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<!--Weave of 'Scaled Arithmetic Values' generated by Inweb-->
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<div class="breadcrumbs">
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<ul class="crumbs"><li><a href="../index.html">Home</a></li><li><a href="../compiler.html">Inform7 Modules</a></li><li><a href="index.html">kinds</a></li><li><a href="index.html#2">Chapter 2: Kinds</a></li><li><b>Scaled Arithmetic Values</b></li></ul></div>
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<p class="purpose">To manage the scalings and offsets used when storing arithmetic values at run-time, and/or when using scaled units to refer to them.</p>
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<ul class="toc"><li><a href="2-sav.html#SP1">§1. Definitions</a></li><li><a href="2-sav.html#SP6">§6. Logging</a></li><li><a href="2-sav.html#SP7">§7. Definition</a></li><li><a href="2-sav.html#SP10">§10. Enlarging and contracting</a></li><li><a href="2-sav.html#SP11">§11. Using scalings</a></li><li><a href="2-sav.html#SP14">§14. Scaled arithmetic at compile-time</a></li><li><a href="2-sav.html#SP17">§17. Scaled arithmetic at run-time</a></li></ul><hr class="tocbar">
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<p class="commentary firstcommentary"><a id="SP1"></a><b>§1. Definitions. </b></p>
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<p class="commentary firstcommentary"><a id="SP2"></a><b>§2. </b>Some literal patterns allow us to give values using scaled units. For
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example, "1 g" and "1 kg" might both define constant values of the same
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kind, but the "1" is read differently in the two cases: it's worth 1000
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times as much in the second case.
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</p>
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<p class="commentary">A "scaling transformation" defines the relationship between the number
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as written and the number stored at runtime. The conversion between the
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two is always a linear function: a number written as <span class="extract"><span class="extract-syntax">x kg</span></span> is stored
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as <span class="extract"><span class="extract-syntax">M*x + O</span></span> at run-time for constants <span class="extract"><span class="extract-syntax">M</span></span> and <span class="extract"><span class="extract-syntax">O</span></span>, the "multiplier"
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and "offset". <span class="extract"><span class="extract-syntax">M</span></span> must be positive, <span class="extract"><span class="extract-syntax">O</span></span> must be positive or zero.
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</p>
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<p class="commentary">Units typically have a range of different literal patterns with different
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scalings: for example, "1 mm", "1 cm", "1 m", "1 km". One of these patterns
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is designated as the "benchmark": in the case of length, probably "1 m".
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This is the one we think of abstractly as the natural notation to use
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when we don't know that the value is particularly large or small.
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</p>
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<p class="commentary firstcommentary"><a id="SP3"></a><b>§3. </b>We have to implement all of this twice, in subtly different ways, to
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cope with the fact that some units use integer arithmetic and others
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use real.
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</p>
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<ul class="items"><li>(a) Real units are easier. A value of <span class="extract"><span class="extract-syntax">1.0</span></span> stored at run-time equals
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1 benchmark unit: in our length example, 1 m. Thus the <span class="extract"><span class="extract-syntax">M</span></span> value for the
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benchmark scaling is always 1.0.
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</li><li>(b) Integer units are harder. If we stored 1 m as the integer 1, we
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would be unable to express any distance smaller than that, and "1 cm"
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or "1 mm" would vanish completely. Instead we scale so that the value
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1 stored at run-time equals 1 unit of our smallest scale: in the length
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example, 1 mm. The <span class="extract"><span class="extract-syntax">M</span></span> value for the benchmark is now usually not 1 —
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in this example, it's 1000, because one benchmark unit (1 m) is stored
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as the integer 1000.
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</li></ul>
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<p class="commentary firstcommentary"><a id="SP4"></a><b>§4. </b>The benchmark <span class="extract"><span class="extract-syntax">M</span></span> has a special significance because it affects the
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result of arithmetic (unless it equals 1). For example, suppose we
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multiply 2 m by 3 m to get 6 square meters, and suppose the benchmark
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<span class="extract"><span class="extract-syntax">M</span></span> is 1000 for both length and area. Then the 2 m and 3 m are stored
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as 2000 and 3000. Simply multiplying those as integers gives 6000000,
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but that corresponds to 6000 square meters, not 6. So the result of the
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multiplication must be rescaled to give the right answer.
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</p>
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<p class="commentary">Since, as noted above, benchmark <span class="extract"><span class="extract-syntax">M</span></span> is always 1 for real values, there's
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no need for rescaling with real arithmetic.
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</p>
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<p class="commentary firstcommentary"><a id="SP5"></a><b>§5. </b>Scalings are defined one at a time, and usually in terms of each other.
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We can't know the values of <span class="extract"><span class="extract-syntax">M</span></span> they end up with until all have been
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defined.
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</p>
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<pre class="definitions code-font"><span class="definition-keyword">define</span> <span class="constant-syntax">LP_SCALED_UP</span><span class="plain-syntax"> </span><span class="constant-syntax">1</span>
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<span class="definition-keyword">define</span> <span class="constant-syntax">LP_SCALED_DOWN</span><span class="plain-syntax"> -1</span>
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<span class="definition-keyword">define</span> <span class="constant-syntax">LP_SCALED_AT</span><span class="plain-syntax"> </span><span class="constant-syntax">2</span>
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</pre>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="reserved-syntax">typedef</span><span class="plain-syntax"> </span><span class="reserved-syntax">struct</span><span class="plain-syntax"> </span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> {</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">use_integer_scaling</span><span class="plain-syntax">; </span><span class="comment-syntax"> or if not, use real</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">int_O</span><span class="plain-syntax">; </span><span class="comment-syntax"> the </span>\(O\)<span class="comment-syntax"> value described above, if integers used</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">int_M</span><span class="plain-syntax">; </span><span class="comment-syntax"> the </span>\(M\)<span class="comment-syntax"> value described above</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">double</span><span class="plain-syntax"> </span><span class="identifier-syntax">real_O</span><span class="plain-syntax">; </span><span class="comment-syntax"> the </span>\(O\)<span class="comment-syntax"> value described above, if real numbers used</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">double</span><span class="plain-syntax"> </span><span class="identifier-syntax">real_M</span><span class="plain-syntax">; </span><span class="comment-syntax"> the </span>\(M\)<span class="comment-syntax"> value described above</span>
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<span class="plain-syntax"> </span><span class="comment-syntax"> used only in the definition process</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">scaling_mode</span><span class="plain-syntax">; </span><span class="comment-syntax"> one of the </span><span class="extract"><span class="extract-syntax">LP_SCALED_*</span></span><span class="comment-syntax"> constants</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">int_scalar</span><span class="plain-syntax">; </span><span class="comment-syntax"> whichever of these is relevant according to the integer/real mode</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">double</span><span class="plain-syntax"> </span><span class="identifier-syntax">real_scalar</span><span class="plain-syntax">;</span>
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<span class="plain-syntax">} </span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax">;</span>
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</pre>
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<ul class="endnotetexts"><li>The structure scaling_transformation is private to this section.</li></ul>
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<p class="commentary firstcommentary"><a id="SP6"></a><b>§6. Logging. </b></p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::describe</span><span class="plain-syntax">(</span><span class="identifier-syntax">OUTPUT_STREAM</span><span class="plain-syntax">, </span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">WRITE</span><span class="plain-syntax">(</span><span class="string-syntax">"scaling: x units --> "</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="identifier-syntax">use_integer_scaling</span><span class="plain-syntax">)</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">WRITE</span><span class="plain-syntax">(</span><span class="string-syntax">"%d x + %x stored at runtime (int)"</span><span class="plain-syntax">, </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</span><span class="plain-syntax">, </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_O</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">else</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">WRITE</span><span class="plain-syntax">(</span><span class="string-syntax">"%g x + %g stored at runtime (real)"</span><span class="plain-syntax">, </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_M</span><span class="plain-syntax">, </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_O</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">switch</span><span class="plain-syntax"> (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">scaling_mode</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">case</span><span class="plain-syntax"> </span><span class="identifier-syntax">LP_SCALED_UP:</span><span class="plain-syntax"> </span><span class="identifier-syntax">WRITE</span><span class="plain-syntax">(</span><span class="string-syntax">" (defined as benchmark * "</span><span class="plain-syntax">); </span><span class="reserved-syntax">break</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">case</span><span class="plain-syntax"> </span><span class="identifier-syntax">LP_SCALED_DOWN:</span><span class="plain-syntax"> </span><span class="identifier-syntax">WRITE</span><span class="plain-syntax">(</span><span class="string-syntax">" (defined as benchmark / "</span><span class="plain-syntax">); </span><span class="reserved-syntax">break</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">case</span><span class="plain-syntax"> </span><span class="identifier-syntax">LP_SCALED_AT:</span><span class="plain-syntax"> </span><span class="identifier-syntax">WRITE</span><span class="plain-syntax">(</span><span class="string-syntax">" (defined as scaled at "</span><span class="plain-syntax">); </span><span class="reserved-syntax">break</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> }</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="identifier-syntax">use_integer_scaling</span><span class="plain-syntax">) </span><span class="identifier-syntax">WRITE</span><span class="plain-syntax">(</span><span class="string-syntax">"%d)"</span><span class="plain-syntax">, </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_scalar</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">else</span><span class="plain-syntax"> </span><span class="identifier-syntax">WRITE</span><span class="plain-syntax">(</span><span class="string-syntax">"%g)"</span><span class="plain-syntax">, </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_scalar</span><span class="plain-syntax">);</span>
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<span class="plain-syntax">}</span>
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</pre>
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<p class="commentary firstcommentary"><a id="SP7"></a><b>§7. Definition. </b>A new scaling is given with a scale factor either pegging it absolutely, or
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relative to the benchmark. At initial definition time, we don't calculate <span class="extract"><span class="extract-syntax">M</span></span>:
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we just take notes for later.
