libdpf/test/tests/constant_lut_test.cpp

#include <gtest/gtest.h>
#include <tuple>

#include "dpf.hpp"
#include "grotto/constant_lut.hpp"
#include "grotto/prefix_parity.hpp"

#include <array>
#include <cmath>
#include <cstdint>
#include <limits>
#include <random>
#include <string>
#include <vector>

namespace
{

using grotto::exact_constant;
using u128 = unsigned __int128;

const exact_constant kAll[] = {
    exact_constant::signum,
    exact_constant::positive,
    exact_constant::negative,
    exact_constant::nonneg,
    exact_constant::nonpos,
    exact_constant::zero,
    exact_constant::nonzero,
    exact_constant::ilogb,
    exact_constant::ceil_ilogb,
    exact_constant::ilog10,
    exact_constant::clz,
    exact_constant::clrsb,
};

const char * name_of(exact_constant which)
{
    switch (which)
    {
    case exact_constant::signum: return "signum";
    case exact_constant::positive: return "positive";
    case exact_constant::negative: return "negative";
    case exact_constant::nonneg: return "nonneg";
    case exact_constant::nonpos: return "nonpos";
    case exact_constant::zero: return "zero";
    case exact_constant::nonzero: return "nonzero";
    case exact_constant::ilogb: return "ilogb";
    case exact_constant::ceil_ilogb: return "ceil_ilogb";
    case exact_constant::ilog10: return "ilog10";
    case exact_constant::clz: return "clz";
    case exact_constant::clrsb: return "clrsb";
    }
    return "?";
}

unsigned __int128 magnitude(std::int64_t raw)
{
    if (raw >= 0)
        return static_cast<unsigned __int128>(raw);
    if (raw == std::numeric_limits<std::int64_t>::min())
        return u128{1} << 63;
    return static_cast<unsigned __int128>(-raw);
}

int shift_log2(unsigned __int128 mag)
{
    int lg = 0;
    while (mag > 1)
    {
        mag >>= 1;
        ++lg;
    }
    return lg;
}

int shift_clz64(std::uint64_t t)
{
    int n = 0;
    if (t == 0)
        return 64;
    while ((t & (std::uint64_t{1} << 63)) == 0)
    {
        t <<= 1;
        ++n;
    }
    return n;
}

bool ge_pow10(unsigned __int128 mag, int k, unsigned fractional_bits)
{
    if (k >= 0)
    {
        unsigned __int128 thresh = 1;
        for (int i = 0; i < k; ++i)
        {
            if (thresh > (~u128{0}) / 10)
                return false;
            thresh *= 10;
        }
        if (fractional_bits >= 128
            || thresh > (~u128{0} >> fractional_bits))
            return false;
        return mag >= (thresh << fractional_bits);
    }
    unsigned __int128 scaled = mag;
    for (int i = 0; i < -k; ++i)
    {
        if (scaled > (~u128{0}) / 10)
            return true;
        scaled *= 10;
    }
    return fractional_bits < 128 && scaled >= (u128{1} << fractional_bits);
}

std::int64_t toward_zero(std::int64_t raw, unsigned fractional_bits)
{
    const unsigned __int128 mag = magnitude(raw);
    const unsigned __int128 q = mag >> fractional_bits;
    if (raw >= 0)
        return static_cast<std::int64_t>(q);
    if (q > static_cast<unsigned __int128>(std::numeric_limits<std::int64_t>::max()))
        return std::numeric_limits<std::int64_t>::min();
    return -static_cast<std::int64_t>(q);
}

