RosettaCodeData/Task/Hamming-numbers/Phix/hamming-numbers-2.phix

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 <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
 <span style="color: #000080;font-style:italic;">-- numbers kept as {log,{pow2,pow3,pow5}},
 --  value is ~= exp(log), == (2^pow2)*(3^pow3)*(5^pow5)</span>
 <span style="color: #008080;">enum</span> <span style="color: #000000;">LOG</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">POWS</span>
 <span style="color: #008080;">enum</span> <span style="color: #000000;">POW2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">POW3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">POW5</span>

 <span style="color: #008080;">function</span> <span style="color: #000000;">lnmin</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
     <span style="color: #008080;">return</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">LOG</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">LOG</span><span style="color: #0000FF;">]?</span><span style="color: #000000;">a</span><span style="color: #0000FF;">:</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>

 <span style="color: #008080;">constant</span> <span style="color: #000000;">ln1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">log</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">ln2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">log</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">ln3</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">log</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">ln5</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">log</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)</span>

 <span style="color: #008080;">function</span> <span style="color: #000000;">hamming</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">N</span><span style="color: #0000FF;">)</span>
 <span style="color: #004080;">sequence</span> <span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">N</span><span style="color: #0000FF;">)</span>
 <span style="color: #004080;">sequence</span> <span style="color: #000000;">x2</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">ln2</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}},</span>
          <span style="color: #000000;">x3</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">ln3</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}},</span>
          <span style="color: #000000;">x5</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">ln5</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}}</span>
 <span style="color: #004080;">integer</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">j</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
     <span style="color: #000000;">h</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">ln1</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}}</span>
     <span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">N</span> <span style="color: #008080;">do</span>
         <span style="color: #000000;">h</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lnmin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lnmin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x5</span><span style="color: #0000FF;">)))</span>
         <span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">POWS</span><span style="color: #0000FF;">]</span>
         <span style="color: #008080;">if</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">=</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">[</span><span style="color: #000000;">POWS</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #000000;">x2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span> <span style="color: #000000;">x2</span><span style="color: #0000FF;">[</span><span style="color: #000000;">LOG</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">ln2</span> <span style="color: #000000;">x2</span><span style="color: #0000FF;">[</span><span style="color: #000000;">POWS</span><span style="color: #0000FF;">][</span><span style="color: #000000;">POW2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
         <span style="color: #008080;">if</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">=</span><span style="color: #000000;">x3</span><span style="color: #0000FF;">[</span><span style="color: #000000;">POWS</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> <span style="color: #000000;">j</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #000000;">x3</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">])</span> <span style="color: #000000;">x3</span><span style="color: #0000FF;">[</span><span style="color: #000000;">LOG</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">ln3</span> <span style="color: #000000;">x3</span><span style="color: #0000FF;">[</span><span style="color: #000000;">POWS</span><span style="color: #0000FF;">][</span><span style="color: #000000;">POW3</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
         <span style="color: #008080;">if</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">=</span><span style="color: #000000;">x5</span><span style="color: #0000FF;">[</span><span style="color: #000000;">POWS</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #000000;">x5</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">])</span> <span style="color: #000000;">x5</span><span style="color: #0000FF;">[</span><span style="color: #000000;">LOG</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">ln5</span> <span style="color: #000000;">x5</span><span style="color: #0000FF;">[</span><span style="color: #000000;">POWS</span><span style="color: #0000FF;">][</span><span style="color: #000000;">POW5</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
     <span style="color: #008080;">return</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">[</span><span style="color: #000000;">N</span><span style="color: #0000FF;">]</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>

 <span style="color: #008080;">function</span> <span style="color: #000000;">hint</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">hm</span><span style="color: #0000FF;">)</span>
 <span style="color: #000080;font-style:italic;">-- (obviously not accurate above 53 bits on a 32-bit system, or 64 bits on a 64 bit system)</span>
     <span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">hm</span><span style="color: #0000FF;">[</span><span style="color: #000000;">POWS</span><span style="color: #0000FF;">]</span>
     <span style="color: #008080;">return</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">POW2</span><span style="color: #0000FF;">])*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">POW3</span><span style="color: #0000FF;">])*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">POW5</span><span style="color: #0000FF;">])</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>

 <span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
 <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">20</span> <span style="color: #008080;">do</span>
     <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">hint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hamming</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)))</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"hamming[1..20]: %v\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">s</span><span style="color: #0000FF;">})</span>
 <span style="color: #0000FF;">?</span><span style="color: #000000;">hint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hamming</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1691</span><span style="color: #0000FF;">))</span>
 <span style="color: #0000FF;">?</span><span style="color: #000000;">hint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hamming</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1000000</span><span style="color: #0000FF;">))</span>
 <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" %d (approx)\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">hint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hamming</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1000000</span><span style="color: #0000FF;">)))</span>

 <span style="color: #008080;">include</span> <span style="color: #000000;">builtins</span><span style="color: #0000FF;">\</span><span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>

 <span style="color: #008080;">function</span> <span style="color: #000000;">mpz_hint</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">hm</span><span style="color: #0000FF;">)</span>
 <span style="color: #000080;font-style:italic;">-- (as accurate as you like)</span>
     <span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p5</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">hm</span><span style="color: #0000FF;">[</span><span style="color: #000000;">POWS</span><span style="color: #0000FF;">]</span>
     <span style="color: #004080;">mpz</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">tmp2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tmp3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tmp5</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
     <span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmp2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">)</span>
     <span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmp3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p3</span><span style="color: #0000FF;">)</span>
     <span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmp5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p5</span><span style="color: #0000FF;">)</span>
     <span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmp3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tmp3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tmp5</span><span style="color: #0000FF;">)</span>
     <span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmp2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tmp2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tmp3</span><span style="color: #0000FF;">)</span>
     <span style="color: #008080;">return</span> <span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmp2</span><span style="color: #0000FF;">)</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>

 <span style="color: #0000FF;">?</span><span style="color: #000000;">mpz_hint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hamming</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1000000</span><span style="color: #0000FF;">))</span>
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