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</p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::new</span><span class="plain-syntax">(</span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">integer_valued</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">scaled</span><span class="plain-syntax">, </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">int_s</span><span class="plain-syntax">, </span><span class="reserved-syntax">double</span><span class="plain-syntax"> </span><span class="identifier-syntax">real_s</span><span class="plain-syntax">, </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">offset</span><span class="plain-syntax">, </span><span class="reserved-syntax">double</span><span class="plain-syntax"> </span><span class="identifier-syntax">real_offset</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">use_integer_scaling</span><span class="plain-syntax"> = </span><span class="identifier-syntax">integer_valued</span><span class="plain-syntax">;</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_O</span><span class="plain-syntax"> = </span><span class="constant-syntax">0</span><span class="plain-syntax">; </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_O</span><span class="plain-syntax"> = </span><span class="constant-syntax">0</span><span class="plain-syntax">.0;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">integer_valued</span><span class="plain-syntax">) </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_O</span><span class="plain-syntax"> = </span><span class="identifier-syntax">offset</span><span class="plain-syntax">; </span><span class="reserved-syntax">else</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_O</span><span class="plain-syntax"> = (</span><span class="reserved-syntax">double</span><span class="plain-syntax">) </span><span class="identifier-syntax">real_offset</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</span><span class="plain-syntax"> = </span><span class="constant-syntax">1</span><span class="plain-syntax">; </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_M</span><span class="plain-syntax"> = </span><span class="constant-syntax">1</span><span class="plain-syntax">.0;</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">scaling_mode</span><span class="plain-syntax"> = </span><span class="identifier-syntax">scaled</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_scalar</span><span class="plain-syntax"> = </span><span class="identifier-syntax">int_s</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_scalar</span><span class="plain-syntax"> = </span><span class="identifier-syntax">real_s</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">;</span>
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<span class="plain-syntax">}</span>
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</pre>
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<p class="commentary firstcommentary"><a id="SP8"></a><b>§8. </b>Soon after definition, we may realise that real arithmetic is needed after
|
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all, even though we previously expected it to use integers. So:
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</p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::convert_to_real</span><span class="plain-syntax">(</span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> *</span><span class="identifier-syntax">sc</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">use_integer_scaling</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">real_O</span><span class="plain-syntax"> = (</span><span class="reserved-syntax">double</span><span class="plain-syntax">) </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_O</span><span class="plain-syntax">; </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_O</span><span class="plain-syntax"> = </span><span class="constant-syntax">0</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">real_M</span><span class="plain-syntax"> = (</span><span class="reserved-syntax">double</span><span class="plain-syntax">) </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_M</span><span class="plain-syntax">; </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_M</span><span class="plain-syntax"> = </span><span class="constant-syntax">1</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">real_scalar</span><span class="plain-syntax"> = (</span><span class="reserved-syntax">double</span><span class="plain-syntax">) </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_scalar</span><span class="plain-syntax">; </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_scalar</span><span class="plain-syntax"> = </span><span class="constant-syntax">1</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">use_integer_scaling</span><span class="plain-syntax"> = </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax">}</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP9"></a><b>§9. </b>Each new scaling in turn is added to the list of those in use for a given
|
|
kind. For example, when the "1 km" scaling is added to those for lengths,
|
|
perhaps "1 cm" and "1 m" (the benchmark) already exist, but "1 mm" doesn't.
|
|
We call the following routine to calculate a suitable <span class="extract"><span class="extract-syntax">M</span></span> for the scaling.
|
|
It returns a value which is either <span class="extract"><span class="extract-syntax">-1</span></span>, or else a scale factor by which
|
|
to increase the <span class="extract"><span class="extract-syntax">M</span></span> values of everything else in the list.
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::determine_M</span><span class="plain-syntax">(</span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> *</span><span class="identifier-syntax">sc</span><span class="plain-syntax">,</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> *</span><span class="identifier-syntax">benchmark_sc</span><span class="plain-syntax">,</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">first</span><span class="plain-syntax">, </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">equiv</span><span class="plain-syntax">, </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">alt</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">rescale_the_others_by_this</span><span class="plain-syntax"> = </span><span class="constant-syntax">1</span><span class="plain-syntax">; </span><span class="comment-syntax"> in effect, don't</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">first</span><span class="plain-syntax">) </span><span class="named-paragraph-container code-font"><a href="2-sav.html#SP9_1" class="named-paragraph-link"><span class="named-paragraph">Determine M for the first scaling of the list</span><span class="named-paragraph-number">9.1</span></a></span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">else</span><span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-sav.html#SP9_2" class="named-paragraph-link"><span class="named-paragraph">Determine M for a subsequent scaling of the list</span><span class="named-paragraph-number">9.2</span></a></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">rescale_the_others_by_this</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax">}</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP9_1"></a><b>§9.1. </b>This is the easy case — there's no list yet, and no benchmark yet. The <span class="extract"><span class="extract-syntax">M</span></span>
|
|
value will usually therefore be 1, unless the source text explicitly asked
|
|
for it to be something else:
|
|
</p>
|
|
|
|
<blockquote>
|
|
<p>1m specifies a length scaled at 10000.</p>
|
|
</blockquote>
|
|
|
|
<p class="commentary">in which case, of course, <span class="extract"><span class="extract-syntax">M</span></span> is 10000. Since there's no benchmark yet, it
|
|
must be a problem message if the unit is defined scaled up or down from the
|
|
benchmark; and similarly if the new notation is claimed to be equivalent to
|
|
some existing notation, in which case the <span class="extract"><span class="extract-syntax">equiv</span></span> flag is set.
