Engel expansion: Difference between revisions

Content added Content deleted
m (→‎{{header|Phix}}: changed dp from 180 to 134 (min rqd))
m (→‎{{header|Phix}}: removed the 70 limit now improves the p2js output)
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<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: #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: #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;">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;">do</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_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: #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>
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{{out}}
{{out}}
I could only get pi accurate to 125 decimal places and root2 to 87, so cut the input strings accordingly.<br>
I could only get pi accurate to 125 decimal places and root2 to 87, so cut the input strings accordingly.<br>
In fact the 1 digit error on desktop/Phix (below) don't happen in a browser. <br>
Increasing the precision helps but only up to a (relatively small) point, ie that 134 ''is'' needed, nowt greater helps at all. <br>
Increasing the precision helps but only up to a (relatively small) point, ie that 134 ''is'' needed, nowt greater helps at all. <br>
You may or may not have better luck with completely rewriting this to use mpq (rationals).
You may or may not have better luck with completely rewriting this to use mpq (rationals).<br>
In fact it works slightly better in a browser (which uses rationals behind the scenes) than on desktop/Phix, as shown below. <br>
<pre>
<pre>
Rational number : 3.14159265358979
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
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)
Number of terms : 83, places : 14 (14 correct)
Back to rational: 3.14159265358979
Back to rational: 3.14159265358979


Rational number : 2.71828182845904
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
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)
Number of terms : 101, places : 14 (14 correct)
Back to rational: 2.71828182845904
Back to rational: 2.71828182845904


Rational number : 1.414213562373095
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
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)
Number of terms : 67, places : 15 (15 correct)
Back to rational: 1.414213562373095
Back to rational: 1.414213562373095


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Rational number : 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384
Rational number : 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384
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 424342175 2147483647 2147483647 2147483647 2147483647
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 424342175 2147483647 2147483647 2147483647 2147483647
Number of terms : 70, places : 125 (125 correct)
Number of terms : 181, places : 125 (125 correct)
Back to rational: 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384
Back to rational: 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384


Rational number : 2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642743
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
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)
Number of terms : 222, places : 101 (101 correct)
Back to rational: 2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642743
Back to rational: 2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642742


Rational number : 1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387
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
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)
Number of terms : 175, places : 87 (87 correct)
Back to rational: 1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387
Back to rational: 1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387


Rational number : 25.628906
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
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)
Number of terms : 65, places : 6 (6 correct)
Back to rational: 25.628906
Back to rational: 25.628906
</pre>
Output under p2js:
<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
Number of terms : 18, 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
Number of terms : 27, 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
Number of terms : 17, 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 : 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384
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 424342175 2717375531 323878055376 339280401894 386771504748
Number of terms : 161, places : 125 (125 correct)
Back to rational: 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384

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 : 150, places : 101 (101 correct)
Back to rational: 2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642743

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 7855284583 34680535992 47012263568 82957997141 1709576125547 42630379527673 164312229775505 404736776022426
Number of terms : 110, 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 : 34, places : 6 (6 correct)
Back to rational: 25.628906
</pre>
</pre>


Retrieved from "https://rosettacode.org/wiki/Engel_expansion"