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====== 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 </r> (phase 0) <r>0.0s0 </r> (phase ([[CL:Functions:cis]] 30)) <r>-1.4159266 </r> (phase #c(0 1)) <r>1.5707964 </r> </blockquote> ====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}