tl;dr: The article presents novel bit-manipulation techniques for computing day-of-week from a day count, outperforming existing solutions (Hinnant, Neri) by 2-3x through exploiting that 7 is a Mersenne number (2³-1), enabling modulus via multiply-add-shift with a rotation constant. Several full-range 32-bit variants are shown, with the fastest achieving just 3 x86 instructions plus a constant load. The techniques generalize to other divisors like x%24 and x%60 via a "power-of-2 padding" formula (n + n/d*k) & mask, which appears novel and is useful for timekeeping code.