Sylvester's sequence: Difference between revisions
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→{{header|Haskell}}: Applied Hlint, Ormolu, reduced (product over map) to fold, showed additional fold for output. |
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Sum of reciprocals of first 10: 0.9999999999999999999999999999999999999999999999999999999999999999999999999999914
</pre>
=={{header|Phix}}==
=== standard precision ===
<!--<lang Phix>(phixonline)-->
<span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">machine_bits</span><span style="color: #0000FF;">()=</span><span style="color: #000000;">32</span><span style="color: #0000FF;">?</span><span style="color: #000000;">53</span><span style="color: #0000FF;">:</span><span style="color: #000000;">64</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</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: #000000;">2</span><span style="color: #0000FF;">:</span><span style="color: #000000;">n</span><span style="color: #0000FF;">*</span><span style="color: #000000;">n</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: #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: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">lim</span><span style="color: #0000FF;">?</span><span style="color: #008000;">"%d: %d\n"</span><span style="color: #0000FF;">:</span><span style="color: #008000;">"%d: %g\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: #000000;">rn</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">n</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;">"sum of reciprocals: %g\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">rn</span><span style="color: #0000FF;">})</span>
<!--</lang>-->
{{out}}
<pre>
1: 2
2: 3
3: 7
4: 43
5: 1807
6: 3263443
7: 10650056950807
8: 1.13424e+26
9: 1.2865e+52
10: 1.65507e+104
sum of reciprocals: 1
</pre>
=== mpfr version ===
Note the (minimal) precision settings of 698 and 211 were found by trial and error.
<!--<lang Phix>(notonline)-->
<span style="color: #008080;">include</span> <span style="color: #7060A8;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #7060A8;">mpz</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">nm1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">mpfr_set_default_prec</span><span style="color: #0000FF;">(</span><span style="color: #000000;">698</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpfr</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">rn</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">tmp</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mpfr_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">></span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">mpz_sub_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nm1</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: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nm1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_add_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</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: #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;">"%d: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)})</span>
<span style="color: #000000;">mpfr_set_z</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmp</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">mpfr_si_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmp</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tmp</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">mpfr_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tmp</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"sum of reciprocals: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpfr_sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%.211Rf"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rn</span><span style="color: #0000FF;">))})</span>
<!--</lang>-->
{{out}}
<pre>
1: 2
2: 3
3: 7
4: 43
5: 1807
6: 3263443
7: 10650056950807
8: 113423713055421844361000443
9: 12864938683278671740537145998360961546653259485195807
10: 165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
sum of reciprocals: 0.999999999999999999...99999999999999999635 (213 digits)
</pre>
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