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<span class="Comment">//: Arithmetic primitives</span>

<span class="Delimiter">:(before &quot;End Primitive Recipe Declarations&quot;)</span>
ADD<span class="Delimiter">,</span>
<span class="Delimiter">:(before &quot;End Primitive Recipe Numbers&quot;)</span>
Recipe_number[<span class="Constant">&quot;add&quot;</span>] = ADD<span class="Delimiter">;</span>
<span class="Delimiter">:(before &quot;End Primitive Recipe Implementations&quot;)</span>
case ADD: <span class="Delimiter">{</span>
  double result = <span class="Constant">0</span><span class="Delimiter">;</span>
  for <span class="Delimiter">(</span>long long int i = <span class="Constant">0</span><span class="Delimiter">;</span> i &lt; SIZE<span class="Delimiter">(</span>ingredients<span class="Delimiter">);</span> ++i<span class="Delimiter">)</span> <span class="Delimiter">{</span>
    assert<span class="Delimiter">(</span>scalar<span class="Delimiter">(</span>ingredients<span class="Delimiter">.</span>at<span class="Delimiter">(</span>i<span class="Delimiter">)));</span>
    result += ingredients<span class="Delimiter">.</span>at<span class="Delimiter">(</span>i<span class="Delimiter">).</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">);</span>
  <span class="Delimiter">}</span>
  products<span class="Delimiter">.</span>resize<span class="Delimiter">(</span><span class="Constant">1</span><span class="Delimiter">);</span>
  products<span class="Delimiter">.</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">).</span>push_back<span class="Delimiter">(</span>result<span class="Delimiter">);</span>
  <span class="Identifier">break</span><span class="Delimiter">;</span>
<span class="Delimiter">}</span>

<span class="Delimiter">:(scenario add_literal)</span>
recipe main [
  <span class="Constant">1</span>:number<span class="Special"> &lt;- </span>add <span class="Constant">23</span>:literal<span class="Delimiter">,</span> <span class="Constant">34</span>:literal
]
<span class="traceContains">+mem: storing 57 in location 1</span>

<span class="Delimiter">:(scenario add)</span>
recipe main [
  <span class="Constant">1</span>:number<span class="Special"> &lt;- </span>copy <span class="Constant">23</span>:literal
  <span class="Constant">2</span>:number<span class="Special"> &lt;- </span>copy <span class="Constant">34</span>:literal
  <span class="Constant">3</span>:number<span class="Special"> &lt;- </span>add <span class="Constant">1</span>:number<span class="Delimiter">,</span> <span class="Constant">2</span>:number
]
<span class="traceContains">+mem: storing 57 in location 3</span>

<span class="Delimiter">:(scenario add_multiple)</span>
recipe main [
  <span class="Constant">1</span>:number<span class="Special"> &lt;- </span>add <span class="Constant">3</span>:literal<span class="Delimiter">,</span> <span class="Constant">4</span>:literal<span class="Delimiter">,</span> <span class="Constant">5</span>:literal
]
<span class="traceContains">+mem: storing 12 in location 1</span>

<span class="Delimiter">:(before &quot;End Primitive Recipe Declarations&quot;)</span>
SUBTRACT<span class="Delimiter">,</span>
<span class="Delimiter">:(before &quot;End Primitive Recipe Numbers&quot;)</span>
Recipe_number[<span class="Constant">&quot;subtract&quot;</span>] = SUBTRACT<span class="Delimiter">;</span>
<span class="Delimiter">:(before &quot;End Primitive Recipe Implementations&quot;)</span>
case SUBTRACT: <span class="Delimiter">{</span>
  assert<span class="Delimiter">(</span>scalar<span class="Delimiter">(</span>ingredients<span class="Delimiter">.</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">)));</span>
  double result = ingredients<span class="Delimiter">.</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">).</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">);</span>
  for <span class="Delimiter">(</span>long long int i = <span class="Constant">1</span><span class="Delimiter">;</span> i &lt; SIZE<span class="Delimiter">(</span>ingredients<span class="Delimiter">);</span> ++i<span class="Delimiter">)</span> <span class="Delimiter">{</span>
    assert<span class="Delimiter">(</span>scalar<span class="Delimiter">(</span>ingredients<span class="Delimiter">.</span>at<span class="Delimiter">(</span>i<span class="Delimiter">)));</span>
    result -= ingredients<span class="Delimiter">.</span>at<span class="Delimiter">(</span>i<span class="Delimiter">).</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">);</span>
  <span class="Delimiter">}</span>
  products<span class="Delimiter">.</span>resize<span class="Delimiter">(</span><span class="Constant">1</span><span class="Delimiter">);</span>
  products<span class="Delimiter">.</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">).</span>push_back<span class="Delimiter">(</span>result<span class="Delimiter">);</span>
  <span class="Identifier">break</span><span class="Delimiter">;</span>
<span class="Delimiter">}</span>

