KOKO\Mimi
303 lines
14 KiB
C++
303 lines
14 KiB
C++
#include "hex8_pair_simd.h"
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#if defined(FESA_HEX8_PAIR_AVX2) && defined(_MSC_VER) && defined(_M_X64)
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#include <cstring>
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#include <immintrin.h>
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#include <intrin.h>
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#include <limits>
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namespace fesa::hex8_internal {
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namespace {
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struct VectorPair {
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__m256d high;
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__m256d low;
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};
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// TU-local predicates mirror the checked scalar premises without publishing
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// AVX2-compiled common math or HighLow COMDAT definitions to baseline callers.
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/// @brief Reads binary64 fields without FP classification or comparison.
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std::uint64_t ScalarBits(double value) {
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static_assert(sizeof(double) == sizeof(std::uint64_t) &&
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std::numeric_limits<double>::is_iec559 &&
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std::numeric_limits<double>::digits == 53);
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std::uint64_t bits = 0;
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std::memcpy(&bits, &value, sizeof(bits));
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return bits;
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}
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/// @brief Bitwise finite gate before any scalar FP comparison.
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bool FiniteScalar(double value) {
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return (ScalarBits(value) & 0x7ff0000000000000ULL) !=
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0x7ff0000000000000ULL;
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}
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/// @brief Exact least-bit exponent; caller has checked finite/nonzero first.
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int LowestBitExponentScalar(double value) {
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const auto bits = ScalarBits(value);
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const auto encoded_exponent = (bits >> 52U) & 0x7ffU;
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auto significand = bits & 0xfffffffffffffULL;
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const int exponent = encoded_exponent == 0U
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? -1074
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: static_cast<int>(encoded_exponent) - 1075;
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if (encoded_exponent != 0U) significand |= 1ULL << 52U;
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unsigned long trailing = 0;
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_BitScanForward64(&trailing, significand);
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return exponent + static_cast<int>(trailing);
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}
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/// @brief Proves the exact tail bound using integer exponents only.
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/// @pre Both operands are finite and nonzero; false requires the exact scans.
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bool TailBoundGuaranteed(double left, double right) {
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const auto left_exponent = (ScalarBits(left) >> 52U) & 0x7ffU;
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const auto right_exponent = (ScalarBits(right) >> 52U) & 0x7ffU;
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const auto left_adjusted = left_exponent == 0 ? 1U : left_exponent;
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const auto right_adjusted = right_exponent == 0 ? 1U : right_exponent;
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// LBE >= adjusted exponent - 1075, including nonzero subnormals.
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return left_adjusted + right_adjusted >= 1076U;
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}
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/// @brief Selects each lane without evaluating additional FP arithmetic.
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__m256d Select(__m256d mask, __m256d selected, __m256d other) {
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return _mm256_blendv_pd(other, selected, mask);
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}
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/// @brief Produces independent finite masks without signaling NaN compares.
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__m256d Finite(__m256d value) {
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const auto exponent = _mm256_set1_epi64x(0x7ff0000000000000LL);
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const auto nonfinite = _mm256_cmpeq_epi64(
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_mm256_and_si256(_mm256_castpd_si256(value), exponent), exponent);
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return _mm256_castsi256_pd(_mm256_xor_si256(
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nonfinite, _mm256_set1_epi64x(-1)));
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}
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/// @brief Recognizes both signed zero encodings using integer fields.
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__m256d Zero(__m256d value) {
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return _mm256_castsi256_pd(_mm256_cmpeq_epi64(
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_mm256_and_si256(_mm256_castpd_si256(value),
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_mm256_set1_epi64x(0x7fffffffffffffffLL)),
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_mm256_setzero_si256()));
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}
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/// @brief Preserves finite/canonical-zero/RN64 gates for active lanes only.
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/// @note Both sum operands and equality RHS are neutral before FP evaluation.
