speed optimization #436

I suggest following optimizations in the scalar_4x64_imp.h file:

CHANGE:

#define muladd_fast(a,b) { \
    uint64_t tl, th; \
    { \
        uint128_t t = (uint128_t)a * b; \
        th = t >> 64;         /* at most 0xFFFFFFFFFFFFFFFE */ \
        tl = t; \
    } \
    c0 += tl;                 /* overflow is handled on the next line */ \
    th += (c0 < tl) ? 1 : 0;  /* at most 0xFFFFFFFFFFFFFFFF */ \
    c1 += th;                 /* never overflows by contract (verified in the next line) */ \
    VERIFY_CHECK(c1 >= th); \
}

TO:

#define muladd_fast(a,b) { \
    uint64_t tl, th; \
    uint128_t t = (uint128_t)a * b + c0; \
    c0 = (uint64_t)t; \
    c1 += (uint64_t)(t >> 64);  /* never overflows by contract (verified in the next line) */ \
    VERIFY_CHECK(c1 >= t >> 64); \
}

This is repeated in multiple macros.

Better remove declaration of tl and th to avoid compiler warnings.

#define muladd_fast(a,b) { \
    uint128_t t = (uint128_t)a * b + c0; \
    c0 = (uint64_t)t; \
    c1 += (uint64_t)(t >> 64);  /* never overflows by contract (verified in the next line) */ \
    VERIFY_CHECK(c1 >= t >> 64); \
}

Sorry for the very slow response, but this looks correct. We don't need the more complicated overflow handling when c2 is not affected.

Does someone care to make a PR implementing this change? @msotoodeh maybe?

I've pasted that into Godbolt a few days ago and it seems actually slower than the current version with -O2 and -O3 (minimally slower on gcc and somewhat slower on clang): https://godbolt.org/z/dndn44. For the full truth in the context of the rest of the code, we need a benchmark though.