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  ANSI Common Lisp   12 Numbers   12.2 Dictionary of Numbers

12.2.49 phase Function

Syntax:
phase number    phase

Arguments and Values:
number - a number.

phase - a number.

Description:
phase returns the phase of number (the angle part of its polar representation) in radians, in the range - pi (exclusive) if minus zero is not supported, or - pi (inclusive) if minus zero is supported, to pi (inclusive). The phase of a positive real number is zero; that of a negative real number is pi . 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 - pi (exclusive) and  pi (inclusive).

The mathematical definition of phase is as follows:

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

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

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

See Also:
Section 12.1.3.3 Rule of Float Substitutability

Allegro CL Implementation Details:
None.

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