D.2 complex

Complex numbers are represented according to the ISO C standard as arrays of two IEEE double precision floating point numbers of 8 bytes each, with the number representing the real part first.

A small selection of operations on complex numbers is available by function calls of the form library('complex',f). These functions are implemented by the host system’s C library.

One example is library('complex','create') which takes a pair of floating point numbers (x,y) to a complex number whose real part is x and whose imaginary part is y. See math for information about constructing floating point numbers.

Other than that, the complex library functions f fall into three main groups, which are the real valued unary operations, the complex valued unary operations, and the complex valued binary operations. All of these operations are designated by their standard C names as documented elsewhere, such as the GNU libc reference manual, except as noted.

• real valued unary operations

creal cimag cabs carg

• complex valued unary operations

ccos cexp clog conj csin csqrt ctan csinh ccosh ctanh casinh cacosh catanh casin cacos catan

• complex valued binary operations

cpow vid bus mul add sub div

The last four correspond to the C language operators *, +, -, and / for complex numbers. The functions named vid and bus are similar to div and sub, respectively, but with the operands interchanged. That is,

library('complex','vid') (x,y)

is equivalent to

library('complex','div') (y,x)

All functions in this library taking complex numbers as input may also operate on real numbers, and binary operators can have either or both operands real. For real operands, a value of zero is inferred as the imaginary part. The result type of the function is the same regardless.

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