Decoding method, encoding method and related devices

Abstract

A method of decoding compressed video or image data, or encoding uncompressed video or image data, using an 8-bit primary transform kernel matrix. The method can include determining whether to use a first transform kernel matrix having a first size type or a second transform kernel matrix having a second size type that is smaller than the first size type. When the result of the determination is to use the first transform kernel matrix, an 8-bit primary transform kernel matrix having a size of 64 points or more is used to encode or decode a target file. Otherwise, the method can include extracting the second transform kernel matrix of the second size type from the first transform matrix, and using the extracted second transform kernel matrix to encode or decode the target file.

Description

[0001] Priority information

[0002] This application claims priority to U.S. Provisional Application No. 62 / 692,658, filed June 29, 2018, and U.S. Application No. 16 / 225,982, filed December 19, 2018, the entire disclosure of which is incorporated herein by reference.

[0003] This application is a divisional application of Chinese patent application No. 201980013988.6, filed on June 3, 2019, entitled "Method, Apparatus and Medium for Decoding or Encoding". Technical Field

[0004] This application relates to image processing technology, and more particularly to video coding / decoding technology, including video coding / decoding technology based on High Efficiency Video Coding (HEVC), such as Universal Video Coding (VVC). Background Technology

[0005] Video encoding and decoding using motion-compensated inter-frame image prediction has been known for decades. Uncompressed digital video can consist of a series of images, each with spatial dimensions, for example, 1920×1080 luma samples and associated chroma samples. This series of images can have a fixed or variable image rate (informally also called frame rate), such as 60 images per second or 60 Hz. Uncompressed video has very high bitrate requirements. For example, 1080p60 4:2:0 video with 8 bits per sample (1920×1080 luma sample resolution at a frame rate of 60 Hz) requires close to 1.5 Gbit / s of bandwidth. One hour of such video would require more than 600 GB of storage space.

[0006] One objective of video encoding and decoding is to reduce redundancy in the input video signal through compression. In some cases, compression can help reduce bandwidth or storage requirements by two orders of magnitude or more. Lossless compression, lossy compression, and combinations thereof can be employed. Lossless compression refers to a technique that reconstructs an exact copy of the original signal from the compressed original signal. When using lossy compression, the reconstructed signal may differ from the original signal, but the distortion between the original and reconstructed signals is small enough that the reconstructed signal is useful for the intended application. In the case of video, lossy compression is widely used. The amount of distortion tolerated depends on the application; for example, users of some consumer streaming applications may tolerate higher distortion than users of television streaming applications. The achievable compression ratio reflects the higher the allowable / tolerable distortion, the higher the achievable compression ratio.

[0007] Those skilled in the art will generally understand video compression / decompression techniques. Typically, to compress video or image data, a series of functional steps are performed to produce a compressed video or image file. While images such as 360° images (e.g., images captured by a 360° camera device) are suitable for compression, video file compression will be described for ease of reading. To generate a compressed video file, under common standards (e.g., H.264, H.265), the uncompressed video sample stream received from the video source can be segmented or parsed to obtain sample blocks of two or more reference images.

[0008] Bidirectional prediction can involve techniques that predict a prediction unit (PU) from two motion-compensated sample blocks of two or more reference images. Bidirectional prediction was first introduced into the MPEG-1 video coding standard and has also been incorporated into other video coding techniques and standards such as MPEG-2 Part 2 (or H.262), H.264, and H.265.

[0009] When decompressing a compressed video file, during the reconstruction of the bidirectional prediction (PU) samples, the motion-compensated and interpolated input samples from each reference block can be multiplied by a different weighting factor for each reference block, and these weighted sample values ​​from two reference blocks can be added together to generate the samples in the reconstruction. Such samples can also be further processed using mechanisms such as loop filtering.

[0010] In MPEG-1 and MPEG-2, weighting factors can be determined based on the relative temporal distance between the picture to which the reconstructed PU belongs and two reference pictures. This is possible because, in MPEG-1 and MPEG-2, one of the two reference I or P pictures is in the "past" of the reconstructed B picture, and the other is in the "future" of the reconstructed B picture (in the order of presentation), and because, in MPEG-1 and MPEG-2, for any reconstructed picture, a well-defined timing relationship is established relative to its reference pictures.

[0011] Starting with H.264, the concept of reference image selection for bidirectional prediction images was relaxed, allowing the reference image to only need to be earlier in the decoding order, not in the rendering order. Furthermore, the concept of time was also relaxed, as neither H.264 nor H.265 requires constrained / fixed image intervals in the temporal domain. Therefore, the decoder can no longer calculate weighting factors based on timing information available in the bitstream. Instead, H.264 and H.265 include a "default value" of 0.5 as the weighting factor for the reference samples of the bidirectional prediction images. This default value can be overridden using syntax available in the slice header called `pred_weight_table()`. The default value of 0.5 or the information in `pred_weight_table` can be applied to all bidirectional prediction PUs in a given slice.

[0012] Non-patent document 1 illustrates the H.265 / HEVC standard. However, the inventors have investigated the need for standardization of future video coding technologies with compression capabilities significantly exceeding the HEVC standard (including its extensions).

[0013] Non-Patent Document 2 discloses a recently introduced standardized format for next-generation video coding on top of HEVC, known as Universal Video Coding (VVC) with Version VTM (VVC Test Model). VVC typically uses a 10-bit integer matrix to provide a large (e.g., 64-point or higher) transform core.

[0014] List of related technologies

[0015] Non-Patent Document 1: “Transform design for HEVC with 16-bit intermediate data representation”; published by the Joint Collaborative Working Group on Video Coding (JCT-VC) of ITU-T SG16 WP3 and ISO / IEC JTC1 / SC29 / WG11, 5th Meeting: Geneva, Switzerland, March 16-23, 2011 (Document: JCTVC-E243). The H.265 / HEVC (High Efficiency Video Coding) standard may include Version 1 (2013), Version 2 (2014), Version 3 (2015), and Version 4 (2016) published by ITU-T VCEG (Q6 / 16) and ISO / IEC MPEG (JTC 1 / SC 29 / WG11).

[0016] Non-Patent Document 2: “Algorithm description for Versatile Video Coding and Test Model 1 (VTM 1)”; published by the Joint Video Experts Group (JVET) of ITU-T SG 16WP 3 and ISO / IEC JTC 1 / SC 29 / WG 11, 10th meeting: San Diego, USA, April 10-20, 2018 (Document: JVET-Jl002-v2).

[0017] The problem to be solved

[0018] Typically, it is not possible to extract 8-bit 2-point, 4-point, 8-point, 16-point, and 32-point DCT-2 transform cores from, for example, a 10-bit 64-point DCT-2 transform core in a traditional VVC. This inevitably increases the cost of applying the main transform, as a separate 64-point transform core would require additional storage and logic to implement. Summary of the Invention

[0019] According to one aspect of this disclosure, a method for decoding compressed video or image data, or encoding uncompressed video or image data, using an 8-bit master transform core matrix, may include:

[0020] Receive information relating to a target file for encoding or decoding, wherein the target file for encoding or decoding is one of the following: a compressed video or image data file, or an uncompressed video or image data file; during the encoding or decoding of the target file, determine whether to use a first transform core matrix having a first size type or a second transform core matrix having a second size type smaller than the first size type, wherein the first size type is an 8-bit master transform core matrix having a core matrix represented by 8 bits and having a size of 64 points or greater.

[0021] The method according to the aspects described in this disclosure may further include: when it is determined that a first transform core matrix of the first size type is used, encoding or decoding the target file for encoding or decoding using the 8-bit master transform core matrix having a size of 64 points or greater; and when it is determined that a second transform core matrix of the second size type is used, extracting a second transform core matrix of the second size type from the 8-bit master transform core matrix having a size of 64 points or greater, and encoding or decoding the target file for encoding or decoding using the extracted second transform core matrix of the second size type.

[0022] According to one aspect of this disclosure, an apparatus for decoding compressed video or image data or decoding uncompressed video or image data using an 8-bit master transform core matrix may include: at least one memory configured to store computer program code, and at least one processor configured to access the at least one memory and operate according to the computer program code. The computer program code may include first application code, second application code, third application code, and fourth application code.

[0023] The first application code can be configured to cause the at least one processor to receive information relating to a target file for encoding or decoding. The target file for encoding or decoding is one of the following: a compressed video or image data file, or an uncompressed video or image data file.

[0024] The second application code can be configured to, during the process of encoding or decoding the target file, determine whether to use a first transform core matrix of a first size type or a second transform core matrix of a second size type smaller than the first size type, wherein the first size type is an 8-bit master transform core matrix having a core matrix represented by 8 bits and having a size of 64 points or greater.

[0025] The third application code can be configured to cause the at least one processor, when determining that a first transform core matrix of the first size type is to be used, to encode or decode the target file for the encoding or decoding using the 8-bit master transform core matrix of a size of 64 points or greater.

[0026] The fourth application code is configured to cause the at least one processor, when determining that a second transform core matrix of the second size type smaller than the first size type is used, to extract a second transform core matrix of the second size type from an 8-bit master transform core matrix of size 64 points or larger, and to encode or decode the target file for encoding or decoding using the extracted second transform core matrix of the second size type.

[0027] According to one aspect of this disclosure, an apparatus for decoding compressed video or image data or decoding uncompressed video or image data using an 8-bit master transform core matrix may include:

[0028] A receiving module is configured to receive information relating to a target file for encoding or decoding, wherein the target file for encoding or decoding is one of the following: a compressed video or image data file, or an uncompressed video or image data file;

[0029] The determination module is used to determine, during the encoding or decoding of the target file, whether to use a first transform core matrix of a first size type or a second transform core matrix of a second size type smaller than the first size type, wherein the first size type is an 8-bit master transform core matrix, and the 8-bit master transform core matrix has a core matrix represented by 8 bits and having a size of 64 points or greater.

[0030] The first processing module is configured to encode or decode the target file for encoding or decoding using the 8-bit master transform core matrix with a size of 64 points or greater when it is determined that a first transform core matrix of the first size type is used.

[0031] The second processing module is configured to, when it is determined that a second transform core matrix of the second size type smaller than the first size type is used, extract a second transform core matrix of the second size type from the 8-bit master transform core matrix of the second size type with a size of 64 points or larger, and use the extracted second transform core matrix of the second size type to encode or decode the information of the target file used for encoding or decoding.

[0032] According to one aspect of this disclosure, a non-transitory computer-readable storage medium may store instructions to cause one or more computers to perform the following operations: receiving information relating to a target file for encoding or decoding, said target file being one of: a compressed video or image data file, or an uncompressed video or image data file; and determining, for the encoding or decoding of said target file, whether to use a first transform core matrix having a first size type or a second transform core matrix having a second size type smaller than the first size type, wherein the first size type is an 8-bit master transform core matrix having a core matrix represented by 8 bits and having a size of 64 points or greater.

[0033] The storage instructions of the non-transitory computer-readable storage medium may also cause one or more processors to perform the following operations: when the determined result is the use of a first transform core matrix of the first size type, to encode or decode the target file using the 8-bit master transform core matrix of the first size type; and when the determined result is the use of a second transform core matrix of the second size type smaller than the first size type, to extract a second transform core matrix of the second size type from the 8-bit master transform core matrix of the second size type of the second size type, and to encode or decode the target file using the extracted second transform core matrix of the second size type.

[0034] The decoding or encoding method provided in this application requires an 8-bit (e.g., 64-bit or higher) core in the VVC to reduce complexity, reduce the memory used to store the transform core, and / or reduce the input bit width of multipliers / additions / subtractions. Compared to a 10-bit main transform core, an 8-bit main transform core reduces complexity by reducing the memory used to store the transform core and reducing the input bit width of multipliers / additions / subtractions. Attached Figure Description

[0035] Other features, properties, and various advantages of the disclosed subject matter will become more apparent from the following detailed description and accompanying drawings, in which:

[0036] Figure 1 It is a schematic diagram of a simplified block diagram of a communication system according to one embodiment;

[0037] Figure 2 This is a schematic diagram of a simplified block diagram of a streaming system according to one embodiment;

[0038] Figure 3 This is a schematic diagram of a simplified block diagram of a decoder according to one embodiment;

[0039] Figure 4 This is a schematic diagram of a simplified block diagram of an encoder according to one embodiment;

[0040] Figure 5 This is a schematic illustration of an exemplary method of encoding or decoding according to one embodiment;

[0041] Figure 6 This is a schematic diagram of the output transformation core matrix according to one embodiment;

[0042] Figure 7 This is a schematic diagram of a computer system according to one embodiment. Detailed Implementation

[0043] Figure 1 A simplified block diagram of a communication system (100) according to one embodiment of the present disclosure is shown. The system (100) may include at least two terminals (110, 120) interconnected via a network (150). For unidirectional data transmission, the first terminal (110) may encode video data locally for transmission to the other terminal (120) via the network (150). The second terminal (120) may receive the encoded video data from the other terminal from the network (150), decode the encoded video data, and display the restored video data. Unidirectional data transmission is common in media service applications, etc.

[0044] Figure 1A second pair of terminals (130, 140) is shown, which are provided to support bidirectional transmission of encoded video that may occur, for example, during a video conference. For bidirectional data transmission, each terminal (130, 140) can encode video data captured at a local location for transmission to the other terminal via a network (150). Each terminal (130, 140) can also receive encoded video data transmitted by the other terminal, decode the encoded video data, and display the recovered video data on a local display device.

[0045] exist Figure 1 In this disclosure, terminals (110-140) may be exemplified as laptop computer 110, server 120, and smartphones 130 and 140, but the principles of this disclosure are not limited thereto. Embodiments of this disclosure can be applied to other devices, including but not limited to laptop computers, tablet computers, media players, and / or dedicated video conferencing equipment. Network (150) refers to any number of networks that transmit encoded video data between terminals (110-440), including, for example, wired and / or wireless communication networks. Communication networks (150) may exchange data in circuit-switched and / or packet-switched channels. Representative networks include telecommunications networks, local area networks (LANs), wide area networks (WANs), and / or the Internet. For the purposes of this application, unless explained below, the architecture and topology of the network (150) may be irrelevant to the operation of this disclosure.

[0046] As an example of the application of the disclosed topic, Figure 2 The placement of a video encoder and decoder in a streaming environment is illustrated. The disclosed subject matter is equally applicable to other video-enabled applications, including, for example, video conferencing, digital TV, and storing compressed video on digital media including CDs, DVDs, memory sticks, etc.

[0047] The streaming system may include a capture subsystem (213) that may include a video source (201) capable of creating an uncompressed video sample stream (202), such as a digital camera device. The sample stream (202) is depicted as a thick line to emphasize the high data volume when compared with an encoded video bitstream. The sample stream (202) may be processed by an encoder (203) coupled to the camera device (201). The encoder (203) may include hardware (e.g., a processor or circuitry and memory), software, or a combination thereof to implement or enforce aspects of the disclosed subject matter as described in more detail below. The encoded video bitstream (204) is depicted as a thin line to emphasize the lower data volume when compared with the sample stream. The encoded video bitstream (204) may be stored on a streaming server (205) for future use. One or more streaming clients (206, 208) may access the streaming server (205) to retrieve copies (207, 209) of the encoded video bitstream (204). The client (206) may include a video decoder (210) that decodes an incoming copy (207) of an encoded video bitstream and creates an outgoing video sample stream (211) that can be displayed on a display (212) or other presentation device (not depicted).

[0048] Figure 3 A functional block diagram of a video decoder (210) according to one embodiment of the present disclosure is shown. Figure 3 As shown, the receiver (310) can receive one or more codec video sequences to be decoded by the decoder (210); in the same embodiment or another embodiment, one encoded video sequence is received at a time, wherein the decoding of each encoded video sequence is independent of the other encoded video sequences. The encoded video sequences can be received from a channel (312), which can be a hardware / software link to a storage device storing the encoded video data. The receiver (310) can receive the encoded video data as well as other data, such as encoded audio data and / or auxiliary data streams that can be forwarded to their respective user entities (not depicted). The receiver (310) can separate the encoded video sequences from other data. To prevent network jitter, a buffer memory (315) can be coupled between the receiver (310) and the entropy decoder / parser (320) (hereinafter referred to as the "parser"). The buffer memory (315) may not be required when the receiver (310) receives data from a store / forward device with sufficient bandwidth and controllability or from an isochronous synchronization network, or the buffer memory (315) may be small. For use on optimal packet networks such as the Internet, a buffer memory (315) may be required, which can be relatively large and can advantageously have an adaptive size.

[0049] The video decoder (210) may include a parser (320) to reconstruct symbols (321) from an entropy-encoded video sequence. These symbols include information for managing the operation of the decoder (210), and potential information for controlling presentation devices such as displays (212) that are not part of the decoder but may be coupled to it. Figure 2 and 3 As shown. Control information for (one or more) presentation devices may be in the form of supplementary enhancement information (SEI messages) or video availability information (VUI) parameter set fragments (not depicted). The parser (320) may parse / entropy decode the received encoded video sequence. The encoding of the encoded video sequence may be performed according to video coding techniques or standards and may follow principles known to those skilled in the art, including: variable length coding, Huffman coding, arithmetic coding with or without context sensitivity, etc. The parser (320) may extract a subgroup parameter set of at least one subgroup of pixels in the subgroup of the video decoder from the encoded video sequence based on at least one parameter corresponding to the group. Subgroups may include: group of pictures (GOP), pictures, tiles, slices, macroblocks, coding units (CU), blocks, transform units (TU), prediction units (PU), etc. The entropy decoder / parser may also extract information such as transform coefficients, quantizer parameter values, motion vectors, etc. from the encoded video sequence.

[0050] The parser (320) can perform entropy decoding / parsing operations on the video sequence received from the buffer memory (315) to create symbols (321). Depending on the type of encoded video pictures or portions thereof (e.g., inter-frame and intra-frame pictures, inter-frame and intra-frame blocks) and other factors, the reconstruction of the symbols (321) can involve multiple different units. Which units are involved and how they are involved can be controlled by subgroup control information parsed by the parser (320) from the encoded video sequence. For brevity, such subgroup control information flow between the parser (320) and the following multiple units is not described.

[0051] In addition to the functional blocks already mentioned, decoder 210 can be conceptually subdivided into a number of functional units as described below. In a practical implementation operating under commercial constraints, many of these units interact closely with each other and can be at least partially integrated with one another. However, for the purposes of describing the disclosed subject matter, a conceptual subdivision into the functional units described below is appropriate.

[0052] The first unit is the scaler / inverse transform unit (351). The scaler / inverse transform unit (351) receives from the parser (320) quantization transform coefficients as (one or more) symbols (321) and control information, including the transform method used, block size, quantization factor, quantization scaling matrix, etc. The scaler / inverse transform unit (351) can output a block containing sample values ​​that can be input into the aggregator (355).

[0053] In some cases, the output samples of the scaler / inverse transform unit (351) may belong to intra-coded blocks; that is, blocks that do not use predictive information from previously reconstructed images but can use predictive information from previously reconstructed portions of the current image. Such predictive information can be provided by the intra-prediction unit (352). In some cases, the intra-prediction unit (352) uses surrounding reconstructed information extracted from the current (partially reconstructed) image (356) to generate blocks of the same size and shape as the blocks in the reconstruction. In some cases, the aggregator (355) adds the predictive information generated by the intra-prediction unit (352) to the output sample information provided by the scaler / inverse transform unit (351) based on each sample.

[0054] In other cases, the output samples of the scaler / inverse transform unit (351) may belong to inter-frame coding and latent motion compensation blocks. In such cases, the motion compensation prediction unit (353) can access the reference image buffer (357) to extract samples for prediction. After motion compensation of the extracted samples according to the symbols (321) belonging to the block, these samples can be added by the aggregator (355) to the output of the scaler / inverse transform unit (351) (referred to as residual samples or residual signals in this case) to generate output sample information. The address in the reference image buffer (357) from which the motion compensation prediction unit (353) extracts its prediction samples can be controlled by motion vectors, which are provided to the motion compensation prediction unit (353) in the form of symbols (321), which may have, for example, X, Y, and reference image components. Motion compensation may also include interpolation of sample values ​​extracted from the reference image memory when using subsample precise motion vectors, motion vector prediction mechanisms, etc.

[0055] The output samples of the aggregator (355) can employ various loop filtering techniques in the loop filter unit (356). The video compression technique may include an in-loop filtering technique, which is controlled by parameters included in the encoded video sequence and available to the loop filter unit (356) as symbols (321) from the parser (320). However, the video compression technique may also respond to metadata obtained during decoding of a previous (in the decoding order) portion of the encoded picture or encoded video sequence, and to previously reconstructed and loop-filtered sample values.

[0056] The output of the loop filter unit (356) can be a sample stream, which can be output to the presentation device (212) and stored in the reference image buffer (357) for future inter-frame image prediction.

[0057] Once fully reconstructed, some of the encoded images can be used as reference images for future predictions. For example, once the encoded images have been fully reconstructed and the encoded images (by, for example, the parser (320)) are identified as reference images, the current reference image (356) can become part of the reference image cache (357), and a new current image memory can be reallocated before the reconstruction of subsequent encoded images begins.

[0058] The video decoder 210 can perform decoding operations according to predetermined video compression techniques in standards such as ITU-T Recommendation H.265. An encoded video sequence may conform to the syntax specified by the video compression technique or standard used, in the sense that it follows the syntax of the video compression technique or standard as indicated in the video compression technique document or standard and its configuration file. For compliance, the complexity of the encoded video sequence is also required to be within the limits defined by the hierarchy of the video compression technique or standard. In some cases, the hierarchy limits the maximum picture size, maximum frame rate, maximum reconstruction sampling rate (measured in, for example, megasamples per second), and / or maximum reference picture size. In some cases, the limitations set by the hierarchy can be further limited by the assumed reference decoder (HRD) specification and metadata managed by the HRD buffer, which is signaled in the encoded video sequence.

[0059] In one embodiment, the receiver (310) may receive supplemental (redundant) data and encoded video. The supplemental data may be included as part of one or more encoded video sequences. The supplemental data may be used by the video decoder (210) to correctly decode the data and / or more accurately reconstruct the original video data. The supplemental data may be in the form of, for example, temporal, spatial, or SNR enhancement layers, redundant slices, redundant images, forward error correction codes, etc.

[0060] Figure 4 This may be a functional block diagram of a video encoder (203) according to one embodiment of the present disclosure.

[0061] The encoder (203) can receive video samples from a video source (201) (not part of the encoder) that can capture one or more video images to be encoded by the encoder (203).

[0062] A video source (201) can provide a source video sequence in the form of a digital video sample stream to be encoded by an encoder (203). This digital video sample stream can have any suitable bit depth (e.g., 8-bit, 10-bit, 12-bit…), any color space (e.g., BT.601 YCrCb, RGB…), and any suitable sampling structure (e.g., YCrCb 4:2:0, YCrCb 4:4:4). In a media service system, the video source (201) can be a storage device storing previously prepared video, which may include a memory and a processor. In a video conferencing system, the video source (201) may include a camera device that captures local image information as a video sequence. Video data can be provided as multiple individual pictures that are given motion when viewed in sequence. The pictures themselves can be organized as spatial pixel arrays, where each pixel may include one or more samples, depending on the sampling structure, color space, etc., used. The relationship between pixels and samples will be readily understood by those skilled in the art. The following description focuses on samples.

[0063] According to one embodiment, the encoder (203) can encode and compress images of a source video sequence into an encoded video sequence in real time or under any other time constraints required by the application. Implementing an appropriate encoding rate is a function of the controller (450). The controller (450) controls and is functionally coupled to other functional units described below. For simplicity, the coupling is not depicted. Parameters set by the controller (450) may include rate control-related parameters (e.g., image skipping, quantizer, λ value of rate-distortion optimization techniques, etc.), image size, group of images (GOP) layout, maximum motion vector search range, etc. Those skilled in the art can readily identify other functions of the controller (450) that are optimized for certain system designs of the video encoder (203).

[0064] Some video encoders operate in a manner readily recognized by those skilled in the art as an “encoding loop.” In a very simple description, an encoding loop may include an encoding section (430) of the encoder (hereinafter referred to as the “source encoder”), responsible for creating a symbol stream based on the input picture to be encoded and (one or more) reference pictures, and a (local) decoder (433) embedded in the encoder (203). The decoder (433) reconstructs the symbols to create sample data that the (remote) decoder will also create (because in the video compression techniques considered in the disclosed subject matter, any compression between the symbols and the encoded video bitstream is lossless). The reconstructed sample stream is input to a reference picture memory (434). Since the decoding of the symbol stream produces a bit-precise result independent of the decoder’s location (local or remote), the contents of the reference picture memory (434) are also bit-precise between the local encoder and the remote encoder. In other words, the reference picture samples “seen” by the encoder’s prediction section are exactly the same sample values ​​that the decoder will “see” during prediction. The basic principles of synchronization of this reference image (and the drift that occurs when synchronization cannot be maintained, for example, due to channel errors) are also well known to those skilled in the art.

[0065] The operation of the “local” decoder (433) can be combined with, for example, the one already mentioned above. Figure 3 The operation is the same as that of the "remote" decoder (210) described in detail. However, a brief reference is also provided. Figure 3 When symbols are available and the entropy encoder (445) and parser (320) can losslessly encode / decode the symbols into an encoded video sequence, the entropy decoding portion of the decoder (210), which includes the channel (312), receiver (310), buffer memory (315), and parser (320), may not be fully implemented in the local decoder (433).

[0066] It can then be observed that any decoder technique other than parsing / entropy decoding, which exists in the decoder, must also exist in the corresponding encoder in essentially the same functional form. The description of the encoder technique is the inverse of the description of the decoder technique. This is only necessary in certain areas and is described in more detail below.

[0067] As part of its operation, the source encoder (430) can perform motion-compensated predictive coding, which predictively codes the input frame with reference to one or more previously encoded frames in the video sequence designated as "reference frames". In this way, the encoding engine (432) encodes the differences between the pixel blocks of the input frame and the pixel blocks of the reference frames (one or more) that can be selected as prediction references for the input frame.

[0068] The local video decoder (433) can decode encoded video data of frames that can be designated as reference frames based on symbols created by the source encoder (430). The operation of the encoding engine (432) can advantageously be lossy. When encoded video data can be decoded by the video decoder (433), Figure 4 When decoded at (not shown), the reconstructed video sequence can typically be a copy of the source video sequence with some errors. The local video decoder (433) replicates the decoding process performed on the reference frame by the video decoder and can store the reconstructed reference frame in the reference image memory (434). In this way, the video encoder (203) can locally store a copy of the reconstructed reference frame that shares the same content (no transmission errors) as the reconstructed reference frame that will be obtained by the remote video decoder.

[0069] The predictor (435) can perform a prediction search against the encoding engine (432). That is, for a new frame to be encoded, the predictor (435) can search in the reference image memory (434) for sample data (as candidate reference pixel blocks) or certain metadata, such as reference image motion vectors, block shapes, etc., that can be used as appropriate prediction references for the new frame. The predictor (435) can operate pixel-by-pixel based on the sample blocks to find appropriate prediction references. In some cases, as determined by the search results obtained by the predictor (435), the input image may have prediction references obtained from multiple reference images stored in the reference image memory (434).

[0070] The controller (450) can manage the encoding operations of the source encoder (430), including, for example, setting parameters and subgroup parameters for encoding video data.

[0071] The outputs of all the aforementioned functional units can be entropy encoded in the entropy encoder (445). The entropy encoder (445) converts the symbols generated by the various functional units into an encoded video sequence by lossless compression of the symbols, based on techniques known to those skilled in the art, such as Huffman coding, variable-length coding, and arithmetic coding.

[0072] The transmitter (440) can buffer (one or more) encoded video sequences created by the entropy encoder (445) in preparation for transmission via a communication channel (460), which can be a hardware / software link to a storage device where the encoded video data will be stored. The transmitter (440) can combine encoded video data from the source encoder (430) with other data to be transmitted, such as encoded audio data and / or auxiliary data streams (source not shown).

[0073] The controller (450) can manage the operation of the encoder (203). During encoding, the controller (450) can assign each encoded picture to certain encoded picture types that may affect the encoding techniques that can be applied to the corresponding picture. For example, pictures can typically be assigned to one of the following frame types: for example, intra-frame picture (I picture), predictive picture (P picture), and bidirectional predictive picture (B picture).

[0074] Intra-frame pictures (I-pictures) are pictures that can be encoded and decoded without using any other frames in the sequence as a source for prediction. Some video codecs allow different types of intra-frame pictures, including, for example, pictures refreshed by a separate decoder. Those skilled in the art will understand the variations of I-pictures and their corresponding applications and characteristics.

[0075] Predictive images (P-images) are images that can be encoded and decoded using intra-frame or inter-frame prediction with at most one motion vector and reference index to predict sample values ​​for each block.

[0076] Bidirectional predictive images (B-images) are images that can be encoded and decoded using intra-frame or inter-frame prediction with up to two motion vectors and reference indices to predict sample values ​​for each block. Similarly, multiple predictive images can use more than two reference images and associated metadata for the reconstruction of a single block.

[0077] Source images are typically spatially subdivided into multiple sample blocks (e.g., blocks of 4×4, 8×8, 4×8, or 16×16 samples each) and encoded block by block. These blocks can be predictively coded with reference to other (already coded) blocks, which are determined by the coding assignments of the corresponding images applied to the blocks. For example, blocks of an I-image can be non-predictively coded, or blocks can be predictively coded (spatial or intra-frame prediction) with reference to already coded blocks of the same image. Pixel blocks of a P-image can be predictively coded with reference to a previously coded reference image via spatial or temporal prediction. Blocks of a B-image can be predictively coded with reference to one or two previously coded reference images via spatial or temporal prediction.

[0078] The video encoder (203) can perform encoding operations according to a predetermined video coding technique or standard, such as that specified in ITU-T H.265 Recommendation. In its operation, the video encoder (203) can perform various compression operations, including predictive coding operations that utilize temporal and spatial redundancy in the input video sequence. Therefore, the encoded video data can conform to the syntax specified by the video coding technique or standard used.

[0079] In one embodiment, the transmitter (440) may transmit additional data and encoded video. The source encoder (430) may include such data as part of the encoded video sequence. The additional data may include temporal / spatial / SNR enhancement layers, other forms of redundant data such as redundant pictures and slices, auxiliary enhancement information (SEI) messages, video availability information (VUI) parameter set fragments, etc.

[0080] As mentioned above, the encoding of a pre-encoded video sequence can be performed according to video coding techniques or standards, and can follow principles known to those skilled in the art, including variable-length coding, Huffman coding, and arithmetic coding with or without context sensitivity. In some streaming systems, the video bitstream (204, 207, 209) can be encoded according to certain video coding / compression standards. An example of those standards includes the ITU-T HEVC Recommendation for H.265.

[0081] In HEVC, the principal transform can have a 4-point, 8-point, 16-point, or 32-point DCT-2 transform core matrix, and the transform core matrix can be represented using an 8-bit integer (i.e., an 8-bit transform core matrix). The HEVC transform core matrix of a smaller DCT-2 is a subset of that of a larger DCT-2, as shown below:

[0082] 4x4 DCT-2 Transform

[0083]

[0084] 8x8 DCT-2 Transform

[0085]

[0086] 16x16 DCT-2 Transform

[0087]

[0088] 32x32 DCT-2 Transform

[0089]

[0090] As shown above, each element in the DCT-2 core exhibits symmetric / antisymmetric properties. Therefore, a so-called "partial butterfly" implementation can be supported to reduce the number of operation counts (multiplication, addition / subtraction, shift), and the same results as matrix multiplication can be obtained using a partial butterfly implementation. More details regarding the HEVC transform design can be found in Non-Patent Literature 1.

[0091] The video coding standard currently under development is informally known as Universal Video Coding (VVC). The topics presented can be used within the context of VVC.

[0092] For the main transform in VVC, in addition to the 4-point, 8-point, 16-point, and 32-point DCT-2 transforms identical to those in HEVC, it can also include additional 2-point, 64-point, and 128-point DCT-2 transforms. The 2-point DCT-2 core can be an 8-bit integer matrix aligned with the HEVC main transform design, but the 64-point and 128-point DCT-2 use 10-bit transform cores, meaning that the 2-point, 4-point, 8-point, 16-point, and 32-point DCT-2 transforms cannot be extracted from the 64-point or 128-point DCT-2 cores in VVC.

[0093] The following shows a portion of an exemplary 64-point DCT-2 core defined in VVC, where {aa,ab,ac,ad,ae,af,ag,ah,ai,aj,ak,al,am,an,ao,ap,aq,ar,as,at,au,av,aw,ax,ay,az,ba,bb,bc,bd,be,bf,bg,bh,bi,bj,bk,bl,bm,bn,bo,bp,bq,br,bs,bt,bu,bv,bw,bx,by,bz,ca,cb,cc,cd,ce,cf,cg,ch,ci,cj,ck}={256,334} 139,355,301,201,71,360,346,319,280,230,171,105,35,362,358,351,341,327,311,291,268,243,216,186,155,122,88,53,18,362,361,359,357,353,349,344,338,331,323,315,306,296,285,274,262,250,236,223,208,194,178,163,147,130,114,97,79,62,44,27,9}:

[0094] {aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa ,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa,aa}

[0095] {bf,bg,bh,bi,bj,bk,bl,bm,bn,bo,bp,bq,br,bs,bt,bu,bv,bw,bx,by,bz,ca,cb,cc,cd,ce,cf,cg,ch,ci,cj,ck,-ck,-cj,-ci,-ch ,-cg,-cf,-ce,-cd,-cc,-cb,-ca,-bz,-by,-bx,-bw,-bv,-bu,-bt,-bs,-br,-bq,-bp,-bo,-bn,-bm,-bl,-bk,-bj,-bi,-bh,-bh,-bf}}

[0096] {ap,aq,ar,as,at,au,av,aw,ax,ay,az,ba,bb,bc,bd,be,-be,-bd,-bc,-bb,-ba,-az,-ay,-ax,-aw,-av,-au,-at,-as,-ar,-aq,-ap ,-ap,-aq,-ar,-as,-at,-au,-av,-aw,-ax,-ay,-az,-ba,-bb,-bc,-bd,-be,be,bd,bc,bb,ba,az,ay,ax,aw,av,au,at,as,ar,aq,ap}

[0097] {bg,bj,bm,bp,bs,bv,by,cb,ce,ch,ck,-ci,-cf,-cc,-bz,-bw,-bt,-bq,-bn,-bk,-bh,-bf,-bi,-bl,-bo,-br,-bu,-bx,-ca,-cd,-cd g,-cj,cj,cg,cd,ca,bx,bu,br,bo,bl,bi,bf,bh,bk,bn,bq,bt,bw,bz,cc,cf,ci,-ck,-ch,-ce,-cb,-by,-bv,-bs,-bp,-bm,-bj,-bg}}

[0098] {ah,ai,aj,ak,al,am,an,ao,-ao,-an,-am,-al,-ak,-aj,-ai,-ah,-ah,-ai,-aj,-ak,-al,-am,-an,-ao,ao,an,am,al,ak,aj,ai,ah ,ah,ai,aj,ak,al,am,an,ao,-ao,-an,-am,-al,-ak,-aj,-ai,-ah,-ah,-ai,-aj,-ak,-al,-am,-an,-ao,ao,an,am,al,ak,aj,ai,ah}

[0099] {bh,bm,br,bw,cb,cg,-ck,-cf,-ca,-bv,-bq,-bl,-bg,-bi,-bn,-bs,-bx,-cc,-ch,cj,ce,bz,bu,bp,bk,bf,bj,bo,bt,by-,cd i,-cd,-by,-bt,-bo,-bj,-bf,-bk,-bp,-bu,-bz,-ce,-cj,ch,cc,bx,bs,bn,bi,bg,bl,bq,bv,ca,cf,ck,-cg,-cb,-bw,-br,-b

[0100] {aq,at,aw,-av,-as,-ap,-ar,-au,-ax,-ba,-bd,bd,ba,ax,au,ar,ap,as,av,ay,bb,be,-bc,-az,-aw,-at,-aq ,-aq,b,ay,av,as,ap,ar,au,ax,ba,bd,-bd,-ba,-ax,-au,-ar,-ap,-as,-av,-ay,-bb,-be,bc,az,aw,at,aq}

[0101] {bi,bp,bw,cd,ck,-ce,-bx,-bq,-bj,-bh,-bo,-bv,-cc,-cj,cf,by,br,bk,bg,bn,bu,cb,ci,-cg,-bz,-bs,-bl,-bf,-bm,-b ch,ch,ca,bt,bm,bf,bl,bs,bz,cg,-ci,-cb,-bu,-bn,-bg,-bk,-br,-by,-cf,cj,cc,bv,bo,bh,bj,bq,bx,ce,-ck,-cd,-bw,-bp

[0102] {ad,ae,af,ag,-ag,-af,-ae,-ad,-ad,-ae,-af,-ag,ag,af,ae,ad,ad,ae,af,ag,-ag,-af,-ae,-ad,-ad,-ae,-af,-ag,ag,af,ae,ad ,ad,ae,af,ag,-ag,-af,-ae,-ad,-ad,-ae,-af,-ag,ag,af,ae,ad,ad,ae,af,ag,-ag,-af,-ae,-ad,-ad,-ae,-af,-ag,ag,af,ae,ad}

[0103] {bj,bs,cb,ck,-cc,-bt,-bk,-bi,-br,-ca,-cj,cd,bu,bl,bh,bq,bz,ci,-ce,-bv,-bm,-bg,-bp,-by,-ch,cf,bw,bn,bf,bo,bx,-cg cg,-bx,-bo,-bf,-bn,-bw,-cf,ch,by,bp,bg,bm,bv,ce,-ci,-bz,-bq,-bh,-bl,-bu,-cd,cj,ca,br,bi,bk,bt,cc,-ck,-cb,-bj,-bj}}

[0104] {ar,aw,bb,-bd,-ay,-at,-ap,-au,-az,-be,ba,av,aq,as,ax,bc,-bc,-ax,-as,-aq,-av,-ba,be,az,au,ap,at,ay,bd,-bb,-aw,-ar ,-ar,-aw,-bb,bd,ay,at,ap,au,az,be,-ba,-av,-aq,-as,-ax,-bc,bc,ax,as,aq,av,ba,-be,-az,-au,-ap,-at,-ay,-bd,bb,aw,ar}

[0105] {bk,bv,cg,-ce,-bt,-bi,-bm,-bx,-ci,cc,br,bg,bo,bz,ck,-ca,-bp,-bf,-bq,-cb,cj,by,bn,bh,bs,cd,-ch,-bw,-bl,-bj,-bu,-c f,cf,bu,bj,bl,bw,ch,-cd,-bs,-bh,-bn,-by,-cj,cb,bq,bf,bp,ca,-ck,-bz,-bo,-bg,-br,-cc,ci,bx,bm,bi,bt,ce,-cg,-bv,-bk}}

[0106] {ai,al,ao,-am,-aj,-ah,-ak,-an,an,ak,ah,aj,am,-ao,-al,-ai,-ai,-al,-ao,am,aj,ah,ak,an,-ak,-ah,-aj,-am,ao,al,ai ,ai,al,ao,-am,-aj,-ah,-ak,-an,an,ak,ah,aj,am,-ao,-al,-ai,-ai,-al,-ao,am,aj,ah,ak,an,-ak,-ah,-aj,-am,ao,al,ai}

[0107] {bl,by,-ck,-bx,-bk,-bm,-bz,cj,bw,bj,bn,ca,-ci,-bv,-bi,-bo,-cb,ch,bu,bh,bp,cc,-cg,-bt,-bg,-bq,-cd,cf,bs,ce,bf, -ce,br,-bf,-bs,-cf,cd,bq,bg,bt,cg,-cc,-bp,-bh,-bu,-ch,cb,bo,bi,bv,ci,-ca,-bn,-bj,-bw,-cj,bz,bm,bk,bybx-bck,}-

[0108] {as,az,-bd,-aw,-ap,-av,-bc,ba,at,ar,ay,-be,-ax,-aq,-au,-bb,bb,au,aq,ax,be,-ay,-ar,-at,-ba,bc,av,ap,aw,bd,-az,-as ,-as,-az,bd,aw,ap,av,bc,-ba,-at,-ar,-ay,be,ax,aq,au,bb,-bb,-au,-aq,-ax,-be,ay,ar,at,ba,-bc,-av,-ap,-aw,-bd,az,as}

[0109] {bm,cb,-cf,-bq,-bi,-bx,cj,bu,bf,bt,ci,-by,-bj,-bp,-ce,cc,bn,bl,ca,-cg,-br,-bh,-bw,ck,bv,bg,bs,ch,-bz,-bk,-bk, ,cd,bo,bk,bz,-ch,-bs,-bg,-bv,-ck,bw,bh,br,cg,-ca,-bl,-bn,-cc,ce,bp,bj,by,-ci,-bt,-bf,-bu,-cj,bx,bi,bq,-cf,-c

[0110] {ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab ,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab}

[0111] {bn,ce,-ca,-bj,-br,-ci,bw,bf,bv,-cj,-bs,-bi,-bz,cf,bo,bm,cd,-cb,-bk,-bq,-ch,bx,bg,bu,-ck,-bt,-bh,-by,bcg,ccbp ,-cc,-bl,-bp,-cg,by,bh,bt,ck,-bu,-bg,-bx,ch,bq,bk,cb,-cd,-bm,-bo,-cf,bz,bi,bs,cj,-bv,-bf,-bw,ci,br,bj,bn,}-

[0112] {at,bc,-ay,-ap,-ax,bd,au,as,bb,-az,-aq,-aw,be,av,ar,ba,-ba,-ar,-av,-be,aw,aq,az,-bb,-as,-au,-bd,ax,ap,ay,-bc,-at ,-at,-bc,ay,ap,ax,-bd,-au,-as,-bb,az,aq,aw,-be,-av,-ar,-ba,ba,ar,av,be,-aw,-aq,-az,bb,as,au,bd,-ax,-ap,-ay,bc,at}

[0113] {bo,ch,-bv,-bh,-ca,cc,bj,bt,-cj,-bq,-bm,-cf,bx,bf,by,-ce,-bl,-br,-ck,bs,bk,cd,-bz,-bg,-bw,cg,bn,bp,bi,-c,-bu, b,cb,bi,bu,-ci,-bp,-bn,-cg,bw,bg,bz,-cd,-bk,-bs,ck,br,bl,ce,-by,-bf,-bx,cf,bm,bq,cj,-bt,-bj,-cc,ca,bh,-bov}-