|
|
</p>
|
|
|
|
<p class="commentary"><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">Determine M for the first scaling of the list</span><span class="named-paragraph-number">9.1</span></span><span class="comment-syntax"> =</span>
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (((</span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_scalar</span><span class="plain-syntax"> != </span><span class="constant-syntax">1</span><span class="plain-syntax">) || (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">real_scalar</span><span class="plain-syntax"> != </span><span class="constant-syntax">1</span><span class="plain-syntax">.0)) &&</span>
|
|
<span class="plain-syntax"> ((</span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">scaling_mode</span><span class="plain-syntax"> == </span><span class="constant-syntax">LP_SCALED_UP</span><span class="plain-syntax">) ||</span>
|
|
<span class="plain-syntax"> (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">scaling_mode</span><span class="plain-syntax"> == </span><span class="constant-syntax">LP_SCALED_DOWN</span><span class="plain-syntax">) ||</span>
|
|
<span class="plain-syntax"> (</span><span class="identifier-syntax">equiv</span><span class="plain-syntax">) ||</span>
|
|
<span class="plain-syntax"> ((</span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">scaling_mode</span><span class="plain-syntax"> == </span><span class="constant-syntax">LP_SCALED_AT</span><span class="plain-syntax">) && (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">use_integer_scaling</span><span class="plain-syntax"> == </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">))))</span>
|
|
<span class="plain-syntax"> </span><a href="2-knd.html#SP38" class="function-link"><span class="function-syntax">Kinds::problem_handler</span></a><span class="plain-syntax">(</span><span class="constant-syntax">LPCantScaleYet_KINDERROR</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_M</span><span class="plain-syntax"> = </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_scalar</span><span class="plain-syntax">;</span>
|
|
</pre>
|
|
<ul class="endnotetexts"><li>This code is used in <a href="2-sav.html#SP9">§9</a>.</li></ul>
|
|
<p class="commentary firstcommentary"><a id="SP9_2"></a><b>§9.2. </b>The harder case, when some scalings already exist for this kind. Firstly,
|
|
you can't create an alternative set of scalings (e.g. Imperial units such
|
|
as feet and inches) with its own absolute scale factor, because the existing
|
|
scalings (metric units such as mm, km, etc.) already have their <span class="extract"><span class="extract-syntax">M</span></span> value.
|
|
</p>
|
|
|
|
<p class="commentary"><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">Determine M for a subsequent scaling of the list</span><span class="named-paragraph-number">9.2</span></span><span class="comment-syntax"> =</span>
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (((</span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_scalar</span><span class="plain-syntax"> != </span><span class="constant-syntax">1</span><span class="plain-syntax">) || (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">real_scalar</span><span class="plain-syntax"> != </span><span class="constant-syntax">1</span><span class="plain-syntax">.0)) &&</span>
|
|
<span class="plain-syntax"> ((</span><span class="identifier-syntax">alt</span><span class="plain-syntax">) && (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">scaling_mode</span><span class="plain-syntax"> == </span><span class="constant-syntax">LP_SCALED_AT</span><span class="plain-syntax">)))</span>
|
|
<span class="plain-syntax"> </span><a href="2-knd.html#SP38" class="function-link"><span class="function-syntax">Kinds::problem_handler</span></a><span class="plain-syntax">(</span><span class="constant-syntax">LPCantScaleTwice_KINDERROR</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">, </span><span class="identifier-syntax">NULL</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">equiv</span><span class="plain-syntax">)</span>
|
|
<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-sav.html#SP9_2_1" class="named-paragraph-link"><span class="named-paragraph">Calculate the multiplier for this equivalent scaling</span><span class="named-paragraph-number">9.2.1</span></a></span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">else</span>
|
|
<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-sav.html#SP9_2_2" class="named-paragraph-link"><span class="named-paragraph">Calculate the multiplier for the LP relative to the benchmark</span><span class="named-paragraph-number">9.2.2</span></a></span><span class="plain-syntax">;</span>
|
|
</pre>
|
|
<ul class="endnotetexts"><li>This code is used in <a href="2-sav.html#SP9">§9</a>.</li></ul>
|
|
<p class="commentary firstcommentary"><a id="SP9_2_1"></a><b>§9.2.1. </b>An equivalent unit exactly specifies its <span class="extract"><span class="extract-syntax">M</span></span>-value. For example:
|
|
</p>
|
|
|
|
<blockquote>
|
|
<p>1 pencil specifies a length equivalent to 18cm.</p>
|
|
</blockquote>
|
|
|
|
<p class="commentary">What happens here is that "18cm" is parsed and turned not into 18, but into
|
|
the "1 cm" scaling applied to 18, and that's the value in our scalar,
|
|
which then becomes <span class="extract"><span class="extract-syntax">M</span></span>.
|
|
</p>
|
|
|
|
<p class="commentary"><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">Calculate the multiplier for this equivalent scaling</span><span class="named-paragraph-number">9.2.1</span></span><span class="comment-syntax"> =</span>
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">use_integer_scaling</span><span class="plain-syntax">)</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_M</span><span class="plain-syntax"> = </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_scalar</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">else</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">real_M</span><span class="plain-syntax"> = </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">real_scalar</span><span class="plain-syntax">;</span>
|
|
</pre>
|
|
<ul class="endnotetexts"><li>This code is used in <a href="2-sav.html#SP9_2">§9.2</a>.</li></ul>
|
|
<p class="commentary firstcommentary"><a id="SP9_2_2"></a><b>§9.2.2. </b>Finally the trickiest case. We calculate <span class="extract"><span class="extract-syntax">M</span></span> based on scaling the benchmark
|
|
either up or down.
|
|
</p>
|
|
|
|
<p class="commentary">Scaling up by <span class="extract"><span class="extract-syntax">k</span></span> is no problem: the <span class="extract"><span class="extract-syntax">M</span></span> value is just <span class="extract"><span class="extract-syntax">k</span></span> times the benchmark
|
|
<span class="extract"><span class="extract-syntax">M</span></span>, which we call <span class="extract"><span class="extract-syntax">B</span></span>.
|
|
</p>
|
|
|
|
<p class="commentary">Scaling down might look similar: we want <span class="extract"><span class="extract-syntax">M = B/k</span></span>. But in integer arithmetic
|
|
<span class="extract"><span class="extract-syntax">k</span></span> probably doesn't divide <span class="extract"><span class="extract-syntax">B</span></span>, and extreme cases frequently occur: for
|
|
example, where <span class="extract"><span class="extract-syntax">k</span></span> is 1000 and <span class="extract"><span class="extract-syntax">B</span></span> is 1.
|
|
</p>
|
|
|
|
<p class="commentary">We get around this by increasing every <span class="extract"><span class="extract-syntax">M</span></span>-value in the list by a factor of:
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> k / gcd(B, k)</span>
|
|
</pre>
|
|
<p class="commentary">Note that <span class="extract"><span class="extract-syntax">B</span></span> also increases in this process, and in fact becomes
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> Bk / gcd(B, k)</span>
|
|
</pre>
|
|
<p class="commentary">which is the smallest multiple of <span class="extract"><span class="extract-syntax">B</span></span> which has <span class="extract"><span class="extract-syntax">k</span></span> as a factor. (If in fact
|
|
<span class="extract"><span class="extract-syntax">k</span></span> always divided <span class="extract"><span class="extract-syntax">B</span></span>, then the scale multiple is 1 and no change is made.)
|
|
That means that the new value of <span class="extract"><span class="extract-syntax">B</span></span> divided by <span class="extract"><span class="extract-syntax">k</span></span> will be
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> B / gcd(B, k)</span>
|
|
</pre>
|
|
<p class="commentary">so this is what we set <span class="extract"><span class="extract-syntax">M</span></span> to.
