Faster 16bit multiplication algorithm for 8-bit MCU

Question

I\'m searching for an algorithm to multiply two integer numbers that is better than the one below. Do you have a good idea about that? (The MCU - AT Tiny 84/85 or similar - wher

Answer 1

At long last, an answer, if a cheeky one: I couldn't (yet) get the AVR-C-compiler from the GCC fit it into 8K code. (For an assembler rendition, see AVR multiplication: No Holds Barred).
The approach is what everyone who used Duff's device tried for a second attempt:
use a switch. Using macros, the source code looks entirely harmless, if massaged:

#define low(mp)     case mp: p = a0 * (uint8_t)(mp) << 8; break
#define low4(mp)    low(mp); low(mp + 1); low(mp + 2); low(mp + 3)
#define low16(mp)   low4(mp); low4(mp + 4); low4(mp + 8); low4(mp + 12)
#define low64(mp)   low16(mp); low16(mp + 16); low16(mp + 32); low16(mp + 48)
#if preShift
# define CASE(mp)   case mp: return p + a * (mp)
#else
# define CASE(mp)   case mp: return (p0<<8) + a * (mp)
#endif
#define case4(mp)   CASE(mp); CASE(mp + 1); CASE(mp + 2); CASE(mp + 3)
#define case16(mp)  case4(mp); case4(mp + 4); case4(mp + 8); case4(mp + 12)
#define case64(mp)  case16(mp); case16(mp + 16); case16(mp + 32); case16(mp + 48)

extern "C" __attribute__ ((noinline))
 uint16_t mpy16NHB16(uint16_t a, uint16_t b)
{
    uint16_t p = 0;
    uint8_t b0 = (uint8_t)b, b1 = (uint8_t)(b>>8);
    uint8_t a0 = (uint8_t)a, p0;

    switch (b1) {
        case64(0);
        case64(64);
        case64(128);
        case64(192);
    }
#if preShift
    p = p0 << 8;
#endif
#if preliminaries
    if (0 == b0) {
        p = -a;
        if (b & 0x8000)
            p += a << 9;
        if (b & 0x4000)
            p += a << 8;
        return p;
    }
    while (b0 & 1) {
        a <<= 1;
        b0 >>= 1;
    }
#endif
    switch (b0) {
        low64(0);
        low64(64);
        low64(128);
        low64(192);
    }
    return ~0;
}
int main(int ac, char const *const av[])
{
    char buf[22];
    for (uint16_t a = 0 ; a < a+1 ; a++)
      for (uint16_t m = 0 ; m <= a ; m++)
        puts(itoa(//shift4(ac)+shift3MaskAdd((uint16_t)av[0], ac)
    //      +shift4Add(ac, (uint16_t)av[0])
    //           + mpy16NHB16(ac, (ac + 105))
                 mpy16NHB16(a, m), buf, 10));
}