Abstract: A method of image compression, including, receiving at least one unprocessed image frame, transforming a domain of the at least one unprocessed image frame to output a transformed domain dataset, block processing the transformed domain dataset to yield a blocked dataset, quantizing the blocked dataset to produce a quantized dataset and entropy encoding the quantized dataset to construct at least one compressed image frame.

Abstract: A processor for a cryptosystem. The processor comprises a hybrid processor architecture including a hardware processor, a software processor and an interconnection interface arranged to exchange data between the hardware processor and the software processor; wherein the hardware processor comprises a plurality of hardware accelerator modules arranged to perform computational tasks including at least one of number theoretic transforms (NTT) computation, arithmetic operations which are more time-consuming when being performed instead by the software-processor.

Abstract: A method is provided that includes performing, by a processor in response to a vector matrix multiply instruction, multiplying an m×n matrix (A matrix) and a n×p matrix (B matrix) to generate elements of an m×p matrix (R matrix), and storing the elements of the R matrix in a storage location specified by the vector matrix multiply instruction.

Abstract: A method, decoder, and program code for controlling a concealment method for a lost audio frame is provided. A first audio frame and a second audio frame of the received audio signal are decoded to obtain modified discrete cosine transform (MDCT) coefficients. Values of a first spectral shape based upon the MDCT coefficients decoded from the first audio frame decoded and values of a second spectral shape based upon MDCT coefficients decoded from the second audio frame decoded are determined, the spectral shapes each comprising a number of sub-bands. The values of the spectral shapes and frame energies of the first audio frame and second audio frame are transformed into representations of FFT based spectral analyses. A transient condition is detected based on the representations of the FFTs. Responsive to detecting the transient condition, the concealment method is modified by selectively adjusting a spectrum magnitude of a substitution frame spectrum.

Abstract: A non-volatile memory device includes a memory cell array to which an arithmetic internal data is written; and an arithmetic circuitry configured to receive an arithmetic input data and the arithmetic internal data for an arithmetic operation of a neural network with the arithmetic internal data and the arithmetic input data in response to an arithmetic command, perform the arithmetic operation using the arithmetic internal data and the arithmetic input data to generate an arithmetic result data, and output the arithmetic result data of the arithmetic operation of the neural network.

Abstract: An apparatus for generating an encoded signal includes: a window sequence controller for generating a window sequence information for windowing an audio or image signal, the window sequence information indicating a first window for generating a first frame of spectral values, a second window function and at least one third window function for generating a second frame of spectral values, wherein the first window function, the second window function and the one or more third window functions overlap within a multi-overlap region; a preprocessor for windowing a second block of samples corresponding to the second window function and the at least one third window functions using an auxiliary window function to acquire a second block of windowed samples, a spectrum converter for applying an aliasing-introducing transform; and a processor for processing the first frame and the second frame to acquire encoded frames of the audio or image signal.

Abstract: A method for replaying a vector image. The method includes: (a) extracting replay information and work environment information of each of the vector lines from an original vector image; (b) receiving a selection of regions of specific vector lines from a user; (c) changing and updating replay settings of the vector lines selected in step (b); (d) replaying the vector image selected by the user; and (e) storing the updated information of the vector image or ending the method for replaying the vector image. Therefore, it is possible to sequentially store every step of drawing work and even a work environment, in addition to vector line information, and replay the stored vector image, as if a scene in which an actual artist was drawing a picture were recorded, while breaking away from the conventional batch replay method of a vector image.

Abstract: Disclosed approaches may provide for non-blocking video processing pipelines that have the ability to efficiently share transform hardware resources. Transform hardware resources may be shared across processing parameters, such as pixel block dimensions, transform types, video stream bit depths, and/or multiple coding formats, as well as for inter-frame and intra-frame encoding. The video processing pipeline may be divided into phases, each phase having half-butterfly circuits to perform a respective portion of computations of a transform. The phases may be selectable and configurable to perform transforms for multiple different combinations of the processing parameters. In each configuration, the phases may be capable of performing a transform by a sequential pass through at least some of the phases resulting in high throughput. Approaches are also described related to improving the performance and efficiency of transpose operations of transforms.

