phase number → phase

number — a number.

phase — a number.

phase returns the phase of number (the angle part of its polar representation) in radians, in the range −π (exclusive) if minus zero is not supported, or −π (inclusive) if minus zero is supported, to π (inclusive). The phase of a positive real number is zero; that of a negative real number is π. The phase of zero is defined to be zero.

If number is a complex float, the result is a float of the same type as the components of number. If number is a float, the result is a float of the same type. If number is a rational or a complex rational, the result is a single float.

The branch cut for phase lies along the negative real axis, continuous with quadrant II. The range consists of that portion of the real axis between −π (exclusive) and π (inclusive).

The mathematical definition of phase is as follows:

(phase x) = (atan (imagpart x) (realpart x))

(phase 1) → 0.0s0 
(phase 0) → 0.0s0 
(phase (cis 30)) → -1.4159266 
(phase #c(0 1)) → 1.5707964

Should signal type-error if its argument is not a number. Might signal arithmetic-error.

Section 12.1.3.3 (Rule of Float Substitutability)