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Record Grotto half-ulp tables and comparison geneval, and factor shared beaver terms before the quotient.

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Horner and window evaluation need those tables in the tree. Comparison geneval opens the same value words as a Doerner–Shelat key. A factor common to every polynomial term is multiplied first so that preprocessing stays smaller.

Co-authored-by: Cursor <cursoragent@cursor.com>
This commit is contained in:
Ryan Henry 2026-09-24 15:16:21 -06:00
parent 3f10e05176
commit 875f09fec1
14 changed files with 42668 additions and 184 deletions
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81
test/tests/principal_lut_test.cpp
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@ -169,3 +169,84 @@ TEST(PrincipalLut, RejectsBadPrecisionAndDomain)
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));
}