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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} | ||