// Independent of grotto::detail: shift loops and the xor form of clrsb,
// not the builtins the LUT builder calls.
std::int64_t reference(exact_constant which, std::int64_t raw, unsigned fractional_bits)
{
    const unsigned __int128 mag = magnitude(raw);
    switch (which)
    {
    case exact_constant::signum:
        return raw < 0 ? -1 : (raw > 0 ? 1 : 0);
    case exact_constant::positive:
        return raw > 0;
    case exact_constant::negative:
        return raw < 0;
    case exact_constant::nonneg:
        return raw >= 0;
    case exact_constant::nonpos:
        return raw <= 0;
    case exact_constant::zero:
        return raw == 0;
    case exact_constant::nonzero:
        return raw != 0;
    case exact_constant::ilogb:
        if (mag == 0)
            return -64;
        if (fractional_bits >= 64
            && mag <= (u128{1} << (fractional_bits - 64)))
            return -64;
        return shift_log2(mag) - static_cast<std::int64_t>(fractional_bits);
    case exact_constant::ceil_ilogb:
        if (mag == 0)
            return -64;
        if (fractional_bits >= 64
            && mag <= (u128{1} << (fractional_bits - 64)))
            return -64;
        {
            const auto floor_exp = shift_log2(mag) - static_cast<std::int64_t>(fractional_bits);
            const bool power = (mag & (mag - 1)) == 0;
            return power ? floor_exp : floor_exp + 1;
        }
    case exact_constant::ilog10:
        if (mag == 0 || !ge_pow10(mag, -19, fractional_bits))
            return -19;
        {
            int k = -19;
            while (k < 40 && ge_pow10(mag, k + 1, fractional_bits))
                ++k;
            return k;
        }
    case exact_constant::clz:
        if (raw < 0)
            return 0;
        if (fractional_bits >= 128 || mag < (u128{1} << fractional_bits))
            return 64;
        return shift_clz64(static_cast<std::uint64_t>(mag >> fractional_bits));
    case exact_constant::clrsb:
    {
        const std::int64_t trunc = toward_zero(raw, fractional_bits);
        const std::uint64_t u = static_cast<std::uint64_t>(trunc);
        const std::uint64_t y = u ^ static_cast<std::uint64_t>(trunc >> 1);
        if (y == 0)
            return 63;
        return shift_clz64(y) - 1;
    }
    }
    return 0;
}

template <typename Raw>
void expect_partition(const grotto::constant_lut<Raw> & lut)
{
    using lim = std::numeric_limits<Raw>;
    ASSERT_FALSE(lut.bounds.empty());
    ASSERT_EQ(lut.bounds.size(), lut.values.size());
    EXPECT_EQ(lut.bounds.front(), lim::min());
    for (std::size_t i = 1; i < lut.bounds.size(); ++i)
    {
        EXPECT_LT(lut.bounds[i - 1], lut.bounds[i]);
        EXPECT_NE(lut.values[i - 1], lut.values[i]);
        EXPECT_EQ(lut(static_cast<Raw>(lut.bounds[i] - 1)), lut.values[i - 1]);
    }
    EXPECT_EQ(lut(lim::max()), lut.values.back());
    for (std::size_t i = 0; i < lut.bounds.size(); ++i)
        EXPECT_EQ(lut(lut.bounds[i]), lut.values[i]);
}

template <typename Raw, std::size_t N>
bool segment_product_matches(const grotto::constant_lut<Raw> & lut, Raw alpha)
{
    std::array<Raw, N> ends{};
    for (std::size_t i = 0; i < N; ++i)
        ends[i] = lut.bounds[i];
    auto [k0, k1] = dpf::make_dpf(alpha, dpf::bit::one);
    const auto s0 = grotto::segment_parities(k0, ends);
    const auto s1 = grotto::segment_parities(k1, ends);
    __int128 a0 = 0;
    __int128 a1 = 0;
    __int128 u0 = 0;
    __int128 u1 = 0;
    int hot = 0;
    int hot_at = -1;
    for (std::size_t i = 0; i < N; ++i)
    {
        const int b0 = s0[i] ? 1 : 0;
        const int b1 = s1[i] ? 1 : 0;
        a0 += __int128(lut.values[i]) * b0;
        a1 += __int128(lut.values[i]) * b1;
        u0 += b0;
        u1 += b1;
        if ((b0 ^ b1) != 0)
        {
            ++hot;
            hot_at = static_cast<int>(i);
        }
    }
    if (hot != 1)
        return false;
    const std::int64_t opened = static_cast<std::int64_t>((u0 - u1) * (a0 - a1));
    return opened == lut.values[static_cast<std::size_t>(hot_at)]
        && opened == lut(alpha);
}

template <std::size_t N>
bool dispatch_segments(const grotto::constant_lut<std::int8_t> & lut, std::int8_t alpha)
{
    if (lut.bounds.size() == N)
        return segment_product_matches<std::int8_t, N>(lut, alpha);
    if constexpr (N > 1)
        return dispatch_segments<N - 1>(lut, alpha);
    return false;
}

