├── .gitignore ├── .travis.yml ├── LICENSE ├── README.md ├── example.c ├── include └── fastdelta.h ├── makefile ├── src └── fastdelta.c └── tests └── unit.c /.gitignore: -------------------------------------------------------------------------------- 1 | # Object files 2 | *.o 3 | *.ko 4 | *.obj 5 | *.elf 6 | 7 | # Precompiled Headers 8 | *.gch 9 | *.pch 10 | 11 | # Libraries 12 | *.lib 13 | *.a 14 | *.la 15 | *.lo 16 | 17 | # Shared objects (inc. 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The downside 15 | of this improved compressibility is the need to recover the original integers by 16 | computing the prefix sum. 17 | 18 | Programmers are often tempted to computer a prefix sum in the straight-forward manner: 19 | 20 | ```C 21 | for (size_t i=1;i 2 | #include 3 | 4 | #include "fastdelta.h" 5 | 6 | int main() { 7 | uint32_t datain[] = {1,14,15,25,100}; 8 | int N = sizeof(datain) / sizeof(uint32_t); 9 | printf("starting from: "); 10 | for(int k = 0; k < N; ++k) printf(" %d ",datain[k]); 11 | printf("\n"); 12 | 13 | compute_deltas_inplace(datain,N,0); 14 | 15 | printf("deltas: "); 16 | for(int k = 0; k < N; ++k) printf(" %d ",datain[k]); 17 | printf("\n"); 18 | 19 | compute_prefix_sum_inplace(datain,N,0); 20 | 21 | 22 | printf("recovered: "); 23 | for(int k = 0; k < N; ++k) printf(" %d ",datain[k]); 24 | printf("\n"); 25 | 26 | // you can also, similarly, write values to another buffer with compute_deltas, and compute_prefix_sum 27 | 28 | } 29 | 30 | 31 | -------------------------------------------------------------------------------- /include/fastdelta.h: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | /*** 4 | * These functions compute fast successive differences, and recover the original 5 | * values from the fast successive differences (i.e., they compute a prefix sum) 6 | * using fast SIMD instructions. 7 | * 8 | * Reference : 9 | * Daniel Lemire, Nathan Kurz, Leonid Boytsov, SIMD Compression and the Intersection of Sorted 10 | * Integers, Software: Practice and Experience (to appear) 11 | * http://arxiv.org/abs/1401.6399 12 | */ 13 | 14 | 15 | // write to output the successive differences of input (input[0]-starting_point, input[1]-input[2], ...) 16 | // there are "length" values in input and output 17 | // input and output must be distinct 18 | // it can make sense to set to zero by default 19 | void compute_deltas(const uint32_t * __restrict__ input, size_t length, uint32_t * __restrict__ output, uint32_t starting_point); 20 | 21 | 22 | 23 | // write to buffer the successive differences of buffer (buffer[0]-starting_point, buffer[1]-buffer[2], ...) 24 | // there are "length" values in buffer 25 | // it can make sense to set to zero by default 26 | void compute_deltas_inplace(uint32_t * buffer, size_t length, uint32_t starting_point); 27 | 28 | 29 | // write to output the successive differences of input (input[0]-starting_point, input[1]-input[2], ...) 30 | // there are "length" values in input and output 31 | // input and output must be distinct 32 | void compute_prefix_sum(const uint32_t * __restrict__ input, size_t length, uint32_t * __restrict__ output, uint32_t starting_point); 33 | 34 | 35 | // write to buffer the successive differences of buffer (buffer[0]-starting_point, buffer[1]-buffer[2], ...) 