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__m256d Normalized(VectorPair value, __m256d active) {
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const auto finite_active = _mm256_and_pd(active,
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_mm256_and_pd(Finite(value.high), Finite(value.low)));
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const auto both_zero = _mm256_and_pd(Zero(value.high), Zero(value.low));
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const auto canonical_zero = _mm256_castsi256_pd(_mm256_and_si256(
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_mm256_cmpeq_epi64(_mm256_castpd_si256(value.high),
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_mm256_setzero_si256()),
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_mm256_cmpeq_epi64(_mm256_castpd_si256(value.low),
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_mm256_setzero_si256())));
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const auto sum_active = _mm256_andnot_pd(both_zero, finite_active);
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const auto high = Select(sum_active, value.high, _mm256_setzero_pd());
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const auto low = Select(sum_active, value.low, _mm256_setzero_pd());
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const auto equality = _mm256_cmp_pd(_mm256_add_pd(high, low), high, _CMP_EQ_OQ);
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return _mm256_and_pd(finite_active,
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Select(both_zero, canonical_zero, equality));
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}
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/// @brief Retains left-to-right normalized short-circuit for every lane.
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bool NormalizedInputs(VectorPair left, VectorPair right) {
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const auto all = _mm256_castsi256_pd(_mm256_set1_epi64x(-1));
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const auto left_valid = Normalized(left, all);
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return _mm256_movemask_pd(Normalized(right, left_valid)) == 15;
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}
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/// @brief Preserves valid lanes and encodes invalid lanes as quiet NaN/+0.
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VectorPair InvalidOutside(VectorPair value, __m256d valid) {
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return {Select(valid, value.high, _mm256_castsi256_pd(
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_mm256_set1_epi64x(0x7ff8000000000000LL))),
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Select(valid, value.low, _mm256_setzero_pd())};
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}
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/// @brief Loads raw high/low fields in lane order 0..3, with no normalization.
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VectorPair Load(const PairPacket& value) {
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return {_mm256_setr_pd(value.values[0].high, value.values[1].high,
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value.values[2].high, value.values[3].high),
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_mm256_setr_pd(value.values[0].low, value.values[1].low,
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value.values[2].low, value.values[3].low)};
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}
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/// @brief Replicates one raw first product without changing either component.
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VectorPair Splat(PacketPair value) {
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return {_mm256_set1_pd(value.high), _mm256_set1_pd(value.low)};
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}
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/// @brief Stores raw high/low fields without rounding or lane reduction.
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PairPacket Store(VectorPair value) {
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double high[4];
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double low[4];
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_mm256_storeu_pd(high, value.high);
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_mm256_storeu_pd(low, value.low);
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return {{{high[0], low[0]}, {high[1], low[1]},
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{high[2], low[2]}, {high[3], low[3]}}};
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}
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/// @brief Retains finite-sum error association; false requests original graph.
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/// @note False leaves output unreadable and preserves the necessary sum flags.
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/// Prefix flags still require optimized scalar-oracle/codegen validation.
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bool TwoSum(__m256d left, __m256d right, VectorPair* output) {
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const auto sum = _mm256_add_pd(left, right);
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// Do not speculate Inf-Inf error arithmetic beyond a failed first sum.
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// The caller retains original inputs for its existing baseline bridge.
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if (_mm256_movemask_pd(Finite(sum)) != 15) return false;
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const auto bridge = _mm256_sub_pd(sum, left);
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const auto restored = _mm256_sub_pd(sum, bridge);
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const auto error = _mm256_add_pd(_mm256_sub_pd(left, restored),
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_mm256_sub_pd(right, bridge));
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const auto valid = _mm256_and_pd(_mm256_and_pd(Finite(sum), Finite(bridge)),
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_mm256_and_pd(Finite(restored), Finite(error)));
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const auto exact_zero = _mm256_and_pd(Zero(sum), Zero(error));
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*output = InvalidOutside({Select(exact_zero, _mm256_setzero_pd(), sum),
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Select(exact_zero, _mm256_setzero_pd(), error)}, valid);
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return true;
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}
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/// @brief Routes exceptional packets to baseline checked Add in lane order.
