Neptune-defined arithmetic

README.md

@@ -1,6 +1,6 @@
 # Inform 7
 
-[Version](notes/versioning.md): 10.2.0-beta+6X48 'Krypton' (26 April 2024)
+[Version](notes/versioning.md): 10.2.0-beta+6X49 'Krypton' (27 April 2024)
 
 ## About Inform
 

build.txt

@@ -1,3 +1,3 @@
 Prerelease: beta
-Build Date: 26 April 2024
-Build Number: 6X48
+Build Date: 27 April 2024
+Build Number: 6X49

docs/BasicInformKit/S-mth.html

@@ -64,9 +64,23 @@ <h1><a href="../index.html">
     <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></div>
 <p class="purpose">Mathematical functions which involve integers.</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. SignedCompare</a></li></ul><hr class="tocbar">
+<ul class="toc"><li><a href="S-mth.html#SP1">&#167;1. Modular arithmetic</a></li><li><a href="S-mth.html#SP2">&#167;2. Square Root</a></li><li><a href="S-mth.html#SP3">&#167;3. Cube Root</a></li><li><a href="S-mth.html#SP4">&#167;4. Absolute value</a></li><li><a href="S-mth.html#SP5">&#167;5. IntegerDivide</a></li><li><a href="S-mth.html#SP6">&#167;6. IntegerRemainder</a></li><li><a href="S-mth.html#SP7">&#167;7. SignedCompare</a></li></ul><hr class="tocbar">
 
-<p class="commentary firstcommentary"><a id="SP1" class="paragraph-anchor"></a><b>&#167;1. Square Root. </b>We only calculate by hand if we have to.
+<p class="commentary firstcommentary"><a id="SP1" class="paragraph-anchor"></a><b>&#167;1. Modular arithmetic. </b>For every integer n there is a unique congruence class 0, 1, ..., m-1 modulo m
+to which that integer belongs, and this function returns it. Note that the
+normal I6 operation % is signed, which is why we need this function.
+</p>
+
+<pre class="displayed-code all-displayed-code code-font">
+<span class="plain-syntax">[ </span><span class="identifier-syntax">CongruenceClass</span><span class="plain-syntax"> </span><span class="identifier-syntax">n</span><span class="plain-syntax"> </span><span class="identifier-syntax">modulus</span><span class="plain-syntax">;</span>
+<span class="plain-syntax">    </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">modulus</span><span class="plain-syntax"> &gt; </span><span class="constant-syntax">0</span><span class="plain-syntax">) {</span>
+<span class="plain-syntax">        </span><span class="identifier-syntax">n</span><span class="plain-syntax"> = </span><span class="identifier-syntax">n</span><span class="plain-syntax">%</span><span class="identifier-syntax">modulus</span><span class="plain-syntax">;</span>
+<span class="plain-syntax">        </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">n</span><span class="plain-syntax"> &lt; </span><span class="constant-syntax">0</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">n</span><span class="plain-syntax"> + </span><span class="identifier-syntax">modulus</span><span class="plain-syntax">;</span>
+<span class="plain-syntax">    }</span>
+<span class="plain-syntax">    </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">n</span><span class="plain-syntax">;</span>
+<span class="plain-syntax">];</span>
+</pre>
+<p class="commentary firstcommentary"><a id="SP2" class="paragraph-anchor"></a><b>&#167;2. Square Root. </b>We only calculate by hand if we have to.
 </p>
 
 <p class="commentary">The slower integer method is an old algorithm for extracting binary square
@@ -106,7 +120,7 @@ <h1><a href="../index.html">
 <span class="plain-syntax">    </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">res</span><span class="plain-syntax">;</span>
 <span class="plain-syntax">];</span>
 </pre>
-<p class="commentary firstcommentary"><a id="SP2" class="paragraph-anchor"></a><b>&#167;2. Cube Root. </b>Again, the technique here is a fallback measure. It's an iterative scheme for
+<p class="commentary firstcommentary"><a id="SP3" class="paragraph-anchor"></a><b>&#167;3. Cube Root. </b>Again, the technique here is a fallback measure. It's 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.
@@ -121,13 +135,13 @@ <h1><a href="../index.html">
 <span class="plain-syntax">    </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">x</span><span class="plain-syntax">;</span>
 <span class="plain-syntax">];</span>
 </pre>
-<p class="commentary firstcommentary"><a id="SP3" class="paragraph-anchor"></a><b>&#167;3. Absolute value. </b>Of an integer:
+<p class="commentary firstcommentary"><a id="SP4" class="paragraph-anchor"></a><b>&#167;4. Absolute value. </b>Of an integer:
 </p>
 