Abstract: The present disclosure discloses an image decompression method, device, and display terminal. The method includes: a step of acquiring image compression data; a step of performing inverse quantization on the image compression data based on a preset inverse quantization factor to obtain inversely quantized data; wherein the inverse quantization factor is in integer form; and a step of performing an inverse discrete cosine transformation (DCT) on the inversely quantized data to obtain image data; wherein the inverse DCT includes bit-shift operations and addition operations.

Abstract: A processing element includes an input zero detector to detect whether the input from the neighbor processing element contains a zero. When the input from the neighbor processing element contains the zero, a zero disable circuit controls the input from the neighbor processing element and respective data of the memory to both appear as unchanged to the arithmetic logic unit for the operation. A controller of an array of processing elements adds a row of error-checking values to a matrix of coefficients, each error-checking value of the row of error-checking values being a negative sum of a respective column of the matrix of coefficients. The controller controls a processing element to perform an operation with the matrix of coefficients and an input vector to accumulate a result vector. Owing to the error-checking values, when a sum of elements of the result vector is non-zero, an error is detected.

Abstract: Disclosed in some examples are methods, systems, devices, and machine-readable mediums that provide for techniques for scrambling and/or updating meta-data that enable an efficient internal copyback operation. In some examples, in order to update the meta-data, the meta-data and host-data are separated and the only the meta-data is sent to the controller to be updated during a modified internal copyback operation. The host-data is not transmitted to the controller. While sending the meta-data utilizes resources of the communication link between the memory dies and the controller, it uses much fewer resources than if the host-data were also transmitted.

Abstract: A convolutional deep neural network architecture can detect malicious executable files by reading the raw sequence of bytes, that is, without any domain-specific feature extraction or preprocessing.

Abstract: An image decoding apparatus that includes circuitry that performs filter processing on an image using both filter coefficients and a number of filter taps being set based on an orthogonal transform size, and decodes the image obtained through the filter processing.

Abstract: A fast vector multiplication and accumulation circuit is applied to an artificial neural network accelerator and configured to calculate an inner product of a multiplier vector and a multiplicand vector. A scheduler is configured to arrange a plurality of multiplicands of the multiplicand vector into a plurality of scheduled operands according to a plurality of multipliers of the multiplier vector, respectively. A self-accumulating adder is signally connected to the scheduler and includes a compressor, at least two delay elements and at least one shifter. The compressor is configured to add the scheduled operands to generate a plurality of compressed operands. The at least two delay elements are connected to the compressor. The shifter is configured to shift one of the compressed operands. An adder is signally connected to the output ports of the compressor so as to add the compressed operands to generate the inner product.

Abstract: A first computation unit acquires a first variation coefficient representing characteristics of linear variation of first time-series data, and calculates a value of a start time point and a value of an end time point of the first time-series data. A second computation unit acquires a second variation coefficient representing characteristics of linear variation of second time-series data, and calculates a commencing time point in the second time-series data, and a completing time point obtained by adding a time width between the start time point and the end time point to the commencing time point. A difference integrated value is calculated between paired time points which are in the same positional relationship in a range from the start time point to the end time point and in a range from the commencing time point to the completing time point, without calculating values of intervening time points.

Abstract: Fully homomorphic encryption integrated circuit (IC) chips, systems and associated methods are disclosed. In one embodiment, a number theoretic transform (NTT) butterfly circuit is disclosed. The (NTT) butterfly circuit includes a high input word path cross-coupled with a low word path. The high input word path includes a first adder/subtractor, a first multiplier, and first selection circuitry coupled to the first adder/subtractor and the first multiplier. Respective bypass paths selectively bypass the first adder/subtractor and the first multiplier. The low input word path includes a second adder/subtractor, a second multiplier, and second selection circuitry coupled to the second adder/subtractor and the second multiplier. Respective bypass paths selectively bypass the second adder/subtractor and the second multiplier. The first and second selection circuitry is responsive to different mode control signals to reconfigure the low and high input word paths into different logic processing units.

