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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<!--Weave of 'Mathematics Template' generated by 7-->
<ul class="crumbs"><li><a href="../index.html">Home</a></li><li><a href="../extensions.html">Kits</a></li><li><a href="index.html">BasicInformKit</a></li><li><b>Mathematics Template</b></li></ul><p class="purpose">Mathematical functions, especially for real numbers.</p>
<ul class="toc"><li><a href="S-mth.html#SP1">&#167;1. Square Root</a></li><li><a href="S-mth.html#SP2">&#167;2. Cube Root</a></li><li><a href="S-mth.html#SP3">&#167;3. Absolute value</a></li><li><a href="S-mth.html#SP4">&#167;4. IntegerDivide</a></li><li><a href="S-mth.html#SP5">&#167;5. IntegerRemainder</a></li><li><a href="S-mth.html#SP6">&#167;6. UnsignedCompare</a></li><li><a href="S-mth.html#SP7">&#167;7. SignedCompare</a></li><li><a href="S-mth.html#SP8">&#167;8. Printing reals</a></li></ul><hr class="tocbar">
<p class="inwebparagraph"><a id="SP1"></a><b>&#167;1. Square Root. </b>Although this routine performs integer square root, it does so using Glulx's
floating-point operations if available (with code contributed by Andrew
Plotkin): this is fast and remains accurate up to about 16 million.
</p>
<p class="inwebparagraph">The slower integer method is an old algorithm for extracting binary square
roots, taking 2 bits at a time. We start out with <code class="display"><span class="extract">one</span></code> at the highest bit
which isn't the sign bit; that used to be worked out as <code class="display"><span class="extract">WORD_HIGHBIT/2</span></code>, but
this caused unexpected portability problems (exposing a minor bug in Inform
and also glulxe) because of differences in how C compilers handle signed
division of constants in the case where the dividend is \(-2^{31}\), the unique
number which cannot be negated in 32-bit twos complement arithmetic.
</p>
<pre class="display">
<span class="plain">[ </span><span class="identifier">SquareRoot</span><span class="plain"> </span><span class="identifier">num</span>
<span class="identifier">op</span><span class="plain"> </span><span class="identifier">res</span><span class="plain"> </span><span class="identifier">one</span><span class="plain"> </span><span class="identifier">n</span><span class="plain"> </span><span class="identifier">x</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">num</span><span class="plain"> &lt; </span><span class="constant">0</span><span class="plain">) { </span><span class="identifier">RunTimeProblem</span><span class="plain">(</span><span class="identifier">RTP_NEGATIVEROOT</span><span class="plain">); </span><span class="reserved">return</span><span class="plain"> </span><span class="constant">1</span><span class="plain">; }</span>
<span class="comment">Use floating-point ops if available.</span>
<span class="plain">#</span><span class="identifier">ifdef</span><span class="plain"> </span><span class="identifier">TARGET_GLULX</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">gestalt</span><span class="plain"> </span><span class="constant">11</span><span class="plain"> </span><span class="constant">0</span><span class="plain"> </span><span class="identifier">n</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">n</span><span class="plain">) {</span>
<span class="plain">@</span><span class="identifier">numtof</span><span class="plain"> </span><span class="identifier">num</span><span class="plain"> </span><span class="identifier">x</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">sqrt</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">x</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">ftonumz</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">num</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">num</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="plain"> #</span><span class="identifier">endif</span><span class="plain">;</span>
<span class="identifier">op</span><span class="plain"> = </span><span class="identifier">num</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">num</span><span class="plain"> &lt; </span><span class="constant">0</span><span class="plain">) { </span><span class="identifier">RunTimeProblem</span><span class="plain">(</span><span class="identifier">RTP_NEGATIVEROOT</span><span class="plain">); </span><span class="reserved">return</span><span class="plain"> </span><span class="constant">1</span><span class="plain">; }</span>
<span class="comment">"one" starts at the highest power of four &lt;= the argument.</span>
<span class="reserved">for</span><span class="plain"> (</span><span class="identifier">one</span><span class="plain"> = </span><span class="identifier">WORD_NEXTTOHIGHBIT</span><span class="plain">: </span><span class="identifier">one</span><span class="plain"> &gt; </span><span class="identifier">op</span><span class="plain">: </span><span class="identifier">one</span><span class="plain"> = </span><span class="identifier">one</span><span class="plain">/4) ;</span>
<span class="reserved">while</span><span class="plain"> (</span><span class="identifier">one</span><span class="plain"> ~= </span><span class="constant">0</span><span class="plain">) {</span>
<span class="comment">print "Round: op = ", op, " res = ", res, ", res**2 = ", res*res, " one = ", one, " nthb = ", WORD_NEXTTOHIGHBIT, "^";</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">op</span><span class="plain"> &gt;= </span><span class="identifier">res</span><span class="plain"> + </span><span class="identifier">one</span><span class="plain">) {</span>
<span class="identifier">op</span><span class="plain"> = </span><span class="identifier">op</span><span class="plain"> - </span><span class="identifier">res</span><span class="plain"> - </span><span class="identifier">one</span><span class="plain">;</span>
<span class="identifier">res</span><span class="plain"> = </span><span class="identifier">res</span><span class="plain">/2 + </span><span class="identifier">one</span><span class="plain">;</span>
<span class="plain">} </span><span class="reserved">else</span><span class="plain"> {</span>
<span class="identifier">res</span><span class="plain"> = </span><span class="identifier">res</span><span class="plain">/2;</span>
<span class="plain">}</span>
<span class="identifier">one</span><span class="plain"> = </span><span class="identifier">one</span><span class="plain">/4;</span>
<span class="plain">}</span>
<span class="comment">print "Res is ", res, "^";</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">res</span><span class="plain">;</span>
<span class="plain">];</span>
</pre>
<p class="inwebparagraph"></p>
<p class="inwebparagraph"><a id="SP2"></a><b>&#167;2. Cube Root. </b>The following, again, uses floating-point arithmetic if it's available:
this is fast and gives good accuracy for smallish numbers, but limited
precision begins to tell at around 2000000.
</p>
<p class="inwebparagraph">The alternative is an iterative scheme for finding cube roots by
Newton-Raphson approximation, not a great method but which, on the narrow
ranges of integers we deal with, just about good enough. The square root is
used only as a sighting shot.
</p>
<pre class="display">
<span class="plain">[ </span><span class="identifier">CubeRoot</span><span class="plain"> </span><span class="identifier">num</span><span class="plain"> </span><span class="identifier">neg</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">n</span><span class="plain">;</span>
<span class="comment">Use floating-point ops if available.</span>
<span class="plain">#</span><span class="identifier">ifdef</span><span class="plain"> </span><span class="identifier">TARGET_GLULX</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">gestalt</span><span class="plain"> </span><span class="constant">11</span><span class="plain"> </span><span class="constant">0</span><span class="plain"> </span><span class="identifier">n</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">n</span><span class="plain">) {</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">num</span><span class="plain"> &lt; </span><span class="constant">0</span><span class="plain">) {</span>
<span class="identifier">neg</span><span class="plain"> = </span><span class="reserved">true</span><span class="plain">;</span>
<span class="identifier">num</span><span class="plain"> = -</span><span class="identifier">num</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="plain">@</span><span class="identifier">numtof</span><span class="plain"> </span><span class="identifier">num</span><span class="plain"> </span><span class="identifier">x</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">pow</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="constant">1051372203</span><span class="plain"> </span><span class="identifier">x</span><span class="plain">; </span><span class="comment">pow(x, 0.3333)</span>
<span class="plain">@</span><span class="identifier">ftonumz</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">num</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">neg</span><span class="plain">)</span>
<span class="reserved">return</span><span class="plain"> -</span><span class="identifier">num</span><span class="plain">;</span>
<span class="reserved">else</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">num</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="plain">#</span><span class="identifier">endif</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">num</span><span class="plain"> &lt; </span><span class="constant">0</span><span class="plain">) </span><span class="identifier">x</span><span class="plain"> = -</span><span class="identifier">SquareRoot</span><span class="plain">(-</span><span class="identifier">num</span><span class="plain">); </span><span class="reserved">else</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> = </span><span class="identifier">SquareRoot</span><span class="plain">(</span><span class="identifier">num</span><span class="plain">);</span>
<span class="reserved">for</span><span class="plain"> (</span><span class="identifier">n</span><span class="plain">=0: (</span><span class="identifier">y</span><span class="plain"> ~= </span><span class="identifier">x</span><span class="plain">) &amp;&amp; (</span><span class="identifier">n</span><span class="plain">++ &lt; </span><span class="constant">100</span><span class="plain">): </span><span class="identifier">y</span><span class="plain"> = </span><span class="identifier">x</span><span class="plain">, </span><span class="identifier">x</span><span class="plain"> = (2*</span><span class="identifier">x</span><span class="plain"> + </span><span class="identifier">num</span><span class="plain">/</span><span class="identifier">x</span><span class="plain">/</span><span class="identifier">x</span><span class="plain">)/3) ;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">x</span><span class="plain">;</span>
<span class="plain">];</span>
</pre>
<p class="inwebparagraph"></p>
<p class="inwebparagraph"><a id="SP3"></a><b>&#167;3. Absolute value. </b>Of an integer:
</p>
<pre class="display">
<span class="plain">[ </span><span class="identifier">NUMBER_TY_Abs</span><span class="plain"> </span><span class="identifier">x</span><span class="plain">; </span><span class="reserved">if</span><span class="plain"> (</span><span class="identifier">x</span><span class="plain">&lt;0) </span><span class="reserved">return</span><span class="plain"> -</span><span class="identifier">x</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">x</span><span class="plain">; ];</span>
</pre>
<p class="inwebparagraph"></p>
<p class="inwebparagraph"><a id="SP4"></a><b>&#167;4. IntegerDivide. </b>We can't simply use I6's <code class="display"><span class="extract">/</span></code> operator, as that translates directly into a
virtual machine opcode which crashes on divide by zero.
