Grid encryption method and device based on filling curve

Abstract

The invention relates to a grid encryption method and device based on a filling curve, and the method comprises the steps: employing an SIMD instruction to accelerate the coordinates of a calculation unit, then employing a parent element of the calculation unit, including the subordinate level of the parent element of the calculation unit, the coordinates of an anchor point of the parent element, the type of the parent element, and a subunit of the calculation unit, comprising the steps of calculating coordinates and levels of anchor points of subunits, mapping grid units in a high-dimensional space to a one-dimensional index by fully utilizing a filling curve technology, quickly realizing encryption of the grid units, and processing a plurality of grid units through an SIMD technology, so that the calculation efficiency is greatly improved.

Description

Technical Field

[0001] The invention belongs to the technical field of grid data processing, and relates to a grid encryption method and device based on a filling curve. Background Art

[0002] Numerical solution of partial differential equations has a wide range of applications in academia and industrial computing. Most numerical solution methods (including finite difference, finite volume method, etc.) use grids to discretize the computational domain. One of the core technologies to improve the performance of numerical simulation is grid encryption. Filling curves are a special type of continuous mapping that maps points in one-dimensional space to points in high-dimensional space and maintains spatial proximity to a certain extent. Common filling curves include Hilbert curves and Z curves. The application of filling curves in grid generation is mainly reflected in technical fields such as grid encryption, grid sorting and optimization, and parallel computing.

[0003] Mesh encryption plays an important role in numerical simulation. By increasing the mesh density in the area of ​​interest, mesh adaptive encryption ensures both the accuracy and efficiency of the calculation results. Mesh adaptive encryption is widely used in technical fields such as computational fluid dynamics (CFD) and electromagnetic simulation. Nevertheless, there are still several challenges in adaptive mesh encryption. For example, the mesh encryption process must ensure mesh quality and consistency, especially in parallel computing environments. In addition, efficiently handling data migration and synchronization in distributed memory systems remains a complex task. Therefore, studying how to quickly achieve mesh encryption remains one of the technical issues to be solved. Summary of the invention

[0004] In view of the problems existing in the above-mentioned traditional technology, the present invention proposes a mesh encryption method based on a filling curve and a mesh encryption device based on a filling curve, which can quickly realize mesh encryption.

[0005] In order to achieve the above objectives, the embodiments of the present invention adopt the following technical solutions: In one aspect, a mesh encryption method based on a filling curve is provided, comprising the steps of: Loading the grid cells to be processed; the grid cells to be processed include two-dimensional cells and three-dimensional cells; Calculate the fill curve index of the cell for the grid cell; According to the encryption rule and the filling curve index of the cell, the coordinates of the cell are calculated using SIMD instructions; Calculate the parent element of the cell according to the coordinates of the cell; calculating the parent element of the cell includes calculating the type of the parent element, the coordinates of the anchor point of the parent element and the level to which it belongs; According to the parent element of the cell obtained by calculation, the child unit of the cell is calculated, and the mesh encryption of the mesh cell to be processed is completed; the child unit of the cell is calculated including the coordinates of the anchor point of the child unit and the level to which it belongs.

[0006] On the other hand, a grid encryption device based on a filling curve is also provided, comprising: A unit loading module is used to load the grid units to be processed; the grid units to be processed include two-dimensional units and three-dimensional units; An index calculation module, used to calculate the filling curve index of the grid cell; A cell coordinate calculation module, used to calculate the coordinates of the cell using SIMD instructions according to the encryption rule and the filling curve index of the cell; A parent element calculation module is used to calculate the parent element of a cell according to the coordinates of the cell; calculating the parent element of a cell includes calculating the type of the parent element, the coordinates of the anchor point of the parent element and the level to which it belongs; The sub-unit calculation module is used to calculate the sub-units of the unit according to the parent element of the unit obtained by calculation, and complete the grid encryption of the grid unit to be processed; the sub-units of the unit are calculated including the coordinates of the anchor point of the sub-unit and the level to which it belongs.