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VectorPair ScalarAdd(VectorPair left, VectorPair right) {
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const auto a = Store(left);
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const auto b = Store(right);
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PairPacket result;
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ScalarPacketAdd(a, b, &result);
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return Load(result);
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}
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/// @brief Routes exceptional packets to baseline checked MultiplyPair.
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VectorPair ScalarMultiply(const PairPacket& left, const PairPacket& right) {
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PairPacket result;
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ScalarPacketMultiply(left, right, &result);
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return Load(result);
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}
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/// @brief Retains normalized/zero branches and the checked per-lane Add graph.
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VectorPair Add(VectorPair left, VectorPair right, bool pair_shortcuts) {
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if (!NormalizedInputs(left, right))
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return ScalarAdd(left, right);
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const int left_zero = _mm256_movemask_pd(
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_mm256_and_pd(Zero(left.high), Zero(left.low)));
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const int right_zero = _mm256_movemask_pd(
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_mm256_and_pd(Zero(right.high), Zero(right.low)));
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if (pair_shortcuts) {
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if (left_zero == 15)
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return {right.high, Select(Zero(right.low), _mm256_setzero_pd(), right.low)};
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if (right_zero == 15)
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return {left.high, Select(Zero(left.low), _mm256_setzero_pd(), left.low)};
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if (left_zero != 0 || right_zero != 0)
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return ScalarAdd(left, right);
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}
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VectorPair head;
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VectorPair tail;
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VectorPair middle;
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VectorPair joined;
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if (!TwoSum(left.high, right.high, &head) ||
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!TwoSum(left.low, right.low, &tail) ||
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!TwoSum(head.low, tail.high, &middle) ||
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!TwoSum(head.high, middle.high, &joined))
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return ScalarAdd(left, right);
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const auto remainder = _mm256_add_pd(
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_mm256_add_pd(joined.low, middle.low), tail.low);
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const auto valid = _mm256_and_pd(Finite(remainder), _mm256_and_pd(
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_mm256_and_pd(Finite(head.high), Finite(head.low)), _mm256_and_pd(
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_mm256_and_pd(Finite(tail.high), Finite(tail.low)), _mm256_and_pd(
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_mm256_and_pd(Finite(middle.high), Finite(middle.low)),
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_mm256_and_pd(Finite(joined.high), Finite(joined.low))))));
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// Original Add returns before its last TwoSum when a prior finite gate fails.
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VectorPair result;
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if (!TwoSum(Select(valid, joined.high, _mm256_setzero_pd()),
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Select(valid, remainder, _mm256_setzero_pd()), &result))
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return ScalarAdd(left, right);
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return InvalidOutside(result, valid);
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}
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/// @brief Checks finite/zero/tail premises before products; neutralizes rejected
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/// lanes before the explicit residual FMA and final TwoSum.
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VectorPair Product(__m256d left, __m256d right) {
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double a[4];
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double b[4];
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_mm256_storeu_pd(a, left);
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_mm256_storeu_pd(b, right);
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bool special = false;
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for (std::size_t lane = 0; lane < 4; ++lane)
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if (!FiniteScalar(a[lane]) ||
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!FiniteScalar(b[lane]) ||
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a[lane] == 0 || b[lane] == 0 ||
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(!TailBoundGuaranteed(a[lane], b[lane]) &&
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LowestBitExponentScalar(a[lane]) +
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LowestBitExponentScalar(b[lane]) < -1074))
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special = true;
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if (special) {
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PairPacket result;
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ScalarPacketTwoProduct(a, b, &result);
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return Load(result);
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}
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const auto product = _mm256_mul_pd(left, right);
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const auto product_valid = Finite(product);
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const auto one = _mm256_set1_pd(1.0);
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// Invalid products never reach the residual FMA in the original helper.