</p>
<pre class="display">
<span class="plain">[ </span><span class="identifier">IntegerDivide</span><span class="plain"> </span><span class="identifier">A</span><span class="plain"> </span><span class="identifier">B</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">B</span><span class="plain"> == </span><span class="constant">0</span><span class="plain">) { </span><span class="identifier">RunTimeProblem</span><span class="plain">(</span><span class="identifier">RTP_DIVZERO</span><span class="plain">); </span><span class="reserved">rfalse</span><span class="plain">; }</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">A</span><span class="plain">/</span><span class="identifier">B</span><span class="plain">;</span>
<span class="plain">];</span>
</pre>
<p class="inwebparagraph"></p>
<p class="inwebparagraph"><a id="SP5"></a><b>&#167;5. IntegerRemainder. </b>Similarly.
</p>
<pre class="display">
<span class="plain">[ </span><span class="identifier">IntegerRemainder</span><span class="plain"> </span><span class="identifier">A</span><span class="plain"> </span><span class="identifier">B</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">B</span><span class="plain"> == </span><span class="constant">0</span><span class="plain">) { </span><span class="identifier">RunTimeProblem</span><span class="plain">(</span><span class="identifier">RTP_DIVZERO</span><span class="plain">); </span><span class="reserved">rfalse</span><span class="plain">; }</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">A</span><span class="plain">%</span><span class="identifier">B</span><span class="plain">;</span>
<span class="plain">];</span>
</pre>
<p class="inwebparagraph"></p>
<p class="inwebparagraph"><a id="SP6"></a><b>&#167;6. UnsignedCompare. </b>Comparison of I6 integers is normally signed, that is, treating the word as
a twos-complement signed number, so that <code class="display"><span class="extract">$FFFF</span></code> is less than <code class="display"><span class="extract">0</span></code>, for
instance. If we want to construe words as being unsigned integers, or as
addresses, we need to compare them with the following routine, which returns
1 if \(x&gt;y\), 0 if \(x=y\) and \(-1\) if \(x&lt;y\).
</p>
<pre class="display">
<span class="plain">[ </span><span class="identifier">UnsignedCompare</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">u</span><span class="plain"> </span><span class="identifier">v</span><span class="plain">;</span>
<span class="plain">#</span><span class="identifier">Ifdef</span><span class="plain"> </span><span class="identifier">TARGET_GLULX</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">jleu</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> ?</span><span class="identifier">lesseq</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="constant">1</span><span class="plain">;</span>
<span class="plain">.</span><span class="identifier">lesseq</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">jeq</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> ?</span><span class="identifier">equal</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> -1;</span>
<span class="plain">.</span><span class="identifier">equal</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="constant">0</span><span class="plain">;</span>
<span class="plain">#</span><span class="identifier">Ifnot</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">x</span><span class="plain"> == </span><span class="identifier">y</span><span class="plain">) </span><span class="reserved">return</span><span class="plain"> </span><span class="constant">0</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">x</span><span class="plain"> &lt; </span><span class="constant">0</span><span class="plain"> &amp;&amp; </span><span class="identifier">y</span><span class="plain"> &gt;= </span><span class="constant">0</span><span class="plain">) </span><span class="reserved">return</span><span class="plain"> </span><span class="constant">1</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">x</span><span class="plain"> &gt;= </span><span class="constant">0</span><span class="plain"> &amp;&amp; </span><span class="identifier">y</span><span class="plain"> &lt; </span><span class="constant">0</span><span class="plain">) </span><span class="reserved">return</span><span class="plain"> -1;</span>
<span class="identifier">u</span><span class="plain"> = </span><span class="identifier">x</span><span class="plain">&amp;~</span><span class="identifier">WORD_HIGHBIT</span><span class="plain">; </span><span class="identifier">v</span><span class="plain">= </span><span class="identifier">y</span><span class="plain">&amp;~</span><span class="identifier">WORD_HIGHBIT</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">u</span><span class="plain"> &gt; </span><span class="identifier">v</span><span class="plain">) </span><span class="reserved">return</span><span class="plain"> </span><span class="constant">1</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> -1;</span>
<span class="plain">#</span><span class="identifier">Endif</span><span class="plain">;</span>
<span class="plain">];</span>
</pre>
<p class="inwebparagraph"></p>
<p class="inwebparagraph"><a id="SP7"></a><b>&#167;7. SignedCompare. </b>This routine is hardly ever needed; it wraps up ordinary comparisons.
</p>
<pre class="display">
<span class="plain">[ </span><span class="identifier">SignedCompare</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">x</span><span class="plain"> &gt; </span><span class="identifier">y</span><span class="plain">) </span><span class="reserved">return</span><span class="plain"> </span><span class="constant">1</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">x</span><span class="plain"> == </span><span class="identifier">y</span><span class="plain">) </span><span class="reserved">return</span><span class="plain"> </span><span class="constant">0</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> -1;</span>
<span class="plain">];</span>
</pre>
<p class="inwebparagraph"></p>
<p class="inwebparagraph"><a id="SP8"></a><b>&#167;8. Printing reals. </b>Most of the code in this section is by Andrew Plotkin, and derives from test
cases used to check the floating-point extensions to Glulx.
