View source for Self numbers\Phix

My humiliatingly bad prior attempts at [[Self_numbers#Phix|this task]]:

Translation of [[Self_numbers#Go|Go]].
Replacing the problematic sv[a+b+... line with a bit of dirty inline assembly improved performance by 90%<br>
(Of course you lose bounds checking, type checking, negative subscripts, fraction handling, and all that jazz.)<br>
We use a string of Y/N for the sieve to force one byte per element ('\0' and 1 would be equally valid).
<!--<syntaxhighlight lang="phix">(phixonline)-->
 <span style="color: #008080;">if</span> <span style="color: #7060A8;">machine_bits</span><span style="color: #0000FF;">()=</span><span style="color: #000000;">32</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">crash</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"requires 64 bit"</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
 
 <span style="color: #008080;">function</span> <span style="color: #000000;">sieve</span><span style="color: #0000FF;">()</span>
     <span style="color: #004080;">string</span> <span style="color: #000000;">sv</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'N'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">1e9</span><span style="color: #0000FF;">+</span><span style="color: #000000;">9</span><span style="color: #0000FF;">*</span><span style="color: #000000;">9</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (1.86GB)</span>
     <span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
     <span style="color: #008080;">for</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
         <span style="color: #008080;">for</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
             <span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
                 <span style="color: #008080;">for</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>                  
                    <span style="color: #008080;">for</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
                         <span style="color: #008080;">for</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>                         
                             <span style="color: #008080;">for</span> <span style="color: #000000;">g</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
                                 <span style="color: #008080;">for</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
                                     <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
                                         <span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>                                         
 <span style="color: #000080;font-style:italic;">--                                         n += 1
 --                                         sv[a+b+c+d+e+f+g+h+i+j+n] = 'Y'</span>
 #<span style="color: #7060A8;">ilASM</span><span style="color: #0000FF;">{</span>
   <span style="color: #0000FF;">[</span><span style="color: #000000;">32</span><span style="color: #0000FF;">]</span>  <span style="color: #000080;font-style:italic;">-- (allows clean compilation on 32 bit, before crash as above)</span>
   <span style="color: #0000FF;">[</span><span style="color: #000000;">64</span><span style="color: #0000FF;">]</span>
     <span style="color: #000000;">mov</span> <span style="color: #000000;">rax</span><span style="color: #0000FF;">,[</span><span style="color: #000000;">a</span><span style="color: #0000FF;">]</span>
     <span style="color: #000000;">mov</span> <span style="color: #000000;">r12</span><span style="color: #0000FF;">,[</span><span style="color: #000000;">b</span><span style="color: #0000FF;">]</span>
     <span style="color: #000000;">mov</span> <span style="color: #000000;">r13</span><span style="color: #0000FF;">,[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span>
     <span style="color: #000000;">mov</span> <span style="color: #000000;">r14</span><span style="color: #0000FF;">,[</span><span style="color: #000000;">d</span><span style="color: #0000FF;">]</span>
     <span style="color: #000000;">mov</span> <span style="color: #000000;">r15</span><span style="color: #0000FF;">,[</span><span style="color: #000000;">e</span><span style="color: #0000FF;">]</span>
     <span style="color: #000000;">add</span> <span style="color: #000000;">r12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r13</span>
     <span style="color: #000000;">add</span> <span style="color: #000000;">r14</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r15</span>
     <span style="color: #000000;">add</span> <span style="color: #000000;">rax</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r12</span> 
     <span style="color: #000000;">mov</span> <span style="color: #000000;">rdi</span><span style="color: #0000FF;">,[</span><span style="color: #000000;">sv</span><span style="color: #0000FF;">]</span>
     <span style="color: #000000;">add</span> <span style="color: #000000;">rax</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r14</span> 
     <span style="color: #000000;">mov</span> <span style="color: #000000;">r12</span><span style="color: #0000FF;">,[</span><span style="color: #000000;">f</span><span style="color: #0000FF;">]</span>
     <span style="color: #000000;">mov</span> <span style="color: #000000;">r13</span><span style="color: #0000FF;">,[</span><span style="color: #000000;">g</span><span style="color: #0000FF;">]</span>
     <span style="color: #000000;">mov</span> <span style="color: #000000;">r14</span><span style="color: #0000FF;">,[</span><span style="color: #000000;">h</span><span style="color: #0000FF;">]</span>
     <span style="color: #000000;">mov</span> <span style="color: #000000;">r15</span><span style="color: #0000FF;">,[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
     <span style="color: #000000;">add</span> <span style="color: #000000;">r12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r13</span>
     <span style="color: #000000;">shl</span> <span style="color: #000000;">rdi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span>
     <span style="color: #000000;">mov</span> <span style="color: #000000;">rcx</span><span style="color: #0000FF;">,[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span>
     <span style="color: #000000;">mov</span> <span style="color: #000000;">r13</span><span style="color: #0000FF;">,[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
     <span style="color: #000000;">add</span> <span style="color: #000000;">r14</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r15</span>
     <span style="color: #000000;">add</span> <span style="color: #000000;">rax</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r12</span> 
     <span style="color: #000000;">add</span> <span style="color: #000000;">rax</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r14</span> 
     <span style="color: #000000;">add</span> <span style="color: #000000;">r13</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rcx</span>
     <span style="color: #000000;">add</span> <span style="color: #000000;">rax</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r13</span> 
     <span style="color: #000000;">add</span> <span style="color: #000000;">rcx</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span>
     <span style="color: #000000;">mov</span> <span style="color: #000000;">byte</span><span style="color: #0000FF;">[</span><span style="color: #000000;">rdi</span><span style="color: #0000FF;">+</span><span style="color: #000000;">rax</span><span style="color: #0000FF;">],</span><span style="color: #008000;">'Y'</span>
     <span style="color: #000000;">mov</span> <span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">],</span><span style="color: #000000;">rcx</span> <span style="color: #0000FF;">}</span>
                                         <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
                                     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>                                  
                                 <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
                             <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>  
                         <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
                     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
                 <span style="color: #008080;">end</span> <span style="color: #008080;">for</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;">"%d,%d\r"</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: #000080;font-style:italic;">-- (show progress)</span>
         <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
     <span style="color: #008080;">return</span> <span style="color: #000000;">sv</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
  