[0007] One of the above technical solutions has the following advantages and beneficial effects: The above-mentioned grid encryption method and device based on filling curves, by using SIMD instructions to accelerate the calculation of the coordinates of the cell and then calculate the parent element of the cell, including the level to which the parent element of the cell belongs, the coordinates of the anchor point of the parent element and the type of the parent element, and then calculate the child unit of the cell, including the coordinates and level to which the anchor point of the child unit belongs. The filling curve technology is fully utilized to map the grid cells in the high-dimensional space to a one-dimensional index, and the encryption of the grid cells is quickly realized. Multiple grid cells are processed by SIMD technology, which greatly improves the computing efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the conventional technology, the drawings required for use in the embodiments or the conventional technology descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0009] Figure 1 A schematic diagram of a flow chart of a mesh encryption method based on a filling curve in one embodiment; Figure 2 A schematic diagram of a car model and encrypted visualization in one embodiment, wherein: Figure 2 (a) is a car model. Figure 2(b) Visualization result of mesh encryption for the car model; Figure 3 A rabbit model and encrypted visualization diagram in one embodiment, wherein: Figure 3 (a) is the rabbit model. Figure 3 (b) Visualization result of mesh encryption of rabbit model; Figure 4 A schematic diagram of a module framework of a grid encryption device based on a filling curve in an embodiment. DETAILED DESCRIPTION

[0010] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with the accompanying drawings and Examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those generally understood by those skilled in the art of the present invention. The terms used in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0011] It should be noted that the reference to "embodiment" in this article means that the specific features, structures or characteristics described in conjunction with the embodiment may be included in at least one embodiment of the present invention. The presentation of this phrase at various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It will be appreciated by those skilled in the art that the embodiments described herein may be combined with other embodiments. The term "and / or" used in the specification and appended claims of the present invention refers to any combination of one or more of the associated listed items and all possible combinations, and includes these combinations.

[0012] The following will describe the implementation of the present invention in detail with reference to the accompanying drawings in the embodiment diagram of the present invention.

[0013] By sorting the grid cells through the filling curve, the areas that need to be refined or coarsened can be quickly marked. At the same time, the locality of the filling curve can be used to balance the workload of each computing node as much as possible.

[0014] In one embodiment, Figure 1 As shown, a mesh encryption method based on a filling curve is provided, which may include the following steps S10 to S16: S10, loading the mesh units to be processed; the mesh units to be processed include two-dimensional units and three-dimensional units, which may be units on various geometric models to be processed.

[0015] S11, calculate the filling curve index of the grid cell.

[0016] It can be understood that an encrypted grid is constructed first. Specifically, the grid units to be processed include two-dimensional units and three-dimensional units. For 2D (two-dimensional) units, four sub-units can be constructed by connecting the midpoints of each edge to obtain an encrypted grid of the 2D unit. For 3D (three-dimensional) units, they can be processed according to the construction rule of cutting along the midline of each vertex to form four sub-units and dividing the remaining part along the diagonal to form a total of eight sub-units. After construction processing according to this construction rule, an encrypted grid of the 3D unit can be obtained.

[0017] Then calculate the cell index. Specifically, according to the given encryption rule, for any cell of the encrypted grid T l , which consists of units T 0 (The initial grid obtained by reading the grid file) l The unit is encrypted T l The level is l . For any unit, compare the coordinates of each vertex of the unit, and call the vertex with the smallest coordinate components the anchor point. In 2D space, the unit square can be divided into 2 different types of triangles, which can be represented by the numbers 0 and 1. They share the edge from (0,0) to (1,1). In 3D space, the unit cube can be divided into 6 different types of tetrahedrons, which can be represented by the numbers 0-5 respectively. They all share the edge from (0,0,0) to (1,1,1). Therefore, for any level l Unit T , the index of its fill curve I ( T ) can be uniquely determined by formula (1): (1) in, Z , Y and X Respectively represent units T The coordinate components of the anchor point, is the bit interleaver, B Indicated by unit T The ancestor type is composed of l Tuple.

[0018] S12, using SIMD instructions to calculate the coordinates of the cell according to the encryption rule and the filling curve index of the cell.

[0019] It can be understood that the coordinates are initialized first. According to the given encryption rules, any unit is obtained by shrinking and translating its parent element, and the coordinates of the anchor point of the unit can be obtained in the process of the filling curve index of the above-mentioned calculation unit. Combining the two and introducing SIMD can quickly calculate the vertex coordinates of each unit. The coordinates of the anchor point of any unit and the remaining vertices (initialized to 0) are loaded into the vector register by using the SIMD instruction __mm_set_ps. Among them, __mm_set_ps is an intrinsic function provided by the SSE instruction set, which is used to initialize a 128-bit register __m128 containing 4 single-precision floating-point numbers (32-bit floating-point numbers of the IEEE754 standard). In the SIMD architecture, the __m128 type register can store and process 4 single-precision floating-point numbers at the same time, thereby realizing data-level parallelism.

