nx_f64_sqrt.nx

nx_f64_sqrt.nx -- IEEE 754 binary64 square root (standalone file). Digit-pair (2-bits-per-iteration) restoring square root on the radicand sig * 2^54, fed MSB-first as 54 bit-pairs (27 pairs from the 54-bit adjusted significand, then 27 zero pairs). Produces a 54-bit root = 53-bit mantissa + explicit guard; sticky = remainder nonzero. Correctly rounded RNE for all finite positive inputs including subnormals. Bounds: root < 2^54, trial = (root<<2)|1 < 2^56, rem <= 2*root + pair so rem << 2 < 2^57 -- all comfortably inside i64. IEEE specials: sqrt(+0) = +0, sqrt(-0) = -0, sqrt(+inf) = +inf, sqrt(negative) = NaN, sqrt(NaN) = NaN. license_tier: ORIGINAL