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<!--Weave of 'Mathematics Template' generated by Inweb-->
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<p class="purpose">Mathematical functions.</p>
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<ul class="toc"><li><a href="S-mth.html#SP1">§1. Unsigned integer comparison</a></li><li><a href="S-mth.html#SP2">§2. Integer roots</a></li><li><a href="S-mth.html#SP3">§3. Real number support</a></li></ul><hr class="tocbar">
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<p class="commentary firstcommentary"><a id="SP1" class="paragraph-anchor"></a><b>§1. Unsigned integer comparison. </b>Comparison of integers is normally signed, that is, treating the word as
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a twos-complement signed number, so that <span class="extract"><span class="extract-syntax">$FFFF</span></span> is less than <span class="extract"><span class="extract-syntax">0</span></span>, for
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instance. If we want to construe words as being unsigned integers, or as
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addresses, we need to compare them with the following routine, which returns
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1 if \(x>y\), 0 if \(x=y\) and \(-1\) if \(x<y\).
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</p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="plain-syntax">[ </span><span class="identifier-syntax">UnsignedCompare</span><span class="plain-syntax"> </span><span class="identifier-syntax">x</span><span class="plain-syntax"> </span><span class="identifier-syntax">y</span><span class="plain-syntax"> </span><span class="identifier-syntax">u</span><span class="plain-syntax"> </span><span class="identifier-syntax">v</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">x</span><span class="plain-syntax"> == </span><span class="identifier-syntax">y</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">0</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">x</span><span class="plain-syntax"> < </span><span class="constant-syntax">0</span><span class="plain-syntax"> && </span><span class="identifier-syntax">y</span><span class="plain-syntax"> >= </span><span class="constant-syntax">0</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">1</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">x</span><span class="plain-syntax"> >= </span><span class="constant-syntax">0</span><span class="plain-syntax"> && </span><span class="identifier-syntax">y</span><span class="plain-syntax"> < </span><span class="constant-syntax">0</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> -1;</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">u</span><span class="plain-syntax"> = </span><span class="identifier-syntax">x</span><span class="plain-syntax">&~</span><span class="identifier-syntax">WORD_HIGHBIT</span><span class="plain-syntax">; </span><span class="identifier-syntax">v</span><span class="plain-syntax">= </span><span class="identifier-syntax">y</span><span class="plain-syntax">&~</span><span class="identifier-syntax">WORD_HIGHBIT</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">u</span><span class="plain-syntax"> > </span><span class="identifier-syntax">v</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">1</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> -1;</span>
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<span class="plain-syntax">];</span>
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</pre>
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<p class="commentary firstcommentary"><a id="SP2" class="paragraph-anchor"></a><b>§2. Integer roots. </b>We are unable to provide VM support for taking square or cube roots rapidly:
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</p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="plain-syntax">[ </span><span class="identifier-syntax">VM_SquareRoot</span><span class="plain-syntax"> </span><span class="identifier-syntax">num</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">0</span><span class="plain-syntax">;</span>
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<span class="plain-syntax">];</span>
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<span class="plain-syntax">[ </span><span class="identifier-syntax">VM_CubeRoot</span><span class="plain-syntax"> </span><span class="identifier-syntax">num</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">0</span><span class="plain-syntax">;</span>
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<span class="plain-syntax">];</span>
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</pre>
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<p class="commentary firstcommentary"><a id="SP3" class="paragraph-anchor"></a><b>§3. Real number support. </b>These need to exist, but are likely never to be used.
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</p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="plain-syntax">[ </span><span class="identifier-syntax">REAL_NUMBER_TY_Say</span><span class="plain-syntax"> </span><span class="identifier-syntax">real</span><span class="plain-syntax">; </span><span class="reserved-syntax">print</span><span class="plain-syntax"> </span><span class="identifier-syntax">real</span><span class="plain-syntax">; ];</span>
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<span class="plain-syntax">[ </span><span class="identifier-syntax">REAL_NUMBER_TY_Compare</span><span class="plain-syntax"> </span><span class="identifier-syntax">r1</span><span class="plain-syntax"> </span><span class="identifier-syntax">r2</span><span class="plain-syntax">; </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">UnsignedCompare</span><span class="plain-syntax">(</span><span class="identifier-syntax">r1</span><span class="plain-syntax">, </span><span class="identifier-syntax">r2</span><span class="plain-syntax">); ];</span>
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