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>float | Common Lisp Nova Spec</TITLE
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><DIV CLASS="matter"
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><DIV CLASS="com"
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><TABLE WIDTH="100%" CELLSPACING="0" CELLPADDING="0"
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><TR
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><TD ALIGN="LEFT" VALIGN="BASELINE" WIDTH="100%" CLASS="name"
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><SPAN CLASS="idx" DATA-KIND="idxref" DATA-TERM="float"
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></SPAN
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><B
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>float</B
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></TD
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><TD ALIGN="RIGHT" VALIGN="BASELINE" WIDTH="0" NOWRAP="NOWRAP" CLASS="ftype"
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><I
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>System</I
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> <I
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>Class</I
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></TD
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></TR
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></TABLE
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><HR
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></DIV
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><UL CLASS="subtoc"
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></UL
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><DL
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><DT
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><B
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>Class Precedence List</B
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></DT
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><DD
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><P CLASS="j"
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><A HREF="t_float.html" CLASS="typeref"
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><B
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>float</B
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></A
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>, <A HREF="t_real.html" CLASS="typeref"
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><B
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>real</B
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></A
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>, <A HREF="t_number.html" CLASS="typeref"
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><B
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>number</B
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></A
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>, <A HREF="t_t.html" CLASS="typeref"
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><B
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>t</B
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></A
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></P
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></DD
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><DT
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><B
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>Description</B
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></DT
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><DD
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><P CLASS="j"
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>A <A HREF="26_1_Glossary.html#float"
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><EM CLASS="term"
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>float</EM
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></A
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> is a mathematical rational (but <I CLASS="i"
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><I
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>not</I
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></I
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> a Common Lisp <A HREF="26_1_Glossary.html#rational"
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><EM CLASS="term"
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>rational</EM
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></A
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>) of the form <I
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>s</I
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> · <I
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>f</I
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> · <I
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>b</I
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><SUP CLASS="sup"
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><I
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>e</I
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> <SPAN CLASS="cmsy"
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>−</SPAN
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> <I
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>p</I
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></SUP
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>, where <I
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>s</I
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> is +1 or −1, the <I CLASS="i"
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><I
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>sign</I
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></I
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>; <I
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>b</I
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> is an <A HREF="26_1_Glossary.html#integer"
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><EM CLASS="term"
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>integer</EM
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></A
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> greater than 1, the <I CLASS="i"
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><I
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>base</I
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></I
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> or <I CLASS="i"
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><I
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>radix</I
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></I
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> of the representation; <I
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>p</I
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> is a positive <A HREF="26_1_Glossary.html#integer"
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><EM CLASS="term"
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>integer</EM
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></A
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>, the <I CLASS="i"
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><I
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>precision</I
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></I
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> (in base-<I
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>b</I
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> digits) of the <A HREF="26_1_Glossary.html#float"
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><EM CLASS="term"
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>float</EM
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></A
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>; <I
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>f</I
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> is a positive <A HREF="26_1_Glossary.html#integer"
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><EM CLASS="term"
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>integer</EM
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></A
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> between b<SUP CLASS="sup"
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><SPAN CLASS="cmr"
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>p-1</SPAN
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></SUP
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> and b<SUP CLASS="sup"
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><SPAN CLASS="cmr"
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>p</SPAN
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></SUP
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>-1 (inclusive), the significand; and <I
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>e</I
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> is an <A HREF="26_1_Glossary.html#integer"
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><EM CLASS="term"
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>integer</EM
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></A
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>, the exponent. The value of <I
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>p</I
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> and the range of <I
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>e</I
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> depends on the implementation and on the type of <A HREF="26_1_Glossary.html#float"
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><EM CLASS="term"
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>float</EM
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></A
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> within that implementation. In addition, there is a floating-point zero; depending on the implementation, there can also be a “minus zero”. If there is no minus zero, then 0<I
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>.</I
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>0 and −0<I
