Sun Studio 12 Update 1: C++ User's Guide

15.3 Mathematical Functions

The complex arithmetic library provides a number of mathematical functions. Some are peculiar to complex numbers; the rest are complex-number versions of functions in the standard C mathematical library.

All of these functions produce a result for every possible argument. If a function cannot produce a mathematically acceptable result, it calls complex_error and returns some suitable value. In particular, the functions try to avoid actual overflow and call complex_error with a message instead. The following tables describe the remainder of the complex arithmetic library functions.

Note –

The implementation of the sqrt and atan2 functions is aligned with the C99 csqrt Annex G specification.

Table 15–1 Complex Arithmetic Library Functions


Complex Arithmetic Library Function	Description
`double abs(const complex)`	Returns the magnitude of a complex number.
`double arg(const complex)`	Returns the angle of a complex number.
`complex conj(const complex)`	Returns the complex conjugate of its argument.
`double imag(const complex&)`	Returns the imaginary part of a complex number.
`double norm(const complex)`	Returns the square of the magnitude of its argument. Faster than `abs`, but more likely to cause an overflow. For comparing magnitudes.
`complex polar(double mag, double ang=0.0)`	Takes a pair of polar coordinates that represent the magnitude and angle of a complex number and returns the corresponding complex number.
`double real(const complex&)`	Returns the real part of a complex number.

Table 15–2 Complex Mathematical and Trigonometric Functions


Complex Arithmetic Library Function	Description
`complex acos(const complex)`	Returns the angle whose cosine is its argument.
`complex asin(const complex)`	Returns the angle whose sine is its argument.
`complex atan(const complex)`	Returns the angle whose tangent is its argument.
`complex cos(const complex)`	Returns the cosine of its argument.
`complex cosh(const complex)`	Returns the hyperbolic cosine of its argument.
`complex exp(const complex)`	Computes `e**x`, where `e` is the base of the natural logarithms, and `x` is the argument given to `exp`.
`complex log(const complex)`	Returns the natural logarithm of its argument.
`complex log10(const complex)`	Returns the common logarithm of its argument.
`complex pow(double b, const complex exp)` `complex pow(const complex b, int exp)` `complex pow(const complex b, double exp)` `complex pow(const complex b, const` `complex exp)`	Takes two arguments: `pow(b, exp)`. It raises `b` to the power of `exp`.
`complex sin(const complex)`	Returns the sine of its argument.
`complex sinh(const complex)`	Returns the hyperbolic sine of its argument.
`complex sqrt(const complex)`	Returns the square root of its argument.
`complex tan(const complex)`	Returns the tangent of its argument.
`complex tanh(const complex)`	Returns the hyperbolic tangent of its argument.