[0020] Then we enter the calculation phase and use SIMD instructions to perform addition calculations. To do this, we first pass through the level of the current unit l and the maximum level of the grid L Calculate the scaling factor for this unit h ,Right now h =2 (L-l) ; Secondly, the coordinate components of the vertices to be calculated are determined by the type of tetrahedron i , j , the calculation formula is as follows: (2) (3) in, T.type Indicates the type of unit. Finally, the parallel vector is updated. The SIMD instruction __mm_add_ps is used to parallelize the subsequent coordinates. The calculation formula can be as follows: (4) in, and Respectively represent the i Peace j dimensional unit vector, x [0] indicates the coordinates of the anchor point. If it is a 2D unit, there is no need to calculate the coordinates. x [3], [ ] T Indicates transpose. __mm_add_ps is a single instruction multiple data instruction in the SSE instruction set, which is used to perform parallel addition operations on four single-precision floating-point numbers in two 128-bit XMM registers. That is, it can add the floating-point numbers in corresponding positions in the two registers at the same time, completing the addition operation of four groups of floating-point numbers at a time, greatly improving the data processing efficiency. It is suitable for scenarios that require a large number of floating-point numbers to be calculated in parallel, such as vector and matrix operations in computer graphics, data processing in scientific computing, etc.

[0021] S14, calculating the parent element of the cell according to the coordinates of the cell; this includes calculating the type of the parent element, the coordinates of the anchor point, and the level to which it belongs.

[0022] It can be understood that the level of the unit minus 1 is the parent element level. The type of the parent element of a unit is uniquely determined by the type of the cube where the unit is located and the type of the unit itself. To this end, the type of the cube where the unit is located must be calculated first. For any unit, the corresponding cube type can be obtained by formula (5).

[0023] (5) in, Tx , Ty and Tz They represent the coordinate components of the anchor point of unit T, ∧ represents the bitwise AND operation, h =2 (L -l) After that, the coordinates of the anchor point of the cell and the level at which it is located are used to calculate the coordinates of the anchor point of the parent element. The calculation formula is as follows: (6) in, Px , Py and Pz Respectively represent the coordinate components of the parent element's anchor point, Indicates the bitwise inversion operation. H =2 (L-T.l) If it is a 2D unit, no calculation is required Pz .

[0024] S16, according to the parent element of the cell obtained by calculation, the child cells of the cell are calculated to complete the mesh encryption of the mesh cell to be processed; this includes calculating the coordinates of the anchor point of the child cell and the level to which it belongs.

[0025] It can be understood that the level of the unit plus 1 is the sub-unit level. The coordinates of the anchor point of the sub-unit can be obtained through the coordinates of the anchor point of the parent element. The calculation formula can be as follows: (7) in, Indicates e The coordinates of the anchor points of the subunits, e ∈{0,…,7}, x [ j e] can be calculated by formula (4). The SIMD broadcast instruction _mm256_set1_ps is used to load the coordinates of the parent element's anchor point into the register, and the SIMD instruction ___mm256_i32gather_ps is used to extract the coordinates of the sub-unit from the vertex coordinate array of the parent element by index. Then, the mean coordinates of the eight sub-units are calculated in parallel through vector addition and vector multiplication operations. In this way, eight sub-unit data are processed each time, further improving the overall processing performance.

[0026] The above-mentioned grid encryption method based on filling curves, by using SIMD instructions to accelerate the calculation of the coordinates of the cell and then calculate the parent element of the cell, including the level to which the parent element of the cell belongs, the coordinates of the anchor point of the parent element and the type of the parent element, and then calculates the child unit of the cell, including the coordinates and the level to which the anchor point of the child unit belongs. It makes full use of the filling curve technology, maps the grid cells in the high-dimensional space to the one-dimensional index, quickly realizes the encryption of the grid cells, and processes multiple grid cells through SIMD technology, thereby greatly improving the computing efficiency.

[0027] In one embodiment, regarding the above step S11, SIMD acceleration technology is used to efficiently calculate the filling curve index of the unit.

[0028] Specifically, SIMD (Single Instruction Multiple Data, a parallel processing technology in computer architecture) can be used to generate the filling curve. This embodiment uses SIMD acceleration technology to efficiently calculate the filling curve index of the unit. For the implementation of bit interleaving, specifically, let the coordinate component Z Keep the lowest position, Y The coordinate components are shifted left by 1. X The bits are shifted left by 2 bits, and the displacement is realized by __mm_slli_epi32. After that, they are merged by __mm_or_si128. Finally, B Direct and interleaved Z , Y , X Merge, and use the shift operation to B Fill in the bits.

