Check Machin-like formulas: Difference between revisions
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<br><br>
=={{header|BASIC}}==
==={{header|FreeBASIC}}===
{{libheader|GMP}}
<syntaxhighlight lang="freebasic">' version 07-04-2018
' compile with: fbc -s console
#Include "gmp.bi"
#Define _a(Q) (@(Q)->_mp_num) 'a
#Define _b(Q) (@(Q)->_mp_den) 'b
Data "[1, 1, 2] [1, 1, 3]"
Data "[2, 1, 3] [1, 1, 7]"
Data "[4, 1, 5] [-1, 1, 239]"
Data "[5, 1, 7] [2, 3, 79]"
Data "[1, 1, 2] [1, 1, 5] [1, 1, 8]"
Data "[4, 1, 5] [-1, 1, 70] [1, 1, 99]"
Data "[5, 1, 7] [4, 1, 53] [2, 1, 4443]"
Data "[6, 1, 8] [2, 1, 57] [1, 1, 239]"
Data "[8, 1, 10] [-1, 1, 239] [-4, 1, 515]"
Data "[12, 1, 18] [8, 1, 57] [-5, 1, 239]"
Data "[16, 1, 21] [3, 1, 239] [4, 3, 1042]"
Data "[22, 1, 28] [2, 1, 443] [-5, 1, 1393] [-10, 1, 11018]"
Data "[22, 1, 38] [17, 7, 601] [10, 7, 8149]"
Data "[44, 1, 57] [7, 1, 239] [-12, 1, 682] [24, 1, 12943]"
Data "[88, 1, 172] [51, 1, 239] [32, 1, 682] [44, 1, 5357] [68, 1, 12943]"
Data "[88, 1, 172] [51, 1, 239] [32, 1, 682] [44, 1, 5357] [68, 1, 12944]"
Data ""
Sub work2do (ByRef a As LongInt, f1 As mpq_ptr)
Dim As LongInt flag = -1
Dim As Mpq_ptr x, y, z
x = Allocate(Len(__mpq_struct)) : Mpq_init(x)
y = Allocate(Len(__mpq_struct)) : Mpq_init(y)
z = Allocate(Len(__mpq_struct)) : Mpq_init(z)
Dim As Mpz_ptr temp1, temp2
temp1 = Allocate(Len(__Mpz_struct)) : Mpz_init(temp1)
temp2 = Allocate(Len(__Mpz_struct)) : Mpz_init(temp2)
mpq_set(y, f1)
While a > 0
If (a And 1) = 1 Then
If flag = -1 Then
mpq_set(x, y)
flag = 0
Else
Mpz_mul(temp1, _a(x), _b(y))
Mpz_mul(temp2, _b(x), _a(y))
Mpz_add(_a(z), temp1, temp2)
Mpz_mul(temp1, _b(x), _b(y))
Mpz_mul(temp2, _a(x), _a(y))
Mpz_sub(_b(z), temp1, temp2)
mpq_canonicalize(z)
mpq_set(x, z)
End If
End If
Mpz_mul(temp1, _a(y), _b(y))
Mpz_mul(temp2, _b(y), _a(y))
Mpz_add(_a(z), temp1, temp2)
Mpz_mul(temp1, _b(y), _b(y))
Mpz_mul(temp2, _a(y), _a(y))
Mpz_sub(_b(z), temp1, temp2)
mpq_canonicalize(z)
mpq_set(y, z)
a = a Shr 1
Wend
mpq_set(f1, x)
End Sub
' ------=< MAIN >=------
Dim As Mpq_ptr f1, f2, f3
f1 = Allocate(Len(__mpq_struct)) : Mpq_init(f1)
f2 = Allocate(Len(__mpq_struct)) : Mpq_init(f2)
f3 = Allocate(Len(__mpq_struct)) : Mpq_init(f3)
Dim As Mpz_ptr temp1, temp2
temp1 = Allocate(Len(__Mpz_struct)) : Mpz_init(temp1)
temp2 = Allocate(Len(__Mpz_struct)) : Mpz_init(temp2)
Dim As mpf_ptr float
float = Allocate(Len(__mpf_struct)) : Mpf_init(float)
Dim As LongInt m1, a1, b1, flag, t1, t2, t3, t4
