2016 Update

Task/Benfords-law/Pascal/benfords-law.pascal

@@ -0,0 +1,53 @@
+program fibFirstdigit;
+{$IFDEF FPC}{$MODE Delphi}{$ELSE}{$APPTYPE CONSOLE}{$ENDIF}
+uses
+  sysutils;
+type
+  tDigitCount = array[0..9] of LongInt;
+var
+  s: Ansistring;
+  dgtCnt,
+  expectedCnt : tDigitCount;
+
+procedure GetFirstDigitFibonacci(var dgtCnt:tDigitCount;n:LongInt=1000);
+//summing up only the first 9 digits
+//n = 1000 -> difference to first 9 digits complete fib < 100 == 2 digits
+var
+  a,b,c : LongWord;//about 9.6 decimals
+Begin
+  for a in dgtCnt do dgtCnt[a] := 0;
+  a := 0;b := 1;
+  while n > 0 do
+  Begin
+    c := a+b;
+    //overflow? round and divide by base 10
+    IF c < a then
+      Begin a := (a+5) div 10;b := (b+5) div 10;c := a+b;end;
+    a := b;b := c;
+    s := IntToStr(a);inc(dgtCnt[Ord(s[1])-Ord('0')]);
+    dec(n);
+  end;
+end;
+
+procedure InitExpected(var dgtCnt:tDigitCount;n:LongInt=1000);
+var
+  i: integer;
+begin
+  for i := 1 to 9  do
+    dgtCnt[i] := trunc(n*ln(1 + 1 / i)/ln(10));
+end;
+
+var
+  reldiff: double;
+  i,cnt: integer;
+begin
+  cnt := 1000;
+  InitExpected(expectedCnt,cnt);
+  GetFirstDigitFibonacci(dgtCnt,cnt);
+  writeln('Digit  count  expected  rel diff');
+  For i := 1 to 9 do
+  Begin
+    reldiff := 100*(expectedCnt[i]-dgtCnt[i])/expectedCnt[i];
+    writeln(i:5,dgtCnt[i]:7,expectedCnt[i]:10,reldiff:10:5,' %');
+  end;
+end.