}  // namespace

TEST(ConstantLut, RejectsFractionalBitsPastTheRawWidth)
{
    EXPECT_THROW(grotto::make_exact_constant_lut<std::int8_t>(exact_constant::signum, 9), std::invalid_argument);
    EXPECT_THROW(grotto::make_exact_constant_lut<std::int64_t>(exact_constant::clz, 65), std::invalid_argument);
}

TEST(ConstantLut, PaperPartCountsOnInt64With16FractionalBits)
{
    // Appendix D, 64-bit fixed point, 16 fractional bits.
    // `zero`, `nonzero`, and `ilog10` are counted after the two end pieces
    // join across the wrap (they hold the same constant). `clrsb` is the
    // linear count the generator emits; joining its equal ends would make 94.
    struct row
    {
        exact_constant which;
        std::size_t linear;
        std::size_t wrapped;
    };
    const row rows[] = {
        {exact_constant::signum, 3, 3},
        {exact_constant::positive, 2, 2},
        {exact_constant::negative, 2, 2},
        {exact_constant::nonneg, 2, 2},
        {exact_constant::nonpos, 2, 2},
        {exact_constant::zero, 3, 2},
        {exact_constant::nonzero, 3, 2},
        {exact_constant::ilogb, 128, 128},
        {exact_constant::ilog10, 41, 40},
        {exact_constant::clz, 49, 49},
        {exact_constant::clrsb, 95, 94},
    };
    for (const row & r : rows)
    {
        const auto lut = grotto::make_exact_constant_lut<std::int64_t>(r.which, 16);
        expect_partition(lut);
        EXPECT_EQ(lut.linear_parts(), r.linear) << name_of(r.which);
        EXPECT_EQ(lut.wrapped_parts(), r.wrapped) << name_of(r.which);
    }
}

TEST(ConstantLut, AnchorsMatchTheDefinitions)
{
    const auto sgn = grotto::make_exact_constant_lut<std::int64_t>(exact_constant::signum, 16);
    EXPECT_EQ(sgn(0), 0);
    EXPECT_EQ(sgn(-1), -1);
    EXPECT_EQ(sgn(1), 1);
    EXPECT_EQ(sgn(std::numeric_limits<std::int64_t>::min()), -1);
    EXPECT_EQ(sgn(std::numeric_limits<std::int64_t>::max()), 1);

    const auto pos = grotto::make_exact_constant_lut<std::int64_t>(exact_constant::positive, 0);
    const auto neg = grotto::make_exact_constant_lut<std::int64_t>(exact_constant::negative, 0);
    const auto nn = grotto::make_exact_constant_lut<std::int64_t>(exact_constant::nonneg, 0);
    const auto np = grotto::make_exact_constant_lut<std::int64_t>(exact_constant::nonpos, 0);
    const auto z = grotto::make_exact_constant_lut<std::int64_t>(exact_constant::zero, 0);
    const auto nz = grotto::make_exact_constant_lut<std::int64_t>(exact_constant::nonzero, 0);
    EXPECT_EQ(pos(0), 0);
    EXPECT_EQ(pos(1), 1);
    EXPECT_EQ(pos(-1), 0);
    EXPECT_EQ(neg(0), 0);
    EXPECT_EQ(neg(-1), 1);
    EXPECT_EQ(nn(0), 1);
    EXPECT_EQ(nn(-1), 0);
    EXPECT_EQ(np(0), 1);
    EXPECT_EQ(np(1), 0);
    EXPECT_EQ(z(0), 1);
    EXPECT_EQ(z(1), 0);
    EXPECT_EQ(z(-1), 0);
    EXPECT_EQ(nz(0), 0);
    EXPECT_EQ(nz(1), 1);

