[Issue 7885] New: std.rationals too

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http://d.puremagic.com/issues/show_bug.cgi?id=7885

           Summary: std.rationals too
           Product: D
           Version: D2
          Platform: All
        OS/Version: All
            Status: NEW
          Severity: enhancement
          Priority: P2
         Component: Phobos
        AssignedTo: nobody at puremagic.com
        ReportedBy: bearophile_hugs at eml.cc


--- Comment #0 from bearophile_hugs at eml.cc 2012-04-10 15:35:23 PDT ---
I suggest to add to Phobos rational numbers, based on BigInts.
A simple implementation from the RosettaCode site:
http://rosettacode.org/wiki/Arithmetic/Rational#D


import std.bigint, std.traits;

T gcd(T)(/*in*/ T a, /*in*/ T b) /*pure nothrow*/ {
    // std.numeric.gcd doesn't work with BigInt
    return (b != 0) ? gcd(b, a % b) : (a < 0) ? -a : a;
}

T lcm(T)(/*in*/ T a, /*in*/ T b) {
    return a / gcd(a, b) * b;
}

BigInt toBig(T : BigInt)(/*const*/ ref T n) pure nothrow { return n; }

BigInt toBig(T)(const ref T n) pure nothrow if (isIntegral!T) {
    return BigInt(n);
}

struct Rational {
    /*const*/ private BigInt num, den; // numerator & denominator

    private enum Type { NegINF = -2,
                        NegDEN = -1,
                        NaRAT  =  0,
                        NORMAL =  1,
                        PosINF =  2 };

    this(U : Rational)(U n) pure nothrow {
        num = n.num;
        den = n.den;
    }

    this(U)(in U n) pure nothrow if (isIntegral!U) {
        num = toBig(n);
        den = 1UL;
    }

    this(U, V)(/*in*/ U n, /*in*/ V d) /*pure nothrow*/ {
        num = toBig(n);
        den = toBig(d);
        /*const*/ BigInt common = gcd(num, den);
        if (common != 0) {
            num /= common;
            den /= common;
        } else { // infinite or NOT a Number
            num = (num == 0) ? 0 : (num < 0) ? -1 : 1;
            den = 0;
        }
        if (den < 0) { // assure den is non-negative
            num = -num;
            den = -den;
        }
    }

    BigInt nomerator() /*const*/ pure nothrow @property {
        return num;
    }

    BigInt denominator() /*const*/ pure nothrow @property {
        return den;
    }

    string toString() /*const*/ {
        if (den == 0) {
            if (num == 0)
                return "NaRat";
            else
                return ((num < 0) ? "-" : "+") ~ "infRat";
        }
        return toDecimalString(num) ~
               (den == 1 ? "" : ("/" ~ toDecimalString(den)));
    }

    Rational opBinary(string op)(/*in*/ Rational r)
    /*const pure nothrow*/ if (op == "+" || op == "-") {
        BigInt common = lcm(den, r.den);
        BigInt n = mixin("common / den * num" ~ op ~
                         "common / r.den * r.num" );
        return Rational(n, common);
    }

    Rational opBinary(string op)(/*in*/ Rational r)
    /*const pure nothrow*/ if (op == "*") {
        return Rational(num * r.num, den * r.den);
    }

    Rational opBinary(string op)(/*in*/ Rational r)
    /*const pure nothrow*/ if (op == "/") {
        return Rational(num * r.den, den * r.num);
    }

    Rational opBinary(string op, T)(in T r)
    /*const pure nothrow*/ if (isIntegral!T && (op == "+" ||
                               op == "-" || op == "*" || op == "/")) {
        return opBinary!op(Rational(r));
    }

    Rational opBinary(string op)(in size_t p)
    /*const pure nothrow*/ if (op == "^^") {
        return Rational(num ^^ p, den ^^ p);
    }

    Rational opBinaryRight(string op, T)(in T l)
    /*const pure nothrow*/ if (isIntegral!T) {
        return Rational(l).opBinary!op(Rational(num, den));
    }

    Rational opUnary(string op)()
    /*const pure nothrow*/ if (op == "+" || op == "-") {
        return Rational(mixin(op ~ "num"), den);
    }

    int opCmp(T)(/*in*/ T r) /*const pure nothrow*/ {
        Rational rhs = Rational(r);
        if (type() == Type.NaRAT || rhs.type() == Type.NaRAT)
            throw new Exception("Compare invlove an NaRAT.");
        if (type() != Type.NORMAL ||
            rhs.type() != Type.NORMAL) // for infinite
            return (type() == rhs.type()) ? 0 :
                ((type() < rhs.type()) ? -1 : 1);
        BigInt diff = num * rhs.den - den * rhs.num;
        return (diff == 0) ? 0 : ((diff < 0) ? -1 : 1);
    }

    int opEquals(T)(/*in*/ T r) /*const pure nothrow*/ {
        Rational rhs = Rational(r);
        if (type() == Type.NaRAT || rhs.type() == Type.NaRAT)
            return false;
        return num == rhs.num && den == rhs.den;
    }

    Type type() /*const pure nothrow*/ {
        if (den > 0) return Type.NORMAL;
        if (den < 0) return Type.NegDEN;
        if (num > 0) return Type.PosINF;
        if (num < 0) return Type.NegINF;
        return Type.NaRAT;
    }
}

version (arithmetic_rational_main) { // test part
void main() {
    import std.stdio, std.math;

    foreach (p; 2 .. 2 ^^ 19) {
        auto sum = Rational(1, p);
        immutable limit = 1 + cast(uint)sqrt(cast(real)p);
        foreach (factor; 2 .. limit)
            if (p % factor == 0)
                sum = sum + Rational(1, factor) + Rational(factor, p);
        if (sum.denominator == 1)
            writefln("Sum of recipr. factors of %6s = %s exactly%s",
                     p, sum, (sum == 1) ? ", perfect." : ".");
    }
}
}

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