|
|
</p>
|
|
|
|
<p class="commentary"><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">Calculate the multiplier for the LP relative to the benchmark</span><span class="named-paragraph-number">9.2.2</span></span><span class="comment-syntax"> =</span>
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">benchmark_sc</span><span class="plain-syntax"> == </span><span class="identifier-syntax">NULL</span><span class="plain-syntax">) </span><span class="identifier-syntax">internal_error</span><span class="plain-syntax">(</span><span class="string-syntax">"no benchmark for comparison"</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">sc</span><span class="plain-syntax">-></span><span class="element-syntax">scaling_mode</span><span class="plain-syntax"> == </span><span class="constant-syntax">LP_SCALED_DOWN</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">sc</span><span class="plain-syntax">-></span><span class="element-syntax">use_integer_scaling</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">B</span><span class="plain-syntax"> = </span><span class="identifier-syntax">benchmark_sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_M</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">k</span><span class="plain-syntax"> = </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_scalar</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">g</span><span class="plain-syntax"> = </span><a href="2-dmn.html#SP20" class="function-link"><span class="function-syntax">Kinds::Dimensions::gcd</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">B</span><span class="plain-syntax">, </span><span class="identifier-syntax">k</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_M</span><span class="plain-syntax"> = </span><span class="identifier-syntax">B</span><span class="plain-syntax">/</span><span class="identifier-syntax">g</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">rescale_the_others_by_this</span><span class="plain-syntax"> = </span><span class="identifier-syntax">k</span><span class="plain-syntax">/</span><span class="identifier-syntax">g</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> } </span><span class="reserved-syntax">else</span><span class="plain-syntax"> {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">double</span><span class="plain-syntax"> </span><span class="identifier-syntax">B</span><span class="plain-syntax"> = </span><span class="identifier-syntax">benchmark_sc</span><span class="plain-syntax">-></span><span class="element-syntax">real_M</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">double</span><span class="plain-syntax"> </span><span class="identifier-syntax">k</span><span class="plain-syntax"> = </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">real_scalar</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">real_M</span><span class="plain-syntax"> = </span><span class="identifier-syntax">B</span><span class="plain-syntax">/</span><span class="identifier-syntax">k</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> } </span><span class="reserved-syntax">else</span><span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">scaling_mode</span><span class="plain-syntax"> == </span><span class="constant-syntax">LP_SCALED_UP</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">sc</span><span class="plain-syntax">-></span><span class="element-syntax">use_integer_scaling</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">B</span><span class="plain-syntax"> = </span><span class="identifier-syntax">benchmark_sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_M</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">k</span><span class="plain-syntax"> = </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_scalar</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">int_M</span><span class="plain-syntax"> = </span><span class="identifier-syntax">B</span><span class="plain-syntax">*</span><span class="identifier-syntax">k</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> } </span><span class="reserved-syntax">else</span><span class="plain-syntax"> {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">double</span><span class="plain-syntax"> </span><span class="identifier-syntax">B</span><span class="plain-syntax"> = </span><span class="identifier-syntax">benchmark_sc</span><span class="plain-syntax">-></span><span class="element-syntax">real_M</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">double</span><span class="plain-syntax"> </span><span class="identifier-syntax">k</span><span class="plain-syntax"> = </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">real_scalar</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">-></span><span class="element-syntax">real_M</span><span class="plain-syntax"> = </span><span class="identifier-syntax">B</span><span class="plain-syntax">*</span><span class="identifier-syntax">k</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> }</span>
|
|
</pre>
|
|
<ul class="endnotetexts"><li>This code is used in <a href="2-sav.html#SP9_2">§9.2</a>.</li></ul>
|
|
<p class="commentary firstcommentary"><a id="SP10"></a><b>§10. Enlarging and contracting. </b>Note that the offset values <span class="extract"><span class="extract-syntax">O</span></span> are not affected here. The idea is this:
|
|
suppose we have a unit such as temperature, and have defined centigrade as
|
|
a scaling with offset 273. Then suppose we want a unit equal to 0.1 of a
|
|
degree centigrade: we want to scale down C by 10, but preserve offset 273,
|
|
so that the value "1 deciC" (or whatever) is 273.1 degrees, not 27.4.
|
|
(In practice, and wisely, scientists never scale units with offsets, so
|
|
this seldom arises.)
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::enlarge</span><span class="plain-syntax">(</span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">, </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">F</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">sc</span><span class="plain-syntax">.</span><span class="identifier-syntax">use_integer_scaling</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="identifier-syntax">int_M</span><span class="plain-syntax"> *= </span><span class="identifier-syntax">F</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> } </span><span class="reserved-syntax">else</span><span class="plain-syntax"> {</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="identifier-syntax">real_M</span><span class="plain-syntax"> *= </span><span class="identifier-syntax">F</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">sc</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax">}</span>
|
|
|
|
<span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::contract</span><span class="plain-syntax">(</span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">, </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">F</span><span class="plain-syntax">,</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> *</span><span class="identifier-syntax">loses_accuracy</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> *</span><span class="identifier-syntax">loses_accuracy</span><span class="plain-syntax"> = </span><span class="identifier-syntax">FALSE</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">sc</span><span class="plain-syntax">.</span><span class="identifier-syntax">use_integer_scaling</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">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</span><span class="plain-syntax"> % </span><span class="identifier-syntax">F</span><span class="plain-syntax"> != </span><span class="constant-syntax">0</span><span class="plain-syntax">) *</span><span class="identifier-syntax">loses_accuracy</span><span class="plain-syntax"> = </span><span class="identifier-syntax">TRUE</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="identifier-syntax">int_M</span><span class="plain-syntax"> /= </span><span class="identifier-syntax">F</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> } </span><span class="reserved-syntax">else</span><span class="plain-syntax"> {</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="identifier-syntax">real_M</span><span class="plain-syntax"> /= </span><span class="identifier-syntax">F</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">sc</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax">}</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP11"></a><b>§11. Using scalings. </b>First, here's a <span class="extract"><span class="extract-syntax">strcmp</span></span>-like routine to report which scaling is smaller
|
|
out of two; it's used for sorting scalings into ascending order of magnitude.
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::compare</span><span class="plain-syntax">(</span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">A</span><span class="plain-syntax">, </span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">B</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">A</span><span class="plain-syntax">.</span><span class="identifier-syntax">use_integer_scaling</span><span class="plain-syntax"> != </span><span class="identifier-syntax">B</span><span class="plain-syntax">.</span><span class="element-syntax">use_integer_scaling</span><span class="plain-syntax">)</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">internal_error</span><span class="plain-syntax">(</span><span class="string-syntax">"scalings incomparable"</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">A</span><span class="plain-syntax">.</span><span class="identifier-syntax">use_integer_scaling</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">A</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</span><span class="plain-syntax"> > </span><span class="identifier-syntax">B</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">1</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">A</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</span><span class="plain-syntax"> < </span><span class="identifier-syntax">B</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> -1;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">A</span><span class="plain-syntax">.</span><span class="element-syntax">int_O</span><span class="plain-syntax"> > </span><span class="identifier-syntax">B</span><span class="plain-syntax">.</span><span class="element-syntax">int_O</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">1</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">A</span><span class="plain-syntax">.</span><span class="element-syntax">int_O</span><span class="plain-syntax"> < </span><span class="identifier-syntax">B</span><span class="plain-syntax">.</span><span class="element-syntax">int_O</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> -1;</span>
|
|
<span class="plain-syntax"> } </span><span class="reserved-syntax">else</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">A</span><span class="plain-syntax">.</span><span class="element-syntax">real_M</span><span class="plain-syntax"> > </span><span class="identifier-syntax">B</span><span class="plain-syntax">.</span><span class="element-syntax">real_M</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">1</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">A</span><span class="plain-syntax">.</span><span class="element-syntax">real_M</span><span class="plain-syntax"> < </span><span class="identifier-syntax">B</span><span class="plain-syntax">.</span><span class="element-syntax">real_M</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> -1;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">A</span><span class="plain-syntax">.</span><span class="element-syntax">real_O</span><span class="plain-syntax"> > </span><span class="identifier-syntax">B</span><span class="plain-syntax">.</span><span class="element-syntax">real_O</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">1</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">A</span><span class="plain-syntax">.</span><span class="element-syntax">real_O</span><span class="plain-syntax"> < </span><span class="identifier-syntax">B</span><span class="plain-syntax">.</span><span class="element-syntax">real_O</span><span class="plain-syntax">) </span><span class="reserved-syntax">return</span><span class="plain-syntax"> -1;</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><span class="constant-syntax">0</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax">}</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP12"></a><b>§12. </b>Second, the following returns <span class="extract"><span class="extract-syntax">M</span></span> unless we're in real mode, in which case it
|
|
returns 1.