36 | // there are "length" values in buffer 37 | void compute_prefix_sum_inplace(uint32_t * buffer, size_t length, uint32_t starting_point); 38 | -------------------------------------------------------------------------------- /makefile: -------------------------------------------------------------------------------- 1 | # minimalist makefile 2 | .SUFFIXES: 3 | # 4 | .SUFFIXES: .cpp .o .c .h 5 | ifeq ($(DEBUG),1) 6 | CFLAGS = -fPIC -std=c99 -ggdb -msse4.1 -march=native -Wall -Wextra -Wshadow -fsanitize=undefined -fno-omit-frame-pointer -fsanitize=address 7 | else 8 | CFLAGS = -fPIC -std=c99 -O3 -msse4.1 -march=native -Wall -Wextra -Wshadow 9 | endif # debug 10 | all: unit 11 | test: 12 | ./unit 13 | 14 | HEADERS=./include/fastdelta.h 15 | 16 | OBJECTS= fastdelta.o 17 | 18 | fastdelta.o: ./src/fastdelta.c $(HEADERS) 19 | $(CC) $(CFLAGS) -c ./src/fastdelta.c -Iinclude 20 | 21 | example: ./example.c $(HEADERS) $(OBJECTS) 22 | $(CC) $(CFLAGS) -o example ./example.c -Iinclude $(OBJECTS) 23 | 24 | unit: ./tests/unit.c $(HEADERS) $(OBJECTS) 25 | $(CC) $(CFLAGS) -o unit ./tests/unit.c -Iinclude $(OBJECTS) 26 | clean: 27 | rm -f unit *.o example 28 | -------------------------------------------------------------------------------- /src/fastdelta.c: -------------------------------------------------------------------------------- 1 | #include "fastdelta.h" 2 | #if defined(_MSC_VER) 3 | /* Microsoft C/C++-compatible compiler */ 4 | #include 5 | #elif defined(__GNUC__) && (defined(__x86_64__) || defined(__i386__)) 6 | /* GCC-compatible compiler, targeting x86/x86-64 */ 7 | #include 8 | #elif defined(__GNUC__) && defined(__ARM_NEON__) 9 | /* GCC-compatible compiler, targeting ARM with NEON */ 10 | #include 11 | #elif defined(__GNUC__) && defined(__IWMMXT__) 12 | /* GCC-compatible compiler, targeting ARM with WMMX */ 13 | #include 14 | #elif (defined(__GNUC__) || defined(__xlC__)) && (defined(__VEC__) || defined(__ALTIVEC__)) 15 | /* XLC or GCC-compatible compiler, targeting PowerPC with VMX/VSX */ 16 | #include 17 | #elif defined(__GNUC__) && defined(__SPE__) 18 | /* GCC-compatible compiler, targeting PowerPC with SPE */ 19 | #include 20 | #endif 21 | 22 | // write to output the successive differences of input (input[0]-starting_point, input[1]-input[2], ...) 23 | // there are "length" values in input and output 24 | // input and output must be distinct 25 | void compute_deltas(const uint32_t * __restrict__ input, size_t length, uint32_t * __restrict__ output, uint32_t starting_point) { 26 | __m128i prev = _mm_set1_epi32(starting_point); 27 | size_t i = 0; 28 | for(; i < length/4; i++) { 29 | __m128i curr = _mm_lddqu_si128 (( const __m128i*) input + i ); 30 | __m128i delta = _mm_sub_epi32(curr, 31 | _mm_alignr_epi8(curr, prev, 12)); 32 | _mm_storeu_si128((__m128i*)output + i,delta); 33 | prev = curr; 34 | } 35 | uint32_t lastprev = _mm_extract_epi32(prev,3); 36 | for(i = 4 * i; i < length; ++i) { 37 | uint32_t curr = input[i]; 38 | output[i] = curr - lastprev; 39 | lastprev = curr; 40 | } 41 | } 42 | 43 | // write to buffer the successive differences of buffer (buffer[0]-starting_point, buffer[1]-buffer[2], ...) 44 | // there are "length" values in buffer 45 | void compute_deltas_inplace(uint32_t * buffer, size_t length, uint32_t starting_point) { 46 | __m128i prev = _mm_set1_epi32(starting_point); 47 | size_t i = 0; 48 | for(; i < length/4; i++) { 49 | __m128i curr = _mm_lddqu_si128 (( const __m128i*) buffer + i ); 50 | __m128i delta = _mm_sub_epi32(curr, 51 | _mm_alignr_epi8(curr, prev, 12)); 52 | _mm_storeu_si128((__m128i*)buffer + i,delta); 53 | prev = curr; 54 | } 55 | uint32_t lastprev = _mm_extract_epi32(prev,3); 56 | for(i = 4 * i; i < length; ++i) { 57 | uint32_t curr = buffer[i]; 58 | buffer[i] = curr - lastprev; 59 | lastprev = curr; 60 | } 61 | } 62 | 63 | // write to output the successive differences of input (input[0]-starting_point, input[1]-input[2], ...) 