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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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20
include/grotto/principal_lut.hpp
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@ -5,8 +5,12 @@
/// Chebfun). A requested precision only rounds those coefficients
/// down to `k + 16` fractional bits. `coth` is different: its
/// principal function depends on `k` through
/// `beta = ln(2^{k+1}+1)/2`, so each precision has its own uniform
/// partition. The returned raw value is
/// `beta = ln(2^{k+1}+1)/2`, so each precision has its own
/// partition. `inv` (1/x), `rsqrt` (1/sqrt(x)), and `invsq`
/// (1/x^2) are also per precision: each is a longest-feasible
/// cubic march on the closed principal interval [1/2, 1], with
/// absolute error at most half an ulp at that precision. They do
/// not apply an exponent lift. The returned raw value is
/// `round_half_away(p(x) * 2^k)`. On the closed principal domain,
/// `p` stays within one unit in the last place of that precision.
@ -33,6 +37,9 @@ enum class principal : unsigned
sec,
gsec,
csch,
inv,
rsqrt,
invsq,
};
inline constexpr unsigned principal_precisions[] = {8u, 12u, 16u, 20u, 24u, 28u, 32u};
@ -71,6 +78,7 @@ struct table_ref
};
#include "grotto/principal_tables.inc"
#include "grotto/principal_recip_tables.inc"
struct w256
{
@ -288,6 +296,14 @@ inline const table_ref & table_for(principal which, unsigned fractional_bits)
const unsigned slot = fractional_bits / 4u - 2u;
return *COTH_BY_K[slot];
}
if (which == principal::inv || which == principal::rsqrt || which == principal::invsq)
{
const unsigned slot = fractional_bits / 4u - 2u;
const table_ref * const * bank = which == principal::inv
? INV_BY_K
: which == principal::rsqrt ? RSQRT_BY_K : INVSQ_BY_K;
return *bank[slot];
}
return *SHARED_TABLE[index];
}