Abstract: A method of decoding or encoding that includes generating a new multi-transform data structure by embedding one or more non-recursive transforms into a larger recursive transform. The method may further include receiving information regarding a target data block and determining whether to use a recursive transform or a non-recursive transform. When the determination is to use the recursive transform, the method may include generating the recursive transform using a multi-transform data structure and causing the target data block to be encoded or decoded using the generated recursive transform. If not, the method may include causing the target data block to be encoded or decoded using one of the one or more the non-recursive transforms embedded in the multi-transform data structure.

Abstract: A data processing apparatus comprises a processing circuit and instruction decoder. A bitfield manipulation instruction controls the processing apparatus to generate at least one result data element from corresponding first and second source data elements. Each result data element includes a portion corresponding to a bitfield of the corresponding first source data element. Bits of the result data element that are more significant than the inserted bitfield have a prefix value that is selected, based on a control value specified by the instruction, as one of a first prefix value having a zero value, a second prefix value having the value of a portion of the corresponding second source data element, and a third prefix value corresponding to a sign extension of the bitfield of the first source data element.

Abstract: An arithmetic processing apparatus, includes: an arithmetic operation execution circuit configured to execute an arithmetic operation; a first register configured to store data to be used for an arithmetic operation by the arithmetic operation execution circuit; a first buffer configured to store data; a first controller configured to store, when an array of data is changed and the changed data is stored into the first register as the data to be used for the arithmetic operation, a plurality of data groups, which are successively received, into the first buffer; and a second controller configured to successively output, every time each of the plurality of data groups is stored into the first buffer, data included in the data groups stored in the first buffer to the first register.

Abstract: An error-concealing audio decoding method comprises: receiving a packet comprising a set of MDCT coefficients encoding a frame of time-domain samples of an audio signal; identifying the received packet as erroneous; generating estimated MDCT coefficients to replace the set of MDCT coefficients of the erroneous packet, based on corresponding MDCT coefficients associated with a received packet directly preceding the erroneous packet; assigning signs of a first subset of MDCT coefficients of the estimated MDCT coefficients, wherein the first subset comprises such MDCT coefficients that are associated with tonal-like spectral bins, to coincide with signs of corresponding MDCT coefficients of said preceding packet; randomly assigning signs of a second subset of MDCT coefficients of the estimated MDCT coefficients, wherein the second subset comprises MDCT coefficients associated with noise-like spectral bins; replacing the erroneous packet by a concealment packet containing the estimated MDCT coefficients and the s

Abstract: There is disclosed a method comprising receiving a set of coefficients; and determining whether a sign of a coefficient in the set of coefficients can be embedded in a bitstream. If the determining indicates that the sign of the coefficient in the set of coefficients can be embedded in the bitstream, an indication of the embedded sign is inserted into the bitstream. There is also disclosed a method comprising receiving a set of decoded coefficients; and determining whether a bitstream contains an indication of an embedded sign of a coefficient. If the determining indicates that the bitstream contains the indication of an embedded sign of a coefficient, the sign is determined on the basis of the decoded coefficients; and the sign of the coefficient is modified on the basis of the determined sign.

Abstract: The present embodiments relate to an address generator circuit for addressing a storage circuit. The address generator circuit may generate address signals for read and write access operations at the storage circuit. The write access operation may store a two-dimensional array in the storage circuit and the read access operation may retrieve a transpose of the two-dimensional array from the storage circuit. The address generator circuit may include a status flag generation circuit that generates status flag signals, a modulo adder circuit that receives first and second signals and computes a modulo adder output signal, and an address processing circuit. The address processing circuit may receive the modulo adder output signal from the modulo adder circuit and the plurality of status flag signals from the status flag generation circuit and provide the first and second signals to the modulo adder circuit.