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::get_integer_multiplier</span><span class="plain-syntax">(</span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</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">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax">}</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP13"></a><b>§13. </b>Finally, this simply detects the presence of a scale factor, real or integer:
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::involves_scale_change</span><span class="plain-syntax">(</span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</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">sc</span><span class="plain-syntax">.</span><span class="identifier-syntax">int_M</span><span class="plain-syntax"> != </span><span class="constant-syntax">1</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><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="identifier-syntax">real_M</span><span class="plain-syntax"> != </span><span class="constant-syntax">1</span><span class="plain-syntax">.0) </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>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP14"></a><b>§14. Scaled arithmetic at compile-time. </b>The "quantum" of a scaling is the run-time value corresponding to 1 unit:
|
|
for example, for kilometers, it's the run-time value which "1 km" translates
|
|
into.
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::quantum</span><button class="popup" onclick="togglePopup('usagePopup1')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup1">Usage of <span class="code-font"><span class="function-syntax">Kinds::Scalings::quantum</span></span>:<br/><a href="2-sav.html#SP20">§20</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> (</span><span class="reserved-syntax">int</span><span class="plain-syntax">) </span><a href="2-sav.html#SP15" class="function-link"><span class="function-syntax">Kinds::Scalings::quanta_to_value</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">sc</span><span class="plain-syntax">, </span><span class="constant-syntax">1</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax">}</span>
|
|
|
|
<span class="reserved-syntax">double</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::real_quantum</span><button class="popup" onclick="togglePopup('usagePopup2')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup2">Usage of <span class="code-font"><span class="function-syntax">Kinds::Scalings::real_quantum</span></span>:<br/><a href="2-sav.html#SP20">§20</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> </span><a href="2-sav.html#SP15" class="function-link"><span class="function-syntax">Kinds::Scalings::real_quanta_to_value</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">sc</span><span class="plain-syntax">, </span><span class="constant-syntax">1</span><span class="plain-syntax">.0);</span>
|
|
<span class="plain-syntax">}</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP15"></a><b>§15. </b>More generally, the following takes a number of quanta and turns it into
|
|
the run-time value that stores as:
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::quanta_to_value</span><button class="popup" onclick="togglePopup('usagePopup3')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup3">Usage of <span class="code-font"><span class="function-syntax">Kinds::Scalings::quanta_to_value</span></span>:<br/><a href="2-sav.html#SP14">§14</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">, </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">q</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">q</span><span class="plain-syntax">*</span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</span><span class="plain-syntax"> + </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_O</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax">}</span>
|
|
|
|
<span class="reserved-syntax">double</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::real_quanta_to_value</span><button class="popup" onclick="togglePopup('usagePopup4')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup4">Usage of <span class="code-font"><span class="function-syntax">Kinds::Scalings::real_quanta_to_value</span></span>:<br/><a href="2-sav.html#SP14">§14</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">, </span><span class="reserved-syntax">double</span><span class="plain-syntax"> </span><span class="identifier-syntax">q</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">q</span><span class="plain-syntax">*</span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_M</span><span class="plain-syntax"> + </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_O</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax">}</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP16"></a><b>§16. </b>In integer arithmetic, the inverse of this function won't generally
|
|
exist, since division can't be performed exactly. The following is the
|
|
best we can do.
|
|
</p>
|
|
|
|
<p class="commentary">So consider the run-time value <span class="extract"><span class="extract-syntax">v</span></span>, and let's try to express it as a
|
|
whole number of quanta plus a fractional remainder. For example, if the
|
|
scaling is for "1 m", with offset 0 and multiplier 1000, then the value
|
|
<span class="extract"><span class="extract-syntax">v = 2643</span></span> produces 2 quanta and remainder 643/1000ths.
|
|
</p>
|
|
|
|
<p class="commentary">In real arithmetic, on the other hand, the inverse straightforwardly exists.
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::value_to_quanta</span><span class="plain-syntax">(</span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">v</span><span class="plain-syntax">, </span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">, </span><span class="reserved-syntax">int</span><span class="plain-syntax"> *</span><span class="identifier-syntax">q</span><span class="plain-syntax">, </span><span class="reserved-syntax">int</span><span class="plain-syntax"> *</span><span class="identifier-syntax">r</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">sc</span><span class="plain-syntax">.</span><span class="identifier-syntax">use_integer_scaling</span><span class="plain-syntax"> == </span><span class="identifier-syntax">FALSE</span><span class="plain-syntax">) </span><span class="identifier-syntax">internal_error</span><span class="plain-syntax">(</span><span class="string-syntax">"inversion unimplemented"</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">r</span><span class="plain-syntax">) *</span><span class="identifier-syntax">r</span><span class="plain-syntax"> = (</span><span class="identifier-syntax">v</span><span class="plain-syntax"> - </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_O</span><span class="plain-syntax">) % (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</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">q</span><span class="plain-syntax">) *</span><span class="identifier-syntax">q</span><span class="plain-syntax"> = (</span><span class="identifier-syntax">v</span><span class="plain-syntax"> - </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_O</span><span class="plain-syntax">) / (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax">}</span>
|
|
|
|
<span class="reserved-syntax">double</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::real_value_to_quanta</span><span class="plain-syntax">(</span><span class="reserved-syntax">double</span><span class="plain-syntax"> </span><span class="identifier-syntax">v</span><span class="plain-syntax">, </span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">) {</span>
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|
<span class="plain-syntax"> </span><span class="reserved-syntax">return</span><span class="plain-syntax"> (</span><span class="identifier-syntax">v</span><span class="plain-syntax"> - </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_O</span><span class="plain-syntax">) / (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="identifier-syntax">real_M</span><span class="plain-syntax">);</span>
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<span class="plain-syntax">}</span>
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|
</pre>
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|
<p class="commentary firstcommentary"><a id="SP17"></a><b>§17. Scaled arithmetic at run-time. </b>We begin with routines to compile code which, at run-time, performs these
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same operations: quanta to value, value to quanta and remainder. The
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value is held in the I6 variable named <span class="extract"><span class="extract-syntax">V_var</span></span>.
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</p>
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|
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<pre class="displayed-code all-displayed-code code-font">
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<span class="plain-syntax">#</span><span class="identifier-syntax">ifdef</span><span class="plain-syntax"> </span><span class="identifier-syntax">CORE_MODULE</span>
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<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::compile_quanta_to_value</span><span class="plain-syntax">(</span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">inter_name</span><span class="plain-syntax"> *</span><span class="identifier-syntax">V_var</span><span class="plain-syntax">, </span><span class="identifier-syntax">inter_symbol</span><span class="plain-syntax"> *</span><span class="identifier-syntax">sgn_var</span><span class="plain-syntax">, </span><span class="identifier-syntax">inter_symbol</span><span class="plain-syntax"> *</span><span class="identifier-syntax">x_var</span><span class="plain-syntax">, </span><span class="identifier-syntax">inter_symbol</span><span class="plain-syntax"> *</span><span class="identifier-syntax">label</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="identifier-syntax">use_integer_scaling</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax"> </span><a href="2-sav.html#SP18" class="function-link"><span class="function-syntax">Kinds::Scalings::compile_scale_and_add</span></a><span class="plain-syntax">(</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">InterNames::to_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">V_var</span><span class="plain-syntax">), </span><span class="identifier-syntax">sgn_var</span><span class="plain-syntax">, </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</span><span class="plain-syntax">, </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_O</span><span class="plain-syntax">, </span><span class="identifier-syntax">x_var</span><span class="plain-syntax">, </span><span class="identifier-syntax">label</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> } </span><span class="reserved-syntax">else</span><span class="plain-syntax"> {</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_M</span><span class="plain-syntax"> != </span><span class="constant-syntax">1</span><span class="plain-syntax">.0) {</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">STORE_BIP</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::ref_iname</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_call_iname</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">Hierarchy::find</span><span class="plain-syntax">(</span><span class="identifier-syntax">REAL_NUMBER_TY_TIMES_HL</span><span class="plain-syntax">));</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_iname</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_real</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_M</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</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">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_O</span><span class="plain-syntax"> != </span><span class="constant-syntax">0</span><span class="plain-syntax">.0) {</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">STORE_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::ref_iname</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_call_iname</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">Hierarchy::find</span><span class="plain-syntax">(</span><span class="identifier-syntax">REAL_NUMBER_TY_PLUS_HL</span><span class="plain-syntax">));</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_iname</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_real</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_O</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">IF_BIP</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_call_iname</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">Hierarchy::find</span><span class="plain-syntax">(</span><span class="identifier-syntax">REAL_NUMBER_TY_NAN_HL</span><span class="plain-syntax">));</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_iname</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::code</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">JUMP_BIP</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::lab</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">label</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax">}</span>
|
|
<span class="plain-syntax">#</span><span class="identifier-syntax">endif</span>
|
|
</pre>
|
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<p class="commentary firstcommentary"><a id="SP18"></a><b>§18. </b>The integer case of this is extracted as a utility routine because it's useful
|
|
for other calculations too. This performs the operation
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> v --> kv + l</span>
|
|
</pre>
|
|
<p class="commentary">carefully checking that the result does not overflow the virtual machine's
|
|
signed integer size limit in the process. <span class="extract"><span class="extract-syntax">k</span></span> is a constant known at compile
|
|
time, but <span class="extract"><span class="extract-syntax">l</span></span> is an arbitrary I6 expression whose value can't be known until
|
|
run-time. If an overflow occurs, we jump to the given label.