    const auto ilogb = grotto::make_exact_constant_lut<std::int64_t>(exact_constant::ilogb, 16);
    EXPECT_EQ(ilogb(0), -64);
    EXPECT_EQ(ilogb(1), -16);
    EXPECT_EQ(ilogb(-1), -16);
    EXPECT_EQ(ilogb(65536), 0);
    EXPECT_EQ(ilogb(-65536), 0);
    EXPECT_EQ(ilogb(std::numeric_limits<std::int64_t>::min()), 47);

    const auto ilog10 = grotto::make_exact_constant_lut<std::int64_t>(exact_constant::ilog10, 16);
    EXPECT_EQ(ilog10(0), -19);
    EXPECT_EQ(ilog10(1), -5);
    EXPECT_EQ(ilog10(-1), -5);
    EXPECT_EQ(ilog10(65536), 0);
    EXPECT_EQ(ilog10(655360), 1);

    const auto clz = grotto::make_exact_constant_lut<std::int64_t>(exact_constant::clz, 16);
    EXPECT_EQ(clz(0), 64);
    EXPECT_EQ(clz(1), 64);
    EXPECT_EQ(clz(65535), 64);
    EXPECT_EQ(clz(65536), 63);
    EXPECT_EQ(clz(131072), 62);
    EXPECT_EQ(clz(-1), 0);
    EXPECT_EQ(clz(std::int64_t{1} << 62), 17);

    const auto clrsb = grotto::make_exact_constant_lut<std::int64_t>(exact_constant::clrsb, 16);
    EXPECT_EQ(clrsb(0), 63);
    EXPECT_EQ(clrsb(65536), 62);
    EXPECT_EQ(clrsb(-65536), 63);
    EXPECT_EQ(clrsb(std::numeric_limits<std::int64_t>::min()), 16);
}

TEST(ConstantLut, EveryInt8AndInt16Point)
{
    const unsigned widths_f_8[] = {0, 1, 4, 7, 8};
    for (unsigned fractional_bits : widths_f_8)
    {
        for (exact_constant which : kAll)
        {
            const auto lut = grotto::make_exact_constant_lut<std::int8_t>(which, fractional_bits);
            expect_partition(lut);
            for (int raw = -128; raw <= 127; ++raw)
            {
                const auto r = static_cast<std::int8_t>(raw);
                EXPECT_EQ(lut(r), reference(which, r, fractional_bits))
                    << name_of(which) << " F=" << fractional_bits << " raw=" << raw;
            }
        }
    }

    const unsigned widths_f_16[] = {0, 1, 4, 8, 12, 15, 16};
    for (unsigned fractional_bits : widths_f_16)
    {
        for (exact_constant which : kAll)
        {
            const auto lut = grotto::make_exact_constant_lut<std::int16_t>(which, fractional_bits);
            expect_partition(lut);
            for (int raw = -32768; raw <= 32767; ++raw)
            {
                const auto r = static_cast<std::int16_t>(raw);
                EXPECT_EQ(lut(r), reference(which, r, fractional_bits))
                    << name_of(which) << " F=" << fractional_bits << " raw=" << raw;
            }
        }
    }
}