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const auto error = _mm256_fmsub_pd(Select(product_valid, left, one),
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Select(product_valid, right, one), Select(product_valid, product, one));
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const auto valid = _mm256_and_pd(product_valid, Finite(error));
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VectorPair result;
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if (!TwoSum(Select(valid, product, _mm256_setzero_pd()),
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Select(valid, error, _mm256_setzero_pd()), &result)) {
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PairPacket scalar;
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ScalarPacketTwoProduct(a, b, &scalar);
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return Load(scalar);
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}
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return InvalidOutside(result, valid);
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}
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/// @brief Uses uniform low-zero branches with original four-product association;
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/// mixed or invalid packets preserve the baseline checked path.
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VectorPair Multiply(VectorPair left, VectorPair right) {
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if (!NormalizedInputs(left, right))
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return ScalarMultiply(Store(left), Store(right));
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const int left_low_zero = _mm256_movemask_pd(Zero(left.low));
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const int right_low_zero = _mm256_movemask_pd(Zero(right.low));
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if ((left_low_zero != 0 && left_low_zero != 15) ||
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(right_low_zero != 0 && right_low_zero != 15))
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return ScalarMultiply(Store(left), Store(right));
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const int branch = (left_low_zero == 0 ? 1 : 0) |
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(right_low_zero == 0 ? 2 : 0);
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auto product = Product(left.high, right.high);
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if (branch == 3) {
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product = Add(product, Product(left.high, right.low), false);
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product = Add(product, Product(left.low, right.high), false);
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return Add(product, Product(left.low, right.low), false);
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}
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const VectorPair zero{_mm256_setzero_pd(), _mm256_setzero_pd()};
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if ((branch & 2) != 0)
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product = Add(product, Product(left.high, right.low), true);
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else if ((branch & 1) != 0)
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product = Add(product, zero, true);
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if ((branch & 1) != 0)
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product = Add(product, Product(left.low, right.high), true);
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return Add(product, zero, true);
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}
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} // namespace
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void EvaluateMaterialPacketAvx2(const MaterialPacketInput& input,
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PairPacket* output) {
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const auto first = Multiply(Load(input.deviatoric_left),
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Load(input.deviatoric_right));
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const auto second = Multiply(Load(input.shear_left), Load(input.shear_right));
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const auto third = Multiply(Load(input.tensor_left), Load(input.gradient_dot));
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const auto material = Add(Add(first, second, true), third, true);
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const PairPacket weight{{input.weight, input.weight, input.weight, input.weight}};
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*output = Store(Add(Load(input.accumulated),
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Multiply(material, Load(weight)), true));
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}
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void EvaluateGeometryPacketAvx2(const GeometryPacketInput& input,
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GeometryPacketOutput* output) {
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VectorPair dot{_mm256_setzero_pd(), _mm256_setzero_pd()};
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for (std::size_t i = 0; i < 3; ++i)
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dot = Add(dot, Multiply(Splat(input.gradient_a[i]),
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Load(input.gradient_b[i])), true);
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VectorPair geo{_mm256_setzero_pd(), _mm256_setzero_pd()};
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for (std::size_t j = 0; j < 3; ++j)
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for (std::size_t l = 0; l < 3; ++l)
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geo = Add(geo, Multiply(Splat(input.gradient_stress[j][l]),
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Load(input.gradient_b[l])), true);
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output->gradient_dot = Store(dot);
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output->weighted_geometric = Store(Multiply(geo, Splat(input.weight)));
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}
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} // namespace fesa::hex8_internal
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#else
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namespace fesa::hex8_internal {
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void EvaluateMaterialPacketAvx2(const MaterialPacketInput& input,
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PairPacket* output) {
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EvaluateMaterialPacketScalar(input, output);
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}
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void EvaluateGeometryPacketAvx2(const GeometryPacketInput& input,
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GeometryPacketOutput* output) {
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EvaluateGeometryPacketScalar(input, output);
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}
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} // namespace fesa::hex8_internal
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#endif
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