 <pre class="displayed-code all-displayed-code code-font">
 <span class="plain-syntax">[ </span><span class="identifier-syntax">NUMBER_TY_Abs</span><span class="plain-syntax"> </span><span class="identifier-syntax">x</span><span class="plain-syntax">; </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">x</span><span class="plain-syntax">&lt;0) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> -</span><span class="identifier-syntax">x</span><span class="plain-syntax">; </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">x</span><span class="plain-syntax">; ];</span>
 </pre>
-<p class="commentary firstcommentary"><a id="SP4" class="paragraph-anchor"></a><b>&#167;4. IntegerDivide. </b>We can't simply use I6's <span class="extract"><span class="extract-syntax">/</span></span> operator, as that translates directly into a
+<p class="commentary firstcommentary"><a id="SP5" class="paragraph-anchor"></a><b>&#167;5. IntegerDivide. </b>We can't simply use I6's <span class="extract"><span class="extract-syntax">/</span></span> operator, as that translates directly into a
 virtual machine opcode which crashes on divide by zero.
 </p>
 
@@ -137,7 +151,7 @@ <h1><a href="../index.html">
 <span class="plain-syntax">    </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">A</span><span class="plain-syntax">/</span><span class="identifier-syntax">B</span><span class="plain-syntax">;</span>
 <span class="plain-syntax">];</span>
 </pre>
-<p class="commentary firstcommentary"><a id="SP5" class="paragraph-anchor"></a><b>&#167;5. IntegerRemainder. </b>Similarly.
+<p class="commentary firstcommentary"><a id="SP6" class="paragraph-anchor"></a><b>&#167;6. IntegerRemainder. </b>Similarly.
 </p>
 
 <pre class="displayed-code all-displayed-code code-font">
@@ -146,7 +160,7 @@ <h1><a href="../index.html">
 <span class="plain-syntax">    </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">A</span><span class="plain-syntax">%</span><span class="identifier-syntax">B</span><span class="plain-syntax">;</span>
 <span class="plain-syntax">];</span>
 </pre>
-<p class="commentary firstcommentary"><a id="SP6" class="paragraph-anchor"></a><b>&#167;6. SignedCompare. </b>This routine is hardly ever needed; it wraps up ordinary comparisons.
+<p class="commentary firstcommentary"><a id="SP7" class="paragraph-anchor"></a><b>&#167;7. SignedCompare. </b>This routine is hardly ever needed; it wraps up ordinary comparisons.
 </p>
 
 <pre class="displayed-code all-displayed-code code-font">

docs/WorldModelKit/S-tm.html

@@ -56,9 +56,7 @@ <h1><a href="../index.html">
 
 <pre class="displayed-code all-displayed-code code-font">
 <span class="plain-syntax">[ </span><span class="identifier-syntax">NUMBER_TY_to_TIME_TY</span><span class="plain-syntax"> </span><span class="identifier-syntax">n</span><span class="plain-syntax">;</span>
-<span class="plain-syntax">    </span><span class="identifier-syntax">n</span><span class="plain-syntax"> = </span><span class="identifier-syntax">n</span><span class="plain-syntax">%1440;</span>
-<span class="plain-syntax">    </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">n</span><span class="plain-syntax"> &lt; </span><span class="constant-syntax">0</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">n</span><span class="plain-syntax"> + </span><span class="constant-syntax">1440</span><span class="plain-syntax">;</span>
-<span class="plain-syntax">    </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">n</span><span class="plain-syntax">;</span>
+<span class="plain-syntax">    </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">CongruenceClass</span><span class="plain-syntax">(</span><span class="identifier-syntax">n</span><span class="plain-syntax">, </span><span class="constant-syntax">1440</span><span class="plain-syntax">);</span>
 <span class="plain-syntax">];</span>
 </pre>
 <p class="commentary firstcommentary"><a id="SP2" class="paragraph-anchor"></a><b>&#167;2. Digital Printing. </b>For instance, "2:06 am".

