Mathematical functions.

• §1. Unsigned integer comparison
• §2. Fully random word
• §3. Integer roots
• §4. Real number support

§1. Unsigned integer comparison. Comparison of integers is normally signed, that is, treating the word as a twos-complement signed number, so that $FFFF is less than 0, for instance. If we want to construe words as being unsigned integers, or as addresses, we need to compare them with the following routine, which returns 1 if \(x>y\), 0 if \(x=y\) and \(-1\) if \(x<y\).

[ UnsignedCompare x y u v;
    if (x == y) return 0;
    if (x < 0 && y >= 0) return 1;
    if (x >= 0 && y < 0) return -1;
    u = x&~WORD_HIGHBIT; v= y&~WORD_HIGHBIT;
    if (u > v) return 1;
    return -1;
];

§2. Fully random word. This should be our best try at a single word consisting of 16 uniformly random bits. random($100)-1 is a fully random byte.

[ FullyRandomWord;
    return (random($100)-1)*$100 + (random($100)-1);
];

§3. Integer roots. We are unable to provide VM support for taking square or cube roots rapidly:

[ VM_SquareRoot num;
    return 0;
];

[ VM_CubeRoot num;
    return 0;
];

§4. Real number support. These need to exist, but are likely never to be used.

[ REAL_NUMBER_TY_Say real; print real; ];

[ REAL_NUMBER_TY_Compare r1 r2; return UnsignedCompare(r1, r2); ];