|
|
</p>
|
|
|
|
<p class="commentary">If, at run-time, the variable <span class="extract"><span class="extract-syntax">sgn</span></span> is negative, then we are performing this
|
|
on the absolute value of what will be a negative number; since we're using
|
|
twos-complement arithmetic, this increases the maxima by 1. Thus 32768 or
|
|
2147483648 will overflow in the positive domain, but not the negative.
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax">#</span><span class="identifier-syntax">ifdef</span><span class="plain-syntax"> </span><span class="identifier-syntax">CORE_MODULE</span>
|
|
<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::compile_scale_and_add</span><button class="popup" onclick="togglePopup('usagePopup5')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup5">Usage of <span class="code-font"><span class="function-syntax">Kinds::Scalings::compile_scale_and_add</span></span>:<br/><a href="2-sav.html#SP17">§17</a></span></button><span class="plain-syntax">(</span><span class="identifier-syntax">inter_symbol</span><span class="plain-syntax"> *</span><span class="identifier-syntax">var</span><span class="plain-syntax">, </span><span class="identifier-syntax">inter_symbol</span><span class="plain-syntax"> *</span><span class="identifier-syntax">sgn_var</span><span class="plain-syntax">,</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">scale_factor</span><span class="plain-syntax">, </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">to_add</span><span class="plain-syntax">, </span><span class="identifier-syntax">inter_symbol</span><span class="plain-syntax"> *</span><span class="identifier-syntax">var_to_add</span><span class="plain-syntax">, </span><span class="identifier-syntax">inter_symbol</span><span class="plain-syntax"> *</span><span class="identifier-syntax">label</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">scale_factor</span><span class="plain-syntax"> > </span><span class="constant-syntax">1</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">long</span><span class="plain-syntax"> </span><span class="reserved-syntax">long</span><span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">max</span><span class="plain-syntax"> = </span><span class="constant-syntax">2147483647</span><span class="identifier-syntax">LL</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">TargetVMs::is_16_bit</span><span class="plain-syntax">(</span><span class="identifier-syntax">Task::vm</span><span class="plain-syntax">())) </span><span class="identifier-syntax">max</span><span class="plain-syntax"> = </span><span class="constant-syntax">32767</span><span class="identifier-syntax">LL</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">IFELSE_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">EQ_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">sgn_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_object</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, </span><span class="constant-syntax">1</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::code</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-sav.html#SP18_1" class="named-paragraph-link"><span class="named-paragraph">Compile the overflow check</span><span class="named-paragraph-number">18.1</span></a></span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::code</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">max</span><span class="plain-syntax">++;</span>
|
|
<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-sav.html#SP18_1" class="named-paragraph-link"><span class="named-paragraph">Compile the overflow check</span><span class="named-paragraph-number">18.1</span></a></span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">STORE_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::ref_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">PLUS_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">TIMES_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, (</span><span class="identifier-syntax">inter_t</span><span class="plain-syntax">) </span><span class="identifier-syntax">scale_factor</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">var</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">PLUS_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, (</span><span class="identifier-syntax">inter_t</span><span class="plain-syntax">) </span><span class="identifier-syntax">to_add</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">var_to_add</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax">}</span>
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<span class="plain-syntax">#</span><span class="identifier-syntax">endif</span>
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</pre>
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<p class="commentary firstcommentary"><a id="SP18_1"></a><b>§18.1. </b><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">Compile the overflow check</span><span class="named-paragraph-number">18.1</span></span><span class="comment-syntax"> =</span>
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</p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">IF_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">OR_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">GT_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">var</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, (</span><span class="identifier-syntax">inter_t</span><span class="plain-syntax">) (</span><span class="identifier-syntax">max</span><span class="plain-syntax">/</span><span class="identifier-syntax">scale_factor</span><span class="plain-syntax">));</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">AND_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">EQ_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">var</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, (</span><span class="identifier-syntax">inter_t</span><span class="plain-syntax">) (</span><span class="identifier-syntax">max</span><span class="plain-syntax">/</span><span class="identifier-syntax">scale_factor</span><span class="plain-syntax">));</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">GT_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">PLUS_BIP</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, (</span><span class="identifier-syntax">inter_t</span><span class="plain-syntax">) </span><span class="identifier-syntax">to_add</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">var_to_add</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, (</span><span class="identifier-syntax">inter_t</span><span class="plain-syntax">) (</span><span class="identifier-syntax">max</span><span class="plain-syntax">/</span><span class="identifier-syntax">scale_factor</span><span class="plain-syntax">));</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::code</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">JUMP_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::lab</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">label</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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</pre>
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<ul class="endnotetexts"><li>This code is used in <a href="2-sav.html#SP18">§18</a> (twice).</li></ul>
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<p class="commentary firstcommentary"><a id="SP19"></a><b>§19. </b>And conversely... Note that in the real case, the remainder variable <span class="extract"><span class="extract-syntax">R_var</span></span>
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is ignored, since the division can be performed "exactly".
|
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</p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="plain-syntax">#</span><span class="identifier-syntax">ifdef</span><span class="plain-syntax"> </span><span class="identifier-syntax">CORE_MODULE</span>
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<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::compile_value_to_quanta</span><button class="popup" onclick="togglePopup('usagePopup6')"><span class="comment-syntax">?</span><span class="popuptext" id="usagePopup6">Usage of <span class="code-font"><span class="function-syntax">Kinds::Scalings::compile_value_to_quanta</span></span>:<br/><a href="2-sav.html#SP21">§21</a></span></button><span class="plain-syntax">(</span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">,</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">inter_symbol</span><span class="plain-syntax"> *</span><span class="identifier-syntax">V_var</span><span class="plain-syntax">, </span><span class="identifier-syntax">inter_symbol</span><span class="plain-syntax"> *</span><span class="identifier-syntax">R_var</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="identifier-syntax">use_integer_scaling</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_O</span><span class="plain-syntax"> != </span><span class="constant-syntax">0</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">STORE_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::ref_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">MINUS_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, (</span><span class="identifier-syntax">inter_t</span><span class="plain-syntax">) </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_O</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
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<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">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</span><span class="plain-syntax"> != </span><span class="constant-syntax">1</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">R_var</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">STORE_BIP</span><span class="plain-syntax">);</span>
|
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::ref_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">R_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">MODULO_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, (</span><span class="identifier-syntax">inter_t</span><span class="plain-syntax">) </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">STORE_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::ref_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
|
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">DIVIDE_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, (</span><span class="identifier-syntax">inter_t</span><span class="plain-syntax">) </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
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<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> } </span><span class="reserved-syntax">else</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">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</span><span class="plain-syntax"> != </span><span class="constant-syntax">0</span><span class="plain-syntax">.0) {</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">STORE_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::ref_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_call_iname</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">Hierarchy::find</span><span class="plain-syntax">(</span><span class="identifier-syntax">REAL_NUMBER_TY_MINUS_HL</span><span class="plain-syntax">));</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_real</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_O</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</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">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_M</span><span class="plain-syntax"> != </span><span class="constant-syntax">1</span><span class="plain-syntax">.0) {</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">STORE_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::ref_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_call_iname</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">Hierarchy::find</span><span class="plain-syntax">(</span><span class="identifier-syntax">REAL_NUMBER_TY_DIVIDE_HL</span><span class="plain-syntax">));</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_real</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">real_M</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax">}</span>
|
|
<span class="plain-syntax">#</span><span class="identifier-syntax">endif</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP20"></a><b>§20. </b>The following compiles a valid condition to test whether the value in the
|
|
named I6 variable is equal to, greater than, less than or equal to, etc., the
|
|
quantum for the scaling. <span class="extract"><span class="extract-syntax">op</span></span> contains the textual form of the comparison
|
|
operator to use: say, <span class="extract"><span class="extract-syntax">">="</span></span>.
