A calculator includes: registers each including sub-registers that hold pieces of data for use in operation; an operator that executes, in parallel, operations of the pieces of data; and a memory configured to hold a first vector and second vectors to be compared with the first vector. Each second vector is divided into sub-vectors and sub-vector groups each including the sub-vectors of the second vectors are arranged in units of sub-vector groups. A first process of transferring one of sub-vectors of the first vector to sub-registers of a first register among the registers, a second process of transferring the sub-vector group of the second vectors corresponding to the transferred sub-vector of the first vector to sub-registers of a second register, the sub-vector group being held in the memory, and a third process of calculating and integrating numbers of mismatches between bit values of the sub-vectors held are repeatedly executed.

Various embodiments include a modulo operation generator associated with a cache memory in a computer-based system. The modulo operation generator generates a first sum by performing an addition and/or a subtraction function on an input address. A first portion of the first sum is applied to a lookup table that generates a correction value. The correction value is then added to a second portion of the first sum to generate a second sum. The second sum is adjusted, as needed, to be less than the divisor. The adjusted second sum forms a residue value that identifies a cache memory slice in which the input data value corresponding to the input address is stored. By generating the residue value in this manner, the cache memory efficiently distributes input data values among the slices in a cache memory even when the number of slices is not a power of two.

Various embodiments include a modulo operation generator associated with a cache memory in a computer-based system. The modulo operation generator generates a first sum by performing an addition and/or a subtraction function on an input address. A first portion of the first sum is applied to a lookup table that generates a correction value. The correction value is then added to a second portion of the first sum to generate a second sum. The second sum is adjusted, as needed, to be less than the divisor. The adjusted second sum forms a residue value that identifies a cache memory slice in which the input data value corresponding to the input address is stored. By generating the residue value in this manner, the cache memory efficiently distributes input data values among the slices in a cache memory even when the number of slices is not a power of two.

A binary logic circuit for determining the ratio x/d where x is a variable integer input, the binary logic circuit comprising: a logarithmic tree of modulo units each configured to calculate x[a:b]mod d for respective block positions a and b in x where b>a with the numbering of block positions increasing from the most significant bit of x up to the least significant bit of x, the modulo units being arranged such that a subset of M−1 modulo units of the logarithmic tree provide x[0:m]mod d for all m∈{1, M}, and, on the basis that any given modulo unit introduces a delay of 1: all of the modulo units are arranged in the logarithmic tree within a delay envelope of ┌log .sub.2M┐; and more than M−2.sup.u of the subset of modulo units are arranged at the maximal delay of ┌log .sub.2M┐, where 2.sup.u is the power of 2 immediately smaller than M.

A hardware logic representation of a circuit to implement an operation to perform multiplication by an invariant rational is generated by truncating an infinite single summation array (which is represented in a finite way). The truncation is performed by identifying a repeating section and then discarding all but a finite number of the repeating sections whilst still satisfying a defined error bound. To further reduce the size of the summation array, the binary representation of the invariant rational is converted into canonical signed digit notation prior to creating the finite representation of the infinite array.

A method, performed by a computing device, includes (a) building a data structure that describes dependence relationships between components of a virtual appliance, the components comprising respective computational processes which may be invoked during booting, a dependence relationship indicating that one component must complete before a second component may be invoked, (b) identifying, with reference to the data structure and an essential set of components which were pre-defined to be essential to the virtual appliance, a set of components that must complete for booting to be considered finished, and, after identifying the required set of components, repeatedly (c) querying each required component for its respective completion status, (d) calculating an estimated completion percentage for booting the virtual appliance with reference to the respective completion statuses of each required component versus all required components, and (e) displaying an indication of the completion percentage to a user via a user interface.

An arithmetic processing method is provided using a binary fixed-point arithmetic processing circuit to carry out an operation of multiplicatively dividing a dividend by a divisor. The method comprises shifting the divisor by a specific number of bits when the absolute value of the divisor is within a specific range, and holding the divisor without shifting the divisor when the absolute value of the divisor is out of the specific range, acquiring an initial value of approximation calculation for the divisor that is shifted or held without being shifted, calculating a reciprocal of the divisor by performing asymptotic approximation of the acquired initial value more than once, and calculating a product of the calculated reciprocal and the dividend, and shifting the calculated product by the specific number of bits when the divisor is shifted.

An arithmetic processing method is provided using a binary fixed-point arithmetic processing circuit to carry out an operation of multiplicatively dividing a dividend by a divisor. The method comprises shifting the divisor by a specific number of bits when the absolute value of the divisor is within a specific range, and holding the divisor without shifting the divisor when the absolute value of the divisor is out of the specific range, acquiring an initial value of approximation calculation for the divisor that is shifted or held without being shifted, calculating a reciprocal of the divisor by performing asymptotic approximation of the acquired initial value more than once, and calculating a product of the calculated reciprocal and the dividend, and shifting the calculated product by the specific number of bits when the divisor is shifted.

A device is provided. In some examples, the device includes a division logic circuit having input lines including a first least significant input line. The division logic circuit further includes temporary output lines including a second least significant line. The device also includes a first multiplexer having a first data input coupled to the first least significant input line. The first multiplexer further includes a second data input coupled to the second least significant line.

A device is provided. In some examples, the device includes a division logic circuit having input lines including a first least significant input line. The division logic circuit further includes temporary output lines including a second least significant line. The device also includes a first multiplexer having a first data input coupled to the first least significant input line. The first multiplexer further includes a second data input coupled to the second least significant line.