Abstract: An apparatus and method are described for performing SIMD reduction operations. For example, one embodiment of a processor comprises: a value vector register containing a plurality of data element values to be reduced; an index vector register to store a plurality of index values indicating which values in the value vector register are associated with one another; single instruction multiple data (SIMD) reduction logic to perform reduction operations on the data element values within the value vector register by combining data element values from the value vector register which are associated with one another as indicated by the index values in the index vector register; and an accumulation vector register to store results of the reduction operations generated by the SIMD reduction logic.

Abstract: Embodiments of the present application provide a method for decoding a video and an apparatus for decoding a video, which increases accuracy of data processing while simplifying a micro architecture design of inverse discrete cosine transform in video decoding process. The method comprises: storing received data to be decoded in a plurality of first data registers and a plurality of second data registers that are spaced with each other in sequence; performing shift and look-up table processing on the data to be decoded that is stored in the first data registers and the second data register, to obtain a look-up table result corresponding to a first coefficient matrix and a look-up table result corresponding to a second coefficient matrix respectively; performing a distributed computing on the look-up table result corresponding to the first coefficient matrix and the look-up table result corresponding to the second coefficient matrix, to obtain decoded data.

Abstract: A common sub-expression elimination method for simplifying hardware logic of a hardware filter circuit by eliminating a common sub-expression included in a plurality of sub-expressions is provided. Each of the sub-expressions includes a corresponding two or more of inputs constituting a plurality of coefficients used by the hardware filter circuit. The method is implemented on a computing device and includes: identifying for each coefficient of the plurality of coefficients, a combination of the inputs constituting the coefficient; counting occurrences of the sub-expressions in each of the coefficients; identifying one or more of the sub-expressions having a maximum one of the counts and including the corresponding two or more of the inputs; selecting one of the one or more of the sub-expressions as the common sub-expression; eliminating the common sub-expression; and repeating these steps to eliminate more of the sub-expressions common to multiple ones of the coefficients.

Abstract: The document relates to modulated sub-sampled digital filter banks, as well as to methods and systems for the design of such filter banks. In particular, the present document proposes a method and apparatus for the improvement of low delay modulated digital filter banks. The method employs modulation of an asymmetric low-pass prototype filter and a new method for optimizing the coefficients of this filter. Further, a specific design for a 64 channel filter bank using a prototype filter length of 640 coefficients and a system delay of 319 samples is given. The method substantially reduces artifacts due to aliasing emerging from independent modifications of subband signals, for example when using a filter bank as a spectral equalizer. The method is preferably implemented in software, running on a standard PC or a digital signal processor (DSP), but can also be hardcoded on a custom chip.

Abstract: Techniques for efficiently performing full and scaled transforms on data received via full and scaled interfaces, respectively, are described and comprise (1) performing a first transform on a block of first input values to obtain a block of first output values by scaling the block to obtain scaled input values, performing a scaled one-dimensional (1D) transform on each row of the block, and performing a scaled 1D transform on each column of the block; and (2) performing a second transform on a block of second input values to obtain a block of second output values by performing a scaled 1D transform on each row of the block, performing a scaled 1D transform on each column of the block, and scaling the block.

Abstract: Provided is a fast Fourier transform circuit including: a first butterfly circuit and a second butterfly circuit which perform butterfly calculations corresponding to calculation bit-widths being different from each other; and a control means which controls selection of the first and second butterfly circuits in accordance with any one of a plurality of operation modes including: a first operation mode in which a calculation is performed by both of the first and second butterfly circuits; and a second operation mode in which a calculation is performed by any one of the first and second butterfly circuits.

Abstract: A method and system may identify a video data block using a video codec and apply a transform kernel of a butterfly asymmetric discrete sine transform (ADST) to the video data block in a pipeline.

Abstract: An image processing system includes a first flip-flop bank and a second flip-flop bank, and a control system configured to control JPEG processing of image data. The control system is further configured to, during a first period, use one of the first or second flip-flop banks as a write bank and the other of the first or second flip-flop banks as a read bank and, during a second period, alternate the use of the first and second flip-flop banks as the write bank and the read bank. Further, the control system is configured to, after alternating the use, initialize the read bank to zero.

