From 754bbf7a25a8dda49b5d08ef0d0443bbf5af0e36 Mon Sep 17 00:00:00 2001 From: Craig Jennings Date: Sun, 7 Apr 2024 13:41:34 -0500 Subject: new repository --- devdocs/c/numeric%2Fcomplex%2Fclog.html | 74 +++++++++++++++++++++++++++++++++ 1 file changed, 74 insertions(+) create mode 100644 devdocs/c/numeric%2Fcomplex%2Fclog.html (limited to 'devdocs/c/numeric%2Fcomplex%2Fclog.html') diff --git a/devdocs/c/numeric%2Fcomplex%2Fclog.html b/devdocs/c/numeric%2Fcomplex%2Fclog.html new file mode 100644 index 00000000..3cc04584 --- /dev/null +++ b/devdocs/c/numeric%2Fcomplex%2Fclog.html @@ -0,0 +1,74 @@ +

clogf, clog, clogl

Defined in header <complex.h> 
float complex       clogf( float complex z );
+		 (1) (since C99) 
double complex      clog( double complex z );
+		 (2) (since C99) 
long double complex clogl( long double complex 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 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,

+

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

#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

See also

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

+ © cppreference.com
Licensed under the Creative Commons Attribution-ShareAlike Unported License v3.0.
+ https://en.cppreference.com/w/c/numeric/complex/clog +

+
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