</p>
<pre class="display">
<span class="plain">#</span><span class="identifier">Ifdef</span><span class="plain"> </span><span class="identifier">TARGET_GLULX</span><span class="plain">;</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Say</span><span class="plain"> </span><span class="identifier">fp</span><span class="plain">;</span>
<span class="reserved">print</span><span class="plain"> (</span><span class="identifier">Float</span><span class="plain">) </span><span class="identifier">fp</span><span class="plain">;</span>
<span class="plain">];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Compare</span><span class="plain"> </span><span class="identifier">r1</span><span class="plain"> </span><span class="identifier">r2</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">jflt</span><span class="plain"> </span><span class="identifier">r1</span><span class="plain"> </span><span class="identifier">r2</span><span class="plain"> ?</span><span class="identifier">less</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">jfeq</span><span class="plain"> </span><span class="identifier">r1</span><span class="plain"> </span><span class="identifier">r2</span><span class="plain"> </span><span class="constant">0</span><span class="plain"> ?</span><span class="identifier">same</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="constant">1</span><span class="plain">;</span>
<span class="plain">.</span><span class="identifier">same</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="constant">0</span><span class="plain">;</span>
<span class="plain">.</span><span class="identifier">less</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> -1;</span>
<span class="plain">];</span>
<span class="plain">[ </span><span class="identifier">NUMBER_TY_to_REAL_NUMBER_TY</span><span class="plain"> </span><span class="identifier">int</span><span class="plain"> </span><span class="identifier">real</span><span class="plain">; @</span><span class="identifier">numtof</span><span class="plain"> </span><span class="identifier">int</span><span class="plain"> </span><span class="identifier">real</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">real</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_to_NUMBER_TY</span><span class="plain"> </span><span class="identifier">real</span><span class="plain"> </span><span class="identifier">int</span><span class="plain">; @</span><span class="identifier">ftonumn</span><span class="plain"> </span><span class="identifier">real</span><span class="plain"> </span><span class="identifier">int</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">int</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Sin</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">sin</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Cos</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">cos</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Tan</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">tan</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Arcsin</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">asin</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Arccos</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">acos</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Arctan</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">atan</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Sinh</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">tmp</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">exp</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">tmp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fsub</span><span class="plain"> </span><span class="identifier">M_0</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="reserved">in</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">exp</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fadd</span><span class="plain"> </span><span class="identifier">tmp</span><span class="plain"> </span><span class="identifier">out</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fmul</span><span class="plain"> </span><span class="identifier">out</span><span class="plain"> </span><span class="identifier">M_HALF</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="plain">];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Cosh</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">tmp</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">exp</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">tmp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fsub</span><span class="plain"> </span><span class="identifier">M_0</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="reserved">in</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">exp</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fsub</span><span class="plain"> </span><span class="identifier">tmp</span><span class="plain"> </span><span class="identifier">out</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fmul</span><span class="plain"> </span><span class="identifier">out</span><span class="plain"> </span><span class="identifier">M_HALF</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="plain">];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Tanh</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">tmp</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="identifier">tmp</span><span class="plain"> = </span><span class="identifier">REAL_NUMBER_TY_Sinh</span><span class="plain">(</span><span class="reserved">in</span><span class="plain">);</span>
<span class="reserved">in</span><span class="plain"> = </span><span class="identifier">REAL_NUMBER_TY_Cosh</span><span class="plain">(</span><span class="reserved">in</span><span class="plain">);</span>
<span class="plain">@</span><span class="identifier">fdiv</span><span class="plain"> </span><span class="identifier">tmp</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="plain">];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Reciprocal</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">fdiv</span><span class="plain"> </span><span class="identifier">M_1</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Negate</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">fsub</span><span class="plain"> </span><span class="identifier">M_0</span><span class="plain"> </span><span class="reserved">in</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Plus</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">fadd</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Minus</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">fsub</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Times</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">fmul</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Divide</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">fdiv</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Remainder</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">r</span><span class="plain"> </span><span class="identifier">q</span><span class="plain">; @</span><span class="identifier">fmod</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">r</span><span class="plain"> </span><span class="identifier">q</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">r</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Approximate</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">quotient</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fdiv</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">quotient</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fadd</span><span class="plain"> </span><span class="identifier">quotient</span><span class="plain"> </span><span class="identifier">M_HALF</span><span class="plain"> </span><span class="identifier">quotient</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">floor</span><span class="plain"> </span><span class="identifier">quotient</span><span class="plain"> </span><span class="identifier">quotient</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fmul</span><span class="plain"> </span><span class="identifier">quotient</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="plain">];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Root</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">sqrt</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Cube_Root</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">pow</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">M_THIRD</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Pow</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">pow</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">y</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Exp</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">exp</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Log</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">log</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_BLog</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">n</span><span class="plain"> </span><span class="identifier">d</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">log</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">n</span><span class="plain"> == </span><span class="constant">10</span><span class="plain">) </span><span class="identifier">d</span><span class="plain"> = </span><span class="identifier">M_LOG10</span><span class="plain">;</span>
<span class="reserved">else</span><span class="plain"> {</span>
<span class="plain">@</span><span class="identifier">numtof</span><span class="plain"> </span><span class="identifier">n</span><span class="plain"> </span><span class="identifier">d</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">log</span><span class="plain"> </span><span class="identifier">d</span><span class="plain"> </span><span class="identifier">d</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="plain">@</span><span class="identifier">fdiv</span><span class="plain"> </span><span class="identifier">out</span><span class="plain"> </span><span class="identifier">d</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">;</span>
