Module ComplexL

module ComplexL: sig .. end

type t

The type of long double complex values

val make : LDouble.t -> LDouble.t -> t

make x y creates the long double complex value x + y * i

val of_complex : Stdlib.Complex.t -> t

create a long double complex from a Complex.t

val to_complex : t -> Stdlib.Complex.t

Convert a long double complex to a Complex.t. The real and imaginary components are converted by calling LDouble.to_float which can produce unspecified results.

val zero : t

0 + i0

val one : t

1 + i0

val i : t

0 + i

val re : t -> LDouble.t

return the real part of the long double complex

val im : t -> LDouble.t

return the imaginary part of the long double complex

val neg : t -> t

Unary negation

val conj : t -> t

Conjugate: given the complex x + i.y, returns x - i.y.

val add : t -> t -> t

Addition

val sub : t -> t -> t

Subtraction

val mul : t -> t -> t

Multiplication

val div : t -> t -> t

Division

val inv : t -> t

Multiplicative inverse (1/z).

val sqrt : t -> t

Square root.

val norm2 : t -> LDouble.t

Norm squared: given x + i.y, returns x^2 + y^2.

val norm : t -> LDouble.t

Norm: given x + i.y, returns sqrt(x^2 + y^2).

val polar : LDouble.t -> LDouble.t -> t

polar norm arg returns the complex having norm norm and argument arg.

val arg : t -> LDouble.t

Argument. The argument of a complex number is the angle in the complex plane between the positive real axis and a line passing through zero and the number.

val exp : t -> t

Exponentiation. exp z returns e to the z power.

val log : t -> t

Natural logarithm (in base e).

val pow : t -> t -> t

Power function. pow z1 z2 returns z1 to the z2 power.