NAME

cexp, cexpf, cexpl —

complex exponential functions

LIBRARY

Math Library (libm, -lm)

SYNOPSIS

#include <complex.h>

double complex
cexp(double complex z);

float complex
cexpf(float complex z);

long double complex
cexpl(long double complex z);

DESCRIPTION

The cexp(), cexpf(), and cexpl() functions compute the complex exponential of z, also known as cis(z).

RETURN VALUES

For real numbers x and y, cexp() behaves according to Euler's formula:

cexp(x + I*y) = (e**x * cos(y)) + (I * e**x * sin(y))

Generally speaking, infinities, zeroes and NaNs are handled as would be expected from this identity given the usual rules of floating-point arithmetic. However, care is taken to avoid generating NaNs when they are not deserved. For example, mathematically we expect that cimag(cexp(x + I*0)); = 0 regardless of the value of x, and cexp() preserves this identity even if x is infinity or NaN. Likewise, cexp(-infinity + I*y) = 0 and creal(cexp(infinity + I*y)); = infinity for any y (even though the latter property is only mathematically true for representable y.) If y is not finite, the sign of the result is indeterminate.

STANDARDS

The cexp(), cexpf(), and cexpl() functions conform to ISO/IEC 9899:1999 (“ISO C99”).