Operator Overloading

The following implementation passes all of the unit tests. The design decisions have been included as code comments.

Some of the functions of this struct can be implemented to run more efficiently. Additionally, it would be beneficial to also normalize the numerator and denominator. For example, instead of keeping the values 20 and 60, the values could be divided by their greatest common divisor and the numerator and the denominator can be stored as 1 and 3 instead. Otherwise, most of the operations on the object would cause the values of the numerator and the denominator to increase.

import std.exception;
import std.conv;

struct Fraction {
    long num;  // numerator
    long den;  // denominator

    /* As a convenience, the constructor uses the default
     * value of 1 for the denominator. */
    this(long num, long den = 1) {
        enforce(den != 0, "The denominator cannot be zero");

        this.num = num;
        this.den = den;

        /* Ensuring that the denominator is always positive
         * will simplify the definitions of some of the
         * operator functions. */
        if (this.den < 0) {
            this.num = -this.num;
            this.den = -this.den;
        }
    }

    /* Unary -: Returns the negative of this fraction. */
    Fraction opUnary(string op)() const
            if (op == "-") {
        /* Simply constructs and returns an anonymous
         * object. */
        return Fraction(-num, den);
    }

    /* ++: Increments the value of the fraction by one. */
    ref Fraction opUnary(string op)()
            if (op == "++") {
        /* We could have used 'this += Fraction(1)' here. */
        num += den;
        return this;
    }

    /* --: Decrements the value of the fraction by one. */
    ref Fraction opUnary(string op)()
            if (op == "--") {
        /* We could have used 'this -= Fraction(1)' here. */
        num -= den;
        return this;
    }

    /* +=: Adds the right-hand fraction to this one. */
    ref Fraction opOpAssign(string op)(Fraction rhs)
            if (op == "+") {
        /* Addition formula: a/b + c/d = (a*d + c*b)/(b*d) */
        num = (num * rhs.den) + (rhs.num * den);
        den *= rhs.den;
        return this;
    }

    /* -=: Subtracts the right-hand fraction from this one. */
    ref Fraction opOpAssign(string op)(Fraction rhs)
            if (op == "-") {
        /* We make use of the already-defined operators += and
         * unary - here. Alternatively, the subtraction
         * formula could explicitly be applied similar to the
         * += operator above.
         *
         * Subtraction formula: a/b - c/d = (a*d - c*b)/(b*d)
         */
        this += -rhs;
        return this;
    }

    /* *=: Multiplies the fraction by the right-hand side. */
    ref Fraction opOpAssign(string op)(Fraction rhs)
            if (op == "*") {
        /* Multiplication formula: a/b * c/d = (a*c)/(b*d) */
        num *= rhs.num;
        den *= rhs.den;
        return this;
    }

    /* /=: Divides the fraction by the right-hand side. */
    ref Fraction opOpAssign(string op)(Fraction rhs)
            if (op == "/") {
        enforce(rhs.num != 0, "Cannot divide by zero");

        /* Division formula: (a/b) / (c/d) = (a*d)/(b*c) */
        num *= rhs.den;
        den *= rhs.num;
        return this;
    }

    /* Binary +: Produces the result of adding this and the
     * right-hand side fractions. */
    Fraction opBinary(string op)(Fraction rhs) const
            if (op == "+") {
        /* Takes a copy of this fraction and adds the
         * right-hand side fraction to that copy. */
        Fraction result = this;
        result += rhs;
        return result;
    }

    /* Binary -: Produces the result of subtracting the
     * right-hand side fraction from this one. */
    Fraction opBinary(string op)(Fraction rhs) const
            if (op == "-") {
        /* Uses the already-defined -= operator. */
        Fraction result = this;
        result -= rhs;
        return result;
    }

    /* Binary *: Produces the result of multiplying this
     * fraction with the right-hand side fraction. */
    Fraction opBinary(string op)(Fraction rhs) const
            if (op == "*") {
        /* Uses the already-defined *= operator. */
        Fraction result = this;
        result *= rhs;
        return result;
    }

    /* Binary /: Produces the result of dividing this fraction
     * by the right-hand side fraction. */
    Fraction opBinary(string op)(Fraction rhs) const
            if (op == "/") {
        /* Uses the already-defined /= operator. */
        Fraction result = this;
        result /= rhs;
        return result;
    }

    /* Returns the value of the fraction as double. */
    double opCast(T : double)() const {
        /* A simple division. However, as dividing values of
         * type long would lose the part of the value after
         * the decimal point, we could not have written
         * 'num/den' here. */
        return to!double(num) / den;
    }

