Double-double: 31 digits of precision without leaving the FPU

A double-double pairs two doubles to yield ~31 decimal digits at roughly 9x the cost of a plain double, filling the gap between double and arbitrary-precision libraries. The post explains error-free transformations (two-sum, quick two-sum, two-product) and benchmarks against MPFR, showing double-double is about 9x faster than MPFR at matched precision.