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  1. #include <iostream>
  2. #include <random>
  3. #include <ctime>
  4. #include <cassert>
  5. #include <chrono>
  6. #include <immintrin.h>
  7.  
  8. const int Q = 30000000;
  9. const int N = 1 << 24;
  10.  
  11. using T = uint32_t;
  12. T a[2 * N];
  13.  
  14. const T identity_element = 0;
  15. T reduce(T u, T v) { return u + v; }
  16. __attribute__((target("sse4.1"))) __m128i reduce(__m128i u, __m128i v) { return _mm_add_epi32(u, v); }
  17. __attribute__((target("avx2"))) __m256i reduce(__m256i u, __m256i v) { return _mm256_add_epi32(u, v); }
  18.  
  19. static_assert(sizeof(T) == 4, "Segment tree elements must be 32-bit");
  20.  
  21. T query_recursive_inner(int v, int vl, int vr, int l, int r) 
  22. {
  23. 	if(l >= r) return identity_element;
  24. 	if(l <= vl && vr <= r) return a[v];
  25. 	int vm = (vl + vr) >> 1;
  26. 	return reduce(query_recursive_inner(v << 1, vl, vm, l, std::min(r, vm)), query_recursive_inner((v << 1) | 1, vm, vr, std::max(l, vm), r));
  27. }
  28.  
  29. T query_recursive_inner(int l, int r) 
  30. {
  31. 	return query_recursive_inner(1, 0, N, l, r + 1);
  32. }
  33.  
  34. T query_recursive_outer(int v, int vl, int vr, int l, int r) 
  35. {
  36. 	if(vl == l && vr == r) return a[v];
  37.  
  38. 	int vm = (vl + vr) >> 1;
  39. 	if(r <= vm) return query_recursive_outer(v << 1, vl, vm, l, r);
  40. 	if(l >= vm) return query_recursive_outer((v << 1) | 1, vm, vr, l, r);
  41. 	return reduce(query_recursive_outer(v << 1, vl, vm, l, vm), query_recursive_outer((v << 1) | 1, vm, vr, vm, r));
  42. }
  43.  
  44. T query_recursive_outer(int l, int r) 
  45. {
  46. 	return query_recursive_outer(1, 0, N, l, r + 1);
  47. }
  48.  
  49. T query_bottom_up(int l, int r) 
  50. {
  51. 	l += N;
  52. 	r += N;
  53. 	T ans = identity_element;
  54. 	while(l <= r) 
  55. 	{
  56. 		if(l & 1) 
  57. 		{
  58. 			ans = reduce(ans, a[l]);
  59. 			l++;
  60. 		}
  61. 		if(!(r & 1)) 
  62. 		{
  63. 			ans = reduce(ans, a[r]);
  64. 			r--;
  65. 		}
  66. 		l >>= 1;
  67. 		r >>= 1;
  68. 	}
  69. 	return ans;
  70. }
  71.  
  72.  
  73. int ffs(unsigned int x) { return sizeof(unsigned int) * 8 - 1 - __builtin_clz(x); }
  74.  
  75. __attribute__((target("avx2"))) T query_parallel(int l, int r) 
  76. {
  77. 	if(l == r) return a[l + N];
  78.  
  79. 	int mbit = ffs(l ^ r);
  80. 	int reset = ((1 << mbit) - 1);
  81. 	int m = r & ~reset;
  82.  
  83. 	using vecint = T __attribute__((vector_size(32)));
  84. 	__m256i identity_vec = _mm256_set1_epi32(identity_element);
  85. 	vecint vec_ans = (vecint)identity_vec;
  86. 	__m256i indexes = _mm256_set_epi32(7, 6, 5, 4, 3, 2, 1, 0);
  87.  
  88. 	if((l & reset) != 0) {
  89. 		int ll = l - 1 + N;
  90. 		int rr = m - 1 + N;
  91.  
  92. 		int modbit = 0;
  93. 		int maxmodbit = ffs(ll ^ rr) + 1;
  94.  
  95. 		vecint ll_vec = (vecint)_mm256_srav_epi32(_mm256_set1_epi32(ll), indexes);
  96.  
  97. #define LOOP(content) if(modbit + 8 <= maxmodbit) { \
  98. 			vec_ans = (vecint)reduce((__m256i)vec_ans, _mm256_i32gather_epi32((int*)a, (__m256i)(((ll_vec & 1) - 1) & (ll_vec | 1)), 4)); \
  99. 			ll_vec >>= 8; \
  100. 			modbit += 8; \
  101. 			content \
  102. 		}
  103. 		LOOP(LOOP(LOOP(LOOP())))
  104. #undef LOOP
  105.  
  106. 		__m256i tmp = _mm256_i32gather_epi32((int*)a, (__m256i)(((ll_vec & 1) - 1) & (ll_vec | 1)), 4);
  107. 		__m256i mask = _mm256_cmpgt_epi32(_mm256_set1_epi32(maxmodbit & 7), indexes);
  108. 		vec_ans = (vecint)reduce((__m256i)vec_ans, _mm256_blendv_epi8(identity_vec, tmp, mask));
  109. 	} 
  110. 	else 
  111. 		vec_ans[0] = reduce(vec_ans[0], a[(l + N) >> mbit]);
  112.  