Dim As String s, s1, s2, s3, sign
Dim As ZString Ptr zstr
Do
Read s
If s = "" Then Exit Do
flag = -1
While s <> ""
t1 = InStr(s, "[") +1
t2 = InStr(t1, s, ",") +1
t3 = InStr(t2, s, ",") +1
t4 = InStr(t3, s, "]")
s1 = Trim(Mid(s, t1, t2 - t1 -1))
s2 = Trim(Mid(s, t2, t3 - t2 -1))
s3 = Trim(Mid(s, t3, t4 - t3))
m1 = Val(s1)
a1 = Val(s2)
b1 = Val(s3)
sign = IIf(m1 < 0, " - ", " + ")
If m1 < 0 Then a1 = -a1 : m1 = Abs(m1)
s = Mid(s, t4 +1)
Print IIf(flag = 0, sign, ""); IIf(m1 = 1, "", Str(m1));
Print "Atn("; s2; "/" ;s3; ")";
If flag = -1 Then
flag = 0
Mpz_set_si(_a(f1), a1)
Mpz_set_si(_b(f1), b1)
If m1 > 1 Then work2do(m1, f1)
Continue While
End If
Mpz_set_si(_a(f2), a1)
Mpz_set_si(_b(f2), b1)
If m1 > 1 Then work2do(m1, f2)
Mpz_mul(temp1, _a(f1), _b(f2))
Mpz_mul(temp2, _b(f1), _a(f2))
Mpz_add(_a(f3), temp1, temp2)
Mpz_mul(temp1, _b(f1), _b(f2))
Mpz_mul(temp2, _a(f1), _a(f2))
Mpz_sub(_b(f3), temp1, temp2)
mpq_canonicalize(f3)
mpq_set(f1, f3)
Wend
If Mpz_cmp_ui(_b(f1), 1) = 0 AndAlso Mpz_cmp(_a(f1), _b(f1)) = 0 Then
Print " = 1"
Else
Mpf_set_q(float, f1)
gmp_printf(!" = %.*Ff\n", 15, float)
End If
Loop
' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End</syntaxhighlight>
{{out}}
<pre>Atn(1/2) + Atn(1/3) = 1
2Atn(1/3) + Atn(1/7) = 1
4Atn(1/5) - Atn(1/239) = 1
5Atn(1/7) + 2Atn(3/79) = 1
Atn(1/2) + Atn(1/5) + Atn(1/8) = 1
4Atn(1/5) - Atn(1/70) + Atn(1/99) = 1
5Atn(1/7) + 4Atn(1/53) + 2Atn(1/4443) = 1
6Atn(1/8) + 2Atn(1/57) + Atn(1/239) = 1
8Atn(1/10) - Atn(1/239) - 4Atn(1/515) = 1
12Atn(1/18) + 8Atn(1/57) - 5Atn(1/239) = 1
16Atn(1/21) + 3Atn(1/239) + 4Atn(3/1042) = 1
22Atn(1/28) + 2Atn(1/443) - 5Atn(1/1393) - 10Atn(1/11018) = 1
22Atn(1/38) + 17Atn(7/601) + 10Atn(7/8149) = 1
44Atn(1/57) + 7Atn(1/239) - 12Atn(1/682) + 24Atn(1/12943) = 1
88Atn(1/172) + 51Atn(1/239) + 32Atn(1/682) + 44Atn(1/5357) + 68Atn(1/12943) = 1
88Atn(1/172) + 51Atn(1/239) + 32Atn(1/682) + 44Atn(1/5357) + 68Atn(1/12944) = 0.999999188225744</pre>
==={{header|Visual Basic .NET}}===
'''BigRat''' class based on the Arithmetic/Rational#C here at Rosetta Code.<br/>
The parser here allows for some flexibility in the input text. Case is ignored, and a variable number of spaces are allowed. Atan(), arctan(), atn() are all recognized as valid. If one of those three are not found, a warning will appear. The coefficient need not have a multiplication sign between it and the "arctan()". The left side of the equation must be pi / 4, otherwise a warning will appear.