    /* Sort order operator: Returns a negative value if this
     * fraction is before, a positive value if this fraction
     * is after, and zero if both fractions have the same sort
     * order. */
    int opCmp(const Fraction rhs) const {
        immutable result = this - rhs;
        /* Being a long, num cannot be converted to int
         * automatically; it must be converted explicitly by
         * 'to' (or cast). */
        return to!int(result.num);
    }

    /* Equality comparison: Returns true if the fractions are
     * equal.
     *
     * The equality comparison had to be defined for this type
     * because the compiler-generated one would be comparing
     * the members one-by-one, without regard to the actual
     * values that the objects represent.
     *
     * For example, although the values of both Fraction(1,2)
     * and Fraction(2,4) are 0.5, the compiler-generated
     * opEquals would decide that they were not equal on
     * account of having members of different values. */
    bool opEquals(const Fraction rhs) const {
        /* Checking whether the return value of opCmp is zero
         * is sufficient here. */
        return opCmp(rhs) == 0;
    }
}

unittest {
    /* Must throw when denominator is zero. */
    assertThrown(Fraction(42, 0));

    /* Let's start with 1/3. */
    auto a = Fraction(1, 3);

    /* -1/3 */
    assert(-a == Fraction(-1, 3));

    /* 1/3 + 1 == 4/3 */
    ++a;
    assert(a == Fraction(4, 3));

    /* 4/3 - 1 == 1/3 */
    --a;
    assert(a == Fraction(1, 3));

    /* 1/3 + 2/3 == 3/3 */
    a += Fraction(2, 3);
    assert(a == Fraction(1));

    /* 3/3 - 2/3 == 1/3 */
    a -= Fraction(2, 3);
    assert(a == Fraction(1, 3));

    /* 1/3 * 8 == 8/3 */
    a *= Fraction(8);
    assert(a == Fraction(8, 3));

    /* 8/3 / 16/9 == 3/2 */
    a /= Fraction(16, 9);
    assert(a == Fraction(3, 2));

    /* Must produce the equivalent value in type 'double'.
     *
     * Note that although double cannot represent every value
     * precisely, 1.5 is an exception. That is why this test
     * is being applied at this point. */
    assert(to!double(a) == 1.5);

    /* 1.5 + 2.5 == 4 */
    assert(a + Fraction(5, 2) == Fraction(4, 1));

    /* 1.5 - 0.75 == 0.75 */
    assert(a - Fraction(3, 4) == Fraction(3, 4));

    /* 1.5 * 10 == 15 */
    assert(a * Fraction(10) == Fraction(15, 1));

    /* 1.5 / 4 == 3/8 */
    assert(a / Fraction(4) == Fraction(3, 8));

    /* Must throw when dividing by zero. */
    assertThrown(Fraction(42, 1) / Fraction(0));

    /* The one with lower numerator is before. */
    assert(Fraction(3, 5) < Fraction(4, 5));

    /* The one with larger denominator is before. */
    assert(Fraction(3, 9) < Fraction(3, 8));
    assert(Fraction(1, 1_000) > Fraction(1, 10_000));

    /* The one with lower value is before. */
    assert(Fraction(10, 100) < Fraction(1, 2));

    /* The one with negative value is before. */
    assert(Fraction(-1, 2) < Fraction(0));
    assert(Fraction(1, -2) < Fraction(0));

    /* The ones with equal values must be both <= and >=.  */
    assert(Fraction(-1, -2) <= Fraction(1, 2));
    assert(Fraction(1, 2) <= Fraction(-1, -2));
    assert(Fraction(3, 7) <= Fraction(9, 21));
    assert(Fraction(3, 7) >= Fraction(9, 21));

    /* The ones with equal values must be equal. */
    assert(Fraction(1, 3) == Fraction(20, 60));

    /* The ones with equal values with sign must be equal. */
    assert(Fraction(-1, 2) == Fraction(1, -2));
    assert(Fraction(1, 2) == Fraction(-1, -2));
}

void main() {
}

As has been mentioned in the chapter, string mixins can be used to combine the definitions of some of the operators. For example, the following definition covers the four arithmetic operators:

    /* Binary arithmetic operators. */
    Fraction opBinary(string op)(Fraction rhs) const
        if ((op == "+") || (op == "-") ||
            (op == "*") || (op == "/")) {
       /* Takes a copy of this fraction and applies the
        * right-hand side fraction to that copy. */
        Fraction result = this;
        mixin ("result " ~ op ~ "= rhs;");
        return result;
    }