Engel expansion: Difference between revisions
→{{header|Phix}}
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0.0+sq2_179-from_engle to_engle sq2_179
9.66281e_196</lang>
=={{header|Phix}}==
<!--<lang Phix>(phixonline)-->
<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>
<span style="color: #7060A8;">mpfr_set_default_precision</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">180</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- see notes</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">toEngel</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">engel</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #004080;">mpfr</span> <span style="color: #000000;">u</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">while</span> <span style="color: #7060A8;">mpfr_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">u</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">0</span>
<span style="color: #008080;">and</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">engel</span><span style="color: #0000FF;">)<</span><span style="color: #000000;">70</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">mpfr_si_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">u</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpfr_ceil</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">engel</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">mpfr_get_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">u</span><span style="color: #0000FF;">,</span><span style="color: #000000;">u</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpfr_sub_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">u</span><span style="color: #0000FF;">,</span><span style="color: #000000;">u</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: #008080;">return</span> <span style="color: #000000;">engel</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">fromEngel</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">engel</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">mpfr</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">prod</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">e</span> <span style="color: #008080;">in</span> <span style="color: #000000;">engel</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">mpfr_set_d</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpfr_si_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">prod</span><span style="color: #0000FF;">,</span><span style="color: #000000;">prod</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpfr_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">prod</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">rats</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span>
<span style="color: #008000;">"3.14159265358979"</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"2.71828182845904"</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"1.414213562373095"</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"7.59375"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642743"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"25.628906"</span>
<span style="color: #0000FF;">}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">rat</span> <span style="color: #008080;">in</span> <span style="color: #000000;">rats</span> <span style="color: #008080;">do</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;">"Rational number : %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rat</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">engel</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">toEngel</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rat</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">dix</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'.'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rat</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">places</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rat</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">dix</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">engel</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">cp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fromEngel</span><span style="color: #0000FF;">(</span><span style="color: #000000;">engel</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">places</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;">places</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">dix</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">rat</span><span style="color: #0000FF;">[</span><span style="color: #000000;">dix</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">dix</span><span style="color: #0000FF;">]</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: #000000;">cp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</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;">"Engel expansion : %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">engel</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">)],</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%d"</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;">"Number of terms : %d, places : %d (%d correct)\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">l</span><span style="color: #0000FF;">,</span><span style="color: #000000;">places</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cp</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;">"Back to rational: %s\n\n"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</lang>-->
{{out}}
I could only get pi accurate to 125 decimal places and root2 to 87, so cut the input strings accordingly, and later
had to lop another 10 dp off pi to avoid a crash under p2js.<br>
In fact the 1 digit error on desktop/Phix (below) don't happen in a browser. Increasing the precision helps but only up to a (relatively small) point. <br>
You may or may not have better luck with completely rewriting this to use mpq (rationals).
<pre>
Rational number : 3.14159265358979
Engel expansion : 1 1 1 8 8 17 19 300 1991 2768 4442 4830 10560 37132 107315 244141 651042 1953125 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647
Number of terms : 70, places : 14 (14 correct)
Back to rational: 3.14159265358979
Rational number : 2.71828182845904
Engel expansion : 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 82 144 321 2289 9041 21083 474060 887785 976563 1953125 2147483647 2147483647 2147483647
Number of terms : 70, places : 14 (14 correct)
Back to rational: 2.71828182845904
Rational number : 1.414213562373095
Engel expansion : 1 3 5 5 16 18 78 102 120 144 260 968 18531 46065 63005 65105 78125 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647
Number of terms : 70, places : 15 (15 correct)
Back to rational: 1.414213562373095
Rational number : 7.59375
Engel expansion : 1 1 1 1 1 1 1 2 6 8
Number of terms : 10, places : 5 (5 correct)
Back to rational: 7.59375
Rational number : 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823
Engel expansion : 1 1 1 8 8 17 19 300 1991 2492 7236 10586 34588 63403 70637 1236467 5417668 5515697 5633167 7458122 9637848 9805775 41840855 58408380 213130873 460586654 1017925067 1626739591 2147483647 2147483647
Number of terms : 70, places : 115 (115 correct)
Back to rational: 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823
Rational number : 2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642743
Engel expansion : 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Number of terms : 70, places : 101 (100 correct)
Back to rational: 2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642742
Rational number : 1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387
Engel expansion : 1 3 5 5 16 18 78 102 120 144 251 363 1402 31169 88630 184655 259252 298770 4196070 38538874 616984563 1975413038 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647 2147483647
Number of terms : 70, places : 87 (87 correct)
Back to rational: 1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387
Rational number : 25.628906
Engel expansion : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 4 33 33 35
Number of terms : 54, places : 6 (6 correct)
Back to rational: 25.628906
</pre>
=={{header|Raku}}==
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