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Square form factorization: Difference between revisions

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Square form factorization (view source)

Revision as of 22:45, 23 March 2021

20,119 bytes added ,  3 years ago
m
→‎{{header|Phix}}: added syntax colouring the hard way
m (added a category.)
m (→‎{{header|Phix}}: added syntax colouring the hard way)
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=={{header|Phix}}==
{{trans|C|<small>(Classical heuristic - fixes the two incorrectly failing cases of the previous version)</small>}}
<!--<lang Phix>-->
<lang Phix>--requires(64) -- (decided to limit 32-bit explicitly instead)
<span style="color: #000080;font-style:italic;">--requires(64) -- (decided to limit 32-bit explicitly instead)</span>
constant MxN = power(2,iff(machine_bits()=32?53:63)),
<span style="color: #008080;">constant</span> <span style="color: #000000;">MxN</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power<span style="color: #0000FF;">(<span style="color: #000000;">2<span style="color: #0000FF;">,<span style="color: #008080;">iff<span style="color: #0000FF;">(<span style="color: #7060A8;">machine_bits<span style="color: #0000FF;">(<span style="color: #0000FF;">)<span style="color: #0000FF;">=<span style="color: #000000;">32<span style="color: #0000FF;">?<span style="color: #000000;">53<span style="color: #0000FF;">:<span style="color: #000000;">63<span style="color: #0000FF;">)<span style="color: #0000FF;">)<span style="color: #0000FF;">,</span>
m = {1, 3, 5, 7, 11}
<span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{<span style="color: #000000;">1<span style="color: #0000FF;">,</span> <span style="color: #000000;">3<span style="color: #0000FF;">,</span> <span style="color: #000000;">5<span style="color: #0000FF;">,</span> <span style="color: #000000;">7<span style="color: #0000FF;">,</span> <span style="color: #000000;">11<span style="color: #0000FF;">}</span>
function squfof(atom N)
<span style="color: #008080;">function</span> <span style="color: #000000;">squfof<span style="color: #0000FF;">(<span style="color: #004080;">atom</span> <span style="color: #000000;">N<span style="color: #0000FF;">)</span>
-- square form factorization
<span style="color: #000080;font-style:italic;">-- square form factorization</span>
 