docs/assertions-module/5-ptd.html

@@ -816,8 +816,15 @@ <h1><a href="../index.html">
 <span class="plain-syntax">}</span>
 
 <span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="function-syntax">IDTypeData::is_arithmetic_phrase</span><span class="plain-syntax">(</span><span class="reserved-syntax">id_body</span><span class="plain-syntax"> *</span><span class="identifier-syntax">idb</span><span class="plain-syntax">) {</span>
-<span class="plain-syntax">    </span><span class="reserved-syntax">if</span><span class="plain-syntax"> ((</span><a href="5-ptd.html#SP24" class="function-link"><span class="function-syntax">IDTypeData::arithmetic_operation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">idb</span><span class="plain-syntax">) &gt;= </span><span class="constant-syntax">0</span><span class="plain-syntax">) &amp;&amp;</span>
-<span class="plain-syntax">        (</span><a href="5-ptd.html#SP24" class="function-link"><span class="function-syntax">IDTypeData::arithmetic_operation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">idb</span><span class="plain-syntax">) &lt; </span><span class="identifier-syntax">NO_OPERATIONS</span><span class="plain-syntax">)) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">TRUE</span><span class="plain-syntax">;</span>
+<span class="plain-syntax">    </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="5-ptd.html#SP24" class="function-link"><span class="function-syntax">IDTypeData::arithmetic_operation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">idb</span><span class="plain-syntax">) == </span><span class="identifier-syntax">PLUS_OPERATION</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">TRUE</span><span class="plain-syntax">;</span>
+<span class="plain-syntax">    </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="5-ptd.html#SP24" class="function-link"><span class="function-syntax">IDTypeData::arithmetic_operation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">idb</span><span class="plain-syntax">) == </span><span class="identifier-syntax">MINUS_OPERATION</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">TRUE</span><span class="plain-syntax">;</span>
+<span class="plain-syntax">    </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="5-ptd.html#SP24" class="function-link"><span class="function-syntax">IDTypeData::arithmetic_operation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">idb</span><span class="plain-syntax">) == </span><span class="identifier-syntax">TIMES_OPERATION</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">TRUE</span><span class="plain-syntax">;</span>
+<span class="plain-syntax">    </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="5-ptd.html#SP24" class="function-link"><span class="function-syntax">IDTypeData::arithmetic_operation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">idb</span><span class="plain-syntax">) == </span><span class="identifier-syntax">DIVIDE_OPERATION</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">TRUE</span><span class="plain-syntax">;</span>
+<span class="plain-syntax">    </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="5-ptd.html#SP24" class="function-link"><span class="function-syntax">IDTypeData::arithmetic_operation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">idb</span><span class="plain-syntax">) == </span><span class="identifier-syntax">REMAINDER_OPERATION</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">TRUE</span><span class="plain-syntax">;</span>
+<span class="plain-syntax">    </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="5-ptd.html#SP24" class="function-link"><span class="function-syntax">IDTypeData::arithmetic_operation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">idb</span><span class="plain-syntax">) == </span><span class="identifier-syntax">APPROXIMATE_OPERATION</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">TRUE</span><span class="plain-syntax">;</span>
+<span class="plain-syntax">    </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="5-ptd.html#SP24" class="function-link"><span class="function-syntax">IDTypeData::arithmetic_operation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">idb</span><span class="plain-syntax">) == </span><span class="identifier-syntax">ROOT_OPERATION</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">TRUE</span><span class="plain-syntax">;</span>
+<span class="plain-syntax">    </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="5-ptd.html#SP24" class="function-link"><span class="function-syntax">IDTypeData::arithmetic_operation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">idb</span><span class="plain-syntax">) == </span><span class="identifier-syntax">REALROOT_OPERATION</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">TRUE</span><span class="plain-syntax">;</span>
+<span class="plain-syntax">    </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><a href="5-ptd.html#SP24" class="function-link"><span class="function-syntax">IDTypeData::arithmetic_operation</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">idb</span><span class="plain-syntax">) == </span><span class="identifier-syntax">CUBEROOT_OPERATION</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">TRUE</span><span class="plain-syntax">;</span>
 <span class="plain-syntax">    </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">;</span>
 <span class="plain-syntax">}</span>