<span class="plain">];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Floor</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">floor</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Ceiling</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; @</span><span class="identifier">ceil</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">out</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Abs</span><span class="plain"> </span><span class="identifier">x</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> &amp; </span><span class="constant">$7fffffff</span><span class="plain">; ];</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Nan</span><span class="plain"> </span><span class="identifier">x</span><span class="plain">; @</span><span class="identifier">jisnan</span><span class="plain"> </span><span class="identifier">x</span><span class="plain"> ?</span><span class="identifier">Nan</span><span class="plain">; </span><span class="reserved">rfalse</span><span class="plain">; .</span><span class="identifier">Nan</span><span class="plain">; </span><span class="reserved">rtrue</span><span class="plain">; ];</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_0</span><span class="plain"> = </span><span class="constant">$0</span><span class="plain">;</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_1</span><span class="plain"> = </span><span class="constant">$3F800000</span><span class="plain">;</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_HALF</span><span class="plain"> = </span><span class="constant">$3F000000</span><span class="plain">; </span><span class="comment">1/3</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_THIRD</span><span class="plain"> = </span><span class="constant">$3EAAAAAB</span><span class="plain">; </span><span class="comment">1/3</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_LOG10</span><span class="plain"> = </span><span class="constant">$40135D8E</span><span class="plain">; </span><span class="comment">log(10)</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_N1</span><span class="plain"> = </span><span class="constant">$BF800000</span><span class="plain">; </span><span class="comment">-1</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_PI</span><span class="plain"> = </span><span class="constant">$40490FDB</span><span class="plain">;</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_NPI</span><span class="plain"> = </span><span class="constant">$C0490FDB</span><span class="plain">;</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_2PI</span><span class="plain"> = </span><span class="constant">$40C90FDB</span><span class="plain">; </span><span class="comment">2*pi</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_PI2</span><span class="plain"> = </span><span class="constant">$3FC90FDB</span><span class="plain">; </span><span class="comment">pi/2</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_NPI2</span><span class="plain"> = </span><span class="constant">$BFC90FDB</span><span class="plain">;</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_E</span><span class="plain"> = </span><span class="constant">$402DF854</span><span class="plain">;</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_E2</span><span class="plain"> = </span><span class="constant">$40EC7326</span><span class="plain">; </span><span class="comment">e^2</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_N0</span><span class="plain"> = </span><span class="constant">$80000000</span><span class="plain">; </span><span class="comment">negative zero</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_INF</span><span class="plain"> = </span><span class="constant">$7F800000</span><span class="plain">; </span><span class="comment">infinity</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_NINF</span><span class="plain"> = </span><span class="constant">$FF800000</span><span class="plain">; </span><span class="comment">negative infinity</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_NAN</span><span class="plain"> = </span><span class="constant">$7F800001</span><span class="plain">; </span><span class="comment">one of many NaN values</span>
<span class="reserved">Constant</span><span class="plain"> </span><span class="identifier">M_NNAN</span><span class="plain"> = </span><span class="constant">$FF800001</span><span class="plain">; </span><span class="comment">another, with a sign bit</span>
<span class="comment">Floating-point parsing routines.</span>
<span class="comment">Parse a float from a text buffer. Returns a float value, or FLOAT_NAN if</span>
<span class="comment">no value was understood.</span>
<span class="comment">The recognized format, if you'll pardon a slightly bastardized regexp</span>
<span class="comment">syntax, is "S?D*(PD*)?(ES?D+)?" where S is a sign character "+" or "-",</span>
<span class="comment">D is a decimal digit "0" to "9", P is a decimal point ".",</span>
<span class="comment">and E is the exponential modifier "E" or "e".</span>
<span class="comment">For flexibility, the string "M10^" is also accepted for E, where M is</span>
<span class="comment">"X", "x", "*", or the multiplication sign @{D7}. Optional spaces are</span>
<span class="comment">allowed before and after the M sign. (But only for the "10^" form of</span>
<span class="comment">the exponent, not the "e" form.)</span>
<span class="comment">This routine does not try to recognize special names for infinity or NaN,</span>
<span class="comment">but it can return FLOAT_INFINITY or FLOAT_NINFINITY if the exponent is too</span>
<span class="comment">large.</span>
<span class="comment">This routine relies on floating-point math. Therefore, the same string</span>
<span class="comment">may parse to slightly different float values on different interpreters!</span>
<span class="comment">Be warned.</span>
<span class="comment">If useall is true, this insists on using all len characters from the buffer.</span>
<span class="comment">(It returns FLOAT_NAN if any unrecognized characters are left over.)</span>
<span class="comment">Contrariwise, if useall is false, unused characters at the end of the buffer</span>
<span class="comment">are fine. (But not at the beginning; the float must start at the beginning</span>
<span class="comment">of the buffer.)</span>
<span class="plain">[ </span><span class="identifier">FloatParse</span><span class="plain"> </span><span class="identifier">buf</span><span class="plain"> </span><span class="identifier">len</span><span class="plain"> </span><span class="identifier">useall</span>
<span class="identifier">res</span><span class="plain"> </span><span class="identifier">ix</span><span class="plain"> </span><span class="identifier">val</span><span class="plain"> </span><span class="identifier">ch</span><span class="plain"> </span><span class="identifier">ten</span><span class="plain"> </span><span class="identifier">negative</span><span class="plain"> </span><span class="identifier">intpart</span><span class="plain"> </span><span class="identifier">fracpart</span><span class="plain"> </span><span class="identifier">fracdiv</span>
<span class="identifier">expon</span><span class="plain"> </span><span class="identifier">expnegative</span><span class="plain"> </span><span class="identifier">count</span><span class="plain">;</span>
<span class="comment">print "FloatParse &lt;";</span>
<span class="comment">for (ix=0: ix&lt;len: ix++) print (char) buf-&gt;ix;</span>
<span class="comment">print "&gt;^";</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">len</span><span class="plain"> == </span><span class="constant">0</span><span class="plain">)</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">FLOAT_NAN</span><span class="plain">;</span>
<span class="identifier">ix</span><span class="plain"> = </span><span class="constant">0</span><span class="plain">;</span>
<span class="identifier">negative</span><span class="plain"> = </span><span class="reserved">false</span><span class="plain">;</span>
<span class="identifier">intpart</span><span class="plain"> = </span><span class="constant">0</span><span class="plain">;</span>
<span class="identifier">fracpart</span><span class="plain"> = </span><span class="constant">0</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">numtof</span><span class="plain"> </span><span class="constant">10</span><span class="plain"> </span><span class="identifier">ten</span><span class="plain">;</span>
<span class="comment">Sign character (optional)</span>
<span class="identifier">ch</span><span class="plain"> = </span><span class="identifier">buf</span><span class="plain">-&gt;</span><span class="identifier">ix</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">ch</span><span class="plain"> == </span><span class="character">'-'</span><span class="plain">) {</span>
<span class="identifier">negative</span><span class="plain"> = </span><span class="reserved">true</span><span class="plain">;</span>
<span class="identifier">ix</span><span class="plain">++;</span>
<span class="plain">}</span>
<span class="reserved">else</span><span class="plain"> </span><span class="reserved">if</span><span class="plain"> (</span><span class="identifier">ch</span><span class="plain"> == </span><span class="character">'+'</span><span class="plain">) {</span>
<span class="identifier">ix</span><span class="plain">++;</span>
<span class="plain">}</span>
<span class="comment">Some digits (optional)</span>
<span class="reserved">for</span><span class="plain"> (</span><span class="identifier">count</span><span class="plain">=0 : </span><span class="identifier">ix</span><span class="plain">&lt;</span><span class="identifier">len</span><span class="plain"> : </span><span class="identifier">ix</span><span class="plain">++, </span><span class="identifier">count</span><span class="plain">++) {</span>
<span class="identifier">ch</span><span class="plain"> = </span><span class="identifier">buf</span><span class="plain">-&gt;</span><span class="identifier">ix</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">ch</span><span class="plain"> &lt; </span><span class="character">'0'</span><span class="plain"> || </span><span class="identifier">ch</span><span class="plain"> &gt; </span><span class="character">'9'</span><span class="plain">)</span>
<span class="reserved">break</span><span class="plain">;</span>
<span class="identifier">val</span><span class="plain"> = (</span><span class="identifier">ch</span><span class="plain"> - </span><span class="character">'0'</span><span class="plain">);</span>
<span class="plain">@</span><span class="identifier">numtof</span><span class="plain"> </span><span class="identifier">val</span><span class="plain"> </span><span class="identifier">val</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fmul</span><span class="plain"> </span><span class="identifier">intpart</span><span class="plain"> </span><span class="identifier">ten</span><span class="plain"> </span><span class="identifier">intpart</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fadd</span><span class="plain"> </span><span class="identifier">intpart</span><span class="plain"> </span><span class="identifier">val</span><span class="plain"> </span><span class="identifier">intpart</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="comment">Decimal point and more digits (optional)</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">ix</span><span class="plain">&lt;</span><span class="identifier">len</span><span class="plain"> &amp;&amp; </span><span class="identifier">buf</span><span class="plain">-&gt;</span><span class="identifier">ix</span><span class="plain"> == </span><span class="character">'.'</span><span class="plain">) {</span>
<span class="identifier">ix</span><span class="plain">++;</span>
<span class="plain">@</span><span class="identifier">numtof</span><span class="plain"> </span><span class="constant">1</span><span class="plain"> </span><span class="identifier">fracdiv</span><span class="plain">;</span>