integer h, a=0, b, c, u=0, v, w, rN, q, r, t
<span style="color: #004080;">integer</span> <span style="color: #000000;">h<span style="color: #0000FF;">,</span> <span style="color: #000000;">a<span style="color: #0000FF;">=<span style="color: #000000;">0<span style="color: #0000FF;">,</span> <span style="color: #000000;">b<span style="color: #0000FF;">,</span> <span style="color: #000000;">c<span style="color: #0000FF;">,</span> <span style="color: #000000;">u<span style="color: #0000FF;">=<span style="color: #000000;">0<span style="color: #0000FF;">,</span> <span style="color: #000000;">v<span style="color: #0000FF;">,</span> <span style="color: #000000;">w<span style="color: #0000FF;">,</span> <span style="color: #000000;">rN<span style="color: #0000FF;">,</span> <span style="color: #000000;">q<span style="color: #0000FF;">,</span> <span style="color: #000000;">r<span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span>
if remainder(N,2)==0 then return 2 end if
<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder<span style="color: #0000FF;">(<span style="color: #000000;">N<span style="color: #0000FF;">,<span style="color: #000000;">2<span style="color: #0000FF;">)<span style="color: #0000FF;">==<span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">2</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
h = floor(sqrt(N) + 0.5)
<span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor<span style="color: #0000FF;">(<span style="color: #7060A8;">sqrt<span style="color: #0000FF;">(<span style="color: #000000;">N<span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">0.5<span style="color: #0000FF;">)</span>
if h*h==N then return h end if
<span style="color: #008080;">if</span> <span style="color: #000000;">h<span style="color: #0000FF;">*<span style="color: #000000;">h<span style="color: #0000FF;">==<span style="color: #000000;">N</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">h</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
for k=1 to length(m) do
<span style="color: #008080;">for</span> <span style="color: #000000;">k<span style="color: #0000FF;">=<span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length<span style="color: #0000FF;">(<span style="color: #000000;">m<span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
integer mk = m[k]
<span style="color: #004080;">integer</span> <span style="color: #000000;">mk</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">m<span style="color: #0000FF;">[<span style="color: #000000;">k<span style="color: #0000FF;">]</span>
if mk>1 and remainder(N,mk)==0 then return mk end if
<span style="color: #008080;">if</span> <span style="color: #000000;">mk<span style="color: #0000FF;">><span style="color: #000000;">1</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">remainder<span style="color: #0000FF;">(<span style="color: #000000;">N<span style="color: #0000FF;">,<span style="color: #000000;">mk<span style="color: #0000FF;">)<span style="color: #0000FF;">==<span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">mk</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
//check overflow m * N
<span style="color: #000080;font-style:italic;">//check overflow m * N</span>
if N>MxN/mk then exit end if
<span style="color: #008080;">if</span> <span style="color: #000000;">N<span style="color: #0000FF;">><span style="color: #000000;">MxN<span style="color: #0000FF;">/<span style="color: #000000;">mk</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>
atom mN = N*mk
<span style="color: #004080;">atom</span> <span style="color: #000000;">mN</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">N<span style="color: #0000FF;">*<span style="color: #000000;">mk</span>
r = floor(sqrt(mN))
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor<span style="color: #0000FF;">(<span style="color: #7060A8;">sqrt<span style="color: #0000FF;">(<span style="color: #000000;">mN<span style="color: #0000FF;">)<span style="color: #0000FF;">)</span>
if r*r>mN then r -= 1 end if
<span style="color: #008080;">if</span> <span style="color: #000000;">r<span style="color: #0000FF;">*<span style="color: #000000;">r<span style="color: #0000FF;">><span style="color: #000000;">mN</span> <span style="color: #008080;">then</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
rN = r
<span style="color: #000000;">rN</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span>
//principal form
<span style="color: #000080;font-style:italic;">//principal form</span>
{b,a} = {r,1}
<span style="color: #0000FF;">{<span style="color: #000000;">b<span style="color: #0000FF;">,<span style="color: #000000;">a<span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{<span style="color: #000000;">r<span style="color: #0000FF;">,<span style="color: #000000;">1<span style="color: #0000FF;">}</span>
h = floor((rN+b)/a)*a-b
<span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor<span style="color: #0000FF;">(<span style="color: #0000FF;">(<span style="color: #000000;">rN<span style="color: #0000FF;">+<span style="color: #000000;">b<span style="color: #0000FF;">)<span style="color: #0000FF;">/<span style="color: #000000;">a<span style="color: #0000FF;">)<span style="color: #0000FF;">*<span style="color: #000000;">a<span style="color: #0000FF;">-<span style="color: #000000;">b</span>
c = floor((mN-h*h)/a)
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor<span style="color: #0000FF;">(<span style="color: #0000FF;">(<span style="color: #000000;">mN<span style="color: #0000FF;">-<span style="color: #000000;">h<span style="color: #0000FF;">*<span style="color: #000000;">h<span style="color: #0000FF;">)<span style="color: #0000FF;">/<span style="color: #000000;">a<span style="color: #0000FF;">)</span>
for i=2 to floor(sqrt(2*r)) * 4-1 do
<span style="color: #008080;">for</span> <span style="color: #000000;">i<span style="color: #0000FF;">=<span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">floor<span style="color: #0000FF;">(<span style="color: #7060A8;">sqrt<span style="color: #0000FF;">(<span style="color: #000000;">2<span style="color: #0000FF;">*<span style="color: #000000;">r<span style="color: #0000FF;">)<span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">4<span style="color: #0000FF;">-<span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
//search principal cycle
<span style="color: #000080;font-style:italic;">//search principal cycle</span>
{a,c,t} = {c,a,b}
<span style="color: #0000FF;">{<span style="color: #000000;">a<span style="color: #0000FF;">,<span style="color: #000000;">c<span style="color: #0000FF;">,<span style="color: #000000;">t<span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{<span style="color: #000000;">c<span style="color: #0000FF;">,<span style="color: #000000;">a<span style="color: #0000FF;">,<span style="color: #000000;">b<span style="color: #0000FF;">}</span>
q = floor((rN+b)/a)
<span style="color: #000000;">q</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor<span style="color: #0000FF;">(<span style="color: #0000FF;">(<span style="color: #000000;">rN<span style="color: #0000FF;">+<span style="color: #000000;">b<span style="color: #0000FF;">)<span style="color: #0000FF;">/<span style="color: #000000;">a<span style="color: #0000FF;">)</span>
b = q*a-b
<span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">q<span style="color: #0000FF;">*<span style="color: #000000;">a<span style="color: #0000FF;">-<span style="color: #000000;">b</span>
c += q*(t-b)
<span style="color: #000000;">c</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">q<span style="color: #0000FF;">*<span style="color: #0000FF;">(<span style="color: #000000;">t<span style="color: #0000FF;">-<span style="color: #000000;">b<span style="color: #0000FF;">)</span>
 