<span class="Delimiter">:(scenario subtract_literal)</span>
recipe main [
  <span class="Constant">1</span>:number<span class="Special"> &lt;- </span>subtract <span class="Constant">5</span>:literal<span class="Delimiter">,</span> <span class="Constant">2</span>:literal
]
<span class="traceContains">+mem: storing 3 in location 1</span>

<span class="Delimiter">:(scenario subtract)</span>
recipe main [
  <span class="Constant">1</span>:number<span class="Special"> &lt;- </span>copy <span class="Constant">23</span>:literal
  <span class="Constant">2</span>:number<span class="Special"> &lt;- </span>copy <span class="Constant">34</span>:literal
  <span class="Constant">3</span>:number<span class="Special"> &lt;- </span>subtract <span class="Constant">1</span>:number<span class="Delimiter">,</span> <span class="Constant">2</span>:number
]
<span class="traceContains">+mem: storing -11 in location 3</span>

<span class="Delimiter">:(scenario subtract_multiple)</span>
recipe main [
  <span class="Constant">1</span>:number<span class="Special"> &lt;- </span>subtract <span class="Constant">6</span>:literal<span class="Delimiter">,</span> <span class="Constant">3</span>:literal<span class="Delimiter">,</span> <span class="Constant">2</span>:literal
]
<span class="traceContains">+mem: storing 1 in location 1</span>

<span class="Delimiter">:(before &quot;End Primitive Recipe Declarations&quot;)</span>
MULTIPLY<span class="Delimiter">,</span>
<span class="Delimiter">:(before &quot;End Primitive Recipe Numbers&quot;)</span>
Recipe_number[<span class="Constant">&quot;multiply&quot;</span>] = MULTIPLY<span class="Delimiter">;</span>
<span class="Delimiter">:(before &quot;End Primitive Recipe Implementations&quot;)</span>
case MULTIPLY: <span class="Delimiter">{</span>
  double result = <span class="Constant">1</span><span class="Delimiter">;</span>
  for <span class="Delimiter">(</span>long long int i = <span class="Constant">0</span><span class="Delimiter">;</span> i &lt; SIZE<span class="Delimiter">(</span>ingredients<span class="Delimiter">);</span> ++i<span class="Delimiter">)</span> <span class="Delimiter">{</span>
    assert<span class="Delimiter">(</span>scalar<span class="Delimiter">(</span>ingredients<span class="Delimiter">.</span>at<span class="Delimiter">(</span>i<span class="Delimiter">)));</span>
    result *= ingredients<span class="Delimiter">.</span>at<span class="Delimiter">(</span>i<span class="Delimiter">).</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">);</span>
  <span class="Delimiter">}</span>
  products<span class="Delimiter">.</span>resize<span class="Delimiter">(</span><span class="Constant">1</span><span class="Delimiter">);</span>
  products<span class="Delimiter">.</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">).</span>push_back<span class="Delimiter">(</span>result<span class="Delimiter">);</span>
  <span class="Identifier">break</span><span class="Delimiter">;</span>
<span class="Delimiter">}</span>

<span class="Delimiter">:(scenario multiply_literal)</span>
recipe main [
  <span class="Constant">1</span>:number<span class="Special"> &lt;- </span>multiply <span class="Constant">2</span>:literal<span class="Delimiter">,</span> <span class="Constant">3</span>:literal
]
<span class="traceContains">+mem: storing 6 in location 1</span>

