CLOG 3CW "12 August 2009" "mathcw-1.00"

Table of contents


NAME

clogf, clog, clogl, clogw, clogq, clogll, clogdf, clogd, clogdl, clogdll - complex natural (base-e) logarithm function

SYNOPSIS

cc [ flags ] -I/usr/local/include file(s) -L/usr/local/lib -lmcw [ ... ]

#include <mathcw.h>

#include <complexcw.h>

extern float complex clogf (float complex z);

extern double complex clog (double complex z);

extern long double complex clogl (long double complex z);

extern __float80 complex clogw (__float80 complex z);

extern __float128 complex clogq (__float128 complex z);

extern long_long_double complex clogll (long_long_double complex z);

extern decimal_float complex clogdf (decimal_float complex z);

extern decimal_double complex clogd (decimal_double complex z);

extern decimal_long_double complex clogdl (decimal_long_double complex z);

extern decimal_long_long_double complex clogdll (decimal_long_long_double complex z);

NB: Functions with prototypes containing underscores in type names may be available only with certain extended compilers.


DESCRIPTION

Compute the complex natural logarithm of the complex value z, that is, the logarithm to the base e (= 2.718281828...) of z.

If the argument in Cartesian form is z = x + y I, where x and y are real, then in polar form, z = r exp(t I), where r = |z| = cabs(z) = hypot(x, y) and t = carg(z) = atan2(y, x). We then have clog(z) = clog(r exp(t I)) = log(r) + t I. Accuracy of the complex logarithm function then depends on that of three real functions.

When compiler support for complex types is lacking, consider using the cx family of functions instead.


BRANCH CUTS

To be written.

RETURN VALUES

Return the complex natural logarithm.

ERRORS

For finite complex arguments, the returned value is complex and finite. For infinite arguments, at least one component of the returned value is Infinity. Otherwise, for NaN arguments, at least one component of the returned value is a quiet NaN.

SEE ALSO

atan2(3CW), cabs(3CW), carg(3CW), cexp(3CW), cexpm1(3CW), clog1p(3CW), hypot(3CW), log(3CW), log1p(3CW).