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- // Euler0013_first_10_digits_of_bignum_sum_v2.linq
- // 2016-04-27
- //
- // http://codereview.stackexchange.com/a/110527/56653
- #define TRACE
- // CarryGuardDigits == 2: 0,005 ms/rnd 0,943 ms/big 0,018 ms/pfx // 222806 tests
- const int N = 100, D = 50, K = 10;
- static Random g_rng = new Random(42);
- static long g_extended_rounds = 0;
- static int CarryGuardDigits = 2;
- void Main ()
- {
- #if true
- var s = input_text;
- // System.IO.File.WriteAllText("x:/temp/foo.txt", s);
- var a = s.Split('\n').Where((si) => si.Length > 1).ToArray();
- var r = via_BigInteger(a);
- var t = via_BigInteger(a);
- Console.WriteLine("{0} {1} {2}", t, t == r ? "==" : "<>", r);
- #endif
- test();
- }
- static void test (int n = N, int length = D, int result_digits = K)
- {
- var tt = Stopwatch.StartNew();
- var tg = new Stopwatch();
- var tb = new Stopwatch();
- var tx = new Stopwatch();
- var a = new string[n];
- for (long tests = 1; ; ++tests)
- {
- tg.Start(); fill_with_random_decimal_strings(a, length); tg.Stop();
- tb.Start(); var b = via_BigInteger(a, result_digits); tg.Stop();
- tx.Start(); var x = sum_prefix(a, result_digits); tx.Stop();
- if (b != x)
- throw new Exception("FAIL!");
- if (tt.ElapsedMilliseconds > 1999)
- {
- Console.WriteLine("{0:N3} ms/rnd {1:N3} ms/big {2:N3} ms/pfx // {3} tests, {4} extended rounds ({5:N3}%)",
- (double)tg.ElapsedMilliseconds / tests,
- (double)tb.ElapsedMilliseconds / tests,
- (double)tx.ElapsedMilliseconds / tests,
- tests,
- g_extended_rounds,
- g_extended_rounds * 100.0 / tests );
- tt.Restart();
- }
- }
- }
- static string via_BigInteger (string[] values, int digits = 10)
- {
- var sum = new System.Numerics.BigInteger(0);
- foreach (var s in values)
- sum += System.Numerics.BigInteger.Parse(s);
- return sum.ToString().Substring(0, digits);
- }
- const int FULL_DIGITS_PER_LONG = 18;
- static string sum_prefix (string[] values, int result_digits = K)
- {
- Trace.Assert(values.Length > 0);
- int n = values.Length;
- int r = (int)Math.Ceiling(Math.Log10(n)) + CarryGuardDigits; // # of overflow reserve digits
- int u = FULL_DIGITS_PER_LONG - r; // # of remaining/usable digits per long
- int m = (int)Math.Pow(10, r); // modulus for the overflow reserve digits
- Trace.Assert(u >= result_digits + r - CarryGuardDigits); // result not guaranteed to fit in a single limb otherwise
- Trace.Assert(m >= n); // ward off oopses
- int l = values[0].Length;
- Trace.Assert(l >= result_digits + r);
- Trace.Assert(values.Where((si) => si.Length != l).Count() == 0);
- Trace.Assert(values.Where((sj) => sj[0] != '0').Count() > 0);
- var sum_limbs = new List<long>();
- int digits = result_digits + r; // in the first round, use exactly what's needed
- long sum; // final values of sum and digits needed after the loop
- for (int offset = 0; ; offset += digits, digits = u)
- {
- digits = Math.Min(digits, l - offset); // # of source digits in this round
- sum = 0;
- foreach (string s in values)
- sum += long.Parse(s.Substring(offset, digits));
- if (sum % m < m - (n - 1) || offset >= l - digits) // worst-case carry can be absorbed
- break;
- ++g_extended_rounds;
- sum_limbs.Add(sum);
- }
- for (int i = sum_limbs.Count; --i >= 0; digits = u)
- {
- long carry = sum / (long)Math.Pow(10, digits);
- sum = sum_limbs[i] + carry;
- }
- return sum.ToString().Substring(0, result_digits);
- }
- static string[] fill_with_random_decimal_strings (string[] result, int length = D)
- {
- var sb = new StringBuilder(length);
- int first_digit_bits = 0;
- for (int i = 0; i < result.Length; ++i)
- {
- sb.Length = 0;
- while (sb.Length < length)
- {
- string s = (g_rng.Next() & int.MaxValue).ToString();
- sb.Append(s.Substring(s[0] == '2' ? 2 : 1));
- }
- sb.Length = length;
- result[i] = sb.ToString();
- first_digit_bits |= sb[0] - '0';
- }
- // all strings start with '0' -> set a random string to start with a random non-zero digit
- if (first_digit_bits == 0)
- {
- int k = g_rng.Next(result.Length);
- var s = result[k];
- result[k] = (char)('1' + g_rng.Next(9)) + s.Substring(1);
- }
- return result;
- }
- static readonly string input_text = @"
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- 46376937677490009712648124896970078050417018260538
- 74324986199524741059474233309513058123726617309629
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- 20849603980134001723930671666823555245252804609722
- 53503534226472524250874054075591789781264330331690
- ";
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