#include "CpuGenerators.h" #include #include #include #include #include using mnd::CpuGenerator; namespace mnd { template class CpuGenerator; template class CpuGenerator; } struct VecPair { __m256d a; __m256d b; }; static inline VecPair quickTwoSum(__m256d a, __m256d b) { __m256d s = _mm256_add_pd(a, b); __m256d e = _mm256_sub_pd(b, _mm256_sub_pd(s, a)); return { s, e }; } static inline VecPair quickTwoDiff(__m256d a, __m256d b) { __m256d s = _mm256_sub_pd(a, b); __m256d e = _mm256_sub_pd(_mm256_sub_pd(a, s), b); return { s, e }; } static inline VecPair twoSum(__m256d a, __m256d b) { __m256d s = _mm256_add_pd(a, b); __m256d bb = _mm256_sub_pd(s, a); __m256d e = _mm256_add_pd(_mm256_sub_pd(a, _mm256_sub_pd(s, bb)), _mm256_sub_pd(b, bb)); return { s, e }; } static inline VecPair twoDiff(__m256d a, __m256d b) { __m256d s = _mm256_sub_pd(a, b); __m256d bb = _mm256_sub_pd(s, a); __m256d e = _mm256_sub_pd(_mm256_sub_pd(a, _mm256_sub_pd(s, bb)), _mm256_add_pd(b, bb)); return { s, e }; } /* static inline VecPair split(__m256d a) { static const __m256d SPLIT_THRESH = { 6.69692879491417e+299, 6.69692879491417e+299, 6.69692879491417e+299, 6.69692879491417e+299 }; static const __m256d MINUS_SPLIT_THRESH = { -6.69692879491417e+299, -6.69692879491417e+299, -6.69692879491417e+299, -6.69692879491417e+299 }; static const __m256d SPLITTER = { 134217729.0, 134217729.0, 134217729.0, 134217729.0}; __m256d temp; __m256i cmp1 = _mm256_castpd_si256(_mm256_cmp_pd(a, SPLIT_THRESH, _CMP_GT_OQ)); __m256i cmp2 = _mm256_castpd_si256(_mm256_cmp_pd(a, MINUS_SPLIT_THRESH, _CMP_LT_OQ)); __m256i cmp = _mm256_or_si256 }*/ static inline VecPair twoProd(__m256d a, __m256d b) { //#ifdef CPUID_FMA __m256d p = _mm256_mul_pd(a, b); __m256d e = _mm256_fmsub_pd(a, b, p); return { p, e }; //#else /* double a_hi, a_lo, b_hi, b_lo; __m256d p = _mm256_mul_ps(a, b); split(a, a_hi, a_lo); split(b, b_hi, b_lo); err = ((a_hi * b_hi - p) + a_hi * b_lo + a_lo * b_hi) + a_lo * b_lo; return p;*/ //#endif } struct AvxDoubleDouble { __m256d x[2]; inline AvxDoubleDouble(__m256d a, __m256d b) : x{ a, b } {} inline AvxDoubleDouble operator + (const AvxDoubleDouble& sm) const { auto[s, e] = twoSum(x[0], sm.x[0]); e = _mm256_add_pd(e, _mm256_add_pd(x[1], sm.x[1])); auto[r1, r2] = quickTwoSum(s, e); return AvxDoubleDouble{ r1, r2 }; } inline AvxDoubleDouble operator - (const AvxDoubleDouble& sm) const { auto[s, e] = twoDiff(x[0], sm.x[0]); e = _mm256_add_pd(e, x[1]); e = _mm256_sub_pd(e, sm.x[1]); auto[r1, r2] = quickTwoSum(s, e); return AvxDoubleDouble{ r1, r2 }; } inline AvxDoubleDouble operator * (const AvxDoubleDouble& sm) const { auto[p1, p2] = twoProd(this->x[0], sm.x[0]); p2 = _mm256_add_pd(p2, _mm256_add_pd(_mm256_mul_pd(sm.x[1], x[0]), _mm256_mul_pd(sm.x[0], x[1])) ); auto[r1, r2] = quickTwoSum(p1, p2); return AvxDoubleDouble{ r1, r2 }; } }; template void CpuGenerator::generate(const mnd::MandelInfo& info, float* data) { const MandelViewport& view = info.view; using T = DoubleDouble; T viewx = mnd::convert(view.x); T viewy = mnd::convert(view.y); T wpp = mnd::convert(view.width / info.bWidth); T hpp = mnd::convert(view.height / info.bHeight); // if constexpr(parallel) // omp_set_num_threads(2 * omp_get_num_procs()); //#pragma omp parallel for schedule(static, 1) if (parallel) for (long j = 0; j < info.bHeight; j++) { T y = viewy + T(double(j)) * hpp; __m256d y0s = { y.x[0], y.x[0], y.x[0], y.x[0] }; __m256d y1s = { y.x[1], y.x[1], y.x[1], y.x[1] }; AvxDoubleDouble ys{ y0s, y1s }; long i = 0; for (i; i < info.bWidth; i += 4) { T x1 = viewx + T(double(i)) * wpp; T x2 = x1 + wpp; T x3 = x2 + wpp; T x4 = x3 + wpp; __m256d x0s = { x1.x[0], x2.x[0], x3.x[0], x4.x[0], }; __m256d x1s = { x1.x[1], x2.x[1], x3.x[1], x4.x[1], }; AvxDoubleDouble xs{ x0s, x1s }; int itRes[4] = { 0, 0, 0, 0 }; __m256d threshold = { 16.0, 16.0, 16.0, 16.0 }; __m256d counter = { 0, 0, 0, 0 }; __m256d adder = { 1, 1, 1, 1 }; AvxDoubleDouble a = xs; AvxDoubleDouble b = ys; __m256d resultsa; __m256d resultsb; for (int k = 0; k < info.maxIter; k++) { AvxDoubleDouble aa = a * a; AvxDoubleDouble bb = b * b; AvxDoubleDouble abab = a * b; abab = abab + abab; a = aa - bb + xs; b = abab + ys; __m256d cmp = _mm256_cmp_pd(_mm256_add_pd(aa.x[0], bb.x[0]), threshold, _CMP_LE_OQ); if (info.smooth) { resultsa = _mm256_or_pd(_mm256_andnot_pd(cmp, resultsa), _mm256_and_pd(cmp, a.x[0])); resultsb = _mm256_or_pd(_mm256_andnot_pd(cmp, resultsb), _mm256_and_pd(cmp, b.x[0])); } adder = _mm256_and_pd(adder, cmp); counter = _mm256_add_pd(counter, adder); if (_mm256_testz_si256(_mm256_castpd_si256(cmp), _mm256_castpd_si256(cmp)) != 0) { break; } } auto alignVec = [](double* data) -> double* { void* aligned = data; ::size_t length = 64; std::align(32, 4 * sizeof(double), aligned, length); return static_cast(aligned); }; double resData[8]; double* ftRes = alignVec(resData); double* resa = (double*) &resultsa; double* resb = (double*) &resultsb; _mm256_store_pd(ftRes, counter); for (int k = 0; k < 4 && i + k < info.bWidth; k++) { if (info.smooth) data[i + k + j * info.bWidth] = ftRes[k] <= 0 ? info.maxIter : ftRes[k] >= info.maxIter ? info.maxIter : ((float)ftRes[k]) + 1 - ::log(::log(resa[k] * resa[k] + resb[k] * resb[k]) / 2) / ::log(2.0f); else data[i + k + j * info.bWidth] = ftRes[k] > 0 ? float(ftRes[k]) : info.maxIter; } } } return; for (long j = 0; j < info.bHeight; j++) { T y = viewy + T(double(j)) * hpp; __m256d y0s = { y.x[0], y.x[0], y.x[0], y.x[0] }; __m256d y1s = { y.x[1], y.x[1], y.x[1], y.x[1] }; AvxDoubleDouble ys{ y0s, y1s }; long i = 0; for (i; i < info.bWidth; i += 4) { T x1 = viewx + T(double(i)) * wpp; T x2 = viewx + T(double(i + 1)) * wpp; T x3 = viewx + T(double(i + 2)) * wpp; T x4 = viewx + T(double(i + 3)) * wpp; __m256d x0s = { x1.x[0], x2.x[0], x3.x[0], x4.x[0], }; __m256d x1s = { x1.x[1], x2.x[1], x3.x[1], x4.x[1], }; AvxDoubleDouble xs{ x0s, x1s }; int itRes[4] = { 0, 0, 0, 0 }; __m256d threshold = { 16.0, 16.0, 16.0, 16.0 }; __m256d counter = { 0, 0, 0, 0 }; __m256d adder = { 1, 1, 1, 1 }; AvxDoubleDouble a = xs; AvxDoubleDouble b = ys; for (int k = 0; k < info.maxIter; k++) { AvxDoubleDouble aa = a * a; AvxDoubleDouble bb = b * b; AvxDoubleDouble abab = a * b; abab = abab + abab; a = aa - bb + xs; b = abab + ys; __m256i cmp = _mm256_castpd_si256(_mm256_cmp_pd(_mm256_add_pd(aa.x[0], bb.x[0]), threshold, _CMP_LE_OQ)); /*if (info.smooth) { resultsa = _mm256_or_pd(_mm256_andnot_ps(cmp, resultsa), _mm256_and_ps(cmp, a)); resultsb = _mm256_or_ps(_mm256_andnot_ps(cmp, resultsb), _mm256_and_ps(cmp, b)); }*/ adder = _mm256_and_pd(adder, _mm256_castsi256_pd(cmp)); counter = _mm256_add_pd(counter, adder); if ((k & 7) == 0 && _mm256_testz_si256(cmp, cmp) != 0) { break; } } auto alignVec = [](double* data) -> double* { void* aligned = data; ::size_t length = 64; std::align(32, 4 * sizeof(double), aligned, length); return static_cast(aligned); }; double resData[8]; double* ftRes = alignVec(resData); _mm256_store_pd(ftRes, counter); for (int k = 0; k < 4 && i + k < info.bWidth; k++) data[i + k + j * info.bWidth] = ftRes[k] > 0 ? float(ftRes[k]) : info.maxIter; } } }