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====== Function SIGNUM ====== ====Syntax==== * **signum** //number// → //signed-prototype// ====Arguments and Values==== * //number// - a //[[CL:Glossary:number]]//. * //signed-prototype// - a //[[CL:Glossary:number]]//. ====Description==== **signum** determines a numerical value that indicates whether //number// is negative, zero, or positive. For a //[[CL:Glossary:rational]]//, **signum** returns one of ''-1'', ''0'', or ''1'' according to whether //number// is negative, zero, or positive. For a //[[CL:Glossary:float]]//, the result is a //[[CL:Glossary:float]]// of the same format whose value is minus one, zero, or one. For a //[[CL:Glossary:complex]]// number //z//, ''(signum //z//)'' is a complex number of the same phase but with unit magnitude, unless //z// is a complex zero, in which case the result is //z//. For //[[CL:Glossary:rational]]// //[[CL:Glossary:arguments]]//, **signum** is a rational function, but it may be irrational for //[[CL:Glossary:complex]]// //[[CL:Glossary:arguments]]//. If //number// is a //[[CL:Glossary:float]]//, the result is a //[[CL:Glossary:float]]//. If //number// is a //[[CL:Glossary:rational]]//, the result is a //[[CL:Glossary:rational]]//. If //number// is a //[[CL:Glossary:complex float]]//, the result is a //[[CL:Glossary:complex float]]//. If //number// is a //[[CL:Glossary:complex rational]]//, the result is a //[[CL:Glossary:complex]]//, but it is //[[CL:Glossary:implementation-dependent]]// whether that result is a //[[CL:Glossary:complex rational]]// or a //[[CL:Glossary:complex float]]//. ====Examples==== <blockquote> (signum 0) <r>0 </r> (signum 99) <r>1 </r> (signum 4/5) <r>1 </r> (signum -99/100) <r>-1 </r> (signum 0.0) <r>0.0 </r> (signum #c(0 33)) <r>#C(0.0 1.0) </r> (signum #c(7.5 10.0)) <r>#C(0.6 0.8) </r> (signum #c(0.0 -14.7)) <r>#C(0.0 -1.0) </r> ([[CL:Functions:eql]] (signum -0.0) -0.0) <r>//[[CL:Glossary:true]]// </r> </blockquote> ====Side Effects==== None. ====Affected By==== None. ====Exceptional Situations==== None. ====See Also==== * {\secref\FloatSubstitutability} ====Notes==== <blockquote> (signum x) ≡ ([[CL:Special Operators:if]] ([[CL:Functions:zerop]] x) x ([[CL:Functions:math-divide|/]] x ([[CL:Functions:abs]] x))) </blockquote>