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Humble numbers: Difference between revisions

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Humble numbers (view source)

Revision as of 18:16, 11 June 2021

13,192 bytes added ,  2 years ago
m
→‎{{header|Phix}}: added syntax colouring the hard way
m (Added Delphi reference to Pascal code)
m (→‎{{header|Phix}}: added syntax colouring the hard way)
Line 3,987:
It will go all the way to 100 digits if you give it time (18 mins, on 64bit - 32bit runs out of memory after printing the 99th line)<br>
I also tried a log version (similar to [[Hamming_numbers#A_much_faster_logarithmic_version|Hamming_numbers]]) but inaccuracies with floor(h[n][LOG]) crept in quite early, at just 10 digits.
<!--<lang Phix>(phixonline)-- demo/rosetta/humble.exw>
<span style="color: #000080;font-style:italic;">-- demo/rosetta/humble.exw</span>
include mpfr.e
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
procedure humble(integer n, bool countdigits=false)
-- if countdigits is false: show first n humble numbers,
<span style="color: #008080;">procedure</span> <span style="color: #000000;">humble</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;">bool</span> <span style="color: #000000;">countdigits</span><span style="color: #0000FF;">=</span><span style="color: #004600;">false</span><span style="color: #0000FF;">)</span>
-- if countdigits is true: count them up to n digits.
<span style="color: #000080;font-style:italic;">-- if countdigits is false: show first n humble numbers,
sequence humble = {mpz_init(1)},
-- if countdigits is true: count them up to n digits.</span>
nexts = {2,3,5,7},
<span style="color: #004080;">sequence</span> <span style="color: #000000;">humble</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)},</span>
indices = repeat(1,4)
<span style="color: #000000;">nexts</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">},</span>
for i=1 to 4 do nexts[i] = mpz_init(nexts[i]) end for
<span style="color: #000000;">indices</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span>
integer digits = 1,
<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;">4</span> <span style="color: #008080;">do</span> <span style="color: #000000;">nexts</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: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nexts</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>
count = 1,
<span style="color: #004080;">integer</span> <span style="color: #000000;">digits</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
dead = 1,
<span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
tc = 0
<span style="color: #000000;">dead</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
atom t0 = time()
<span style="color: #000000;">tc</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
mpz p10 = mpz_init(10)
<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>
while ((not countdigits) and length(humble)<n)
<span style="color: #004080;">mpz</span> <span style="color: #000000;">p10</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
or (countdigits and digits<=n) do
<span style="color: #008080;">while</span> <span style="color: #0000FF;">((</span><span style="color: #008080;">not</span> <span style="color: #000000;">countdigits</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">humble</span><span style="color: #0000FF;">)<</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
mpz x = mpz_init_set(mpz_min(nexts))
<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">countdigits</span> <span style="color: #008080;">and</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
humble = append(humble,x)
<span style="color: #004080;">mpz</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init_set</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nexts</span><span style="color: #0000FF;">))</span>
if countdigits then
<span style="color: #000000;">humble</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">humble</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
if mpz_cmp(x,p10)>=0 then
<span style="color: #008080;">if</span> <span style="color: #000000;">countdigits</span> <span style="color: #008080;">then</span>
mpz_mul_si(p10,p10,10)
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p10</span><span style="color: #0000FF;">)>=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
integer d = min(indices)
<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
for k=dead to d-1 do
<span style="color: #004080;">integer</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">indices</span><span style="color: #0000FF;">)</span>
humble[k] = mpz_free(humble[k])
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">dead</span> <span style="color: #008080;">to</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
end for
<span style="color: #000000;">humble</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: #7060A8;">mpz_free</span><span style="color: #0000FF;">(</span><span style="color: #000000;">humble</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">])</span>
dead = d
string s<span style="color: iff(digits#008080;">end</span> <span style=1?""color: #008080;"s"),>for</span>
<span style="color: #000000;">dead</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d</span>
e = elapsed(time()-t0)
<span style="color: #004080;">string</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">?</span><span style="color: #008000;">""</span><span style="color: #0000FF;">:</span><span style="color: #008000;">"s"</span><span style="color: #0000FF;">),</span>
tc += count
<span style="color: #000000;">e</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>
-- e &= sprintf(", %,d dead",{dead-1})
<span style="color: #000000;">tc</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">count</span>
e &= sprintf(", total:%,d",{tc})
<span style="color: #000080;font-style:italic;">-- e &= sprintf(", %,d dead",{dead-1})</span>
printf(1,"%,12d humble numbers have %d digit%s (%s)\n",{count,digits,s,e})
<span style="color: #000000;">e</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">", total:%,d"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">tc</span><span style="color: #0000FF;">})</span>
digits += 1
<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 humble numbers have %d digit%s (%s)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">})</span>
count = 1
<span style="color: #000000;">digits</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
else
<span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
count += 1
end if<span style="color: #008080;">else</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
for j=1 to 4 do
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
if mpz_cmp(nexts[j],x)<=0 then
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">4</span> <span style="color: #008080;">do</span>
indices[j] += 1
<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nexts</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)<=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
mpz_mul_si(nexts[j],humble[indices[j]],get_prime(j))
<span style="color: #000000;">indices</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;">1</span>
end if
<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nexts</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span><span style="color: #000000;">humble</span><span style="color: #0000FF;">[</span><span style="color: #000000;">indices</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]],</span><span style="color: #7060A8;">get_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">j</span><span style="color: #0000FF;">))</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end while
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
if not countdigits then
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
for i=1 to length(humble) do
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">countdigits</span> <span style="color: #008080;">then</span>
humble[i] = shorten(mpz_get_str(humble[i]),ml:=10)
<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;">humble</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
end for
<span style="color: #000000;">humble</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: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">humble</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]),</span><span style="color: #000000;">ml</span><span style="color: #0000FF;">:=</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
printf(1,"First %d humble numbers: %s\n\n",{n,join(humble," ")})
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end if
<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;">"First %d humble numbers: %s\n\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">humble</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">)})</span>
end procedure
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
 
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
humble(50)
humble(42,true)</lang>
<span style="color: #000000;">humble</span><span style="color: #0000FF;">(</span><span style="color: #000000;">50</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">humble</span><span style="color: #0000FF;">(</span><span style="color: #000000;">42</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
<!--</lang>-->
{{out}}
<pre>
Petelomax
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