nx_f32.nx

nx_f32.nx -- IEEE 754 binary32 (single-precision float) bits-up. L4 of the bits-up numeric tower (see docs/NISHI_BITS_UP_NUMERIC_TOWER_ROADMAP.md). Substrate-side IEEE 754 conformant f32 arithmetic on i64 backend. No libm, no soft-float linker stubs, no compiler-builtin lowerings. Bit layout (IEEE 754-2019): bit 31: sign (1 = negative) bits 30..23: exponent (biased by 127; 0 = subnormal/zero; 255 = inf/NaN) bits 22..0: mantissa (23 bits; implicit leading 1 for normal) Real value = (-1)^sign * 2^(exp - 127) * (1.mantissa) for normal = (-1)^sign * 2^-126 * (0.mantissa) for subnormal Storage convention: an f32 value is stored in the LOW 32 bits of an i64. Pack/unpack helpers enforce zero high bits. This brick ships multiplication first because it is THE load-bearing op for matmul (which is THE load-bearing op for ML inference). Add/sub/div/sqrt land in follow-on bricks (L4 v2-v5). Operations in v1: nx_f32_classify(x) -- NX_F32_CLS_* (zero / normal / subnormal / inf / nan) nx_f32_is_nan(x) nx_f32_is_inf(x) nx_f32_is_zero(x) nx_f32_neg(x) nx_f32_abs(x) nx_f32_eq(a, b) -- IEEE 754 equality (NaN != NaN) nx_f32_mul(a, b) -- IEEE 754 multiply, round-to-nearest-even nx_f32_add(a, b) -- IEEE 754 addition, round-to-nearest-even with guard/round/sticky alignment + cancellation nx_f32_sub(a, b) -- a + (-b) Reference (research absorbed bits-up; no code copied): IEEE 754-2019 standard Goldberg 1991 "What Every Computer Scientist Should Know..." Müller 2018 "Handbook of Floating-Point Arithmetic"