<syntaxhighlight lang="vbnet">Imports System.Numerics
Public Class BigRat ' Big Rational Class constructed with BigIntegers
Implements IComparable
Public nu, de As BigInteger
Public Shared Zero = New BigRat(BigInteger.Zero, BigInteger.One),
One = New BigRat(BigInteger.One, BigInteger.One)
Sub New(bRat As BigRat)
nu = bRat.nu : de = bRat.de
End Sub
Sub New(n As BigInteger, d As BigInteger)
If d = BigInteger.Zero Then _
Throw (New Exception(String.Format("tried to set a BigRat with ({0}/{1})", n, d)))
Dim bi As BigInteger = BigInteger.GreatestCommonDivisor(n, d)
If bi > BigInteger.One Then n /= bi : d /= bi
If d < BigInteger.Zero Then n = -n : d = -d
nu = n : de = d
End Sub
Shared Operator -(x As BigRat) As BigRat
Return New BigRat(-x.nu, x.de)
End Operator
Shared Operator +(x As BigRat, y As BigRat)
Return New BigRat(x.nu * y.de + x.de * y.nu, x.de * y.de)
End Operator
Shared Operator -(x As BigRat, y As BigRat) As BigRat
Return x + (-y)
End Operator
Shared Operator *(x As BigRat, y As BigRat) As BigRat
Return New BigRat(x.nu * y.nu, x.de * y.de)
End Operator
Shared Operator /(x As BigRat, y As BigRat) As BigRat
Return New BigRat(x.nu * y.de, x.de * y.nu)
End Operator
Public Function CompareTo(obj As Object) As Integer Implements IComparable.CompareTo
Dim dif As BigRat = New BigRat(nu, de) - obj
If dif.nu < BigInteger.Zero Then Return -1
If dif.nu > BigInteger.Zero Then Return 1
Return 0
End Function
Shared Operator =(x As BigRat, y As BigRat) As Boolean
Return x.CompareTo(y) = 0
End Operator
Shared Operator <>(x As BigRat, y As BigRat) As Boolean
Return x.CompareTo(y) <> 0
End Operator
Overrides Function ToString() As String
If de = BigInteger.One Then Return nu.ToString
Return String.Format("({0}/{1})", nu, de)
End Function
Shared Function Combine(a As BigRat, b As BigRat) As BigRat
Return (a + b) / (BigRat.One - (a * b))
End Function
End Class
Public Structure Term ' coefficent, BigRational construction for each term
Dim c As Integer, br As BigRat
Sub New(cc As Integer, bigr As BigRat)
c = cc : br = bigr
End Sub
End Structure
Module Module1
Function Eval(c As Integer, x As BigRat) As BigRat
If c = 1 Then Return x Else If c < 0 Then Return Eval(-c, -x)
Dim hc As Integer = c \ 2
Return BigRat.Combine(Eval(hc, x), Eval(c - hc, x))
End Function
Function Sum(terms As List(Of Term)) As BigRat
If terms.Count = 1 Then Return Eval(terms(0).c, terms(0).br)
Dim htc As Integer = terms.Count / 2
Return BigRat.Combine(Sum(terms.Take(htc).ToList), Sum(terms.Skip(htc).ToList))
End Function
Function ParseLine(ByVal s As String) As List(Of Term)
ParseLine = New List(Of Term) : Dim t As String = s.ToLower, p As Integer, x As New Term(1, BigRat.Zero)
While t.Contains(" ") : t = t.Replace(" ", "") : End While
p = t.IndexOf("pi/4=") : If p < 0 Then _
Console.WriteLine("warning: tan(left side of equation) <> 1") : ParseLine.Add(x) : Exit Function
t = t.Substring(p + 5)
For Each item As String In t.Split(")")
If item.Length > 5 Then
If (Not item.Contains("tan") OrElse item.IndexOf("a") < 0 OrElse
item.IndexOf("a") > item.IndexOf("tan")) AndAlso Not item.Contains("atn") Then
Console.WriteLine("warning: a term is mising a valid arctangent identifier on the right side of the equation: [{0})]", item)
ParseLine = New List(Of Term) : ParseLine.Add(New Term(1, BigRat.Zero)) : Exit Function
End If
x.c = 1 : x.br = New BigRat(BigRat.One)
p = item.IndexOf("/") : If p > 0 Then