Abstract: An apparatus for generating real-valued output audio samples is disclosed. The apparatus includes a memory that stores complex-valued input subband samples, real-valued demodulated samples, and the real-valued output audio samples. The apparatus also incudes a phase shifter that shifts a phase of the complex-valued input subband samples by an amount equal to a previously added phase shift and a complex-valued synthesis filter bank that generates the real-valued output audio samples in response to the complex-valued input subband samples, the real-valued demodulated samples, and prototype filter coefficients.

Abstract: A product of an integer value and an irrational value may be determined by a sign-symmetric algorithm. A process may determine possible algorithms that minimize metrics such as mean asymmetry, mean error, variance of error, and magnitude of error. Given an integer variable x and rational dyadic constants that approximate the irrational fraction, a series of intermediate values may be produced that are sign-symmetric. The intermediate values may include a sequence of addition, subtraction and right shift operations the when summed together approximate the product of the integer and irrational value. Other operations, such as additions or subtractions of 0s or shifts by 0 bits may be removed.

Abstract: A method of encoding a video stream in a video encoder is provided that includes computing an offset into a transform matrix based on a transform block size, wherein a size of the transform matrix is larger than the transform block size, and wherein the transform matrix is one selected from a group consisting of a DCT transform matrix and an IDCT transform matrix, and transforming a residual block to generate a DCT coefficient block, wherein the offset is used to select elements of rows and columns of a DCT submatrix of the transform block size from the transform matrix.

Abstract: A processing unit, method, and medium for decompressing or generating textures within a graphics processing unit (GPU). The textures are compressed with a variable-rate compression scheme such as JPEG. The compressed textures are retrieved from system memory and transferred to local cache memory on the GPU without first being decompressed. A table is utilized by the cache to locate individual blocks within the compressed texture. A decompressing shader processor receives compressed blocks and then performs on-the-fly decompression of the blocks. The decompressed blocks are then processed as usual by a texture consuming shader processor of the GPU.

Abstract: A data processing apparatus and method are provided for performing a transform between spatial and frequency domains when processing video data. The data processing apparatus comprises transform circuitry configured to receive N input values and to perform a sequence of operations to generate N output values representing the transform of the N input values between the spatial and frequency domains. In doing this, the transform circuitry employs a base circuitry that is configured to receive M internal input values generated by the transform circuitry, where M is greater than or equal to 4, and to perform a base operation equivalent to matrix multiplication of the M internal input values by a Hankel matrix, which is a square matrix with constant skew diagonals, where each element of the array identifies a coefficient, performance of the base operation generating M internal output values for returning to the transform circuitry.

Abstract: A first set of discrete cosine transform (DCT) blocks is obtained. Each DCT block from the first set of DCT blocks has a first block size. When performing a split operation on the first set of DCT blocks, a filter is applied to the first set of DCT blocks. A second set of data blocks is generated based on the first set of DC blocks using a transform function. Each block in the second set of data blocks has a second block size. When performing a merge operation, the filter is applied to the second set of data blocks.

Abstract: Discrete cosine transform/inverse discrete cosine transform method and device are provided. The discrete cosine transform/inverse discrete cosine transform method includes: generating a table index for only an input value other than 0 (zero) out of input values of coordinates in an input block; reading one or more partial values corresponding to the table index out of a plurality of table information pieces which are generated and stored in advance so as to include partial values corresponding to a multiplication of a weight value and an index; and adding the read partial value and calculating the resultant value of each coordinate in an output block. Accordingly, it is possible to perform a fast DCT/IDCT operation and to reduce the energy consumption for the transform.

Abstract: A method for adaptively performing video decoding includes: performing decoding complexity management based upon bit stream information of an input bit stream, in order to determine whether to reduce decoding complexity of at least one component of a plurality of components within an adaptive complexity video decoder; and selectively reducing decoding complexity of a portion of components within the adaptive complexity video decoder. An associated adaptive complexity video decoder and an associated adaptive audio/video playback system are also provided. In particular, the adaptive complexity video decoder includes a plurality of components and a decoding complexity manager. When needed, the decoding complexity manager delays audio playback of audio information.