[0114] {aj,ao,-ak,-ai,-an,al,ah,am,-am,-ah,-al,an,ai,ak,-ao,-aj,-aj,-ao,ak,ai,an,-ah,-am,am,ah,al,-an,-ai,-ak,ao,aj ,aj,ao,-ak,-ai,-an,al,ah,am,-am,-ah,-al,an,ai,ak,-ao,-aj,-aj,-ao,ak,ai,an,-ah,-am,am,ah,al,-an,-ai,-ak,ao,aj}

[0115] {bp,ck,-bq,-bo,-cj,br,bn,ci,-bs,-bm,-ch,bt,bl,cg,-bu,-bk,-cf,bv,bj,ce,-bw,-bi,-cd,bx,bh,cc,-by,-bg,-cb,bz,bf,ca -ca,-bf,-bz,cb,bg,by,-cc,-bh,-bx,cd,bi,bw,-ce,-bj,-bv,cf,bk,bu,-cg,-bl,-bt,ch,bm,bs,-ci,-bn,-br,cj,bo,bq,-bp}}

[0116] {au,-be,-at,-av,bd,as,aw,-bc,-ar,-ax,bb,aq,ay,-ba,-ap,-az,az,ap,ba,-ay,-aq,-bb,ax,ar,bc,-aw,-as,-bd,av,at,be,-au ,-au,be,at,av,-bd,-as,-aw,bc,ar,ax,-bb,-aq,-ay,ba,ap,az,-az,-ap,-ba,ay,aq,bb,-ax,-ar,-bc,aw,as,bd,-av,-at,-be,au}

[0117] {bq,-ci,-bl,-bv,cd,bg,ca,-by,-bi,-cf,bt,bn,ck,-bo,-bs,cg,bj,bx,-cb,-bf,-cc,bw,bk,ch,-br,-bp,cj,bm,bu,-ce,-bz,-bz ,bz,bh,ce,-bu,-bm,-cj,bp,br,-ch,-bk,-bw,cc,bf,cb,-bx,-bj,-cg,bs,bo,-ck,-bn,-bt,cf,bi,by,-ca,-bg,-cd,bv,bl,ci,-bq}}

[0118] {ae,-ag,-ad,-af,af,ad,ag,-ae,-ae,ag,ad,af,-af,-ad,-ag,ae,ae,-ag,-ad,-af,af,ad,ag,-ae,-ae,ag,ad,af,-af,-ad,-ag,ae ,ae,-ag,-ad,-af,af,ad,ag,-ae,-ae,ag,ad,af,-af,-ad,-ag,ae,ae,-ag,-ad,-af,af,ad,ag,-ae,-ae,ag,ad,af,-af,-ad,-ag,ae}

[0119] {br,-cf,-bg,-cc,bu,bo,-ci,-bj,-bz,bx,bl,ck,-bm,-bw,ca,bi,ch,-bp,-bt,cd,bf,ce,-bs,-bq,cg,bh,cb,-bv,-bkn,bycj-b by,-bk,-cj,bn,bv,-cb,-bh,-cg,bq,bs,-ce,-bf,-cd,bt,bp,-ch,-bi,-ca,bj,bm,-ck,-bl,-bx,bz,bj,ci,-bo,-bu,cc,bg,bg,cf

[0120] {av,-bb,-ap,-bc,au,aw,-ba,-aq,-bd,at,ax,-az,-ar,-be,as,ay,-ay,-as,be,ar,az,-ax,-at,bd,aq,ba,-aw,-au,bc,ap,bb,-av ,-av,bb,ap,bc,-au,-aw,ba,aq,bd,-at,-ax,az,ar,be,-as,-ay,ay,as,-be,-ar,-az,ax,at,-bd,-aq,-ba,aw,au,-bc,-ap,-bb,av}

[0121] {bs,-cc,-bi,-cj,bl,bz,-bv,-bp,cf,bf,cg,-bo,-bw,by,bm,-ci,-bh,-cd,br,bt,-cb,-bj,-ck,bk,ca,-bu,-bq,ce,bng,-ch-, x,bx,bn,-ch,-bg,-ce,bq,bu,-ca,-bk,ck,bj,cb,-bt,-br,cd,bh,ci,-bm,-by,bw,bo,-cg,-bf,-cf,bp,bv,-bz,-bl,cc,-cb,bi,bi,

[0122] {ak,-am,-ai,ao,ah,an,-aj,-al,al,aj,-an,-ah,-ao,ai,am,-ak,-ak,am,ai,-ao,-ah,-an,aj,al,-al,-aj,an,ah,ao,-ai,-am,ak ,ak,-am,-ai,ao,ah,an,-aj,-al,al,aj,-an,-ah,-ao,ai,am,-ak,-ak,am,ai,-ao,-ah,-an,aj,al,-al,-aj,an,ah,ao,-ai,-am,ak}

[0123] {bt,-bz,-bn,cf,bh,ck,-bi,-ce,bo,by,-bu,-bs,ca,bm,-cg,-bg,-cj,bj,cd,-bp,-bx,bv,br,-cb,-bl,ch,bf,ci,-bk,-cc,bq,bw, -bw,-bq,cc,bk,-ci,-bf,-ch,bl,cb,-br,-bv,bx,bp,-cd,-bj,cj,bg,cg,-bm,-ca,bs,bu,-by,-bo,ce,bi,-ck,-bh,-cf,bn,bz,-bt}}

[0124] {aw,-ay,-au,ba,as,-bc,-aq,be,ap,bd,-ar,-bb,at,az,-av,-ax,ax,av,-az,-at,bb,ar,-bd,-ap,-be,aq,bc,-as,-ba,au,ay,-aw ,-aw,ay,au,-ba,-as,bc,aq,-be,-ap,-bd,ar,bb,-at,-az,av,ax,-ax,-av,az,at,-bb,-ar,bd,ap,be,-aq,-bc,as,ba,-au,-ay,aw}

[0125] {bu,-bw,-bs,by,bq,-ca,-bo,cc,bm,-ce,-bk,cg,bi,-ci,-bg,ck,bf,cj,-bh,-ch,bj,cf,-bl,-cd,bn,cb,-bp,-bz,br,bx,-b ,bv,bt,-bx,-br,bz,bp,-cb,-bn,cd,bl,-cf,-bj,ch,bh,-cj,-bf,-ck,bg,ci,-bi,-cg,bk,ce,-bm,-cc,bo,ca,-bq,-bw,-bu},bs

[0126] {Ah,-aa,-aa,aa,aa,aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa being being ,aa,-aa,-aa,aa,aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa being being

[0127] {bv,-bt,-bx,br,bz,-bp,-cb,bn,cd,-bl,-cf,bj,ch,-bh,-cj,bf,-ck,-bg,ci,bi,-cg,-bk,ce,bm,-cc,-bo,ca,bq,bq,-wby,bu,-bs ,-bu,-bw,bs,by,-bq,-ca,bo,cc,-bm,-ce,bk,cg,-bi,-ci,bg,ck,-bf,cj,bh,-ch,-bj,cf,bl,-cd,-bn,cb,bp,-bz,-br,,bx,}b

[0128] {ax,-av,-az,at,bb,-ar,-bd,ap,-be,-aq,bc,as,-ba,-au,ay,aw,-aw,-ay,au,ba,-as,-bc,aq,be,-ap,bd,ar,-bb,-at,az,av,-ax ,-ax,av,az,-at,-bb,ar,bd,-ap,be,aq,-bc,-as,ba,au,-ay,-aw,aw,ay,-au,-ba,as,bc,-aq,-be,ap,-bd,-ar,bb,at,-az,-av,ax} {bw,-bq,-cc,bk,ci,-bf,ch,bl,-cb,-br,bv,bx,-bp,-cd,bj,cj,-bg,cg,bm,-ca,-bs,bu,by,-bo,-ce,bi,ck,-bh,cf,bn,-bz,-bt,-bt bt,bz,-bn,-cf,bh,-ck,-bi,ce,bo,-by,-bu,bs,ca,-bm,-cg,bg,-cj,-bj,cd,bp,-bx,-bv,br,cb,-bl,-ch,bf,-ci,-bk,cc,bq,-bw}}

[0129] {al,-aj,-an,ah,-ao,-ai,am,ak,-ak,-am,ai,ao,-ah,an,aj,-al,-al,aj,an,-ah,ao,ai,-am,-ak,ak,am,-ai,-ao,ah,-an,-aj,al ,al,-aj,-an,ah,-ao,-ai,am,ak,-ak,-am,ai,ao,-ah,an,aj,-al,-al,aj,an,-ah,ao,ai,-am,-ak,ak,am,-ai,-ao,ah,-an,-aj,al}

[0130] {bx,-bn,-ch,bg,-ce,-bq,bu,ca,-bk,-ck,bj,-cb,-bt,br,cd,-bh,ci,bm,-by,-bw,bo,cg,-bf,cf,bp,-bv,-bz,bl,cj,-bi,cc,bs -bs,-cc,bi,-cj,-bl,bz,bv,-bp,-cf,bf,-cg,-bo,bw,by,-bm,-ci,bh,-cd,-br,bt,cb,-bj,ck,bk,-ca,-bu,bq,ce,-bg,ch,bn,-bx}}

[0131] {ay,-as,-be,ar,-az,-ax,at,bd,-aq,ba,aw,-au,-bc,ap,-bb,-av,av,bb,-ap,bc,au,-aw,-ba,aq,-bd,-at,ax,az,-ar,be,as,-ay ,-ay,as,be,-ar,az,ax,-at,-bd,aq,-ba,-aw,au,bc,-ap,bb,av,-av,-bb,ap,-bc,-au,aw,ba,-aq,bd,at,-ax,-az,ar,-be,-as,ay}

[0132] {by,-bk,cj,bn,-bv,-cb,bh,-cg,-bq,bs,ce,-bf,cd,bt,-bp,-ch,bi,-ca,-bw,bm,ck,-bl,bx,bz,-bj,ci,bo,-bu,-ccf,bg,- ,br,cf,-bg,cc,bu,-bo,-ci,bj,-bz,-bx,bl,-ck,-bm,bw,ca,-bi,ch,bp,-bt,-cd,bf,-ce,-bs,bq,cg,-bh,cb,bv,-bn,-by}cj,

[0133] {af,-ad,ag,ae,-ae,-ag,ad,-af,-af,ad,-ag,-ae,ae,ag,-ad,af,af,-ad,ag,ae,-ae,-ag,ad,-af,-af,ad,-ag,-ae,ae,ag,-ad,af ,af,-ad,ag,ae,-ae,-ag,ad,-af,-af,ad,-ag,-ae,ae,ag,-ad,af,af,-ad,ag,ae,-ae,-ag,ad,-af,-af,ad,-ag,-ae,ae,ag,-ad,af}

[0134] {bz,-bh,ce,bu,-bm,cj,bp,-br,-ch,bk,-bw,-cc,bf,-cb,-bx,bj,-cg,-bs,bo,ck,-bn,bt,cf,-bi,by,ca,-bg,cd,bv,b,-b,-ci bq,-ci,bl,-bv,-cd,bg,-ca,-by,bi,-cf,-bt,bn,-ck,-bo,bs,cg,-bj,bx,cb,-bf,cc,bw,-bk,ch,br,-bp,-cj,bm,-bu,-bz,-bh

[0135] {az,-ap,ba,ay,-aq,bb,ax,-ar,bc,aw,-as,bd,av,-at,be,au,-au,-be,at,-av,-bd,as,-aw,-bc,ar,-ax,-bb,aq,-ay,-ba,ap,-az ,-az,ap,-ba,-ay,aq,-bb,-ax,ar,-bc,-aw,as,-bd,-av,at,-be,-au,au,be,-at,av,bd,-as,aw,bc,-ar,ax,bb,-aq,ay,ba,-ap,az}

[0136] {ca,-bf,bz,cb,-bg,by,cc,-bh,bx,cd,-bi,bw,ce,-bj,bv,cf,-bk,bu,cg,-bl,bt,ch,-bm,bs,ci,-bn,br,cj,-bo,bq,ck,-bp,-bp ck,-bq,bo,-cj,-br,bn,-ci,-bs,bm,-ch,-bt,bl,-cg,-bu,bk,-cf,-bv,bj,-ce,-bw,bi,-cd,-bx,bh,-cc,-by,bg,-cb,-bf,-ca}

[0137] {am,-ah,al,an,-ai,ak,ao,-aj,aj,-ao,-ak,ai,-an,-al,ah,-am,-am,ah,-al,-an,ai,-ak,-ao,aj,-aj,ao,ak,-ai,an,al,-ah,am ,am,-ah,al,an,-ai,ak,ao,-aj,aj,-ao,-ak,ai,-an,-al,ah,-am,-am,ah,-al,-an,ai,-ak,-ao,aj,-aj,ao,ak,-ai,an,al,-ah,am}

[0138] {cb,-bi,bu,ci,-bp,bn,-cg,-bw,bg,-bz,-cd,bk,-bs,-ck,br,-bl,ce,by,-bf,bx,cf,-bm,bq,-cj,-bt,bj,-cc,-ca,bh,-bv,-bv o,-bo,ch,bv,-bh,ca,cc,-bj,bt,cj,-bq,bm,-cf,-bx,bf,-by,-ce,bl,-br,ck,bs,-bk,cd,bz,-bg,bw,cg,-bn,bp,-ci,-bu,bi,-cb}

[0139] {ba,-ar,av,-be,-aw,aq,-az,-bb,as,-au,bd,ax,-ap,ay,bc,-at,at,-bc,-ay,ap,-ax,-bd,au,-as,bb,az,-aq,aw,be,-av,ar,-ba ,-ba,ar,-av,be,aw,-aq,az,bb,-as,au,-bd,-ax,ap,-ay,-bc,at,-at,bc,ay,-ap,ax,bd,-au,as,-bb,-az,aq,-aw,-be,av,-ar,ba}

[0140] {cc,-bl,bp,-cg,-by,bh,-bt,ck,bu,-bg,bx,ch,-bq,bk,-cb,-cd,bm,-bo,cf,bz,-bi,bs,-cj,-bv,bf,-bw,-ci,br,ce,-bj,ca, ,bn,-ce,-ca,bj,-br,ci,bw,-bf,bv,cj,-bs,bi,-bz,-cf,bo,-bm,cd,cb,-bk,bq,-ch,-bx,bg,-bu,-ck,bt,-bh,by,cl,-ccp

[0141] {ac,-ab,ab,-ac,-ac,-ab,-ab,ac,ac,-ab,-ac,-ac,-ab,-ab,ac,ac,-ab,-ac,-ac,-ab,-ab,ac,ac,-ab,-ac,-ac,ab,-ab,ac ,ac,-ab,ab,-ac,-ac,-ab,-ab,ac,ac,-ab,-ac,-ac,-ab,-ab,ac,ac,-ab,-ac,-ac,-ab,-ab,ac,ac,-ab,-ac,-ac,ab,-ab,ac}

[0142] {cd,-bo,bk,-bz,-ch,bs,-bg,bv,-ck,-bw,bh,-br,cg,ca,-bl,bn,-cc,-ce,bp,-bj,by,ci,-bt,bf,-bu,cj,bx,-bi,bcb,-cf,- ,-bm,cb,cf,-bq,bi,-bx,-cj,bu,-bf,bt,-ci,-by,bj,-bp,ce,cc,-bn,bl,-ca,-cg,br,-bh,bw,ck,-bv,bg,-bs,ch,bz,-cd,bk}

[0143] {bb,-au,aq,-ax,be,ay,-ar,at,-ba,-bc,av,-ap,aw,-bd,-az,as,-as,az,bd,-aw,ap,-av,bc,ba,-at,ar,-ay,-be,ax,-aq,au,-bb ,-bb,au,-aq,ax,-be,-ay,ar,-at,ba,bc,-av,ap,-aw,bd,az,-as,as,-az,-bd,aw,-ap,av,-bc,-ba,at,-ar,ay,be,-ax,aq,-au,bb}

[0144] {ce,-br,bf,-bs,cf,cd,-bq,bg,-bt,cg,cc,-bp,bh,-bu,ch,cb,-bo,bi,-bv,ci,ca,-bn,bj,-bw,cj,bz,-bm,bk,-bx,ck,by,-bl,bl ,-by,-ck,bx,-bk,bm,-bz,-cj,bw,-bj,bn,-ca,-ci,bv,-bi,bo,-cb,-ch,bu,-bh,bp,-cc,-cg,bt,-bg,bq,-cd,-cf,bs,-bf,-br}}

[0145] {an,-ak,ah,-aj,am,ao,-al,ai,-ai,al,-ao,-am,aj,-ah,ak,-an,-an,ak,-ah,aj,-am,-ao,al,-ai,ai,-al,ao,am,-aj,ah,-ak,an ,an,-ak,ah,-aj,am,ao,-al,ai,-ai,al,-ao,-am,aj,-ah,ak,-an,-an,ak,-ah,aj,-am,-ao,al,-ai,ai,-al,ao,am,-aj,ah,-ak,an}

[0146] {cf,-bu,bj,-bl,bw,-ch,-cd,bs,-bh,bn,-by,cj,cb,-bq,bf,-bp,ca,ck,-bz,bo,-bg,br,-cc,-ci,bx,-bm,bi,-bt,ce,cg,- -bk,bv,-cg,-ce,bt,-bi,bm,-bx,ci,cc,-br,bg,-bo,bz,-ck,-ca,bp,-bf,bq,-cb,-cj,by,-bn,bh,-bs,cd,ch,-bw,bl,-cf}

[0147] {bc,-ax,as,-aq,av,-ba,-be,az,-au,ap,-at,ay,-bd,-bb,aw,-ar,ar,-aw,bb,bd,-ay,at,-ap,au,-az,be,ba,-av,aq,-as,ax,-bc ,-bc,ax,-as,aq,-av,ba,be,-az,au,-ap,at,-ay,bd,bb,-aw,ar,-ar,aw,-bb,-bd,ay,-at,ap,-au,az,-be,-ba,av,-aq,as,-ax,bc}

[0148] {cg,-bx,bo,-bf,bn,-bw,cf,ch,-by,bp,-bg,bm,-bv,ce,ci,-bz,bq,-bh,bl,-bu,cd,cj,-ca,br,-bi,bk,-bt,cc,ck,-bjb,bs, j,-bs,cb,-ck,-cc,bt,-bk,bi,-br,ca,-cj,-cd,bu,-bl,bh,-bq,bz,-ci,-ce,bv,-bm,bg,-bp,by,-ch,-cf,bw,-bn,bf,-cg,}b

[0149] {ag,-af,ae,-ad,ad,-ae,af,-ag,-ag,af,-ae,ad,-ad,ae,-af,ag,ag,-af,ae,-ad,-ae,af,-ag,-ag,af,-ae,ad,-ad,ae,-af,ag ,ag,-af,ae,-ad,ad,-ae,af,-ag,-ag,af,-ae,ad,-ad,ae,-af,ag,ag,-af,ae,-ad,-ae,af,-ag,-ag,af,-ae,ad,-ad,ae,-af,ag}

[0150] {ch,-ca,bt,-bm,bf,-bl,bs,-bz,cg,ci,-cb,bu,-bn,bg,-bk,br,-by,cf,cj,-cc,bv,-bo,bh,-bj,bq,-bx,ce,ck,-cd,bw,-bp,-bi,-b bi,bp,-bw,cd,-ck,-ce,bx,-bq,bj,-bh,bo,-bv,cc,-cj,-cf,by,-br,bk,-bg,bn,-bu,cb,-ci,-cg,bz,-bs,bl,-bf,bm,-bt,ca,-ch}}

[0151] {bd,-ba,ax,-au,ar,-ap,as,-av,ay,-bb,be,bc,-az,aw,-at,aq,-aq,at,-aw,az,-bc,-be,bb,-ay,av,-as,ap,-ar,au,-ax,ba,-bd ,-bd,ba,-ax,au,-ar,ap,-as,av,-ay,bb,-be,-bc,az,-aw,at,-aq,aq,-at,aw,-az,bc,be,-bb,ay,-av,as,-ap,ar,-au,ax,-ba,bd}

[0152] {ci,-cd,by,-bt,bo,-bj,bf,-bk,bp,-bu,bz,-ce,cj,ch,-cc,bx,-bs,bn,-bi,bg,-bl,bq,-bv,ca,-cf,ck,cg,-cb,bw,-br,bm,-bh bh,-bm,br,-bw,cb,-cg,-ck,cf,-ca,bv,-bq,bl,-bg,bi,-bn,bs,-bx,cc,-ch,-cj,ce,-bz,bu,-bp,bk,-bf,bj,-bo,bt,-bp,-cd,-ci}

[0153] {ao,-an,am,-al,ak,-aj,ai,-ah,ah,-ai,aj,-ak,al,-am,an,-ao,-ao,an,-am,al,-ak,aj,-ai,ah,-ah,ai,-aj,ak,-al,am,-an,ao ,ao,-an,am,-al,ak,-aj,ai,-ah,ah,-ai,aj,-ak,al,-am,an,-ao,-ao,an,-am,al,-ak,aj,-ai,ah,-ah,ai,-aj,ak,-al,am,-an,ao}

[0154] {cj,-cg,cd,-ca,bx,-bu,br,-bo,bl,-bi,bf,-bh,bk,-bn,bq,-bt,bw,-bz,cc,-cf,ci,ck,-ch,ce,-cb,by,-bv,bs,-bj,bg,- -bg,bj,-bm,bp,-bs,bv,-by,cb,-ce,ch,-ck,-ci,cf,-cc,bz,-bw,bt,-bq,bn,-bk,bh,-bf,bi,-bl,bo,-br,bu,-bx,ca,-cj,}c

[0155] {be,-bd,bc,-bb,ba,-az,ay,-ax,aw,-av,au,-at,as,-ar,aq,-ap,ap,-aq,ar,-as,at,-au,av,-aw,ax,-ay,az,-ba,bb,-bc,bd,-be ,-be,bd,-bc,bb,-ba,az,-ay,ax,-aw,av,-au,at,-as,ar,-aq,ap,-ap,aq,-ar,as,-at,au,-av,aw,-ax,ay,-az,ba,-bb,bc,-bd,be}

[0156] {ck,-cj,ci,-ch,cg,-cf,ce,-cd,cc,-cb,ca,-bz,by,-bx,bw,-bv,bu,-bt,bs,-br,bq,-bp,bo,-bn,bm,-bl,bk,-bj,bi,-bh,b ,bf,-bg,bh,-bi,bj,-bk,bl,-bm,bn,-bo,bp,-bq,br,-bs,bt,-bu,bv,-bw,bx,-by,bz,-ca,cb,-cc,cd,-ce,cf,-cj,ch,-ck,ci,

[0157] The following shows an exemplary 128-point DCT-2 core defined in VVC, where {aa,ab,ac,ad,ae,af,ag,ah,ai,aj,ak,al,am,an,ao,ap,aq,ar,as,at,au,av,aw,ax,ay,az,ba,bb,bc,bd,be,bf,bg,bh,bi,bj,bk,bl,bm,bn,bo,bp,bq,br,bs,bt,bu,bv,bw,bx,by,bz,ca,cb,cc,cd,ce,cf,cg,ch,ci,cj,ck,cl,c m,cn,co,cp,cq,cr,cs,ct,cu,cv,cw,cx,cy,cz,da,db,dc,dd,de,df,dg,dh,di,dj,dk,dl,dm,dn,d_,dp,dq,dr,ds,dt,du,dv,dw,dx ,dy,dz,ea,eb,ec,ed,ee,ef,eg,eh,ei,ej,ek,el,em,en,eo,ep,eq,er,es,et,eu,ev,ew}={256,334,139,355,301,201,71,360,346, 319,280,230,171,105,35,362,358,351,341,327,311,291,268,243,216,186,155,122,88,53,18,362,361,359,357,353,349,344,338,331,323,315,306,296,285,274,262,250,236,223,208,194,178,163,147,130,114,97,79,62,44,27,9,362,362,361,361,360, 359,357,356,354,352,350,348,345,342,339,336,333,329,325,321,317,313,308,303,299,293,288,283,277,271,265,259,253,246,240,233,226,219,212,205,197,190,182,175,167,159,151,143,134,126,118,109,101,92,84,75,66,58,49,40,31,22,13,4}.

[0158] The following shows a 128-point DCT-2 core, describing only the left half of the 128x128 transform core. The right half can be derived based on the symmetry / antisymmetry properties of DCT-2:

[0159] {Ah,aa,aa,aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaoahaaaaaaaaaaaaaaaaaaaaaaxias'a'a'a'a'a'a'a'a'a'a'a'a','a'a'a'a,'a'a'a' ,aa,aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa,aaaaaaaaaaaaaaaaaaaaaaaughaaaa,aa,aaaaaaaaaaaaaaaaaaaaaaaaaaaa,aaaaaaaaaaaaaaaaaah,aaaaaaaaaaaaaaaaaaaaaaaaaaaa,aaaaaaaaaaaaaaaaah,aaaaaaaaaaaaaaaaaaaaa,aaaaaaaaaaaaaaaah,aa,aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa,aaaaaaaaaaaaaaaah,aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

[0160] {cl,cm,cn,co,cp,cq,cr,cs,ct,cu,cv,cw,cx,cy,cz,da,db,dc,dd,d,df,dg,dh,dj,dk,dl,dm,dn,d_,dp,dq ,dr,ds,dt,du,dv,dw,dx,dz,ea,eb,ec,ed,ee,ef,eg,eh,ei,ej,ek,el,em,en,eo,ep,eq,er,es,et,eu,ev,ew}

[0161] {bf,bg,bh,bi,bj,bk,bl,bm,bn,bo,bp,bq,br,bz,bt,bu,bv,bw,bx,bx,ca,cb,cc,cd,ce,cf,cg,ch,ci,cj,ck,-ck,-chj,-ci ,-cg,-cf,-ce,-cd,-cc,-cb,-ca,-bz,-by,-bx,-bw,-bv,-bu,-bt,-bs,-br,-bq,-bp,-bo,-bn,-bm,-bl,-bk,-bj,-fg,-bi,-bh

[0162] {cm,cp,cs,cv,cy,db,de,dh,dk,dn,dq,dt,dw,dz,ec,ef,ei,el,eo,er,eu,-ew,-et,-eq,-en,-ek,-eh,-ee,-eb,-dy,-dv,-ds,-dp,-dm j,-dg,-dd,-da,-cx,-cu,-cr,-co,-cl,-cn,-cq,-ct,-cw,-cz,-dc,-df,-di,-dl,-d_,-dr,-du,-dx,-ea,-ed,-eg,-ej,-es,-ep

[0163] {ap,aq,ar,as,at,au,av,aw,ax,ay,az,ba,bb,bc,bd,be,-be,-bd,-bc,-bb,-ba,-az,-ay,-ax,-aw,-av,-au,-at,-as,-ar,-aq,-ap ,-ap,-aq,-ar,-as,-at,-au,-av,-aw,-ax,-ay,-az,-ba,-bb,-bc,-bd,-be,be,bd,bc,bb,ba,az,ay,ax,aw,av,au,at,as,ar,aq,ap}

[0164] {cn,cs,cx,dc,dh,dm,dr,dw,eb,eg,el,eq,ev,-et,-eo,-ej,-ee,-dz,-du,-dp,-dk,-df,-da,-cv,-cq,-cl,-cp,-cu,-cz,-de,- dj,-d_,-dt,-dy,-ed,-ei,-en,-es,ew,er,em,eh,ec,dx,ds,dn,di,dd,cy,ct,co,cm,cr,cw,db,dg,dl,dq,dv,ea,ef,ek,ep,eu}

[0165] {bg,bj,bm,bp,bs,bv,by,cb,ce,ch,ck,-ci,-cf,-cc,-bz,-bw,-bt,-bq,-bn,-bk,-bh,-bf,-bi,-bl,-bo,-br,-bu,-cd,-ca,- g,-cj,cj,cg,cd,ca,bx,bu,br,bo,bl,bi,bf,bh,bk,bn,bq,bt,bw,bz,cc,cf,ci,-ck,-ch,-ce,-cb,-by,-bv,-bs,-bp,-bm,-bj

[0166] {co,cv,dc,dj,dq,dx,ee,el,es,-eu,-en,-eg,-dz,-ds,-dl,-de,-cx,-cq,-cm,-ct,-da,-dh,-d_,-dv,-ec,-ej,-eq,ew,ep,ei,eb,du ,dn,dg,cz,cs,cl,cr,cy,df,dm,dt,ea,eh,eo,ev,-er,-ek,-ed,-dw,-dp,-di,-db,-cu,-cn,-cp,-cw,-dd,-dk,-dr,-emdy,-et}-ef,

[0167] {ah,ai,aj,ak,al,am,an,ao,-ao,-an,-am,-al,-ak,-aj,-ai,-ah,-ah,-ai,-aj,-ak,-al,-am,-an,-ao,ao,an,am,al,ak,-aj,ai,ah ,ah,ai,aj,ak,al,am,an,ao,-ao,-an,-am,-al,-ak,-aj,-ai,-ah,-ah,-ai,-ah,-ah,-ak,-al,-am,-an,-ao,-an,am,al,ak,-aj,ai,-ah}

[0168] {cp,cy,dh,dq,dz,ei,er,-et,-ek,-eb,-ds,-dj,-da,-cr,-cn,-cw,-df,-d_,-dx,-eg,-ep,ev,em,ed,du,dl,dc,ct,cl,cu,dd,dm ,dv,ee,en,ew,-eo,-ef,-dw,-dn,-de,-cv,-cm,-cs,-db,-dk,-dt,-ec,-el,-eu,eq,eh,dy,dp,dg,cx,co,cq,cz,di,dr,ea,ej,es}

[0169] {bh,bm,br,bw,cb,cg,-ck,-cf,-ca,-bv,-bq,-bl,-bg,-bi,-bn,-bs,-bx,-cc,-ch,cj,ce,bz,bu,bp,bk,bf,bj,bo,bt,by,cd,ci,-c i,-cd,-by,-bt,-bo,-bj,-bf,-bk,-bp,-bu,-bz,-ce,-cj,ch,cc,bx,bs,bn,bi,bg,bl,bq,bv,ca,cf,ck,-cg,-cb,-bw,-br,-bm,-bh}

[0170] {cq,db,dm,dx,ei,et,-ep,-ee,-dt,-di,-cx,-cm,-cu,-df,-dq,-eb,-em,ew,el,ea,dp,de,ct,cn,cy,dj,du,ef,eq,-es,-eh,-dw,-dl ,-da,-cp,-cr,-dc,-dn,-dy,-ej,-eu,eo,ed,ds,dh,cw,cl,cv,dg,dr,ec,en,-ev,-ek,-dz,-d_,-dd,-cs,-co,-cz,-dk,-dv,-eg,-er}

[0171] {aq,at,aw,-av,-as,-ap,-ar,-au,-ax,-ba,-bd,bd,ba,ax,au,ar,ap,as,av,ay,bb,be,-bc,-az,-aw,-at,-aq ,-aq,b,ay,av,as,ap,ar,au,ax,ba,bd,-bd,-ba,-ax,-au,-ar,-ap,-as,-av,-ay,-bb,-be,bc,az,aw,at,aq}

[0172] {cr,de,dr,ee,er,-ep,-ec,-dp,-dc,-cp,-ct,-dg,-dt,-eg,-et,en,ea,dn,da,cn,cv,di,dv,ei,ev,-el,-dy,-dl,-cy,-cl,-cx,- dk,-dx,-ek,ew,ej,dw,dj,cw,cm,cz,dm,dz,-eu,-eh,-du,-dh,-cu,-co,-db,-d_,-eb,-eo,es,f,df,cs,cq,dd,dq,ed,eq}

[0173] {bi,bp,bw,cd,ck,-ce,-bx,-bq,-bj,-bh,-bo,-bv,-cc,-cj,cf,by,br,bk,bg,bn,bu,cb,ci,-cg,-bz,-bs,-bl,-bf,-bm,-b ch,ch,ca,bt,bm,bf,bl,bs,bz,cg,-ci,-cb,-bu,-bn,-bg,-bk,-br,-by,-cf,cj,cc,bv,bo,bh,bj,bq,bx,ce,-ck,-cd,-bw,-bp

[0174] {cs,dh,dw,el,-et,-ee,-dp,-da,-cl,-cz,-d_,-ed,-es,em,dx,di,ct,cr,dg,dv,ek,-eu,-ef,-dq,-db,-cm,-cy,-dn,-ec,-er,en,dy ,dj,cu,cq,df,du,ej,-ev,-eg,-dr,-dc,-cn,-cx,-dm,-eb,-eq,eo,dz,dk,cv,cp,de,dt,ei,-ew,-eh,-ds,-dd,-co,-cw,-dl,-

[0175] {ad,ae,af,ag,-ag,-af,-ae,-ad,-ad,-ae,-af,-ag,ag,af,ae,ad,ad,ae,af,ag,-ag,-af,-ae,-ad,-ad,-ae,-af,-ag,ag,af,ae,ad ,ad,ae,af,ag,-ag,-af,-ae,-ad,-ad,-ae,-af,-ag,ag,af,ae,ad,ad,ae,af,ag,-ag,-af,-ae,-ad,-ad,-ae,-af,-ag,ag,af,ae,ad}

[0176] {ct,dk,eb,es,-ek,-dt,-dc,-cl,-db,-ds,-ej,et,ec,dl,cu,cs,dj,ea,er,-el,-du,-dd,-cm,-da,-dr,-ei,eu,ed,dm,cv,cr,di ,dz,eq,-em,-dv,-de,-cn,-cz,-dq,-eh,ev,ee,dn,cw,cq,dh,dy,ep,-en,-dw,-df,-co,-cy,-dp,-eg,ew,ef,d_,cx,cp,dg},dx,eo

[0177] {bj,bs,cb,ck,-cc,-bt,-bk,-bi,-br,-ca,-cj,cd,bu,bl,bh,bq,bz,ci,-ce,-bv,-bm,-bg,-bp,-by,-ch,cf,bw,bn,bf,bg,bo,-bx cg,-bx,-bo,-bf,-bn,-bw,-cf,ch,by,bp,bg,bm,bv,ce,-ci,-bz,-bq,-bh,-bl,-bu,-cd,cj,ca,br,bi,bk,bt,cc,-ck,-bj,-bs

[0178] {cu,dn,eg,-eu,-eb,-di,-cp,-cz,-ds,-el,ep,dw,dd,cl,de,dx,eq,-ek,-dr,-cy,-cq,-dj,-ec,-ev,ef,dm,ct,cv,d_,eh,-et,-ea dh,-co,-da,-dt,-em,eo,dv,dc,cm,df,dy,er,-ej,-dq,-cx,-cr,-dk,-ed,-ew,ee,dl,cs,cw,dp,ei,-es,-dz,-dg,-cn,-db,-du,du

[0179] {ar,aw,bb,-bd,-ay,-at,-ap,-au,-az,-be,ba,av,aq,as,ax,bc,-bc,-ax,-as,-aq,-av,-ba,be,az,au,ap,at,ay,bd,-bb,-aw,-ar ,-ar,-aw,-bb,b,bd,ay,at,ap,au,az,be,-ba,-av,-aq,-as,-ax,-bc,bc,ax,as,aq,av,ba,-be,-az,-au,-ap,-at,-ay,-bd,bb,aw,ar}

[0180] {cv,dq,el,-en,-ds,-cx,-ct,-d_,-ej,ep,du,cz,cr,dm,eh,-er,-dw,-db,-cp,-dk,-ef,et,dy,dd,cn,di,ed,-ev,-ea,-df,-cl,-d g,-eb,-ew,ec,dh,cm,de,dz,eu,-ee,-dj,-co,-dc,-dx,-es,eg,dl,cq,da,dv,eq,-ei,-dn,-cs,-cy,-dt,-eo,ek,dp,cu,cw,dr,em}

[0181] {bk,bv,cg,-ce,-bt,-bi,-bm,-bx,-ci,cc,br,bg,bo,bz,ck,-ca,-bp,-bf,-bq,-cb,cj,by,bn,bh,bs,cd,-ch,-bw,-bl,-bj, f,cf,bu,bj,bl,bw,ch,-cd,-bs,-bh,-bn,-by,-cj,cb,bq,bf,bp,ca,-ck,-bz,-bo,-bg,-br,-cc,ci,bx,bm,bi,bt,ce,-cg,-bv

[0182] {cw,dt,eq,-eg,-dj,-cm,-dg,-ed,et,dw,cz,ct,dq,en,-ej,-dm,-cp,-dd,-ea,ew,dz,dc,cq,dn,ek,-em,-dp,-cs,-da,-ecx,,-eu df,cn,dk,eh,-ep,-ds,-cv,-cx,-du,-er,ef,di,cl,dh,ee,-es,-dv,-cy,-cu,-dr,-eo,ei,dl,co,de,eb,-ev,-dy,-db,-cr,-d_,-el}

[0183] {ai,al,ao,-am,-aj,-ah,-ak,-an,an,ak,ah,aj,am,-ao,-al,-ai,-ai,-al,-ao,am,-ah,ak,an,-an,-ak,-ah,-aj,-am,ao,al,ai ,ai,al,ao,-am,-aj,-ah,-ak,-an,an,ak,ah,aj,am,-ao,-al,-ai,-ai,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al,-al

[0184] {cx,dw,ev,-dz,-da,-cu,-dt,-es,ec,dd,cr,dq,ep,-ef,-dg,-co,-dn,-em,ei,dj,cl,dk,ej,-el,-dm,-cn,-dh,-eg,eo,dp,cq,de ,ed,-er,-ds,-ct,-db,-ea,eu,dv,cw,cy,dx,ew,-dy,-cz,-cv,-du,-et,eb,dc,cs,dr,eq,-ee,-df,-cp,-d_,-en,eh,di,cm,dl,ek}

[0185] {bl,by,-ck,-bx,-bk,-bm,-bz,cj,bw,bj,bn,ca,-ci,-bv,-bi,-bo,-cb,ch,bu,bh,bp,cc,-cg,-bt,-bg,-bq,-cd,cf,bs,bf,br,ce, -ce,-br,-bf,-bs,-cf,cd,bq,bg,bt,cg,-cc,-bp,-bh,-bu,-ch,cb,bo,bi,bv,ci,-ca,-bn,-bj,-bw,-cj,bz,bm,bk,bx,ck,-by,-bl}

[0186] {cy,dz,-et,-ds,-cr,-df,-eg,em,dl,cl,dm,en,-ef,-de,-cs,-dt,-eu,dy,cx,cz,ea,-es,-dr,-cq,-dg,-eh,el,dk,cm,dn,eo,-ee,- dd,-ct,-du,-ev,dx,cw,da,eb,-er,-dq,-cp,-dh,-ei,ek,dj,cn,d_,ep,-ed,-dc,-cu,-dv,-ew,dw,cv,db,ec,-eq,-dp,-co,-di,-ej}

[0187] {as,az,-bd,-aw,-ap,-av,-bc,ba,at,ar,ay,-be,-ax,-aq,-au,-bb,bb,au,aq,ax,be,-ay,-ar,-at,-ba,bc,av,ap,aw,bd,-az,-as ,-as,-az,bd,aw,ap,av,bc,-ba,-at,-ar,-ay,be,ax,aq,au,bb,-bb,-au,-aq,-ax,-be,ay,ar,at,ba,-bc,-av,-ap,-aw,-bd,az,as}

[0188] {cz,ec,-eo,-dl,-cn,-dq,-et,dx,cu,de,eh,-ej,-dg,-cs,-dv,ev,ds,cp,dj,em,-ee,-db,-cx,-ea,eq,dn,cl,d_,er,-dz,-cw, ,-ef,el,di,cq,dt,ew,-du,-cr,-dh,-ek,eg,dd,cv,dy,-es,-dp,-cm,-dm,-ep,eb,cy,da,ed,-en,-dk,-co,-dr,-eu,dw,ct,df,ei}

[0189] {bm,cb,-cf,-bq,-bi,-bx,cj,bu,bf,bt,ci,-by,-bj,-bp,-ce,cc,bn,bl,ca,-cg,-br,-bh,-bw,ck,bv,bg,bs,ch,-bz,-bk,-bk, ,cd,bo,bk,bz,-ch,-bs,-bg,-bv,-ck,bw,bh,br,cg,-ca,-bl,-bn,-cc,ce,bp,bj,by,-ci,-bt,-bf,-bu,-cj,bx,bi,bq,-cf,-c

[0190] {da,f,-ej,-de,-cw,-eb,en,di,cs,dx,-er,-dm,-co,-dt,ev,dq,cl,dp,eu,-du,-cp,-dl,-eq,dy,ct,dh,em,-ec,-cx,-dd,-ei,eg ,db,cz,ee,-ek,-df,-cv,-ea,eo,dj,cr,dw,-es,-dn,-cn,-ds,ew,dr,cm,d_,et,-dv,-cq,-dk,-ep,dz,cu,dg,el,-ed,-eh,}-dc

[0191] {ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab ,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab,ab,ac,-ac,-ab,-ab,-ac,ac,ab}

[0192] {db,ei,-ee,-cx,-df,-em,ea,ct,dj,eq,-dw,-cp,-dn,-eu,ds,cl,dr,-ev,-d_,-co,-dv,er,dk,cs,dz,-en,-dg,-cw,-ed,ej,dc,da ,eh,-ef,-cy,-de,-el,eb,cu,di,ep,-dx,-cq,-dm,-et,dt,cm,dq,-ew,-dp,-cn,-du,es,dl,cr,dy,-eo,-dh,-cv,-ec,ek,dd,cz,eg}

[0193] {bn,ce,-ca,-bj,-br,-ci,bw,bf,bv,-cj,-bs,-bi,-bz,cf,bo,bm,cd,-cb,-bk,-bq,-ch,bx,bg,bu,-ck,-bt,-bh,-by,cg,bp,bl,cc ,-cc,-bl,-bp,-cg,by,bh,bt,ck,-bu,-bg,-bx,ch,bq,bk,cb,-cd,-bm,-bo,-cf,bz,bi,bs,cj,-bv,-bf,-bw,ci,br,bj,ca,-ce,-bn}