 <span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
 <span style="color: #004080;">string</span> <span style="color: #000000;">sv</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sieve</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;">"sieve build took %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)})</span>
 <span style="color: #004080;">integer</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</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;">"The first 50 self numbers are:\n"</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: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sv</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
     <span style="color: #008080;">if</span> <span style="color: #000000;">sv</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'N'</span> <span style="color: #008080;">then</span>
         <span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
         <span style="color: #008080;">if</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;"><=</span> <span style="color: #000000;">50</span> <span style="color: #008080;">then</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;">"%3d "</span><span style="color: #0000FF;">,</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: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</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;">"\n"</span><span style="color: #0000FF;">)</span>
             <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
         <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
         <span style="color: #008080;">if</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">1e8</span> <span style="color: #008080;">then</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;">"\nThe %,dth self number is %,d (%s)\n"</span><span style="color: #0000FF;">,</span>
                      <span style="color: #0000FF;">{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</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: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)})</span>
             <span style="color: #008080;">exit</span>
         <span style="color: #008080;">end</span> <span style="color: #008080;">if</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>
<!--</syntaxhighlight>-->
{{out}}
<pre>
sieve build took 6.6s
The first 50 self numbers are:
  1   3   5   7   9  20  31  42  53  64
 75  86  97 108 110 121 132 143 154 165
176 187 198 209 211 222 233 244 255 266
277 288 299 310 312 323 334 345 356 367
378 389 400 411 413 424 435 446 457 468