<span class="reserved">for</span><span class="plain"> ( : </span><span class="identifier">ix</span><span class="plain">&lt;</span><span class="identifier">len</span><span class="plain"> : </span><span class="identifier">ix</span><span class="plain">++, </span><span class="identifier">count</span><span class="plain">++) {</span>
<span class="identifier">ch</span><span class="plain"> = </span><span class="identifier">buf</span><span class="plain">-&gt;</span><span class="identifier">ix</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">ch</span><span class="plain"> &lt; </span><span class="character">'0'</span><span class="plain"> || </span><span class="identifier">ch</span><span class="plain"> &gt; </span><span class="character">'9'</span><span class="plain">)</span>
<span class="reserved">break</span><span class="plain">;</span>
<span class="identifier">val</span><span class="plain"> = (</span><span class="identifier">ch</span><span class="plain"> - </span><span class="character">'0'</span><span class="plain">);</span>
<span class="plain">@</span><span class="identifier">numtof</span><span class="plain"> </span><span class="identifier">val</span><span class="plain"> </span><span class="identifier">val</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fmul</span><span class="plain"> </span><span class="identifier">fracpart</span><span class="plain"> </span><span class="identifier">ten</span><span class="plain"> </span><span class="identifier">fracpart</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fadd</span><span class="plain"> </span><span class="identifier">fracpart</span><span class="plain"> </span><span class="identifier">val</span><span class="plain"> </span><span class="identifier">fracpart</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fmul</span><span class="plain"> </span><span class="identifier">fracdiv</span><span class="plain"> </span><span class="identifier">ten</span><span class="plain"> </span><span class="identifier">fracdiv</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="plain">@</span><span class="identifier">fdiv</span><span class="plain"> </span><span class="identifier">fracpart</span><span class="plain"> </span><span class="identifier">fracdiv</span><span class="plain"> </span><span class="identifier">fracpart</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="comment">If there are no digits before *or* after the decimal point, fail.</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">count</span><span class="plain"> == </span><span class="constant">0</span><span class="plain">)</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">FLOAT_NAN</span><span class="plain">;</span>
<span class="comment">Combine the integer and fractional parts.</span>
<span class="plain">@</span><span class="identifier">fadd</span><span class="plain"> </span><span class="identifier">intpart</span><span class="plain"> </span><span class="identifier">fracpart</span><span class="plain"> </span><span class="identifier">res</span><span class="plain">;</span>
<span class="comment">Exponent (optional)</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">ix</span><span class="plain">&lt;</span><span class="identifier">len</span><span class="plain"> &amp;&amp; </span><span class="identifier">buf</span><span class="plain">-&gt;</span><span class="identifier">ix</span><span class="plain"> == </span><span class="character">'e'</span><span class="plain"> </span><span class="reserved">or</span><span class="plain"> </span><span class="character">'E'</span><span class="plain"> </span><span class="reserved">or</span><span class="plain"> </span><span class="character">' '</span><span class="plain"> </span><span class="reserved">or</span><span class="plain"> </span><span class="character">'*'</span><span class="plain"> </span><span class="reserved">or</span><span class="plain"> </span><span class="character">'x'</span><span class="plain"> </span><span class="reserved">or</span><span class="plain"> </span><span class="character">'X'</span><span class="plain"> </span><span class="reserved">or</span><span class="plain"> </span><span class="constant">$D7</span><span class="plain">) {</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">buf</span><span class="plain">-&gt;</span><span class="identifier">ix</span><span class="plain"> == </span><span class="character">'e'</span><span class="plain"> </span><span class="reserved">or</span><span class="plain"> </span><span class="character">'E'</span><span class="plain">) {</span>
<span class="comment">no spaces, just the 'e'</span>
<span class="identifier">ix</span><span class="plain">++;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">ix</span><span class="plain"> == </span><span class="identifier">len</span><span class="plain">)</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">FLOAT_NAN</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="reserved">else</span><span class="plain"> {</span>
<span class="comment">any number of spaces, "*", any number of spaces more, "10^"</span>
<span class="reserved">while</span><span class="plain"> (</span><span class="identifier">ix</span><span class="plain"> &lt; </span><span class="identifier">len</span><span class="plain"> &amp;&amp; </span><span class="identifier">buf</span><span class="plain">-&gt;</span><span class="identifier">ix</span><span class="plain"> == </span><span class="character">' '</span><span class="plain">)</span>
<span class="identifier">ix</span><span class="plain">++;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">ix</span><span class="plain"> == </span><span class="identifier">len</span><span class="plain">)</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">FLOAT_NAN</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">buf</span><span class="plain">-&gt;</span><span class="identifier">ix</span><span class="plain"> ~= </span><span class="character">'*'</span><span class="plain"> </span><span class="reserved">or</span><span class="plain"> </span><span class="character">'x'</span><span class="plain"> </span><span class="reserved">or</span><span class="plain"> </span><span class="character">'X'</span><span class="plain"> </span><span class="reserved">or</span><span class="plain"> </span><span class="constant">$D7</span><span class="plain">)</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">FLOAT_NAN</span><span class="plain">;</span>
<span class="identifier">ix</span><span class="plain">++;</span>
<span class="reserved">while</span><span class="plain"> (</span><span class="identifier">ix</span><span class="plain"> &lt; </span><span class="identifier">len</span><span class="plain"> &amp;&amp; </span><span class="identifier">buf</span><span class="plain">-&gt;</span><span class="identifier">ix</span><span class="plain"> == </span><span class="character">' '</span><span class="plain">)</span>
<span class="identifier">ix</span><span class="plain">++;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">ix</span><span class="plain"> == </span><span class="identifier">len</span><span class="plain">)</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">FLOAT_NAN</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">buf</span><span class="plain">-&gt;</span><span class="identifier">ix</span><span class="plain"> ~= </span><span class="character">'1'</span><span class="plain">)</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">FLOAT_NAN</span><span class="plain">;</span>
<span class="identifier">ix</span><span class="plain">++;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">buf</span><span class="plain">-&gt;</span><span class="identifier">ix</span><span class="plain"> ~= </span><span class="character">'0'</span><span class="plain">)</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">FLOAT_NAN</span><span class="plain">;</span>
<span class="identifier">ix</span><span class="plain">++;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">buf</span><span class="plain">-&gt;</span><span class="identifier">ix</span><span class="plain"> ~= </span><span class="constant">$5E</span><span class="plain">)</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">FLOAT_NAN</span><span class="plain">;</span>
<span class="identifier">ix</span><span class="plain">++;</span>
<span class="plain">}</span>
<span class="comment">Sign character (optional)</span>
<span class="identifier">expnegative</span><span class="plain"> = </span><span class="reserved">false</span><span class="plain">;</span>
<span class="identifier">ch</span><span class="plain"> = </span><span class="identifier">buf</span><span class="plain">-&gt;</span><span class="identifier">ix</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">ch</span><span class="plain"> == </span><span class="character">'-'</span><span class="plain">) {</span>
<span class="identifier">expnegative</span><span class="plain"> = </span><span class="reserved">true</span><span class="plain">;</span>
<span class="identifier">ix</span><span class="plain">++;</span>
<span class="plain">}</span>
<span class="reserved">else</span><span class="plain"> </span><span class="reserved">if</span><span class="plain"> (</span><span class="identifier">ch</span><span class="plain"> == </span><span class="character">'+'</span><span class="plain">) {</span>
<span class="identifier">ix</span><span class="plain">++;</span>
<span class="plain">}</span>
<span class="identifier">expon</span><span class="plain"> = </span><span class="constant">0</span><span class="plain">;</span>
<span class="comment">Some digits (mandatory)</span>
<span class="reserved">for</span><span class="plain"> (</span><span class="identifier">count</span><span class="plain">=0 : </span><span class="identifier">ix</span><span class="plain">&lt;</span><span class="identifier">len</span><span class="plain"> : </span><span class="identifier">ix</span><span class="plain">++, </span><span class="identifier">count</span><span class="plain">++) {</span>
<span class="identifier">ch</span><span class="plain"> = </span><span class="identifier">buf</span><span class="plain">-&gt;</span><span class="identifier">ix</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">ch</span><span class="plain"> &lt; </span><span class="character">'0'</span><span class="plain"> || </span><span class="identifier">ch</span><span class="plain"> &gt; </span><span class="character">'9'</span><span class="plain">)</span>
<span class="reserved">break</span><span class="plain">;</span>
<span class="identifier">expon</span><span class="plain"> = </span><span class="constant">10</span><span class="plain">*</span><span class="identifier">expon</span><span class="plain"> + (</span><span class="identifier">ch</span><span class="plain"> - </span><span class="character">'0'</span><span class="plain">);</span>
<span class="plain">}</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">count</span><span class="plain"> == </span><span class="constant">0</span><span class="plain">)</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">FLOAT_NAN</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">expnegative</span><span class="plain">)</span>