[0194] {dc,el,-dz,-cq,-d_,ew,dn,cr,ea,-ek,-db,-dd,-em,dy,cp,dp,-ev,-dm,-cs,-eb,ej,da,de,en,-dx,-co,-dq,eu,dl,ct,ec,-ei,- cz,-df,-eo,dw,cn,dr,-et,-dk,-cu,-ed,eh,cy,dg,ep,-dv,-cm,-ds,es,dj,cv,ee,-eg,-cx,-dh,-eq,du,cl,dt,-er,-di,-cw,-ef

[0195] {at,bc,-ay,-ap,-ax,bd,au,as,bb,-az,-aq,-aw,be,av,ar,ba,-ba,-ar,-av,-be,aw,aq,az,-bb,-as,-au,-bd,ax,ap,ay,-bc,-at ,-at,-bc,ay,ap,ax,-bd,-au,-as,-bb,az,aq,aw,-be,-av,-ar,-ba,ba,ar,av,be,-aw,-aq,-az,bb,as,au,bd,-ax,-ap,-ay,bc,at}

[0196] {dd,eo,-du,-cm,-dx,el,da,dg,er,-dr,-cp,-ea,ei,cx,dj,eu,-d_,-cs,-ed,ef,cu,dm,-ew,-dl,-cv,-eg,ec,cr,dp,-et,,-cy,- -ej,dz,co,ds,-eq,-df,-db,-em,dw,cl,dv,-en,-dc,-de,-ep,dt,cn,dy,-ek,-cz,-dh,-es,dq,cq,eb,-eh,-cw,-dk,-ev,dn,ct,ee}

[0197] {bo,ch,-bv,-bh,-ca,cc,bj,bt,-cj,-bq,-bm,-cf,bx,bf,by,-ce,-bl,-br,-ck,bs,bk,cd,-bz,-bg,-bw,cg,bn,bp,bi,-c,-bu, b,cb,bi,bu,-ci,-bp,-bn,-cg,bw,bg,bz,-cd,-bk,-bs,ck,br,bl,ce,-by,-bf,-bx,cf,bm,bq,cj,-bt,-bj,-cc,ca,bh,-bv}-

[0198] {de,er,-dp,-ct,-eg,ea,cn,dv,-el,-cy,-dk,ew,dj,cz,em,-du,-co,-eb,ef,cs,dq,-eq,-dd,-df,-es,d_,cu,eh,-dz,-cm,-dw,ek ,cx,dl,-ev,-di,-da,-en,dt,cp,ec,-ee,-cr,-dr,ep,dc,dg,et,-dn,-cv,-ei,dy,cl,dx,-ej,-cw,-dm,eu,dh,db,eo,-ds,-cq,-ed}

[0199] {aj,ao,-ak,-ai,-an,al,ah,am,-am,-ah,-al,an,ai,ak,-ak,-ao,-aj,-aj,-ao,-an,-al,-ah,-am,am,ah,al,-an,-ai,-ak,ao,-aj ,aj,ao,-ak,-am,-am,-ah,-al,an,ai,-ak,-ao,-aj,-aj,-ao,------------------------------------------------------luat-ao,----------

[0200] {df,eu,-dk,-da,-ep,dp,cv,ek,-du,-cq,-ef,dz,cl,ea,-ee,-cp,-dv,ej,cu,dq,-eo,-cz,-dl,et,de,dg,ev,-dj,-db,-eq,d_,cw ,el,-dt,-cr,-eg,dy,cm,eb,-ed,-co,-dw,ei,ct,dr,-en,-cy,-dm,es,dd,dh,ew,-di,-dc,-er,dn,cx,em,-ds,-cs,-eh,dx,cn,ec}

[0201] {bp,ck,-bq,-bo,-cj,br,bn,ci,-bs,-bm,-ch,bt,bl,cg,-bu,-bk,-cf,bv,bj,ce,-bw,-bi,-cd,bx,bh,cc,-by,-bg,-cb,bz,bf,ca, -ca,-bf,-bz,cb,bg,by,-cc,-bh,-bx,cd,bi,bw,-ce,-bj,-bv,cf,bk,bu,-cg,-bl,-bt,ch,bm,bs,-ci,-bn,-br,cj,bo,bq,-ck,-bp}

[0202] {dg,-ew,-df,-dh,ev,de,di,-eu,-dd,-dj,et,dc,dk,-es,-db,-dl,er,da,dm,-eq,-cz,-dn,ep,cy,d_,-eo,-cx,-dp,en,cw,dq -cv,-dr,el,cu,ds,-ek,-ct,-dt,ej,cs,du,-ei,-cr,-dv,eh,cq,dw,-eg,-cp,-dx,ef,co,dy,-ee,-cn,-dz,ed,cm,ea,-ec,-cl,-eb}

[0203] {au,-be,-at,-av,bd,as,aw,-bc,-ar,-ax,bb,aq,ay,-ba,-ap,-az,az,ap,ba,-ay,-aq,-bb,ax,ar,bc,-aw,-as,-bd,av,at,be,-au ,-au,be,at,av,-bd,-as,-aw,bc,ar,ax,-bb,-aq,-ay,ba,ap,az,-az,-ap,-ba,ay,aq,bb,-ax,-ar,-bc,aw,as,bd,-av,-at,-be,au}

[0204] {dh,-et,-da,-d_,em,ct,dv,-ef,-cm,-ec,dy,cq,ej,-dr,-cx,-eq,dk,de,-ew,-dd,-dl,ep,cw,ds,-ei,-cp,-dz,eb,cn,eg,-du,-c u,-en,dn,db,eu,-dg,-di,es,cz,dp,-el,-cs,-dw,ee,cl,ed,-dx,-cr,-ek,dq,cy,er,-dj,-df,ev,DC,dm,-eo,-cv,-dt},eh,co

[0205] {bq,-ci,-bl,-bv,cd,bg,ca,-by,-bi,-cf,bt,bn,ck,-bo,-bs,cg,bj,bx,-cb,-bf,-cc,bw,bk,ch,-br,-bp,cj,bm,bu,-ce,- ,bz,bh,ce,-bu,-bm,-cj,bp,br,-ch,-bk,-bw,cc,bf,cb,-bx,-bj,-cg,bs,bo,-ck,-bn,-bt,cf,bi,by,-ca,-bg,-cd,bv,-bql}

[0206] {di,-eq,-cv,-dv,ed,cn,ei,-dq,-da,-ev,dd,dn,-el,-cq,-ea,dy,cs,en,-dl,-df,et,cy,ds,-eg,-cl,-ef,dt,cx,es,-dg,-dk,eo ct,dx,-eb,-cp,-ek,d_,dc,-ew,-db,-dp,ej,co,ec,-dw,-cu,-ep,dj,dh,-er,-cw,-du,ee,cm,eh,-dr,-cz,-eu,de,dm,-em,-dz,}-cr,-

[0207] {ae,-ag,-ad,-af,af,ad,ag,-ae,-ae,ag,ad,af,-af,-ad,-ag,ae,ae,-ag,-ad,-af,af,ad,ag,-ae,-ae,ad,af,-af,-ad,-ag,ae ,ae,-ag,-ad,-af,af,ad,ag,-ae,-ae,ag,ad,af,-af,-ad,-ag,ae,ae,-ag,-ad,-af,af,ad,ag,-ae,-ae,ag,ad,af,-af,-ad,-ag,ae}

[0208] {dj,-en,-cq,-ec,du,cy,ev,-db,-dr,ef,cn,ek,-dm,-dg,eq,ct,dz,-dx,-cv,-es,de,d_,-ei,-cl,-eh,dp,dd,-et,-cw,-dw,ea,c s,ep,-dh,-dl,el,co,ee,-ds,-da,ew,cz,dt,-ed,-cp,-em,dk,di,-eo,-cr,-eb,dv,cx,eu,-dc,-dq,eg,cm,ej,-dn,-df,er,cu,dy}

[0209] {br,-cf,-bg,-cc,bu,bo,-ci,-bj,-bz,bx,bl,ck,-bm,-bw,ca,bi,ch,-bp,-bt,cd,bf,ce,-bs,-bq,cg,bh,cb,-bv,-bkn,bycj-b by,-bk,-cj,bn,bv,-cb,-bh,-cg,bq,bs,-ce,-bf,-cd,bt,bp,-ch,-bi,-ca,bj,bm,-ck,-bl,-bx,bz,bj,ci,-bo,-bu,cc,-bg,bg,cf

[0210] {dk,-ek,-cl,-ej,dl,dj,-el,-cm,-ei,dm,di,-em,-cn,-eh,dn,dh,-en,-co,-eg,d_,dg,-eo,-cp,-ef,dp,df,-ep,-cq,-ee,dq,de,-eq, -cr,-ed,dr,dd,-er,-cs,-ec,ds,dc,-es,-ct,-eb,dt,db,-et,-cu,-ea,du,da,-eu,-cv,-dz,dv,cz,-ev,-cw,-dy,dw,cy,-ew,-cx,-dx}}

[0211] {av,-bb,-ap,-bc,au,aw,-ba,-aq,-bd,at,ax,-az,-ar,-be,as,ay,-ay,-as,be,ar,az,-ax,-at,bd,aq,ba,-aw,-au,bc,ap,bb,-av ,-av,bb,ap,bc,-au,-aw,ba,aq,bd,-at,-ax,az,ar,be,-as,-ay,ay,as,-be,-ar,-az,ax,at,-bd,-aq,-ba,aw,au,-bc,-ap,-bb,av}

[0212] {dl,-eh,-cp,-eq,dc,du,-dy,-cy,eu,ct,ed,-dp,-dh,el,cl,em,-dg,-dq,ec,cu,ev,-cx,-dz,dt,dd,-ep,-co,-ei,dk,dm,-eg,-cq ,-er,db,dv,-dx,-cz,et,cs,ee,-d_,-di,ek,cm,en,-df,-dr,eb,cv,ew,-cw,-ea,ds,de,-eo,-cn,-ej,dj,dn,-ef,-cr,-es,da,dw}

[0213] {bs,-cc,-bi,-cj,bl,bz,-bv,-bp,cf,bf,cg,-bo,-bw,by,bm,-ci,-bh,-cd,br,bt,-cb,-bj,-ck,bk,ca,-bu,-bq,ce,bg,ch,-bn,-b x,bx,bn,-ch,-bg,-ce,bq,bu,-ca,-bk,ck,bj,cb,-bt,-br,cd,bh,ci,-bm,-by,bw,bo,-cg,-bf,-cf,bp,bv,-bz,-bl,cj,bi,cc,-bs}

[0214] {dm,-ee,-cu,ew,ct,ef,-dl,-dn,ed,cv,-ev,-cs,-eg,dk,d_,-ec,-cw,eu,cr,eh,-dj,-dp,eb,cx,-et,-cq,-ei,di,dq,-ea,-cy,es ,cp,ej,-dh,-dr,dz,cz,-er,-co,-ek,dg,ds,-dy,-da,eq,cn,el,-df,-dt,dx,db,-ep,-cm,-em,de,du,-dw,-dc,eo,cl,en,-dd,-dv}

[0215] {ak,-am,-ai,ao,ah,an,-aj,-al,al,aj,-an,-ah,-ao,ai,am,-ak,-ak,am,ai,-ao,-ah,-an,aj,al,-al,-aj,an,ah,ao,-ai,-am,ak ,ak,-am,-ai,ao,ah,an,-aj,-al,al,aj,-an,-ah,-ao,ai,am,-ak,-ak,am,ai,-ao,-ah,-an,-al,-al,-aj,an,ah,ao,-ai,-am,ak}

[0216] {dn,-eb,-cz,ep,cl,eq,-cy,-ec,dm,d_,-ea,-da,eo,cm,er,-cx,-ed,dl,dp,-dz,-db,en,cn,es,-cw,-ee,dk,dq,-dy,-dc,em,co ,et,-cv,-ef,dj,dr,-dx,-dd,el,cp,eu,-cu,-eg,di,ds,-dw,-de,ek,cq,ev,-ct,-eh,dh,dt,-dv,-df,ej,cr,ew,-cs,-ei,dg,du}

[0217] {bt,-bz,-bn,cf,bh,ck,-bi,-ce,bo,by,-bu,-bs,ca,bm,-cg,-bg,-cj,bj,cd,-bp,-bx,bv,br,-cb,-bl,ch,bf,ci,-bq,b,-cc,b -bw,-bq,cc,bk,-ci,-bf,-ch,bl,cb,-br,-bv,bx,bp,-cd,-bj,cj,bg,cg,-bm,-ca,bs,bu,-by,-bo,ce,bi,ck,-bh,-cf,-bn,bn,bn,

[0218] {d_,-dy,-de,ei,cu,-es,-cl,-er,cv,eh,-df,-dx,dp,dn,-dz,-dd,ej,ct,-et,-cm,-eq,cw,eg,-dg,-dw,dq,dm,-ea,-dc,ek,,cs,- -cn,-ep,cx,ef,-dh,-dv,dr,dl,-eb,-db,el,cr,-ev,-co,-eo,cy,ee,-di,-du,ds,dk,-ec,-da,em,cq,-ew,-cp,-en,cz,ed,-dj,-dt

[0219] {aw,-ay,-au,ba,as,-bc,-aq,be,ap,bd,-ar,-bb,at,az,-av,-ax,ax,av,-az,-at,bb,ar,-bd,-ap,-be,aq,bc,-as,-ba,au,ay,-aw ,-aw,ay,au,-ba,-as,bc,aq,-be,-ap,-bd,ar,bb,-at,-az,av,ax,-ax,-av,az,at,-bb,-ar,bd,ap,be,-aq,-bc,as,ba,-au,-ay,aw}

[0220] {dp,-dv,-dj,eb,dd,-eh,-cx,en,cr,-et,-cl,-eu,cq,eo,-cw,-ei,dc,ec,-di,-dw,d_,dq,-du,-dk,ea,de,-eg,-cy,em,csm,-es,-es, ,-ev,cp,ep,-cv,-ej,db,ed,-dh,-dx,dn,dr,-dt,-dl,dz,df,-ef,-cz,el,ct,-er,-cn,-ew,co,eq,-cu,-ek,da,ee,-dg,-dy,dm,ds}

[0221] {bu,-bw,-bs,by,bq,-ca,-bo,cc,bm,-ce,-bk,cg,bi,-ci,-bg,ck,bf,cj,-bh,-ch,bj,cf,-bl,-cd,bn,cb,-bp,-bz,br,bx,-b ,bv,bt,-bx,-br,bz,bp,-cb,-bn,cd,bl,-cf,-bj,ch,bh,-cj,-bf,-ck,bg,ci,-bi,-cg,bk,ce,-bm,-cc,bo,ca,-bq,-bw,-bu},bs

[0222] {dq,-ds,-d_,du,dm,-dw,-dk,dy,di,-ea,-dg,ec,de,-ee,-dc,eg,da,-ei,-cy,ek,cw,-em,-cu,eo,cs,-eq,-cq,es,co,-eu,-cm,ew ,cl,ev,-cn,-et,cp,er,-cr,-ep,ct,en,-cv,-el,cx,ej,-cz,-eh,db,ef,-dd,-ed,df,eb,-dh,-dz,dj,dx,-dl,-dv,dn,dt,-}dp,-

[0223] {Ah,-aa,-aa,aa,aa,aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa being being ,aa,-aa,-aa,aa,aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa being being

[0224] {dr,-dp,-dt,dn,dv,-dl,-dx,dj,dz,-dh,-eb,df,ed,-dd,-ef,db,eh,-cz,-ej,cx,el,-cv,-en,ct,ep,-cr,-er,cp,et,-cl,-ev ,-ew,-cm,eu,co,-es,-cq,eq,cs,-eo,-cu,em,cw,-ek,-cy,ei,da,-eg,-dc,ee,de,-ec,-dg,ea,di,-dy,-dk,dw,dm,-du,-d_,ds,dq}

[0225] {bv,-bt,-bx,br,bz,-bp,-cb,bn,cd,-bl,-cf,bj,ch,-bh,-cj,bf,-ck,-bg,ci,bi,-cg,-bk,ce,bm,-cc,-bo,ca,bq,bq,-wby,-bs ,-bu,-bw,bs,by,-bq,-ca,bo,cc,-bm,-ce,bk,cg,-bi,-ci,bg,ck,-bf,cj,bh,-ch,-bj,cf,bl,-cd,-bn,cb,bp,-bz,-br,,bx,}b

[0226] {ds,-dm,-dy,dg,ee,-da,-ek,cu,eq,-co,-ew,cn,-er,-ct,el,cz,-ef,-df,dz,dl,-dt,-dr,dn,dx,-dh,-ed,db,ej,-cv,-ep,cp,ev, -cm,es,cs,-em,-cy,eg,de,-ea,-dk,du,dq,-d_,-dw,di,ec,-dc,-ei,cw,eo,-cq,-eu,cl,-et,-cr,en,cx,-eh,-dd,eb,dj,-}dv,-dk

[0227] {ax,-av,-az,at,bb,-ar,-bd,ap,-be,-aq,bc,as,-ba,-au,ay,aw,-aw,-ay,au,ba,-as,-bc,aq,be,-ap,bd,ar,-bb,-at,az,av,-ax ,-ax,av,az,-at,-bb,ar,bd,-ap,be,aq,-bc,-as,ba,au,-ay,-aw,aw,ay,-au,-ba,as,bc,-aq,-be,ap,-bd,-ar,bb,at,-az,-av,ax}

[0228] {dt,-dj,-ed,cz,en,-cp,ew,cq,-em,-da,ec,dk,-ds,-du,di,ee,-cy,-eo,co,-ev,-cr,el,db,-eb,-dl,dr,dv,-dh,-ef,cx,ep,-cn ,eu,cs,-ek,-dc,ea,dm,-dq,-dw,dg,eg,-cw,-eq,cm,-et,-ct,ej,dd,-dz,-dn,dp,dx,-df,-eh,cv,er,-cl,es,cu,-ei,-de,dy,d_}

[0229] {bw,-bq,-cc,bk,ci,-bf,ch,bl,-cb,-br,bv,bx,-bp,-cd,bj,cj,-bg,cg,bm,-ca,-bs,bu,by,-bo,-ce,bi,ck,-bh,cf,bn,-bz,-bt, bt,bz,-bn,-cf,bh,-ck,-bi,ce,bo,-by,-bu,bs,ca,-bm,-cg,bg,-cj,-bj,cd,bp,-bx,-bv,br,cb,-bl,-ch,bf,-ci,-bk,cc,bq,-bw}

[0230] {du,-dg,-ei,cs,ew,-cr,ej,df,-dv,-dt,dh,eh,-ct,-ev,cq,-ek,-de,dw,ds,-di,-eg,cu,eu,-cp,el,dd,-dx,-dr,dj,ef,-cv,-et ,co,-em,-dc,dy,dq,-dk,-ee,cw,es,-cn,en,db,-dz,-dp,dl,ed,-cx,-er,cm,-eo,-da,ea,d_,-dm,-ec,cy,eq,-cl,ep,cz,-eb,-dn}

[0231] {al,-aj,-an,ah,-ao,-ai,am,ak,-ak,-am,ai,ao,-ah,an,aj,-al,-al,aj,an,-ah,ao,ai,-am,-ak,ak,am,-ai,-ao,ah,-an,-aj,al ,al,-aj,-an,ah,-ao,-ai,am,ak,-ak,-am,ai,ao,-ah,an,aj,-al,-al,aj,an,-ah,ao,ai,-am,-ak,ak,am,-ai,-ao,ah,-an,-an,-aj,al}

[0232] {dv,-dd,-en,cl,-eo,-dc,dw,du,-de,-em,cm,-ep,-db,dx,dt,-df,-el,cn,-eq,-da,dy,ds,-dg,-ek,co,-er,-cz,dz,dr,-pdh,-ej,c ,-es,-cy,ea,dq,-di,-ei,cq,-et,-cx,eb,dp,-dj,-eh,cr,-eu,-cw,ec,d_,-dk,-eg,cs,-ev,-cv,ed,d,-dl,-ef,ct,-dm,-cu,ee

[0233] {bx,-bn,-ch,bg,-ce,-bq,bu,ca,-bk,-ck,bj,-cb,-bt,br,cd,-bh,ci,bm,-by,-bw,bo,cg,-bf,cf,bp,-bv,-bz,bl,,ccb,-bi -bs,cc,bi,-cj,-bl,bz,bv,-bp,-cf,bf,-cg,-bo,bw,by,-bm,-ci,bh,-cd,-br,bt,cb,-bj,ck,bk,-ca,-bu,bq,ce,}-bg,bx,b

[0234] {dw,-da,-es,cr,-ef,-dn,dj,ej,-cn,eo,de,-ds,-ea,cw,ew,-cv,eb,dr,-df,-en,cm,-ek,-di,d_,ee,-cs,et,cz,-dx,-dv,db,er cq,eg,dm,-dk,-ei,co,-ep,-dd,dt,dz,-cx,-ev,cu,-ec,-dq,dg,em,-cl,el,dh,-dp,-ed,ct,-eu,-cy,dy,du,-dc,-eq,cp,-eh,-dl}

[0235] {ay,-as,-be,ar,-az,-ax,at,bd,-aq,ba,aw,-au,-bc,ap,-bb,-av,av,bb,-ap,bc,au,-aw,-ba,aq,-bd,-at,ax,az,-ar,be,as,-ay ,-ay,as,be,-ar,az,ax,-at,-bd,aq,-ba,-aw,au,bc,-ap,bb,av,-av,-bb,ap,-bc,-au,aw,ba,-aq,bd,at,-ax,-az,ar,-be,-as,ay}

[0236] {dx,-cx,ew,cy,-dw,-dy,cw,-ev,-cz,dv,dz,-cv,eu,da,-du,-ea,cu,-et,-db,dt,eb,-ct,es,dc,-ds,-ec,cs,-er,-dd,dr,ed,-cr ,eq,de,-dq,-ee,cq,-ep,-df,dp,ef,-cp,eo,dg,-d_,-eg,co,-en,-dh,dn,eh,-cn,em,di,-dm,-ei,cm,-el,-dj,dl,ej,-cl},ek,dk

[0237] {by,-bk,cj,bn,-bv,-cb,bh,-cg,-bq,bs,ce,-bf,cd,bt,-bp,-ch,bi,-ca,-bw,bm,ck,-bl,bx,bz,-bj,ci,bo,-bu,-ccf,bg,- ,br,cf,-bg,cc,bu,-bo,-ci,bj,-bz,-bx,bl,-ck,-bm,bw,ca,-bi,ch,bp,-bt,-cd,bf,-ce,-bs,bq,cg,-bh,cb,bv,-bn,-by}cj,

[0238] {dy,-cu,er,df,-dn,-ej,cm,-eg,-dq,dc,eu,-cx,dv,eb,-cr,eo,di,-dk,-em,cp,-ed,-dt,cz,-ew,-da,ds,ee,-co,el,dl,,-dh,-ep cs,-ea,-dw,cw,-et,-dd,dp,eh,-cl,ei,d_,-de,-es,cv,-dx,-dz,ct,-eq,-dg,dm,ek,-cn,ef,dr,-db,-ev,cy,-du,-ec,cq,}-en,-dj

[0239] {af,-ad,ag,ae,-ae,-ag,ad,-af,-af,ad,-ag,-ae,ae,ag,-ad,af,af,-ad,ag,ae,-ae,-ag,ad,-af,-af,ad,-ag,-ae,ae,ag,-ad,af ,af,-ad,ag,ae,-ae,-ag,ad,-af,-af,ad,-ag,-ae,ae,ag,-ad,af,af,-ad,ag,ae,-ae,-ag,ad,-af,-af,ad,-ag,-ae,ae,ag,-ad,af}

[0240] {dz,-cr,em,dm,-de,-eu,cz,-dr,-eh,cm,-ee,-du,cw,-er,-dh,dj,ep,-cu,dw,ec,-co,ej,dp,-db,ew,dc,-d_,-ek,cp,-eb,-dx,c t,-eo,-dk,dg,es,-cx,dt,ef,-cl,eg,ds,-cy,et,df,-dl,-en,cs,-dy,-ea,cq,-el,-dn,dd,ev,-da,dq,ei,-cn,ed,d,dv,-cv,eq,di}

[0241] {bz,-bh,ce,bu,-bm,cj,bp,-br,-ch,bk,-bw,-cc,bf,-cb,-bx,bj,-cg,-bs,bo,ck,-bn,bt,cf,-bi,by,ca,-bg,cd,bv,b,q,-ci bq,-ci,bl,-bv,-cd,bg,-ca,-by,bi,-cf,-bt,bn,-ck,-bo,bs,cg,-bj,bx,cb,-bf,cc,bw,-bk,ch,br,-bp,-cj,bm,-bu,-bce,bh

[0242] {ea,-co,eh,dt,-cv,eo,dm,-dc,ev,df,-dj,-er,cy,-dq,-ek,cr,-dx,-ed,cl,-ee,-dw,cs,-el,-dp,cz,-es,-di,dg,eu,-end,db,d -cu,du,eg,-cn,eb,dz,-cp,ei,ds,-cw,ep,dl,-dd,ew,de,-dk,-eq,cx,-dr,-ej,cq,-dy,-ec,cm,-ef,-dv,ct,-em,-d_,da,-et,-dh}

[0243] {az,-ap,ba,ay,-aq,bb,ax,-ar,bc,aw,-as,bd,av,-at,be,au,-au,-be,at,-av,-bd,as,-aw,-bc,ar,-ax,-bb,aq,-ay,-ba,ap,-az ,-az,ap,-ba,-ay,aq,-bb,-ax,ar,-bc,-aw,as,-bd,-av,at,-be,-au,au,be,-at,av,bd,-as,aw,bc,-ar,ax,bb,-aq,ay,ba,-ap,az}

[0244] {eb,-cl,ec,ea,-cm,ed,dz,-cn,ee,dy,-co,ef,dx,-cp,eg,dw,-cq,eh,dv,-cr,ei,du,-cs,ej,dt,-ct,ek,ds,-cu,el,dr,-cv ,em,dq,-cw,en,dp,-cx,eo,d_,-cy,ep,dn,-cz,eq,dm,-da,er,dl,-db,es,dk,-dc,et,dj,-dd,eu,di,-de,ev,dh,-df,ew,dg}

[0245] {ca,-bf,bz,cb,-bg,by,cc,-bh,bx,cd,-bi,bw,ce,-bj,bv,cf,-bk,bu,cg,-bl,bt,ch,-bm,bs,ci,-bn,br,cj,-bo,bq,ck,-bp,bp,- ck,-bq,bo,-cj,-br,bn,-ci,-bs,bm,-ch,-bt,bl,-cg,-bu,bk,-cf,-bv,bj,-ce,-bw,bi,-cd,-bx,bh,-cc,-by,bg,-cb,-bz,bf,-ca}

[0246] {ec,-cn,dx,eh,-cs,ds,em,-cx,dn,er,-dc,di,ew,-dh,dd,-es,-dm,cy,-en,-dr,ct,-ei,-dw,co,-ed,-eb,cm,-dy,-eg,cr,-dt,- el,cw,-d_,-eq,db,-dj,-ev,dg,-de,et,dl,-cz,eo,dq,-cu,ej,dv,-cp,ee,ea,-cl,dz,ef,-cq,du,ek,-cv,dp,ep,-da,dk,eu,-df}

[0247] {am,-ah,al,an,-ai,ak,ao,-aj,aj,-ao,-ak,ai,-an,-al,ah,-am,-am,ah,-al,-an,ai,-ak,-ao,aj,-aj,ao,ak,-ai,an,al,-ah,am ,am,-ah,al,an,-ai,ak,ao,-aj,aj,-ao,-ak,-ai,-an,-al,ah,-am,-am,ah,-al,-an,ai,-ak,-ao,-aj,-aj,-ao,ak,-ai,an,al,-ah,am}

[0248] {ed,-cq,ds,eo,-db,dh,-eu,-dm,cw,-ej,-dx,cl,-dy,-ei,cv,-dn,-et,dg,-dc,ep,dr,-cr,ee,ec,-cp,dt,en,-da,di,-ev,-dl -ek,-dw,cm,-dz,-eh,cu,-d_,-es,df,-dd,eq,dq,-cs,ef,eb,-co,du,em,-cz,dj,-ew,-dk,cy,-el,-dv,cn,-ea,-eg,ct,-dp,-er,de}

[0249] {cb,-bi,bu,ci,-bp,bn,-cg,-bw,bg,-bz,-cd,bk,-bs,-ck,br,-bl,ce,by,-bf,bx,cf,-bm,bq,-cj,-bt,bj,-cc,-ca,bh,-b o,-bo,ch,bv,-bh,ca,cc,-bj,bt,cj,-bq,bm,-cf,-bx,bf,-by,-ce,bl,-br,ck,bs,-bk,cd,bz,-bg,bw}cg,-bn,bp,-ci,-bu,bi

[0250] {ee,-ct,dn,ev,-dk,cw,-eh,-eb,cq,-dq,-es,dh,-cz,ek,dy,-cn,dt,ep,-de,dc,-en,-dv,cl,-dw,-em,db,-df,eq,ds,-co,dz,ej, -cy,di,-et,-dp,cr,-ec,-eg,cv,-dl,ew,dm,-cu,ef,ed,-cs,d_,eu,-dj,cx,-ei,-ea,cp,-dr,-er,dg,-da,el,dx,-cm,du,eo,-dd}

[0251] {ba,-ar,av,-be,-aw,aq,-az,-bb,as,-au,bd,ax,-ap,ay,bc,-at,at,-bc,-ay,ap,-ax,-bd,au,-as,bb,az,-aq,aw,be,-av,ar,-ba ,-ba,ar,-av,be,aw,-aq,az,bb,-as,au,-bd,-ax,ap,-ay,-bc,at,-at,bc,ay,-ap,ax,bd,-au,as,-bb,-az,aq,-aw,-be,av,-ar,ba}

[0252] {ef,-cw,di,-er,-dt,cl,-du,-eq,dh,-cx,eg,ee,-cv,dj,-es,-ds,cm,-dv,-ep,dg,-cy,eh,ed,-cu,dk,-et,-dr,cn,-dw,-eo,df ,ei,ec,-ct,dl,-eu,-dq,co,-dx,-en,de,-da,ej,eb,-cs,dm,-ev,-dp,cp,-dy,-em,dd,-db,ek,ea,-cr,dn,-ew,-d_,cq,-dz,-el,dc}

[0253] {cc,-bl,bp,-cg,-by,bh,-bt,ck,bu,-bg,bx,ch,-bq,bk,-cb,-cd,bm,-bo,cf,bz,-bi,bs,-cj,-bv,bf,-bw,-ci,br,ce,-bj,ca, ,bn,-ce,-ca,bj,-br,ci,bw,-bf,bv,cj,-bs,bi,-bz,-cf,bo,-bm,cd,cb,-bk,bq,-ch,-bx,bg,-bu,-ck,bt,-bh,by,cl,-ccp

[0254] {eg,-cz,dd,-ek,-ec,cv,-dh,eo,dy,-cr,dl,-es,-du,cn,-dp,ew,dq,-cm,dt,et,-dm,cq,-dx,-ep,di,-cu,eb,el,-de,cy,-ef,-eh ,da,-dc,ej,ed,-cw,dg,-en,-dz,cs,-dk,er,dv,-co,d_,-ev,-dr,cl,-ds,-eu,dn,-cp,dw,eq,-dj,ct,-ea,-em,df,-cx,bee},ei,-d

[0255] {ac,-ab,ab,-ac,-ac,-ab,-ab,ac,ac,-ab,-ac,-ac,-ab,-ab,ac,ac,-ab,-ac,-ac,-ab,-ab,ac,ac,-ab,-ac,-ac,ab,-ab,ac ,ac,-ab,ab,-ac,-ac,-ab,-ab,ac,ac,-ab,-ac,-ac,-ab,-ab,ac,ac,-ab,-ac,-ac,-ab,-ab,ac,ac,-ab,-ac,-ac,ab,-ab,ac}

[0256] {eh,-dc,cy,-ed,-el,dg,-cu,dz,ep,-dk,cq,-dv,-et,d_,-cm,dr,-ew,-ds,cn,-dn,es,dw,-cr,dj,-eo,-ea,cv,-df,ek,deb,-cz ,-eg,-ei,dd,-cx,ec,em,-dh,ct,-dy,-eq,dl,-cp,du,eu,-dp,cl,-dq,ev,dt,-co,dm,-er,-dx,cs,-di,en,eb,-cw,de,-ej,-ef,da}

[0257] {cd,-bo,bk,-bz,-ch,bs,-bg,bv,-ck,-bw,bh,-br,cg,ca,-bl,bn,-cc,-ce,bp,-bj,by,ci,-bt,bf,-bu,cj,bx,-bi,bcb,-cf,- ,-bm,cb,cf,-bq,bi,-bx,-cj,bu,-bf,bt,-ci,-by,bj,-bp,ce,cc,-bn,bl,-ca,-cg,br,-bh,bw,ck,-bv,bg,-bs,ch,bz,-cd,bk}

[0258] {ei,-df,ct,-dw,-eu,dr,-co,dk,-en,-ed,da,-cy,eb,ep,-dm,cm,-dp,es,dy,-cv,dd,-eg,-ek,dh,-cr,du,ew,-dt,cq,-di,el,ef, -dc,cw,-dz,-er,d_,-cl,dn,-eq,-ea,cx,-db,ee,em,-dj,cp,-ds,ev,dv,-cs,dg,-ej,-eh,de,-cu,dx,et,-dq,cn,-dl,ezo},ec,-

[0259] {bb,-au,aq,-ax,be,ay,-ar,at,-ba,-bc,av,-ap,aw,-bd,-az,as,-as,az,bd,-aw,ap,-av,bc,ba,-at,ar,-ay,-be,ax,-aq,au,-bb ,-bb,au,-aq,ax,-be,-ay,ar,-at,ba,bc,-av,ap,-aw,bd,az,-as,as,-az,-bd,aw,-ap,av,-bc,-ba,at,-ar,ay,be,-ax,aq,-au,bb}

[0260] {ej,-di,co,-dp,eq,ec,-db,cv,-dw,-ew,dv,-cu,dc,-ed,-ep,d_,-cn,dj,-ek,-ei,dh,-cp,dq,-er,-eb,da,-cw,dx,ev,-du,ct,-dd ,ee,eo,-dn,cm,-dk,el,eh,-dg,cq,-dr,es,ea,-cz,cx,-dy,-eu,dt,-cs,de,-ef,-en,dm,-cl,dl,-em,-eg,df,-cr,ds,-}et,-dz

[0261] {ce,-br,bf,-bs,cf,cd,-bq,bg,-bt,cg,cc,-bp,bh,-bu,ch,cb,-bo,bi,-bv,ci,ca,-bn,bj,-bw,cj,bz,-bm,bk,-bx,ck,bb,by,- ,-by,-ck,bx,-bk,bm,-bz,-cj,bw,-bj,bn,-ca,-ci,bv,-bi,bo,-cb,-ch,bu,-bh,bp,-cc,-cg,bt,-bg,bq,-cd,-cf,bs,-bf,}

[0262] {ek,-dl,cm,-di,eh,en,-d_,cp,-df,ee,eq,-dr,cs,-dc,eb,et,-du,cv,-cz,dy,ew,-dx,cy,-cw,dv,-eu,-ea,db,-ct,ds,-er,-ed,d e,-cq,dp,-eo,-eg,dh,-cn,dm,-el,-ej,dk,-cl,dj,-ei,-em,dn,-co,dg,-ef,-ep,dq,-cr,dd,-ec,-es,dt,-cu,da,-dz,-ev,-cx,dw,

[0263] {an,-ak,ah,-aj,am,ao,-al,ai,-ai,al,-ao,-am,aj,-ah,ak,-an,-an,ak,-ah,-al,-am,-a,-al,ao,am,-aj,ah,-ak,-an ,an,-ak,ah,-aj,am,ao,-al,ai,-ai,al,-ao,-am,aj,-ah,ak,-an,-an,-ak,-ah,-al,-ak,-ah,-al,ao,-am,-al,-ao,-am,-am,-am,-ah,-ah,-an,-ak,-ah,-al,-ah,-ak,-ah}

[0264] {el,-d_,cr,-db,dy,-ev,-eb,de,-co,dl,-ei,-eo,dr,-cu,cy,-dv,es,ee,-dh,cl,-di,ef,er,-du,cx,-cv,ds,-ep,-eh,dk,-cn,df ,-ec,-eu,dx,-da,cs,-dp,em,ek,-dn,cq,-dc,dz,-ew,-ea,dd,-cp,dm,-ej,-en,dq,-ct,cz,-dw,et,ed,-dg,cm,-dj,eg,eq,-dt,cw}

[0265] {cf,-bu,bj,-bl,bw,-ch,-cd,bs,-bh,bn,-by,cj,cb,-bq,bf,-bp,ca,ck,-bz,bo,-bg,br,-cc,-ci,bx,-bm,bi,-bt,ce,cg,-bv,bk, -bk,bv,-cg,-ce,bt,-bi,bm,-bx,ci,cc,-br,bg,-bo,bz,-ck,-ca,bp,-bf,bq,-cb,-cj,by,-bn,bh,-bs,cd,ch,-bw,bl,-bj,bu,-cf}

[0266] {em,-dr,cw,-cu,dp,-ek,-eo,dt,-cy,cs,-dn,ei,eq,-dv,da,-cq,dl,-eg,-es,dx,-dc,co,-dj,ee,eu,-dz,de,-cm,dh,-ec,-ew,eb, -dg,cl,-df,ea,-ev,-ed,di,-cn,dd,-dy,et,ef,-dk,cp,-db,dw,-er,-eh,dm,-cr,cz,-du,ep,ej,-d_,ct,-cx,ds,-en,-el,dq,-cv}

[0267] {bc,-ax,as,-aq,av,-ba,-be,az,-au,ap,-at,ay,-bd,-bb,aw,-ar,ar,-aw,bb,bd,-ay,at,-ap,au,-az,be,ba,-av,aq,-as,ax,-bc ,-bc,ax,-as,aq,-av,ba,be,-az,au,-ap,at,-ay,bd,bb,-aw,ar,-ar,aw,-bb,-bd,ay,-at,ap,-au,az,-be,-ba,av,-aq,as,-ax,bc}

[0268] {en,-du,db,-cn,dg,-dz,es,ei,-dp,cw,-cs,dl,-ee,-ew,ed,-dk,cr,-cx,dq,-ej,-er,dy,-df,cm,-dc,dv,-eo,-em,dt,-da,co,co, h,ea,-et,-eh,d_,-cv,ct,-dm,ef,ev,-ec,dj,-cq,cy,-dr,ek,eq,-dx,de,-cl,dd,-dw,ep,el,-ds,cz,-cp,di,-eb,eu,eg,-dn,cu}

[0269] {cg,-bx,bo,-bf,bn,-bw,cf,ch,-by,bp,-bg,bm,-bv,ce,ci,-bz,bq,-bh,bl,-bu,cd,cj,-ca,br,-bi,bk,-bt,cc,ck,-bjb,bs, j,-bs,cb,-ck,-cc,bt,-bk,bi,-br,ca,-cj,-cd,bu,-bl,bh,-bq,bz,-ci,-ce,bv,-bm,bg,-bp,by,-ch,-cf,bw,-bn,bf,-cg,}b

[0270] {eo,-dx,dg,-cp,cx,-d_,ef,-ew,-eg,dp,-cy,co,-df,dw,-en,-ep,dy,-dh,cq,-cw,dn,-ee,ev,eh,-dq,cz,-cn,de,-dv,em,eq ,di,-cr,cv,-dm,ed,-eu,-ei,dr,-da,cm,-dd,du,-el,-er,ea,-dj,cs,-cu,dl,-ec,et,ej,-ds,db,-cl,dc,-dt,ek,es,-eb,dk,-ct}

[0271] {ag,-af,ae,-ad,ad,-ae,af,-ag,-ag,af,-ae,ad,-ad,ae,-af,ag,ag,-af,ae,-ad,-ae,af,-ag,-ag,af,-ae,ad,-ad,ae,-af,ag ,ag,-af,ae,-ad,ad,-ae,af,-ag,-ag,af,-ae,ad,-ad,ae,-af,ag,ag,-af,ae,-ad,-ae,af,-ag,-ag,af,-ae,ad,-ad,ae,-af,ag}

[0272] {ep,-ea,dl,-cw,co,-dd,ds,-eh,ew,ei,-dt,de,-cp,cv,-dk,dz,-eo,-eq,eb,-dm,cx,-cn,dc,-dr,eg,-ev,-ej,du,-df,cj,-cu,d ,-dy,en,er,-ec,dn,-cy,cm,-db,dq,-ef,eu,ek,-dv,dg,-cr,ct,-di,dx,-em,-es,ed,-d_,cz,-cl,da,-dp,ee,-et,-el,dw,-dh,cs}

[0273] {ch,-ca,bt,-bm,bf,-bl,bs,-bz,cg,ci,-cb,bu,-bn,bg,-bk,br,-by,cf,cj,-cc,bv,-bo,bh,-bj,bq,-bx,ce,ck,-cd,biw,-bx,ce,ck,-cd,bw,- bi,bp,-bx,cd,-ck,-ce,bx,-bq,bj,-bh,bo,-bv,cc,-cj,-cf,by,-br,bk,-bg,bn,-bu,cb,-ci,-cg,bz,-bs,bl,-bf,cam,-ch}bt,

[0274] {eq,-ed,dq,-dd,cq,-cs,df,-ds,ef,-es,-eo,eb,-d_,db,-co,cu,-dh,du,-eh,eu,em,-dz,dm,-cz,cm,-cw,dj,-dw,ej,-ew,-ek,dx, -dk,cx,-cl,cy,-dl,dy,-el,-ev,ei,-dv,di,-cv,cn,-da,dn,-ea,en,et,-eg,dt,-dg,ct,-cp,dc,-dp,ec,-ep,-er,ee,-dr},de,-c

[0275] {bd,-ba,ax,-au,ar,-ap,as,-av,ay,-bb,be,bc,-az,aw,-at,aq,-aq,at,-aw,az,-bc,-be,bb,-ay,av,-as,ap,-ar,au,-ax,ba,-bd ,-bd,ba,-ax,au,-ar,ap,-as,av,-ay,bb,-be,-bc,az,-aw,at,-aq,aq,-at,aw,-az,bc,be,-bb,ay,-av,as,-ap,ar,-au,ax,-ba,bd}

[0276] {er,-eg,dv,-dk,cz,-co,cs,-dd,d_,-dz,ek,-ev,-en,ec,-dr,dg,-cv,cl,-cw,dh,-ds,ed,-eo,-eu,ej,-dy,dn,-dc,cr,-dlp,da ,dw,-eh,es,eq,-ef,du,-dj,cy,-cn,ct,-de,dp,-ea,el,-ew,-em,eb,-dq,df,-cu,cm,-cx,di,-dt,ee,-ep,-et,ei,-dx,dm,-db,cq}

[0277] {ci,-cd,by,-bt,bo,-bj,bf,-bk,bp,-bu,bz,-ce,cj,ch,-cc,bx,-bs,bn,-bi,bg,-bl,bq,-bv,ca,-cf,ck,cg,-cb,bw,-br,bm bh,-bm,br,-bw,cb,-cg,-ck,cf,-ca,bv,-bq,bl,-bg,bi,-bn,bs,-bx,cc,-ch,-cj,ce,-bz,bu,-bp,bk,-bf,bj,-bo,bt,-ci},c

[0278] {es,-ej,ea,-dr,di,-cz,cq,-co,cx,-dg,dp,-dy,eh,-eq,-eu,el,-ec,dt,-dk,db,-cs,cm,-cv,de,-dn,dw,-ef,eo,ew,-en,ee,-dv ,dm,-dd,cu,-cl,ct,-dc,dl,-du,ed,-em,ev,ep,-eg,dx,-d_,df,-cw,cn,-cr,da,-dj,ds,-eb,ek,-et,-er,ei,-dz,dq,-dh,cy,-cp}

[0279] {ao,-an,am,-al,ak,-aj,ai,-ah,ah,-ai,aj,-ak,al,-am,an,-am,-al,-ak,----------------------------------------------------------in ,ao,-an,am,-al,ak,-aj,ai,-ah,ah,-ai,-al,-ak,al,-am,-an,-ao,-ao,-an,-am,-al,-ak,-a,-ai,-ah,-ah,ai,-ai,-ak,-al,am,-an,ao}

[0280] {et,-em,ef,-dy,dr,-dk,dd,-cw,cp,-cn,cu,-db,di,-dp,dw,-ed,ek,-er,-ev,eo,-eh,ea,-dt,dm,-df,cy,-cr,cl,-cs,cz,-dg,dn ,-du,eb,-ei,ep,-ew,-eq,ej,-ec,dv,-d_,dh,-da,ct,-cm,cq,-cx,de,-dl,ds,-dz,eg,-en,eu,es,-el,ee,-dx,dq,-dj,dc,-cv,co}

[0281] {cj,-cg,cd,-ca,bx,-bu,br,-bo,bl,-bi,bf,-bh,bk,-bn,bq,-bt,bw,-bz,cc,-cf,ci,ck,-ch,ce,-cb,by,-bv,bs,-bp,bm,-bj,bg, -bg,bj,-bm,bp,-bs,bv,-by,cb,-ce,ch,-ck,-ci,cf,-cc,bz,-bw,bt,-bq,bn,-bk,bh,-bf,bi,-bl,bo,-br,bu,-bx,ca,-cd,cg,-cj}

[0282] {eu,-ep,ek,-ef,ea,-dv,dq,-dl,dg,-db,cw,-cr,cm,-co,ct,-cy,dd,-di,dn,-ds,dx,-ec,eh,-em,er,-ew,-es,en,-ei,ed,-dy,dt, -d_,dj,-de,cz,-cu,cp,-cl,cq,-cv,da,-df,dk,-dp,du,-dz,ee,-ej,eo,-et,-ev,eq,-el,eg,-eb,dw,-dr,dm,-dh,dc,-cx,-cx,cs

[0283] {be,-bd,bc,-bb,ba,-az,ay,-ax,aw,-av,au,-at,as,-ar,aq,-ap,ap,-aq,ar,-as,at,-au,av,-aw,ax,-ay,az,-ba,bb,-bc,bd,-be ,-be,bd,-bc,bb,-ba,az,-ay,ax,-aw,av,-au,at,-as,ar,-aq,ap,-ap,aq,-ar,as,-at,au,-av,aw,-ax,ay,-az,ba,-bb,bc,-bd,be}

[0284] {ev,-es,ep,-em,ej,-eg,ed,-ea,dx,-du,dr,-d_,dl,-di,df,-dc,cz,-cw,ct,-cq,cn,-cl,co,-cr,cu,-cx,da,-dd,dg,-dj,dm ,ds,-dv,dy,-eb,ee,-eh,ek,-en,eq,-et,ew,eu,-er,eo,-el,ei,-ef,ec,-dz,dw,-dt,dq,-dn,dk,-dh,de,-db,cy,-cv,cs,-cp,cm}

[0285] {ck,-cj,ci,-ch,cg,-cf,ce,-cd,cc,-cb,ca,-bz,by,-bx,bw,-bv,bu,-bt,bs,-br,bq,-bp,bo,-bn,bm,-bl,bk,-bj,bi,-bh,b ,bf,-bg,bh,-bi,bj,-bk,bl,-bm,bn,-bo,bp,-bq,br,-bs,bt,-bu,bv,-bw,bx,-by,bz,-ca,cb,-cc,cd,-ce,cf,-cj,ch,-ck,ci,

[0286] {ew,-ev,eu,-et,es,-er,eq,-ep,eo,-en,em,-el,ek,-ej,ei,-eh,eg,-ef,ee,-ed,ec,-eb,ea,-dz,dy,-dx,dw,-dv,du,-dt,ds,-dr, dq,-dp,d_,-dn,dm,-dl,dk,-dj,di,-dh,dg,-df,de,-dd,dc,-db,da,-cz,cy,-cx,cw,-cv,cu,-ct,cs,-cr,cq,-cp,co,-cn,cm,-cl}.