if remainder(i,2)==0 then
<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder<span style="color: #0000FF;">(<span style="color: #000000;">i<span style="color: #0000FF;">,<span style="color: #000000;">2<span style="color: #0000FF;">)<span style="color: #0000FF;">==<span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
r = floor(sqrt(c)+0.5)
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor<span style="color: #0000FF;">(<span style="color: #7060A8;">sqrt<span style="color: #0000FF;">(<span style="color: #000000;">c<span style="color: #0000FF;">)<span style="color: #0000FF;">+<span style="color: #000000;">0.5<span style="color: #0000FF;">)</span>
if r*r==c then
<span style="color: #008080;">if</span> <span style="color: #000000;">r<span style="color: #0000FF;">*<span style="color: #000000;">r<span style="color: #0000FF;">==<span style="color: #000000;">c</span> <span style="color: #008080;">then</span>
//square form found
<span style="color: #000080;font-style:italic;">//square form found
//inverse square root
q =//inverse square floor((rN-b)root</r)span>
<span style="color: #000000;">q</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor<span style="color: #0000FF;">(<span style="color: #0000FF;">(<span style="color: #000000;">rN<span style="color: #0000FF;">-<span style="color: #000000;">b<span style="color: #0000FF;">)<span style="color: #0000FF;">/<span style="color: #000000;">r<span style="color: #0000FF;">)</span>
v = q*r+b
<span style="color: #000000;">v</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">q<span style="color: #0000FF;">*<span style="color: #000000;">r<span style="color: #0000FF;">+<span style="color: #000000;">b</span>
w = floor((mN-v*v)/r)
<span style="color: #000000;">w</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor<span style="color: #0000FF;">(<span style="color: #0000FF;">(<span style="color: #000000;">mN<span style="color: #0000FF;">-<span style="color: #000000;">v<span style="color: #0000FF;">*<span style="color: #000000;">v<span style="color: #0000FF;">)<span style="color: #0000FF;">/<span style="color: #000000;">r<span style="color: #0000FF;">)</span>
//search ambiguous cycle
u <span style="color: #000080;font-style:italic;">//search ambiguous rcycle</span>
<span style="color: #000000;">u</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span>
while true do
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
{u,w,r} = {w,u,v}
<span style="color: #0000FF;">{<span style="color: #000000;">u<span style="color: #0000FF;">,<span style="color: #000000;">w<span style="color: #0000FF;">,<span style="color: #000000;">r<span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{<span style="color: #000000;">w<span style="color: #0000FF;">,<span style="color: #000000;">u<span style="color: #0000FF;">,<span style="color: #000000;">v<span style="color: #0000FF;">}</span>
q = floor((rN+v)/u)
<span style="color: #000000;">q</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor<span style="color: #0000FF;">(<span style="color: #0000FF;">(<span style="color: #000000;">rN<span style="color: #0000FF;">+<span style="color: #000000;">v<span style="color: #0000FF;">)<span style="color: #0000FF;">/<span style="color: #000000;">u<span style="color: #0000FF;">)</span>
v = q*u-v
<span style="color: #000000;">v</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">q<span style="color: #0000FF;">*<span style="color: #000000;">u<span style="color: #0000FF;">-<span style="color: #000000;">v</span>
if v==r then exit end if
<span style="color: #008080;">if</span> <span style="color: #000000;">v<span style="color: #0000FF;">==<span style="color: #000000;">r</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>
w += q*(r-v)
<span style="color: #000000;">w</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">q<span style="color: #0000FF;">*<span style="color: #0000FF;">(<span style="color: #000000;">r<span style="color: #0000FF;">-<span style="color: #000000;">v<span style="color: #0000FF;">)</span>
end while
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
 
