Method log2_fp

src/fl/math/fixed_point/base.h:344–373

Fixed-point log base 2 for positive values. Uses 4-term minimax polynomial for log2(1+t), t in [0,1). Horner evaluation uses intermediate precision (IFRAC) to minimize rounding error, then converts back to FRAC_BITS.

    // Horner evaluation uses intermediate precision (IFRAC) to minimize
    // rounding error, then converts back to FRAC_BITS.
    static FASTLED_FORCE_INLINE Derived log2_fp(Derived x) {
        constexpr int IFRAC = traits::IFRAC;

        unsigned_raw_type val = static_cast<unsigned_raw_type>(x.mValue);
        int msb = highest_bit(static_cast<u32>(val));
        raw_type int_part = msb - FRAC_BITS;
        raw_type t;
        if (msb >= FRAC_BITS) {
            t = static_cast<raw_type>(
                (val >> (msb - FRAC_BITS)) - (static_cast<unsigned_raw_type>(1) << FRAC_BITS));
        } else {
            t = static_cast<raw_type>(
                (val << (FRAC_BITS - msb)) - (static_cast<unsigned_raw_type>(1) << FRAC_BITS));
        }

        // 4-term minimax coefficients for log2(1+t), t in [0,1).
        // Coefficients scaled by 2^IFRAC.
        // Use poly_intermediate_type (i32 or i64 based on IFRAC).
        using poly_type = poly_intermediate_type;
        constexpr poly_type c0 = static_cast<poly_type>(1.44179 * (1LL << IFRAC));
        constexpr poly_type c1 = static_cast<poly_type>(-0.69907 * (1LL << IFRAC));
        constexpr poly_type c2 = static_cast<poly_type>(0.36348 * (1LL << IFRAC));
        constexpr poly_type c3 = static_cast<poly_type>(-0.10660 * (1LL << IFRAC));

        // Extend t to IFRAC fractional bits
        poly_type t_ifrac = static_cast<poly_type>(t) << (IFRAC - FRAC_BITS);

        // Horner: t * (c0 + t * (c1 + t * (c2 + t * c3)))
        return log2_horner(int_part, t_ifrac, c0, c1, c2, c3, fl::bool_constant<(IFRAC <= 16)>());
    }

    // log2 Horner evaluation for i32 intermediates (IFRAC <= 16)
    template<typename PolyType>