Metallic ratios: Difference between revisions

Line 657:

Golden ratio, where b = 1:

Value after 615 iterations: 1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374847540880753868917521266338622235369317931800607667263544333890865959395829056383226613199282902678806752087668925017116962070322210432162695486262963136144</pre>

=={{header|J}}==

It's perhaps worth noting that we can compute the fibonacci ratio to 256 digits in ten iterations, if we use an appropriate form of iteration:

258j256":%~/+/+/ .*~^:10 x:*i.2 2

1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374847540880753868917521266338622235369317931800607667263544333890865959395829056383226613199282902678806752087668925017116962070322210432162695486262963136144

</lang>

However, the task implies we should use a different form of iteration, so we should probably stick to that here.

task=:{{

32 task y

:

echo 'b=',":y

echo 'seq=',":(,(1,y) X _2{.])^:15]1 1x

k=. 0

prev=.val=. ''

rat=. 1 1x

whilst.-.prev-:val do.

k=. k+1

prev=. val

rat=. }.rat,rat X 1,y

val=. (j./2 0+x)":%~/rat

end.

echo (":k),' iterations: ',val

}}

task 0

b=0

seq=1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

2 iterations: 1.00000000000000000000000000000000

task 1

b=1

seq=1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597

78 iterations: 1.61803398874989484820458683436564

task 2

b=2

seq=1 1 3 7 17 41 99 239 577 1393 3363 8119 19601 47321 114243 275807 665857

44 iterations: 2.41421356237309504880168872420970

task 3

b=3

seq=1 1 4 13 43 142 469 1549 5116 16897 55807 184318 608761 2010601 6640564 21932293 72437443

34 iterations: 3.30277563773199464655961063373525

task 4

b=4

seq=1 1 5 21 89 377 1597 6765 28657 121393 514229 2178309 9227465 39088169 165580141 701408733 2971215073

28 iterations: 4.23606797749978969640917366873128

task 5

b=5

seq=1 1 6 31 161 836 4341 22541 117046 607771 3155901 16387276 85092281 441848681 2294335686 11913527111 61861971241

25 iterations: 5.19258240356725201562535524577016

task 6

b=6

seq=1 1 7 43 265 1633 10063 62011 382129 2354785 14510839 89419819 551029753 3395598337 20924619775 128943316987 794584521697

23 iterations: 6.16227766016837933199889354443272

task 7

b=7

seq=1 1 8 57 407 2906 20749 148149 1057792 7552693 53926643 385039194 2749201001 19629446201 140155324408 1000716717057 7145172343807

22 iterations: 7.14005494464025913554865124576352

task 8

b=8

seq=1 1 9 73 593 4817 39129 317849 2581921 20973217 170367657 1383914473 11241683441 91317382001 741780739449 6025563297593 48946287120193

20 iterations: 8.12310562561766054982140985597408

task 9

b=9

seq=1 1 10 91 829 7552 68797 626725 5709322 52010623 473804929 4316254984 39320099785 358197153049 3263094477226 29726047448083 270797521509973

20 iterations: 9.10977222864644365500113714088140

256 task 1

b=1

seq=1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597

615 iterations: 1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374847540880753868917521266338622235369317931800607667263544333890865959395829056383226613199282902678806752087668925017116962070322210432162695486262963136144

</lang>

=={{header|Java}}==