[0287] In addition to DCT-2 and 4x4 DST-7 already used in HEVC, an Adaptive Multiple Transform (AMT, or Enhanced Multiple Transform (EMT)) scheme is proposed for redundant coding of both inter-frame and intra-frame coding blocks. Besides the current transforms in HEVC, AMT can use several selectable transforms from the DCT / DST family. The newly introduced transform matrices can include DST-7, DCT-8, DST-1, and DCT-5. Table 1 below shows exemplary basic functions for the selected DST / DCT.

[0288] Table 1: Basic Transform Functions for N-Point Inputs of DCT-II / V / VIII and DST-I / VII

[0289]

[0290] To maintain the orthogonality of the transform matrix, it can be quantized more precisely using 10 bits instead of the 8 bits used in HEVC, compared to the transform matrix in HEVC. After the horizontal and vertical transforms, to keep the intermediate values ​​of the transformed coefficients within the 16-bit range, all coefficients can be shifted 2 bits to the right compared to the right shift used in the current HEVC transform. AMT can be applied to coding units (CUs) with a width and height of 64 or less, and whether AMT is applied can be controlled by a CU-level flag. When the CU-level flag is equal to 0, DCT-2 can be applied in the CU to encode the residuals. For the luminance coding block within a CU with AMT enabled, two additional flags can be used to indicate the horizontal and vertical transforms to be used.

[0291] For intra-frame residual coding, due to the different residual statistics of different intra-frame prediction modes, mode-related transform candidate selection can be used. As follows:

[0292] As shown in Table 2, three transform subsets can be defined, and the transform subsets can be selected based on the intra-frame prediction mode, such as...

[0293] The following are specified in Table 3.

[0294] Table 2: Three predefined candidate sets of transformations

[0295]

[0296] Using the concept of subsets, we can first identify transform subsets based on Table 3 using the intra-prediction mode of the CU with the CU-level AMT flag equal to 1. Then, for each of the horizontal and vertical transforms, based on explicitly representing them with a signal using a flag, we can select one of the two transform candidates from the identified transform subsets according to Table 2.

[0297] Table 3: Selected (H) Horizontal and (V) Vertical Transform Sets for Each Intra-Frame Prediction Mode

[0298]

[0299] However, for inter-frame prediction residuals, only one transform set consisting of DST-7 and DCT-8 can be used for all inter-frame modes, as well as horizontal and vertical transforms. Of the four additional transform types—DST-7, DCT-8, DST-1, and DCT-5—DST-7 and DCT-8 are the most efficient. It should be noted that DCT-8 essentially flips the DST-7 basis horizontally using sign changes; therefore, DCT-8 and DST-7 can essentially share the same transform basis.

[0300] It should be noted that 8 bits means 8 bits in total. Each bit represents either 0 or 1 (i.e., a binary number), so 8 bits means 8 binary numbers. 8-bit DST-7 indicates that the value of each element in the matrix is ​​an 8-bit binary number.

[0301] The core of the DST-7 transformation, which is a matrix composed of basis vectors, can also be represented as follows:

[0302] 4 o'clock DST-7:

[0303]

[0304] 8 o'clock DST-7:

[0305]

[0306] 16 o'clock DST-7:

[0307]

[0308] 32 points DST-7:

[0309]

[0310] 64 points DST-7:

[0311] {aa,ab,ac,ad,ae,af,ag,ah,ai,aj,ak,al,am,an,ao,ap,aq,ar,as,at,au,av,aw,ax,ay,az,ba,bb,bc,bd,be,bf, bg,bh,bi,bj,bk,bl,bm,bn,bo,bp,bq,br,bs,bt,bu,bv,bw,bx,by,bz,ca,cb,cc,cd,ce,cf,cg,ch,ci,cj,ck,cl,}

[0312] {ab,ae,ah,ak,an,aq,at,aw,az,bc,bf,bi,bl,bo,br,bu,bx,ca,cd,cg,cj,cl,ci,cf,cc,bz,bw,bt,bq,bn,bk,bh,be,bb,ay,a v,as,ap,am,aj,ag,ad,aa,-ac,-af,-ai,-al,-ao,-ar,-au,-ax,-ba,-bd,-bg,-bj,-bm,-bp,-bs,-bv,-by,-cb,-ce,-ch,-ck,}

[0313] {ac,ah,am,ar,aw,bb,bg,bl,bq,bv,ca,cf,ck,ci,cd,by,bt,bo,bj,be,az,au,ap,ak,af,aa,-ae,-aj,-ao,-at,-ay,-bd,-bi,-b n,-bs,-bx,-cc,-ch,-cl,-cg,-cb,-bw,-br,-bm,-bh,-bc,-ax,-as,-an,-ai,-ad,ab,ag,al,aq,av,ba,bf,bk,bp,bu,bz,ce,cj,}

[0314] {ad,ak,ar,ay,bf,bm,bt,ca,ch,cj,cc,bv,bo,bh,ba,at,am,af,-ab,-ai,-ap,-aw,-bd,-bk,-br,-by,-cf,-cl,-ce,-bx,-bq,-bj, -bc,-av,-ao,-ah,-aa,ag,an,au,bb,bi,bp,bw,cd,ck,cg,bz,bs,bl,be,ax,aq,aj,ac,-ae,-al,-as,-az,-bg,-bn,-bu,-cb,-ci,}

[0315] {ae,an,aw,bf,bo,bx,cg,ci,bz,bq,bh,ay,ap,ag,-ac,-al,-au,-bd,-bm,-bv,-ce,-ck,-cb,-bs,-bj,-ba,-ar,-ai,aa,aj,as,bb, bk,bt,cc,cl,cd,bu,bl,bc,at,ak,ab,-ah,-aq,-az,-bi,-br,-ca,-cj,-cf,-bw,-bn,-be,-av,-am,-ad,af,ao,ax,bg,bp,by,ch,}

[0316] {af,aq,bb,bm,bx,ci,ce,bt,bi,ax,am,ab,-aj,-au,-bf,-bq,-cb,-cl,-ca,-bp,-be,-at,-ai,ac,an,ay,bj,bu,cf,ch,bw,bl,ba, ap,ae,-ag,-ar,-bc,-bn,-by,-cj,-cd,-bs,-bh,-aw,-al,-aa,ak,av,bg,br,cc,ck,bz,bo,bd,as,ah,-ad,-ao,-az,-bk,-bv,-cg,}

[0317] {ag,at,bg,bt,cg,ce,br,be,ar,ae,-ai,-av,-bi,-bv,-ci,-cc,-bp,-bc,-ap,-ac,ak,ax,bk,bx,ck,ca,bn,ba,an,aa,-am,-az,-b m,-bz,-cl,-by,-bl,-ay,-al,ab,ao,bb,bo,cb,cj,bw,bj,aw,aj,-ad,-aq,-bd,-bq,-cd,-ch,-bu,-bh,-au,-ah,af,as,bf,bs,cf,}

[0318] {ah,aw,bl,ca,ci,bt,be,ap,aa,-ao,-bd,-bs,-ch,-cb,-bm,-ax,-ai,ag,av,bk,bz,cj,bu,bf,aq,ab,-an,-bc,-br,-cg,-cc,-bn, -ay,-aj,af,au,bj,by,ck,bv,bg,ar,ac,-am,-bb,-bq,-cf,-cd,-bo,-az,-ak,ae,at,bi,bx,cl,bw,bh,as,ad,-al,-ba,-bp,-ce,}

[0319] {ai,az,bq,ch,bz,bi,ar,aa,-aq,-bh,-by,-ci,-br,-ba,-aj,ah,ay,bp,cg,ca,bj,as,ab,-ap,-bg,-bx,-cj,-bs,-bb,-ak,ag,ax, bo,cf,cb,bk,at,ac,-ao,-bf,-bw,-ck,-bt,-bc,-al,af,aw,bn,ce,cc,bl,au,ad,-an,-be,-bv,-cl,-bu,-bd,-am,ae,av,bm,cd,}

[0320] {aj,bc,bv,cj,bq,ax,ae,-ao,-bh,-ca,-ce,-bl,-as,aa,at,bm,cf,bz,bg,an,-af,-ay,-br,-ck,-bu,-bb,-ai,ak,bd,bw,ci,bp,a w,ad,-ap,-bi,-cb,-cd,-bk,-ar,ab,au,bn,cg,by,bf,am,-ag,-az,-bs,-cl,-bt,-ba,-ah,al,be,bx,ch,bo,av,ac,-aq,-bj,-cc,}

[0321] {ak,bf,ca,cc,bh,am,-ai,-bd,-by,-ce,-bj,-ao,ag,bb,bw,cg,bl,aq,-ae,-az,-bu,-ci,-bn,-as,ac,ax,bs,ck,bp,au,-aa,-av,- bq,-cl,-br,-aw,-ab,at,bo,cj,bt,ay,ad,-ar,-bm,-ch,-bv,-ba,-af,ap,bk,cf,bx,bc,ah,-an,-bi,-cd,-bz,-be,-aj,al,bg,cb,}

[0322] {al,bi,cf,bv,ay,ab,-av,-bs,-ci,-bl,-ao,ai,bf,cc,by,bb,ae,-as,-bp,-cl,-bo,-ar,of,bc,bz,cb,be,ah,-ap,-bm,-cj,-br,- au,ac,az,bw,ce,bh,ak,-am,-bj,-cg,-bu,-ax,-aa,aw,bt,ch,bk,an,-aj,-bg,-cd,-bx,-ba,-ad,at,bq,ck,bn,aq,-ag,-bd,-ca,}

[0323] {am,bl,ck,bo,ap,-aj,-bi,-ch,-br,-as,ag,bf,ce,bu,av,-ad,-bc,-cb,-bx,-ay,aa,az,by,ca,bb,ac,-aw,-bv,-cd,-be,-af,at, bs,cg,bh,ai,-aq,-bp,-cj,-bk,-al,an,bm,cl,bn,ao,-ak,-bj,-ci,-bq,-ar,ah,bg,cf,bt,au,-ae,-bd,-cc,-bw,-ax,ab,ba,bz,}

[0324] {an,bo,ci,bh,ag,-au,-bv,-cb,-ba,aa,bb,cc,bu,at,-ah,-bi,-cj,-bn,-am,ao,bp,ch,bg,af,-av,-bw,-ca,-az,ab,bc,cd,bt,a s,-ai,-bj,-ck,-bm,-al,ap,bq,cg,bf,ae,-aw,-bx,-bz,-ay,ac,bd,ce,bs,ar,-aj,-bk,-cl,-bl,-ak,aq,br,cf,be,ad,-ax,-by,}

[0325] {ao,br,cd,ba,-ac,-bf,-ci,-bm,-aj,at,bw,by,av,-ah,-bk,-ck,-bh,-ae,ay,cb,bt,aq,-am,-bp,-cf,-bc,aa,bd,cg,bo,al,-ar, -bu,-ca,-ax,af,bi,cl,bj,ag,-aw,-bz,-bv,-as,ak,bn,ch,be,ab,-bb,-ce,-bq,-an,ap,bs,cc,az,-ad,-bg,-cj,-bl,-ai,au,bx,}

[0326] {ap,bu,by,at,-al,-bq,-cc,-ax,ah,bm,cg,bb,-ad,-bi,-ck,-bf,-aa,be,cj,bj,ae,-ba,-cf,-bn,-ai,aw,cb,br,am,-as,-bx,-bv, -aq,ao,bt,bz,au,-ak,-bp,-cd,-ay,ag,bl,ch,bc,-ac,-bh,-cl,-bg,-ab,bd,ci,bk,af,-az,-ce,-bo,-aj,av,ca,bs,an,-ar,-bw,}

[0327] {aq,bx,bt,am,-au,-cb,-bp,-ai,ay,cf,bl,ae,-bc,-cj,-bh,-aa,bg,ck,bd,-ad,-bk,-cg,-az,ah,bo,cc,av,-al,-bs,-by,-ar,ap, bw,bu,an,-at,-ca,-bq,-aj,ax,ce,bm,af,-bb,-ci,-bi,-ab,bf,cl,be,-ac,-bj,-ch,-ba,ag,bn,cd,aw,-ak,-br,-bz,-as,ao,bv,}

[0328] {ar,ca,bo,of,-bd,-cl,-bc,ag,bp,bz,aq,-as,-cb,-bn,-ae,be,ck,bb,-ah,-bq,-by,-ap,at,cc,bm,ad,-bf,-cj,-ba,ai,br,bx,a o,-au,-cd,-bl,-ac,bg,ci,az,-aj,-bs,-bw,-an,av,ce,bk,ab,-bh,-ch,-ay,ak,bt,bv,am,-aw,-cf,-bj,-aa,bi,cg,ax,-al,-bu,}

[0329] {as,cd,bj,-ab,-bm,-ca,-ap,av,cg,bg,-ae,-bp,-bx,-am,ay,cj,bd,-ah,-bs,-bu,-aj,bb,cl,ba,-ak,-bv,-br,-ag,be,ci,ax,-an ,-by,-bo,-ad,bh,cf,au,-aq,-cb,-bl,-aa,bk,cc,ar,-at,-ce,-bi,ac,bn,bz,ao,-aw,-ch,-bf,of,bq,bw,al,-az,-ck,-bc,ai,bt,}

[0330] {at,cg,be,-ai,-bv,-bp,-ac,bk,ca,an,-az,-cl,-ay,ao,cb,bj,-ad,-bq,-bu,-ah,bf,cf,as,-au,-ch,-bd,aj,bw,bo,ab,-bl,-bz, -am,ba,ck,ax,-ap,-cc,-bi,ae,br,bt,ag,-bg,-ce,-ar,av,ci,bc,-ak,-bx,-bn,-aa,bm,by,al,-bb,-cj,-aw,aq,cd,bh,-af,-bs,}

[0331] {au,cj,az,-ap,-ce,-be,ak,bz,bj,-of,-bu,-bo,aa,bp,bt,ae,-bk,-by,-aj,bf,cd,ao,-ba,-ci,-at,av,ck,ay,-aq,-cf,-bd,al, ca,bi,-ag,-bv,-bn,ab,bq,bs,ad,-bl,-bx,-ai,bg,cc,an,-bb,-ch,-as,aw,cl,ax,-ar,-cg,-bc,am,cb,bh,-ah,-bw,-bm,ac,br,}

[0332] {av,cl,au,-aw,-ck,-at,ax,cj,as,-ay,-ci,-ar,az,ch,aq,-ba,-cg,-ap,bb,cf,ao,-bc,-ce,-an,bd,cd,am,-be,-cc,-al,bf,cb, ak,-bg,-ca,-aj,bh,bz,ai,-bi,-by,-ah,bj,bx,ag,-bk,-bw,-af,bl,bv,ae,-bm,-bu,-ad,bn,bt,ac,-bo,-bs,-ab,bp,br,aa,-bq,}

[0333] {aw,ci,ap,-bd,-cb,-ai,bk,bu,ab,-br,-bn,af,by,bg,-am,-cf,-az,at,cl,as,-ba,-ce,-al,bh,bx,ae,-bo,-bq,ac,bv,bj,-aj,- cc,-bc,aq,cj,av,-ax,-ch,-ao,be,ca,ah,-bl,bt,-aa,bs,bm,-ag,-bz,-bf,an,cg,ay,-au,-ck,-ar,bb,cd,ak,-bi,-bw,-ad,bp,}

[0334] {ax,cf,ak,-bk,-bs,ac,bx,bf,-ap,-ck,-as,bc,ca,af,-bp,-bn,ah,cc,ba,-au,-ci,-an,bh,bv,aa,-bu,-bi,am,ch,av,-az,-cd,- ai,bm,bq,-ae,-bz,-bd,ar,cl,aq,-be,-by,-ad,br,bl,-aj,-ce,-ay,aw,cg,al,-bj,-bt,ab,bw,bg,-ao,-cj,-at,bb,cb,ag,-bo,}

[0335] {ay,cc,af,-br,-bj,an,ck,aq,-bg,-bu,ac,bz,bb,-av,-cf,-ai,bo,bm,-ak,-ch,-at,bd,bx,aa,-bw,-be,as,ci,al,-bl,-bp,ah,c e,aw,-ba,-ca,-ad,bt,bh,-ap,-cl,-ao,bi,bs,-ae,-cb,-az,ax,cd,ag,-bq,-bk,am,cj,ar,-bf,-bv,ab,by,bc,-au,-cg,-aj,bn,}

[0336] {az,bz,aa,-by,-ba,ay,ca,ab,-bx,-bb,ax,cb,ac,-bw,-bc,aw,cc,ad,-bv,-bd,av,cd,ae,-bu,-be,au,ce,af,-bt,-bf,at,cf, ag,-bs,-bg,as,cg,ah,-br,-bh,ar,ch,ai,-bq,-bi,aq,ci,aj,-bp,-bj,ap,cj,ak,-bo,-bk,ao,ck,al,-bn,-bl,an,cl,am,-bm,}

[0337] {ba,bw,-ae,-cf,-ar,bj,bn,-an,-cj,-ai,bs,be,-aw,-ca,aa,cb,av,-bf,-br,aj,ck,am,-bo,-bi,as,ce,ad,-bx,-az,bb,bv,-af, -cg,-aq,bk,bm,-ao,-ci,-ah,bt,bd,-ax,-bz,ab,cc,au,-bg,-bq,ak,cl,al,-bp,-bh,at,cd,ac,-by,-ay,bc,bu,-ag,-ch,-ap,bl,}

[0338] {bb,bt,-aj,-cl,-ai,bu,ba,-bc,-bs,ak,ck,ah,-bv,-az,bd,br,-al,-cj,-ag,bw,ay,-be,-bq,am,ci,af,-bx,-ax,bf,bp,-an,-ch, -ae,by,aw,-bg,-bo,ao,cg,ad,-bz,-av,bh,bn,-ap,-cf,-ac,ca,au,-bi,-bm,aq,ce,ab,-cb,-at,bj,bl,-ar,-cd,-aa,cc,as,-bk,}

[0339] {bc,bq,-ao,-ce,aa,cf,an,-br,-bb,bd,bp,-ap,-cd,ab,cg,am,-bs,-ba,be,bo,-aq,-cc,ac,ch,al,-bt,-az,bf,bn,-ar,-cb,ad, ci,ak,-bu,-ay,bg,bm,-as,-ca,ae,cj,aj,-bv,-ax,bh,bl,-at,-bz,af,ck,ai,-bw,-aw,bi,bk,-au,-by,ag,cl,ah,-bx,-av,bj,}

[0340] {bd,bn,-at,-bx,aj,ch,aa,-cg,-ak,bw,au,-bm,-be,bc,bo,-as,-by,ai,ci,ab,-cf,-al,bv,av,-bl,-bf,bb,bp,-ar,-bz,ah,cj, ac,-ce,-am,bu,aw,-bk,-bg,ba,bq,-aq,-ca,ag,ck,ad,-cd,-an,bt,ax,-bj,-bh,az,br,-ap,-cb,af,cl,ae,-cc,-ao,bs,ay,-bi,}

[0341] {be,bk,-ay,-bq,as,bw,-am,-cc,ag,ci,-aa,-cj,-af,cd,al,-bx,-ar,br,ax,-bl,-bd,bf,bj,-az,-bp,at,bv,-an,-cb,ah,ch,-ab, -ck,-ae,ce,ak,-by,-aq,bs,aw,-bm,-bc,bg,bi,-ba,-bo,au,bu,-ao,-ca,ai,cg,-ac,-cl,-ad,cf,aj,-bz,-ap,bt,av,-bn,-bb,bh,}

[0342] {bf,bh,-bd,-bj,bb,bl,-az,-bn,ax,bp,-av,-br,at,bt,-ar,-bv,ap,bx,-an,-bz,al,cb,-aj,-cd,ah,cf,-af,-ch,ad,cj,-ab,-cl, -aa,ck,ac,-ci,-ae,cg,ag,-ce,-ai,cc,ak,-ca,-am,by,ao,-bw,-aq,bu,as,-bs,-au,bq,aw,-bo,-ay,bm,ba,-bk,-bc,bi,be,-bg,}

[0343] {bg,be,-bi,-bc,bk,ba,-bm,-ay,bo,aw,-bq,-au,bs,as,-bu,-aq,bw,ao,-by,-am,ca,ak,-cc,-ai,ce,ag,-cg,-ae,ci,ac,-ck,-aa, cl,-ab,-cj,ad,ch,-of,-cf,ah,cd,-aj,-cb,al,bz,-an,-bx,ap,bv,-ar,-bt,at,br,-av,-bp,ax,bn,-az,-bl,bb,bj,-bd,-bh,bf,}

[0344] {bh,bb,-bn,-av,bt,ap,-bz,-aj,cf,ad,-cl,ac,cg,-ai,-ca,ao,bu,-au,-bo,ba,bi,-bg,-bc,bm,aw,-bs,-aq,by,ak,-ce,-ae,ck, -ab,-ch,ah,cb,-an,-bv,at,bp,-az,-bj,bf,bd,-bl,-ax,br,ar,-bx,-al,cd,af,-cj,aa,ci,-ag,-cc,am,bw,-as,-bq,ay,bk,-be,}

[0345] {bi,ay,-bs,-ao,cc,ae,-cl,af,cb,-ap,-br,az,bh,-bj,-ax,bt,an,-cd,-ad,ck,-ag,-ca,aq,bq,-ba,-bg,bk,aw,-bu,-am,ce,ac, -cj,ah,bz,-ar,-bp,bb,bf,-bl,-av,bv,al,-cf,-ab,ci,-ai,-by,as,bo,-bc,-be,bm,au,-bw,-ak,cg,aa,-ch,aj,bx,-at,-bn,bd,}

[0346] {bj,av,-bx,-ah,cl,-ag,-by,au,bk,-bi,-aw,bw,ai,-ck,af,bz,-at,-bl,bh,ax,-bv,-aj,cj,-ae,-ca,as,bm,-bg,-ay,bu,ak,-ci, ad,cb,-ar,-bn,bf,az,-bt,-al,ch,-ac,-cc,aq,bo,-be,-ba,bs,am,-cg,ab,cd,-ap,-bp,bd,bb,-br,-an,cf,-aa,-ce,ao,bq,-bc,}

[0347] {bk,as,-cc,-aa,cd,-ar,-bl,bj,at,-cb,-ab,ce,-aq,-bm,bi,au,-ca,-ac,cf,-ap,-bn,bh,av,-bz,-ad,cg,-ao,-bo,bg,aw,-by,-ae, ch,-an,-bp,bf,ax,-bx,-af,ci,-am,-bq,be,ay,-bw,-ag,cj,-al,-br,bd,az,-bv,-ah,ck,-ak,-bs,bc,ba,-bu,-ai,cl,-aj,-bt,bb,}

[0348] {bl,ap,-ch,ag,bu,-bc,-ay,by,ac,-cd,at,bh,-bp,-al,cl,-ak,-bq,bg,au,-cc,ab,bz,-ax,-bd,bt,ah,-ci,ao,bm,-bk,-aq,cg,- af,-bv,bb,az,-bx,-ad,ce,-as,-bi,bo,am,-ck,aj,br,-bf,-av,cb,-aa,-ca,aw,be,-bs,-ai,cj,-an,-bn,bj,ar,-cf,ae,bw,-ba,}

[0349] {bm,am,-cl,an,bl,-bn,-al,ck,-ao,-bk,bo,ak,-cj,ap,bj,-bp,-aj,ci,-aq,-bi,bq,ai,-ch,ar,bh,-br,-ah,cg,-as,-bg,bs,ag, -cf,at,bf,-bt,-af,ce,-au,-be,bu,ae,-cd,av,bd,-bv,-ad,cc,-aw,-bc,bw,ac,-cb,ax,bb,-bx,-ab,ca,-ay,-ba,by,aa,-bz,az,}

[0350] {bn,aj,-cg,au,bc,-by,ab,bv,-bf,-ar,cj,-am,-bk,bq,ag,-cd,ax,az,-cb,ae,bs,-bi,-ao,cl,-ap,-bh,bt,ad,-ca,ba,aw,-ce,a h,bp,-bl,-al,ci,-as,-be,bw,aa,-bx,bd,at,-ch,ak,bm,-bo,-ai,cf,-av,-bb,bz,-ac,-bu,bg,aq,-ck,an,bj,-br,-of,cc,-ay,}

[0351] {bo,ag,-cb,bb,at,-cj,ao,bg,-bw,ab,bt,-bj,-al,cg,-aw,-ay,ce,-aj,-bl,br,ad,-by,be,aq,-cl,ar,bd,-bz,ae,bq,-bm,-ai,c d,-az,-av,ch,-am,-bi,bu,aa,-bv,bh,an,-ci,au,ba,-cc,ah,bn,-bp,-af,ca,-bc,-as,ck,-ap,-bf,bx,-ac,-bs,bk,ak,-cf,ax,}

[0352] {bp,ad,-bw,bi,ak,-cd,bb,ar,-ck,au,ay,-cg,an,bf,-bz,ag,bm,-bs,-aa,bt,-bl,-ah,ca,-be,-ao,ch,-ax,-av,cj,-aq,-bc,cc, -aj,-bj,bv,-ac,-bq,bo,ae,-bx,bh,al,-ce,ba,as,-cl,at,az,-cf,am,bg,-by,af,bn,-br,-ab,bu,-bk,-ai,cb,-bd,-ap,ci,-aw,}

[0353] {bq,aa,-br,bp,ab,-bs,bo,ac,-bt,bn,ad,-bu,bm,ae,-bv,bl,af,-bw,bk,ag,-bx,bj,ah,-by,bi,ai,-bz,bh,aj,-ca,bg,ak, -cb,bf,al,-cc,be,am,-cd,bd,an,-ce,bc,ao,-cf,bb,ap,-cg,ba,aq,-ch,az,ar,-ci,ay,as,-cj,ax,at,-ck,aw,au,-cl,av,}

[0354] {br,-ac,-bm,bw,-ah,-bh,cb,-am,-bc,cg,-ar,-ax,cl,-aw,-as,ch,-bb,-an,cc,-bg,-ai,bx,-bl,-ad,bs,-bq,ab,bn,-bv,ag,bi,-c a,al,bd,-cf,aq,ay,-ck,av,at,-ci,ba,ao,-cd,bf,aj,-by,bk,ae,-bt,bp,-aa,-bo,bu,-af,-bj,bz,-ak,-be,ce,-ap,-az,cj,-au,}

[0355] {bs,-af,-bh,cd,-aq,-aw,cj,-bb,-al,by,-bm,-aa,bn,-bx,ak,bc,-ci,av,ar,-ce,bg,ag,-bt,br,-ae,-bi,cc,-ap,-ax,ck,-ba,-am ,bz,-bl,-ab,bo,-bw,aj,bd,-ch,au,as,-cf,bf,ah,-bu,bq,-ad,-bj,cb,-ao,-ay,cl,-az,-an,ca,-bk,-ac,bp,-bv,ai,be,-cg,at,}

[0356] {bt,-ai,-bc,ck,-az,-al,bw,-bq,of,bf,-ch,aw,ao,-bz,bn,-ac,-bi,ce,-at,-ar,cc,-bk,-aa,bl,-cb,aq,au,-cf,bh,ad,-bo,by, -an,-ax,ci,-be,-ag,br,-bv,ak,ba,-cl,bb,aj,-bu,bs,-ah,-bd,cj,-ay,-am,bx,-bp,ae,bg,-cg,av,ap,-ca,bm,-ab,-bj,cd,-as,}

[0357] {bu,-al,-ax,cg,-bi,-aa,bj,-cf,aw,am,-bv,bt,-ak,-ay,ch,-bh,-ab,bk,-ce,av,an,-bw,bs,-aj,-az,ci,-bg,-ac,bl,-cd,au,ao, -bx,br,-ai,-ba,cj,-bf,-ad,bm,-cc,at,ap,-by,bq,-ah,-bb,ck,-be,-ae,bn,-cb,as,aq,-bz,bp,-ag,-bc,cl,-bd,-af,bo,-ca,ar,}

[0358] {bv,-ao,-as,bz,-br,ak,aw,-cd,bn,-ag,-ba,ch,-bj,ac,be,-cl,bf,ab,-bi,ci,-bb,-af,bm,-ce,ax,aj,-bq,ca,-at,-an,bu,-bw, ap,ar,-by,bs,-al,-av,cc,-bo,ah,az,-cg,bk,-ad,-bd,ck,-bg,-aa,bh,-cj,bc,ae,-bl,cf,-ay,-ai,bp,-cb,au,am,-bt,bx,-aq,}

[0359] {bw,-ar,-an,bs,-ca,av,aj,-bo,ce,-az,-af,bk,-ci,bd,ab,-bg,cl,-bh,ac,bc,-ch,bl,-ag,-ay,cd,-bp,ak,au,-bz,bt,-ao,-aq, bv,-bx,as,am,-br,cb,-aw,-ai,bn,-cf,ba,ae,-bj,cj,-be,-aa,bf,-ck,bi,-ad,-bb,cg,-bm,ah,ax,-cc,bq,-al,-at,by,-bu,ap,}

[0360] {bx,-au,-ai,bl,-cj,bg,-ad,-az,cc,-bs,ap,an,-bq,ce,-bb,-ab,be,-ch,bn,-ak,-as,bv,-bz,aw,ag,-bj,cl,-bi,af,ax,-ca,bu, -ar,-al,bo,-cg,bd,-aa,-bc,cf,-bp,am,aq,-bt,cb,-ay,-ae,bh,-ck,bk,-ah,-av,by,-bw,at,aj,-bm,ci,-bf,ac,ba,-cd,br,-ao,}

[0361] {by,-ax,-ad,be,-cf,br,-aq,-ak,bl,-cl,bk,-aj,-ar,bs,-ce,bd,-ac,-ay,bz,-bx,aw,ae,-bf,cg,-bq,ap,al,-bm,ck,-bj,ai,as, -bt,cd,-bc,ab,az,-ca,bw,-av,-af,bg,-ch,bp,-ao,-am,bn,-cj,bi,-ah,-at,bu,-cc,bb,-aa,-ba,cb,-bv,au,ag,-bh,ci,-bo,an,}

[0362] {bz,-ba,ab,ax,-bw,cc,-bd,ae,au,-bt,cf,-bg,ah,ar,-bq,ci,-bj,ak,ao,-bn,cl,-bm,an,al,-bk,cj,-bp,aq,ai,-bh,cg,-bs,at ,af,-be,cd,-bv,aw,ac,-bb,ca,-by,az,-aa,-ay,bx,-cb,bc,-ad,-av,bu,-ce,bf,-ag,-as,br,-ch,bi,-aj,-ap,bo,-ck,bl,-am,}

[0363] {ca,-bd,ag,aq,-bn,ck,-bq,at,ad,-ba,bx,-cd,bg,-aj,-an,bk,-ch,bt,-aw,-aa,ax,-bu,cg,-bj,am,ak,-bh,ce,-bw,az,-ac,-au, br,-cj,bm,-ap,-ah,be,-cb,bz,-bc,af,ar,-bo,cl,-bp,as,ae,-bb,by,-cc,bf,-ai,-ao,bl,-ci,bs,-av,-ab,ay,-bv,cf,-bi,al,}

[0364] {cb,-bg,al,aj,-be,bz,-cd,bi,-an,-ah,bc,-bx,cf,-bk,ap,af,-ba,bv,-ch,bm,-ar,-ad,ay,-bt,cj,-bo,at,ab,-aw,br,-cl,bq, -av,aa,au,-bp,ck,-bs,ax,-ac,-as,bn,-ci,bu,-az,ae,aq,-bl,cg,-bw,bb,-ag,-ao,bj,-ce,by,-bd,ai,am,-bh,cc,-ca,bf,-ak,}

[0365] {cc,-bj,aq,ac,-av,bo,-ch,bx,-be,al,ah,-ba,bt,-cl,bs,-az,ag,am,-bf,by,-cg,bn,-au,ab,ar,-bk,cd,-cb,bi,-ap,-ad,aw,- bp,ci,-bw,bd,-ak,-ai,bb,-bu,ck,-br,ay,-af,-an,bg,-bz,cf,-bm,at,-aa,-as,bl,-ce,ca,-bh,ao,ae,-ax,bq,-cj,bv,-bc,aj,}

[0366] {cd,-bm,av,-ae,-am,bd,-bu,cl,-bv,be,-an,-ad,au,-bl,cc,-ce,bn,-aw,af,al,-bc,bt,-ck,bw,-bf,ao,ac,-at,bk,-cb,cf,-bo, ax,-ag,-ak,bb,-bs,cj,-bx,bg,-ap,-ab,as,-bj,ca,-cg,bp,-ay,ah,aj,-ba,br,-ci,by,-bh,aq,aa,-ar,bi,-bz,ch,-bq,az,-ai,}

[0367] {ce,-bp,ba,-al,-ad,as,-bh,bw,-cl,bx,-bi,at,-ae,-ak,az,-bo,cd,-cf,bq,-bb,am,ac,-ar,bg,-bv,ck,-by,bj,-au,af,aj,-ay, bn,-cc,cg,-br,bc,-an,-ab,aq,-bf,bu,-cj,bz,-bk,av,-ag,-ai,ax,-bm,cb,-ch,bs,-bd,ao,aa,-ap,be,-bt,ci,-ca,bl,-aw,ah,}

[0368] {cf,-bs,bf,-as,af,ah,-au,bh,-bu,ch,-cd,bq,-bd,aq,-ad,-aj,aw,-bj,bw,-cj,cb,-bo,bb,-ao,ab,al,-ay,bl,-by,cl,-bz,bm, -az,am,aa,-an,ba,-bn,ca,-ck,bx,-bk,ax,-ak,-ac,ap,-bc,bp,-cc,ci,-bv,bi,-av,ai,ae,-ar,be,-br,ce,-cg,bt,-bg,at,-ag,}

[0369] {cg,-bv,bk,-az,ao,-ad,-ah,as,-bd,bo,-bz,ck,-cc,br,-bg,av,-ak,-aa,al,-aw,bh,-bs,cd,-cj,by,-bn,bc,-ar,ag,ae,-ap,ba, -bl,bw,-ch,cf,-bu,bj,-ay,an,-ac,-ai,at,-be,bp,-ca,cl,-cb,bq,-bf,au,-aj,-ab,am,-ax,bi,-bt,ce,-ci,bx,-bm,bb,-aq,af,}

[0370] {ch,-by,bp,-bg,ax,-ao,af,ad,-am,av,-be,bn,-bw,cf,-cj,ca,-br,bi,-az,aq,-ah,-ab,ak,-at,bc,-bl,bu,-cd,cl,-cc,bt,-bk, bb,-as,aj,-aa,-ai,ar,-ba,bj,-bs,cb,-ck,ce,-bv,bm,-bd,au,-al,ac,ag,-ap,ay,-bh,bq,-bz,ci,-cg,bx,-bo,bf,-aw,an,-ae,}

[0371] {ci,-cb,bu,-bn,bg,-az,as,-al,ae,ac,-aj,aq,-ax,be,-bl,bs,-bz,cg,-ck,cd,-bw,bp,-bi,bb,-au,an,-ag,-aa,ah,-ao,av,-bc, bj,-bq,bx,-ce,cl,-cf,by,-br,bk,-bd,aw,-ap,ai,-ab,-af,am,-at,ba,-bh,bo,-bv,cc,-cj,ch,-ca,bt,-bm,bf,-ay,ar,-ak,ad,}

[0372] {cj,-ce,bz,-bu,bp,-bk,bf,-ba,av,-aq,al,-ag,ab,ad,-ai,an,-as,ax,-bc,bh,-bm,br,-bw,cb,-cg,cl,-ch,cc,-bx,bs,-bn,bi, -bd,ay,-at,ao,-aj,ae,aa,-af,ak,-ap,au,-az,be,-bj,bo,-bt,by,-cd,ci,-ck,cf,-ca,bv,-bq,bl,-bg,bb,-aw,ar,-am,ah,-ac,}

[0373] {ck,-ch,ce,-cb,by,-bv,bs,-bp,bm,-bj,bg,-bd,ba,-ax,au,-ar,ao,-al,ai,-af,ac,aa,-ad,ag,-aj,am,-ap,as,-av,ay,-bb,be, -bh,bk,-bn,bq,-bt,bw,-bz,cc,-cf,ci,-cl,cj,-cg,cd,-ca,bx,-bu,br,-bo,bl,-bi,bf,-bc,az,-aw,at,-aq,an,-ak,ah,-ae,ab,}

[0374] {cl,-ck,cj,-ci,ch,-cg,cf,-ce,cd,-cc,cb,-ca,bz,-by,bx,-bw,bv,-bu,bt,-bs,br,-bq,bp,-bo,bn,-bm,bl,-bk,bj,-bi,bh,-bg, bf,-be,bd,-bc,bb,-ba,az,-ay,ax,-aw,av,-au,at,-as,ar,-aq,ap,-ao,an,-am,al,-ak,aj,-ai,ah,-ag,af,-ae,ad,-ac,ab,-aa,}

[0375] The variables a, bc, ..., aa, ab, ac, ..., cl can be derived based on the formulas for DST-7 shown in Table 1, and their values ​​can differ for different sizes of DST-7. For example, the value of "a" can be different for 4-point DST-7 and 8-point DST-7. To avoid floating-point operations, similar to the DCT-2 core used in HEVC, the DST-7 transformation core can be controlled by predefined factors, such as... (corresponding to an 8-bit transformation core) or (Corresponding to a 10-bit transform core), to perform scaling and round to the nearest integer, or further adjust by offset, such as +1 / -1.