TEST(ConstantLut, Int32AndInt64BoundariesAndSamples)
{
    const unsigned widths_f_32[] = {0, 1, 8, 16, 31, 32};
    const unsigned widths_f_64[] = {0, 1, 4, 8, 12, 16, 20, 32, 48, 63, 64};
    std::mt19937 rng(0x108u);
    for (exact_constant which : kAll)
    {
        for (unsigned fractional_bits : widths_f_32)
        {
            const auto lut = grotto::make_exact_constant_lut<std::int32_t>(which, fractional_bits);
            expect_partition(lut);
            for (std::int32_t raw : lut.bounds)
                EXPECT_EQ(lut(raw), reference(which, raw, fractional_bits));
            EXPECT_EQ(lut(0), reference(which, 0, fractional_bits));
            EXPECT_EQ(lut(-1), reference(which, -1, fractional_bits));
            EXPECT_EQ(lut(1), reference(which, 1, fractional_bits));
            EXPECT_EQ(lut(std::numeric_limits<std::int32_t>::min()),
                reference(which, std::numeric_limits<std::int32_t>::min(), fractional_bits));
            EXPECT_EQ(lut(std::numeric_limits<std::int32_t>::max()),
                reference(which, std::numeric_limits<std::int32_t>::max(), fractional_bits));
            std::uniform_int_distribution<std::int32_t> dist;
            for (int n = 0; n < 256; ++n)
            {
                const std::int32_t raw = dist(rng);
                EXPECT_EQ(lut(raw), reference(which, raw, fractional_bits))
                    << name_of(which) << " F=" << fractional_bits;
            }
        }
        for (unsigned fractional_bits : widths_f_64)
        {
            const auto lut = grotto::make_exact_constant_lut<std::int64_t>(which, fractional_bits);
            expect_partition(lut);
            for (std::size_t i = 0; i < lut.bounds.size(); ++i)
            {
                const std::int64_t raw = lut.bounds[i];
                EXPECT_EQ(lut(raw), reference(which, raw, fractional_bits))
                    << name_of(which) << " F=" << fractional_bits << " bound " << i;
                if (i + 1 < lut.bounds.size())
                {
                    const std::int64_t before = static_cast<std::int64_t>(lut.bounds[i + 1] - 1);
                    EXPECT_EQ(lut(before), reference(which, before, fractional_bits));
                }
            }
            std::uniform_int_distribution<std::int64_t> dist;
            for (int n = 0; n < 128; ++n)
            {
                const std::int64_t raw = dist(rng);
                EXPECT_EQ(lut(raw), reference(which, raw, fractional_bits))
                    << name_of(which) << " F=" << fractional_bits << " raw=" << raw;
            }
        }
    }
}

TEST(ConstantLut, LibmAgreesOnPowersOfTwo)
{
    for (unsigned fractional_bits : {0u, 4u, 8u, 12u, 16u, 20u})
    {
        const auto ilogb = grotto::make_exact_constant_lut<std::int64_t>(
            exact_constant::ilogb, fractional_bits);
        const auto ilog10 = grotto::make_exact_constant_lut<std::int64_t>(
            exact_constant::ilog10, fractional_bits);
        for (int k = 0; k <= 62; ++k)
        {
            const std::int64_t raw = std::int64_t{1} << k;
            const double x = std::ldexp(static_cast<double>(raw), -static_cast<int>(fractional_bits));
            if (x == 0.0 || !std::isfinite(x))
                continue;
            EXPECT_EQ(ilogb(raw), std::ilogb(x)) << "F=" << fractional_bits << " k=" << k;
            EXPECT_EQ(ilogb(-raw), std::ilogb(-x)) << "F=" << fractional_bits << " k=" << k;
            const int from_log10 = static_cast<int>(std::floor(std::log10(std::fabs(x))));
            EXPECT_EQ(ilog10(raw), from_log10) << "F=" << fractional_bits << " k=" << k;
            EXPECT_EQ(ilog10(-raw), from_log10) << "F=" << fractional_bits << " k=" << k;
        }
    }
}

TEST(ConstantLut, PartCountsScaleWithTheDomain)
{
    // clz pieces: one negative piece, the [0, 1) piece, then one piece per
    // power of two that still fits. For a 64-bit word and F fractional bits
    // with F <= 62 that is 63 - F + 2.
    for (unsigned fractional_bits : {0u, 4u, 8u, 16u, 20u, 32u})
    {
        const auto clz = grotto::make_exact_constant_lut<std::int64_t>(
            exact_constant::clz, fractional_bits);
        EXPECT_EQ(clz.linear_parts(), 63u - fractional_bits + 2u) << fractional_bits;
    }
    // No positive power of two fits once every value is strictly inside (-1, 1).
    EXPECT_EQ(grotto::make_exact_constant_lut<std::int64_t>(exact_constant::clz, 63).linear_parts(), 2u);
    EXPECT_EQ(grotto::make_exact_constant_lut<std::int64_t>(exact_constant::clz, 64).linear_parts(), 2u);