<span class="Delimiter">:(scenario multiply)</span>
recipe main [
  <span class="Constant">1</span>:number<span class="Special"> &lt;- </span>copy <span class="Constant">4</span>:literal
  <span class="Constant">2</span>:number<span class="Special"> &lt;- </span>copy <span class="Constant">6</span>:literal
  <span class="Constant">3</span>:number<span class="Special"> &lt;- </span>multiply <span class="Constant">1</span>:number<span class="Delimiter">,</span> <span class="Constant">2</span>:number
]
<span class="traceContains">+mem: storing 24 in location 3</span>

<span class="Delimiter">:(scenario multiply_multiple)</span>
recipe main [
  <span class="Constant">1</span>:number<span class="Special"> &lt;- </span>multiply <span class="Constant">2</span>:literal<span class="Delimiter">,</span> <span class="Constant">3</span>:literal<span class="Delimiter">,</span> <span class="Constant">4</span>:literal
]
<span class="traceContains">+mem: storing 24 in location 1</span>

<span class="Delimiter">:(before &quot;End Primitive Recipe Declarations&quot;)</span>
DIVIDE<span class="Delimiter">,</span>
<span class="Delimiter">:(before &quot;End Primitive Recipe Numbers&quot;)</span>
Recipe_number[<span class="Constant">&quot;divide&quot;</span>] = DIVIDE<span class="Delimiter">;</span>
<span class="Delimiter">:(before &quot;End Primitive Recipe Implementations&quot;)</span>
case DIVIDE: <span class="Delimiter">{</span>
  assert<span class="Delimiter">(</span>scalar<span class="Delimiter">(</span>ingredients<span class="Delimiter">.</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">)));</span>
  double result = ingredients<span class="Delimiter">.</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">).</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">);</span>
  for <span class="Delimiter">(</span>long long int i = <span class="Constant">1</span><span class="Delimiter">;</span> i &lt; SIZE<span class="Delimiter">(</span>ingredients<span class="Delimiter">);</span> ++i<span class="Delimiter">)</span> <span class="Delimiter">{</span>
    assert<span class="Delimiter">(</span>scalar<span class="Delimiter">(</span>ingredients<span class="Delimiter">.</span>at<span class="Delimiter">(</span>i<span class="Delimiter">)));</span>
    result /= ingredients<span class="Delimiter">.</span>at<span class="Delimiter">(</span>i<span class="Delimiter">).</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">);</span>
  <span class="Delimiter">}</span>
  products<span class="Delimiter">.</span>resize<span class="Delimiter">(</span><span class="Constant">1</span><span class="Delimiter">);</span>
  products<span class="Delimiter">.</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">).</span>push_back<span class="Delimiter">(</span>result<span class="Delimiter">);</span>
  <span class="Identifier">break</span><span class="Delimiter">;</span>
<span class="Delimiter">}</span>

<span class="Delimiter">:(scenario divide_literal)</span>
recipe main [
  <span class="Constant">1</span>:number<span class="Special"> &lt;- </span>divide <span class="Constant">8</span>:literal<span class="Delimiter">,</span> <span class="Constant">2</span>:literal
]
<span class="traceContains">+mem: storing 4 in location 1</span>

<span class="Delimiter">:(scenario divide)</span>
recipe main [
  <span class="Constant">1</span>:number<span class="Special"> &lt;- </span>copy <span class="Constant">27</span>:literal
  <span class="Constant">2</span>:number<span class="Special"> &lt;- </span>copy <span class="Constant">3</span>:literal
  <span class="Constant">3</span>:number<span class="Special"> &lt;- </span>divide <span class="Constant">1</span>:number<span class="Delimiter">,</span> <span class="Constant">2</span>:number
]
<span class="traceContains">+mem: storing 9 in location 3</span>

<span class="Delimiter">:(scenario divide_multiple)</span>
recipe main [
  <span class="Constant">1</span>:number<span class="Special"> &lt;- </span>divide <span class="Constant">12</span>:literal<span class="Delimiter">,</span> <span class="Constant">3</span>:literal<span class="Delimiter">,</span> <span class="Constant">2</span>:literal
]
<span class="traceContains">+mem: storing 2 in location 1</span>