<span class="identifier">expon</span><span class="plain"> = -</span><span class="identifier">expon</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">expon</span><span class="plain">) {</span>
<span class="plain">@</span><span class="identifier">numtof</span><span class="plain"> </span><span class="identifier">expon</span><span class="plain"> </span><span class="identifier">expon</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">pow</span><span class="plain"> </span><span class="identifier">ten</span><span class="plain"> </span><span class="identifier">expon</span><span class="plain"> </span><span class="identifier">val</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fmul</span><span class="plain"> </span><span class="identifier">res</span><span class="plain"> </span><span class="identifier">val</span><span class="plain"> </span><span class="identifier">res</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="plain">}</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">negative</span><span class="plain">) {</span>
<span class="comment">set the value's sign bit</span>
<span class="identifier">res</span><span class="plain"> = </span><span class="constant">$80000000</span><span class="plain"> | </span><span class="identifier">res</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">useall</span><span class="plain"> &amp;&amp; </span><span class="identifier">ix</span><span class="plain"> ~= </span><span class="identifier">len</span><span class="plain">)</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">FLOAT_NAN</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">res</span><span class="plain">;</span>
<span class="plain">];</span>
<span class="comment">Floating-point printing routines. (These are based on code in</span>
<span class="comment">Glulxercise.inf, but modified.)</span>
<span class="comment">Print a float. This uses exponential notation ("[-]N.NNNe[+-]NN") if</span>
<span class="comment">the exponent is not between 6 and -4. If it is (that is, if the</span>
<span class="comment">absolute value is near 1.0) then it uses decimal notation ("[-]NNN.NNNNN").</span>
<span class="comment">The precision is the number of digits after the decimal point</span>
<span class="comment">(at least one, no more than eight). The default is five, because</span>
<span class="comment">beyond that rounding errors creep in, and even exactly-represented</span>
<span class="comment">float values are printed with trailing fudgy digits.</span>
<span class="comment">Trailing zeroes are trimmed.</span>
<span class="plain">[ </span><span class="identifier">Float</span><span class="plain"> </span><span class="identifier">val</span><span class="plain"> </span><span class="identifier">prec</span><span class="plain"> </span><span class="identifier">pval</span><span class="plain">;</span>
<span class="identifier">pval</span><span class="plain"> = </span><span class="identifier">val</span><span class="plain"> &amp; </span><span class="constant">$7FFFFFFF</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">jz</span><span class="plain"> </span><span class="identifier">pval</span><span class="plain"> ?</span><span class="identifier">UseFloatDec</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">jfge</span><span class="plain"> </span><span class="identifier">pval</span><span class="plain"> </span><span class="constant">$49742400</span><span class="plain"> ?</span><span class="identifier">UseFloatExp</span><span class="plain">; </span><span class="comment">1000000.0</span>
<span class="plain">@</span><span class="identifier">jflt</span><span class="plain"> </span><span class="identifier">pval</span><span class="plain"> </span><span class="constant">$38D1B717</span><span class="plain"> ?</span><span class="identifier">UseFloatExp</span><span class="plain">; </span><span class="comment">0.0001</span>
<span class="plain">.</span><span class="identifier">UseFloatDec</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">FloatDec</span><span class="plain">(</span><span class="identifier">val</span><span class="plain">, </span><span class="identifier">prec</span><span class="plain">);</span>
<span class="plain">.</span><span class="identifier">UseFloatExp</span><span class="plain">;</span>
<span class="reserved">return</span><span class="plain"> </span><span class="identifier">FloatExp</span><span class="plain">(</span><span class="identifier">val</span><span class="plain">, </span><span class="identifier">prec</span><span class="plain">);</span>
<span class="plain">];</span>
<span class="reserved">Array</span><span class="plain"> </span><span class="identifier">PowersOfTen</span><span class="plain"> --&gt; </span><span class="constant">1</span><span class="plain"> </span><span class="constant">10</span><span class="plain"> </span><span class="constant">100</span><span class="plain"> </span><span class="constant">1000</span><span class="plain"> </span><span class="constant">10000</span><span class="plain"> </span><span class="constant">100000</span><span class="plain"> </span><span class="constant">1000000</span><span class="plain"> </span><span class="constant">10000000</span><span class="plain"> </span><span class="constant">100000000</span><span class="plain"> </span><span class="constant">1000000000</span><span class="plain">;</span>
<span class="comment">Print a float in exponential notation: "[-]N.NNNe[+-]NN".</span>
<span class="comment">The precision is the number of digits after the decimal point</span>
<span class="comment">(at least one, no more than eight). The default is five, because</span>
<span class="comment">beyond that rounding errors creep in, and even exactly-represented</span>
<span class="comment">float values are printed with trailing fudgy digits.</span>
<span class="comment">Trailing zeroes are trimmed.</span>
<span class="plain">[ </span><span class="identifier">FloatExp</span><span class="plain"> </span><span class="identifier">val</span><span class="plain"> </span><span class="identifier">prec</span><span class="plain"> </span><span class="identifier">log10val</span><span class="plain"> </span><span class="identifier">expo</span><span class="plain"> </span><span class="identifier">fexpo</span><span class="plain"> </span><span class="identifier">idig</span><span class="plain"> </span><span class="identifier">ix</span><span class="plain"> </span><span class="identifier">pow10</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">prec</span><span class="plain"> == </span><span class="constant">0</span><span class="plain">)</span>
<span class="identifier">prec</span><span class="plain"> = </span><span class="constant">5</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">prec</span><span class="plain"> &gt; </span><span class="constant">8</span><span class="plain">)</span>
<span class="identifier">prec</span><span class="plain"> = </span><span class="constant">8</span><span class="plain">;</span>
<span class="identifier">pow10</span><span class="plain"> = </span><span class="identifier">PowersOfTen</span><span class="plain"> --&gt; </span><span class="identifier">prec</span><span class="plain">;</span>
<span class="comment">Knock off the sign bit first.</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">val</span><span class="plain"> &amp; </span><span class="constant">$80000000</span><span class="plain">) {</span>
<span class="plain">@</span><span class="identifier">streamchar</span><span class="plain"> </span><span class="character">'-'</span><span class="plain">;</span>
<span class="identifier">val</span><span class="plain"> = </span><span class="identifier">val</span><span class="plain"> &amp; </span><span class="constant">$7FFFFFFF</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="plain">@</span><span class="identifier">jisnan</span><span class="plain"> </span><span class="identifier">val</span><span class="plain"> ?</span><span class="identifier">IsNan</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">jisinf</span><span class="plain"> </span><span class="identifier">val</span><span class="plain"> ?</span><span class="identifier">IsInf</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">val</span><span class="plain"> == </span><span class="constant">$0</span><span class="plain">) {</span>
<span class="identifier">expo</span><span class="plain"> = </span><span class="constant">0</span><span class="plain">;</span>
<span class="identifier">idig</span><span class="plain"> = </span><span class="constant">0</span><span class="plain">;</span>
<span class="reserved">jump</span><span class="plain"> </span><span class="identifier">DoPrint</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="comment">Take as an example val=123.5, with precision=6. The desired</span>
<span class="comment">result is "1.23000e+02".</span>
<span class="plain">@</span><span class="identifier">log</span><span class="plain"> </span><span class="identifier">val</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fdiv</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="constant">$40135D8E</span><span class="plain"> </span><span class="identifier">log10val</span><span class="plain">; </span><span class="comment">\(40135D8E is log(10)</span>
<span class="plain">@</span><span class="identifier">floor</span><span class="plain"> </span><span class="identifier">log10val</span><span class="plain"> </span><span class="identifier">fexpo</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">ftonumn</span><span class="plain"> </span><span class="identifier">fexpo</span><span class="plain"> </span><span class="identifier">expo</span><span class="plain">;</span>
<span class="comment">expo is now the exponent (as an integer). For our example, expo=2.</span>
<span class="plain">@</span><span class="identifier">fsub</span><span class="plain"> </span><span class="identifier">log10val</span><span class="plain"> </span><span class="identifier">fexpo</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">numtof</span><span class="plain"> </span><span class="identifier">prec</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fadd</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fmul</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="constant">$40135D8E</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">exp</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="comment">The stack value is now exp((log10val - fexpo + prec) * log(10)).</span>
<span class="comment">We've shifted the decimal point left by expo digits (so that</span>
<span class="comment">it's after the first nonzero digit), and then right by prec</span>
<span class="comment">digits. In our example, that would be 1235000.0.</span>
<span class="plain">@</span><span class="identifier">ftonumn</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="identifier">idig</span><span class="plain">;</span>
