libdpf/test/tests/window_lut_test.cpp

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

#include "grotto/window_lut.hpp"

#include <cmath>
#include <cstdint>

namespace
{

struct sample
{
    int which;
    unsigned k;
    std::int64_t raw;
    std::int64_t y;
};

const sample kExact[] = {
#include "window_samples.inc"
};

const sample kTruth[] = {
#include "window_accuracy.inc"
};

long double sigmoid(long double x) { return 1.0L / (1.0L + expl(-x)); }

long double softplus(long double x)
{
    if (x > 40.0L)
        return x;
    if (x < -40.0L)
        return expl(x);
    return log1pl(expl(x));
}

long double reference(grotto::window which, unsigned k, long double x)
{
    switch (which)
    {
    case grotto::window::smoothstep:
        if (x <= -0.5L)
            return 0;
        if (x >= 0.5L)
            return 1;
        return -2.0L * x * x * x + 1.5L * x + 0.5L;
    case grotto::window::sigmoid:
        return sigmoid(x);
    case grotto::window::tanh:
        return tanhl(x);
    case grotto::window::erf:
        return erfl(x);
    case grotto::window::erfc:
        return erfcl(x);
    case grotto::window::softplus:
        return softplus(x);
    case grotto::window::softminus:
        return x - softplus(x);
    case grotto::window::logsigmoid:
        return -softplus(-x);
    case grotto::window::gelu:
        return x * (1.0L + erfl(x / sqrtl(2.0L))) / 2.0L;
    case grotto::window::silu:
        return x * sigmoid(x);
    case grotto::window::mish:
        return x * tanhl(softplus(x));
    case grotto::window::elish:
        return x < 0 ? expm1l(x) * sigmoid(x) : x * sigmoid(x);
    case grotto::window::serf:
        return x * erfl(softplus(x));
    case grotto::window::tanhexp:
        return x * tanhl(expl(x));
    case grotto::window::asin:
        return asinl(x);
    case grotto::window::acos:
        return acosl(x);
    case grotto::window::probit:
        return 0;
    case grotto::window::hardelish:
        if (x <= -1.0L)
            return 0;
        if (x >= 1.0L)
            return x;
        if (x >= 0.0L)
            return x * (x + 1.0L) / 2.0L;
        return expm1l(x) * (x + 1.0L) / 2.0L;
    case grotto::window::lecun_tanh:
        return 1.7159L * tanhl(2.0L * x / 3.0L);
    case grotto::window::one_minus_sigmoid:
        return 1.0L - sigmoid(x);
    }
    return 0;
}

void expect_close(grotto::window which, unsigned k, std::int64_t raw)
{
    const auto y = grotto::eval_window(which, k, raw);
    const long double x = ldexpl(static_cast<long double>(raw), -static_cast<int>(k));
    const long double truth = reference(which, k, x) * ldexpl(1.0L, static_cast<int>(k));
    EXPECT_LE(fabsl(static_cast<long double>(y) - truth), 1.5L)
        << static_cast<int>(which) << " k=" << k << " raw=" << raw << " y=" << y;
}

}  // namespace

TEST(WindowLut, HornerMatchesGeneratedSamples)
{
    for (const sample & point : kExact)
    {
        EXPECT_EQ(grotto::eval_window(static_cast<grotto::window>(point.which), point.k, point.raw), point.y)
            << point.which << " k=" << point.k << " raw=" << point.raw;
    }
}

TEST(WindowLut, WithinOneUlpOfLibm)
{
    for (const sample & point : kTruth)
    {
        if (point.which == static_cast<int>(grotto::window::probit))
            continue;
        expect_close(static_cast<grotto::window>(point.which), point.k, point.raw);
    }
}

TEST(WindowLut, ProbitMatchesMpmathRounding)
{
    for (const sample & point : kTruth)
    {
        if (point.which != static_cast<int>(grotto::window::probit))
            continue;
        const auto y = grotto::eval_window(grotto::window::probit, point.k, point.raw);
        EXPECT_LE(std::llabs(y - point.y), 1) << "k=" << point.k << " raw=" << point.raw;
    }
}