[0376] In an exemplary design of AMT, when AMT is applied, all the main converter cores, including DCT-2, can be represented by 10-bit integers, i.e., 10-bit converter cores. However, it is possible that at least one (but not all) of the main converter cores are represented by 10-bit integers.

[0377] The master transform in VVC can apply 8-bit (e.g., for all transform sizes except 64 points and larger) and 10-bit (e.g., for 64-point transforms and larger) transform cores. In this application, it's impossible to extract 2, 4, 8, 16, and 32-point DCT-2 transform cores from, for example, a 64-point DCT-2 transform core. This inevitably increases the cost of applying the master transform, as a separate 64-point transform core would require additional storage and logic for implementation. Compared to a 10-bit master transform core, an 8-bit master transform core reduces complexity due to reduced memory used to store the transform core and a smaller input bit width for multipliers / additions / subtractions.

[0378] Therefore, this disclosure provides a set of 8-bit master transform cores for all transform size types applicable to the exemplary AMT, including DCT-2, DCT-5, DCT-8, DST-1, and DST-7. The methods presented below can be used individually or in combination in any order.

[0379] Reference Figure 5 In a first simple example, a method for decoding compressed video or image data or encoding uncompressed video or image data using an 8-bit master transform core matrix may include:

[0380] Step 501: Receive information related to the target file used for encoding or decoding. The target file used for encoding or decoding can be one of the following: a compressed video or image data file, or an uncompressed video or image data file.

[0381] Figure 5 The method may further include step 502. Step 502 includes: encoding or decoding the target file to determine whether to use a first transform core matrix of a first size type or a second transform core matrix of a second size type smaller than the first size type. The first size type may be an 8-bit master transform core matrix having a core matrix represented by 8 bits and having a size of 64 points or greater.

[0382] The method according to one aspect of this disclosure may further include step 503. Step 503 includes: when the determined result is a first transform core matrix of a first size type, using an 8-bit master transform core matrix of size 64 points or larger to encode or decode the target file for encoding or decoding.

[0383] Figure 5The method may further include step 504. Step 504 includes: when the determined result is to use a second transform core matrix of a second size type smaller than the first size type, extracting a second transform core matrix of the second size type from an 8-bit master transform core matrix of size 64 points or larger, and using the extracted second transform core matrix of the second size type to encode or decode the target file for encoding or decoding.

[0384] Figure 5 The method shown may also include processing steps 501 to 504 being performed by one or more processors. Figure 5 The method shown may also include pre-storing an 8-bit master transform core matrix in memory by one or more processors before executing steps 501 to 504.

[0385] Figure 5 The method shown may further include: the first transformation core matrix is ​​a 64-point 8-bit principal transformation core matrix, constructed using 33 integers for constructing a 32-point 8-bit principal transformation core matrix and an additional 32 integers, wherein the additional 32 integers include: bf, bg, bh, bi, bj, bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb, cc, cd, ce, cf, cg, ch, ci, cj, and ck plus their respective sign changes, and the additional... The thirty-two integers {bf, bg, bh, bi, bj, bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb, cc, cd, ce, cf, cg, ch, ci, cj, ck} equal {91, 90, 90, 90, 88, 87, 86, 84, 83, 81, 79, 77, 73, 71, 69, 65, 62, 59, 56, 52, 48, 44, 41, 37, 33, 28, 24, 20, 15, 11, 7, 2}.

[0386] Figure 5The method shown may further include: constructing a 128-point 8-bit master transform core using 65 integers for constructing a 64-point 8-bit master transform core matrix and an additional 64 integers, wherein the additional 64 integers include: cl,cm,cn,co,cp,cq,cr,cs,ct,cu,cv,cw,cx,cy,cz,da,db,dc,dd,de,df,dg,dh,di,dj,dk,dl,dm,dn,d_,dp,dq ,dr,ds,dt,du,dv,dw,dx,dy,dz,ea,eb,ec,ed,ee,ef,eg,eh,ei,ej,ek,el,em,en,eo,ep,eq,er,es,et,eu,ev andew plus their sign changes, and these additional 64 integers are {cl,cm,cn,co,cp,cq,cr,cs,ct,cu,cv,cw,cx,cy,cz,da, db,dc,dd,de,df,dg,dh,di,dj,dk,dl,dm,dn,d_,dp,dq,dr,ds,dt,du,dv,dw,dx,dy,dz,ea,eb,ec, ed,ee,ef,eg,eh,ei,ej,ek,el,em,en,eo,ep,eq,er,es,et,eu,ev,ew} is equal to {90,90,90,90,90,90,89, 89,89,88,88,87,86,86,85,84,83,82,81,80,79,78,77,76,75,73,72,71,69,68,66,65,63,62,60,58,58,55,53,51,49,48,45,44,42,40,38,36,34,32,29,27,25,23,21,19,17,15,12,10,8,6,3,1}.

[0387] Figure 5 The method shown may also include: the size of the 8-bit master transform core matrix is ​​64 points or 128 points.

[0388] also, Figure 5 The method shown may further include: the left or right half of the even or odd rows of the 8-bit master transform core matrix forming a matrix similar to the second transform core matrix, wherein the 8-bit master transform core matrix is ​​one of the following: DCT-2, DCT-5, DCT-8, DST-1 and DST-7, and / or the second transform core matrix is ​​one of the following: DCT-2, DCT-5, DCT-8, DST-1 and DST-7.

[0389] Figure 5The method shown may also include: the 8-bit master transform core matrix and the second transform core matrix being the same of the following: DCT-2, DCT-5, DCT-8, DST-1 and DST-7.

[0390] Figure 5 The method shown may further include: the 8-bit master transform core matrix is ​​an 8-bit 64-point DCT-2 transform matrix, and / or the second transform core matrix is ​​an 8-bit 32-point DCT-2 transform matrix.

[0391] Figure 5 The method shown may also include: via Figure 6 The following steps are shown to derive an 8-bit N-point master transform core matrix consisting of M unique numbers. Figure 6 Step 601 is illustrated. Step 601 includes deriving an initial transformation core matrix by scaling the original transformation core using a scaling factor. For example, step 601 may include deriving an initial transformation core matrix T1 by scaling the original transformation core T0, which consists of floating-point numbers, using a scaling factor of 2B-2×log2(N) such that T1 = T0×2B-2×log2(N), where B = 8, and the row vectors of T0, which serve as basis vectors, are orthogonal to each other, and the norm of each row vector is 1.

[0392] Figure 6 The method may also include step 602. Step 602 includes deriving the adjusted transformation core matrix. For example, step 602 may include deriving the adjusted transformation core matrix (T2) by adding an offset to a selected set of M unique numbers used to construct the adjusted master transformation core matrix T2.

[0393] Figure 6 The method may also include step 603. Step 603 includes: calculating the cost C as the sum of the absolute values ​​of all elements. For example, step 603 may include: calculating the cost C as the sum of the absolute values ​​of all elements of (T1*T1T-22B-4×log2(N)2×I), where I is an N×N identity matrix.

[0394] Figure 6 The method may also include step 604. Step 604 includes updating the adjusted transformation matrix. For example, step 604 may include updating the adjusted transformation matrix T2 by adding the calculated offset value to T2, which minimizes the cost to T2, and the adjusted transformation matrix T2 can be output as an 8-bit N-point principal transformation core matrix.

[0395] exist Figure 6 In the method, the offset value for each of the M unique numbers can include one or more of the following values: -2, -1, 0, +1, +2.

[0396] also, Figure 6 The method may also include: after minimizing the cost C by trying all possible combinations of offset values ​​on a selected set of M unique numbers, outputting T2 as an 8-bit N-point master transformation core matrix.

[0397] Next, we will explain the different types of transform cores (transform core matrices). For example, a 64-point DCT-2 transform core can be represented using an 8-bit integer, where the left half of the even-numbered rows (rows 0, 2, 4, ..., 30) of the transform core matrix forms the same matrix as a 32-point DCT-2 transform core matrix. In one embodiment, a 64-point DCT-2 core matrix can be derived by setting the parameters as follows: {aa,ab,ac,ad,ae,af,ag,ah,ai,aj,ak,al,am,an,ao,ap,aq,ar,as,at,au,av,aw,ax,ay,az,ba,bb,bc,bd,be,bf,bg,bh,bi,bj,bk,bl,bm,bn,bo,bp,bq,br,bs,bt,bu,bv,bw,bx,by,bz,ca,cb,cc,cd,ce, cf,cg,ch,ci,cj,ck}={64,83,36,89,75,50,18,90,87,80,70,57,43,25,9,90,90,88,85,82,78,73,67,61,54,46,38,31, 22,13,4,91,90,90,90,88,87,86,84,83,81,79,77,73,71,69,65,62,59,56,52,48,44,41,37,33,28,24,20,15,11,7,2}.

[0398] A 128-point DCT-2 transform core can be represented using an 8-bit integer, and the left half of the even-numbered rows (rows 0, 2, 4, ..., 126) of the transform core matrix can form the same matrix as the 64-point DCT-2 transform core matrix. In one embodiment, the 128-point DCT-2 core matrix can be derived by setting the parameters as follows: {aa,ab,ac,ad,ae,af,ag,ah,ai,aj,ak,al,am,an,ao,ap,aq,ar,as,at,au,av,aw,ax,ay,az,ba,bb,bc,bd,be,bf,bg,bh,bi,bj,bk,bl,bm,bn,bo,bp,bq,br,bs,bt,bu,bv,bw,bx,by,bz,ca,cb, cc,cd,ce,cf,cg,ch,ci,cj,ck,cl,cm,cn,co,cp,cq,cr,cs,ct,cu,cv,cw,cx,cy,cz,da,db,dc,dd,de,df,dg,dh,di, dj,dk,dl,dm,dn,d_,dp,dq,dr,ds,dt,du,dv,dw,dx,dy,dz,ea,eb,ec,ed,ee,ef,eg,eh,ei,ej,ek,el,em,en,eo,ep, eq,er,es,et,eu,ev,ew}={64,83,36,89,75,50,18,90,87,80,70,57,43,25,9,90,90,88,85,82,78,73,67,61,54,46 ,38,31,22,13,4,91,90,90,90,88,87,86,84,83,81,79,77,73,71,69,65,62,59,56,52,48,44,41,37,33,28,24,20, 15,11,7,2,90,90,90,90,90,90,89,89,89,88,88,87,86,86,85,84,83,82,81,80,79,78,77,76,75,73,72,71,69,68,66,65,63,62,60,58,58,55,53,51,49,48,45,44,42,40,38,36,34,32,29,27,25,23,21,19,17,15,12,10,8,6,3,1}.

[0399] The B-bit N-point master transform core consisting of M unique numbers (albeit signed and zero) can be derived through the following steps: (a) the initial transform core matrix T1 is derived by scaling the original transform core, such as T0, consisting of floating-point numbers using a scaling factor of 2B-2×log2(N), i.e., Tl = T0×2B-2×log2(N), where the row vectors, i.e., the basis vectors, of T0 are orthogonal to each other and each row vector has a norm of 1; (b) the adjusted transform core T2 is derived by attempting to add offsets to a selected set of the M unique numbers used to construct the master transform core T2; and (c) the cost C is calculated as the sum of the absolute values ​​of all elements of (T1*T1T-22B-4×log2(N)2×I), where I is an N×N identity matrix. The offset value that minimizes the cost value can then be added to T2, and T2 can be updated. Example offset values ​​for each of the M unique numbers can include, but are not limited to: -2, -1, 0, +1, +2. After minimizing the cost by trying all possible combinations of offset values ​​for a selected set of M unique numbers, T2 can be output as the B-bit N-point master transform core.

[0400] When deriving N-point DCT-8 and DST-7 transform cores, it may be limited that the set of M unique numbers used to construct the N-point DCT-8 core matrix is ​​the same as the set of M unique numbers used to construct the N-point DST-7 core matrix. In one embodiment, M equals N. In one embodiment, an 8-bit DCT-8 and DST-7 transform core is shown below. For example, in a 4-point DST-7 core, there can be four unique numbers including 28, 55, 74, and 84, and this is the same set of four unique numbers used to construct the 4-point DCT-8 core.

[0401] 4 o'clock DST-7:

[0402]

[0403] 8-bit DST-7:

[0404]

[0405] 16-bit DST-7:

[0406]

[0407] 32-bit DST-7:

[0408] {4,9,13,17,21,26,30,34,38,42,45,50,53,56,60,63,66,68,72,74,77,78,80,82,84,85,86,88,88,89,90,90,}

[0409] {13,26,38,50,60,68,77,82,86,89,90,88,85,80,74,66,56,45,34,21,9,-4,-17,-30,-42,-53,-63,-72,-78,-84,-88,-90,}

[0410] {21,42,60,74,84,89,89,84,74,60,42,21,0,-21,-42,-60,-74,-84,-89,-89,-84,-74,-60,-42,-21,0,21,42,60,74,84,89,}{30,56,77,88,89,80,63,38,9,-21,-50,-72,-85,-90,-84,-68,-45,-17,13,42,66,82,90,86,74,53,26,-4,-34,-60,-78,-88,}

[0411] {38,68,86,88,74,45,9,-30,-63,-84,-90,-78,-53,-17,21,56,80,90,82,60,26,-13,-50,-77,-89,-85,-66,-34,4,42,72,88,}

[0412] {45,78,90,77,42,-4,-50,-80,-90,-74,-38,9,53,82,89,72,34,-13,-56,-84,-88,-68,-30,17,60,85,88,66,26,-21,-63,-86,}

[0413] {53,85,85,53,0,-53,-85,-85,-53,0,53,85,85,53,0,-53,-85,-85,-53,0,53,85,85,53,0,-53,-85,-85,-53,0,53,85,}

[0414] {60,89,74,21,-42,-84,-84,-42,21,74,89,60,0,-60,-89,-74,-21,42,84,84,42,-21,-74,-89,-60,0,60,89,74,21,-42,-84,}

[0415] {66,90,56,-13,-74,-88,-45,26,80,84,34,-38,-85,-78,-21,50,88,72,9,-60,-90,-63,4,68,89,53,-17,-77,-86,-42,30,82,}

[0416] {72,86,34,-45,-89,-63,13,78,82,21,-56,-90,-53,26,84,77,9,-66,-88,-42,38,88,68,-4,-74,-85,-30,50,90,60,-17,-80,}

[0417] {77,80,9,-72,-84,-17,66,86,26,-60,-88,-34,53,90,42,-45,-90,-50,38,89,56,-30,-88,-63,21,85,68,-13,-82,-74,4,78,}

[0418] {80,72,-17,-86,-60,34,90,45,-50,-89,-30,63,85,13,-74,-78,4,82,68,-21,-88,-56,38,90,42,-53,-88,-26,66,84,9,-77,}

[0419] {84,60,-42,-89,-21,74,74,-21,-89,-42,60,84,0,-84,-60,42,89,21,-74,-74,21,89,42,-60,-84,0,84,60,-42,-89,-21,74,}

[0420] {86,45,-63,-78,21,90,26,-77,-66,42,88,4,-85,-50,60,80,-17,-90,-30,74,68,-38,-88,-9,84,53,-56,-82,13,89,34,-72,}

[0421] {88,30,-78,-56,60,77,-34,-88,4,89,26,-80,-53,63,74,-38,-86,9,90,21,-82,-50,66,72,-42,-85,13,90,17,-84,-45,68,}

[0422] {90,13,-88,-26,84,38,-78,-50,72,60,-63,-68,53,77,-42,-82,30,86,-17,-89,4,90,9,-88,-21,85,34,-80,-45,74,56,-66,}

[0423] {90,-4,-90,9,89,-13,-88,17,88,-21,-86,26,85,-30,-84,34,82,-38,-80,42,78,-45,-77,50,74,-53,-72,56,68,-60,-66,63,}

[0424] {89,-21,-84,42,74,-60,-60,74,42,-84,-21,89,0,-89,21,84,-42,-74,60,60,-74,-42,84,21,-89,0,89,-21,-84,42,74,-60,}

[0425] {88,-38,-72,68,42,-86,-4,88,-34,-74,66,45,-85,-9,89,-30,-77,63,50,-84,-13,90,-26,-78,60,53,-82,-17,90,-21,-80,56,}

[0426] {85,-53,-53,85,0,-85,53,53,-85,0,85,-53,-53,85,0,-85,53,53,-85,0,85,-53,-53,85,0,-85,53,53,-85,0,85,-53,}

[0427] {82,-66,-30,90,-42,-56,86,-13,-77,74,17,-88,53,45,-89,26,68,-80,-4,84,-63,-34,90,-38,-60,85,-9,-78,72,21,-88,50,}

[0428] {78,-77,-4,80,-74,-9,82,-72,-13,84,-68,-17,85,-66,-21,86,-63,-26,88,-60,-30,88,-56,-34,89,-53,-38,90,-50,-42,90,-45,}

[0429] {74,-84,21,60,-89,42,42,-89,60,21,-84,74,0,-74,84,-21,-60,89,-42,-42,89,-60,-21,84,-74,0,74,-84,21,60,-89,42,}

[0430] {68,-88,45,30,-84,78,-17,-56,90,-60,-13,77,-85,34,42,-88,72,-4,-66,89,-50,-26,82,-80,21,53,-90,63,9,-74,86,-38,}

[0431] {63,-90,66,-4,-60,90,-68,9,56,-89,72,-13,-53,88,-74,17,50,-88,77,-21,-45,86,-78,26,42,-85,80,-30,-38,84,-82,34,}

[0432] {56,-88,80,-38,-21,72,-90,68,-17,-42,82,-86,53,4,-60,88,-78,34,26,-74,90,-66,13,45,-84,85,-50,-9,63,-89,77,-30,}

[0433] {50,-82,88,-66,21,30,-72,90,-78,42,9,-56,85,-86,60,-13,-38,77,-90,74,-34,-17,63,-88,84,-53,4,45,-80,89,-68,26,}

[0434] {42,-74,89,-84,60,-21,-21,60,-84,89,-74,42,0,-42,74,-89,84,-60,21,21,-60,84,-89,74,-42,0,42,-74,89,-84,60,-21,}

[0435] {34,-63,82,-90,84,-66,38,-4,-30,60,-80,90,-85,68,-42,9,26,-56,78,-89,86,-72,45,-13,-21,53,-77,88,-88,74,-50,17,}

[0436] {26,-50,68,-82,89,-88,80,-66,45,-21,-4,30,-53,72,-84,90,-88,78,-63,42,-17,-9,34,-56,74,-85,90,-86,77,-60,38,-13,}

[0437] {17,-34,50,-63,74,-82,88,-90,88,-84,77,-66,53,-38,21,-4,-13,30,-45,60,-72,80,-86,90,-89,85,-78,68,-56,42,-26,9,}

[0438] {9,-17,26,-34,42,-50,56,-63,68,-74,78,-82,85,-88,89,-90,90,-88,86,-84,80,-77,72,-66,60,-53,45,-38,30,-21,13,-4,}

[0439] 64-bit DST-7:

[0440] {2,5,7,8,11,13,15,17,20,22,23,26,29,30,32,34,37,38,41,42,44,46,48,49,52,53,55,58,59,60,62,64,65,66,68,69,72,72,74,73,76,77,78,79,81,80,82,83,85,84,85,86,87,87,88,89,89,90,89,90,90,90,90,90,}

[0441] {7,13,20,26,32,38,44,49,55,60,65,69,74,77,81,83,85,87,89,90,90,90,90,89,87,85,83,81,77,74,69,65,60,55,49,44,38,32,26,20,13,7,0,-7,-13,-20,-26,-32,-38,-44,-49,-55,-60,-65,-69,-74,-77,-81,-83,-85,-87,-89,-90,-90,}

[0442] {11,22,32,42,52,60,68,73,81,84,88,90,90,89,87,85,79,74,66,59,49,41,30,20,8,-2,-13,-23,-34,-44,-53,-62,-69,-76,-80,-85,-89,-90,-90,-90,-87,-83,-78,-72,-65,-58,-48,-38,-29,-17,-7,5,15,26,37,46,55,64,72,77,82,86,89,90,}

[0443] {15,30,44,58,68,77,85,89,90,89,86,81,72,62,49,37,22,7,-8,-23,-38,-52,-64,-74,-80,-87,-90,-90,-88,-83,-76,-66,-55,-42,-29,-13,2,17,32,46,59,69,78,84,89,90,90,85,79,72,60,48,34,20,5,-11,-26,-41,-53,-65,-73,-82,-87,-90,}

[0444] {20,38,55,69,81,87,90,89,83,74,60,44,26,7,-13,-32,-49,-65,-77,-85,-90,-90,-85,-77,-65,-49,-32,-13,7,26,44,60,74,83,89,90,87,81,69,55,38,20,0,-20,-38,-55,-69,-81,-87,-90,-89,-83,-74,-60,-44,-26,-7,13,32,49,65,77,85,90,}

[0445] {23,46,65,79,88,90,86,76,60,41,17,-7,-30,-52,-69,-82,-90,-90,-85,-72,-55,-34,-11,13,37,58,74,84,90,89,80,68,49,29,5,-20,-42,-62,-77,-87,-90,-87,-78,-64,-44,-22,2,26,48,66,81,89,90,85,73,59,38,15,-8,-32,-53,-72,-83,-89,}

[0446] {29,53,74,86,90,85,72,52,26,-2,-30,-55,-73,-87,-90,-84,-72,-49,-23,5,32,58,76,87,90,85,69,48,22,-7,-34,-59,-77,-88,-90,-83,-68,-46,-20,8,37,60,78,89,90,82,66,44,17,-11,-38,-62,-79,-89,-89,-80,-65,-42,-15,13,41,64,81,90,}

[0447] {32,60,81,90,87,74,49,20,-13,-44,-69,-85,-90,-83,-65,-38,-7,26,55,77,89,89,77,55,26,-7,-38,-65,-83,-90,-85,-69,-44,-13,20,49,74,87,90,81,60,32,0,-32,-60,-81,-90,-87,-74,-49,-20,13,44,69,85,90,83,65,38,7,-26,-55,-77,-89,}

[0448] {37,66,85,90,79,55,22,-15,-49,-76,-90,-87,-72,-42,-7,30,62,83,90,82,60,29,-8,-44,-72,-88,-89,-73,-48,-13,23,58,81,90,84,65,34,-2,-38,-68,-86,-90,-78,-53,-20,17,52,77,89,87,69,41,5,-32,-64,-85,-90,-80,-59,-26,11,46,74,89,}

[0449] {41,72,89,87,66,32,-8,-48,-77,-90,-85,-60,-23,17,55,80,90,81,53,15,-26,-62,-84,-90,-76,-46,-7,34,68,87,89,72,38,-2,-42,-74,-90,-86,-65,-30,11,49,78,90,83,59,22,-20,-58,-82,-90,-79,-52,-13,29,64,85,89,73,44,5,-37,-69,-88,}

[0450] {44,77,90,81,49,7,-38,-74,-90,-83,-55,-13,32,69,89,85,60,20,-26,-65,-87,-87,-65,-26,20,60,85,89,69,32,-13,-55,-83,-90,-74,-38,7,49,81,90,77,44,0,-44,-77,-90,-81,-49,-7,38,74,90,83,55,13,-32,-69,-89,-85,-60,-20,26,65,87,}

[0451] {48,80,90,72,30,-20,-64,-88,-85,-58,-11,38,76,90,77,41,-8,-55,-84,-89,-65,-22,29,69,89,82,49,2,-46,-81,-90,-72,-32,17,62,87,86,59,13,-37,-73,-90,-78,-42,7,53,85,89,66,23,-26,-68,-90,-83,-52,-5,44,79,90,74,34,-15,-60,-87,}

[0452] {52,84,87,59,8,-44,-80,-90,-65,-17,37,77,90,72,26,-29,-72,-90,-76,-34,20,66,89,81,42,-11,-60,-88,-85,-49,2,53,85,87,58,7,-46,-82,-89,-64,-15,38,78,90,69,23,-30,-74,-90,-73,-32,22,68,90,79,41,-13,-62,-89,-83,-48,5,55,86,}

[0453] {55,87,83,44,-13,-65,-90,-77,-32,26,74,90,69,20,-38,-81,-89,-60,-7,49,85,85,49,-7,-60,-89,-81,-38,20,69,90,74,26,-32,-77,-90,-65,-13,44,83,87,55,0,-55,-87,-83,-44,13,65,90,77,32,-26,-74,-90,-69,-20,38,81,89,60,7,-49,-85,}

[0454] {59,90,77,29,-34,-81,-88,-53,7,64,90,74,22,-41,-83,-86,-48,13,68,90,69,15,-46,-85,-85,-42,20,72,90,65,8,-52,-87,-80,-37,26,76,89,60,2,-58,-89,-78,-30,32,79,89,55,-5,-62,-90,-73,-23,38,82,87,49,-11,-66,-90,-72,-17,44,84,}

[0455] {62,90,69,11,-53,-89,-76,-22,44,86,80,32,-34,-82,-85,-42,23,77,89,52,-13,-72,-90,-60,2,64,90,68,8,-55,-90,-73,-20,46,87,81,30,-37,-83,-84,-41,26,78,88,49,-15,-72,-90,-59,5,65,90,66,7,-58,-89,-74,-17,48,87,79,29,-38,-85,}

[0456] {65,90,60,-7,-69,-90,-55,13,74,89,49,-20,-77,-87,-44,26,81,85,38,-32,-83,-83,-32,38,85,81,26,-44,-87,-77,-20,49,89,74,13,-55,-90,-69,-7,60,90,65,0,-65,-90,-60,7,69,90,55,-13,-74,-89,-49,20,77,87,44,-26,-81,-85,-38,32,83,}

[0457] {68,89,49,-23,-80,-83,-29,46,89,72,5,-65,-90,-53,20,79,84,32,-42,-88,-74,-8,62,90,58,-15,-77,-86,-37,38,87,76,13,-59,-90,-60,11,73,87,41,-34,-85,-78,-17,55,90,64,-7,-72,-89,-44,30,85,81,22,-52,-90,-66,2,69,90,48,-26,-82,}

[0458] {72,88,38,-41,-89,-69,2,72,87,37,-42,-89,-68,5,74,87,34,-44,-90,-66,7,73,86,32,-46,-89,-65,8,76,85,30,-48,-90,-64,11,77,84,29,-49,-90,-62,13,78,85,26,-52,-90,-60,15,79,83,23,-53,-90,-59,17,81,82,22,-55,-90,-58,20,80,}

[0459] {74,85,26,-55,-90,-49,32,87,69,-7,-77,-83,-20,60,90,44,-38,-89,-65,13,81,81,13,-65,-89,-38,44,90,60,-20,-83,-77,-7,69,87,32,-49,-90,-55,26,85,74,0,-74,-85,-26,55,90,49,-32,-87,-69,7,77,83,20,-60,-90,-44,38,89,65,-13,-81,}

[0460] {76,82,13,-68,-87,-26,59,89,38,-48,-90,-49,37,90,60,-23,-86,-69,11,80,77,2,-73,-83,-15,66,87,29,-58,-90,-41,46,90,52,-34,-89,-62,22,85,72,-8,-81,-78,-5,74,85,17,-65,-88,-30,55,90,42,-44,-90,-53,32,89,64,-20,-84,-72,7,79,}

[0461] {78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,}

[0462] {81,74,-13,-85,-65,26,89,55,-38,-90,-44,49,90,32,-60,-87,-20,69,83,7,-77,-77,7,83,69,-20,-87,-60,32,90,49,-44,-90,-38,55,89,26,-65,-85,-13,74,81,0,-81,-74,13,85,65,-26,-89,-55,38,90,44,-49,-90,-32,60,87,20,-69,-83,-7,77,}

[0463] {82,68,-26,-89,-48,49,90,23,-69,-80,2,83,66,-29,-90,-46,52,89,22,-72,-81,5,85,65,-30,-90,-44,53,89,20,-72,-79,7,84,64,-32,-90,-42,55,88,17,-74,-78,8,85,62,-34,-90,-41,58,87,15,-73,-77,11,86,60,-37,-90,-38,59,87,13,-76,}

[0464] {85,62,-38,-90,-29,69,79,-11,-87,-53,48,89,17,-76,-74,22,89,44,-58,-86,-7,80,66,-32,-90,-34,65,82,-5,-85,-59,42,90,23,-72,-77,15,89,49,-52,-88,-13,78,72,-26,-90,-41,60,84,2,-83,-64,37,90,30,-68,-81,8,87,55,-46,-90,-20,73,}

[0465] {85,55,-49,-87,-7,83,60,-44,-89,-13,81,65,-38,-90,-20,77,69,-32,-90,-26,74,74,-26,-90,-32,69,77,-20,-90,-38,65,81,-13,-89,-44,60,83,-7,-87,-49,55,85,0,-85,-55,49,87,7,-83,-60,44,89,13,-81,-65,38,90,20,-77,-69,32,90,26,-74,}

[0466] {87,48,-60,-80,15,90,34,-72,-74,30,90,20,-79,-64,44,88,5,-85,-52,58,83,-11,-90,-38,68,76,-26,-90,-23,77,66,-41,-89,-8,85,55,-53,-84,7,89,42,-65,-78,22,90,29,-73,-69,37,89,13,-82,-59,49,86,-2,-87,-46,62,81,-17,-90,-32,72,}

[0467] {88,41,-69,-72,37,89,5,-87,-44,66,73,-32,-89,-8,85,48,-64,-77,29,90,13,-85,-52,60,79,-23,-90,-17,82,55,-58,-80,20,90,22,-81,-59,53,83,-15,-90,-26,78,62,-49,-84,11,90,30,-76,-65,46,86,-7,-90,-34,74,68,-42,-87,2,89,38,-72,}

[0468] {89,32,-77,-60,55,81,-26,-90,-7,87,38,-74,-65,49,83,-20,-90,-13,85,44,-69,-69,44,85,-13,-90,-20,83,49,-65,-74,38,87,-7,-90,-26,81,55,-60,-77,32,89,0,-89,-32,77,60,-55,-81,26,90,7,-87,-38,74,65,-49,-83,20,90,13,-85,-44,69,}

[0469] {89,23,-83,-46,72,65,-53,-79,32,88,-8,-90,-15,86,38,-76,-59,60,73,-41,-85,17,90,7,-89,-30,81,52,-66,-69,48,82,-26,-90,2,90,22,-85,-44,72,64,-55,-78,34,87,-11,-90,-13,87,37,-77,-58,62,74,-42,-84,20,90,5,-89,-29,80,49,-68,}

[0470] {90,15,-87,-30,82,44,-73,-58,65,68,-53,-77,41,85,-26,-89,11,90,5,-89,-20,86,34,-81,-48,72,60,-62,-72,49,79,-37,-85,22,90,-7,-90,-8,89,23,-84,-38,78,52,-69,-64,59,74,-46,-80,32,87,-17,-90,2,90,13,-88,-29,83,42,-76,-55,66,}

[0471] {90,7,-90,-13,89,20,-87,-26,85,32,-83,-38,81,44,-77,-49,74,55,-69,-60,65,65,-60,-69,55,74,-49,-77,44,81,-38,-83,32,85,-26,-87,20,89,-13,-90,7,90,0,-90,-7,90,13,-89,-20,87,26,-85,-32,83,38,-81,-44,77,49,-74,-55,69,60,-65,}

[0472] {90,-2,-90,5,90,-7,-90,8,90,-11,-89,13,90,-15,-89,17,89,-20,-88,22,87,-23,-87,26,86,-29,-85,30,84,-32,-85,34,83,-37,-82,38,80,-41,-81,42,79,-44,-78,46,77,-48,-76,49,73,-52,-74,53,72,-55,-72,58,69,-59,-68,60,66,-62,-65,64,}

[0473] {90,-11,-89,22,86,-32,-82,42,77,-52,-72,60,64,-68,-55,73,46,-81,-37,84,26,-88,-15,90,5,-90,7,89,-17,-87,29,85,-38,-79,48,74,-58,-66,65,59,-72,-49,78,41,-83,-30,87,20,-90,-8,90,-2,-90,13,89,-23,-85,34,80,-44,-76,53,69,-62,}

[0474] {90,-20,-85,38,77,-55,-65,69,49,-81,-32,87,13,-90,7,89,-26,-83,44,74,-60,-60,74,44,-83,-26,89,7,-90,13,87,-32,-81,49,69,-65,-55,77,38,-85,-20,90,0,-90,20,85,-38,-77,55,65,-69,-49,81,32,-87,-13,90,-7,-89,26,83,-44,-74,60,}

[0475] {90,-29,-81,53,64,-74,-41,86,13,-90,15,85,-42,-72,65,52,-80,-26,89,-2,-89,30,79,-55,-62,73,38,-87,-11,90,-17,-84,44,72,-66,-49,82,23,-90,5,89,-32,-78,58,60,-76,-37,87,8,-90,20,85,-46,-69,68,48,-83,-22,90,-7,-88,34,77,-59,}

[0476] {89,-37,-74,66,46,-85,-11,90,-26,-79,59,55,-80,-22,90,-15,-85,49,64,-76,-32,90,-5,-87,41,72,-69,-42,87,7,-89,30,77,-62,-52,83,17,-90,20,82,-53,-60,78,29,-90,8,86,-44,-68,72,38,-88,-2,89,-34,-73,65,48,-84,-13,90,-23,-81,58,}

[0477] {87,-44,-65,77,26,-90,20,81,-60,-49,85,7,-89,38,69,-74,-32,90,-13,-83,55,55,-83,-13,90,-32,-74,69,38,-89,7,85,-49,-60,81,20,-90,26,77,-65,-44,87,0,-87,44,65,-77,-26,90,-20,-81,60,49,-85,-7,89,-38,-69,74,32,-90,13,83,-55,}

[0478] {86,-52,-55,84,5,-87,48,59,-83,-8,89,-44,-62,80,13,-90,41,65,-79,-17,90,-37,-68,77,22,-90,32,72,-73,-26,90,-29,-74,72,30,-90,23,76,-69,-34,90,-20,-78,66,38,-89,15,81,-64,-42,89,-11,-82,60,46,-88,7,85,-58,-49,87,-2,-85,53,}

[0479] {84,-59,-44,90,-17,-77,72,29,-90,34,66,-81,-11,88,-49,-53,87,-7,-82,64,38,-90,23,74,-73,-22,90,-41,-62,83,5,-86,55,48,-89,13,79,-68,-32,90,-30,-69,78,15,-89,46,58,-85,2,85,-60,-42,89,-20,-76,72,26,-90,37,65,-80,-8,87,-52,}

[0480] {83,-65,-32,90,-38,-60,85,-7,-81,69,26,-90,44,55,-87,13,77,-74,-20,89,-49,-49,89,-20,-74,77,13,-87,55,44,-90,26,69,-81,-7,85,-60,-38,90,-32,-65,83,0,-83,65,32,-90,38,60,-85,7,81,-69,-26,90,-44,-55,87,-13,-77,74,20,-89,49,}

[0481] {80,-72,-20,88,-58,-38,90,-41,-55,89,-22,-69,82,-2,-81,72,17,-87,59,37,-90,42,53,-89,23,68,-83,5,79,-74,-15,87,-60,-34,90,-44,-52,90,-26,-66,85,-7,-78,73,13,-86,62,32,-90,46,49,-89,29,65,-84,8,77,-76,-11,85,-64,-30,90,-48,}

[0482] {79,-76,-7,82,-72,-13,84,-68,-20,87,-64,-26,89,-59,-32,89,-53,-38,90,-48,-44,90,-42,-49,90,-37,-55,90,-30,-60,88,-23,-65,86,-17,-69,85,-11,-74,80,-5,-77,78,2,-81,73,8,-83,72,15,-85,66,22,-87,62,29,-89,58,34,-90,52,41,-90,46,}

[0483] {77,-81,7,74,-83,13,69,-85,20,65,-87,26,60,-89,32,55,-90,38,49,-90,44,44,-90,49,38,-90,55,32,-89,60,26,-87,65,20,-85,69,13,-83,74,7,-81,77,0,-77,81,-7,-74,83,-13,-69,85,-20,-65,87,-26,-60,89,-32,-55,90,-38,-49,90,-44,}

[0484] {73,-85,20,62,-90,38,46,-90,55,29,-87,69,8,-79,81,-11,-68,87,-30,-53,90,-48,-37,89,-64,-17,83,-76,2,74,-84,22,60,-89,41,44,-90,58,26,-86,72,7,-78,80,-13,-66,88,-32,-52,90,-49,-34,89,-65,-15,82,-77,5,72,-85,23,59,-90,42,}

[0485] {72,-87,32,48,-90,60,17,-80,81,-15,-62,90,-46,-34,87,-72,-2,74,-86,30,49,-90,59,20,-82,79,-13,-64,89,-44,-37,88,-69,-5,73,-85,29,52,-90,58,22,-83,78,-11,-65,90,-42,-38,89,-68,-7,76,-84,26,53,-90,55,23,-85,77,-8,-66,89,-41,}

[0486] {69,-89,44,32,-85,77,-13,-60,90,-55,-20,81,-83,26,49,-90,65,7,-74,87,-38,-38,87,-74,7,65,-90,49,26,-83,81,-20,-55,90,-60,-13,77,-85,32,44,-89,69,0,-69,89,-44,-32,85,-77,13,60,-90,55,20,-81,83,-26,-49,90,-65,-7,74,-87,38,}

[0487] {66,-90,55,15,-76,87,-42,-30,83,-82,29,44,-88,73,-13,-58,90,-65,-2,68,-90,53,17,-77,87,-41,-32,85,-80,26,46,-89,74,-11,-59,90,-64,-5,69,-89,52,20,-78,86,-38,-34,84,-81,23,48,-89,72,-8,-60,90,-62,-7,72,-90,49,22,-79,85,-37,}

[0488] {64,-90,65,-2,-62,90,-66,5,60,-90,68,-7,-59,90,-69,8,58,-90,72,-11,-55,89,-72,13,53,-90,74,-15,-52,89,-73,17,49,-89,76,-20,-48,88,-77,22,46,-87,78,-23,-44,87,-79,26,42,-86,81,-29,-41,85,-80,30,38,-84,82,-32,-37,85,-83,34,}

[0489] {60,-90,74,-20,-44,85,-83,38,26,-77,89,-55,-7,65,-90,69,-13,-49,87,-81,32,32,-81,87,-49,-13,69,-90,65,-7,-55,89,-77,26,38,-83,85,-44,-20,74,-90,60,0,-60,90,-74,20,44,-85,83,-38,-26,77,-89,55,7,-65,90,-69,13,49,-87,81,-32,}

[0490] {58,-89,81,-37,-23,74,-90,66,-13,-46,84,-85,48,11,-65,90,-73,26,34,-79,89,-59,2,55,-88,80,-38,-22,72,-90,68,-15,-44,85,-86,49,8,-64,90,-76,29,32,-78,90,-60,5,53,-87,82,-41,-20,72,-90,69,-17,-42,83,-87,52,7,-62,89,-77,30,}

[0491] {53,-86,85,-52,-2,55,-87,84,-49,-5,58,-87,85,-48,-7,59,-88,83,-46,-8,60,-89,82,-44,-11,62,-89,80,-42,-13,64,-90,81,-41,-15,65,-89,79,-38,-17,66,-90,78,-37,-20,68,-90,77,-34,-22,69,-90,76,-32,-23,72,-90,73,-30,-26,72,-90,74,-29,}

[0492] {49,-83,89,-65,20,32,-74,90,-77,38,13,-60,87,-85,55,-7,-44,81,-90,69,-26,-26,69,-90,81,-44,-7,55,-85,87,-60,13,38,-77,90,-74,32,20,-65,89,-83,49,0,-49,83,-89,65,-20,-32,74,-90,77,-38,-13,60,-87,85,-55,7,44,-81,90,-69,26,}

[0493] {46,-79,90,-76,41,7,-52,82,-90,72,-34,-13,58,-84,89,-68,29,20,-62,87,-87,64,-22,-26,66,-89,85,-59,15,32,-72,89,-83,53,-8,-38,73,-90,81,-48,2,44,-78,90,-77,42,5,-49,80,-90,74,-37,-11,55,-85,90,-69,30,17,-60,86,-88,65,-23,}

[0494] {42,-73,90,-85,59,-20,-23,62,-85,90,-72,38,5,-46,77,-90,82,-55,15,29,-65,87,-89,69,-34,-8,49,-79,90,-81,52,-11,-32,68,-88,87,-66,30,13,-53,80,-90,78,-48,7,37,-72,89,-86,64,-26,-17,58,-83,90,-76,44,-2,-41,74,-89,84,-60,22,}

[0495] {38,-69,87,-89,74,-44,7,32,-65,85,-90,77,-49,13,26,-60,83,-90,81,-55,20,20,-55,81,-90,83,-60,26,13,-49,77,-90,85,-65,32,7,-44,74,-89,87,-69,38,0,-38,69,-87,89,-74,44,-7,-32,65,-85,90,-77,49,-13,-26,60,-83,90,-81,55,-20,}

[0496] {34,-64,83,-90,85,-65,37,-2,-32,62,-82,90,-84,66,-38,5,30,-60,80,-90,85,-68,41,-7,-29,59,-81,90,-86,69,-42,8,26,-58,79,-90,87,-72,44,-11,-23,55,-78,89,-87,72,-46,13,22,-53,77,-90,88,-74,48,-15,-20,52,-76,89,-89,73,-49,17,}