<span class="comment">Round to an integer, and we have 1235000. Notice that this is</span>
<span class="comment">exactly the digits we want to print (if we stick a decimal point</span>
<span class="comment">after the first).</span>
<span class="plain">.</span><span class="identifier">DoPrint</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">idig</span><span class="plain"> &gt;= </span><span class="constant">10</span><span class="plain">*</span><span class="identifier">pow10</span><span class="plain">) {</span>
<span class="comment">Rounding errors have left us outside the decimal range of</span>
<span class="comment">[1.0, 10.0) where we should be. Adjust to the next higher</span>
<span class="comment">exponent.</span>
<span class="identifier">expo</span><span class="plain">++;</span>
<span class="plain">@</span><span class="identifier">div</span><span class="plain"> </span><span class="identifier">idig</span><span class="plain"> </span><span class="constant">10</span><span class="plain"> </span><span class="identifier">idig</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="comment">Trim off trailing zeroes, as long as there's at least one digit</span>
<span class="comment">after the decimal point. (Delete this stanza if you want to</span>
<span class="comment">keep the trailing zeroes.)</span>
<span class="reserved">while</span><span class="plain"> (</span><span class="identifier">prec</span><span class="plain"> &gt; </span><span class="constant">1</span><span class="plain">) {</span>
<span class="plain">@</span><span class="identifier">mod</span><span class="plain"> </span><span class="identifier">idig</span><span class="plain"> </span><span class="constant">10</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">jnz</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> ?</span><span class="identifier">DoneTrimming</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">div</span><span class="plain"> </span><span class="identifier">pow10</span><span class="plain"> </span><span class="constant">10</span><span class="plain"> </span><span class="identifier">pow10</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">div</span><span class="plain"> </span><span class="identifier">idig</span><span class="plain"> </span><span class="constant">10</span><span class="plain"> </span><span class="identifier">idig</span><span class="plain">;</span>
<span class="identifier">prec</span><span class="plain">--;</span>
<span class="plain">}</span>
<span class="plain">.</span><span class="identifier">DoneTrimming</span><span class="plain">;</span>
<span class="reserved">for</span><span class="plain"> (</span><span class="identifier">ix</span><span class="plain">=0 : </span><span class="identifier">ix</span><span class="plain">&lt;=</span><span class="identifier">prec</span><span class="plain"> : </span><span class="identifier">ix</span><span class="plain">++) {</span>
<span class="plain">@</span><span class="identifier">div</span><span class="plain"> </span><span class="identifier">idig</span><span class="plain"> </span><span class="identifier">pow10</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">mod</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="constant">10</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">streamnum</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">ix</span><span class="plain"> == </span><span class="constant">0</span><span class="plain">)</span>
<span class="plain">@</span><span class="identifier">streamchar</span><span class="plain"> </span><span class="character">'.'</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">div</span><span class="plain"> </span><span class="identifier">pow10</span><span class="plain"> </span><span class="constant">10</span><span class="plain"> </span><span class="identifier">pow10</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="comment">Print the exponent. There are two conventions coded here: the</span>
<span class="comment">programmatic ("1.0e+00") and the literary ("1.0 x 10^0").</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">TEMPLATE_CONFIGURATION_BITMAP</span><span class="plain"> &amp; </span><span class="identifier">PROGRAMMING_EXPONENTS_TCBIT</span><span class="plain"> == </span><span class="constant">0</span><span class="plain">) {</span>
<span class="identifier">PrintMultiplicationSign</span><span class="plain">();</span>
<span class="plain">@</span><span class="identifier">streamstr</span><span class="plain"> </span><span class="string">"10"</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">streamchar</span><span class="plain"> </span><span class="constant">$5E</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">streamnum</span><span class="plain"> </span><span class="identifier">expo</span><span class="plain">;</span>
<span class="plain">} </span><span class="reserved">else</span><span class="plain"> {</span>
<span class="comment">Convention is to use at least two digits.</span>
<span class="plain">@</span><span class="identifier">streamchar</span><span class="plain"> </span><span class="character">'e'</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">expo</span><span class="plain"> &lt; </span><span class="constant">0</span><span class="plain">) {</span>
<span class="plain">@</span><span class="identifier">streamchar</span><span class="plain"> </span><span class="character">'-'</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">neg</span><span class="plain"> </span><span class="identifier">expo</span><span class="plain"> </span><span class="identifier">expo</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="reserved">else</span><span class="plain"> {</span>
<span class="plain">@</span><span class="identifier">streamchar</span><span class="plain"> </span><span class="character">'+'</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">expo</span><span class="plain"> &lt; </span><span class="constant">10</span><span class="plain">)</span>
<span class="plain">@</span><span class="identifier">streamchar</span><span class="plain"> </span><span class="character">'0'</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">streamnum</span><span class="plain"> </span><span class="identifier">expo</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="reserved">rtrue</span><span class="plain">;</span>
<span class="plain">.</span><span class="identifier">IsNan</span><span class="plain">;</span>
<span class="identifier">PrintNan</span><span class="plain">();</span>
<span class="reserved">rtrue</span><span class="plain">;</span>
<span class="plain">.</span><span class="identifier">IsInf</span><span class="plain">;</span>
<span class="identifier">PrintInfinity</span><span class="plain">();</span>
<span class="reserved">rtrue</span><span class="plain">;</span>
<span class="plain">];</span>
<span class="comment">Print a float in decimal notation: "[-]NNN.NNNNN".</span>
<span class="comment">The precision is the number of digits after the decimal point</span>
<span class="comment">(at least one, no more than eight). The default is five, because</span>
<span class="comment">beyond that rounding errors creep in, and even exactly-represented</span>
<span class="comment">float values are printed with trailing fudgy digits.</span>
<span class="comment">Trailing zeroes are trimmed.</span>
<span class="plain">[ </span><span class="identifier">FloatDec</span><span class="plain"> </span><span class="identifier">val</span><span class="plain"> </span><span class="identifier">prec</span><span class="plain"> </span><span class="identifier">log10val</span><span class="plain"> </span><span class="identifier">int</span><span class="plain"> </span><span class="identifier">fint</span><span class="plain"> </span><span class="identifier">extra0</span><span class="plain"> </span><span class="identifier">frac</span><span class="plain"> </span><span class="identifier">idig</span><span class="plain"> </span><span class="identifier">ix</span><span class="plain"> </span><span class="identifier">pow10</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">prec</span><span class="plain"> == </span><span class="constant">0</span><span class="plain">)</span>
<span class="identifier">prec</span><span class="plain"> = </span><span class="constant">5</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">prec</span><span class="plain"> &gt; </span><span class="constant">8</span><span class="plain">)</span>
<span class="identifier">prec</span><span class="plain"> = </span><span class="constant">8</span><span class="plain">;</span>
<span class="identifier">pow10</span><span class="plain"> = </span><span class="identifier">PowersOfTen</span><span class="plain"> --&gt; </span><span class="identifier">prec</span><span class="plain">;</span>
<span class="comment">Knock off the sign bit first.</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">val</span><span class="plain"> &amp; </span><span class="constant">$80000000</span><span class="plain">) {</span>
<span class="plain">@</span><span class="identifier">streamchar</span><span class="plain"> </span><span class="character">'-'</span><span class="plain">;</span>
<span class="identifier">val</span><span class="plain"> = </span><span class="identifier">val</span><span class="plain"> &amp; </span><span class="constant">$7FFFFFFF</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="plain">@</span><span class="identifier">jisnan</span><span class="plain"> </span><span class="identifier">val</span><span class="plain"> ?</span><span class="identifier">IsNan</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">jisinf</span><span class="plain"> </span><span class="identifier">val</span><span class="plain"> ?</span><span class="identifier">IsInf</span><span class="plain">;</span>
<span class="comment">Take as an example val=123.5, with precision=6. The desired result</span>
<span class="comment">is "123.50000".</span>
<span class="identifier">extra0</span><span class="plain"> = </span><span class="constant">0</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fmod</span><span class="plain"> </span><span class="identifier">val</span><span class="plain"> </span><span class="constant">$3F800000</span><span class="plain"> </span><span class="identifier">frac</span><span class="plain"> </span><span class="identifier">fint</span><span class="plain">; </span><span class="comment">\(3F800000 is 1.0.</span>
<span class="plain">@</span><span class="identifier">ftonumz</span><span class="plain"> </span><span class="identifier">fint</span><span class="plain"> </span><span class="identifier">int</span><span class="plain">;</span>
<span class="comment">This converts the integer part of the value to an integer value;</span>
<span class="comment">in our example, 123.</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">int</span><span class="plain"> == </span><span class="constant">$7FFFFFFF</span><span class="plain">) {</span>
<span class="comment">Looks like the integer part of the value is bigger than</span>
<span class="comment">we can store in an int variable. (It could be as large</span>