TEST(WindowLut, SmoothstepKnotsAreExact)
{
    EXPECT_EQ(grotto::eval_window(grotto::window::smoothstep, 8, -128), 0);
    EXPECT_EQ(grotto::eval_window(grotto::window::smoothstep, 8, 128), 256);
    EXPECT_EQ(grotto::eval_window(grotto::window::smoothstep, 8, 0), 128);
    EXPECT_EQ(grotto::eval_window(grotto::window::smoothstep, 16, -100000), 0);
    EXPECT_EQ(grotto::eval_window(grotto::window::smoothstep, 16, 100000), 1 << 16);
}

TEST(WindowLut, ExhaustiveLowPrecision)
{
    for (int which_i = 0; which_i <= static_cast<int>(grotto::window::tanhexp); ++which_i)
    {
        if (which_i == static_cast<int>(grotto::window::probit))
            continue;
        const auto which = static_cast<grotto::window>(which_i);
        for (unsigned k : {8u, 12u})
        {
            const std::int64_t span = std::int64_t{30} << k;
            const std::int64_t step = k == 8 ? 1 : 17;
            for (std::int64_t raw = -span; raw <= span; raw += step)
                expect_close(which, k, raw);
        }
    }
    for (unsigned k : {8u, 12u})
    {
        const auto one = std::int64_t{1} << k;
        for (std::int64_t raw = -one; raw <= one; raw += (k == 8 ? 1 : 8))
        {
            expect_close(grotto::window::asin, k, raw);
            expect_close(grotto::window::acos, k, raw);
        }
        const std::int64_t step = k == 8 ? 1 : 17;
        for (std::int64_t raw = -2 * one; raw <= 2 * one; raw += step)
            expect_close(grotto::window::hardelish, k, raw);
        const std::int64_t lecun_span = std::int64_t{20} << k;
        for (std::int64_t raw = -lecun_span; raw <= lecun_span; raw += step)
        {
            expect_close(grotto::window::lecun_tanh, k, raw);
            expect_close(grotto::window::one_minus_sigmoid, k, raw);
        }
    }
}

TEST(WindowLut, HighPrecisionSamples)
{
    for (unsigned k : {16u, 24u, 32u})
    {
        const auto one = std::int64_t{1} << k;
        const auto step = std::int64_t{1} << (k - 8);
        for (std::int64_t raw = -2 * one; raw <= 2 * one; raw += step)
            expect_close(grotto::window::hardelish, k, raw);
        const std::int64_t span = std::int64_t{20} << k;
        const auto wide = std::int64_t{1} << (k - 6);
        for (std::int64_t raw = -span; raw <= span; raw += wide)
        {
            expect_close(grotto::window::lecun_tanh, k, raw);
            expect_close(grotto::window::one_minus_sigmoid, k, raw);
        }
        expect_close(grotto::window::hardelish, k, -one + 1);
        expect_close(grotto::window::hardelish, k, -1);
        expect_close(grotto::window::lecun_tanh, k, 1);
        expect_close(grotto::window::lecun_tanh, k, span);
    }
}

TEST(WindowLut, OneMinusSigmoidComplementsSigmoid)
{
    for (unsigned k : {8u, 16u, 32u})
    {
        const auto one = std::int64_t{1} << k;
        for (std::int64_t raw : {std::int64_t{-8} * one, -one, std::int64_t{0}, one, std::int64_t{8} * one})
        {
            const auto sig = grotto::eval_window(grotto::window::sigmoid, k, raw);
            const auto comp = grotto::eval_window(grotto::window::one_minus_sigmoid, k, raw);
            EXPECT_EQ(sig + comp, one) << k << " " << raw;
        }
    }
}

TEST(WindowLut, RejectsBadDomain)
{
    EXPECT_THROW(grotto::eval_window(grotto::window::sigmoid, 7, 0), std::invalid_argument);
    EXPECT_THROW(grotto::eval_window(grotto::window::asin, 8, 257), std::out_of_range);
    EXPECT_THROW(grotto::eval_window(grotto::window::probit, 8, 0), std::out_of_range);
    EXPECT_THROW(grotto::eval_window(grotto::window::probit, 8, 256), std::out_of_range);
}