Upside-down numbers: Difference between revisions

Line 578:

The 5,000,000,000,000,000th upside down number is the 830,704,575,083,359th 34-digit number (1513835774459212468981566335727959)

The total time taken for this onerous and difficult task: 0s

</pre>

=== higher limits ===

Limited to the ''18,446,744,073,709,551,614th?'', we can do better than that!

with javascript_semantics

atom t0 = time()

include mpfr.e -- (so that nth etc can exceed 64 bits of precision)

function kth_of_n(mpz kth, count, integer digits)

if digits=0 then return "" end if

if digits=1 then return "5" end if

mpz_divexact_ui(count,count,9)

mpz_sub_si(kth,kth,1)

mpz dz = mpz_init()

mpz_fdiv_q(dz,kth,count)

integer d = mpz_get_integer(dz)

mpz_add_ui(kth,kth,1)

mpz_mul(dz,dz,count)

mpz_sub(kth,kth,dz)

return ('1'+d) & kth_of_n(kth,count,digits-2) & ('9'-d)

end function

function get_which(mpz nth)

integer digits = 1

mpz count = mpz_init(1),

first = mpz_init(1),

last = mpz_init(1)

while mpz_cmp(nth,last)>0 do

mpz_add_si(first,last,1)

digits += 1

if even(digits) then mpz_mul_si(count,count,9) end if

mpz_add(last,first,count)

mpz_sub_ui(last,last,1)

end while

mpz kth = mpz_init(1)

mpz_add(kth,kth,nth)

mpz_sub(kth,kth,first)

string ns = mpz_get_str(nth,10,true),

res = kth_of_n(kth,count,digits)

return {ns, res, elapsed(time()-t0)}

end function

mpz wz = mpz_init(10)

mpz_pow_ui(wz,wz,100)

printf(1,"The %sth upside down number is\n %s (%s)\n",get_which(wz))

The 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000th upside down number is

454594394343883179243759282183821923122343988685136868482218367266879951778395152999458916423484426556989121455486626786491256111859517233951132448347298826242479524221767889781982729828153768139722767617615656 (0.0s)

</pre>

@@ Line 578: / Line 578: @@
 The 5,000,000,000,000,000th upside down number is the 830,704,575,083,359th 34-digit number (1513835774459212468981566335727959)
 The total time taken for this onerous and difficult task: 0s
+</pre>
+=== higher limits ===
+Limited to the ''18,446,744,073,709,551,614th?'', we can do better than that!
+<!--<syntaxhighlight lang="phix">(phixonline)-->
+ <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</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: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>  <span style="color: #000080;font-style:italic;">-- (so that nth etc can exceed 64 bits of precision)</span>
+ <span style="color: #008080;">function</span> <span style="color: #000000;">kth_of_n</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpz</span> <span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">count</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">if</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #008000;">""</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+     <span style="color: #008080;">if</span> <span style="color: #000000;">digits</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #008000;">"5"</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+     <span style="color: #7060A8;">mpz_divexact_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_sub_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">mpz</span> <span style="color: #000000;">dz</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
+     <span style="color: #7060A8;">mpz_fdiv_q</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dz</span><span style="color: #0000FF;">,</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">integer</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dz</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_add_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dz</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dz</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dz</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">return</span> <span style="color: #0000FF;">(</span><span style="color: #008000;">'1'</span><span style="color: #0000FF;">+</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">&</span> <span style="color: #000000;">kth_of_n</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</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;">2</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">&</span> <span style="color: #0000FF;">(</span><span style="color: #008000;">'9'</span><span style="color: #0000FF;">-</span><span style="color: #000000;">d</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;">get_which</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpz</span> <span style="color: #000000;">nth</span><span style="color: #0000FF;">)</span>
+     <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: #004080;">mpz</span> <span style="color: #000000;">count</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>
+         <span style="color: #000000;">first</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>
+          <span style="color: #000000;">last</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>
+     <span style="color: #008080;">while</span> <span style="color: #7060A8;">mpz_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">last</span><span style="color: #0000FF;">)></span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
+         <span style="color: #7060A8;">mpz_add_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">first</span><span style="color: #0000FF;">,</span><span style="color: #000000;">last</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</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: #008080;">if</span> <span style="color: #7060A8;">even</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digits</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+         <span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">last</span><span style="color: #0000FF;">,</span><span style="color: #000000;">first</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">)</span>
+         <span style="color: #7060A8;">mpz_sub_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">last</span><span style="color: #0000FF;">,</span><span style="color: #000000;">last</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
+     <span style="color: #004080;">mpz</span> <span style="color: #000000;">kth</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>
+     <span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nth</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpz_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">kth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">first</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">string</span> <span style="color: #000000;">ns</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nth</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">),</span>
+            <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">kth_of_n</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kth</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: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">ns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">res</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;">end</span> <span style="color: #008080;">function</span>
+ <span style="color: #004080;">mpz</span> <span style="color: #000000;">wz</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>
+ <span style="color: #7060A8;">mpz_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">wz</span><span style="color: #0000FF;">,</span><span style="color: #000000;">wz</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</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 %sth upside down number is\n %s (%s)\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">get_which</span><span style="color: #0000FF;">(</span><span style="color: #000000;">wz</span><span style="color: #0000FF;">))</span>
+<!--</syntaxhighlight>-->
+{{out}}
+<pre style="font-size: 7px">
+The 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000th upside down number is
+ 454594394343883179243759282183821923122343988685136868482218367266879951778395152999458916423484426556989121455486626786491256111859517233951132448347298826242479524221767889781982729828153768139722767617615656 (0.0s)
 </pre>