nx_numeric.nx

numeric.nx -- Kahan-discipline numerical primitives. Per W. Kahan ("How Java's Floating-Point Hurts Everyone Everywhere" 1998 + "MxMulEps" matrix-mul precision paper), a numerically sound language must expose substrate-level building blocks for catastrophic-cancellation-resistant arithmetic. This file ships the canonical three: TwoSum, TwoProduct, and Kahan compensated summation. Compilation note: this module uses `f64` types and arithmetic operators directly, which the NishiLang sovereign sibling (nxc.elf) accepts but the C bootstrap (nxc2.exe) does NOT lex. That is the correct division of labor: C bootstrap is one Wheeler-comparator anchor for the integer subset; f64-using modules Wheeler against a different peer (rustc, gcc-riscv64 compiling an equivalent C program, or self-host nxc.elf when it ships). NishiLang is not limited by what its bootstrap can lex; the bootstrap is limited by NishiLang's needs. Calling convention: state structs caller-allocated via sys_mmap, mutated through pointers; scalar helpers return single f64 values. No struct-by-value returns, no &local out-params (pre-existing language constraints). Bibliography: Dekker (1971) "A Floating-Point Technique for Extending the Available Precision" -- TwoSum, TwoProduct, the SPLIT_FACTOR trick Møller (1965) pre-Dekker accumulating-correction summation Kahan (1965) compensated summation algorithm Kahan & Ivory (1995) "Roundoff Degrades an Idealized Cantilever" Ogita-Rump-Oishi (2005) "Accurate Sum and Dot Product" -- compensated dot product