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>.</I
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>0 are both interpreted as simply a floating-point zero. <SPAN CLASS="cmtt"
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>(=</SPAN
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> <SPAN CLASS="cmtt"
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>0.0</SPAN
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> <SPAN CLASS="cmtt"
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>-0.0)</SPAN
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> is always true. If there is a minus zero, <SPAN CLASS="cmtt"
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>(eql</SPAN
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> <SPAN CLASS="cmtt"
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>-0.0</SPAN
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> <SPAN CLASS="cmtt"
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>0.0)</SPAN
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> is <A HREF="26_1_Glossary.html#false"
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><EM CLASS="term"
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>false</EM
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></A
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>, otherwise it is <A HREF="26_1_Glossary.html#true"
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><EM CLASS="term"
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>true</EM
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></A
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>. </P
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><P CLASS="j"
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>The <A HREF="26_1_Glossary.html#type"
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><EM CLASS="term"
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>types</EM
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></A
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> <A HREF="t_short-float.html" CLASS="typeref"
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><B
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>short-float</B
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></A
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>, <A HREF="t_short-float.html" CLASS="typeref"
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><B
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>single-float</B
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></A
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>, <A HREF="t_short-float.html" CLASS="typeref"
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><B
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>double-float</B
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></A
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>, and <A HREF="t_short-float.html" CLASS="typeref"
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><B
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>long-float</B
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></A
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> are <A HREF="26_1_Glossary.html#subtype"
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><EM CLASS="term"
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>subtypes</EM
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></A
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> of <A HREF="26_1_Glossary.html#type"
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><EM CLASS="term"
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>type</EM
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></A
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> <A HREF="t_float.html" CLASS="typeref"
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><B
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>float</B
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></A
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>. Any two of them must be either <A HREF="26_1_Glossary.html#disjoint"
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><EM CLASS="term"
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>disjoint</EM
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></A
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> <A HREF="26_1_Glossary.html#type"
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><EM CLASS="term"
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>types</EM
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></A
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> or the <A HREF="26_1_Glossary.html#same"
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><EM CLASS="term"
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>same</EM
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></A
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> <A HREF="26_1_Glossary.html#type"
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><EM CLASS="term"
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>type</EM
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></A
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>; if the <A HREF="26_1_Glossary.html#same"
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><EM CLASS="term"
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>same</EM
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></A
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> <A HREF="26_1_Glossary.html#type"
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><EM CLASS="term"
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>type</EM
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></A
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>, then any other <A HREF="26_1_Glossary.html#type"
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><EM CLASS="term"
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>types</EM
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></A
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> between them in the above ordering must also be the <A HREF="26_1_Glossary.html#same"
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><EM CLASS="term"
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>same</EM
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></A
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> <A HREF="26_1_Glossary.html#type"
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><EM CLASS="term"
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>type</EM
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></A
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>. For example, if the <A HREF="26_1_Glossary.html#type"
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><EM CLASS="term"
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>type</EM
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></A
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> <A HREF="t_short-float.html" CLASS="typeref"
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><B
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>single-float</B
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></A
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> and the <A HREF="26_1_Glossary.html#type"
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><EM CLASS="term"
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>type</EM
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></A
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> <A HREF="t_short-float.html" CLASS="typeref"
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><B
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>long-float</B
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></A
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> are the <A HREF="26_1_Glossary.html#same"
|
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><EM CLASS="term"
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>same</EM
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></A
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> <A HREF="26_1_Glossary.html#type"
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><EM CLASS="term"
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>type</EM
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></A
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>, then the <A HREF="26_1_Glossary.html#type"
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><EM CLASS="term"
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>type</EM
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></A
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> <A HREF="t_short-float.html" CLASS="typeref"
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><B
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>double-float</B
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></A
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> must be the <A HREF="26_1_Glossary.html#same"
|
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><EM CLASS="term"
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>same</EM
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></A
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> <A HREF="26_1_Glossary.html#type"
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><EM CLASS="term"
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>type</EM
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></A
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> also.</P
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></DD
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><DT
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><B
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>Compound Type Specifier Kind</B
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></DT
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><DD
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><P CLASS="j"
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>Abbreviating.</P
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></DD
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><DT
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><B