[0029] Among them, _mm_slli_epi32 is an intrinsic function of the SSE (Streaming SIMD Extension) instruction set, which is used to perform a logical left shift operation on four 32-bit signed integers in a 128-bit register. _mm is the common prefix of these intrinsic functions, indicating that the SSE instruction set is used to operate on 128-bit registers, slli stands for Signed Logical Left Immediate, and epi32 indicates that the data type of the operation is a 32-bit signed integer. _mm_or_si128 is also an intrinsic function of the SSE instruction set, which is used to perform a bitwise OR operation on the data in two 128-bit registers. It will OR the bits in the corresponding positions of the two 128-bit registers, and the result is stored in a new 128-bit register.

[0030] In one embodiment, regarding the above step S12, in the process of using SIMD instructions to calculate the coordinates of the calculation unit, a SIMD instruction __mm_store__ps is used to write the calculation result of the coordinates of the calculation unit into the memory.

[0031] It can be understood that at the end of the above step S12, the storage stage can also be entered, and the calculation results of the previous calculation stage can be written to the memory using the SIMD instruction __mm_store__ps to persist the calculation results, so as to facilitate the calculation and use of subsequent steps. By introducing SIMD technology to batch process multiple coordinate dimensions at the same time, the processing efficiency is significantly improved. Among them, __mm_store__ps is an instruction for storing data in the SSE instruction set, which stores 4 single-precision floating-point numbers in the 128-bit XMM register (__m128 type) to the specified address in the memory.

[0032] In one embodiment, in the above step S14, SIMD instructions are used to accelerate the calculation process.

[0033] It can be understood that in the above step S14, SIMD instructions can also be used to accelerate the above calculation process. Specifically, each coordinate dimension is a group, and the anchor point coordinates are loaded by SIMD instructions ___mm256___loadu___si256, and SIMD instructions mm256_and_si256 and h Perform a bitwise AND operation and finally update it through the SIMD instruction _mm256bendv___epi8 k . Use SIMD instruction ___mm256_sllv_epi32 to calculate bitwise left shift H , use SIMD instruction mm256_xorsi256 to take XOR bit by bit, and get Finally, the SIMD instruction _mm256___and _si256 is used to implement the bitwise AND operation to obtain the coordinates of the parent element's anchor point. Since all calculations are vectorized bitwise operations, there is no complex conditional judgment. The coordinate calculation of the parent element of the vectorized processing unit further greatly improves the calculation efficiency.

[0034] In some embodiments, Figure 2 and Figure 3 As shown in the figure, the number of meshes obtained after reading the corresponding .brep file and .msh file for the two geometric models are as follows: Figure 2 There are 17,479 units. Figure 3 There are 16,463 units. Figure 2 (a) is a car model. Figure 2 (b) Visualization result of mesh encryption of the car model. Figure 3 (a) is the rabbit model. Figure 3 (b) Visualization of mesh encryption results for the rabbit model. For the car model, it takes 3.7 seconds to encrypt 4.5 billion meshes on 1,200 processes; for the rabbit model, which has a large number of initial meshes and a more complex model, it only takes 3.9 seconds to encrypt 4.3 billion meshes. It can be seen that the above scheme increases the mesh size while greatly reducing the calculation time.

[0035] It should be understood that although Figure 1 The steps in the method are shown in sequence as indicated by the arrows, but the steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of the steps, and the steps can be executed in other orders. Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequentially, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0036] In one embodiment, Figure 4As shown, a grid encryption device 100 based on a filling curve is provided, which may include a unit loading module 11, an index calculation module 13, a unit coordinate calculation module 15, a parent element calculation module 17, and a sub-unit calculation module 19. Among them, the unit loading module 11 is used to load the grid unit to be processed; the grid unit to be processed includes a two-dimensional unit and a three-dimensional unit. The index calculation module 13 is used to calculate the filling curve index of the grid unit. The unit coordinate calculation module 15 is used to calculate the coordinates of the unit using SIMD instructions according to the encryption rule and the filling curve index of the unit. The parent element calculation module 17 is used to calculate the parent element of the unit according to the coordinates of the unit; calculating the parent element of the unit includes calculating the type of the parent element, the coordinates of the anchor point of the parent element, and the level to which it belongs. The sub-unit calculation module 19 is used to calculate the sub-units of the unit according to the parent element of the unit obtained by calculation, and complete the grid encryption of the grid unit to be processed; calculating the sub-units of the unit includes calculating the coordinates of the anchor point of the sub-unit and the level to which it belongs.