The 100,000,000th self number is 1,022,727,208 (11.0s)
</pre>

=== generator dictionary ===
While this is dog-slow (see shocking estimate below), it is interesting to note that even by the time it generates the 
10,000,000th number, it is only having to juggle a mere 27 generators.
Just a shame that we had to push over 10,000,000 generators onto that stack, and tried to push quite a few more.
Memory use is pretty low, around ~4MB.<br>
[unlike the above, this is perfectly happy on both 32 and 64 bit]<br>
Long story short: this works much the same as a prime sieve, in which you only need to eliminate multiples
of previous primes. Here, you only need to eliminate digital additions of previous safe numbers. 
Only after writing this did I understand how to write a sliding sieve, which it turns out is a much better idea (see below).
Still, this is pretty interesting and quite neat.
<!--<syntaxhighlight lang="phix">(phixonline)-->
 <span style="color: #004080;">integer</span> <span style="color: #000000;">gd</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">new_dict</span><span style="color: #0000FF;">(),</span> <span style="color: #000000;">gdhead</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
 
 <span style="color: #008080;">function</span> <span style="color: #000000;">ng</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;">integer</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span>
     <span style="color: #008080;">while</span> <span style="color: #000000;">r</span> <span style="color: #008080;">do</span>
         <span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
         <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">/</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
     <span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
     <span style="color: #008080;">return</span> <span style="color: #000000;">n</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
 <span style="color: #008080;">function</span> <span style="color: #000000;">self</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000080;font-style:italic;">/*i*/</span><span style="color: #0000FF;">)</span>
 <span style="color: #000080;font-style:italic;">-- note: assumes sequentially invoked (arg i unused)</span>
     <span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
     <span style="color: #008080;">while</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">gdhead</span> <span style="color: #008080;">do</span>
         <span style="color: #000000;">gdhead</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">pop_dict</span><span style="color: #0000FF;">(</span><span style="color: #000000;">gd</span><span style="color: #0000FF;">)[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
         <span style="color: #7060A8;">setd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ng</span><span style="color: #0000FF;">(</span><span style="color: #000000;">gdhead</span><span style="color: #0000FF;">),</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">gd</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: #000000;">n</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">gdhead</span><span style="color: #0000FF;">)</span>
     <span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
     <span style="color: #7060A8;">setd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ng</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">gd</span><span style="color: #0000FF;">)</span>
     <span style="color: #008080;">return</span> <span style="color: #000000;">n</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
 <span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</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;">"The first 50 self numbers are:\n"</span><span style="color: #0000FF;">)</span>
 <span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">50</span><span style="color: #0000FF;">),</span><span style="color: #000000;">self</span><span style="color: #0000FF;">),{</span><span style="color: #004600;">pp_IntFmt</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%3d"</span><span style="color: #0000FF;">,</span><span style="color: #004600;">pp_IntCh</span><span style="color: #0000FF;">,</span><span style="color: #004600;">false</span><span style="color: #0000FF;">})</span>
 
 <span style="color: #008080;">constant</span> <span style="color: #000000;">limit</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">10000000</span>
 <span style="color: #004080;">integer</span> <span style="color: #000000;">chk</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">100</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;">"\n          i           n   size time\n"</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;">51</span> <span style="color: #008080;">to</span> <span style="color: #000000;">limit</span> <span style="color: #008080;">do</span>
     <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">self</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
     <span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">chk</span> <span style="color: #008080;">then</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;">"%,11d %,11d %6d %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">dict_size</span><span style="color: #0000FF;">(</span><span style="color: #000000;">gd</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)})</span>
         <span style="color: #000000;">chk</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">10</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: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nEstimated time for %,d :%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">1e8</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">((</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">1e8</span><span style="color: #0000FF;">/</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">)})</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
The first 50 self numbers are:
{  1,  3,  5,  7,  9, 20, 31, 42, 53, 64, 75, 86, 97,108,110,121,132,143,
 154,165,176,187,198,209,211,222,233,244,255,266,277,288,299,310,312,323,
 334,345,356,367,378,389,400,411,413,424,435,446,457,468}

          i           n   size time
        100         973     18 0.1s
      1,000      10,188     13 0.2s
     10,000     102,225     10 1.0s
    100,000   1,022,675     20 9.3s
  1,000,000  10,227,221     17 1 minute and 37s
 10,000,000 102,272,662     27 16 minutes and 40s