Abstract: A system and method for preventing an application program, which is licensed to a customer to be exclusively executed in a processor based on a certain processor design, from being executed properly in unauthorized processors is provided. The system includes a scrambling module and a recovery module. The scrambling module scrambles a selected portion of the application program using an identifier which identifies the authorized processor design. The recovery module adds an unscrambling program to the application program such that when the program is running in a processor, it retrieves a second identifier from the processor and unscrambles the scrambled portion of the application program using the retrieved second identifier. If the second identifier does not correspond to an authorized processor design, the unscrambling operation will incorrectly unscramble the scrambled portion and the application program will not run properly.

Abstract: In general, techniques are described for implementing a 16-point inverse discrete cosine transform (IDCT) that is capable of applying multiple IDCTs of different sizes. For example, an apparatus comprising a 16-point inverse discrete cosine transform of type II (IDCT-II) unit may implement the techniques of this disclosure. The 16-point IDCT-II unit performs these IDCTs-II of different sizes to transform data from a spatial to a frequency domain. The 16-point IDCT-II unit includes an 8-point IDCT-II unit that performs one of the IDCTs-II of size 8 and a first 4-point IDCT-II unit that performs one of the IDCTs-II of size 4. The 8-point IDCT-II unit includes the first 4-point DCT-II unit. The 16-point IDCT-II unit also comprises an inverse 8-point DCT-IV unit that includes a second 4-point IDCT-II unit and a third 4-point IDCT-II unit. Each of the second and third 4-point IDCT-II units performs one of the IDCTs-II of size 4.

Abstract: A texture unit may be used to perform general purpose mathematical computations such as dot products. This enables some general purpose computations and operations to be offloaded from a central processing unit to the texture unit. The texture unit may use linear interpolators in order to perform the dot product calculations.

Abstract: In general, techniques are described for implementing a 16-point discrete cosine transform (DCT) that is capable of applying multiple IDCT of different sizes. For example, an apparatus comprising a 16-point discrete cosine transform of type II (DCT-II) unit may implement the techniques of this disclosure. The 16-point DCT-II unit performs these DCTs-II of different sizes to transform data from a spatial to a frequency domain. The 16-point DCT-II unit includes an 8-point DCT-II unit that performs one of the DCTs-II of size 8 and a first 4-point DCT-II unit that performs one of the DCTs-II of size 4. The 8-point DCT-II unit includes the first 4-point DCT-II unit. The 16-point DCT-II unit also comprises an 8-point DCT-IV unit that includes a second 4-point DCT-II unit and a third 4-point DCT-II unit. Each of the second and third 4-point DCT-II units performs one of the DCTs-II of size 4.

Abstract: A joint optimization iterative algorithm determines optimized mode pairs. Each mode pair includes an intra-predictor and a transform pair that are iteratively modified to determine an optimized intra-predictor and an optimized transform that forms the optimized mode pair. A set of training videos and a set of quantization parameters (QPs) are used as the base data for determining the optimized mode pairs. Each video includes a plurality of pixel blocks, herein referred to as blocks. Block statistics associated with each mode pair are accumulated by separately encoding each block using each mode pair, and selecting the best mode pair for each block according to a measured characteristic of each encoding. The accumulated block statistics are used to modify the intra-predictor and the transform within each mode pair.

Abstract: A recursive type-IV discrete cosine transform system includes a first permutation device, a recursive type-III discrete cosine/sine transform device, a cosine/sine factor generation device, a recursive type-II discrete cosine/sine transform device, a second permutation device. The first permutation device performs two-dimensional order permutation operation on N digital signals for generating N two-dimensional first temporal signals. The recursive type-III discrete cosine/sine transform device repeats a type-III discrete cosine/sine transform for generating second temporal signals. The cosine/sine factor generation device sequentially performs cosine/sine factor multiplication and corresponding addition operations for generating third temporal signals. The recursive type-II discrete cosine/sine transform device repeats a type-II discrete cosine/sine transform for generating fourth temporal signals.