[0037] The above-mentioned grid encryption device 100 based on filling curves, by using SIMD instructions to accelerate the calculation of the coordinates of the cells and then calculates the parent elements of the cells, including the level to which the parent elements of the cells belong, the coordinates of the anchor points of the parent elements, and the type of the parent elements, and then calculates the child units of the cells, including the coordinates and levels to which the anchor points of the child units belong. It makes full use of the filling curve technology, maps the grid cells in the high-dimensional space to one-dimensional indexes, quickly realizes the encryption of the grid cells, and processes multiple grid cells through SIMD technology, thereby greatly improving the computing efficiency.

[0038] In one embodiment, the index calculation module 13 uses SIMD acceleration technology to efficiently calculate the filling curve index of the unit.

[0039] In one embodiment, when the unit coordinate calculation module 15 uses SIMD instructions to calculate the coordinates of the unit, the SIMD instruction __mm_store__ps is used to write the calculation result of the coordinates of the unit into the memory.

[0040] In one embodiment, the parent element calculation module 17 uses SIMD instructions to accelerate the calculation process.

[0041] It can be understood that the explanation of each feature in the above-mentioned grid encryption device 100 based on the filling curve can be understood in the same way as the corresponding explanation in each embodiment of the above-mentioned grid encryption method based on the filling curve. Each module in the above-mentioned grid encryption device 100 based on the filling curve can be fully or partially implemented by software, hardware and a combination thereof. The above-mentioned components can be embedded in or independent of a device with data processing functions in the form of hardware, or can be stored in the memory of the aforementioned device in the form of software, so that the processor can call and execute the operations corresponding to the above modules. The aforementioned device can be, but is not limited to, various types of data processing computers already available in the art.

[0042] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided by the present invention can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus dynamic random access memory (RambusDRAM, referred to as RDRAM) and interface dynamic random access memory (DRDRAM).

[0043] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0044] The above embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of protection of the invention. It should be pointed out that, for those of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the attached claims.

Claims

1. A mesh encryption method based on a filling curve, characterized in that: Includes steps: Loading grid cells to be processed; the grid cells to be processed include two-dimensional cells and three-dimensional cells; Calculating a fill curve index of the cell for the grid cell; According to the encryption rule and the filling curve index of the cell, the coordinates of the cell are calculated using SIMD instructions; Calculate the parent element of the cell according to the coordinates of the cell; calculating the parent element of the cell includes calculating the type of the parent element, the coordinates of the anchor point of the parent element and the level to which it belongs; According to the parent element of the cell obtained by calculation, the child element of the cell is calculated, and the grid encryption of the grid cell to be processed is completed; The sub-unit of the calculation unit includes the coordinates of the anchor point of the calculation sub-unit and the level to which it belongs.

2. The mesh encryption method based on filling curve according to claim 1, characterized in that: In the step of calculating the filling curve index of the grid unit, SIMD acceleration technology is used to efficiently calculate the filling curve index of the unit.

3. The mesh encryption method based on filling curve according to claim 1 or 2, characterized in that: In the process of using SIMD instructions to calculate the coordinates of the unit, the SIMD instruction __mm_store__ps is used to write the calculation results of the coordinates of the calculation unit into the memory.

4. The mesh encryption method based on filling curve according to claim 3 is characterized in that: In the process of calculating the parent element of a cell according to the coordinates of the cell, SIMD instructions are used to accelerate the calculation process.

5. A grid encryption device based on a filling curve, characterized in that: include: A unit loading module is used to load the grid units to be processed; The grid cells to be processed include two-dimensional cells and three-dimensional cells; An index calculation module, used for calculating the filling curve index of the grid cell; A cell coordinate calculation module, used to calculate the coordinates of the cell using SIMD instructions according to the encryption rule and the filling curve index of the cell; A parent element calculation module is used to calculate the parent element of a cell according to the coordinates of the cell; calculating the parent element of a cell includes calculating the type of the parent element, the coordinates of the anchor point of the parent element and the level to which it belongs; A sub-unit calculation module, used for calculating the sub-units of the unit according to the parent element of the unit obtained by calculation, and completing the grid encryption of the grid unit to be processed; The sub-unit of the calculation unit includes the coordinates of the anchor point of the calculation sub-unit and the level to which it belongs.

6. The grid encryption device based on filling curve according to claim 5, characterized in that: The index calculation module uses SIMD acceleration technology to efficiently calculate the filling curve index of the unit.

7. The grid encryption device based on filling curve according to claim 5 or 6, characterized in that: In the process of the unit coordinate calculation module using SIMD instructions to calculate the coordinates of the unit, the SIMD instruction __mm_store__ps is used to write the calculation result of the coordinates of the calculation unit into the memory.

8. The grid encryption device based on filling curve according to claim 7, characterized in that: The parent element calculation module uses SIMD instructions to accelerate the calculation process.

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