x.br.de = UInt64.Parse(item.Substring(p + 1))
item = item.Substring(0, p)
p = item.IndexOf("(") : If p > 0 Then
x.br.nu = UInt64.Parse(item.Substring(p + 1))
p = item.IndexOf("a") : If p > 0 Then
Integer.TryParse(item.Substring(0, p).Replace("*", ""), x.c)
If x.c = 0 Then x.c = 1
If item.Contains("-") AndAlso x.c > 0 Then x.c = -x.c
End If
ParseLine.Add(x)
End If
End If
End If
Next
End Function
Sub Main(ByVal args As String())
Dim nl As String = vbLf
For Each item In ("pi/4 = ATan(1 / 2) + ATan(1/3)" & nl &
"pi/4 = 2Atan(1/3) + ATan(1/7)" & nl &
"pi/4 = 4ArcTan(1/5) - ATan(1 / 239)" & nl &
"pi/4 = 5arctan(1/7) + 2 * atan(3/79)" & nl &
"Pi/4 = 5ATan(29/278) + 7*ATan(3/79)" & nl &
"pi/4 = atn(1/2) + ATan(1/5) + ATan(1/8)" & nl &
"PI/4 = 4ATan(1/5) - Atan(1/70) + ATan(1/99)" & nl &
"pi /4 = 5*ATan(1/7) + 4 ATan(1/53) + 2ATan(1/4443)" & nl &
"pi / 4 = 6ATan(1/8) + 2arctangent(1/57) + ATan(1/239)" & nl &
"pi/ 4 = 8ATan(1/10) - ATan(1/239) - 4ATan(1/515)" & nl &
"pi/4 = 12ATan(1/18) + 8ATan(1/57) - 5ATan(1/239)" & nl &
"pi/4 = 16 * ATan(1/21) + 3ATan(1/239) + 4ATan(3/1042)" & nl &
"pi/4 = 22ATan(1/28) + 2ATan(1/443) - 5ATan(1/1393) - 10 ATan( 1 / 11018 )" & nl &
"pi/4 = 22ATan(1/38) + 17ATan(7/601) + 10ATan(7 / 8149)" & nl &
"pi/4 = 44ATan(1/57) + 7ATan(1/239) - 12ATan(1/682) + 24ATan(1/12943)" & nl &
"pi/4 = 88ATan(1/172) + 51ATan(1/239) + 32ATan(1/682) + 44ATan(1/5357) + 68ATan(1/12943)" & nl &
"pi/4 = 88ATan(1/172) + 51ATan(1/239) + 32ATan(1/682) + 44ATan(1/5357) + 68ATan(1/12944)").Split(nl)
Console.WriteLine("{0}: {1}", If(Sum(ParseLine(item)) = BigRat.One, "Pass", "Fail"), item)
Next
End Sub
End Module</syntaxhighlight>
{{out}}
<pre>Pass: pi/4 = ATan(1 / 2) + ATan(1/3)
Pass: pi/4 = 2Atan(1/3) + ATan(1/7)
Pass: pi/4 = 4ArcTan(1/5) - ATan(1 / 239)
Pass: pi/4 = 5arctan(1/7) + 2 * atan(3/79)
Pass: pi/4 = 5ATan(29/278) + 7*ATan(3/79)
Pass: pi/4 = atn(1/2) + ATan(1/5) + ATan(1/8)
Pass: pi/4 = 4ATan(1/5) - Atan(1/70) + ATan(1/99)
Pass: pi /4 = 5*ATan(1/7) + 4 ATan(1/53) + 2ATan(1/4443)
Pass: pi / 4 = 6ATan(1/8) + 2arctangent(1/57) + ATan(1/239)
Pass: pi/ 4 = 8ATan(1/10) - ATan(1/239) - 4ATan(1/515)
Pass: pi/4 = 12ATan(1/18) + 8ATan(1/57) - 5ATan(1/239)
Pass: pi/4 = 16 * ATan(1/21) + 3ATan(1/239) + 4ATan(3/1042)
Pass: pi/4 = 22ATan(1/28) + 2ATan(1/443) - 5ATan(1/1393) - 10 ATan( 1 / 11018 )
Pass: pi/4 = 22ATan(1/38) + 17ATan(7/601) + 10ATan(7 / 8149)
Pass: pi/4 = 44ATan(1/57) + 7ATan(1/239) - 12ATan(1/682) + 24ATan(1/12943)
Pass: pi/4 = 88ATan(1/172) + 51ATan(1/239) + 32ATan(1/682) + 44ATan(1/5357) + 68ATan(1/12943)
Fail: pi/4 = 88ATan(1/172) + 51ATan(1/239) + 32ATan(1/682) + 44ATan(1/5357) + 68ATan(1/12944)</pre>
=={{header|Clojure}}==
Clojure automatically handles ratio of numbers as fractions
Line 390 ⟶ 715:
} = 10092...08223/10092...39711
</pre>
=={{header|GAP}}==
The formula is entered as a list of pairs [k, x], where each pair means k*atan(x), and all the terms in the list are summed. Like most other solutions, the program will only check that the tangent of the resulting sum is 1. For instance, <code>Check([[5, 1/2], [5, 1/3]]);</code> returns also <code>true</code>, though the result is 5pi/4.
Line 2,784 ⟶ 2,937:
No! 'pi/4 = 88*arctan(1/172) + 51*arctan(1/239) + 32*arctan(1/682) + 44*arctan(1/5357) + 68*arctan(1/12944)' not true
</pre>
=={{header|Wren}}==
{{trans|Kotlin}}
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