Estimated time for 100,000,000 :2 hours, 46 minutes and 37s
</pre>
For the record, I would not be at all surprised should a translation of this beat 20 minutes (for 1e8)

=== sliding sieve ===
Mid-speed, perhaps helped by a slightly smarter way of calculating/updating the digit sums<br>
Similar to some other entries, we (only) need a sieve of 9*9, +1 here as I test an entry after the slide.
<!--<syntaxhighlight lang="phix">(phixonline)-->
 <span style="color: #000080;font-style:italic;">--sequence sieve = repeat(0,82), -- (~25% slower)</span>
 <span style="color: #004080;">sequence</span> <span style="color: #000000;">sieve</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;">8192</span><span style="color: #0000FF;">),</span>
          <span style="color: #000000;">digits</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;">10</span><span style="color: #0000FF;">)</span>
 <span style="color: #004080;">integer</span> <span style="color: #000000;">offset</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span>
         <span style="color: #000000;">digit_sum</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: #000000;">0</span>
         
 <span style="color: #008080;">procedure</span> <span style="color: #000000;">next_self</span><span style="color: #0000FF;">()</span>
     <span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
         <span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
         <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
             <span style="color: #004080;">integer</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
             <span style="color: #008080;">if</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">9</span> <span style="color: #008080;">then</span>
                 <span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span>
                 <span style="color: #000000;">digit_sum</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
                 <span style="color: #008080;">exit</span>
             <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
             <span style="color: #000000;">digits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
             <span style="color: #000000;">digit_sum</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">9</span>
         <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
         <span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">digit_sum</span><span style="color: #0000FF;">-</span><span style="color: #000000;">offset</span>
         <span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sieve</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
             <span style="color: #004080;">integer</span> <span style="color: #000000;">j</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
             <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">offset</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sieve</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
                 <span style="color: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</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: #008080;">end</span> <span style="color: #008080;">for</span>
             <span style="color: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">..$]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
             <span style="color: #000000;">offset</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
             <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">digit_sum</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: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
         <span style="color: #008080;">if</span> <span style="color: #000000;">sieve</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">offset</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
     <span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
     <span style="color: #000080;font-style:italic;">-- (result in n)</span>
 <span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
 
 <span style="color: #008080;">constant</span> <span style="color: #000000;">limit</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">100000000</span>
 <span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</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;">"The first 50 self numbers are:\n"</span><span style="color: #0000FF;">)</span>
 <span style="color: #004080;">integer</span> <span style="color: #000000;">chk</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">100</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;">limit</span> <span style="color: #008080;">do</span>
     <span style="color: #000000;">next_self</span><span style="color: #0000FF;">()</span>
     <span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">50</span> <span style="color: #008080;">then</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;">" %3d%s"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">25</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">?</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">:</span><span style="color: #008000;">""</span><span style="color: #0000FF;">)})</span>
     <span style="color: #008080;">elsif</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">chk</span> <span style="color: #008080;">then</span>
         <span style="color: #008080;">if</span> <span style="color: #000000;">chk</span><span style="color: #0000FF;">=</span><span style="color: #000000;">100</span> <span style="color: #008080;">then</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;">"\n           i             n time\n"</span><span style="color: #0000FF;">)</span>
         <span style="color: #008080;">end</span> <span style="color: #008080;">if</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;">"%,12d %,13d %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)})</span>
         <span style="color: #000000;">chk</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">10</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: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nEstimated time for %,d :%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">1e9</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">((</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">1e9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">)})</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
The first 50 self numbers are:
   1   3   5   7   9  20  31  42  53  64  75  86  97 108 110 121 132 143 154 165 176 187 198 209 211
 222 233 244 255 266 277 288 299 310 312 323 334 345 356 367 378 389 400 411 413 424 435 446 457 468

           i             n time
         100           973 0.1s
       1,000        10,188 0.1s
      10,000       102,225 0.1s
     100,000     1,022,675 0.1s
   1,000,000    10,227,221 0.5s
  10,000,000   102,272,662 4.5s
 100,000,000 1,022,727,208 44.5s

Estimated time for 1,000,000,000 :7 minutes and 25s
</pre>