//symmetry point
h <span style="color: #000080;font-style:italic;">//symmetry gcd(N,u)point</span>
<span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">gcd<span style="color: #0000FF;">(<span style="color: #000000;">N<span style="color: #0000FF;">,<span style="color: #000000;">u<span style="color: #0000FF;">)</span>
if h!=1 then return h end if
<span style="color: #008080;">if</span> <span style="color: #000000;">h<span style="color: #0000FF;">!=<span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">h</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
return 1
<span style="color: #008080;">return</span> <span style="color: #000000;">1</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
constant tests = {2501, 12851, 13289, 75301, 120787, 967009, 997417, 7091569, 5214317, 20834839,
<span style="color: #008080;">constant</span> <span style="color: #000000;">tests</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{<span style="color: #000000;">2501<span style="color: #0000FF;">,</span> <span style="color: #000000;">12851<span style="color: #0000FF;">,</span> <span style="color: #000000;">13289<span style="color: #0000FF;">,</span> <span style="color: #000000;">75301<span style="color: #0000FF;">,</span> <span style="color: #000000;">120787<span style="color: #0000FF;">,</span> <span style="color: #000000;">967009<span style="color: #0000FF;">,</span> <span style="color: #000000;">997417<span style="color: #0000FF;">,</span> <span style="color: #000000;">7091569<span style="color: #0000FF;">,</span> <span style="color: #000000;">5214317<span style="color: #0000FF;">,</span> <span style="color: #000000;">20834839<span style="color: #0000FF;">,</span>
23515517, 33409583, 44524219, 13290059, 223553581, 42854447, 223553581, 2027651281,
<span style="color: #000000;">23515517<span style="color: #0000FF;">,</span> <span style="color: #000000;">33409583<span style="color: #0000FF;">,</span> <span style="color: #000000;">44524219<span style="color: #0000FF;">,</span> <span style="color: #000000;">13290059<span style="color: #0000FF;">,</span> <span style="color: #000000;">223553581<span style="color: #0000FF;">,</span> <span style="color: #000000;">42854447<span style="color: #0000FF;">,</span> <span style="color: #000000;">223553581<span style="color: #0000FF;">,</span> <span style="color: #000000;">2027651281<span style="color: #0000FF;">,</span>
11111111111, 100895598169, 1002742628021, -- (prime/expected to fail)
<span style="color: #000000;">11111111111<span style="color: #0000FF;">,</span> <span style="color: #000000;">100895598169<span style="color: #0000FF;">,</span> <span style="color: #000000;">1002742628021<span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (prime/expected to fail)</span>
60012462237239, 287129523414791, 9007199254740931, 32, -- (limit of 32-bit)
<span style="color: #000000;">60012462237239<span style="color: #0000FF;">,</span> <span style="color: #000000;">287129523414791<span style="color: #0000FF;">,</span> <span style="color: #000000;">9007199254740931<span style="color: #0000FF;">,</span> <span style="color: #000000;">32<span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (limit of 32-bit)</span>
11111111111111111, 314159265358979323, 384307168202281507, 419244183493398773,
<span style="color: #000000;">11111111111111111<span style="color: #0000FF;">,</span> <span style="color: #000000;">314159265358979323<span style="color: #0000FF;">,</span> <span style="color: #000000;">384307168202281507<span style="color: #0000FF;">,</span> <span style="color: #000000;">419244183493398773<span style="color: #0000FF;">,</span>
658812288346769681, 922337203685477563, 1000000000000000127, 1152921505680588799,
<span style="color: #000000;">658812288346769681<span style="color: #0000FF;">,</span> <span style="color: #000000;">922337203685477563<span style="color: #0000FF;">,</span> <span style="color: #000000;">1000000000000000127<span style="color: #0000FF;">,</span> <span style="color: #000000;">1152921505680588799<span style="color: #0000FF;">,</span>
1537228672809128917, 4611686018427387877}
<span style="color: #000000;">1537228672809128917<span style="color: #0000FF;">,</span> <span style="color: #000000;">4611686018427387877<span style="color: #0000FF;">}</span>
 
