pkg/math: remove placeholder

pkg/math/lib/math.dart

-// Copyright (c) 2013, the Dart project authors.  Please see the AUTHORS file
-// for details. All rights reserved. Use of this source code is governed by a
-// BSD-style license that can be found in the LICENSE file.
-
-library dart.pkg.math;
-
-/**
- * Computes the greatest common divisor between [a] and [b].
- *
- * The result is always positive even if either `a` or `b` is negative.
- */
-int gcd(int a, int b) {
-  if (a == null) throw new ArgumentError(a);
-  if (b == null) throw new ArgumentError(b);
-  a = a.abs();
-  b = b.abs();
-
-  // Iterative Binary GCD algorithm.
-  if (a == 0) return b;
-  if (b == 0) return a;
-  int powerOfTwo = 1;
-  while (((a | b) & 1) == 0) {
-    powerOfTwo *= 2;
-    a ~/= 2;
-    b ~/= 2;
-  }
-
-  while (a.isEven) a ~/= 2;
-
-  do {
-    while (b.isEven) b ~/= 2;
-    if (a > b) {
-      int temp = b;
-      b = a;
-      a = temp;
-    }
-    b -= a;
-  } while (b != 0);
-
-  return a * powerOfTwo;
-}
-
-/**
- * Computes the greatest common divisor between [a] and [b], as well as [x] and
- * [y] such that `ax+by == gcd(a,b)`.
- *
- * The return value is a List of three ints: the greatest common divisor, `x`,
- * and `y`, in that order.
- */
-List<int> gcdext(int a, int b) {
-  if (a == null) throw new ArgumentError(a);
-  if (b == null) throw new ArgumentError(b);
-
-  if (a < 0) {
-    List<int> result = gcdext(-a, b);
-    result[1] = -result[1];
-    return result;
-  }
-  if (b < 0) {
-    List<int> result = gcdext(a, -b);
-    result[2] = -result[2];
-    return result;
-  }
-
-  int r0 = a;
-  int r1 = b;
-  int x0, x1, y0, y1;
-  x0 = y1 = 1;
-  x1 = y0 = 0;
-
-  while (r1 != 0) {
-    int q = r0 ~/ r1;
-    int tmp = r0;
-    r0 = r1;
-    r1 = tmp - q*r1;
-
-    tmp = x0;
-    x0 = x1;
-    x1 = tmp - q*x1;
-
-    tmp = y0;
-    y0 = y1;
-    y1 = tmp - q*y1;
-  }
-
-  return new List<int>(3)
-      ..[0] = r0
-      ..[1] = x0
-      ..[2] = y0;
-}
-
-/**
- * Computes the inverse of [a] modulo [m].
- *
- * Throws an [IntegerDivisionByZeroException] if `a` has no inverse modulo `m`:
- *
- *     invert(4, 7); // 2
- *     invert(4, 10); // throws IntegerDivisionByZeroException
- */
-int invert(int a, int m) {
-  List<int> results = gcdext(a, m);
-  int g = results[0];
-  int x = results[1];
-  if (g != 1) {
-    throw new IntegerDivisionByZeroException();
-  }
-  return x % m;
-}
-
-/**
- * Computes the least common multiple between [a] and [b].
- */
-int lcm(int a, int b) {
-  if (a == null) throw new ArgumentError(a);
-  if (b == null) throw new ArgumentError(b);
-  if (a == 0 && b == 0) return 0;
-
-  return a.abs() ~/ gcd(a, b) * b.abs();
-}
-
-/**
- * Computes [base] raised to [exp] modulo [mod].
- *
- * The result is always positive, in keeping with the behavior of modulus
- * operator (`%`).
- *
- * Throws an [IntegerDivisionByZeroException] if `exp` is negative and `base`
- * has no inverse modulo `mod`.
- */
-int powmod(int base, int exp, int mod) {
-  if (base == null) throw new ArgumentError(base);
-  if (exp == null) throw new ArgumentError(exp);
-  if (mod == null) throw new ArgumentError(mod);
-
-  // Right-to-left binary method of modular exponentiation.
-  if (exp < 0) {
-    base = invert(base, mod);
-    exp = -exp;
-  }
-  if (exp == 0) { return 1; }
-
-  int result = 1;
-  base = base % mod;
-  while (true) {
-    if (exp.isOdd) {
-      result = (result * base) % mod;
-    }
-    exp ~/= 2;
-    if (exp == 0) {
-      return result;
-    }
-    base = (base * base) % mod;
-  }
-}