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>Compound Type Specifier Syntax</B
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></DT
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><DD
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><TABLE CELLSPACING="0" CELLPADDING="0" RULES="GROUPS" STYLE="margin: 1ex 0"
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><TBODY
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><TR
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><TD ALIGN="LEFT" VALIGN="BASELINE" STYLE=";"
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><SPAN CLASS="cmtt"
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>(float</SPAN
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> <SPAN CLASS="cmtt"
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>[</SPAN
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><SPAN CLASS="cmssi"
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>lower-limit</SPAN
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> <SPAN CLASS="cmr"
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>[</SPAN
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><SPAN CLASS="cmssi"
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>upper-limit</SPAN
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><SPAN CLASS="cmr"
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>]</SPAN
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><SPAN CLASS="cmtt"
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>])</SPAN
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></TD
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></TR
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></TBODY
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></TABLE
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></DD
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><DT
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><B
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>Compound Type Specifier Arguments</B
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></DT
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><DD
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><P CLASS="j"
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><VAR CLASS="param"
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>lower-limit</VAR
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>, <VAR CLASS="param"
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>upper-limit</VAR
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> — <A HREF="26_1_Glossary.html#interval_designator"
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><EM CLASS="term"
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>interval designators</EM
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></A
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> for <A HREF="26_1_Glossary.html#type"
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><EM CLASS="term"
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>type</EM
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></A
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> <A HREF="t_float.html" CLASS="typeref"
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><B
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>float</B
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></A
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>. The defaults for each of <VAR CLASS="param"
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>lower-limit</VAR
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> and <VAR CLASS="param"
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>upper-limit</VAR
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> is the <A HREF="26_1_Glossary.html#symbol"
|
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><EM CLASS="term"
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>symbol</EM
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></A
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> <SPAN CLASS="misc"
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><B
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>*</B
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></SPAN
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>.</P
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></DD
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><DT
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><B
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>Compound Type Specifier Description</B
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></DT
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><DD
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><P CLASS="j"
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>This denotes the <A HREF="26_1_Glossary.html#float"
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><EM CLASS="term"
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>floats</EM
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></A
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> on the interval described by <VAR CLASS="param"
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>lower-limit</VAR
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> and <VAR CLASS="param"
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>upper-limit</VAR
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>.</P
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></DD
|
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><DT
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><B
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|
>See Also</B
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></DT
|
|
><DD
|
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><P CLASS="j"
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|
>Figure 2–9, <A HREF="2_3_Interpretation_of_Tokens.html#sec_2_3_2" CLASS="secref"
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><SPAN CLASS="cmr"
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>Section</SPAN
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> <SPAN CLASS="cmr"
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>2.3.2</SPAN
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> <SPAN CLASS="cmr"
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>(Constructing</SPAN
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> <SPAN CLASS="cmr"
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>Numbers</SPAN
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> <SPAN CLASS="cmr"
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>from</SPAN
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> <SPAN CLASS="cmr"
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>Tokens)</SPAN
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></A
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>, <A HREF="22_1_The_Lisp_Printer.html#sec_22_1_3_1_3" CLASS="secref"
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><SPAN CLASS="cmr"
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>Section</SPAN
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> <SPAN CLASS="cmr"
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>22.1.3.1.3</SPAN
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> <SPAN CLASS="cmr"
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>(Printing</SPAN
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> <SPAN CLASS="cmr"
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>Floats)</SPAN
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></A
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></P
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></DD
|
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><DT
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><B
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|
>Notes</B
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></DT
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><DD
|
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><P CLASS="j"
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>Note that all mathematical integers are representable not only as Common Lisp <EM CLASS="term"
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>reals</EM
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>, but also as <A HREF="26_1_Glossary.html#complex_float"
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><EM CLASS="term"
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>complex floats</EM
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></A
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>. For example, possible representations of the mathematical number 1 include the <A HREF="26_1_Glossary.html#integer"
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><EM CLASS="term"
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>integer</EM
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></A
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> <CODE CLASS="f"
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>1</CODE
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>, the <A HREF="26_1_Glossary.html#float"
|
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><EM CLASS="term"
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>float</EM
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></A
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> <CODE CLASS="f"
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>1.0</CODE
|
|
>, or the <A HREF="26_1_Glossary.html#complex"
|
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><EM CLASS="term"
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>complex</EM
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></A
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> <CODE CLASS="f"
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>#C(1.0 0.0)</CODE
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|
>.</P
|
|
></DD
|
|
></DL
|
|
></DIV
|
|
></DIV
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><DIV CLASS="footer"
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><DIV CLASS="btmnav"
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