Data commit

Task/Partition-function-P/FreeBASIC/partition-function-p-1.basic

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+Function PartitionsP(n As UInteger) As ULongInt
+    ' if n > 416, the result becomes to large for a unsigned 64bit integer
+    Dim As ULongInt p(n)
+    Dim As UInteger k, j
+
+    p(0) = 1
+    For i As UInteger = 1 To n
+        k = 0
+        While TRUE
+            k += 1
+            j = (k * (3*k - 1)) \ 2
+            If (j > i) Then Exit While
+            If (k And 1) Then
+                p(i) += p(i - j)
+            Else
+                p(i) -= p(i - j)
+            End If
+            'j = (k * (3*k + 1)) \ 2
+            j += k
+            If (j > i) Then Exit While
+            If (k And 1) Then
+                p(i) += p(i - j)
+            Else
+                p(i) -= p(i - j)
+            End If
+        Wend
+    Next i
+    Return p(n)
+End Function
+
+Print !"\nPartitionsP: ";
+For x As UInteger = 0 To 12
+    Print PartitionsP(x);"  ";
+Next x
+
+Print !"\n\ndone"
+Sleep

Task/Partition-function-P/FreeBASIC/partition-function-p-2.basic

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+' version 26-06-2021
+' compile with: fbc -s console
+
+#Include Once "gmp.bi"
+
+Sub PartitionsP(max As ULong, p() As MpZ_ptr)
+    ' based on Numericana code example
+    Dim As ULong a, b, i, k
+    Dim As Long j
+
+    Dim As Mpz_ptr s = Allocate(Len(__mpz_struct)) : Mpz_init(s)
+
+    Mpz_set_ui(p(0), 1)
+
+    For i = 1 To max
+        j = 1 : k = 1 : b = 2 : a = 5
+        While j > 0
+            ' j = i - (3*k*k+k) \ 2
+            j = i - b : b = b + a : a = a + 3
+            If j >= 0 Then
+                If k And 1 Then Mpz_add(s, s, p(j)) Else Mpz_sub(s, s, p(j))
+            End If
+            j = j + k
+            If j >= 0 Then
+                If k And 1 Then Mpz_add(s, s, p(j)) Else Mpz_sub(s, s, p(j))
+            End If
+            k = k +1
+        Wend
+        Mpz_swap(p(i), s)
+    Next
+
+    Mpz_clear(s)
+
+End Sub
+
+' ------=< MAIN >=------
+
+#Define max 6666
+
+Dim As UInteger n
+Dim As ZString Ptr ans
+Dim As Double t = Timer
+
+ReDim big_p(max) As Mpz_ptr
+For n = 0 To max
+    big_p(n) = Allocate(Len(__mpz_struct)) : Mpz_init(big_p(n))
+Next
+
+PartitionsP(max, big_p())
+ans = Mpz_get_str (0, 10, big_p(max))
+Print "PartitionsP("; Str(max); ") = "; "  "; *ans
+
+For n = 0 To max
+    Mpz_clear(big_p(n))
+Next
+
+Print Using "time = ###.## ms"; (Timer - t) * 1000
+
+' empty keyboard buffer
+While InKey <> "" : Wend
+Print : Print "hit any key to end program"
+Sleep
+End