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 cl:functions:phase [2019/07/14 17:00] cl:functions:phase [2020/06/07 09:00] (current) Line 1: Line 1: + ====== Function PHASE ====== + + ====Syntax==== + * **phase** //number// → //phase// + + ====Arguments and Values==== + * //number// - a //​[[CL:​Glossary:​number]]//​. + * //phase// - a //​[[CL:​Glossary:​number]]//​. + + ====Description==== + **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 //​[[CL:​Glossary:​real]]//​ number is zero; that of a negative //​[[CL:​Glossary:​real]]//​ number is ''​π''​. The phase of zero is defined to be zero. + + If //number// is a //​[[CL:​Glossary:​complex float]]//, the result is a //​[[CL:​Glossary:​float]]//​ of the same //​[[CL:​Glossary:​type]]//​ as the components of //number//. If //number// is a //​[[CL:​Glossary:​float]]//,​ the result is a //​[[CL:​Glossary:​float]]//​ of the same //​[[CL:​Glossary:​type]]//​. If //number// is a //​[[CL:​Glossary:​rational]]//​ or a //​[[CL:​Glossary:​complex rational]]//,​ the result is a //​[[CL:​Glossary:​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''​) = ([[CL:​Functions:​atan]] ([[CL:​Functions:​imagpart]] ''​x''​) ([[CL:​Functions:​realpart]] ''​x''​))''​ + + ====Examples==== + <​blockquote> ​ + (phase 1) <​r>​0.0s0 + (phase 0) <​r>​0.0s0 + (phase ([[CL:​Functions:​cis]] 30)) <​r>​-1.4159266 + (phase #c(0 1)) <​r>​1.5707964 + ​ + + ====Side Effects==== + None. + + ====Affected By==== + None. + + ====Exceptional Situations==== + Should signal **[[CL:​Types:​type-error]]** if its argument is not a //​[[CL:​Glossary:​number]]//​. Might signal **[[CL:​Types:​arithmetic-error]]**. + + ====See Also==== + * {\secref\FloatSubstitutability} + + ====Notes==== + None. + + \issue{IEEE-ATAN-BRANCH-CUT:​SPLIT} \issue{REAL-NUMBER-TYPE:​X3J13-MAR-89} \issue{REAL-NUMBER-TYPE:​X3J13-MAR-89} \issue{IEEE-ATAN-BRANCH-CUT:​SPLIT}