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Task/Pythagorean-triples/FreeBASIC/pythagorean-triples-1.freebasic

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+' version 30-05-2016
+' compile with: fbc -s console
+
+' primitive pythagoras triples
+' a = m^2 - n^2, b = 2mn, c = m^2 + n^2
+' m, n are positive integers and m > n
+' m - n = odd and GCD(m, n) = 1
+' p = a + b + c
+
+' max m for give perimeter
+' p = m^2 - n^2 + 2mn + m^2 + n^2
+' p = 2mn + m^2 + m^2 + n^2 - n^2 = 2mn + 2m^2
+' m >> n and n = 1 ==> p = 2m + 2m^2 = 2m(1 + m)
+' m >> 1 ==> p = 2m(m) = 2m^2
+' max m for given perimeter = sqr(p / 2)
+
+Function gcd(x As UInteger, y As UInteger) As UInteger
+
+    Dim As UInteger t
+
+    While y
+        t = y
+        y = x Mod y
+        x = t
+    Wend
+    Return x
+
+End Function
+
+
+Sub pyth_trip(limit As ULongInt, ByRef trip As ULongInt, ByRef prim As ULongInt)
+
+    Dim As ULongInt perimeter, lby2 = limit Shr 1
+    Dim As UInteger m, n
+    Dim As ULongInt a, b, c
+
+    For m = 2 To Sqr(limit / 2)
+        For n = 1 + (m And 1) To (m - 1) Step 2
+            ' common divisor, try next n
+            If (gcd(m, n) > 1) Then Continue For
+            a = CULngInt(m) * m - n * n
+            b = CULngInt(m) * n * 2
+            c = CULngInt(m) * m + n * n
+            perimeter = a + b + c
+            ' perimeter > limit, since n goes up try next m
+            If perimeter >= limit Then Continue For, For
+            prim += 1
+            If perimeter < lby2 Then
+                trip += limit \ perimeter
+            Else
+                trip += 1
+            End If
+        Next n
+    Next m
+
+End Sub
+
+
+' ------=< MAIN >=------
+
+Dim As String str1, buffer = Space(14)
+Dim As ULongInt limit, trip, prim
+Dim As Double t, t1 = Timer
+
+Print "below           triples   primitive            time"
+Print
+
+For x As UInteger = 1 To 12
+    t = Timer
+    limit = 10 ^ x : trip = 0 : prim = 0
+    pyth_trip(limit, trip, prim)
+    LSet buffer, Str(prim) : str1 = buffer
+    Print Using "10^##  ################   "; x; trip;
+    If x > 7 Then
+        Print str1;
+        Print Using "  ######.## sec."; Timer - t
+    Else
+        Print str1
+    End If
+Next x
+
+Print : Print
+Print Using "Total time needed #######.## sec."; Timer - t1
+
+
+' empty keyboard buffer
+While InKey <> "" : Wend
+Print : Print "hit any key to end program"
+Sleep
+End

Task/Pythagorean-triples/FreeBASIC/pythagorean-triples-2.freebasic

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+' version 30-05-2016
+' compile with: fbc -s console
+
+' max m for give perimeter
+' p = m^2 - n^2 + 2mn + m^2 + n^2
+' p = 2mn + m^2 + m^2 + n^2 - n^2 = 2mn + 2m^2
+' m >> n and n = 1 ==> p = 2m + 2m^2 = 2m(1 + m)
+' m >> 1 ==> p = 2m(m) = 2m^2
+' max m for given perimeter = sqr(p / 2)
+
+Function gcd(x As UInteger, y As UInteger) As UInteger
+
+    Dim As UInteger t
+
+    While y
+        t = y
+        y = x Mod y
+        x = t
+    Wend
+    Return x
+
+End Function
+
+Sub pyth_trip_fast(limit As ULongInt, ByRef trip As ULongInt, ByRef prim As ULongInt)
+
+
+    Dim As ULongInt perimeter, lby2 = limit Shr 1
+    Dim As UInteger mx2 = 4
+
+    For m As UInteger = 2 To Sqr(limit / 2)
+        perimeter = (CULngInt(m) * m * 2) - IIf(m And 1, 0, m * 2)
+        mx2 = mx2 + 4
+        For n As UInteger = 1 + (m And 1) To (m - 1) Step 2
+            perimeter += mx2
+            ' common divisor, try next n
+            If (gcd(m, n) > 1) Then Continue For
+            ' perimeter > limit, since n goes up try next m
+            If perimeter >= limit Then Continue For, For
+            prim += 1
+            If perimeter < lby2 Then
+                trip += limit \ perimeter
+            Else
+                trip += 1
+            End If
+        Next n
+    Next m
+
+End Sub
+
+
+' ------=< MAIN >=------
+
+Dim As String str1, buffer = Space(14)
+Dim As ULongInt limit, trip, prim
+Dim As Double t, t1 = Timer
+
+Print "below           triples   primitive            time"
+Print
+
+For x As UInteger = 1 To 12
+    t = Timer
+    limit = 10 ^ x : trip = 0 : prim = 0
+    pyth_trip_fast(limit, trip, prim)
+    LSet buffer, Str(prim) : str1 = buffer
+    Print Using "10^##  ################   "; x; trip;
+    If x > 7 Then
+        Print str1;
+        Print Using "  ######.## sec."; Timer - t
+    Else
+        Print str1
+    End If
+Next x
+
+Print : Print
+Print Using "Total time needed #######.## sec."; Timer - t1
+
+
+' empty keyboard buffer
+While InKey <> "" : Wend
+Print : Print "hit any key to end program"
+Sleep
+End