    // ilogb splits at every raw power of two, on both sides, plus zero: 128
    // pieces for every fractional width that still sees the whole int64 word.
    for (unsigned fractional_bits : {0u, 4u, 8u, 12u, 16u, 20u, 32u, 48u, 63u})
    {
        EXPECT_EQ(grotto::make_exact_constant_lut<std::int64_t>(
            exact_constant::ilogb, fractional_bits).linear_parts(), 128u)
            << fractional_bits;
    }

    // Sign tests do not depend on the fractional width.
    for (unsigned fractional_bits : {0u, 7u, 15u, 16u})
    {
        EXPECT_EQ(grotto::make_exact_constant_lut<std::int16_t>(
            exact_constant::signum, fractional_bits).linear_parts(), 3u);
        EXPECT_EQ(grotto::make_exact_constant_lut<std::int16_t>(
            exact_constant::zero, fractional_bits).wrapped_parts(), 2u);
    }
    for (unsigned fractional_bits : {0u, 16u, 31u, 32u})
    {
        EXPECT_EQ(grotto::make_exact_constant_lut<std::int32_t>(
            exact_constant::positive, fractional_bits).linear_parts(), 2u);
        EXPECT_EQ(grotto::make_exact_constant_lut<std::int64_t>(
            exact_constant::signum, fractional_bits).linear_parts(), 3u);
    }
}

TEST(ConstantLut, OneProgramCoversEveryWidthAndPrecision)
{
    // Sign programs are three constants. Projecting them onto any word yields
    // the same piece values, and the direct evaluator matches the table.
    for (unsigned fractional_bits : {0u, 4u, 8u})
    {
        const auto narrow = grotto::make_exact_constant_lut<std::int8_t>(
            exact_constant::signum, fractional_bits);
        const auto wide = grotto::make_exact_constant_lut<std::int64_t>(
            exact_constant::signum, fractional_bits);
        ASSERT_EQ(narrow.values, wide.values);
        EXPECT_EQ(narrow.values, (std::vector<std::int64_t>{-1, 0, 1}));
        EXPECT_EQ(grotto::evaluate_exact<exact_constant::signum>(std::int8_t{-5}, fractional_bits),
            narrow(-5));
        EXPECT_EQ(grotto::evaluate_exact<exact_constant::signum>(std::int64_t{5}, fractional_bits),
            wide(5));
    }

    // ilogb is floor(log2(|raw|)) - F. Changing F only shifts that one exponent.
    EXPECT_EQ(grotto::evaluate_exact<exact_constant::ilogb>(std::int64_t{1} << 20, 4u),
        grotto::evaluate_exact<exact_constant::ilogb>(std::int64_t{1} << 20, 8u) + 4);

    // ilog10's positive unit boundary is 10^0 from the shared pow10 table,
    // placed at raw = 2^F.
    for (unsigned fractional_bits : {0u, 4u, 8u, 16u})
    {
        const auto lut = grotto::make_exact_constant_lut<std::int64_t>(
            exact_constant::ilog10, fractional_bits);
        const std::int64_t unit = std::int64_t{1} << fractional_bits;
        EXPECT_EQ(lut(unit), 0) << fractional_bits;
        if (unit > 1)
            EXPECT_LT(lut(static_cast<std::int64_t>(unit - 1)), 0) << fractional_bits;
        EXPECT_EQ(grotto::evaluate_exact<exact_constant::ilog10>(unit, fractional_bits), lut(unit));
    }