  113.  
  114. 	if((r & reset) != reset) 
  115. 	{
  116. 		int ll = m + N;
  117. 		int rr = r + 1 + N;
  118.  
  119. 		int modbit = 0;
  120. 		int maxmodbit = ffs(ll ^ rr) + 1;
  121.  
  122. 		vecint rr_vec = (vecint)_mm256_srav_epi32(_mm256_set1_epi32(rr), indexes);
  123.  
  124. #define LOOP(content) if(modbit + 8 <= maxmodbit) { \
  125. 			vec_ans = (vecint)reduce((__m256i)vec_ans, _mm256_i32gather_epi32((int*)a, (__m256i)(~((rr_vec & 1) - 1) & (rr_vec - 1)), 4)); \
  126. 			rr_vec >>= 8; \
  127. 			modbit += 8; \
  128. 			content \
  129. 		}
  130. 		LOOP(LOOP(LOOP(LOOP())))
  131. #undef LOOP
  132.  
  133. 		__m256i tmp = _mm256_i32gather_epi32((int*)a, (__m256i)(~((rr_vec & 1) - 1) & (rr_vec - 1)), 4);
  134. 		__m256i mask = _mm256_cmpgt_epi32(_mm256_set1_epi32(maxmodbit & 7), indexes);
  135. 		vec_ans = (vecint)reduce((__m256i)vec_ans, _mm256_blendv_epi8(identity_vec, tmp, mask));
  136. 	} 
  137. 	else 
  138. 		vec_ans[0] = reduce(vec_ans[0], a[(r + N) >> mbit]);
  139.  
  140. 	// vec_ans = 7 6 5 4 3 2 1 0
  141. 	__m128i low128 = _mm256_castsi256_si128((__m256i)vec_ans); // 3 2 1 0
  142. 	__m128i high128 = _mm256_extractf128_si256((__m256i)vec_ans, 1); // 7 6 5 4
  143. 	__m128i ans128 = reduce(low128, high128); // 7+3 6+2 5+1 4+0
  144. 	T ans = identity_element;
  145. 	for(int i = 0; i < 4; i++) ans = reduce(ans, ((T __attribute__((vector_size(16))))ans128)[i]);
  146. 	return ans;
  147. }
  148.  
  149. T pref[N];
  150. T query_prefix(int l, int r) { return pref[r] - (l == 0 ? 0 : pref[l - 1]); }
  151.  
  152. T fenwick[N];
  153.  
  154. T query_fenwick(int r)
  155. {
  156. 	T ans = 0;
  157. 	for (; r >= 0; r = (r & (r + 1)) - 1) ans += fenwick[r];
  158. 	return ans;
  159. }
  160.  
  161. T query_fenwick(int l, int r)
  162. {
  163. 	return query_fenwick(r) - (l == 0 ? 0 : query_fenwick(l - 1));
  164. }
  165.  
  166. int main() 
  167. {
  168. 	//std::mt19937 rng(1447);
  169. 	std::mt19937 rng(std::chrono::steady_clock::now().time_since_epoch().count());
  170.  
  171. 	std::pair<int, int>* queries = new std::pair<int, int>[Q];
  172. 	for(int i = 0; i < Q; i++) 
  173. 	{
  174. 		int l = rng() % N;
  175. 		int r = rng() % N;
  176. 		if(l > r) std::swap(l, r);
  177. 		queries[i] = {l, r};
  178. 	}
  179. 	for(int i = 0; i < N; i++) a[N + i] = rng() % (32768);
  180. 	for(int i = N - 1; i >= 1; i--) a[i] = reduce(a[i * 2], a[i * 2 + 1]);
  181. 	a[0] = identity_element;
  182.  
  183. 	for(int i = 0; i < N; i++) pref[i] = (i == 0 ? 0 : pref[i - 1]) + a[N + i];
  184.  
  185. 	for(int i = 0; i < N; i++)
  186. 		for (int j = i; j < N; j = (j | (j + 1))) 
  187. 			fenwick[j] += a[N + i];
  188.  
  189. #define CHECK(func) { \
  190. 		auto clock_start = clock(); \
  191. 		T checksum = 0; \
  192. 		for(int i = 0; i < Q; i++) { \
  193. 			checksum += func(queries[i].first, queries[i].second); \
  194. 		} \
  195. 		std::cout << #func << ": " << (double)(clock() - clock_start) / CLOCKS_PER_SEC << " seconds (checksum: " << checksum << ")" << std::endl; \
  196. 	}
  197.  
  198. 	CHECK(query_recursive_inner)
  199. 	CHECK(query_recursive_outer)
  200. 	CHECK(query_bottom_up)
  201. 	CHECK(query_parallel)
  202. 	CHECK(query_fenwick)
  203. 	CHECK(query_prefix)
  204.  
  205. 	delete [] queries;
  206.  
  207. 	return 0;
  208. }
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https://ideone.com/GeqRbp
language:
C++14 (gcc 8.3)
created:
2 years ago
visibility:
public

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