<span class="Comment">//: Integer division</span>

<span class="Delimiter">:(before &quot;End Primitive Recipe Declarations&quot;)</span>
DIVIDE_WITH_REMAINDER<span class="Delimiter">,</span>
<span class="Delimiter">:(before &quot;End Primitive Recipe Numbers&quot;)</span>
Recipe_number[<span class="Constant">&quot;divide-with-remainder&quot;</span>] = DIVIDE_WITH_REMAINDER<span class="Delimiter">;</span>
<span class="Delimiter">:(before &quot;End Primitive Recipe Implementations&quot;)</span>
case DIVIDE_WITH_REMAINDER: <span class="Delimiter">{</span>
  long long int quotient = ingredients<span class="Delimiter">.</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">).</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">)</span> / ingredients<span class="Delimiter">.</span>at<span class="Delimiter">(</span><span class="Constant">1</span><span class="Delimiter">).</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">);</span>
  long long int remainder = static_cast&lt;long long int&gt;<span class="Delimiter">(</span>ingredients<span class="Delimiter">.</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">).</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">))</span> % static_cast&lt;long long int&gt;<span class="Delimiter">(</span>ingredients<span class="Delimiter">.</span>at<span class="Delimiter">(</span><span class="Constant">1</span><span class="Delimiter">).</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">));</span>
  products<span class="Delimiter">.</span>resize<span class="Delimiter">(</span><span class="Constant">2</span><span class="Delimiter">);</span>
  <span class="Comment">// very large integers will lose precision</span>
  products<span class="Delimiter">.</span>at<span class="Delimiter">(</span><span class="Constant">0</span><span class="Delimiter">).</span>push_back<span class="Delimiter">(</span>quotient<span class="Delimiter">);</span>
  products<span class="Delimiter">.</span>at<span class="Delimiter">(</span><span class="Constant">1</span><span class="Delimiter">).</span>push_back<span class="Delimiter">(</span>remainder<span class="Delimiter">);</span>
  <span class="Identifier">break</span><span class="Delimiter">;</span>
<span class="Delimiter">}</span>

<span class="Delimiter">:(scenario divide_with_remainder_literal)</span>
recipe main [
  <span class="Constant">1</span>:number<span class="Delimiter">,</span> <span class="Constant">2</span>:number<span class="Special"> &lt;- </span>divide-with-remainder <span class="Constant">9</span>:literal<span class="Delimiter">,</span> <span class="Constant">2</span>:literal
]
<span class="traceContains">+mem: storing 4 in location 1</span>
<span class="traceContains">+mem: storing 1 in location 2</span>

<span class="Delimiter">:(scenario divide_with_remainder)</span>
recipe main [
  <span class="Constant">1</span>:number<span class="Special"> &lt;- </span>copy <span class="Constant">27</span>:literal
  <span class="Constant">2</span>:number<span class="Special"> &lt;- </span>copy <span class="Constant">11</span>:literal
  <span class="Constant">3</span>:number<span class="Delimiter">,</span> <span class="Constant">4</span>:number<span class="Special"> &lt;- </span>divide-with-remainder <span class="Constant">1</span>:number<span class="Delimiter">,</span> <span class="Constant">2</span>:number
]
<span class="traceContains">+mem: storing 2 in location 3</span>
<span class="traceContains">+mem: storing 5 in location 4</span>

<span class="Delimiter">:(scenario divide_with_decimal_point)</span>
recipe main [
  <span class="Comment"># todo: literal floats?</span>
  <span class="Constant">1</span>:number<span class="Special"> &lt;- </span>divide <span class="Constant">5</span>:literal<span class="Delimiter">,</span> <span class="Constant">2</span>:literal
]
<span class="traceContains">+mem: storing 2.5 in location 1</span>

<span class="Delimiter">:(code)</span>
inline bool scalar<span class="Delimiter">(</span>vector&lt;long long int&gt;&amp; x<span class="Delimiter">)</span> <span class="Delimiter">{</span>
  <span class="Identifier">return</span> SIZE<span class="Delimiter">(</span>x<span class="Delimiter">)</span> == <span class="Constant">1</span><span class="Delimiter">;</span>
<span class="Delimiter">}</span>
inline bool scalar<span class="Delimiter">(</span>vector&lt;double&gt;&amp; x<span class="Delimiter">)</span> <span class="Delimiter">{</span>
  <span class="Identifier">return</span> SIZE<span class="Delimiter">(</span>x<span class="Delimiter">)</span> == <span class="Constant">1</span><span class="Delimiter">;</span>
<span class="Delimiter">}</span>
</pre>
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