libdpf/test/tests/principal_lut_test.cpp

#include <gtest/gtest.h>

#include "grotto/principal_lut.hpp"

#include <cmath>
#include <cstdint>
#include <vector>

namespace
{

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

const sample kSamples[] = {
#include "principal_samples.inc"
};

long double series_coth_minus_inv(long double u)
{
    const long double u2 = u * u;
    return u * (1.0L / 3.0L - u2 / 45.0L + 2.0L * u2 * u2 / 945.0L);
}

long double reference(grotto::principal which, unsigned k, long double x)
{
    constexpr long double pi = 3.141592653589793238462643383279502884L;
    switch (which)
    {
    case grotto::principal::ln:
        return logl(x);
    case grotto::principal::exp:
        return expl(ldexpl(x, -13));
    case grotto::principal::sin:
        return sinl(pi * x / 2);
    case grotto::principal::tanf:
        if (x == 0)
            return 1;
        {
            const long double z = pi * x / 4;
            return tanl(z) / z;
        }
    case grotto::principal::tang:
        if (x < ldexpl(1, -12))
        {
            const long double z = pi * x / 4;
            const long double z2 = z * z;
            return -z / 3 - z2 * z / 45;
        }
        {
            const long double z = pi * x / 4;
            return 1 / tanl(z) - 1 / z;
        }
    case grotto::principal::sinh:
        return sinhl(ldexpl(x, -13));
    case grotto::principal::cosh:
        return coshl(ldexpl(x, -13));
    case grotto::principal::sqrt:
        return sqrtl(x);
    case grotto::principal::coth:
        if (x == 0)
            return 0;
        {
            const long double beta = 0.5L * logl(ldexpl(1, static_cast<int>(k) + 1) + 1);
            const long double u = beta * x;
            if (u < 0.05L)
                return series_coth_minus_inv(u);
            return 1 / tanhl(u) - 1 / u;
        }
    case grotto::principal::sec:
        return 1 / cosl(pi * x / 4);
    case grotto::principal::gsec:
        if (x < ldexpl(1, -12))
        {
            const long double z = pi * x / 4;
            const long double z2 = z * z;
            return z / 6 + 7 * z2 * z / 360;
        }
        {
            const long double z = pi * x / 4;
            return 1 / sinl(z) - 1 / z;
        }
    case grotto::principal::csch:
        if (x < ldexpl(1, -12))
        {
            const long double x2 = x * x;
            return -x / 6 + 7 * x2 * x / 360;
        }
        return 1 / sinhl(x) - 1 / x;
    }
    return 0;
}

std::int64_t domain_left(grotto::principal which, unsigned k)
{
    if (which == grotto::principal::ln || which == grotto::principal::sqrt)
        return std::int64_t{1} << (k - 1);
    return 0;
}

std::int64_t domain_right(unsigned k)
{
    return std::int64_t{1} << k;
}

void expect_close(grotto::principal which, unsigned k, std::int64_t raw)
{
    const auto y = grotto::eval_principal(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, static_cast<int>(k));
    EXPECT_LE(fabsl(static_cast<long double>(y) - truth), 1.5L) << static_cast<int>(which) << " k=" << k << " raw=" << raw;
}

}  // namespace

TEST(PrincipalLut, CoarsenedPieceCountsStayPut)
{
    EXPECT_EQ(grotto::principal_parts(grotto::principal::ln, 8), grotto::principal_parts(grotto::principal::ln, 32));
    EXPECT_EQ(grotto::principal_parts(grotto::principal::sqrt, 8), 393);
    EXPECT_EQ(grotto::principal_parts(grotto::principal::exp, 32), 2u);
    EXPECT_EQ(grotto::principal_parts(grotto::principal::sinh, 16), 1u);
    EXPECT_LT(grotto::principal_parts(grotto::principal::coth, 8), grotto::principal_parts(grotto::principal::coth, 32));
}

TEST(PrincipalLut, EmbeddedHornerMatches)
{
    for (const sample & point : kSamples)
    {
        const auto which = static_cast<grotto::principal>(point.which);
        EXPECT_EQ(grotto::eval_principal(which, point.k, point.raw), point.y)
            << point.which << " k=" << point.k << " raw=" << point.raw;
    }
}