64 | // there are "length" values in input and output 65 | // input and output must be distinct 66 | void compute_prefix_sum(const uint32_t * __restrict__ input, size_t length, uint32_t * __restrict__ output, uint32_t starting_point) { 67 | __m128i prev = _mm_set1_epi32(starting_point); 68 | size_t i = 0; 69 | for(; i < length/4; i++) { 70 | __m128i curr = _mm_lddqu_si128 (( const __m128i*) input + i ); 71 | const __m128i _tmp1 = _mm_add_epi32(_mm_slli_si128(curr, 8), curr); 72 | const __m128i _tmp2 = _mm_add_epi32(_mm_slli_si128(_tmp1, 4), _tmp1); 73 | prev = _mm_add_epi32(_tmp2, _mm_shuffle_epi32(prev, 0xff)); 74 | _mm_storeu_si128((__m128i*)output + i,prev); 75 | } 76 | uint32_t lastprev = _mm_extract_epi32(prev,3); 77 | for(i = 4 * i; i < length; ++i) { 78 | lastprev = lastprev + input[i]; 79 | output[i] = lastprev; 80 | } 81 | } 82 | 83 | // write to buffer the successive differences of buffer (buffer[0]-starting_point, buffer[1]-buffer[2], ...) 84 | // there are "length" values in buffer 85 | void compute_prefix_sum_inplace(uint32_t * buffer, size_t length, uint32_t starting_point) { 86 | __m128i prev = _mm_set1_epi32(starting_point); 87 | size_t i = 0; 88 | for(; i < length/4; i++) { 89 | __m128i curr = _mm_lddqu_si128 (( const __m128i*) buffer + i ); 90 | const __m128i _tmp1 = _mm_add_epi32(_mm_slli_si128(curr, 8), curr); 91 | const __m128i _tmp2 = _mm_add_epi32(_mm_slli_si128(_tmp1, 4), _tmp1); 92 | prev = _mm_add_epi32(_tmp2, _mm_shuffle_epi32(prev, 0xff)); 93 | _mm_storeu_si128((__m128i*)buffer + i,prev); 94 | } 95 | uint32_t lastprev = _mm_extract_epi32(prev,3); 96 | for(i = 4 * i ; i < length; ++i) { 97 | lastprev = lastprev + buffer[i]; 98 | buffer[i] = lastprev; 99 | } 100 | } 101 | -------------------------------------------------------------------------------- /tests/unit.c: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | 4 | #include "fastdelta.h" 5 | 6 | int main() { 7 | int N = 4096; 8 | uint32_t * datain = malloc(N * sizeof(uint32_t)); 9 | uint32_t * buffer = malloc(N * sizeof(uint32_t)); 10 | uint32_t * recovdata = malloc(N * sizeof(uint32_t)); 11 | 12 | 13 | for (int length = 0; length <= N;) { 14 | printf("length = %d \n", length); 15 | for (uint32_t gap = 1; gap <= 387420489; gap *= 3) { 16 | for (int k = 0; k < length; ++k) 17 | datain[k] = gap * (k+1); 18 | compute_deltas(datain, length, buffer, 0); 19 | for (int k = 0; k < length; ++k) { 20 | if(buffer[k] != gap) { 21 | printf("bug. buffer[%d]=%d expected %d \n",k,buffer[k],gap); 22 | return -1; 23 | } 24 | } 25 | 26 | compute_prefix_sum(buffer, length, recovdata, 0); 27 | for(int k = 0; k < length; ++k) { 28 | if(datain[k] != recovdata[k]) { 29 | printf("bug.\n"); 30 | return -1; 31 | } 32 | } 33 | compute_deltas_inplace(datain, length, 0); 34 | for (int k = 0; k < length; ++k) { 35 | if(datain[k] != gap) { 36 | printf("bug."); 37 | return -1; 38 | } 39 | } 40 | compute_prefix_sum_inplace(datain, length, 0); 41 | for(int k = 0; k < length; ++k) { 42 | if(datain[k] != recovdata[k]) { 43 | printf("bug.\n"); 44 | return -1; 45 | } 46 | } 47 | } 48 | 49 | if (length < 128) 50 | ++length; 51 | else { 52 | length *= 2; 53 | } 54 | } 55 | free(datain); 56 | free(buffer); 57 | free(recovdata); 58 | printf("Code looks good.\n"); 59 | return 0; 60 | } 61 | --------------------------------------------------------------------------------