[0497] {30,-58,77,-89,89,-81,62,-37,7,23,-52,74,-87,90,-83,66,-42,13,17,-46,69,-84,90,-85,72,-48,20,11,-41,65,-82,90,-87,73,-53,26,5,-34,60,-79,90,-89,78,-59,32,-2,-29,55,-76,88,-90,80,-64,38,-8,-22,49,-72,86,-90,85,-68,44,-15,}

[0498] {26,-49,69,-83,90,-89,81,-65,44,-20,-7,32,-55,74,-85,90,-87,77,-60,38,-13,-13,38,-60,77,-87,90,-85,74,-55,32,-7,-20,44,-65,81,-89,90,-83,69,-49,26,0,-26,49,-69,83,-90,89,-81,65,-44,20,7,-32,55,-74,85,-90,87,-77,60,-38,13,}

[0499] {22,-42,60,-73,84,-90,89,-85,74,-59,41,-20,-2,23,-44,62,-76,85,-90,90,-83,72,-58,38,-17,-5,26,-46,64,-77,86,-90,89,-82,72,-55,37,-15,-7,29,-48,65,-78,87,-90,89,-80,69,-53,34,-13,-8,30,-49,66,-79,87,-90,88,-81,68,-52,32,-11,}

[0500] {17,-34,49,-64,73,-83,89,-90,89,-85,76,-65,52,-37,20,-2,-15,32,-48,62,-74,82,-88,90,-90,84,-77,66,-53,38,-22,5,13,-30,46,-60,72,-80,87,-90,89,-85,78,-68,55,-41,23,-7,-11,29,-44,59,-72,81,-87,90,-90,86,-79,69,-58,42,-26,8,}

[0501] {13,-26,38,-49,60,-69,77,-83,87,-90,90,-89,85,-81,74,-65,55,-44,32,-20,7,7,-20,32,-44,55,-65,74,-81,85,-89,90,-90,87,-83,77,-69,60,-49,38,-26,13,0,-13,26,-38,49,-60,69,-77,83,-87,90,-90,89,-85,81,-74,65,-55,44,-32,20,-7,}

[0502] {8,-17,26,-34,42,-49,58,-64,69,-73,79,-83,86,-89,90,-90,90,-89,87,-85,81,-76,72,-65,59,-52,44,-37,29,-20,11,-2,-7,15,-23,32,-41,48,-55,62,-68,74,-78,82,-85,88,-89,90,-90,90,-87,84,-80,77,-72,66,-60,53,-46,38,-30,22,-13,5,}

[0503] {5,-8,13,-17,22,-26,30,-34,38,-42,46,-49,53,-58,60,-64,66,-69,72,-73,77,-79,80,-83,84,-86,87,-89,90,-90,90,-90,90,-90,89,-89,88,-87,85,-85,82,-81,78,-76,74,-72,68,-65,62,-59,55,-52,48,-44,41,-37,32,-29,23,-20,15,-11,7,-2,}

[0504] 4-point DCT-8:

[0505]

[0506] 8-point DCT-8:

[0507]

[0508] 16-point DCT-8:

[0509]

[0510]

[0511] 32-point DCT-8:

[0512] {90,90,89,88,88,86,85,84,82,80,78,77,74,72,68,66,63,60,56,53,50,45,42,38,34,30,26,21,17,13,9,4,}

[0513] {90,88,84,78,72,63,53,42,30,17,4,-9,-21,-34,-45,-56,-66,-74,-80,-85,-88,-90,-89,-86,-82,-77,-68,-60,-50,-38,-26,-13,}

[0514] {89,84,74,60,42,21,0,-21,-42,-60,-74,-84,-89,-89,-84,-74,-60,-42,-21,0,21,42,60,74,84,89,89,84,74,60,42,21,}

[0515] {88,78,60,34,4,-26,-53,-74,-86,-90,-82,-66,-42,-13,17,45,68,84,90,85,72,50,21,-9,-38,-63,-80,-89,-88,-77,-56,-30,}

[0516] {88,72,42,4,-34,-66,-85,-89,-77,-50,-13,26,60,82,90,80,56,21,-17,-53,-78,-90,-84,-63,-30,9,45,74,88,86,68,38,}

[0517] {86,63,21,-26,-66,-88,-85,-60,-17,30,68,88,84,56,13,-34,-72,-89,-82,-53,-9,38,74,90,80,50,4,-42,-77,-90,-78,-45,}

[0518] {85,53,0,-53,-85,-85,-53,0,53,85,85,53,0,-53,-85,-85,-53,0,53,85,85,53,0,-53,-85,-85,-53,0,53,85,85,53,}

[0519] {84,42,-21,-74,-89,-60,0,60,89,74,21,-42,-84,-84,-42,21,74,89,60,0,-60,-89,-74,-21,42,84,84,42,-21,-74,-89,-60,}

[0520] {82,30,-42,-86,-77,-17,53,89,68,4,-63,-90,-60,9,72,88,50,-21,-78,-85,-38,34,84,80,26,-45,-88,-74,-13,56,90,66,}

[0521] {80,17,-60,-90,-50,30,85,74,4,-68,-88,-38,42,88,66,-9,-77,-84,-26,53,90,56,-21,-82,-78,-13,63,89,45,-34,-86,-72,}

[0522] {78,4,-74,-82,-13,68,85,21,-63,-88,-30,56,89,38,-50,-90,-45,42,90,53,-34,-88,-60,26,86,66,-17,-84,-72,9,80,77,}

[0523] {77,-9,-84,-66,26,88,53,-42,-90,-38,56,88,21,-68,-82,-4,78,74,-13,-85,-63,30,89,50,-45,-90,-34,60,86,17,-72,-80,}

[0524] {74,-21,-89,-42,60,84,0,-84,-60,42,89,21,-74,-74,21,89,42,-60,-84,0,84,60,-42,-89,-21,74,74,-21,-89,-42,60,84,}

[0525] {72,-34,-89,-13,82,56,-53,-84,9,88,38,-68,-74,30,90,17,-80,-60,50,85,-4,-88,-42,66,77,-26,-90,-21,78,63,-45,-86,}

[0526] {68,-45,-84,17,90,13,-85,-42,72,66,-50,-82,21,90,9,-86,-38,74,63,-53,-80,26,89,4,-88,-34,77,60,-56,-78,30,88,}

[0527] {66,-56,-74,45,80,-34,-85,21,88,-9,-90,-4,89,17,-86,-30,82,42,-77,-53,68,63,-60,-72,50,78,-38,-84,26,88,-13,-90,}

[0528] {63,-66,-60,68,56,-72,-53,74,50,-77,-45,78,42,-80,-38,82,34,-84,-30,85,26,-86,-21,88,17,-88,-13,89,9,-90,-4,90,}

[0529] {60,-74,-42,84,21,-89,0,89,-21,-84,42,74,-60,-60,74,42,-84,-21,89,0,-89,21,84,-42,-74,60,60,-74,-42,84,21,-89,}

[0530] {56,-80,-21,90,-17,-82,53,60,-78,-26,90,-13,-84,50,63,-77,-30,89,-9,-85,45,66,-74,-34,88,-4,-86,42,68,-72,-38,88,}

[0531] {53,-85,0,85,-53,-53,85,0,-85,53,53,-85,0,85,-53,-53,85,0,-85,53,53,-85,0,85,-53,-53,85,0,-85,53,53,-85,}

[0532] {50,-88,21,72,-78,-9,85,-60,-38,90,-34,-63,84,-4,-80,68,26,-89,45,53,-88,17,74,-77,-13,86,-56,-42,90,-30,-66,82,}

[0533] {45,-90,42,50,-90,38,53,-89,34,56,-88,30,60,-88,26,63,-86,21,66,-85,17,68,-84,13,72,-82,9,74,-80,4,77,-78,}

[0534] {42,-89,60,21,-84,74,0,-74,84,-21,-60,89,-42,-42,89,-60,-21,84,-74,0,74,-84,21,60,-89,42,42,-89,60,21,-84,74,}

[0535] {38,-86,74,-9,-63,90,-53,-21,80,-82,26,50,-89,66,4,-72,88,-42,-34,85,-77,13,60,-90,56,17,-78,84,-30,-45,88,-68,}

[0536] {34,-82,84,-38,-30,80,-85,42,26,-78,86,-45,-21,77,-88,50,17,-74,88,-53,-13,72,-89,56,9,-68,90,-60,-4,66,-90,63,}

[0537] {30,-77,89,-63,9,50,-85,84,-45,-13,66,-90,74,-26,-34,78,-88,60,-4,-53,86,-82,42,17,-68,90,-72,21,38,-80,88,-56,}

[0538] {26,-68,89,-80,45,4,-53,84,-88,63,-17,-34,74,-90,77,-38,-13,60,-86,85,-56,9,42,-78,90,-72,30,21,-66,88,-82,50,}

[0539] {21,-60,84,-89,74,-42,0,42,-74,89,-84,60,-21,-21,60,-84,89,-74,42,0,-42,74,-89,84,-60,21,21,-60,84,-89,74,-42,}

[0540] {17,-50,74,-88,88,-77,53,-21,-13,45,-72,86,-89,78,-56,26,9,-42,68,-85,90,-80,60,-30,-4,38,-66,84,-90,82,-63,34,}

[0541] {13,-38,60,-77,86,-90,85,-74,56,-34,9,17,-42,63,-78,88,-90,84,-72,53,-30,4,21,-45,66,-80,88,-89,82,-68,50,-26,}

[0542] {9,-26,42,-56,68,-78,85,-89,90,-86,80,-72,60,-45,30,-13,-4,21,-38,53,-66,77,-84,88,-90,88,-82,74,-63,50,-34,17,}

[0543] {4,-13,21,-30,38,-45,53,-60,66,-72,77,-80,84,-86,88,-90,90,-89,88,-85,82,-78,74,-68,63,-56,50,-42,34,-26,17,-9,}

[0544] 64-point DCT-8:

[0545] {90,90,90,90,90,89,90,89,89,88,87,87,86,85,84,85,83,82,80,81,79,78,77,76,73,74,72,72,69,68,66,65,64,62,60,59,58,55,53,52,49,48,46,44,42,41,38,37,34,32,30,29,26,23,22,20,17,15,13,11,8,7,5,2,}

[0546] {90,90,89,87,85,83,81,77,74,69,65,60,55,49,44,38,32,26,20,13,7,0,-7,-13,-20,-26,-32,-38,-44,-49,-55,-60,-65,-69,-74,-77,-81,-83,-85,-87,-89,-90,-90,-90,-90,-89,-87,-85,-83,-81,-77,-74,-69,-65,-60,-55,-49,-44,-38,-32,-26,-20,-13,-7,}

[0547] {90,89,86,82,77,72,64,55,46,37,26,15,5,-7,-17,-29,-38,-48,-58,-65,-72,-78,-83,-87,-90,-90,-90,-89,-85,-80,-76,-69,-62,-53,-44,-34,-23,-13,-2,8,20,30,41,49,59,66,74,79,85,87,89,90,90,88,84,81,73,68,60,52,42,32,22,11,}

[0548] {90,87,82,73,65,53,41,26,11,-5,-20,-34,-48,-60,-72,-79,-85,-90,-90,-89,-84,-78,-69,-59,-46,-32,-17,-2,13,29,42,55,66,76,83,88,90,90,87,80,74,64,52,38,23,8,-7,-22,-37,-49,-62,-72,-81,-86,-89,-90,-89,-85,-77,-68,-58,-44,-30,-15,}

[0549] {90,85,77,65,49,32,13,-7,-26,-44,-60,-74,-83,-89,-90,-87,-81,-69,-55,-38,-20,0,20,38,55,69,81,87,90,89,83,74,60,44,26,7,-13,-32,-49,-65,-77,-85,-90,-90,-85,-77,-65,-49,-32,-13,7,26,44,60,74,83,89,90,87,81,69,55,38,20,}

[0550] {89,83,72,53,32,8,-15,-38,-59,-73,-85,-90,-89,-81,-66,-48,-26,-2,22,44,64,78,87,90,87,77,62,42,20,-5,-29,-49,-68,-80,-89,-90,-84,-74,-58,-37,-13,11,34,55,72,85,90,90,82,69,52,30,7,-17,-41,-60,-76,-86,-90,-88,-79,-65,-46,-23,}

[0551] {90,81,64,41,13,-15,-42,-65,-80,-89,-89,-79,-62,-38,-11,17,44,66,82,90,89,78,60,37,8,-20,-46,-68,-83,-90,-88,-77,-59,-34,-7,22,48,69,85,90,87,76,58,32,5,-23,-49,-72,-84,-90,-87,-73,-55,-30,-2,26,52,72,85,90,86,74,53,29,}

[0552] {89,77,55,26,-7,-38,-65,-83,-90,-85,-69,-44,-13,20,49,74,87,90,81,60,32,0,-32,-60,-81,-90,-87,-74,-49,-20,13,44,69,85,90,83,65,38,7,-26,-55,-77,-89,-89,-77,-55,-26,7,38,65,83,90,85,69,44,13,-20,-49,-74,-87,-90,-81,-60,-32,}

[0553] {89,74,46,11,-26,-59,-80,-90,-85,-64,-32,5,41,69,87,89,77,52,17,-20,-53,-78,-90,-86,-68,-38,-2,34,65,84,90,81,58,23,-13,-48,-73,-89,-88,-72,-44,-8,29,60,82,90,83,62,30,-7,-42,-72,-87,-90,-76,-49,-15,22,55,79,90,85,66,37,}

[0554] {88,69,37,-5,-44,-73,-89,-85,-64,-29,13,52,79,90,82,58,20,-22,-59,-83,-90,-78,-49,-11,30,65,86,90,74,42,2,-38,-72,-89,-87,-68,-34,7,46,76,90,84,62,26,-15,-53,-81,-90,-80,-55,-17,23,60,85,90,77,48,8,-32,-66,-87,-89,-72,-41,}

[0555] {87,65,26,-20,-60,-85,-89,-69,-32,13,55,83,90,74,38,-7,-49,-81,-90,-77,-44,0,44,77,90,81,49,7,-38,-74,-90,-83,-55,-13,32,69,89,85,60,20,-26,-65,-87,-87,-65,-26,20,60,85,89,69,32,-13,-55,-83,-90,-74,-38,7,49,81,90,77,44,}

[0556] {87,60,15,-34,-74,-90,-79,-44,5,52,83,90,68,26,-23,-66,-89,-85,-53,-7,42,78,90,73,37,-13,-59,-86,-87,-62,-17,32,72,90,81,46,-2,-49,-82,-89,-69,-29,22,65,89,84,55,8,-41,-77,-90,-76,-38,11,58,85,88,64,20,-30,-72,-90,-80,-48,}

[0557] {86,55,5,-48,-83,-89,-62,-13,41,79,90,68,22,-32,-73,-90,-74,-30,23,69,90,78,38,-15,-64,-89,-82,-46,7,58,87,85,53,2,-49,-85,-88,-60,-11,42,81,89,66,20,-34,-76,-90,-72,-29,26,72,90,77,37,-17,-65,-90,-80,-44,8,59,87,84,52,}

[0558] {85,49,-7,-60,-89,-81,-38,20,69,90,74,26,-32,-77,-90,-65,-13,44,83,87,55,0,-55,-87,-83,-44,13,65,90,77,32,-26,-74,-90,-69,-20,38,81,89,60,7,-49,-85,-85,-49,7,60,89,81,38,-20,-69,-90,-74,-26,32,77,90,65,13,-44,-83,-87,-55,}

[0559] {84,44,-17,-72,-90,-66,-11,49,87,82,38,-23,-73,-90,-62,-5,55,89,79,32,-30,-78,-89,-58,2,60,89,76,26,-37,-80,-87,-52,8,65,90,72,20,-42,-85,-85,-46,15,69,90,68,13,-48,-86,-83,-41,22,74,90,64,7,-53,-88,-81,-34,29,77,90,59,}

[0560] {85,38,-29,-79,-87,-48,17,74,89,58,-7,-66,-90,-65,-5,59,90,72,15,-49,-88,-78,-26,41,84,83,37,-30,-81,-87,-46,20,73,90,55,-8,-68,-90,-64,-2,60,90,72,13,-52,-89,-77,-23,42,85,82,34,-32,-80,-86,-44,22,76,89,53,-11,-69,-90,-62,}

[0561] {83,32,-38,-85,-81,-26,44,87,77,20,-49,-89,-74,-13,55,90,69,7,-60,-90,-65,0,65,90,60,-7,-69,-90,-55,13,74,89,49,-20,-77,-87,-44,26,81,85,38,-32,-83,-83,-32,38,85,81,26,-44,-87,-77,-20,49,89,74,13,-55,-90,-69,-7,60,90,65,}

[0562] {82,26,-48,-90,-69,-2,66,90,52,-22,-81,-85,-30,44,89,72,7,-64,-90,-55,17,78,85,34,-41,-87,-73,-11,60,90,59,-13,-76,-87,-38,37,86,77,15,-58,-90,-62,8,74,88,42,-32,-84,-79,-20,53,90,65,-5,-72,-89,-46,29,83,80,23,-49,-89,-68,}

[0563] {80,20,-58,-90,-55,22,82,81,17,-59,-90,-53,23,83,79,15,-60,-90,-52,26,85,78,13,-62,-90,-49,29,84,77,11,-64,-90,-48,30,85,76,8,-65,-89,-46,32,86,73,7,-66,-90,-44,34,87,74,5,-68,-89,-42,37,87,72,2,-69,-89,-41,38,88,72,}

[0564] {81,13,-65,-89,-38,44,90,60,-20,-83,-77,-7,69,87,32,-49,-90,-55,26,85,74,0,-74,-85,-26,55,90,49,-32,-87,-69,7,77,83,20,-60,-90,-44,38,89,65,-13,-81,-81,-13,65,89,38,-44,-90,-60,20,83,77,7,-69,-87,-32,49,90,55,-26,-85,-74,}

[0565] {79,7,-72,-84,-20,64,89,32,-53,-90,-44,42,90,55,-30,-88,-65,17,85,74,-5,-78,-81,-8,72,85,22,-62,-89,-34,52,90,46,-41,-90,-58,29,87,66,-15,-83,-73,2,77,80,11,-69,-86,-23,60,90,37,-49,-90,-48,38,89,59,-26,-87,-68,13,82,76,}

[0566] {78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,0,78,78,0,-78,-78,}

[0567] {77,-7,-83,-69,20,87,60,-32,-90,-49,44,90,38,-55,-89,-26,65,85,13,-74,-81,0,81,74,-13,-85,-65,26,89,55,-38,-90,-44,49,90,32,-60,-87,-20,69,83,7,-77,-77,7,83,69,-20,-87,-60,32,90,49,-44,-90,-38,55,89,26,-65,-85,-13,74,81,}

[0568] {76,-13,-87,-59,38,90,37,-60,-86,-11,77,73,-15,-87,-58,41,90,34,-62,-85,-8,78,74,-17,-88,-55,42,90,32,-64,-84,-7,79,72,-20,-89,-53,44,90,30,-65,-85,-5,81,72,-22,-89,-52,46,90,29,-66,-83,-2,80,69,-23,-90,-49,48,89,26,-68,-82,}

[0569] {73,-20,-90,-46,55,87,8,-81,-68,30,90,37,-64,-83,2,84,60,-41,-90,-26,72,78,-13,-88,-52,49,89,15,-77,-72,23,90,42,-59,-85,-5,82,65,-34,-90,-32,66,80,-7,-86,-58,44,89,22,-74,-76,17,89,48,-53,-87,-11,79,69,-29,-90,-38,62,85,}

[0570] {74,-26,-90,-32,69,77,-20,-90,-38,65,81,-13,-89,-44,60,83,-7,-87,-49,55,85,0,-85,-55,49,87,7,-83,-60,44,89,13,-81,-65,38,90,20,-77,-69,32,90,26,-74,-74,26,90,32,-69,-77,20,90,38,-65,-81,13,89,44,-60,-83,7,87,49,-55,-85,}

[0571] {72,-32,-90,-17,81,62,-46,-87,-2,86,49,-59,-82,13,89,37,-69,-73,29,90,22,-78,-65,42,89,7,-84,-53,55,85,-8,-89,-41,66,77,-23,-90,-26,76,68,-38,-90,-11,83,58,-52,-85,5,88,44,-64,-79,20,90,30,-74,-72,34,90,15,-80,-60,48,87,}

[0572] {72,-38,-89,-2,87,42,-68,-74,34,90,7,-86,-46,65,76,-30,-90,-11,84,49,-62,-78,26,90,15,-83,-53,59,81,-22,-90,-20,80,58,-55,-82,17,90,23,-79,-60,52,85,-13,-90,-29,77,64,-48,-85,8,89,32,-73,-66,44,87,-5,-89,-37,72,69,-41,-88,}

[0573] {69,-44,-85,13,90,20,-83,-49,65,74,-38,-87,7,90,26,-81,-55,60,77,-32,-89,0,89,32,-77,-60,55,81,-26,-90,-7,87,38,-74,-65,49,83,-20,-90,-13,85,44,-69,-69,44,85,-13,-90,-20,83,49,-65,-74,38,87,-7,-90,-26,81,55,-60,-77,32,89,}

[0574] {68,-49,-80,29,89,-5,-90,-20,84,42,-74,-62,58,77,-37,-87,13,90,11,-87,-34,78,55,-64,-72,44,85,-22,-90,-2,90,26,-82,-48,69,66,-52,-81,30,89,-7,-90,-17,85,41,-73,-60,59,76,-38,-86,15,90,8,-88,-32,79,53,-65,-72,46,83,-23,-89,}

[0575] {66,-55,-76,42,83,-29,-88,13,90,2,-90,-17,87,32,-80,-46,74,59,-64,-69,52,78,-38,-84,23,89,-8,-90,-7,90,22,-85,-37,79,49,-72,-62,60,72,-48,-81,34,86,-20,-89,5,90,11,-89,-26,85,41,-77,-53,68,65,-58,-73,44,82,-30,-87,15,90,}

[0576] {65,-60,-69,55,74,-49,-77,44,81,-38,-83,32,85,-26,-87,20,89,-13,-90,7,90,0,-90,-7,90,13,-89,-20,87,26,-85,-32,83,38,-81,-44,77,49,-74,-55,69,60,-65,-65,60,69,-55,-74,49,77,-44,-81,38,83,-32,-85,26,87,-20,-89,13,90,-7,-90,}

[0577] {64,-65,-62,66,60,-68,-59,69,58,-72,-55,72,53,-74,-52,73,49,-76,-48,77,46,-78,-44,79,42,-81,-41,80,38,-82,-37,83,34,-85,-32,84,30,-85,-29,86,26,-87,-23,87,22,-88,-20,89,17,-89,-15,90,13,-89,-11,90,8,-90,-7,90,5,-90,-2,90,}

[0578] {62,-69,-53,76,44,-80,-34,85,23,-89,-13,90,2,-90,8,90,-20,-87,30,83,-41,-78,49,72,-59,-65,66,58,-74,-48,79,38,-85,-29,87,17,-89,-7,90,-5,-90,15,88,-26,-84,37,81,-46,-73,55,68,-64,-60,72,52,-77,-42,82,32,-86,-22,89,11,-90,}

[0579] {60,-74,-44,83,26,-89,-7,90,-13,-87,32,81,-49,-69,65,55,-77,-38,85,20,-90,0,90,-20,-85,38,77,-55,-65,69,49,-81,-32,87,13,-90,7,89,-26,-83,44,74,-60,-60,74,44,-83,-26,89,7,-90,13,87,-32,-81,49,69,-65,-55,77,38,-85,-20,90,}

[0580] {59,-77,-34,88,7,-90,22,83,-48,-68,69,46,-85,-20,90,-8,-87,37,76,-60,-58,78,32,-89,-5,90,-23,-82,49,66,-72,-44,84,17,-90,11,87,-38,-73,62,55,-79,-30,89,2,-89,26,80,-52,-65,72,42,-85,-15,90,-13,-86,41,74,-64,-53,81,29,-90,}

[0581] {58,-81,-23,90,-13,-84,48,65,-73,-34,89,-2,-88,38,72,-68,-44,86,8,-90,29,78,-60,-53,82,20,-90,17,83,-52,-62,77,30,-89,7,87,-42,-69,72,41,-87,-5,90,-32,-76,64,49,-85,-15,90,-22,-80,55,59,-79,-26,90,-11,-85,46,66,-74,-37,89,}

[0582] {55,-83,-13,90,-32,-74,69,38,-89,7,85,-49,-60,81,20,-90,26,77,-65,-44,87,0,-87,44,65,-77,-26,90,-20,-81,60,49,-85,-7,89,-38,-69,74,32,-90,13,83,-55,-55,83,13,-90,32,74,-69,-38,89,-7,-85,49,60,-81,-20,90,-26,-77,65,44,-87,}

[0583] {53,-85,-2,87,-49,-58,85,7,-88,46,60,-82,-11,89,-42,-64,81,15,-89,38,66,-78,-20,90,-34,-69,76,23,-90,30,72,-74,-29,90,-26,-73,72,32,-90,22,77,-68,-37,90,-17,-79,65,41,-90,13,80,-62,-44,89,-8,-83,59,48,-87,5,84,-55,-52,86,}

[0584] {52,-87,8,80,-65,-37,90,-26,-72,76,20,-89,42,60,-85,-2,85,-58,-46,89,-15,-78,69,30,-90,32,68,-79,-13,89,-48,-55,86,-5,-83,62,41,-90,22,73,-74,-23,90,-38,-64,82,7,-87,53,49,-88,11,81,-66,-34,90,-29,-72,77,17,-90,44,59,-84,}

[0585] {49,-89,20,74,-77,-13,87,-55,-44,90,-26,-69,81,7,-85,60,38,-90,32,65,-83,0,83,-65,-32,90,-38,-60,85,-7,-81,69,26,-90,44,55,-87,13,77,-74,-20,89,-49,-49,89,-20,-74,77,13,-87,55,44,-90,26,69,-81,-7,85,-60,-38,90,-32,-65,83,}

[0586] {48,-90,30,64,-85,11,76,-77,-8,84,-65,-29,89,-49,-46,90,-32,-62,86,-13,-73,78,7,-85,66,26,-90,52,44,-90,34,60,-87,15,74,-79,-5,83,-68,-23,89,-53,-42,90,-37,-59,87,-17,-72,81,2,-82,69,22,-89,55,41,-90,38,58,-88,20,72,-80,}

[0587] {46,-90,41,52,-90,34,58,-89,29,62,-87,22,66,-85,15,72,-83,8,73,-81,2,78,-77,-5,80,-74,-11,85,-69,-17,86,-65,-23,88,-60,-30,90,-55,-37,90,-49,-42,90,-44,-48,90,-38,-53,89,-32,-59,89,-26,-64,87,-20,-68,84,-13,-72,82,-7,-76,79,}

[0588] {44,-90,49,38,-90,55,32,-89,60,26,-87,65,20,-85,69,13,-83,74,7,-81,77,0,-77,81,-7,-74,83,-13,-69,85,-20,-65,87,-26,-60,89,-32,-55,90,-38,-49,90,-44,-44,90,-49,-38,90,-55,-32,89,-60,-26,87,-65,-20,85,-69,-13,83,-74,-7,81,-77,}

[0589] {42,-90,59,23,-85,72,5,-77,82,-15,-65,89,-34,-49,90,-52,-32,88,-66,-13,80,-78,7,72,-86,26,58,-90,44,41,-89,60,22,-84,74,2,-76,83,-17,-64,89,-37,-48,90,-53,-30,87,-68,-11,81,-79,8,69,-87,29,55,-90,46,38,-90,62,20,-85,73,}

[0590] {41,-89,66,8,-77,85,-23,-55,90,-53,-26,84,-76,7,68,-89,38,42,-90,65,11,-78,83,-22,-58,90,-52,-29,85,-73,5,69,-88,37,44,-89,64,13,-79,82,-20,-59,90,-49,-30,86,-74,2,72,-87,34,46,-90,62,15,-81,80,-17,-60,90,-48,-32,87,-72,}

[0591] {38,-87,74,-7,-65,90,-49,-26,83,-81,20,55,-90,60,13,-77,85,-32,-44,89,-69,0,69,-89,44,32,-85,77,-13,-60,90,-55,-20,81,-83,26,49,-90,65,7,-74,87,-38,-38,87,-74,7,65,-90,49,26,-83,81,-20,-55,90,-60,-13,77,-85,32,44,-89,69,}

[0592] {37,-85,79,-22,-49,90,-72,7,62,-90,60,8,-72,89,-48,-23,81,-84,34,38,-86,78,-20,-52,89,-69,5,64,-90,59,11,-74,89,-46,-26,80,-85,32,41,-87,77,-17,-53,90,-68,2,65,-90,58,13,-73,88,-44,-29,82,-83,30,42,-87,76,-15,-55,90,-66,}

[0593] {34,-83,85,-37,-32,82,-84,38,30,-80,85,-41,-29,81,-86,42,26,-79,87,-44,-23,78,-87,46,22,-77,88,-48,-20,76,-89,49,17,-73,89,-52,-15,74,-90,53,13,-72,89,-55,-11,72,-90,58,8,-69,90,-59,-7,68,-90,60,5,-66,90,-62,-2,65,-90,64,}

[0594] {32,-81,87,-49,-13,69,-90,65,-7,-55,89,-77,26,38,-83,85,-44,-20,74,-90,60,0,-60,90,-74,20,44,-85,83,-38,-26,77,-89,55,7,-65,90,-69,13,49,-87,81,-32,-32,81,-87,49,13,-69,90,-65,7,55,-89,77,-26,-38,83,-85,44,20,-74,90,-60,}

[0595] {30,-77,89,-62,7,52,-87,83,-42,-17,69,-90,72,-20,-41,82,-87,53,5,-60,90,-78,32,29,-76,90,-64,8,49,-86,85,-44,-15,68,-90,72,-22,-38,80,-88,55,2,-59,89,-79,34,26,-73,90,-65,11,48,-85,84,-46,-13,66,-90,74,-23,-37,81,-89,58,}

[0596] {29,-74,90,-72,26,30,-73,90,-72,23,32,-76,90,-69,22,34,-77,90,-68,20,37,-78,90,-66,17,38,-79,89,-65,15,41,-81,90,-64,13,42,-80,89,-62,11,44,-82,89,-60,8,46,-83,88,-59,7,48,-85,87,-58,5,49,-84,87,-55,2,52,-85,86,-53,}

[0597] {26,-69,90,-81,44,7,-55,85,-87,60,-13,-38,77,-90,74,-32,-20,65,-89,83,-49,0,49,-83,89,-65,20,32,-74,90,-77,38,13,-60,87,-85,55,-7,-44,81,-90,69,-26,-26,69,-90,81,-44,-7,55,-85,87,-60,13,38,-77,90,-74,32,20,-65,89,-83,49,}

[0598] {23,-65,88,-86,60,-17,-30,69,-90,85,-55,11,37,-74,90,-80,49,-5,-42,77,-90,78,-44,-2,48,-81,90,-73,38,8,-53,83,-89,72,-32,-15,59,-85,89,-66,26,22,-64,87,-87,62,-20,-29,68,-89,84,-58,13,34,-72,90,-82,52,-7,-41,76,-90,79,-46,}

[0599] {22,-60,84,-89,74,-41,-2,44,-76,90,-83,58,-17,-26,64,-86,89,-72,37,7,-48,78,-90,80,-53,13,30,-66,87,-88,68,-32,-11,52,-81,90,-79,49,-8,-34,69,-89,87,-65,29,15,-55,82,-90,77,-46,5,38,-72,90,-85,62,-23,-20,59,-85,90,-73,42,}

[0600] {20,-55,81,-90,83,-60,26,13,-49,77,-90,85,-65,32,7,-44,74,-89,87,-69,38,0,-38,69,-87,89,-74,44,-7,-32,65,-85,90,-77,49,-13,-26,60,-83,90,-81,55,-20,-20,55,-81,90,-83,60,-26,-13,49,-77,90,-85,65,-32,-7,44,-74,89,-87,69,-38,}

[0601] {17,-49,73,-89,89,-76,52,-20,-15,48,-74,88,-90,77,-53,22,13,-46,72,-87,89,-78,55,-23,-11,44,-72,87,-90,79,-58,26,8,-42,69,-86,90,-81,59,-29,-7,41,-68,85,-90,80,-60,30,5,-38,66,-84,90,-82,62,-32,-2,37,-65,85,-90,83,-64,34,}

[0602] {15,-44,68,-85,90,-86,72,-49,22,8,-38,64,-80,90,-88,76,-55,29,2,-32,59,-78,89,-90,79,-60,34,-5,-26,53,-73,87,-90,82,-65,41,-11,-20,48,-72,85,-90,84,-69,46,-17,-13,42,-66,83,-90,87,-74,52,-23,-7,37,-62,81,-89,89,-77,58,-30,}

[0603] {13,-38,60,-77,87,-90,85,-74,55,-32,7,20,-44,65,-81,89,-90,83,-69,49,-26,0,26,-49,69,-83,90,-89,81,-65,44,-20,-7,32,-55,74,-85,90,-87,77,-60,38,-13,-13,38,-60,77,-87,90,-85,74,-55,32,-7,-20,44,-65,81,-89,90,-83,69,-49,26,}

[0604] {11,-32,52,-68,81,-88,90,-87,79,-66,49,-30,8,13,-34,53,-69,80,-89,90,-87,78,-65,48,-29,7,15,-37,55,-72,82,-89,90,-86,77,-64,46,-26,5,17,-38,58,-72,83,-90,90,-85,76,-62,44,-23,2,20,-41,59,-74,85,-89,90,-84,73,-60,42,-22,}

[0605] {8,-26,42,-58,69,-79,86,-90,90,-87,81,-72,59,-44,29,-11,-7,23,-41,55,-68,78,-85,89,-90,87,-80,72,-60,46,-30,13,5,-22,38,-53,66,-77,84,-90,90,-88,82,-74,62,-48,32,-15,-2,20,-37,52,-65,76,-85,89,-90,89,-83,73,-64,49,-34,17,}

[0606] {7,-20,32,-44,55,-65,74,-81,85,-89,90,-90,87,-83,77,-69,60,-49,38,-26,13,0,-13,26,-38,49,-60,69,-77,83,-87,90,-90,89,-85,81,-74,65,-55,44,-32,20,-7,-7,20,-32,44,-55,65,-74,81,-85,89,-90,90,-87,83,-77,69,-60,49,-38,26,-13,}

[0607] {5,-13,22,-30,38,-46,53,-60,66,-72,77,-80,84,-87,90,-90,90,-89,88,-85,82,-78,74,-68,62,-55,48,-41,32,-23,15,-7,-2,11,-20,29,-37,44,-52,59,-65,72,-76,81,-85,87,-89,90,-90,90,-89,86,-83,79,-73,69,-64,58,-49,42,-34,26,-17,8,}

[0608] {2,-7,11,-15,20,-23,29,-32,37,-41,44,-48,52,-55,59,-62,65,-68,72,-74,76,-78,81,-82,85,-85,87,-88,89,-89,90,-90,90,-90,90,-90,89,-87,86,-84,83,-80,79,-77,73,-72,69,-66,64,-60,58,-53,49,-46,42,-38,34,-30,26,-22,17,-13,8,-5,}

[0609] After minimizing the cost by trying all possible combinations of offset values ​​for a selected set of M unique numbers, T2 can be output as the B-bit N-point master transform core.

[0610] When deriving the 2N-point DST-1 transform core, the set of M unique numbers for constructing the 2N-point DST-1 core matrix is ​​restricted to be the same as the set of M unique numbers for constructing the N-point DST-7 and / or N-point DCT-8 core matrices. In one embodiment, M equals N. In one embodiment, one of the 8-bit DST-1 transform cores shown below can be used. For example, in 8-point DST-1, there are four unique numbers including 28, 55, 74, and 84, and this is the same set of four unique numbers used to construct the 4-point DST-7 and 4-point DCT-8 cores using the embodiment where M equals N discussed above.

[0611] An 8-bit DST-1 transform core may include:

[0612] 4 points DST-l:

[0613]

[0614] 8 o'clock DST-l:

[0615]

[0616]

[0617] 16:00 DST-l:

[0618]

[0619] 32 DST-l:

[0620] {9,17,25,33,41,49,56,62,66,72,77,81,83,87,89,90,90,89,87,83,81,77,72,66,62,56,49,41,33,25,17,9,}

[0621] {17,33,49,62,72,81,87,90,89,83,77,66,56,41,25,9,-9,-25,-41,-56,-66,-77,-83,-89,-90,-87,-81,-72,-62,-49,-33,-17,}

[0622] {25,49,66,81,89,89,81,66,49,25,0,-25,-49,-66,-81,-89,-89,-81,-66,-49,-25,0,25,49,66,81,89,89,81,66,49,25,}

[0623] {33,62,81,90,83,66,41,9,-25,-56,-77,-89,-87,-72,-49,-17,17,49,72,87,89,77,56,25,-9,-41,-66,-83,-90,-81,-62,-33,}

[0624] {41,72,89,83,62,25,-17,-56,-81,-90,-77,-49,-9,33,66,87,87,66,33,-9,-49,-77,-90,-81,-56,-17,25,62,83,89,72,41,}

[0625] {49,81,89,66,25,-25,-66,-89,-81,-49,0,49,81,89,66,25,-25,-66,-89,-81,-49,0,49,81,89,66,25,-25,-66,-89,-81,-49,}

[0626] {56,87,81,41,-17,-66,-90,-72,-25,33,77,89,62,9,-49,-83,-83,-49,9,62,89,77,33,-25,-72,-90,-66,-17,41,81,87,56,}

[0627] {62,90,66,9,-56,-89,-72,-17,49,87,77,25,-41,-83,-81,-33,33,81,83,41,-25,-77,-87,-49,17,72,89,56,-9,-66,-90,-62,}

[0628] {66,89,49,-25,-81,-81,-25,49,89,66,0,-66,-89,-49,25,81,81,25,-49,-89,-66,0,66,89,49,-25,-81,-81,-25,49,89,66,}

[0629] {72,83,25,-56,-90,-49,33,87,66,-9,-77,-81,-17,62,89,41,-41,-89,-62,17,81,77,9,-66,-87,-33,49,90,56,-25,-83,-72,}

[0630] {77,77,0,-77,-77,0,77,77,0,-77,-77,0,77,77,0,-77,-77,0,77,77,0,-77,-77,0,77,77,0,-77,-77,0,77,77,}

[0631] {81,66,-25,-89,-49,49,89,25,-66,-81,0,81,66,-25,-89,-49,49,89,25,-66,-81,0,81,66,-25,-89,-49,49,89,25,-66,-81,}

[0632] {83,56,-49,-87,-9,81,62,-41,-89,-17,77,66,-33,-90,-25,72,72,-25,-90,-33,66,77,-17,-89,-41,62,81,-9,-87,-49,56,83,}

[0633] {87,41,-66,-72,33,89,9,-83,-49,62,77,-25,-90,-17,81,56,-56,-81,17,90,25,-77,-62,49,83,-9,-89,-33,72,66,-41,-87,}

[0634] {89,25,-81,-49,66,66,-49,-81,25,89,0,-89,-25,81,49,-66,-66,49,81,-25,-89,0,89,25,-81,-49,66,66,-49,-81,25,89,}

[0635] {90,9,-89,-17,87,25,-83,-33,81,41,-77,-49,72,56,-66,-62,62,66,-56,-72,49,77,-41,-81,33,83,-25,-87,17,89,-9,-90,}

[0636] {90,-9,-89,17,87,-25,-83,33,81,-41,-77,49,72,-56,-66,62,62,-66,-56,72,49,-77,-41,81,33,-83,-25,87,17,-89,-9,90,}

[0637] {89,-25,-81,49,66,-66,-49,81,25,-89,0,89,-25,-81,49,66,-66,-49,81,25,-89,0,89,-25,-81,49,66,-66,-49,81,25,-89,}

[0638] {87,-41,-66,72,33,-89,9,83,-49,-62,77,25,-90,17,81,-56,-56,81,17,-90,25,77,-62,-49,83,9,-89,33,72,-66,-41,87,}

[0639] {83,-56,-49,87,-9,-81,62,41,-89,17,77,-66,-33,90,-25,-72,72,25,-90,33,66,-77,-17,89,-41,-62,81,9,-87,49,56,-83,}

[0640] {81,-66,-25,89,-49,-49,89,-25,-66,81,0,-81,66,25,-89,49,49,-89,25,66,-81,0,81,-66,-25,89,-49,-49,89,-25,-66,81,}

[0641] {77,-77,0,77,-77,0,77,-77,0,77,-77,0,77,-77,0,77,-77,0,77,-77,0,77,-77,0,77,-77,0,77,-77,0,77,-77,}

[0642] {72,-83,25,56,-90,49,33,-87,66,9,-77,81,-17,-62,89,-41,-41,89,-62,-17,81,-77,9,66,-87,33,49,-90,56,25,-83,72,}

[0643] {66,-89,49,25,-81,81,-25,-49,89,-66,0,66,-89,49,25,-81,81,-25,-49,89,-66,0,66,-89,49,25,-81,81,-25,-49,89,-66,}

[0644] {62,-90,66,-9,-56,89,-72,17,49,-87,77,-25,-41,83,-81,33,33,-81,83,-41,-25,77,-87,49,17,-72,89,-56,-9,66,-90,62,}

[0645] {56,-87,81,-41,-17,66,-90,72,-25,-33,77,-89,62,-9,-49,83,-83,49,9,-62,89,-77,33,25,-72,90,-66,17,41,-81,87,-56,}

[0646] {49,-81,89,-66,25,25,-66,89,-81,49,0,-49,81,-89,66,-25,-25,66,-89,81,-49,0,49,-81,89,-66,25,25,-66,89,-81,49,}

[0647] {41,-72,89,-83,62,-25,-17,56,-81,90,-77,49,-9,-33,66,-87,87,-66,33,9,-49,77,-90,81,-56,17,25,-62,83,-89,72,-41,}

[0648] {33,-62,81,-90,83,-66,41,-9,-25,56,-77,89,-87,72,-49,17,17,-49,72,-87,89,-77,56,-25,-9,41,-66,83,-90,81,-62,33,}

[0649] {25,-49,66,-81,89,-89,81,-66,49,-25,0,25,-49,66,-81,89,-89,81,-66,49,-25,0,25,-49,66,-81,89,-89,81,-66,49,-25,}

