NAME cplxexp, exp, log, log10, pow, sqrt - functions in the C++ complex number math library SYNOPSIS #include <complex.h> class complex { public: friend complex exp(const complex); friend complex log(const complex); friend complex log10(const complex); friend complex pow(double base, const complex exp); friend complex pow(const complex base, int exp); friend complex pow(const complex base, double exp); friend complex pow(const complex base, const complex exp); friend complex sqrt(const complex); ... // remainder not shown here }; DESCRIPTION These functions are versions of the corresponding floating- point math library functions, overloaded for use with com- plex numbers. complex z = exp(x) Returns e raised to the x power, where x is a complex number, and e is the base of the natural logarithms. complex z = log(x) Returns the natural logarithm (base e) of x, where x is a complex number. complex z = log10(x) Returns the common logarithm (base 10) of x, where x is a complex number. complex z = pow(x, y) Returns x raised to the y power, where x or y (or both) are complex numbers. The library provides versions of this function optimized for various combinations of integer, floating-point, and complex arguments. complex z = sqrt(x) Returns the square root of x, where x is a complex number. The real part of the result will be non- negative. SEE ALSO cplx.intro(3C++), cartpol(3C++), cplxerr(3C++), cplxops(3C++), cplxtrig(3C++), intro(2), C++ Library Refer- ence Manual, Chapter 3, "The Complex Arithmetic Library." DIAGNOSTICS exp(x) If the real part of x is small enough or the imaginary part is large enough to cause overflow, exp() returns (0,0). If the real part is large enough to cause over- flow, returns a value depending on the sine and cosine of the imaginary part of x: ______________________________________________ | x.imag()| x.imag()| returned value | |_________|__________|________________________| | sin>=0 | cos>=0 | (HUGE_VAL, HUGE_VAL) | |_________|__________|________________________| | sin< 0 | cos>=0 | (HUGE_VAL, -HUGE_VAL)| |_________|__________|________________________| | sin>=0 | cos< 0 | (-HUGE_VAL, HUGE_VAL) | |_________|__________|________________________| | sin< 0 | cos< 0 | (-HUGE_VAL, -HUGE_VAL)| |_________|__________|________________________| In all cases, errno is set to ERANGE (see intro(2)). log(x), log10(x) If x is (0,0), returns (-HUGE_VAL, 0), sets errno to EDOM (see intro(2)), and generates a SING error (see cplxerr(3C++)).
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