<span class="comment">as 3e+38.) We're going to have to use a log function to</span>
<span class="comment">reduce it by some number of factors of 10, and then pad</span>
<span class="comment">with zeroes.</span>
<span class="plain">@</span><span class="identifier">log</span><span class="plain"> </span><span class="identifier">fint</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fdiv</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="constant">$40135D8E</span><span class="plain"> </span><span class="identifier">log10val</span><span class="plain">; </span><span class="comment">\(40135D8E is log(10)</span>
<span class="plain">@</span><span class="identifier">ftonumz</span><span class="plain"> </span><span class="identifier">log10val</span><span class="plain"> </span><span class="identifier">extra0</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">sub</span><span class="plain"> </span><span class="identifier">extra0</span><span class="plain"> </span><span class="constant">8</span><span class="plain"> </span><span class="identifier">extra0</span><span class="plain">;</span>
<span class="comment">extra0 is the number of zeroes we'll be padding with.</span>
<span class="plain">@</span><span class="identifier">numtof</span><span class="plain"> </span><span class="identifier">extra0</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fsub</span><span class="plain"> </span><span class="identifier">log10val</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fmul</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="constant">$40135D8E</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">exp</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="comment">The stack value is now exp((log10val - extra0) * log(10)).</span>
<span class="comment">We've shifted the decimal point far enough left to leave</span>
<span class="comment">about eight digits, which is all we can print as an integer.</span>
<span class="plain">@</span><span class="identifier">ftonumz</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="identifier">int</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="comment">Print the integer part.</span>
<span class="plain">@</span><span class="identifier">streamnum</span><span class="plain"> </span><span class="identifier">int</span><span class="plain">;</span>
<span class="reserved">for</span><span class="plain"> (</span><span class="identifier">ix</span><span class="plain">=0 : </span><span class="identifier">ix</span><span class="plain">&lt;</span><span class="identifier">extra0</span><span class="plain"> : </span><span class="identifier">ix</span><span class="plain">++)</span>
<span class="plain">@</span><span class="identifier">streamchar</span><span class="plain"> </span><span class="character">'0'</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">streamchar</span><span class="plain"> </span><span class="character">'.'</span><span class="plain">;</span>
<span class="comment">Now we need to print the frac part, which is .5.</span>
<span class="plain">@</span><span class="identifier">log</span><span class="plain"> </span><span class="identifier">frac</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fdiv</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="constant">$40135D8E</span><span class="plain"> </span><span class="identifier">log10val</span><span class="plain">; </span><span class="comment">\(40135D8E is log(10)</span>
<span class="plain">@</span><span class="identifier">numtof</span><span class="plain"> </span><span class="identifier">prec</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fadd</span><span class="plain"> </span><span class="identifier">log10val</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">fmul</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="constant">$40135D8E</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">exp</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="comment">The stack value is now exp((frac + prec) * log(10)).</span>
<span class="comment">We've shifted the decimal point right by prec</span>
<span class="comment">digits. In our example, that would be 50000.0.</span>
<span class="plain">@</span><span class="identifier">ftonumn</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="identifier">idig</span><span class="plain">;</span>
<span class="comment">Round to an integer, and we have 50000. Notice that this is</span>
<span class="comment">exactly the (post-decimal-point) digits we want to print.</span>
<span class="plain">.</span><span class="identifier">DoPrint</span><span class="plain">;</span>
<span class="reserved">if</span><span class="plain"> (</span><span class="identifier">idig</span><span class="plain"> &gt;= </span><span class="identifier">pow10</span><span class="plain">) {</span>
<span class="comment">Rounding errors have left us outside the decimal range of</span>
<span class="comment">[0.0, 1.0) where we should be. I'm not sure this is possible,</span>
<span class="comment">actually, but we'll just adjust downward.</span>
<span class="identifier">idig</span><span class="plain"> = </span><span class="identifier">pow10</span><span class="plain"> - </span><span class="constant">1</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="comment">Trim off trailing zeroes, as long as there's at least one digit</span>
<span class="comment">after the decimal point. (Delete this stanza if you want to</span>
<span class="comment">keep the trailing zeroes.)</span>
<span class="reserved">while</span><span class="plain"> (</span><span class="identifier">prec</span><span class="plain"> &gt; </span><span class="constant">1</span><span class="plain">) {</span>
<span class="plain">@</span><span class="identifier">mod</span><span class="plain"> </span><span class="identifier">idig</span><span class="plain"> </span><span class="constant">10</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">jnz</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> ?</span><span class="identifier">DoneTrimming</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">div</span><span class="plain"> </span><span class="identifier">pow10</span><span class="plain"> </span><span class="constant">10</span><span class="plain"> </span><span class="identifier">pow10</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">div</span><span class="plain"> </span><span class="identifier">idig</span><span class="plain"> </span><span class="constant">10</span><span class="plain"> </span><span class="identifier">idig</span><span class="plain">;</span>
<span class="identifier">prec</span><span class="plain">--;</span>
<span class="plain">}</span>
<span class="plain">.</span><span class="identifier">DoneTrimming</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">div</span><span class="plain"> </span><span class="identifier">pow10</span><span class="plain"> </span><span class="constant">10</span><span class="plain"> </span><span class="identifier">pow10</span><span class="plain">;</span>
<span class="reserved">for</span><span class="plain"> (</span><span class="identifier">ix</span><span class="plain">=0 : </span><span class="identifier">ix</span><span class="plain">&lt;</span><span class="identifier">prec</span><span class="plain"> : </span><span class="identifier">ix</span><span class="plain">++) {</span>
<span class="plain">@</span><span class="identifier">div</span><span class="plain"> </span><span class="identifier">idig</span><span class="plain"> </span><span class="identifier">pow10</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">mod</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain"> </span><span class="constant">10</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">streamnum</span><span class="plain"> </span><span class="identifier">sp</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">div</span><span class="plain"> </span><span class="identifier">pow10</span><span class="plain"> </span><span class="constant">10</span><span class="plain"> </span><span class="identifier">pow10</span><span class="plain">;</span>
<span class="plain">}</span>
<span class="reserved">rtrue</span><span class="plain">;</span>
<span class="plain">.</span><span class="identifier">IsNan</span><span class="plain">;</span>
<span class="identifier">PrintNan</span><span class="plain">();</span>
<span class="reserved">rtrue</span><span class="plain">;</span>
<span class="plain">.</span><span class="identifier">IsInf</span><span class="plain">;</span>
<span class="identifier">PrintInfinity</span><span class="plain">();</span>
<span class="reserved">rtrue</span><span class="plain">;</span>
<span class="plain">];</span>
<span class="plain">[ </span><span class="identifier">PrintInfinity</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">streamunichar</span><span class="plain"> </span><span class="constant">$221E</span><span class="plain">;</span>
<span class="comment">@streamstr "Inf";</span>
<span class="plain">];</span>
<span class="plain">[ </span><span class="identifier">PrintNan</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">streamunichar</span><span class="plain"> </span><span class="constant">$26a0</span><span class="plain">;</span>
<span class="comment">@streamstr "NaN";</span>
<span class="plain">];</span>
<span class="plain">[ </span><span class="identifier">PrintMultiplicationSign</span><span class="plain">;</span>
<span class="reserved">print</span><span class="plain"> </span><span class="string">" "</span><span class="plain">;</span>
<span class="plain">@</span><span class="identifier">streamunichar</span><span class="plain"> </span><span class="constant">$D7</span><span class="plain">;</span>
<span class="reserved">print</span><span class="plain"> </span><span class="string">" "</span><span class="plain">;</span>
<span class="comment">@streamstr " x ";</span>
<span class="plain">];</span>
<span class="plain">#</span><span class="identifier">Ifnot</span><span class="plain">; </span><span class="comment">TARGET_GLULX</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Say</span><span class="plain"> </span><span class="identifier">real</span><span class="plain">; </span><span class="reserved">print</span><span class="plain"> </span><span class="identifier">real</span><span class="plain">; ]; </span><span class="comment">Needs to exist, but likely never used</span>
<span class="plain">[ </span><span class="identifier">REAL_NUMBER_TY_Compare</span><span class="plain"> </span><span class="identifier">r1</span><span class="plain"> </span><span class="identifier">r2</span><span class="plain">; </span><span class="reserved">return</span><span class="plain"> </span><span class="identifier">UnsignedCompare</span><span class="plain">(</span><span class="identifier">r1</span><span class="plain">, </span><span class="identifier">r2</span><span class="plain">); ];</span>
<span class="plain">#</span><span class="identifier">Endif</span><span class="plain">; </span><span class="comment">TARGET_GLULX</span>
</pre>
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