摘要:
A method and apparatus (20) for performing cryptographic computations employing recursive algorithms to accelerate multiplication and squaring operations. Products and squares of long integer values (24) are recursively reduced to a combination of products and squares reduced-length integer values in a host processor (22). The reduced-length integer values are passed to a co-processor (24). The values may be randomly ordered to prevent disclosure of secret data.
摘要:
Rounding error can be reduced when evaluating binary floating point polynomials utilizing a Floating Point Unit (58) by first computing the sum of products of second and higher order polynomial terms. Next, the Floating Point Unit (58) adds a zero th level term to the product of a first order coefficient and an independent variable to form a "Big" term. The Floating Point Unit (58) calculates as a "Little" term the rounding error resulting from the computation of the "Big" term. The "Little" term is then added to the sum of products of higher order terms to form an "Intermediate" term. Finally, the Floating Point Unit (58) adds the "Big" term to the "Intermediate" term to form the polynomial result corrected by the rounding error introduced by the computation of the low order terms.
摘要:
The method and circuit find the reciprocal value of an input vector signal. The level of the input vector signal (X + jY) is first reduced to (X + jY)/ 2 in an overflow-preventing circuit. A power calculating circuit squares and adds the components of the level-reduced input vector signal, thereby obtaining a power value (X² + Y²)/2 . An initial value of a tap value (K), which represents the reciprocal value to be found, is multiplied twice by a multiplying circuit, thereby obtaining K²(X + Y)²/2 . Further, a differential circuit obtains an error signal (ΔK) = 1/2 - K²(X² + Y²)/2 by subtraction from a reference value. An updating circuit updates the tap value (K) by adding to it the error signal (ΔK). A loop consisting of the multiplication of the tap value, differential operation, and updating of the tap value, is repeated until the error signal (ΔK) is reduced to less than or equal to a predetermined value. The tap value (K) thus obtained is the desired reciprocal value 1/√(X² + Y²) of the amplitude of the input vector signal. The method and circuit can be used for amplitude normalization in a modem, for example.
摘要:
This vector magnitude approximating method uses logarithms of vector's orthogonal components to select multiplier scaling constants (K x ,K y ) and to minimize arithmetic-function and hardware complexity. The vector magnitude is approximated by multiplying (20,22) each component (X,Y) of a complex number representing the vector by selected scaling constants (K x ,K y ) and then by summing (24) the two resulting products (K x X,K y Y). The scaling constants (K x ,K y ) are selected by feeding each orthogonal component (X,Y) into one of two identical logic arrays (10,12) which determine the base-2 logarithm of the absolute value of each component. The resulting logarithm values are fed, in parallel, into a third logic array (14) which outputs an address to real and imaginary constant read-only memory generators (16,18) for providing respective scaling constant pairs (K x ,K y ) which are used in computing the approximate magnitude of the vector or complex number. The apparatus is particularly applicable to a high-throughput, pipelined, digital signal processing application such as radar.
摘要:
The present application relates to a device and method for processing a digital value to thereby determine an estimate of the square of said digital value. This is done by linearly approximating the square function with the help of anchor points that are powers of 2, such that the estimate of the square of a digital value xa is determined on the basis of a first processing value 2i, where 2i ≤x¿a? ∫2?i+1¿, and a second processing value (3x¿a? - 2?i+1¿). The present invention is advantageous in that it allows simple processing steps and a simple processing hardware. It is preferably applied to the mean signal power estimation of a digital signal being sent to a transmitter.
摘要:
A cable modem (20) having a blind equalizer (40) in its equalization function (28) is disclosed. The blind equalizer (40) includes an adaptive equalizer (44) and an approximating update function (42) that provides updated equalization coefficients to the adaptive equalizer (44) using the Constant Modulus Algorithm, wherein the error in the adaptive equalizer output is estimated. The estimates are based upon a determination of the maximum and minimum of the real and imaginary components of symbols output by the adaptive equalizer (44). Efficiency in the computations required for updating the equalizer coefficients is obtained, without sacrificing convergence.
摘要:
The present application relates to a device and method for processing a digital value to thereby determine an estimate of the square of said digital value. This is done by linearly approximating the square function with the help of anchor points that are powers of 2, such that the estimate of the square of a digital value xa is determined on the basis of a first processing value 2i, where 2i ≤x¿a? ∫2?i+1¿, and a second processing value (3x¿a? - 2?i+1¿). The present invention is advantageous in that it allows simple processing steps and a simple processing hardware. It is preferably applied to the mean signal power estimation of a digital signal being sent to a transmitter.