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax">#</span><span class="identifier-syntax">ifdef</span><span class="plain-syntax"> </span><span class="identifier-syntax">CORE_MODULE</span>
|
|
<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::compile_threshold_test</span><span class="plain-syntax">(</span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">,</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">inter_symbol</span><span class="plain-syntax"> *</span><span class="identifier-syntax">V_var</span><span class="plain-syntax">, </span><span class="identifier-syntax">inter_t</span><span class="plain-syntax"> </span><span class="identifier-syntax">op</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">op</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</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">sc</span><span class="plain-syntax">.</span><span class="identifier-syntax">use_integer_scaling</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_call_iname</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">Hierarchy::find</span><span class="plain-syntax">(</span><span class="identifier-syntax">NUMBER_TY_ABS_HL</span><span class="plain-syntax">));</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, (</span><span class="identifier-syntax">inter_t</span><span class="plain-syntax">) </span><a href="2-sav.html#SP14" class="function-link"><span class="function-syntax">Kinds::Scalings::quantum</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">sc</span><span class="plain-syntax">));</span>
|
|
<span class="plain-syntax"> } </span><span class="reserved-syntax">else</span><span class="plain-syntax"> {</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_call_iname</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">Hierarchy::find</span><span class="plain-syntax">(</span><span class="identifier-syntax">REAL_NUMBER_TY_COMPARE_HL</span><span class="plain-syntax">));</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_call_iname</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">Hierarchy::find</span><span class="plain-syntax">(</span><span class="identifier-syntax">REAL_NUMBER_TY_ABS_HL</span><span class="plain-syntax">));</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_real</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><a href="2-sav.html#SP14" class="function-link"><span class="function-syntax">Kinds::Scalings::real_quantum</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">sc</span><span class="plain-syntax">));</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, </span><span class="constant-syntax">0</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax">}</span>
|
|
<span class="plain-syntax">#</span><span class="identifier-syntax">endif</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP21"></a><b>§21. </b>We now compile code to print the value in the variable <span class="extract"><span class="extract-syntax">V_var</span></span> with
|
|
respect to this scaling. We need two other variables at our disposal to
|
|
do this: <span class="extract"><span class="extract-syntax">R_var</span></span>, which is temporary storage to hold the remainder part;
|
|
and <span class="extract"><span class="extract-syntax">S_var</span></span>, which is a scratch variable used as a form of loop counter.
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax">#</span><span class="identifier-syntax">ifdef</span><span class="plain-syntax"> </span><span class="identifier-syntax">CORE_MODULE</span>
|
|
<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::compile_print_in_quanta</span><span class="plain-syntax">(</span><span class="reserved-syntax">scaling_transformation</span><span class="plain-syntax"> </span><span class="identifier-syntax">sc</span><span class="plain-syntax">,</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">inter_symbol</span><span class="plain-syntax"> *</span><span class="identifier-syntax">V_var</span><span class="plain-syntax">, </span><span class="identifier-syntax">inter_symbol</span><span class="plain-syntax"> *</span><span class="identifier-syntax">R_var</span><span class="plain-syntax">, </span><span class="identifier-syntax">inter_symbol</span><span class="plain-syntax"> *</span><span class="identifier-syntax">S_var</span><span class="plain-syntax">) {</span>
|
|
|
|
<span class="plain-syntax"> </span><a href="2-sav.html#SP19" class="function-link"><span class="function-syntax">Kinds::Scalings::compile_value_to_quanta</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">sc</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">, </span><span class="identifier-syntax">R_var</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">sc</span><span class="plain-syntax">.</span><span class="identifier-syntax">use_integer_scaling</span><span class="plain-syntax">) {</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">PRINTNUMBER_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">IF_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">GT_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">R_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, </span><span class="constant-syntax">0</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::code</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-sav.html#SP21_1" class="named-paragraph-link"><span class="named-paragraph">Print a decimal expansion for the remainder</span><span class="named-paragraph-number">21.1</span></a></span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> } </span><span class="reserved-syntax">else</span><span class="plain-syntax"> {</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_call_iname</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">Hierarchy::find</span><span class="plain-syntax">(</span><span class="identifier-syntax">REAL_NUMBER_TY_SAY_HL</span><span class="plain-syntax">));</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">V_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> }</span>
|
|
<span class="plain-syntax">}</span>
|
|
<span class="plain-syntax">#</span><span class="identifier-syntax">endif</span>
|
|
</pre>
|
|
<p class="commentary firstcommentary"><a id="SP21_1"></a><b>§21.1. </b>In the integer case, then, suppose we have determined that our value is
|
|
2 quanta with remainder 26/Mths. We've already printed the 2, and it remains
|
|
to print the best decimal expansion we can to represent 26/Mths.
|
|
</p>
|
|
|
|
<p class="commentary">This splits into two cases. If <span class="extract"><span class="extract-syntax">M</span></span> divides some power of 10 then the fraction
|
|
<span class="extract"><span class="extract-syntax">26/M</span></span> can be written as a positive integer divided by a power of 10, and
|
|
that means the decimal expansion can be printed exactly: there are no
|
|
recurring decimals. If it can't, then we must approximate.
|
|
</p>
|
|
|
|
<p class="commentary"><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">Print a decimal expansion for the remainder</span><span class="named-paragraph-number">21.1</span></span><span class="comment-syntax"> =</span>
|
|
</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">PRINT_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_text</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">I</span><span class="string-syntax">"."</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">M</span><span class="plain-syntax"> = </span><span class="identifier-syntax">sc</span><span class="plain-syntax">.</span><span class="element-syntax">int_M</span><span class="plain-syntax">;</span>
|
|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">cl10M</span><span class="plain-syntax"> = </span><span class="constant-syntax">1</span><span class="plain-syntax">; </span><span class="reserved-syntax">while</span><span class="plain-syntax"> (</span><span class="identifier-syntax">M</span><span class="plain-syntax"> > </span><span class="identifier-syntax">cl10M</span><span class="plain-syntax">) </span><span class="identifier-syntax">cl10M</span><span class="plain-syntax"> = </span><span class="identifier-syntax">cl10M</span><span class="plain-syntax">*10;</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">TEMPORARY_TEXT</span><span class="plain-syntax">(</span><span class="identifier-syntax">C</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">WRITE_TO</span><span class="plain-syntax">(</span><span class="identifier-syntax">C</span><span class="plain-syntax">, </span><span class="string-syntax">"M = %d, ceiling(log_10(M)) = %d"</span><span class="plain-syntax">, </span><span class="identifier-syntax">M</span><span class="plain-syntax">, </span><span class="identifier-syntax">cl10M</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Emit::code_comment</span><span class="plain-syntax">(</span><span class="identifier-syntax">C</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">DISCARD_TEXT</span><span class="plain-syntax">(</span><span class="identifier-syntax">C</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">cl10M</span><span class="plain-syntax"> % </span><span class="identifier-syntax">M</span><span class="plain-syntax"> == </span><span class="constant-syntax">0</span><span class="plain-syntax">)</span>
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<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-sav.html#SP21_1_1" class="named-paragraph-link"><span class="named-paragraph">Use an exact method, since the multiplier divides a power of 10</span><span class="named-paragraph-number">21.1.1</span></a></span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">else</span>
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<span class="plain-syntax"> </span><span class="named-paragraph-container code-font"><a href="2-sav.html#SP21_1_2" class="named-paragraph-link"><span class="named-paragraph">Use an approximate method, since we can't have an exact one in all cases</span><span class="named-paragraph-number">21.1.2</span></a></span><span class="character-syntax">;</span>
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</pre>
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<ul class="endnotetexts"><li>This code is used in <a href="2-sav.html#SP21">§21</a>.</li></ul>
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<p class="commentary firstcommentary"><a id="SP21_1_1"></a><b>§21.1.1. </b>In this exact case,
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</p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="plain-syntax"> M = cl10M / t</span>
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</pre>
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<p class="commentary">for some natural number <span class="extract"><span class="extract-syntax">t</span></span>, which means our example <span class="extract"><span class="extract-syntax">26/M</span></span> is equal to
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</p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="plain-syntax"> 26t/Mt = 26t / cl10M</span>
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</pre>
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<p class="commentary">Once we've done that, we simply work out how many initial 0s there should
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be; print that many zeroes; and then print <span class="extract"><span class="extract-syntax">26t</span></span> as if it's an integer.
