如何找到Java的底数和余数？

Question

Given integers 'a' and 'b', I would like a method that returns the floor and remainder of a / b such that:

• a / b = floor + remainder / |b| (where |b| is the absolute value of b), and
• 0 <= remainder < |b|.

For example, 5/3 = 1 + 2/3.

Here's an attempt that works only for positive a and b :

public static long[] floorAndRemainder(long a, long b) {
  long floor = a / b;
  long remainder = a % b;
  return new long[] { floor, remainder };
}

I need a function that works for all positive and negative numerators and denominators. For example,

• -5/3 = -2 + 1/3
• 5/-3 = -2 + 1/3
• -5/-3 = 1 + 2/3

Answer 1

Implementation 1: Floating Point

Uses floating point math to simplify the logic. Be warned that this will produce incorrect results for large numbers due to loss of precision.

public static long[] floorAndRemainder(long a, long b) {
  long floor = (long) Math.floor(a / (double) b);
  long remainder = Math.abs(a - floor * b);
  return new long[] { floor, remainder };
}

Implementation 2: Find, then Correct

Finds the floor and remainder using integer division and modulus operators, then corrects for negative fractions. This shows that the remainder is relatively difficult to correct without using the floor.

public static long[] floorAndRemainder(long a, long b) {
  long floor = a / b;
  long remainder = a % b;
  boolean isNegative = a < 0 ^ b < 0;
  boolean hasRemainder = remainder != 0;

  // Correct the floor.
  if (isNegative && hasRemainder) {
    floor--;
  }

  // Correct the remainder.
  if (hasRemainder) {
    if (isNegative) {
      if (a < 0) { // then remainder < 0 and b > 0
        remainder += b;
      } else { // then remainder > 0 and b < 0
        remainder = -remainder - b;
      }
    } else {
      if (remainder < 0) {
        remainder = -remainder;
      }
    }
  }
  return new long[] { floor, remainder };
}

Implementation 3: The Best Option

Finds the floor the same way as Implementation 2, then uses the floor to find the remainder like Implementation 1.

public static long[] floorAndRemainder(long a, long b) {
  long floor = a / b;
  if ((a < 0 ^ b < 0) && a % b != 0) {
    floor--;
  }
  long remainder = Math.abs(a - floor * b);
  return new long[] { floor, remainder };
}