Abstract: A codec includes an encoder having a quantization level generator that defines a quantization level specific to a block of values (e.g., transform coefficients), a quantizer that quantizes the block of transform coefficients according to the block-specific quantization level, a run-length encoder, and an entropy encoder. The quantization level is defined to result in at least a predetermined number (k) of quantized coefficients having a predetermined value. The amount of data compression by the encoder is proportional to (k). The codec also includes a decoder having entropy and run-length decoding sections whose throughputs are proportional to (k). The decoder takes advantage of this increased throughput by further decoding coefficients in parallel using a plurality of decoding channels. Methods for encoding and decoding data are also disclosed. The invention is well-suited to quantization, entropy, and/or run-length-based codecs, such as JPEG.

Abstract: In some embodiments, a data processing system including an operation unit including circuitry configurable to perform any selected one of a number of operations on data (e.g., audio data) and a configuration unit configured to assert configuration information to configure the operation unit to perform the selected operation. When the operation includes matrix multiplication of a data vector and a matrix whose coefficients exhibit symmetry, the configuration information preferably includes bits that determine signs of all but magnitudes of only a subset of the coefficients. When the operation includes successive addition and subtraction operations on operand pairs, the configuration information preferably includes bits that configure the operation unit to operate in an alternating addition/subtraction mode to perform successive addition and subtraction operations on each pair of data values of a sequence of data value pairs.

Abstract: A data processing apparatus and method are provided for performing a transform between spatial and frequency domains when processing video data. The data processing apparatus comprises transform circuitry configured to receive N input values and to perform a sequence of operations to generate N output values representing the transform of the N input values between the spatial and frequency domains. In doing this, the transform circuitry employs a base circuitry that is configured to receive M internal input values generated by the transform circuitry, where M is greater than or equal to 4, and to perform a base operation equivalent to matrix multiplication of the M internal input values by a Hankel matrix, which is a square matrix with constant skew diagonals, where each element of the array identifies a coefficient, performance of the base operation generating M internal output values for returning to the transform circuitry.

Abstract: Techniques for efficiently performing full and scaled transforms on data received via full and scaled interfaces, respectively, are described. A full transform is a transform that implements the complete mathematical description of the transform. A full transform operates on or provides full transform coefficients. A scaled transform is a transform that operates on or provides scaled transform coefficients, which are scaled versions of the full transform coefficients. The scaled transform may have lower computational complexity whereas the full transform may be simpler to use by applications. The full and scaled transforms may be for a 2D IDCT, which may be implemented in a separable manner with 1D IDCTs. The full and scaled transforms may also be for a 2D DCT, which may be implemented in a separable manner with 1D DCTs. The 1D IDCTs and 1D DCTs may be implemented in a computationally efficient manner.

Abstract: A product of an integer value and an irrational value may be determined by a sign-symmetric algorithm. A process may determine possible algorithms that minimize metrics such as mean asymmetry, mean error, variance of error, and magnitude of error. Given an integer variable x and rational dyadic constants that approximate the irrational fraction, a series of intermediate values may be produced that are sign-symmetric. The intermediate values may include a sequence of addition, subtraction and right shift operations the when summed together approximate the product of the integer and irrational value. Other operations, such as additions or subtractions of 0s or shifts by 0 bits may be removed.

Abstract: In general, techniques are described that provide for 4×4 transforms for media coding. A number of different 4×4 transforms are described that adhere to these techniques. As one example, an apparatus includes a 4×4 discrete cosine transform (DCT) hardware unit. The DCT hardware unit implements an orthogonal 4×4 DCT having an odd portion that applies first and second internal factors (C, S) that are related to a scaled factor (?) such that the scaled factor equals a square root of a sum of a square of the first internal factor (C) plus a square of the second internal factor (S). The 4×4 DCT hardware unit applies the 4×4 DCT implementation to media data to transform the media data from a spatial domain to a frequency domain. As another example, an apparatus implements a non-orthogonal 4×4 DCT to improve coding gain.