printf(1,"N f N/f\n")
<span style="color: #7060A8;">printf<span style="color: #0000FF;">(<span style="color: #000000;">1<span style="color: #0000FF;">,<span style="color: #008000;">"N f N/f\n"<span style="color: #0000FF;">)</span>
printf(1,"======================================\n")
<span style="color: #7060A8;">printf<span style="color: #0000FF;">(<span style="color: #000000;">1<span style="color: #0000FF;">,<span style="color: #008000;">"======================================\n"<span style="color: #0000FF;">)</span>
for i=1 to length(tests) do
<span style="color: #008080;">for</span> <span style="color: #000000;">i<span style="color: #0000FF;">=<span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length<span style="color: #0000FF;">(<span style="color: #000000;">tests<span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
atom N = tests[i]
<span style="color: #004080;">atom</span> <span style="color: #000000;">N</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tests<span style="color: #0000FF;">[<span style="color: #000000;">i<span style="color: #0000FF;">]</span>
if N=32 then
<span style="color: #008080;">if</span> <span style="color: #000000;">N<span style="color: #0000FF;">=<span style="color: #000000;">32</span> <span style="color: #008080;">then</span>
if machine_bits()=32 then exit end if
<span style="color: #008080;">if</span> <span style="color: #7060A8;">machine_bits<span style="color: #0000FF;">(<span style="color: #0000FF;">)<span style="color: #0000FF;">=<span style="color: #000000;">32</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>
else
<span style="color: #008080;">else</span>
atom f = squfof(N)
<span style="color: #004080;">atom</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">squfof<span style="color: #0000FF;">(<span style="color: #000000;">N<span style="color: #0000FF;">)</span>
printf(1,"%-22d %s\n",{N,iff(f=1?"fail":sprintf("%-10d %d",{f,N/f}))})
<span style="color: #7060A8;">printf<span style="color: #0000FF;">(<span style="color: #000000;">1<span style="color: #0000FF;">,<span style="color: #008000;">"%-22d %s\n"<span style="color: #0000FF;">,<span style="color: #0000FF;">{<span style="color: #000000;">N<span style="color: #0000FF;">,<span style="color: #008080;">iff<span style="color: #0000FF;">(<span style="color: #000000;">f<span style="color: #0000FF;">=<span style="color: #000000;">1<span style="color: #0000FF;">?<span style="color: #008000;">"fail"<span style="color: #0000FF;">:<span style="color: #7060A8;">sprintf<span style="color: #0000FF;">(<span style="color: #008000;">"%-10d %d"<span style="color: #0000FF;">,<span style="color: #0000FF;">{<span style="color: #000000;">f<span style="color: #0000FF;">,<span style="color: #000000;">N<span style="color: #0000FF;">/<span style="color: #000000;">f<span style="color: #0000FF;">}<span style="color: #0000FF;">)<span style="color: #0000FF;">)<span style="color: #0000FF;">}<span style="color: #0000FF;">)</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end for</lang>
<span style="color: #008080;">end</span> <span style="color: #008080;">for
<!--</lang>-->
{{out}}
<small>(on 64-bit, whereas the last 10 entries, ie 11111111111111111 on, are simply omitted on 32-bit)</small>
Petelomax
7,804

edits

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