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>integer-length | Common Lisp Nova Spec</TITLE
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><TD ALIGN="LEFT" VALIGN="BASELINE" WIDTH="100%" CLASS="name"
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></SPAN
><B
>integer-length</B
></TD
><TD ALIGN="RIGHT" VALIGN="BASELINE" WIDTH="0" NOWRAP="NOWRAP" CLASS="ftype"
><I
>Function</I
></TD
></TR
></TABLE
><HR
></DIV
><UL CLASS="subtoc"
></UL
><DL
><DT
><B
>Syntax</B
></DT
><DD
><P CLASS="j"
><B
>integer-length</B
> <SPAN CLASS="cmssi"
>integer</SPAN
> <SPAN CLASS="arrow"
>&#8594;</SPAN
> <SPAN CLASS="cmssi"
>number-of-bits</SPAN
></P
></DD
><DT
><B
>Arguments and Values</B
></DT
><DD
><P CLASS="j"
><VAR CLASS="param"
>integer</VAR
> &#8212; an <A HREF="26_1_Glossary.html#integer"
><EM CLASS="term"
>integer</EM
></A
>. </P
><P CLASS="j"
><VAR CLASS="param"
>number-of-bits</VAR
> &#8212; a non-negative <A HREF="26_1_Glossary.html#integer"
><EM CLASS="term"
>integer</EM
></A
>.</P
></DD
><DT
><B
>Description</B
></DT
><DD
><P CLASS="j"
>Returns the number of bits needed to represent <VAR CLASS="param"
>integer</VAR
> in binary two&#8217;s-complement format.</P
></DD
><DT
><B
>Examples</B
></DT
><DD
><PRE CLASS="screen"
>(integer-length 0) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 0
(integer-length 1) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 1
(integer-length 3) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 2
(integer-length 4) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 3
(integer-length 7) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 3
(integer-length -1) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 0
(integer-length -4) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 2
(integer-length -7) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 3
(integer-length -8) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 3
(integer-length (expt 2 9)) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 10
(integer-length (1- (expt 2 9))) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 9
(integer-length (- (expt 2 9))) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 9
(integer-length (- (1+ (expt 2 9)))) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 10</PRE
></DD
><DT
><B
>Exceptional Situations</B
></DT
><DD
><P CLASS="j"
>Should signal an error of <A HREF="26_1_Glossary.html#type"
><EM CLASS="term"
>type</EM
></A
> <A HREF="t_type-error.html" CLASS="typeref"
><B
>type-error</B
></A
> if <VAR CLASS="param"
>integer</VAR
> is not an <A HREF="26_1_Glossary.html#integer"
><EM CLASS="term"
>integer</EM
></A
>.</P
></DD
><DT
><B
>Notes</B
></DT
><DD
><P CLASS="j"
>This function could have been defined by:</P
><PRE CLASS="screen"
>(defun integer-length (integer)
(ceiling (log (if (minusp integer)
(- integer)
(1+ integer))
2)))</PRE
><P CLASS="j"
>If <VAR CLASS="param"
>integer</VAR
> is non-negative, then its value can be represented in unsigned binary form in a field whose width in bits is no smaller than <SPAN CLASS="cmtt"
>(integer-length</SPAN
> <VAR CLASS="param"
>integer</VAR
><SPAN CLASS="cmtt"
>)</SPAN
>. Regardless of the sign of <VAR CLASS="param"
>integer</VAR
>, its value can be represented in signed binary two&#8217;s-complement form in a field whose width in bits is no smaller than <SPAN CLASS="cmtt"
>(+</SPAN
> <SPAN CLASS="cmtt"
>(integer-length</SPAN
> <VAR CLASS="param"
>integer</VAR
><SPAN CLASS="cmtt"
>)</SPAN
> <SPAN CLASS="cmtt"
>1)</SPAN
>.</P
></DD
></DL
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