Toeplitz Hash Algorithm
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Toeplitz Hash Algorithm
The Toeplitz Hash Algorithm describes hash functions that compute hash values through matrix multiplication of the key with a suitable Toeplitz matrix. The Toeplitz Hash Algorithm is used in many network interface controllers for receive side scaling. As an example, with the Toeplitz matrix T the key k results in a hash h as follows: :h = T\cdot k = \begin1 & 1 & 0 & 1 \\0 & 1 & 1 & 0 \\1 & 0 & 1 & 1 \\\end \cdot \begin1\\1\\0\\0\\\end = \begin0 \\1 \\1 \\\end where the entries are bits and all operations are modulo 2. In implementations the highly redundant matrix is not necessarily explicitly stored. References Hash functions {{compu-prog-stub ...
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Scalable Networking Pack
Scalable Networking Pack (SNP) is a set of additions that adds new features to Microsoft's Windows Server 2003 Service Pack 1 or later with architectural enhancements and APIs to support the new capabilities of network acceleration and hardware-based offload technologies. Features * ''TCP chimney offload'' provides seamlessly integrated support for network adapters with TCP offload engines (TOE) * ''Receive-side scaling A network interface controller (NIC, also known as a network interface card, network adapter, LAN adapter or physical network interface, and by similar terms) is a computer hardware component that connects a computer to a computer network. Ear ...'' dynamically load-balances inbound network connections across multiple processors or cores * ''NetDMA'' enables support for advanced direct memory access technologies, such as Intel I/O Acceleration Technology (Intel I/OAT) References External linksMicrosoft Scalable Networking
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Hash Function
A hash function is any function that can be used to map data of arbitrary size to fixed-size values. The values returned by a hash function are called ''hash values'', ''hash codes'', ''digests'', or simply ''hashes''. The values are usually used to index a fixed-size table called a ''hash table''. Use of a hash function to index a hash table is called ''hashing'' or ''scatter storage addressing''. Hash functions and their associated hash tables are used in data storage and retrieval applications to access data in a small and nearly constant time per retrieval. They require an amount of storage space only fractionally greater than the total space required for the data or records themselves. Hashing is a computationally and storage space-efficient form of data access that avoids the non-constant access time of ordered and unordered lists and structured trees, and the often exponential storage requirements of direct access of state spaces of large or variable-length keys. Use of ...
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Matrix Multiplication
In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices and is denoted as . Matrix multiplication was first described by the French mathematician Jacques Philippe Marie Binet in 1812, to represent the composition of linear maps that are represented by matrices. Matrix multiplication is thus a basic tool of linear algebra, and as such has numerous applications in many areas of mathematics, as well as in applied mathematics, statistics, physics, economics, and engineering. Computing matrix products is a central operation in all computational applications of linear algebra. Notation This article will use the following notati ...
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Toeplitz Matrix
In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to right is constant. For instance, the following matrix is a Toeplitz matrix: :\qquad\begin a & b & c & d & e \\ f & a & b & c & d \\ g & f & a & b & c \\ h & g & f & a & b \\ i & h & g & f & a \end. Any ''n'' × ''n'' matrix ''A'' of the form :A = \begin a_0 & a_ & a_ & \cdots & \cdots & a_ \\ a_1 & a_0 & a_ & \ddots & & \vdots \\ a_2 & a_1 & \ddots & \ddots & \ddots & \vdots \\ \vdots & \ddots & \ddots & \ddots & a_ & a_ \\ \vdots & & \ddots & a_1 & a_0 & a_ \\ a_ & \cdots & \cdots & a_2 & a_1 & a_0 \end is a Toeplitz matrix. If the ''i'', ''j'' element of ''A'' is denoted ''A''''i'', ''j'' then we have :A_ = A_ = a_. A Toeplitz matrix is not necessarily square. Solving a Toeplitz system A matrix equation of the form :Ax = b is called a Toeplitz system ...
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Network Interface Controller
A network interface controller (NIC, also known as a network interface card, network adapter, LAN adapter or physical network interface, and by similar terms) is a computer hardware component that connects a computer to a computer network. Early network interface controllers were commonly implemented on expansion cards that plugged into a computer bus. The low cost and ubiquity of the Ethernet standard means that most newer computers have a network interface built into the motherboard, or is contained into a USB-connected dongle. Modern network interface controllers offer advanced features such as interrupt and DMA interfaces to the host processors, support for multiple receive and transmit queues, partitioning into multiple logical interfaces, and on-controller network traffic processing such as the TCP offload engine. Purpose The network controller implements the electronic circuitry required to communicate using a specific physical layer and data link layer standard such ...
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