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</p>
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<p class="commentary"><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">Use an exact method, since the multiplier divides a power of 10</span><span class="named-paragraph-number">21.1.1</span></span><span class="comment-syntax"> =</span>
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</p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">t</span><span class="plain-syntax"> = </span><span class="identifier-syntax">cl10M</span><span class="plain-syntax">/</span><span class="identifier-syntax">M</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">if</span><span class="plain-syntax"> (</span><span class="identifier-syntax">t</span><span class="plain-syntax"> != </span><span class="constant-syntax">1</span><span class="plain-syntax">) {</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">STORE_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::ref_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">R_var</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">TIMES_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">R_var</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, (</span><span class="identifier-syntax">inter_t</span><span class="plain-syntax">) </span><span class="identifier-syntax">t</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> }</span>
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|
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">STORE_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::ref_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">S_var</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, (</span><span class="identifier-syntax">inter_t</span><span class="plain-syntax">) </span><span class="identifier-syntax">cl10M</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">WHILE_BIP</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">AND_BIP</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">EQ_BIP</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">MODULO_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">R_var</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, </span><span class="constant-syntax">10</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, </span><span class="constant-syntax">0</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">GT_BIP</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">R_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, </span><span class="constant-syntax">0</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::code</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">STORE_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::ref_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">R_var</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">DIVIDE_BIP</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">R_var</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, </span><span class="constant-syntax">10</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">STORE_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::ref_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">S_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">DIVIDE_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">S_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, </span><span class="constant-syntax">10</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">WHILE_BIP</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">LT_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">R_var</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">DIVIDE_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">S_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, </span><span class="constant-syntax">10</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::code</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">PRINT_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_text</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">I</span><span class="string-syntax">"0"</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">STORE_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::ref_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">S_var</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">DIVIDE_BIP</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">S_var</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, </span><span class="constant-syntax">10</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">PRINTNUMBER_BIP</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">R_var</span><span class="plain-syntax">);</span>
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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</pre>
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<ul class="endnotetexts"><li>This code is used in <a href="2-sav.html#SP21_1">§21.1</a>.</li></ul>
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<p class="commentary firstcommentary"><a id="SP21_1_2"></a><b>§21.1.2. </b>In this approximation, <span class="extract"><span class="extract-syntax">R_var</span></span> is measured in units of <span class="extract"><span class="extract-syntax">1/M</span></span>. Thus the first
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digit after the decimal point should be <span class="extract"><span class="extract-syntax">R_var</span></span> times <span class="extract"><span class="extract-syntax">10/M</span></span>, the second
|
|
<span class="extract"><span class="extract-syntax">R_var</span></span> times <span class="extract"><span class="extract-syntax">100/M</span></span>, and so on.
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</p>
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<p class="commentary"><span class="named-paragraph-container code-font"><span class="named-paragraph-defn">Use an approximate method, since we can't have an exact one in all cases</span><span class="named-paragraph-number">21.1.2</span></span><span class="comment-syntax"> =</span>
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</p>
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<pre class="displayed-code all-displayed-code code-font">
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<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">R</span><span class="plain-syntax"> = </span><span class="constant-syntax">1</span><span class="plain-syntax">;</span>
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<span class="plain-syntax"> </span><span class="reserved-syntax">while</span><span class="plain-syntax"> (</span><span class="identifier-syntax">R</span><span class="plain-syntax"><=</span><span class="identifier-syntax">M</span><span class="plain-syntax">) {</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">R</span><span class="plain-syntax"> = </span><span class="identifier-syntax">R</span><span class="plain-syntax">*10;</span>
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|
<span class="plain-syntax"> </span><span class="reserved-syntax">int</span><span class="plain-syntax"> </span><span class="identifier-syntax">g</span><span class="plain-syntax"> = </span><a href="2-dmn.html#SP20" class="function-link"><span class="function-syntax">Kinds::Dimensions::gcd</span></a><span class="plain-syntax">(</span><span class="identifier-syntax">R</span><span class="plain-syntax">, </span><span class="identifier-syntax">M</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">PRINTNUMBER_BIP</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">MODULO_BIP</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">PLUS_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">MODULO_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">DIVIDE_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::inv_primitive</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">TIMES_BIP</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::down</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val_symbol</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_value</span><span class="plain-syntax">, </span><span class="identifier-syntax">R_var</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, (</span><span class="identifier-syntax">inter_t</span><span class="plain-syntax">) (</span><span class="identifier-syntax">R</span><span class="plain-syntax">/</span><span class="identifier-syntax">g</span><span class="plain-syntax">));</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, (</span><span class="identifier-syntax">inter_t</span><span class="plain-syntax">) (</span><span class="identifier-syntax">M</span><span class="plain-syntax">/</span><span class="identifier-syntax">g</span><span class="plain-syntax">));</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, </span><span class="constant-syntax">10</span><span class="plain-syntax">);</span>
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|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, </span><span class="constant-syntax">10</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::val</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">(), </span><span class="identifier-syntax">K_number</span><span class="plain-syntax">, </span><span class="identifier-syntax">LITERAL_IVAL</span><span class="plain-syntax">, </span><span class="constant-syntax">10</span><span class="plain-syntax">);</span>
|
|
<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
|
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<span class="plain-syntax"> </span><span class="identifier-syntax">Produce::up</span><span class="plain-syntax">(</span><span class="identifier-syntax">Emit::tree</span><span class="plain-syntax">());</span>
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<span class="plain-syntax"> }</span>
|
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</pre>
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<ul class="endnotetexts"><li>This code is used in <a href="2-sav.html#SP21_1">§21.1</a>.</li></ul>
|
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<p class="commentary firstcommentary"><a id="SP22"></a><b>§22. </b>And finally:
|
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</p>
|
|
|
|
<pre class="displayed-code all-displayed-code code-font">
|
|
<span class="reserved-syntax">void</span><span class="plain-syntax"> </span><span class="function-syntax">Kinds::Scalings::I6_real_literal</span><span class="plain-syntax">(</span><span class="identifier-syntax">OUTPUT_STREAM</span><span class="plain-syntax">, </span><span class="reserved-syntax">double</span><span class="plain-syntax"> </span><span class="identifier-syntax">x</span><span class="plain-syntax">) {</span>
|
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<span class="plain-syntax"> </span><span class="identifier-syntax">WRITE</span><span class="plain-syntax">(</span><span class="string-syntax">"$"</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">x</span><span class="plain-syntax"> > </span><span class="constant-syntax">0</span><span class="plain-syntax">) </span><span class="identifier-syntax">WRITE</span><span class="plain-syntax">(</span><span class="string-syntax">"+"</span><span class="plain-syntax">);</span>
|
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<span class="plain-syntax"> </span><span class="identifier-syntax">WRITE</span><span class="plain-syntax">(</span><span class="string-syntax">"%g"</span><span class="plain-syntax">, </span><span class="identifier-syntax">x</span><span class="plain-syntax">);</span>
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<span class="plain-syntax">}</span>
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</pre>
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