    // clz reads the integer part. Shifting the raw word and the fractional
    // width by the same amount does not change the count.
    EXPECT_EQ(grotto::evaluate_exact<exact_constant::clz>(std::int64_t{1} << 8, 0u),
        grotto::evaluate_exact<exact_constant::clz>(std::int64_t{1} << 12, 4u));
    EXPECT_EQ(grotto::evaluate_exact<exact_constant::clrsb>(std::int64_t{1} << 8, 0u),
        grotto::evaluate_exact<exact_constant::clrsb>(std::int64_t{1} << 12, 4u));

    const unsigned fractional_bits = 4;
    for (exact_constant which : kAll)
    {
        const auto lut = grotto::make_exact_constant_lut<std::int16_t>(which, fractional_bits);
        for (int raw = -32768; raw <= 32767; raw += 17)
        {
            const auto r = static_cast<std::int16_t>(raw);
            std::int64_t fast = 0;
            switch (which)
            {
            case exact_constant::signum:
                fast = grotto::evaluate_exact<exact_constant::signum>(r, fractional_bits); break;
            case exact_constant::positive:
                fast = grotto::evaluate_exact<exact_constant::positive>(r, fractional_bits); break;
            case exact_constant::negative:
                fast = grotto::evaluate_exact<exact_constant::negative>(r, fractional_bits); break;
            case exact_constant::nonneg:
                fast = grotto::evaluate_exact<exact_constant::nonneg>(r, fractional_bits); break;
            case exact_constant::nonpos:
                fast = grotto::evaluate_exact<exact_constant::nonpos>(r, fractional_bits); break;
            case exact_constant::zero:
                fast = grotto::evaluate_exact<exact_constant::zero>(r, fractional_bits); break;
            case exact_constant::nonzero:
                fast = grotto::evaluate_exact<exact_constant::nonzero>(r, fractional_bits); break;
            case exact_constant::ilogb:
                fast = grotto::evaluate_exact<exact_constant::ilogb>(r, fractional_bits); break;
            case exact_constant::ceil_ilogb:
                fast = grotto::evaluate_exact<exact_constant::ceil_ilogb>(r, fractional_bits); break;
            case exact_constant::ilog10:
                fast = grotto::evaluate_exact<exact_constant::ilog10>(r, fractional_bits); break;
            case exact_constant::clz:
                fast = grotto::evaluate_exact<exact_constant::clz>(r, fractional_bits); break;
            case exact_constant::clrsb:
                fast = grotto::evaluate_exact<exact_constant::clrsb>(r, fractional_bits); break;
            }
            EXPECT_EQ(fast, lut(r)) << name_of(which) << " raw=" << raw;
        }
    }
}

TEST(ConstantLut, SegmentParitiesRecoverEveryInt16Sign)
{
    const exact_constant signs[] = {
        exact_constant::signum,
        exact_constant::positive,
        exact_constant::negative,
        exact_constant::nonneg,
        exact_constant::nonpos,
        exact_constant::zero,
        exact_constant::nonzero,
    };
    for (unsigned fractional_bits : {0u, 8u, 15u})
    {
        for (exact_constant which : signs)
        {
            const auto lut = grotto::make_exact_constant_lut<std::int16_t>(which, fractional_bits);
            ASSERT_LE(lut.bounds.size(), 3u);
            for (int raw = -32768; raw <= 32767; ++raw)
            {
                const auto alpha = static_cast<std::int16_t>(raw);
                const bool ok = lut.bounds.size() == 2
                    ? segment_product_matches<std::int16_t, 2>(lut, alpha)
                    : segment_product_matches<std::int16_t, 3>(lut, alpha);
                EXPECT_TRUE(ok) << name_of(which) << " F=" << fractional_bits
                                << " alpha=" << raw;
            }
        }
    }
}

TEST(ConstantLut, SegmentParitiesRecoverEveryInt8Point)
{
    const unsigned widths[] = {0u, 1u, 4u, 7u};
    for (unsigned fractional_bits : widths)
    {
        for (exact_constant which : kAll)
        {
            const auto lut = grotto::make_exact_constant_lut<std::int8_t>(which, fractional_bits);
            ASSERT_LE(lut.bounds.size(), 40u) << name_of(which);
            for (int raw = -128; raw <= 127; ++raw)
            {
                const auto alpha = static_cast<std::int8_t>(raw);
            EXPECT_TRUE(dispatch_segments<40>(lut, alpha))
                << name_of(which) << " F=" << fractional_bits << " alpha=" << raw
                << " parts=" << lut.bounds.size();
        }
    }
}
}

std::int64_t ref_floor_div(std::int64_t n, std::int64_t d)
{
    if (n >= 0)
        return n / d;
    const __int128 neg = -static_cast<__int128>(n);
    return static_cast<std::int64_t>(-((neg + d - 1) / d));
}

std::int64_t ref_quot(std::int64_t raw, std::int64_t modulus, std::int64_t low, std::int64_t high)
{
    const std::int64_t clipped = raw < low ? low : (raw > high ? high : raw);
    return ref_floor_div(clipped, modulus);
}

