Ed's Big Plans

Here’s a function I developed for Andre about a week ago. The C function takes two arguments. Both arguments are C characters. The first argument corresponds to a degenerate nucleotide as in the below table. The second argument corresponds to a non-degenerate nucleotide {‘A’, ‘C’, ‘G’, ‘T’} or any nucleotide ‘N’. The function returns zero if the logical intersection between the two arguments is zero. The function returns a one-hot binary encoding for the logical intersection if it exists so that {‘A’ = 1, ‘C’ = 2, ‘G’ = 4, ‘T’ = 8} and {‘N’ = 15}. All of this is done treating the lower 5-bits of the ASCII encoding for each character as wires of a circuit.

The premise is that removing all of the logical branching and using only binary operators would make things a bit faster — I’m actually not sure if the following solution is faster because there are twelve variables local to the function scope — we can be assured that at least half of these variables will be stored outside of cache and will have to live in memory. We’d get a moderate speed boost if at all.

/*
    f():
        Bitwise comparison circuit that treats nucleotide and degenerate
        nucleotide ascii characters as mathematical sets.
        The operation performed is set i intersect j.
    arg char i:
        Primer -- accepts ascii |ABCDG HKMNR STVWY| = 15.
    arg char j:
        Sequence -- accepts ascii |ACGTN| = 5.
    return char (k = 0):
        false -- i intersect j is empty.
    return char (k > 0):
        1 -- the intersection is 'A'
        2 -- the intersection is 'C'
        4 -- the intersection is 'G'
        8 -- the intersection is 'T'
       15 -- the intersection is 'N'
    return char (undefined value):
        ? -- if any other characters are placed in i or j.
*/
char f(char i, char j) {

    // break apart Primer into bits ...
    char p = (i >> 4) &1;
    char q = (i >> 3) &1;
    char r = (i >> 2) &1;
    char s = (i >> 1) &1;
    char t =  i       &1;

    // break apart Sequence into bits ...
    char a = (j >> 4) &1;
    char b = (j >> 3) &1;
    char c = (j >> 2) &1;
    char d = (j >> 1) &1;
    char e =  j       &1;

    return

    ( // == PRIMER CIRCUIT ==
        ( // -- A --
            ((p|q|r|s  )^1) &         t |
            ((p|q|  s|t)^1) &     r     |
            ((p|  r|s|t)^1) &   q       |
            ((p|    s  )^1) &   q&r&  t |
            ((p|      t)^1) &   q&r&s   |
            ((  q|    t)^1) & p&s       |
            ((  q      )^1) & p&r&s
        )
        |
        ( // -- C --
            ((p|q|r    )^1) &       s   |
            ((p|  r|s|t)^1) &   q       |
            ((p|    s  )^1) &   q&r&  t |
            ((p|      t)^1) &   q&r&s   |
            ((  q|r    )^1) &       s&t |
            ((  q|    t)^1) & p  &r&s   |
            ((    r|s  )^1) & p&q&    t
        ) << 1
        |
        ( // -- G --
            ((  q|r|  t)^1) &       s   |
            ((p|q|  s|t)^1) &     r     |
            ((p|q      )^1) &     r&s&t |
            ((p|  r    )^1) &   q&  s&t |
            ((p|      t)^1) &   q&r&s   |
            ((  q|r    )^1) & p&    s   |
            ((  q|    t)^1) & p&    s
        ) << 2
        |
        ( // -- T --
            ((p|q|r|  t)^1) &       s   |
            ((  q|  s|t)^1) &     r     |
            ((p|  r|s|t)^1) &   q       |
            ((p|  r    )^1) &   q&  s&t |
            ((p|      t)^1) &   q&r&s   |
            ((  q      )^1) & p&  r&s&t |
            ((    r|s  )^1) & p&q&    t
        ) << 3
    )
    &
    ( // == SEQUENCE CIRCUIT ==
        ( // -- A --
            ((a|b|c|d  )^1) &         e |
            ((a|      e)^1) &   b&c&d
        )
        |
        ( // -- C --
            ((a|b|c    )^1) &       d&e |
            ((a|      e)^1) &   b&c&d
        ) << 1
        |
        ( // -- G --
            ((a|b      )^1) &     c&d&e |
            ((a|      e)^1) &   b&c&d
        ) << 2
        |
        ( // -- T --
            ((a|      e)^1) &   b&c&d   |
            ((  b|  d|e)^1) & a&  c
        ) << 3
    );
}

Andre’s eventual solution was to use a look-up table which very likely proves faster in practice. At the very least, this was a nice refresher and practical example for circuit logic using four sets of minterms (one for each one-hot output wire).

Should you need this logic to build a fast physical circuit or have some magical architecture with a dozen registers (accessible to the compiler), be my guest 😀