[0650] {17,-33,49,-62,72,-81,87,-90,89,-83,77,-66,56,-41,25,-9,-9,25,-41,56,-66,77,-83,89,-90,87,-81,72,-62,49,-33,17,}

[0651] {9,-17,25,-33,41,-49,56,-62,66,-72,77,-81,83,-87,89,-90,90,-89,87,-83,81,-77,72,-66,62,-56,49,-41,33,-25,17,-9,}

[0652] 64 points DST-l:

[0653] {4,9,13,17,21,26,30,34,38,42,45,50,53,56,60,63,66,68,72,74,77,78,80,82,84,85,86,88,88,89,90,90,90,90,89,88,88,86,85,84,82,80,78,77,74,72,68,66,63,60,56,53,50,45,42,38,34,30,26,21,17,13,9,4,}

[0654] {9,17,26,34,42,50,56,63,68,74,78,82,85,88,89,90,90,88,86,84,80,77,72,66,60,53,45,38,30,21,13,4,-4,-13,-21,-30,-38,-45,-53,-60,-66,-72,-77,-80,-84,-86,-88,-90,-90,-89,-88,-85,-82,-78,-74,-68,-63,-56,-50,-42,-34,-26,-17,-9,}

[0655] {13,26,38,50,60,68,77,82,86,89,90,88,85,80,74,66,56,45,34,21,9,-4,-17,-30,-42,-53,-63,-72,-78,-84,-88,-90,-90,-88,-84,-78,-72,-63,-53,-42,-30,-17,-4,9,21,34,45,56,66,74,80,85,88,90,89,86,82,77,68,60,50,38,26,13,}

[0656] {17,34,50,63,74,82,88,90,88,84,77,66,53,38,21,4,-13,-30,-45,-60,-72,-80,-86,-90,-89,-85,-78,-68,-56,-42,-26,-9,9,26,42,56,68,78,85,89,90,86,80,72,60,45,30,13,-4,-21,-38,-53,-66,-77,-84,-88,-90,-88,-82,-74,-63,-50,-34,-17,}

[0657] {21,42,60,74,84,89,89,84,74,60,42,21,0,-21,-42,-60,-74,-84,-89,-89,-84,-74,-60,-42,-21,0,21,42,60,74,84,89,89,84,74,60,42,21,0,-21,-42,-60,-74,-84,-89,-89,-84,-74,-60,-42,-21,0,21,42,60,74,84,89,89,84,74,60,42,21,}

[0658] {26,50,68,82,89,88,80,66,45,21,-4,-30,-53,-72,-84,-90,-88,-78,-63,-42,-17,9,34,56,74,85,90,86,77,60,38,13,-13,-38,-60,-77,-86,-90,-85,-74,-56,-34,-9,17,42,63,78,88,90,84,72,53,30,4,-21,-45,-66,-80,-88,-89,-82,-68,-50,-26,}

[0659] {30,56,77,88,89,80,63,38,9,-21,-50,-72,-85,-90,-84,-68,-45,-17,13,42,66,82,90,86,74,53,26,-4,-34,-60,-78,-88,-88,-78,-60,-34,-4,26,53,74,86,90,82,66,42,13,-17,-45,-68,-84,-90,-85,-72,-50,-21,9,38,63,80,89,88,77,56,30,}

[0660] {34,63,82,90,84,66,38,4,-30,-60,-80,-90,-85,-68,-42,-9,26,56,78,89,86,72,45,13,-21,-53,-77,-88,-88,-74,-50,-17,17,50,74,88,88,77,53,21,-13,-45,-72,-86,-89,-78,-56,-26,9,42,68,85,90,80,60,30,-4,-38,-66,-84,-90,-82,-63,-34,}

[0661] {38,68,86,88,74,45,9,-30,-63,-84,-90,-78,-53,-17,21,56,80,90,82,60,26,-13,-50,-77,-89,-85,-66,-34,4,42,72,88,88,72,42,4,-34,-66,-85,-89,-77,-50,-13,26,60,82,90,80,56,21,-17,-53,-78,-90,-84,-63,-30,9,45,74,88,86,68,38,}

[0662] {42,74,89,84,60,21,-21,-60,-84,-89,-74,-42,0,42,74,89,84,60,21,-21,-60,-84,-89,-74,-42,0,42,74,89,84,60,21,-21,-60,-84,-89,-74,-42,0,42,74,89,84,60,21,-21,-60,-84,-89,-74,-42,0,42,74,89,84,60,21,-21,-60,-84,-89,-74,-42,}

[0663] {45,78,90,77,42,-4,-50,-80,-90,-74,-38,9,53,82,89,72,34,-13,-56,-84,-88,-68,-30,17,60,85,88,66,26,-21,-63,-86,-86,-63,-21,26,66,88,85,60,17,-30,-68,-88,-84,-56,-13,34,72,89,82,53,9,-38,-74,-90,-80,-50,-4,42,77,90,78,45,}

[0664] {50,82,88,66,21,-30,-72,-90,-78,-42,9,56,85,86,60,13,-38,-77,-90,-74,-34,17,63,88,84,53,4,-45,-80,-89,-68,-26,26,68,89,80,45,-4,-53,-84,-88,-63,-17,34,74,90,77,38,-13,-60,-86,-85,-56,-9,42,78,90,72,30,-21,-66,-88,-82,-50,}

[0665] {53,85,85,53,0,-53,-85,-85,-53,0,53,85,85,53,0,-53,-85,-85,-53,0,53,85,85,53,0,-53,-85,-85,-53,0,53,85,85,53,0,-53,-85,-85,-53,0,53,85,85,53,0,-53,-85,-85,-53,0,53,85,85,53,0,-53,-85,-85,-53,0,53,85,85,53,}

[0666] {56,88,80,38,-21,-72,-90,-68,-17,42,82,86,53,-4,-60,-88,-78,-34,26,74,90,66,13,-45,-84,-85,-50,9,63,89,77,30,-30,-77,-89,-63,-9,50,85,84,45,-13,-66,-90,-74,-26,34,78,88,60,4,-53,-86,-82,-42,17,68,90,72,21,-38,-80,-88,-56,}

[0667] {60,89,74,21,-42,-84,-84,-42,21,74,89,60,0,-60,-89,-74,-21,42,84,84,42,-21,-74,-89,-60,0,60,89,74,21,-42,-84,-84,-42,21,74,89,60,0,-60,-89,-74,-21,42,84,84,42,-21,-74,-89,-60,0,60,89,74,21,-42,-84,-84,-42,21,74,89,60,}

[0668] {63,90,66,4,-60,-90,-68,-9,56,89,72,13,-53,-88,-74,-17,50,88,77,21,-45,-86,-78,-26,42,85,80,30,-38,-84,-82,-34,34,82,84,38,-30,-80,-85,-42,26,78,86,45,-21,-77,-88,-50,17,74,88,53,-13,-72,-89,-56,9,68,90,60,-4,-66,-90,-63,}

[0669] {66,90,56,-13,-74,-88,-45,26,80,84,34,-38,-85,-78,-21,50,88,72,9,-60,-90,-63,4,68,89,53,-17,-77,-86,-42,30,82,82,30,-42,-86,-77,-17,53,89,68,4,-63,-90,-60,9,72,88,50,-21,-78,-85,-38,34,84,80,26,-45,-88,-74,-13,56,90,66,}

[0670] {68,88,45,-30,-84,-78,-17,56,90,60,-13,-77,-85,-34,42,88,72,4,-66,-89,-50,26,82,80,21,-53,-90,-63,9,74,86,38,-38,-86,-74,-9,63,90,53,-21,-80,-82,-26,50,89,66,-4,-72,-88,-42,34,85,77,13,-60,-90,-56,17,78,84,30,-45,-88,-68,}

[0671] {72,86,34,-45,-89,-63,13,78,82,21,-56,-90,-53,26,84,77,9,-66,-88,-42,38,88,68,-4,-74,-85,-30,50,90,60,-17,-80,-80,-17,60,90,50,-30,-85,-74,-4,68,88,38,-42,-88,-66,9,77,84,26,-53,-90,-56,21,82,78,13,-63,-89,-45,34,86,72,}

[0672] {74,84,21,-60,-89,-42,42,89,60,-21,-84,-74,0,74,84,21,-60,-89,-42,42,89,60,-21,-84,-74,0,74,84,21,-60,-89,-42,42,89,60,-21,-84,-74,0,74,84,21,-60,-89,-42,42,89,60,-21,-84,-74,0,74,84,21,-60,-89,-42,42,89,60,-21,-84,-74,}

[0673] {77,80,9,-72,-84,-17,66,86,26,-60,-88,-34,53,90,42,-45,-90,-50,38,89,56,-30,-88,-63,21,85,68,-13,-82,-74,4,78,78,4,-74,-82,-13,68,85,21,-63,-88,-30,56,89,38,-50,-90,-45,42,90,53,-34,-88,-60,26,86,66,-17,-84,-72,9,80,77,}

[0674] {78,77,-4,-80,-74,9,82,72,-13,-84,-68,17,85,66,-21,-86,-63,26,88,60,-30,-88,-56,34,89,53,-38,-90,-50,42,90,45,-45,-90,-42,50,90,38,-53,-89,-34,56,88,30,-60,-88,-26,63,86,21,-66,-85,-17,68,84,13,-72,-82,-9,74,80,4,-77,-78,}

[0675] {80,72,-17,-86,-60,34,90,45,-50,-89,-30,63,85,13,-74,-78,4,82,68,-21,-88,-56,38,90,42,-53,-88,-26,66,84,9,-77,-77,9,84,66,-26,-88,-53,42,90,38,-56,-88,-21,68,82,4,-78,-74,13,85,63,-30,-89,-50,45,90,34,-60,-86,-17,72,80,}

[0676] {82,66,-30,-90,-42,56,86,13,-77,-74,17,88,53,-45,-89,-26,68,80,-4,-84,-63,34,90,38,-60,-85,-9,78,72,-21,-88,-50,50,88,21,-72,-78,9,85,60,-38,-90,-34,63,84,4,-80,-68,26,89,45,-53,-88,-17,74,77,-13,-86,-56,42,90,30,-66,-82,}

[0677] {84,60,-42,-89,-21,74,74,-21,-89,-42,60,84,0,-84,-60,42,89,21,-74,-74,21,89,42,-60,-84,0,84,60,-42,-89,-21,74,74,-21,-89,-42,60,84,0,-84,-60,42,89,21,-74,-74,21,89,42,-60,-84,0,84,60,-42,-89,-21,74,74,-21,-89,-42,60,84,}

[0678] {85,53,-53,-85,0,85,53,-53,-85,0,85,53,-53,-85,0,85,53,-53,-85,0,85,53,-53,-85,0,85,53,-53,-85,0,85,53,-53,-85,0,85,53,-53,-85,0,85,53,-53,-85,0,85,53,-53,-85,0,85,53,-53,-85,0,85,53,-53,-85,0,85,53,-53,-85,}

[0679] {86,45,-63,-78,21,90,26,-77,-66,42,88,4,-85,-50,60,80,-17,-90,-30,74,68,-38,-88,-9,84,53,-56,-82,13,89,34,-72,-72,34,89,13,-82,-56,53,84,-9,-88,-38,68,74,-30,-90,-17,80,60,-50,-85,4,88,42,-66,-77,26,90,21,-78,-63,45,86,}

[0680] {88,38,-72,-68,42,86,-4,-88,-34,74,66,-45,-85,9,89,30,-77,-63,50,84,-13,-90,-26,78,60,-53,-82,17,90,21,-80,-56,56,80,-21,-90,-17,82,53,-60,-78,26,90,13,-84,-50,63,77,-30,-89,-9,85,45,-66,-74,34,88,4,-86,-42,68,72,-38,-88,}

[0681] {88,30,-78,-56,60,77,-34,-88,4,89,26,-80,-53,63,74,-38,-86,9,90,21,-82,-50,66,72,-42,-85,13,90,17,-84,-45,68,68,-45,-84,17,90,13,-85,-42,72,66,-50,-82,21,90,9,-86,-38,74,63,-53,-80,26,89,4,-88,-34,77,60,-56,-78,30,88,}

[0682] {89,21,-84,-42,74,60,-60,-74,42,84,-21,-89,0,89,21,-84,-42,74,60,-60,-74,42,84,-21,-89,0,89,21,-84,-42,74,60,-60,-74,42,84,-21,-89,0,89,21,-84,-42,74,60,-60,-74,42,84,-21,-89,0,89,21,-84,-42,74,60,-60,-74,42,84,-21,-89,}

[0683] {90,13,-88,-26,84,38,-78,-50,72,60,-63,-68,53,77,-42,-82,30,86,-17,-89,4,90,9,-88,-21,85,34,-80,-45,74,56,-66,-66,56,74,-45,-80,34,85,-21,-88,9,90,4,-89,-17,86,30,-82,-42,77,53,-68,-63,60,72,-50,-78,38,84,-26,-88,13,90,}

[0684] {90,4,-90,-9,89,13,-88,-17,88,21,-86,-26,85,30,-84,-34,82,38,-80,-42,78,45,-77,-50,74,53,-72,-56,68,60,-66,-63,63,66,-60,-68,56,72,-53,-74,50,77,-45,-78,42,80,-38,-82,34,84,-30,-85,26,86,-21,-88,17,88,-13,-89,9,90,-4,-90,}

[0685] {90,-4,-90,9,89,-13,-88,17,88,-21,-86,26,85,-30,-84,34,82,-38,-80,42,78,-45,-77,50,74,-53,-72,56,68,-60,-66,63,63,-66,-60,68,56,-72,-53,74,50,-77,-45,78,42,-80,-38,82,34,-84,-30,85,26,-86,-21,88,17,-88,-13,89,9,-90,-4,90,}

[0686] {90,-13,-88,26,84,-38,-78,50,72,-60,-63,68,53,-77,-42,82,30,-86,-17,89,4,-90,9,88,-21,-85,34,80,-45,-74,56,66,-66,-56,74,45,-80,-34,85,21,-88,-9,90,-4,-89,17,86,-30,-82,42,77,-53,-68,63,60,-72,-50,78,38,-84,-26,88,13,-90,}

[0687] {89,-21,-84,42,74,-60,-60,74,42,-84,-21,89,0,-89,21,84,-42,-74,60,60,-74,-42,84,21,-89,0,89,-21,-84,42,74,-60,-60,74,42,-84,-21,89,0,-89,21,84,-42,-74,60,60,-74,-42,84,21,-89,0,89,-21,-84,42,74,-60,-60,74,42,-84,-21,89,}

[0688] {88,-30,-78,56,60,-77,-34,88,4,-89,26,80,-53,-63,74,38,-86,-9,90,-21,-82,50,66,-72,-42,85,13,-90,17,84,-45,-68,68,45,-84,-17,90,-13,-85,42,72,-66,-50,82,21,-90,9,86,-38,-74,63,53,-80,-26,89,-4,-88,34,77,-60,-56,78,30,-88,}

[0689] {88,-38,-72,68,42,-86,-4,88,-34,-74,66,45,-85,-9,89,-30,-77,63,50,-84,-13,90,-26,-78,60,53,-82,-17,90,-21,-80,56,56,-80,-21,90,-17,-82,53,60,-78,-26,90,-13,-84,50,63,-77,-30,89,-9,-85,45,66,-74,-34,88,-4,-86,42,68,-72,-38,88,}

[0690] {86,-45,-63,78,21,-90,26,77,-66,-42,88,-4,-85,50,60,-80,-17,90,-30,-74,68,38,-88,9,84,-53,-56,82,13,-89,34,72,-72,-34,89,-13,-82,56,53,-84,-9,88,-38,-68,74,30,-90,17,80,-60,-50,85,4,-88,42,66,-77,-26,90,-21,-78,63,45,-86,}

[0691] {85,-53,-53,85,0,-85,53,53,-85,0,85,-53,-53,85,0,-85,53,53,-85,0,85,-53,-53,85,0,-85,53,53,-85,0,85,-53,-53,85,0,-85,53,53,-85,0,85,-53,-53,85,0,-85,53,53,-85,0,85,-53,-53,85,0,-85,53,53,-85,0,85,-53,-53,85,}

[0692] {84,-60,-42,89,-21,-74,74,21,-89,42,60,-84,0,84,-60,-42,89,-21,-74,74,21,-89,42,60,-84,0,84,-60,-42,89,-21,-74,74,21,-89,42,60,-84,0,84,-60,-42,89,-21,-74,74,21,-89,42,60,-84,0,84,-60,-42,89,-21,-74,74,21,-89,42,60,-84,}

[0693] {82,-66,-30,90,-42,-56,86,-13,-77,74,17,-88,53,45,-89,26,68,-80,-4,84,-63,-34,90,-38,-60,85,-9,-78,72,21,-88,50,50,-88,21,72,-78,-9,85,-60,-38,90,-34,-63,84,-4,-80,68,26,-89,45,53,-88,17,74,-77,-13,86,-56,-42,90,-30,-66,82,}

[0694] {80,-72,-17,86,-60,-34,90,-45,-50,89,-30,-63,85,-13,-74,78,4,-82,68,21,-88,56,38,-90,42,53,-88,26,66,-84,9,77,-77,-9,84,-66,-26,88,-53,-42,90,-38,-56,88,-21,-68,82,-4,-78,74,13,-85,63,30,-89,50,45,-90,34,60,-86,17,72,-80,}

[0695] {78,-77,-4,80,-74,-9,82,-72,-13,84,-68,-17,85,-66,-21,86,-63,-26,88,-60,-30,88,-56,-34,89,-53,-38,90,-50,-42,90,-45,-45,90,-42,-50,90,-38,-53,89,-34,-56,88,-30,-60,88,-26,-63,86,-21,-66,85,-17,-68,84,-13,-72,82,-9,-74,80,-4,-77,78,}

[0696] {77,-80,9,72,-84,17,66,-86,26,60,-88,34,53,-90,42,45,-90,50,38,-89,56,30,-88,63,21,-85,68,13,-82,74,4,-78,78,-4,-74,82,-13,-68,85,-21,-63,88,-30,-56,89,-38,-50,90,-45,-42,90,-53,-34,88,-60,-26,86,-66,-17,84,-72,-9,80,-77,}

[0697] {74,-84,21,60,-89,42,42,-89,60,21,-84,74,0,-74,84,-21,-60,89,-42,-42,89,-60,-21,84,-74,0,74,-84,21,60,-89,42,42,-89,60,21,-84,74,0,-74,84,-21,-60,89,-42,-42,89,-60,-21,84,-74,0,74,-84,21,60,-89,42,42,-89,60,21,-84,74,}

[0698] {72,-86,34,45,-89,63,13,-78,82,-21,-56,90,-53,-26,84,-77,9,66,-88,42,38,-88,68,4,-74,85,-30,-50,90,-60,-17,80,-80,17,60,-90,50,30,-85,74,-4,-68,88,-38,-42,88,-66,-9,77,-84,26,53,-90,56,21,-82,78,-13,-63,89,-45,-34,86,-72,}

[0699] {68,-88,45,30,-84,78,-17,-56,90,-60,-13,77,-85,34,42,-88,72,-4,-66,89,-50,-26,82,-80,21,53,-90,63,9,-74,86,-38,-38,86,-74,9,63,-90,53,21,-80,82,-26,-50,89,-66,-4,72,-88,42,34,-85,77,-13,-60,90,-56,-17,78,-84,30,45,-88,68,}

[0700] {66,-90,56,13,-74,88,-45,-26,80,-84,34,38,-85,78,-21,-50,88,-72,9,60,-90,63,4,-68,89,-53,-17,77,-86,42,30,-82,82,-30,-42,86,-77,17,53,-89,68,-4,-63,90,-60,-9,72,-88,50,21,-78,85,-38,-34,84,-80,26,45,-88,74,-13,-56,90,-66,}

[0701] {63,-90,66,-4,-60,90,-68,9,56,-89,72,-13,-53,88,-74,17,50,-88,77,-21,-45,86,-78,26,42,-85,80,-30,-38,84,-82,34,34,-82,84,-38,-30,80,-85,42,26,-78,86,-45,-21,77,-88,50,17,-74,88,-53,-13,72,-89,56,9,-68,90,-60,-4,66,-90,63,}

[0702] {60,-89,74,-21,-42,84,-84,42,21,-74,89,-60,0,60,-89,74,-21,-42,84,-84,42,21,-74,89,-60,0,60,-89,74,-21,-42,84,-84,42,21,-74,89,-60,0,60,-89,74,-21,-42,84,-84,42,21,-74,89,-60,0,60,-89,74,-21,-42,84,-84,42,21,-74,89,-60,}

[0703] {56,-88,80,-38,-21,72,-90,68,-17,-42,82,-86,53,4,-60,88,-78,34,26,-74,90,-66,13,45,-84,85,-50,-9,63,-89,77,-30,-30,77,-89,63,-9,-50,85,-84,45,13,-66,90,-74,26,34,-78,88,-60,4,53,-86,82,-42,-17,68,-90,72,-21,-38,80,-88,56,}

[0704] {53,-85,85,-53,0,53,-85,85,-53,0,53,-85,85,-53,0,53,-85,85,-53,0,53,-85,85,-53,0,53,-85,85,-53,0,53,-85,85,-53,0,53,-85,85,-53,0,53,-85,85,-53,0,53,-85,85,-53,0,53,-85,85,-53,0,53,-85,85,-53,0,53,-85,85,-53,}

[0705] {50,-82,88,-66,21,30,-72,90,-78,42,9,-56,85,-86,60,-13,-38,77,-90,74,-34,-17,63,-88,84,-53,4,45,-80,89,-68,26,26,-68,89,-80,45,4,-53,84,-88,63,-17,-34,74,-90,77,-38,-13,60,-86,85,-56,9,42,-78,90,-72,30,21,-66,88,-82,50,}

[0706] {45,-78,90,-77,42,4,-50,80,-90,74,-38,-9,53,-82,89,-72,34,13,-56,84,-88,68,-30,-17,60,-85,88,-66,26,21,-63,86,-86,63,-21,-26,66,-88,85,-60,17,30,-68,88,-84,56,-13,-34,72,-89,82,-53,9,38,-74,90,-80,50,-4,-42,77,-90,78,-45,}

[0707] {42,-74,89,-84,60,-21,-21,60,-84,89,-74,42,0,-42,74,-89,84,-60,21,21,-60,84,-89,74,-42,0,42,-74,89,-84,60,-21,-21,60,-84,89,-74,42,0,-42,74,-89,84,-60,21,21,-60,84,-89,74,-42,0,42,-74,89,-84,60,-21,-21,60,-84,89,-74,42,}

[0708] {38,-68,86,-88,74,-45,9,30,-63,84,-90,78,-53,17,21,-56,80,-90,82,-60,26,13,-50,77,-89,85,-66,34,4,-42,72,-88,88,-72,42,-4,-34,66,-85,89,-77,50,-13,-26,60,-82,90,-80,56,-21,-17,53,-78,90,-84,63,-30,-9,45,-74,88,-86,68,-38,}

[0709] {34,-63,82,-90,84,-66,38,-4,-30,60,-80,90,-85,68,-42,9,26,-56,78,-89,86,-72,45,-13,-21,53,-77,88,-88,74,-50,17,17,-50,74,-88,88,-77,53,-21,-13,45,-72,86,-89,78,-56,26,9,-42,68,-85,90,-80,60,-30,-4,38,-66,84,-90,82,-63,34,}

[0710] {30,-56,77,-88,89,-80,63,-38,9,21,-50,72,-85,90,-84,68,-45,17,13,-42,66,-82,90,-86,74,-53,26,4,-34,60,-78,88,-88,78,-60,34,-4,-26,53,-74,86,-90,82,-66,42,-13,-17,45,-68,84,-90,85,-72,50,-21,-9,38,-63,80,-89,88,-77,56,-30,}

[0711] {26,-50,68,-82,89,-88,80,-66,45,-21,-4,30,-53,72,-84,90,-88,78,-63,42,-17,-9,34,-56,74,-85,90,-86,77,-60,38,-13,-13,38,-60,77,-86,90,-85,74,-56,34,-9,-17,42,-63,78,-88,90,-84,72,-53,30,-4,-21,45,-66,80,-88,89,-82,68,-50,26,}

[0712] {21,-42,60,-74,84,-89,89,-84,74,-60,42,-21,0,21,-42,60,-74,84,-89,89,-84,74,-60,42,-21,0,21,-42,60,-74,84,-89,89,-84,74,-60,42,-21,0,21,-42,60,-74,84,-89,89,-84,74,-60,42,-21,0,21,-42,60,-74,84,-89,89,-84,74,-60,42,-21,}

[0713] {17,-34,50,-63,74,-82,88,-90,88,-84,77,-66,53,-38,21,-4,-13,30,-45,60,-72,80,-86,90,-89,85,-78,68,-56,42,-26,9,9,-26,42,-56,68,-78,85,-89,90,-86,80,-72,60,-45,30,-13,-4,21,-38,53,-66,77,-84,88,-90,88,-82,74,-63,50,-34,17,}

[0714] {13,-26,38,-50,60,-68,77,-82,86,-89,90,-88,85,-80,74,-66,56,-45,34,-21,9,4,-17,30,-42,53,-63,72,-78,84,-88,90,-90,88,-84,78,-72,63,-53,42,-30,17,-4,-9,21,-34,45,-56,66,-74,80,-85,88,-90,89,-86,82,-77,68,-60,50,-38,26,-13,}

[0715] {9,-17,26,-34,42,-50,56,-63,68,-74,78,-82,85,-88,89,-90,90,-88,86,-84,80,-77,72,-66,60,-53,45,-38,30,-21,13,-4,-4,13,-21,30,-38,45,-53,60,-66,72,-77,80,-84,86,-88,90,-90,89,-88,85,-82,78,-74,68,-63,56,-50,42,-34,26,-17,9,}

[0716] {4,-9,13,-17,21,-26,30,-34,38,-42,45,-50,53,-56,60,-63,66,-68,72,-74,77,-78,80,-82,84,-85,86,-88,88,-89,90,-90,90,-90,89,-88,88,-86,85,-84,82,-80,78,-77,74,-72,68,-66,63,-60,56,-53,50,-45,42,-38,34,-30,26,-21,17,-13,9,-4,}.

[0717] In one embodiment, one or more 8-bit DCT-5 transform cores can be used for the main transform. As an example, an 8-bit DCT-5 transform core could be:

[0718] 4-point DCT-5:

[0719]

[0720] 8 o'clock DCT-5:

[0721]

[0722] 16-point DCT-5:

[0723]

[0724] 32-point DCT-5:

[0725] {46,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,65,}

[0726] {65,91,89,87,84,80,75,70,64,57,49,42,33,25,16,7,-2,-12,-20,-29,-38,-46,-53,-60,-67,-72,-78,-82,-86,-89,-90,-91,}

[0727] {65,89,84,75,64,49,33,16,-2,-20,-38,-53,-67,-78,-86,-90,-91,-89,-82,-72,-60,-46,-29,-12,7,25,42,57,70,80,87,91,}

[0728] {65,87,75,57,33,7,-20,-46,-67,-82,-90,-90,-82,-67,-46,-20,7,33,57,75,87,92,87,75,57,33,7,-20,-46,-67,-82,-90,}

[0729] {65,84,64,33,-2,-38,-67,-86,-91,-82,-60,-29,7,42,70,87,91,80,57,25,-12,-46,-72,-89,-90,-78,-53,-20,16,49,75,89,}

[0730] {65,80,49,7,-38,-72,-90,-86,-60,-20,25,64,87,89,70,33,-12,-53,-82,-91,-78,-46,-2,42,75,91,84,57,16,-29,-67,-89,}

[0731] {65,75,33,-20,-67,-90,-82,-46,7,57,87,87,57,7,-46,-82,-90,-67,-20,33,75,92,75,33,-20,-67,-90,-82,-46,7,57,87,}

[0732] {65,70,16,-46,-86,-86,-46,16,70,92,70,16,-46,-86,-86,-46,16,70,92,70,16,-46,-86,-86,-46,16,70,92,70,16,-46,-86,}

[0733] {65,64,-2,-67,-91,-60,7,70,91,57,-12,-72,-90,-53,16,75,89,49,-20,-78,-89,-46,25,80,87,42,-29,-82,-86,-38,33,84,}

[0734] {65,57,-20,-82,-82,-20,57,92,57,-20,-82,-82,-20,57,92,57,-20,-82,-82,-20,57,92,57,-20,-82,-82,-20,57,92,57,-20,-82,}

[0735] {65,49,-38,-90,-60,25,87,70,-12,-82,-78,-2,75,84,16,-67,-89,-29,57,91,42,-46,-91,-53,33,89,64,-20,-86,-72,7,80,}

[0736] {65,42,-53,-90,-29,64,87,16,-72,-82,-2,80,75,-12,-86,-67,25,89,57,-38,-91,-46,49,91,33,-60,-89,-20,70,84,7,-78,}

[0737] {65,33,-67,-82,7,87,57,-46,-90,-20,75,75,-20,-90,-46,57,87,7,-82,-67,33,92,33,-67,-82,7,87,57,-46,-90,-20,75,}

[0738] {65,25,-78,-67,42,89,7,-86,-53,57,84,-12,-90,-38,70,75,-29,-91,-20,80,64,-46,-89,-2,87,49,-60,-82,16,91,33,-72,}

[0739] {65,16,-86,-46,70,70,-46,-86,16,92,16,-86,-46,70,70,-46,-86,16,92,16,-86,-46,70,70,-46,-86,16,92,16,-86,-46,70,}

[0740] {65,7,-90,-20,87,33,-82,-46,75,57,-67,-67,57,75,-46,-82,33,87,-20,-90,7,92,7,-90,-20,87,33,-82,-46,75,57,-67,}

[0741] {65,-2,-91,7,91,-12,-90,16,89,-20,-89,25,87,-29,-86,33,84,-38,-82,42,80,-46,-78,49,75,-53,-72,57,70,-60,-67,64,}

[0742] {65,-12,-89,33,80,-53,-67,70,49,-82,-29,89,7,-91,16,87,-38,-78,57,64,-72,-46,84,25,-90,-2,91,-20,-86,42,75,-60,}

[0743] {65,-20,-82,57,57,-82,-20,92,-20,-82,57,57,-82,-20,92,-20,-82,57,57,-82,-20,92,-20,-82,57,57,-82,-20,92,-20,-82,57,}

[0744] {65,-29,-72,75,25,-91,33,70,-78,-20,91,-38,-67,80,16,-90,42,64,-82,-12,89,-46,-60,84,7,-89,49,57,-86,-2,87,-53,}

[0745] {65,-38,-60,87,-12,-78,75,16,-89,57,42,-91,33,64,-86,7,80,-72,-20,89,-53,-46,91,-29,-67,84,-2,-82,70,25,-90,49,}

[0746] {65,-46,-46,92,-46,-46,92,-46,-46,92,-46,-46,92,-46,-46,92,-46,-46,92,-46,-46,92,-46,-46,92,-46,-46,92,-46,-46,92,-46,}

[0747] {65,-53,-29,87,-72,-2,75,-86,25,57,-91,49,33,-89,70,7,-78,84,-20,-60,91,-46,-38,89,-67,-12,80,-82,16,64,-90,42,}

[0748] {65,-60,-12,75,-89,42,33,-86,80,-20,-53,91,-67,-2,70,-90,49,25,-82,84,-29,-46,89,-72,7,64,-91,57,16,-78,87,-38,}

[0749] {65,-67,7,57,-90,75,-20,-46,87,-82,33,33,-82,87,-46,-20,75,-90,57,7,-67,92,-67,7,57,-90,75,-20,-46,87,-82,33,}

[0750] {65,-72,25,33,-78,91,-67,16,42,-82,89,-60,7,49,-86,87,-53,-2,57,-89,84,-46,-12,64,-90,80,-38,-20,70,-91,75,-29,}

[0751] {65,-78,42,7,-53,84,-90,70,-29,-20,64,-89,87,-60,16,33,-72,91,-82,49,-2,-46,80,-91,75,-38,-12,57,-86,89,-67,25,}

[0752] {65,-82,57,-20,-20,57,-82,92,-82,57,-20,-20,57,-82,92,-82,57,-20,-20,57,-82,92,-82,57,-20,-20,57,-82,92,-82,57,-20,}

[0753] {65,-86,70,-46,16,16,-46,70,-86,92,-86,70,-46,16,16,-46,70,-86,92,-86,70,-46,16,16,-46,70,-86,92,-86,70,-46,16,}

[0754] {65,-89,80,-67,49,-29,7,16,-38,57,-72,84,-90,91,-86,75,-60,42,-20,-2,25,-46,64,-78,87,-91,89,-82,70,-53,33,-12,}

[0755] {65,-90,87,-82,75,-67,57,-46,33,-20,7,7,-20,33,-46,57,-67,75,-82,87,-90,92,-90,87,-82,75,-67,57,-46,33,-20,7,}

[0756] {65,-91,91,-90,89,-89,87,-86,84,-82,80,-78,75,-72,70,-67,64,-60,57,-53,49,-46,42,-38,33,-29,25,-20,16,-12,7,-2,}

[0757] 64-point DCT-5:

[0758] {44,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,}

[0759] {64,91,90,90,90,88,87,85,84,82,80,78,75,72,70,66,64,61,58,54,50,46,42,39,34,29,25,22,17,13,7,4,-1,-6,-10,-15,-19,-24,-28,-32,-36,-40,-44,-48,-51,-55,-59,-63,-65,-68,-70,-73,-77,-79,-81,-83,-85,-86,-88,-89,-90,-90,-91,-91,}

[0760] {64,90,90,87,84,80,75,70,64,58,50,42,34,25,17,7,-1,-10,-19,-28,-36,-44,-51,-59,-65,-70,-77,-81,-85,-88,-90,-91,-91,-90,-89,-86,-83,-79,-73,-68,-63,-55,-48,-40,-32,-24,-15,-6,4,13,22,29,39,46,54,61,66,72,78,82,85,88,90,91,}

[0761] {64,90,87,82,75,66,58,46,34,22,7,-6,-19,-32,-44,-55,-65,-73,-81,-86,-90,-91,-90,-88,-83,-77,-68,-59,-48,-36,-24,-10,4,17,29,42,54,64,72,80,85,90,91,90,88,84,78,70,61,50,39,25,13,-1,-15,-28,-40,-51,-63,-70,-79,-85,-89,-91,}

[0762] {64,90,84,75,64,50,34,17,-1,-19,-36,-51,-65,-77,-85,-90,-91,-89,-83,-73,-63,-48,-32,-15,4,22,39,54,66,78,85,90,91,88,82,72,61,46,29,13,-6,-24,-40,-55,-68,-79,-86,-90,-91,-88,-81,-70,-59,-44,-28,-10,7,25,42,58,70,80,87,90,}

[0763] {64,88,80,66,50,29,7,-15,-36,-55,-70,-83,-90,-91,-86,-77,-63,-44,-24,-1,22,42,61,75,85,90,90,84,72,58,39,17,-6,-28,-48,-65,-79,-88,-91,-89,-81,-68,-51,-32,-10,13,34,54,70,82,90,91,87,78,64,46,25,4,-19,-40,-59,-73,-85,-90,}

[0764] {64,87,75,58,34,7,-19,-44,-65,-81,-90,-90,-83,-68,-48,-24,4,29,54,72,85,91,88,78,61,39,13,-15,-40,-63,-79,-89,-91,-85,-70,-51,-28,-1,25,50,70,84,90,90,80,64,42,17,-10,-36,-59,-77,-88,-91,-86,-73,-55,-32,-6,22,46,66,82,90,}

[0765] {64,85,70,46,17,-15,-44,-68,-85,-91,-86,-70,-48,-19,13,42,66,84,91,87,72,50,22,-10,-40,-65,-83,-91,-88,-73,-51,-24,7,39,64,82,90,88,75,54,25,-6,-36,-63,-81,-90,-89,-77,-55,-28,4,34,61,80,90,90,78,58,29,-1,-32,-59,-79,-90,}

[0766] {64,84,64,34,-1,-36,-65,-85,-91,-83,-63,-32,4,39,66,85,91,82,61,29,-6,-40,-68,-86,-91,-81,-59,-28,7,42,70,87,90,80,58,25,-10,-44,-70,-88,-90,-79,-55,-24,13,46,72,88,90,78,54,22,-15,-48,-73,-89,-90,-77,-51,-19,17,50,75,90,}

[0767] {64,82,58,22,-19,-55,-81,-91,-83,-59,-24,17,54,80,91,84,61,25,-15,-51,-79,-91,-85,-63,-28,13,50,78,90,85,64,29,-10,-48,-77,-90,-86,-65,-32,7,46,75,90,87,66,34,-6,-44,-73,-90,-88,-68,-36,4,42,72,90,88,70,39,-1,-40,-70,-89,}

[0768] {64,80,50,7,-36,-70,-90,-86,-63,-24,22,61,85,90,72,39,-6,-48,-79,-91,-81,-51,-10,34,70,90,87,64,25,-19,-59,-85,-90,-73,-40,4,46,78,91,82,54,13,-32,-68,-89,-88,-65,-28,17,58,84,90,75,42,-1,-44,-77,-91,-83,-55,-15,29,66,88,}

[0769] {64,78,42,-6,-51,-83,-90,-70,-32,17,61,87,88,64,22,-28,-68,-90,-85,-55,-10,39,75,91,80,46,-1,-48,-81,-91,-73,-36,13,58,85,90,66,25,-24,-65,-89,-86,-59,-15,34,72,90,82,50,4,-44,-79,-91,-77,-40,7,54,84,90,70,29,-19,-63,-88,}

[0770] {64,75,34,-19,-65,-90,-83,-48,4,54,85,88,61,13,-40,-79,-91,-70,-28,25,70,90,80,42,-10,-59,-88,-86,-55,-6,46,82,90,66,22,-32,-73,-91,-77,-36,17,64,90,84,50,-1,-51,-85,-89,-63,-15,39,78,91,72,29,-24,-68,-90,-81,-44,7,58,87,}

[0771] {64,72,25,-32,-77,-91,-68,-19,39,80,90,64,13,-44,-83,-89,-59,-6,50,85,87,54,-1,-55,-88,-85,-48,7,61,90,82,42,-15,-65,-90,-79,-36,22,70,91,75,29,-28,-73,-91,-70,-24,34,78,90,66,17,-40,-81,-90,-63,-10,46,84,88,58,4,-51,-86,}

[0772] {64,70,17,-44,-85,-86,-48,13,66,91,72,22,-40,-83,-88,-51,7,64,90,75,25,-36,-81,-89,-55,4,61,90,78,29,-32,-79,-90,-59,-1,58,90,80,34,-28,-77,-90,-63,-6,54,88,82,39,-24,-73,-91,-65,-10,50,87,84,42,-19,-70,-91,-68,-15,46,85,}

[0773] {64,66,7,-55,-90,-77,-24,42,85,84,39,-28,-79,-89,-51,13,70,91,64,4,-59,-90,-73,-19,46,87,82,34,-32,-81,-88,-48,17,72,90,61,-1,-63,-91,-70,-15,50,88,80,29,-36,-83,-86,-44,22,75,90,58,-6,-65,-91,-68,-10,54,90,78,25,-40,-85,}

[0774] {64,64,-1,-65,-91,-63,4,66,91,61,-6,-68,-91,-59,7,70,90,58,-10,-70,-90,-55,13,72,90,54,-15,-73,-90,-51,17,75,90,50,-19,-77,-89,-48,22,78,88,46,-24,-79,-88,-44,25,80,87,42,-28,-81,-86,-40,29,82,85,39,-32,-83,-85,-36,34,84,}

[0775] {64,61,-10,-73,-89,-44,29,84,82,25,-48,-90,-70,-6,64,91,58,-15,-77,-88,-40,34,85,80,22,-51,-90,-68,-1,66,90,54,-19,-79,-86,-36,39,87,78,17,-55,-91,-65,4,70,90,50,-24,-81,-85,-32,42,88,75,13,-59,-91,-63,7,72,90,46,-28,-83,}

[0776] {64,58,-19,-81,-83,-24,54,91,61,-15,-79,-85,-28,50,90,64,-10,-77,-86,-32,46,90,66,-6,-73,-88,-36,42,90,70,-1,-70,-89,-40,39,88,72,4,-68,-90,-44,34,87,75,7,-65,-90,-48,29,85,78,13,-63,-91,-51,25,84,80,17,-59,-91,-55,22,82,}

[0777] {64,54,-28,-86,-73,-1,72,87,29,-51,-91,-55,25,85,75,4,-70,-88,-32,50,91,58,-24,-85,-77,-6,70,88,34,-48,-91,-59,22,84,78,7,-68,-89,-36,46,90,61,-19,-83,-79,-10,66,90,39,-44,-90,-63,17,82,80,13,-65,-90,-40,42,90,64,-15,-81,}

[0778] {64,50,-36,-90,-63,22,85,72,-6,-79,-81,-10,70,87,25,-59,-90,-40,46,91,54,-32,-89,-65,17,84,75,-1,-77,-83,-15,66,88,29,-55,-91,-44,42,90,58,-28,-88,-68,13,82,78,4,-73,-85,-19,64,90,34,-51,-91,-48,39,90,61,-24,-86,-70,7,80,}

[0779] {64,46,-44,-91,-48,42,91,50,-40,-91,-51,39,90,54,-36,-90,-55,34,90,58,-32,-90,-59,29,90,61,-28,-89,-63,25,88,64,-24,-88,-65,22,87,66,-19,-86,-68,17,85,70,-15,-85,-70,13,84,72,-10,-83,-73,7,82,75,-6,-81,-77,4,80,78,-1,-79,}

[0780] {64,42,-51,-90,-32,61,88,22,-68,-85,-10,75,80,-1,-81,-73,13,85,66,-24,-89,-59,34,90,50,-44,-91,-40,54,90,29,-63,-88,-19,70,84,7,-77,-79,4,82,72,-15,-86,-65,25,90,58,-36,-91,-48,46,91,39,-55,-90,-28,64,87,17,-70,-83,-6,78,}

[0781] {64,39,-59,-88,-15,75,78,-10,-86,-63,34,91,42,-55,-89,-19,72,80,-6,-85,-65,29,90,46,-51,-90,-24,70,82,-1,-83,-68,25,90,50,-48,-90,-28,66,84,4,-81,-70,22,90,54,-44,-91,-32,64,85,7,-79,-73,17,88,58,-40,-91,-36,61,87,13,-77,}