TEST(ConstantLut, CeilLogStepsUpOffPowersOfTwo)
{
    const auto lut = grotto::make_exact_constant_lut<std::int64_t>(exact_constant::ceil_ilogb, 0);
    expect_partition(lut);
    EXPECT_EQ(lut(0), -64);
    EXPECT_EQ(lut(1), 0);
    EXPECT_EQ(lut(2), 1);
    EXPECT_EQ(lut(3), 2);
    EXPECT_EQ(lut(4), 2);
    EXPECT_EQ(lut(-3), 2);
    EXPECT_EQ(lut(-4), 2);
    // The same real value, written with 4 more fractional bits, has the same ceil log.
    EXPECT_EQ(grotto::evaluate_exact<exact_constant::ceil_ilogb>(std::int64_t{3}, 0u),
        grotto::evaluate_exact<exact_constant::ceil_ilogb>(std::int64_t{3} << 4, 4u));
}

TEST(ConstantLut, ClippedQuotientIntervalAndThreshold)
{
    // quot(3, -4, 10) on the raw grid, including the clip tails.
    const auto quot = grotto::make_clipped_quotient_lut<std::int16_t>(3, -4, 10);
    expect_partition(quot);
    for (int raw = -32768; raw <= 32767; ++raw)
    {
        const auto r = static_cast<std::int16_t>(raw);
        EXPECT_EQ(quot(r), ref_quot(r, 3, -4, 10)) << raw;
    }
    EXPECT_EQ(quot(-5), ref_floor_div(-4, 3));
    EXPECT_EQ(quot(11), ref_floor_div(10, 3));
    EXPECT_EQ(quot(0), 0);
    EXPECT_EQ(quot(3), 1);
    EXPECT_EQ(quot(-3), -1);

    // A mathematical step of 0.5 with 2 fractional bits is raw modulus 2.
    const auto half = grotto::make_clipped_quotient_lut<std::int8_t>(2, -6, 6);
    for (int raw = -128; raw <= 127; ++raw)
        EXPECT_EQ(half(static_cast<std::int8_t>(raw)), ref_quot(raw, 2, -6, 6)) << raw;

    const auto window = grotto::make_interval_lut<std::int8_t>(-2, 5);
    expect_partition(window);
    for (int raw = -128; raw <= 127; ++raw)
    {
        const auto r = static_cast<std::int8_t>(raw);
        EXPECT_EQ(window(r), (r >= -2 && r <= 5) ? 1 : 0) << raw;
    }

    const auto ge = grotto::make_threshold_lut<std::int8_t>(-3, grotto::threshold_cmp::geq);
    const auto lt = grotto::make_threshold_lut<std::int8_t>(-3, grotto::threshold_cmp::lt);
    for (int raw = -128; raw <= 127; ++raw)
    {
        const auto r = static_cast<std::int8_t>(raw);
        EXPECT_EQ(ge(r), r >= -3);
        EXPECT_EQ(lt(r), r < -3);
    }

    EXPECT_THROW(grotto::make_clipped_quotient_lut<std::int16_t>(0, -1, 1), std::invalid_argument);
    EXPECT_THROW(grotto::make_clipped_quotient_lut<std::int16_t>(1, 4, -4), std::invalid_argument);
    EXPECT_THROW(grotto::make_clipped_quotient_lut<std::int32_t>(1, -100000, 100000), std::invalid_argument);
    EXPECT_THROW(grotto::make_interval_lut<std::int8_t>(2, -2), std::invalid_argument);
}