Metallic ratios: Difference between revisions
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Reached after 616 iterations
</pre>
=={{header|Visual Basic .NET}}==
{{trans|C#}}
<lang vbnet>Imports BI = System.Numerics.BigInteger
Module Module1
Function IntSqRoot(v As BI, res As BI) As BI
REM res is the initial guess
Dim term As BI = 0
Dim d As BI = 0
Dim dl As BI = 1
While dl <> d
term = v / res
res = (res + term) >> 1
dl = d
d = term - res
End While
Return term
End Function
Function DoOne(b As Integer, digs As Integer) As String
REM calculates result via square root, not iterations
Dim s = b * b + 4
digs += 1
Dim g As BI = Math.Sqrt(s * Math.Pow(10, digs))
Dim bs = IntSqRoot(s * BI.Parse("1" + New String("0", digs << 1)), g)
bs += b * BI.Parse("1" + New String("0", digs))
bs >>= 1
bs += 4
Dim st = bs.ToString
digs -= 1
Return String.Format("{0}.{1}", st(0), st.Substring(1, digs))
End Function
Function DivIt(a As BI, b As BI, digs As Integer) As String
REM performs division
Dim al = a.ToString.Length
Dim bl = b.ToString.Length
digs += 1
a *= BI.Pow(10, digs << 1)
b *= BI.Pow(10, digs)
Dim s = (a / b + 5).ToString
digs -= 1
Return s(0) + "." + s.Substring(1, digs)
End Function
REM custom formatting
Function Joined(x() As BI) As String
Dim wids() = {1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
Dim res = ""
For i = 0 To x.Length - 1
res += String.Format("{0," + (-wids(i)).ToString + "} ", x(i))
Next
Return res
End Function
Sub Main()
REM calculates and checks each "metal"
Console.WriteLine("Metal B Sq.Rt Iters /---- 32 decimal place value ----\\ Matches Sq.Rt Calc")
Dim t = ""
Dim n As BI
Dim nm1 As BI
Dim k As Integer
Dim j As Integer
For b = 0 To 9
Dim lst(14) As BI
lst(0) = 1
lst(1) = 1
For i = 2 To 14
lst(i) = b * lst(i - 1) + lst(i - 2)
Next
REM since all the iterations (except Pt) are > 15, continue iterating from the end of the list of 15
n = lst(14)
nm1 = lst(13)
k = 0
j = 13
While k = 0
Dim lt = t
t = DivIt(n, nm1, 32)
If lt = t Then
k = If(b = 0, 1, j)
End If
Dim onn = n
n = b * n + nm1
nm1 = onn
j += 1
End While
Console.WriteLine("{0,4} {1} {2,2} {3, 2} {4} {5}" + vbNewLine + "{6,19} {7}", "Pt Au Ag CuSn Cu Ni Al Fe Sn Pb".Split(" ")(b), b, b * b + 4, k, t, t = DoOne(b, 32), "", Joined(lst))
Next
REM now calculate and check big one
n = 1
nm1 = 1
k = 0
j = 1
While k = 0
Dim lt = t
t = DivIt(n, nm1, 256)
If lt = t Then
k = j
End If
Dim onn = n
n += nm1
nm1 = onn
j += 1
End While
Console.WriteLine()
Console.WriteLine("Au to 256 digits:")
Console.WriteLine(t)
Console.WriteLine("Iteration count: {0} Matched Sq.Rt Calc: {1}", k, t = DoOne(1, 256))
End Sub
End Module</lang>
{{out}}
<pre>Metal B Sq.Rt Iters /---- 32 decimal place value ----\\ Matches Sq.Rt Calc
Pt 0 4 1 1.00000000000000000000000000000000 True
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Au 1 5 78 1.61803398874989484820458683436564 True
1 1 2 3 5 8 13 21 34 55 89 144 233 377 610
Ag 2 8 44 2.41421356237309504880168872420970 True
1 1 3 7 17 41 99 239 577 1393 3363 8119 19601 47321 114243
CuSn 3 13 34 3.30277563773199464655961063373525 True
1 1 4 13 43 142 469 1549 5116 16897 55807 184318 608761 2010601 6640564
Cu 4 20 28 4.23606797749978969640917366873128 True
1 1 5 21 89 377 1597 6765 28657 121393 514229 2178309 9227465 39088169 165580141
Ni 5 29 25 5.19258240356725201562535524577016 True
1 1 6 31 161 836 4341 22541 117046 607771 3155901 16387276 85092281 441848681 2294335686
Al 6 40 23 6.16227766016837933199889354443272 True
1 1 7 43 265 1633 10063 62011 382129 2354785 14510839 89419819 551029753 3395598337 20924619775
Fe 7 53 22 7.14005494464025913554865124576352 True
1 1 8 57 407 2906 20749 148149 1057792 7552693 53926643 385039194 2749201001 19629446201 140155324408
Sn 8 68 20 8.12310562561766054982140985597408 True
1 1 9 73 593 4817 39129 317849 2581921 20973217 170367657 1383914473 11241683441 91317382001 741780739449
Pb 9 85 20 9.10977222864644365500113714088140 True
1 1 10 91 829 7552 68797 626725 5709322 52010623 473804929 4316254984 39320099785 358197153049 3263094477226
Au to 256 digits:
1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374847540880753868917521266338622235369317931800607667263544333890865959395829056383226613199282902678806752087668925017116962070322210432162695486262963136144
Iteration count: 616 Matched Sq.Rt Calc: True</pre>
=={{header|Wren}}==
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