320 lines
6.3 KiB
HTML
320 lines
6.3 KiB
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>rational, rationalize | Common Lisp Nova Spec</TITLE
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>rational, rationalize</A
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>←</A
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><A HREF="f_rationalp.html" CLASS="next"
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>→</A
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><DIV CLASS="matter"
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><DIV CLASS="com"
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><DIV CLASS="begincom"
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><HR
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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="rational, rationalize"
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></SPAN
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><B
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>rational, rationalize</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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>Function</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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>Syntax</B
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></DT
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><DD
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><P CLASS="j"
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><B
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>rational</B
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> <SPAN CLASS="cmssi"
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>number</SPAN
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> <SPAN CLASS="arrow"
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>→</SPAN
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> <SPAN CLASS="cmssi"
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>rational</SPAN
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></P
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><P CLASS="j"
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><B
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>rationalize</B
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> <SPAN CLASS="cmssi"
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>number</SPAN
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> <SPAN CLASS="arrow"
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>→</SPAN
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> <SPAN CLASS="cmssi"
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>rational</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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>Arguments and Values</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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>number</VAR
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> — a <EM CLASS="term"
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>real</EM
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>. </P
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><P CLASS="j"
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><VAR CLASS="param"
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>rational</VAR
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> — a <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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>.</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 HREF="f_rational.html" CLASS="funref"
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><B
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>rational</B
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></A
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> and <A HREF="f_rational.html" CLASS="funref"
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><B
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>rationalize</B
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></A
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> convert <EM CLASS="term"
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>reals</EM
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> to <A HREF="26_1_Glossary.html#rational"
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><EM CLASS="term"
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>rationals</EM
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></A
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>. </P
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><P CLASS="j"
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>If <VAR CLASS="param"
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>number</VAR
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> is already <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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>, it is returned. </P
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><P CLASS="j"
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>If <VAR CLASS="param"
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>number</VAR
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> is 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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>, <A HREF="f_rational.html" CLASS="funref"
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><B
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>rational</B
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></A
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> returns a <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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> that is mathematically equal in value to 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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>. <A HREF="f_rational.html" CLASS="funref"
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><B
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>rationalize</B
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></A
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> returns a <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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> that approximates 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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> to the accuracy of the underlying floating-point representation. </P
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><P CLASS="j"
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><A HREF="f_rational.html" CLASS="funref"
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><B
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>rational</B
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></A
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> assumes that 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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> is completely accurate. </P
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><P CLASS="j"
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><A HREF="f_rational.html" CLASS="funref"
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><B
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>rationalize</B
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></A
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> assumes that 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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> is accurate only to the precision of the floating-point representation.</P
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></DD
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><DT
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><B
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>Examples</B
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></DT
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><DD
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><PRE CLASS="screen"
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>(rational 0) <SPAN CLASS="cmsy"
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><SPAN CLASS="arrow"
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>→</SPAN
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></SPAN
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> 0
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(rationalize -11/100) <SPAN CLASS="cmsy"
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><SPAN CLASS="arrow"
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>→</SPAN
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></SPAN
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> -11/100
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(rational .1) <SPAN CLASS="cmsy"
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><SPAN CLASS="arrow"
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>→</SPAN
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></SPAN
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> 13421773/134217728 ;implementation-dependent
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(rationalize .1) <SPAN CLASS="cmsy"
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><SPAN CLASS="arrow"
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>→</SPAN
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></SPAN
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> 1/10</PRE
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></DD
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><DT
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><B
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>Affected By</B
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></DT
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><DD
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><P CLASS="j"
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>The <A HREF="26_1_Glossary.html#implementation"
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><EM CLASS="term"
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>implementation</EM
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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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>Exceptional Situations</B
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></DT
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><DD
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><P CLASS="j"
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>Should signal an error 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_type-error.html" CLASS="typeref"
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><B
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>type-error</B
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></A
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> if <VAR CLASS="param"
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>number</VAR
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> is not a <EM CLASS="term"
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>real</EM
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>. Might signal <A HREF="t_arithmetic-error.html" CLASS="typeref"
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><B
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>arithmetic-error</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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>Notes</B
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></DT
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><DD
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><P CLASS="j"
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>It is always the case that</P
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><PRE CLASS="screen"
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>(float (rational x) x) <SPAN CLASS="cmsy"
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><SPAN STYLE="font-size:16px;vertical-align:-2px"
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>≡</SPAN
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></SPAN
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> x</PRE
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><P CLASS="j"
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>and</P
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><PRE CLASS="screen"
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>(float (rationalize x) x) <SPAN CLASS="cmsy"
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><SPAN STYLE="font-size:16px;vertical-align:-2px"
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>≡</SPAN
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></SPAN
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> x</PRE
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><P CLASS="j"
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>That is, rationalizing 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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> by either method and then converting it back to 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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> of the same format produces the original <VAR CLASS="param"
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>number</VAR
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>.</P
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></DD
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></DL
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></DIV
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><DIV CLASS="footer"
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><DIV CLASS="btmnav"
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><A HREF="f_numerator.html" CLASS="prev"
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>←</A
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>→</A
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><DIV CLASS="trail"
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>Conversion to HTML copyright 2023 by Gilbert Baumann</DIV
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