NaNi - If
zisNaN+yi(for any finite y), the result isNaN+NaNiand FE_INVALID may be raised - If
zisNaN+∞i, the result is+∞+NaNi - If
zisNaN+NaNi, the result isNaN+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 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
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
| (C99)(C99)(C99) |
computes the complex base-e exponential (function) |
| (C99)(C99) |
computes natural (base-e) logarithm (ln(x)) (function) |
| C++ documentation for log
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