[0782] {64,34,-65,-83,4,85,61,-40,-91,-28,70,80,-10,-88,-55,46,90,22,-73,-77,17,90,50,-51,-89,-15,78,72,-24,-90,-44,58,87,7,-81,-68,29,91,39,-63,-85,-1,84,64,-36,-91,-32,66,82,-6,-86,-59,42,90,25,-70,-79,13,88,54,-48,-90,-19,75,}

[0783] {64,29,-70,-77,22,90,39,-65,-81,13,90,46,-59,-85,4,87,54,-51,-88,-6,84,61,-44,-90,-15,80,66,-36,-91,-24,75,72,-28,-91,-32,70,78,-19,-90,-40,64,82,-10,-89,-48,58,85,-1,-86,-55,50,88,7,-83,-63,42,90,17,-79,-68,34,91,25,-73,}

[0784] {64,25,-77,-68,39,90,13,-83,-59,50,87,-1,-88,-48,61,82,-15,-90,-36,70,75,-28,-91,-24,78,66,-40,-90,-10,84,58,-51,-86,4,88,46,-63,-81,17,90,34,-70,-73,29,91,22,-79,-65,42,90,7,-85,-55,54,85,-6,-89,-44,64,80,-19,-91,-32,72,}

[0785] {64,22,-81,-59,54,84,-15,-91,-28,78,64,-48,-86,7,90,34,-73,-68,42,88,-1,-89,-40,70,72,-36,-90,-6,87,46,-65,-77,29,90,13,-85,-51,61,80,-24,-91,-19,82,58,-55,-83,17,91,25,-79,-63,50,85,-10,-90,-32,75,66,-44,-88,4,90,39,-70,}

[0786] {64,17,-85,-48,66,72,-40,-88,7,90,25,-81,-55,61,78,-32,-90,-1,90,34,-77,-63,54,82,-24,-91,-10,87,42,-70,-68,46,85,-15,-91,-19,84,50,-65,-73,39,88,-6,-90,-28,80,58,-59,-79,29,90,4,-89,-36,75,64,-51,-83,22,91,13,-86,-44,70,}

[0787] {64,13,-88,-36,78,58,-63,-73,42,85,-19,-91,-6,90,29,-81,-51,66,70,-48,-83,25,90,-1,-90,-24,84,46,-70,-65,54,80,-32,-89,7,91,17,-86,-40,75,61,-59,-77,39,87,-15,-91,-10,88,34,-79,-55,64,72,-44,-85,22,90,4,-90,-28,82,50,-68,}

[0788] {64,7,-90,-24,85,39,-79,-51,70,64,-59,-73,46,82,-32,-88,17,90,-1,-91,-15,88,29,-83,-44,75,58,-65,-68,54,78,-40,-85,25,90,-10,-91,-6,90,22,-86,-36,80,50,-70,-63,61,72,-48,-81,34,87,-19,-90,4,91,13,-89,-28,84,42,-77,-55,66,}

[0789] {64,4,-91,-10,90,17,-89,-24,87,29,-85,-36,82,42,-79,-48,75,54,-70,-59,66,64,-63,-68,58,72,-51,-77,46,80,-40,-83,34,85,-28,-88,22,90,-15,-90,7,91,-1,-91,-6,90,13,-90,-19,88,25,-86,-32,84,39,-81,-44,78,50,-73,-55,70,61,-65,}

[0790] {64,-1,-91,4,91,-6,-91,7,90,-10,-90,13,90,-15,-90,17,90,-19,-89,22,88,-24,-88,25,87,-28,-86,29,85,-32,-85,34,84,-36,-83,39,82,-40,-81,42,80,-44,-79,46,78,-48,-77,50,75,-51,-73,54,72,-55,-70,58,70,-59,-68,61,66,-63,-65,64,}

[0791] {64,-6,-90,17,88,-28,-85,39,80,-48,-73,58,66,-65,-59,72,50,-79,-40,84,29,-88,-19,90,7,-91,4,90,-15,-89,25,85,-36,-81,46,75,-55,-68,64,61,-70,-51,78,42,-83,-32,87,22,-90,-10,91,-1,-91,13,90,-24,-86,34,82,-44,-77,54,70,-63,}

[0792] {64,-10,-89,29,82,-48,-70,64,58,-77,-40,85,22,-90,-1,90,-19,-86,39,78,-55,-65,70,50,-81,-32,88,13,-91,7,90,-28,-83,46,72,-63,-59,75,42,-85,-24,90,4,-91,17,87,-36,-79,54,66,-68,-51,80,34,-88,-15,91,-6,-90,25,84,-44,-73,61,}

[0793] {64,-15,-86,42,72,-65,-51,82,25,-90,4,90,-32,-79,58,61,-77,-36,88,7,-91,22,84,-48,-68,70,46,-85,-19,91,-10,-88,39,75,-63,-55,80,29,-90,-1,90,-28,-81,54,64,-73,-40,87,13,-91,17,85,-44,-70,66,50,-83,-24,90,-6,-89,34,78,-59,}

[0794] {64,-19,-83,54,61,-79,-28,90,-10,-86,46,66,-73,-36,90,-1,-89,39,72,-68,-44,87,7,-90,29,78,-63,-51,84,17,-91,22,82,-55,-59,80,25,-91,13,85,-48,-65,75,34,-90,4,88,-40,-70,70,42,-88,-6,90,-32,-77,64,50,-85,-15,91,-24,-81,58,}

[0795] {64,-24,-79,64,46,-88,-1,88,-44,-65,78,25,-91,22,80,-63,-48,87,4,-89,42,66,-77,-28,91,-19,-81,61,50,-86,-6,90,-40,-68,75,29,-91,17,82,-59,-51,85,7,-90,39,70,-73,-32,90,-15,-83,58,54,-85,-10,90,-36,-70,72,34,-90,13,84,-55,}

[0796] {64,-28,-73,72,29,-91,25,75,-70,-32,91,-24,-77,70,34,-91,22,78,-68,-36,90,-19,-79,66,39,-90,17,80,-65,-40,90,-15,-81,64,42,-90,13,82,-63,-44,90,-10,-83,61,46,-89,7,84,-59,-48,88,-6,-85,58,50,-88,4,85,-55,-51,87,-1,-86,54,}

[0797] {64,-32,-68,80,13,-89,50,54,-88,7,82,-65,-36,91,-28,-70,78,17,-90,46,58,-86,4,84,-63,-40,90,-24,-73,75,22,-90,42,61,-85,-1,85,-59,-44,90,-19,-77,72,25,-91,39,64,-83,-6,87,-55,-48,90,-15,-79,70,29,-91,34,66,-81,-10,88,-51,}

[0798] {64,-36,-63,85,-6,-81,70,25,-90,46,54,-89,17,75,-77,-15,88,-55,-44,90,-28,-68,82,4,-85,64,34,-91,39,61,-86,7,80,-70,-24,90,-48,-51,90,-19,-73,78,13,-88,58,42,-91,29,66,-83,-1,84,-65,-32,91,-40,-59,87,-10,-79,72,22,-90,50,}

[0799] {64,-40,-55,90,-24,-68,84,-6,-79,75,13,-86,64,29,-90,50,46,-91,34,61,-88,17,72,-81,-1,82,-70,-19,88,-59,-36,91,-44,-51,90,-28,-65,85,-10,-77,78,7,-85,66,25,-90,54,42,-91,39,58,-89,22,70,-83,4,80,-73,-15,87,-63,-32,90,-48,}

[0800] {64,-44,-48,91,-40,-51,90,-36,-55,90,-32,-59,90,-28,-63,88,-24,-65,87,-19,-68,85,-15,-70,84,-10,-73,82,-6,-77,80,-1,-79,78,4,-81,75,7,-83,72,13,-85,70,17,-86,66,22,-88,64,25,-89,61,29,-90,58,34,-90,54,39,-91,50,42,-91,46,}

[0801] {64,-48,-40,90,-55,-32,90,-63,-24,87,-68,-15,84,-73,-6,80,-79,4,75,-83,13,70,-86,22,64,-89,29,58,-90,39,50,-91,46,42,-91,54,34,-90,61,25,-88,66,17,-85,72,7,-81,78,-1,-77,82,-10,-70,85,-19,-65,88,-28,-59,90,-36,-51,91,-44,}

[0802] {64,-51,-32,88,-68,-10,80,-81,13,66,-89,34,50,-91,54,29,-88,70,7,-79,82,-15,-65,90,-36,-48,91,-55,-28,87,-70,-6,78,-83,17,64,-90,39,46,-91,58,25,-86,72,4,-77,84,-19,-63,90,-40,-44,90,-59,-24,85,-73,-1,75,-85,22,61,-90,42,}

[0803] {64,-55,-24,84,-79,13,64,-90,46,34,-88,72,-1,-70,88,-36,-44,90,-65,-10,78,-85,25,54,-91,58,22,-83,80,-15,-63,90,-48,-32,87,-73,4,70,-89,39,42,-90,66,7,-77,85,-28,-51,91,-59,-19,82,-81,17,61,-91,50,29,-86,75,-6,-68,90,-40,}

[0804] {64,-59,-15,78,-86,34,42,-89,72,-6,-65,90,-51,-24,82,-83,25,50,-90,66,4,-70,90,-44,-32,85,-79,17,58,-91,61,13,-77,87,-36,-40,88,-73,7,64,-91,54,22,-81,84,-28,-48,90,-68,-1,70,-90,46,29,-85,80,-19,-55,91,-63,-10,75,-88,39,}

[0805] {64,-63,-6,70,-90,54,17,-77,88,-44,-28,82,-85,34,39,-86,80,-24,-48,90,-73,13,58,-91,66,-1,-65,91,-59,-10,72,-90,50,22,-79,87,-40,-32,84,-83,29,42,-88,78,-19,-51,90,-70,7,61,-91,64,4,-68,90,-55,-15,75,-89,46,25,-81,85,-36,}

[0806] {64,-65,4,61,-91,70,-10,-55,90,-73,17,50,-89,78,-24,-44,87,-81,29,39,-85,84,-36,-32,82,-86,42,25,-79,88,-48,-19,75,-90,54,13,-70,90,-59,-6,66,-91,64,-1,-63,91,-68,7,58,-90,72,-15,-51,90,-77,22,46,-88,80,-28,-40,85,-83,34,}

[0807] {64,-68,13,50,-88,82,-36,-28,78,-90,58,4,-63,90,-73,22,42,-85,85,-44,-19,72,-91,64,-6,-55,90,-79,29,34,-81,88,-51,-10,66,-91,70,-15,-48,87,-83,39,25,-77,90,-59,-1,61,-90,75,-24,-40,84,-86,46,17,-70,91,-65,7,54,-89,80,-32,}

[0808] {64,-70,22,39,-81,90,-59,4,54,-88,84,-44,-15,66,-91,75,-28,-32,78,-90,64,-10,-48,85,-86,50,7,-63,90,-79,34,25,-73,91,-68,17,42,-83,88,-55,-1,58,-89,82,-40,-19,70,-91,72,-24,-36,80,-90,61,-6,-51,87,-85,46,13,-65,90,-77,29,}

[0809] {64,-73,29,25,-70,91,-77,34,22,-68,90,-79,39,17,-65,90,-81,42,13,-63,90,-83,46,7,-59,88,-85,50,4,-55,87,-86,54,-1,-51,85,-88,58,-6,-48,84,-89,61,-10,-44,82,-90,64,-15,-40,80,-90,66,-19,-36,78,-91,70,-24,-32,75,-91,72,-28,}

[0810] {64,-77,39,13,-59,87,-88,61,-15,-36,75,-91,78,-40,-10,58,-86,88,-63,17,34,-73,91,-79,42,7,-55,85,-89,64,-19,-32,72,-91,80,-44,-6,54,-85,90,-65,22,29,-70,90,-81,46,4,-51,84,-90,66,-24,-28,70,-90,82,-48,-1,50,-83,90,-68,25,}

[0811] {64,-79,46,-1,-44,78,-91,80,-48,4,42,-77,91,-81,50,-6,-40,75,-91,82,-51,7,39,-73,90,-83,54,-10,-36,72,-90,84,-55,13,34,-70,90,-85,58,-15,-32,70,-90,85,-59,17,29,-68,90,-86,61,-19,-28,66,-89,87,-63,22,25,-65,88,-88,64,-24,}

[0812] {64,-81,54,-15,-28,64,-86,90,-73,42,-1,-40,72,-90,87,-65,29,13,-51,80,-91,82,-55,17,25,-63,85,-90,75,-44,4,39,-70,90,-88,66,-32,-10,50,-79,91,-83,58,-19,-24,61,-85,90,-77,46,-6,-36,70,-89,88,-68,34,7,-48,78,-91,84,-59,22,}

[0813] {64,-83,61,-28,-10,46,-73,90,-89,72,-44,7,29,-63,84,-91,82,-59,25,13,-48,75,-90,88,-70,42,-6,-32,64,-85,91,-81,58,-24,-15,50,-77,90,-88,70,-40,4,34,-65,85,-91,80,-55,22,17,-51,78,-90,87,-68,39,-1,-36,66,-86,90,-79,54,-19,}

[0814] {64,-85,66,-40,7,25,-55,78,-90,90,-77,54,-24,-10,42,-68,85,-91,84,-65,39,-6,-28,58,-79,90,-89,75,-51,22,13,-44,70,-86,91,-83,64,-36,4,29,-59,80,-90,88,-73,50,-19,-15,46,-70,87,-91,82,-63,34,-1,-32,61,-81,90,-88,72,-48,17,}

[0815] {64,-86,72,-51,25,4,-32,58,-77,88,-91,84,-68,46,-19,-10,39,-63,80,-90,90,-81,64,-40,13,17,-44,66,-83,90,-89,78,-59,34,-6,-24,50,-70,85,-91,87,-73,54,-28,-1,29,-55,75,-88,91,-85,70,-48,22,7,-36,61,-79,90,-90,82,-65,42,-15,}

[0816] {64,-88,78,-63,42,-19,-6,29,-51,70,-83,90,-90,84,-70,54,-32,7,17,-40,61,-77,87,-91,88,-79,64,-44,22,4,-28,50,-68,82,-90,90,-85,72,-55,34,-10,-15,39,-59,75,-86,91,-89,80,-65,46,-24,-1,25,-48,66,-81,90,-91,85,-73,58,-36,13,}

[0817] {64,-89,82,-70,58,-40,22,-1,-19,39,-55,70,-81,88,-91,90,-83,72,-59,42,-24,4,17,-36,54,-68,80,-88,91,-90,84,-73,61,-44,25,-6,-15,34,-51,66,-79,87,-91,90,-85,75,-63,46,-28,7,13,-32,50,-65,78,-86,90,-90,85,-77,64,-48,29,-10,}

[0818] {64,-90,85,-79,70,-59,46,-32,17,-1,-15,29,-44,58,-68,78,-85,90,-91,90,-86,80,-70,61,-48,34,-19,4,13,-28,42,-55,66,-77,84,-89,91,-90,87,-81,72,-63,50,-36,22,-6,-10,25,-40,54,-65,75,-83,88,-91,90,-88,82,-73,64,-51,39,-24,7,}

[0819] {64,-90,88,-85,80,-73,66,-59,50,-40,29,-19,7,4,-15,25,-36,46,-55,64,-70,78,-83,87,-90,91,-91,90,-86,82,-77,70,-63,54,-44,34,-24,13,-1,-10,22,-32,42,-51,61,-68,75,-81,85,-89,90,-91,90,-88,84,-79,72,-65,58,-48,39,-28,17,-6,}

[0820] {64,-91,90,-89,87,-85,82,-79,75,-70,66,-63,58,-51,46,-40,34,-28,22,-15,7,-1,-6,13,-19,25,-32,39,-44,50,-55,61,-65,70,-73,78,-81,84,-86,88,-90,90,-91,91,-90,90,-88,85,-83,80,-77,72,-68,64,-59,54,-48,42,-36,29,-24,17,-10,4,}

[0821] {64,-91,91,-91,90,-90,90,-90,90,-89,88,-88,87,-86,85,-85,84,-83,82,-81,80,-79,78,-77,75,-73,72,-70,70,-68,66,-65,64,-63,61,-59,58,-55,54,-51,50,-48,46,-44,42,-40,39,-36,34,-32,29,-28,25,-24,22,-19,17,-15,13,-10,7,-6,4,-1,}.

[0822] This application also provides an apparatus for decoding compressed video or image data or encoding uncompressed video or image data using an 8-bit master transform core matrix. The apparatus includes:

[0823] A receiving module is configured to receive information relating to a target file for encoding or decoding, wherein the target file for encoding or decoding is one of the following: a compressed video or image data file, or an uncompressed video or image data file;

[0824] The determination module is used to encode or decode the target file and determine whether to use a first transform core matrix with a first size type or a second transform core matrix with a second size type smaller than the first size type, wherein the first size type is an 8-bit master transform core matrix, and the 8-bit master transform core matrix has a core matrix represented by 8 bits and has a size of 64 points or greater.

[0825] The first processing module is configured to encode or decode the target file for encoding or decoding using the 8-bit master transform core matrix with a size of 64 points or larger when the determined result is a first transform core matrix of the first size type.

[0826] The second processing module is configured to extract the second transformation core matrix of the second size type from the 8-bit master transformation core matrix of the second size type when the determined result is a second transformation core matrix of the second size type that is smaller than the first size type, and to encode or decode the target file for encoding or decoding using the extracted second transformation core matrix of the second size type.

[0827] Optionally, the first transformation core matrix is ​​a 64-point 8-bit principal transformation core matrix. This 64-point 8-bit principal transformation core matrix is ​​constructed using thirty-three integers used to construct a 32-point 8-bit principal transformation core matrix and an additional thirty-two integers. The additional thirty-two integers include: bf, bg, bh, bi, bj, bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb, cc, cd, ce, cf, cg, ch, ci, cj, and ck, plus their respective sign changes.

[0828] The additional thirty-two integers {bf,bg,bh,bi,bj,bk,bl,bm,bn,bo,bp,bq,br,bs,bt,bu,bv,bw,bx,by,bz,ca,cb,cc,cd,ce,cf,cg,ch,ci,cj,ck} are equal to {91,90,90,90,88,87,86,84,83,81,79,77,73,71,69,65,62,59,56,52,48,44,41,37,33,28,24,20,15,11,7,2}.

[0829] Optionally, the 128-point 8-bit master transform core is constructed using 65 integers used to construct the 64-point 8-bit master transform core matrix and an additional 64 integers, wherein the additional 64 integers include: cl,cm,cn,co,cp,cq,cr,cs,ct,cu,cv,cw,cx,cy,cz,da,db,dc,dd,de,df,dg,dh,di,dj,dk,dl,dm,dn,d_,dp,dq,dr. ds,dt,du,dv,dw,dx,dy,dz,ea,eb,ec,ed,ee,ef,eg,eh,ei,ej,ek,el,em,en,eo,ep,eq,er,es,et,eu,ev andew plus their sign changes, and these additional 64 integers are {cl,cm,cn,co,cp,cq,cr,cs,ct,cu,cv,cw,cx,cy,cz,da,db, dc,dd,de,df,dg,dh,di,dj,dk,dl,dm,dn,d_,dp,dq,dr,ds,dt,du,dv,dw,dx,dy,dz,ea,eb,ec,ed ,ee,ef,eg,eh,ei,ej,ek,el,em,en,eo,ep,eq,er,es,et,eu,ev,ew} is equal to {90,90,90,90,90,90,89,8 9,89,88,88,87,86,86,85,84,83,82,81,80,79,78,77,76,75,73,72,71,69,68,66,65,63,62,60,58,58,55,53,51,49,48,45,44,42,40,38,36,34,32,29,27,25,23,21,19,17,15,12,10,8,6,3,1}.

[0830] Optionally, the size of the 8-bit master transform core matrix is ​​64 points or 128 points.

[0831] Optionally, the left or right half of the even or odd rows of the 8-bit master transform core matrix forms a matrix similar to the second transform core matrix.

[0832] The 8-bit master transform core matrix is ​​one of the following: DCT-2, DCT-5, DCT-8, DST-1, and DST-7, and

[0833] The second transformation core matrix is ​​one of the following: DCT-2, DCT-5, DCT-8, DST-1, and DST-7.

[0834] Optionally, the 8-bit master transform core matrix and the second transform core matrix are the same one of the following: DCT-2, DCT-5, DCT-8, DST-1, and DST-7.

[0835] Optionally, the 8-bit master transform core matrix is ​​an 8-bit 64-point DCT-2 transform matrix, and the second transform core matrix is ​​an 8-bit 32-point DCT-2 transform matrix.

[0836] Optionally, the device further includes:

[0837] The scaling module is used to scale the original transformation core T0, which consists of floating-point numbers, by using a scaling factor of 2B-2×log2(N) to derive the initial transformation core matrix Tl = T0×2B-2×log2(N), where B = 8, and the row vectors of T0, which serve as basis vectors, are orthogonal to each other, and the norm of each row vector is 1.

[0838] An export module is used to export the adjusted transformation core matrix T2 by adding an offset to a selected set of the M unique numbers used to construct the adjusted master transformation core matrix T2.

[0839] The calculation module is used to calculate the cost C as the sum of the absolute values ​​of all elements of (T1*T1T-22B-4×log2(N)2×I), where I is an N×N identity matrix;

[0840] The output module is used to update the adjusted transformation matrix T2 by adding the calculated offset value to T2, so that the cost value is minimized to T2, and the adjusted transformation matrix T2 is output as the 8-bit N-point main transformation core matrix.

[0841] Optionally, the output module is specifically used for:

[0842] After minimizing the cost C by trying all possible combinations of offset values ​​on a selected set of M unique numbers, T2 is output as the 8-bit N-point master transformation core matrix.

[0843] The encoding / decoding techniques described herein can be implemented by one or more processors that can execute computer software with computer-readable instructions, which can be physically stored in one or more computer-readable media (e.g., hard disk drives). For example, Figure 7 A computer system 700 suitable for implementing certain embodiments of the disclosed subject matter is shown.

[0844] Computer software can be encoded using any suitable machine code or computer language. Mechanisms such as assembling, compiling, and linking can be used to create code that includes instructions that can be executed directly by a computer's central processing unit (CPU), graphics processing unit (GPU), or through interpretation, microcode, etc.

[0845] This instruction can be executed on various types of computers or their components, including, for example, personal computers, tablets, servers, smartphones, gaming devices, and Internet of Things (IoT) devices.

[0846] Figure 7 The components shown for computer system 700 are exemplary in nature and are not intended to impose any limitation on the scope or functionality of computer software implementing embodiments of this disclosure. The configuration of the components should also not be construed as having any dependency or requirement relating to any one or combination of components shown in the exemplary embodiments of computer system 700.

[0847] Computer system 700 may include certain human-machine interface input devices. Such human-machine interface input devices may respond to input from one or more human users via, for example, tactile input (such as keystrokes, swipes, or movement with a data glove), audio input (such as speech or tapping), visual input (such as gestures), or olfactory input (not shown). The human-machine interface device may also be used to capture certain media that are not necessarily directly related to human conscious input, such as audio (such as speech, music, or ambient sound), images (such as scanned images or photographic images obtained from still image capturing devices), and video (such as two-dimensional video or three-dimensional video including stereoscopic video).

[0848] The input human-machine interface device may include one or more of the following (only one of each described): keyboard 701, mouse 702, touchpad 703, touch screen 710, data glove 704, joystick 705, microphone 706, scanner 707, and camera device 708.

[0849] Computer system 700 may also include certain human-machine interface (HMI) output devices. Such HMI output devices can stimulate the senses of one or more human users through, for example, tactile output, sound, light, and smell / taste. Such HMI output devices may include tactile output devices (e.g., tactile feedback via touchscreen 710, data gloves, or joystick 705, but may also include tactile feedback devices that are not used as input devices), audio output devices (e.g., speakers 709, headphones (not shown)), visual output devices (e.g., screens 710, including CRT screens, LCD screens, plasma screens, OLED screens, each with or without touchscreen input capability, each with or without tactile feedback capability—some of which may be able to output two-dimensional or more than three-dimensional visual output in a manner such as stereoscopic image output; virtual reality glasses (not depicted), holographic displays, and ashtrays (not depicted)), and printers (not depicted).

[0850] The computer system 700 may also include human-accessible storage devices and their associated media, such as optical media including CD / DVD ROM / RW 720 with media 721 such as CD / DVD, thumb drives 722, removable hard disk drives or solid-state drives 723, legacy magnetic media such as magnetic tapes and floppy disks (not depicted), devices based on dedicated ROM / ASIC / PLD, such as security dongles (not depicted), etc.

[0851] Those skilled in the art should also understand that the term "computer-readable medium" as used in connection with the presently disclosed subject matter does not cover transmission media, carrier waves, or other transient signals.

[0852] Computer system 700 may also include interfaces to one or more communication networks. These networks can be, for example, wireless, wired connections, or optical networks. Networks can also be local, wide area, metropolitan, vehicle and industrial, real-time, or latency-tolerant networks. Examples of networks include: local area networks such as Ethernet, wireless LANs, cellular networks including GSM, 3G, 4G, 5G, LTE, etc., wired or wireless wide area digital network television including cable television, satellite television, and terrestrial broadcast television, and vehicle and industrial television including CANBus. Some networks typically require external network interface adapters attached to certain general-purpose data ports or peripheral buses (749) (e.g., USB ports of computer system 700); others are typically integrated into the core of computer system 700 by attaching to the system bus as described below (e.g., an Ethernet interface to a PC computer system or a cellular network interface to a smartphone computer system). Using any of these networks, computer system 700 can communicate with other entities. Such communication can be unidirectional, receive-only (e.g., broadcast television), transmit-only (e.g., a CAN bus to some CAN bus device), or bidirectional, such as using a local or wide area digital network to other computer systems. Certain protocols and protocol stacks can be used on each of these networks and network interfaces as described above.

[0853] The aforementioned human-machine interface device, human-machine accessible storage device, and network interface can be attached to the core 740 of the computer system 700.

[0854] The core 740 may include one or more central processing units (CPUs) 741, graphics processing units (GPUs) 742, dedicated programmable processing units in the form of field-programmable gate arrays (FPGAs) 743, hardware accelerators 744 for certain tasks, etc. These devices, along with read-only memory (ROM) 745, random access memory 746, and internal mass storage devices 747 such as internal non-user-accessible hard disk drives (SD drives) or SSDs, can be connected via a system bus 748. In some computer systems, the system bus 748 can be accessed via one or more physical connectors to allow for expansion through additional CPUs, GPUs, etc. Peripheral devices can be attached directly to the core's system bus 748 or via a peripheral bus 749. Peripheral bus architectures include PCI, USB, etc.

[0855] The CPU 741, GPU 742, FPGA 743, and accelerator 744 can execute certain instructions, which can be combined to form the aforementioned computer code. This computer code can be stored in ROM 745 or RAM 746. Transient data can also be stored in RAM 746, while permanent data can be stored, for example, in an internal mass storage device 747. Fast storage and retrieval of any storage device in the storage device can be achieved by using a cache memory, which can be closely associated with one or more CPUs 741, GPUs 742, mass storage devices 747, ROM 745, RAM 746, etc.

[0856] Computer-readable media may have computer code thereon for performing operations of various computer implementations. The media and computer code may be specifically designed and constructed for the purposes of this disclosure, or they may be of a type known and available to those skilled in the art of computer software.

[0857] By way of example and not limitation, a computer system having architecture 700—particularly core 740—can provide functionality by having (one or more) processors (including CPUs, GPUs, FPGAs, accelerators, etc.) execute software embodied in one or more tangible computer-readable media. Such computer-readable media can be media associated with user-accessible mass storage devices as described above, and certain storage devices of the non-transitory core 740, such as core mass storage device 747 or ROM 745. Software implementing various embodiments of this disclosure can be stored in such devices and executed by the core 740. Depending on specific needs, the computer-readable media may include one or more storage devices or chips. The software can cause the core 740—particularly the processors therein (including CPUs, GPUs, FPGAs, etc.)—to execute specific processes or specific portions of specific processes described herein, including defining data structures stored in RAM 746 and modifying such data structures according to the software-defined processes. Alternatively or concurrently, the computer system may provide functionality by means of logic hardwired or otherwise embodied in circuitry (e.g., accelerator 744), which may replace or operate with software to perform a particular process or a particular portion of a particular process described herein. Where appropriate, reference to software may include logic, and vice versa. Where appropriate, reference to computer-readable medium may include circuitry (e.g., integrated circuit (IC)) storing software for execution, circuitry embodying logic for execution, or both. This disclosure includes any suitable combination of hardware and software.

[0858] Although several exemplary embodiments have been described in this disclosure, there are changes, substitutions, and various alternative equivalents that fall within the scope of this disclosure. It will therefore be appreciated that, while not expressly shown or described herein, those skilled in the art will be able to conceive of many systems and methods that embody the principles of this disclosure and thus its spirit and scope.

Claims

1. A decoding method, characterized in that, The method includes: Receive compressed video or image data files; Determine whether to use a first transform core matrix of a first size type or a second transform core matrix of a second size type smaller than the first size type, wherein the first size type is an 8-bit master transform core matrix, the 8-bit master transform core matrix having a core matrix represented by 8 bits and having a size of 64 points or greater; When it is determined that a first transform core matrix of a first size type will be used to decode the video or image data file, an 8-bit DST-7 master transform core matrix is ​​derived based on a set of M unique numbers, and first information is generated to trigger decoding of the video or image data file using the derived master transform core matrix, wherein the first transform core matrix is ​​a DST-7 master transform core matrix represented by 8 bits and having a size of 64 points or greater; and When it is determined that a second transform core matrix of a second size type smaller than the first size type is used to decode the video or image data file, a second transform core matrix is ​​derived based on the M unique numbers, and second information is generated. The second information is used to trigger the decoding of the video or image data file using the derived second transform core matrix. The second transform core matrix is ​​one of DCT-2, DST-7, DCT-8, DST-1, and DCT-5. When the first transform core matrix is ​​a 64-point 8-bit master transform core matrix, it is constructed using 31 integers for constructing a 32-point 8-bit master transform core matrix and an additional 32 integers.

2. A decoding method, characterized in that, The method includes: Receive compressed video or image data files; Determine whether to use a first transform core matrix of a first size type or a second transform core matrix of a second size type smaller than the first size type, wherein the first size type is an 8-bit master transform core matrix, the 8-bit master transform core matrix having a core matrix represented by 8 bits and having a size of 64 points or greater; When it is determined that a first transform core matrix of a first size type will be used to decode the video or image data file, an 8-bit DST-7 master transform core matrix is ​​derived based on a set of M unique numbers, and first information is generated to trigger decoding of the video or image data file using the derived master transform core matrix, wherein the first transform core matrix is ​​a DST-7 master transform core matrix represented by 8 bits and having a size of 64 points or greater; and When it is determined that a second transform core matrix of a second size type smaller than the first size type will be used to decode the video or image data file, a second transform core matrix is ​​derived based on the M unique numbers, and second information is generated. This second information is used to trigger decoding of the video or image data file using the derived second transform core matrix. The second transform core matrix is ​​one of DCT-2, DST-7, DCT-8, DST-1, and DCT-5. When the first transform core matrix is ​​6... The 4-point 8-bit principal transform core matrix is ​​constructed using 31 integers used to construct the 32-point 8-bit principal transform core matrix and an additional 32 integers. The additional 32 integers include: bf, bg, bh, bi, bj, bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb, cc, cd, ce, cf, cg, ch, ci, cj, and ck, plus their respective sign changes. bf, bg, bh, bi, bj, bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb, cc, cd, ce, cf, cg, ch, ci, cj, ck} is equal to {91, 90, 90, 90, 88, 87, 86, 84, 83, 81, 79, 77, 73, 71,69, 65, 62, 59, 56, 52, 48, 44, 41, 37, 33, 28, 24, 20, 15, 11, 7, 2}.

3. An encoding method, characterized in that, The method includes: Receive uncompressed video or image data files; Determine whether to use a first transform core matrix of a first size type or a second transform core matrix of a second size type smaller than the first size type, wherein the first size type is an 8-bit master transform core matrix, the 8-bit master transform core matrix having a core matrix represented by 8 bits and having a size of 64 points or greater; When it is determined that a first transform core matrix of a first size type will be used to encode the video or image data file, an 8-bit DST-7 master transform core matrix is ​​derived based on a set of M unique numbers, and first information is generated to trigger encoding of the video or image data file using the derived master transform core matrix, wherein the first transform core matrix is ​​a DST-7 master transform core matrix represented by 8 bits and having a size of 64 points or greater; and When it is determined that a second transform core matrix of a second size type smaller than the first size type will be used to encode the video or image data file, a second transform core matrix is ​​derived based on the M unique numbers, and second information is generated. The second information is used to trigger the encoding of the video or image data file using the derived second transform core matrix. The second transform core matrix is ​​one of DCT-2, DST-7, DCT-8, DST-1, and DCT-5. When the first transform core matrix is ​​a 64-point 8-bit master transform core matrix, it is constructed using 31 integers for constructing a 32-point 8-bit master transform core matrix and an additional 32 integers.

4. An encoding method, characterized in that, The method includes: Receive uncompressed video or image data files; Determine whether to use a first transform core matrix of a first size type or a second transform core matrix of a second size type smaller than the first size type, wherein the first size type is an 8-bit master transform core matrix, the 8-bit master transform core matrix having a core matrix represented by 8 bits and having a size of 64 points or greater; When it is determined that a first transform core matrix of a first size type will be used to encode the video or image data file, an 8-bit DST-7 master transform core matrix is ​​derived based on a set of M unique numbers, and first information is generated to trigger encoding of the video or image data file using the derived master transform core matrix, wherein the first transform core matrix is ​​a DST-7 master transform core matrix represented by 8 bits and having a size of 64 points or greater; and When it is determined that a second transform core matrix of a second size type smaller than the first size type will be used to encode the video or image data file, a second transform core matrix is ​​derived based on the M unique numbers, and second information is generated. This second information is used to trigger encoding of the video or image data file using the derived second transform core matrix. The second transform core matrix is ​​one of DCT-2, DST-7, DCT-8, DST-1, and DCT-5. When the first transform core matrix is ​​6... The 4-point 8-bit principal transform core matrix is ​​constructed using 31 integers used to construct the 32-point 8-bit principal transform core matrix and an additional 32 integers. The additional 32 integers include: bf, bg, bh, bi, bj, bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb, cc, cd, ce, cf, cg, ch, ci, cj, and ck, plus their respective sign changes. bf, bg, bh, bi, bj, bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb, cc, cd, ce, cf, cg, ch, ci, cj, ck} is equal to {91, 90, 90, 90, 88, 87, 86, 84, 83, 81, 79, 77, 73, 71,69, 65, 62, 59, 56, 52, 48, 44, 41, 37, 33, 28, 24, 20, 15, 11, 7, 2}.

5. The method according to claim 1, 2, 3, or 4, characterized in that, The first transformation core matrix is ​​an 8-point 8-bit DST-7 master transformation core matrix created using 8 integers, including the values ​​of a, b, c, d, e, f, g, and h and their respective sign transformations. The values ​​of the eight integers {a, b, c, d, e, f, g, h} are equal to {17, 32, 46, 60, 71, 78, 85, 86}.

6. The method according to claim 1, 2, 3, or 4, characterized in that, The first transformation core matrix is ​​a 16-point 8-bit DST-7 master transformation core matrix created using 16 integers. These 16 integers include the values ​​of a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, and p, and their respective sign transformations. The values ​​of the 16 integers {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p} are equal to {9, 17, 25, 33, 41, 49, 56, 62, 66, 72, 77, 81, 83, 87, 89, 90}.

7. The method according to claim 1, 2, 3, or 4, characterized in that, The first transformation core matrix is ​​a 32-point 8-bit DST-7 master transformation core matrix created using 32 integers. These 32 integers include the values ​​of a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B, C, D, E, and F, and their respective sign transformations. The values ​​of the 32 integers {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B, C, D, E, F} are equal to {4, 9, 13, 17, 21, 26, 30, 34, 38, 42, 45, 50, 53, 56, 60, 63, 66, 68, 72, 74, 77, 78, 80, 82, 84, 85, 86, 88, 88, 89, 90, 90}.

8. The method according to claim 1, 2, 3, or 4, characterized in that, The first transformation core matrix is ​​a 64-point 8-bit DST-7 master transformation core matrix created using 64 integers. These 64 integers include the values ​​of aa, ab, ac, ad, ae, af, ag, ah, ai, aj, ak, al, am, an, ao, ap, aq, ar, as, at, au, av, aw, ax, ay, az, ba, bb, bc, bd, be, bf, bg, bh, bi, bj, bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb, cc, cd, ce, cf, cg, ch, ci, cj, ck, and cl, and their respective sign transformations. The values ​​of the 64 integers {aa, ab, ac, ad, ae, af, ag, ah, ai, aj, ak, al, am, an, ao, ap, aq, ar, as, at, au, av, aw, ax, ay, az, ba, bb, bc, bd, be, bf, bg, bh, bi, bj, bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb, cc, cd, ce, cf, cg, ch, ci, cj, ck, cl} are equal to {2, 5, 7, 8, 11, 13, 15}. ,17,20 ,22 ,23 ,26 ,29 ,30 ,32 ,34 ,37 ,38 ,41 ,42 ,44 ,46 ,48 ,49 ,52 ,53 ,55 ,58 ,59 ,60 ,62 ,64 ,65 ,66 ,68 ,69 ,72 ,72 ,74 ,73 ,76 ,77 ,78 ,79 ,81 ,80 ,82 ,83 ,85 ,84 ,85 ,86 ,87 ,87 ,88 ,89 ,89 ,90 ,89 ,90 ,90 ,90 ,90 ,90 ,90}.

9. The method according to claim 1, 2, 3, or 4, characterized in that, The second transform core matrix is ​​an 8-point 8-bit DCT-8 master transform core matrix created using 8 integers, including the values ​​of a, b, c, d, e, f, g, and h and their respective sign transformations. The values ​​of the eight integers {a, b, c, d, e, f, g, h} are equal to {86, 85, 78, 71, 60, 46, 32, 17}.

10. The method according to claim 1, 2, 3, or 4, characterized in that, The second transform core matrix is ​​a 16-point 8-bit DCT-8 master transform core matrix created using 16 integers. These 16 integers include the values ​​of a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, and p, and their respective sign transformations. The values ​​of the 16 integers {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p} are equal to {90, 89, 87, 83, 81, 77, 72, 66, 62, 56, 49, 41, 33, 25, 17, 9}.

11. The method according to claim 1, 2, 3, or 4, characterized in that, The second transformation core matrix is ​​a 32-point 8-bit DCT-8 master transformation core matrix created using 32 integers. These 32 integers include the values ​​of a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B, C, D, E, and F, and their respective sign transformations. The 32 integers {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B, C, D, E, F} take values ​​equal to {90, 90, 89, 88, 88, 86, 85, 84, 82, 80, 78, 77, 74, 72, 68, 66, 63, 60, 56, 53, , 50 ,45 , 42 ,38 ,34 ,30 ,26 ,21 ,17 ,13 ,9 ,4}。 12. The method according to claim 1, 2, 3, or 4, characterized in that, The second transformation core matrix is ​​a 64-point 8-bit DCT-8 master transformation core matrix created using 64 integers. These 64 integers include the values ​​of aa, ab, ac, ad, ae, af, ag, ah, ai, aj, ak, al, am, an, ao, ap, aq, ar, as, at, au, av, aw, ax, ay, az, ba, bb, bc, bd, be, bf, bg, bh, bi, bj, bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb, cc, cd, ce, cf, cg, ch, ci, cj, ck, and cl, along with their respective sign transformations. The values ​​of the 64 integers {aa, ab, ac, ad, ae, af, ag, ah, ai, aj, ak, al, am, an, ao, ap, aq, ar, as, at, au, av, aw, ax, ay, az, ba, bb, bc, bd, be, bf, bg, bh, bi, bj, bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb, cc, cd, ce, cf, cg, ch, ci, cj, ck, cl} are equal to {90, 90, 90, 90, 89}. ,90,89 ,89 ,88 ,87 ,87 ,86 ,85 ,84 ,85 ,83 ,82 ,80 ,81 ,79 ,78 ,77 ,76 ,73 ,74 ,72 ,72 ,69 ,68 ,66 ,65 ,64 ,62 ,60 ,59 ,58 ,55 ,53 ,52 ,49 ,48 ,46 ,44 ,42 ,41 ,38 ,37 ,34 ,32 ,30 ,29 ,26 ,23 ,22 ,20 ,17 ,15 ,13 ,11 ,8 ,7,5,2}.

13. The method according to claim 1, 2, 3, or 4, characterized in that, When deriving the N-point 8-bit DCT-8 transform core matrix or the N-point 8-bit DST-7 master transform core matrix, the M unique numbers used to create the N-point DCT-8 core matrix and the M unique numbers used to create the N-point DST-7 core matrix are the same set of M unique numbers with the same values, and M = N.

14. A decoding device, characterized in that, The device includes: Memory, which stores instructions; and A processor that communicates with the memory, wherein, when the processor executes the instructions, the processor is configured to cause the device to perform the method according to any one of claims 1, 2, 5 to 13.

15. An encoding device, characterized in that, The device includes: Memory, which stores instructions; and A processor that communicates with the memory, wherein, when the processor executes the instructions, the processor is configured to cause the device to perform the method according to any one of claims 3 to 13.

16. A non-volatile computer-readable storage medium, characterized in that, The system stores instructions that, when executed by a computer used for encoding or decoding, cause the computer to perform the method described in any one of claims 1-13.

17. A computer device, characterized in that, The device includes one or more processors and one or more memories, the one or more memories storing at least one instruction, the at least one instruction being loaded and executed by the one or more processors to implement the method as claimed in any one of claims 1 to 13.

18. A method for storing video bitstreams, characterized in that, The video encoding method according to any one of claims 3-13 is used to generate a video bitstream; and the video bitstream is stored.

19. A method for transmitting a video bitstream, characterized in that, The video encoding method according to any one of claims 3-13 is used to generate a video bitstream; and the video bitstream is transmitted.

20. A computer-readable storage medium storing a computer program / instructions and a video bitstream thereon, characterized in that, When executed by a processor, the computer program / instructions implement the steps of the video encoding method according to any one of claims 3-13 to generate the video bitstream.

Images