TEST(PrincipalLut, WithinOneUlpOnTheDomain)
{
    for (unsigned which_i = 0; which_i < 12; ++which_i)
    {
        const auto which = static_cast<grotto::principal>(which_i);
        for (unsigned k : {8u, 12u})
        {
            const auto left = domain_left(which, k);
            const auto right = domain_right(k);
            for (std::int64_t raw = left; raw <= right; ++raw)
                expect_close(which, k, raw);
        }
        for (unsigned k : {16u, 20u, 24u, 28u, 32u})
        {
            const auto left = domain_left(which, k);
            const auto right = domain_right(k);
            const std::int64_t step = std::max<std::int64_t>(1, (right - left) / 256);
            expect_close(which, k, left);
            expect_close(which, k, right);
            for (std::int64_t raw = left; raw < right; raw += step)
                expect_close(which, k, raw);
        }
    }
}

TEST(PrincipalLut, RejectsBadPrecisionAndDomain)
{
    EXPECT_THROW(grotto::eval_principal(grotto::principal::ln, 7, 64), std::invalid_argument);
    EXPECT_THROW(grotto::eval_principal(grotto::principal::ln, 8, 0), std::out_of_range);
    EXPECT_THROW(grotto::eval_principal(grotto::principal::exp, 8, -1), std::out_of_range);
    EXPECT_THROW(grotto::eval_principal(grotto::principal::sin, 8, 257), std::out_of_range);
}

long double recip_reference(grotto::principal which, long double x)
{
    switch (which)
    {
    case grotto::principal::inv:
        return 1.0L / x;
    case grotto::principal::rsqrt:
        return 1.0L / sqrtl(x);
    case grotto::principal::invsq:
        return 1.0L / (x * x);
    default:
        return 0;
    }
}

void expect_recip(grotto::principal which, unsigned k, std::int64_t raw)
{
    const auto y = grotto::eval_principal(which, k, raw);
    const long double x = ldexpl(static_cast<long double>(raw), -static_cast<int>(k));
    const long double truth = recip_reference(which, 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;
}

TEST(PrincipalLut, ReciprocalPieceCounts)
{
    const unsigned inv[] = {2u, 3u, 5u, 9u, 18u, 35u, 69u};
    const unsigned rsqrt[] = {1u, 2u, 3u, 6u, 12u, 24u, 48u};
    const unsigned invsq[] = {2u, 4u, 8u, 15u, 29u, 57u, 113u};
    unsigned slot = 0;
    for (unsigned k : grotto::principal_precisions)
    {
        EXPECT_EQ(grotto::principal_parts(grotto::principal::inv, k), inv[slot]);
        EXPECT_EQ(grotto::principal_parts(grotto::principal::rsqrt, k), rsqrt[slot]);
        EXPECT_EQ(grotto::principal_parts(grotto::principal::invsq, k), invsq[slot]);
        ++slot;
    }
}

TEST(PrincipalLut, ReciprocalWithinOneAndAHalfUlp)
{
    const grotto::principal maps[] = {
        grotto::principal::inv,
        grotto::principal::rsqrt,
        grotto::principal::invsq,
    };
    for (const auto which : maps)
    {
        for (unsigned k : {8u, 12u, 16u})
        {
            const auto left = std::int64_t{1} << (k - 1);
            const auto right = std::int64_t{1} << k;
            for (std::int64_t raw = left; raw <= right; ++raw)
                expect_recip(which, k, raw);
        }
        for (unsigned k : {20u, 24u, 28u, 32u})
        {
            const auto left = std::int64_t{1} << (k - 1);
            const auto right = std::int64_t{1} << k;
            const std::int64_t step = std::max<std::int64_t>(1, (right - left) / 4096);
            expect_recip(which, k, left);
            expect_recip(which, k, right);
            for (std::int64_t raw = left; raw < right; raw += step)
                expect_recip(which, k, raw);
        }
    }
}

TEST(PrincipalLut, ReciprocalRejectsOutsidePrincipalInterval)
{
    EXPECT_THROW(grotto::eval_principal(grotto::principal::inv, 7, 128), std::invalid_argument);
    EXPECT_THROW(grotto::eval_principal(grotto::principal::inv, 8, 127), std::out_of_range);
    EXPECT_THROW(grotto::eval_principal(grotto::principal::inv, 8, 257), std::out_of_range);
    EXPECT_THROW(grotto::eval_principal(grotto::principal::rsqrt, 12, 2047), std::out_of_range);
    EXPECT_THROW(grotto::eval_principal(grotto::principal::invsq, 16, (std::int64_t{1} << 16) + 1), std::out_of_range);
    EXPECT_THROW(grotto::eval_principal(grotto::principal::invsq, 8, -1), std::out_of_range);
    EXPECT_NO_THROW(grotto::eval_principal(grotto::principal::inv, 8, 128));
    EXPECT_NO_THROW(grotto::eval_principal(grotto::principal::rsqrt, 8, 256));
    EXPECT_NO_THROW(grotto::eval_principal(grotto::principal::invsq, 12, 4096));
}