log2_fp()

static FASTLED_FORCE_INLINE u12x4 fl::u12x4::log2_fp ( u12x4 x )

inlinestaticprivate

Definition at line 222 of file u12x4.h.

                                                                   {
        u32 val = static_cast<u32>(x.mValue);
        int msb = highest_bit(val);
        u32 int_part = msb - FRAC_BITS;
        u32 t;
        if (msb >= FRAC_BITS) {
            t = static_cast<u32>(
                (val >> (msb - FRAC_BITS)) - (SCALE));
        } else {
            t = static_cast<u32>(
                (val << (FRAC_BITS - msb)) - (SCALE));
        }
        // 4-term minimax coefficients for log2(1+t), t in [0,1).
        // Stored as u32 with 12 fractional bits. Max product ~2^21, fits u32 comfortably.
        constexpr int IFRAC = 12;
        constexpr u32 c0 = 5907;    // 1.44179 * 2^12
        constexpr u32 c1 = 2864;    // 0.69907 * 2^12 (no negation for unsigned)
        constexpr u32 c2 = 1489;    // 0.36348 * 2^12
        constexpr u32 c3 = 437;     // 0.10660 * 2^12 (no negation for unsigned)
        // Extend t from 4 to 12 frac bits.
        u32 t12 = static_cast<u32>(t) << (IFRAC - FRAC_BITS);
        // Simplified Horner for unsigned: t * (c0 + t * c1 + t^2 * c2 + t^3 * c3)
        u32 acc = c3;
        acc = c2 + ((acc * t12) >> IFRAC);
        acc = c1 + ((acc * t12) >> IFRAC);
        acc = c0 + ((acc * t12) >> IFRAC);
        u32 frac_part = (acc * t12) >> IFRAC;
        // Convert from 12 frac bits back to 4.
        u16 frac4 = static_cast<u16>(frac_part >> (IFRAC - FRAC_BITS));
        return from_raw(static_cast<u16>((int_part << FRAC_BITS) + frac4));
    }

References u12x4(), FASTLED_FORCE_INLINE, FL_NOEXCEPT, FRAC_BITS, from_raw(), highest_bit(), SCALE, fl::t, and fl::x.

Referenced by pow().

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