A method for protecting data in a data memory against an undetected change, wherein a functional variable x is encoded via a value, an input constant, an input signature and a timestamp D into a coded variable, where the functional variable is normalized relative to a base to form the integer value from the functional variable.

A method for protecting data in a data memory against an undetected change, wherein a functional variable x is encoded via a value, an input constant, an input signature and a timestamp D into a coded variable, where the functional variable is normalized relative to a base to form the integer value from the functional variable.

A hardware module comprising at least one of: one or more field programmable gate arrays and one or more application specific integrated circuits configured to: receive a number in floating-point representation at a first precision level, the number comprising an exponent and a first mantissa; apply a first random number to the first mantissa to generate a first carry; truncate the first mantissa to a level specified by a second precision level; add the first carry to the least significant bit of the mantissa truncated to the level specified by the second precision level to form a mantissa for the number in floating-point representation at the second precision level.

A hardware module comprising at least one of: one or more field programmable gate arrays and one or more application specific integrated circuits configured to: receive a number in floating-point representation at a first precision level, the number comprising an exponent and a first mantissa; apply a first random number to the first mantissa to generate a first carry; truncate the first mantissa to a level specified by a second precision level; add the first carry to the least significant bit of the mantissa truncated to the level specified by the second precision level to form a mantissa for the number in floating-point representation at the second precision level.

A database engine receives a human-readable database query that includes a subquery, and parses the database query to build an operator tree. The operator tree includes a subtree corresponding to the subquery. The database engine estimates the number of rows that will accessed when the subtree is executed and estimates the fraction of the cardinality of rows that will be filtered out by subsequent operations in the operator tree. In accordance with a determination that the estimated fraction exceeds a first threshold, the database engine inserts a domain constraint into the subtree that restricts rows retrieved by execution of the subtree, thereby forming a modified operator tree. The database engine executes the modified operator tree to form a final result set corresponding to the database query and returns the final result set.

A method compares text strings having Unicode encoding. The method receives a first string S=s.sub.1s.sub.2 . . . s.sub.n and a second string T=t.sub.1t.sub.2 . . . t.sub.m, where s.sub.1, s.sub.2, . . . , s.sub.n and t.sub.1, t.sub.2, . . . , t.sub.m are Unicode characters. The method computes a first string weight for the first string S according to a weight function . When S consists of ASCII characters, (S)=S. When S consists of ASCII characters and some accented ASCII characters that are replaceable by ASCII characters, (S)=g(s.sub.1)g(s.sub.2) . . . g(s.sub.n), where g(s.sub.i)=s.sub.i when s.sub.i is an ASCII character and g(s.sub.i)=s.sub.i when s.sub.i is an accented ASCII character that is replaceable by the corresponding ASCII character s.sub.i. The method also computes a second string weight for the second text string T. Equality of the strings is tested using the string weights.

A method compares text strings having Unicode encoding. The method receives a first string S=s.sub.1s.sub.2 . . . s.sub.n and a second string T=t.sub.1t.sub.2 . . . t.sub.m, where s.sub.1, s.sub.2, . . . , s.sub.n and t.sub.1, t.sub.2, . . . , t.sub.m are Unicode characters. The method computes a first string weight for the first string S according to a weight function . When S consists of ASCII characters, (S)=S. When S consists of ASCII characters and some accented ASCII characters that are replaceable by ASCII characters, (S)=g(s.sub.1)g(s.sub.2) . . . g(s.sub.n), where g(s.sub.i)=s.sub.i when s.sub.i is an ASCII character and g(s.sub.i)=s.sub.i when s.sub.i is an accented ASCII character that is replaceable by the corresponding ASCII character s.sub.i. The method also computes a second string weight for the second text string T. Equality of the strings is tested using the string weights.

A compression system includes an encoder and a decoder. The encoder can be deployed by a sender system to encode a tensor for transmission to a receiver system, and the decoder can be deployed by the receiver system to decode and reconstruct the encoded tensor. The encoder receives a tensor for compression. The encoder also receives a quantization mask and probability data associated with the tensor. Each element of the tensor is quantized using an alphabet size allocated to that element by the quantization mask data. The encoder compresses the tensor by entropy coding each element using the probability data and alphabet size associated with the element. The decoder receives the quantization mask data, the probability data, and the compressed tensor data. The quantization mask and probabilities are used to entropy decode and subsequently reconstruct the tensor.

A compression system includes an encoder and a decoder. The encoder can be deployed by a sender system to encode a tensor for transmission to a receiver system, and the decoder can be deployed by the receiver system to decode and reconstruct the encoded tensor. The encoder receives a tensor for compression. The encoder also receives a quantization mask and probability data associated with the tensor. Each element of the tensor is quantized using an alphabet size allocated to that element by the quantization mask data. The encoder compresses the tensor by entropy coding each element using the probability data and alphabet size associated with the element. The decoder receives the quantization mask data, the probability data, and the compressed tensor data. The quantization mask and probabilities are used to entropy decode and subsequently reconstruct the tensor.

A method compares text strings having Unicode encoding. The method receives a first string S=s.sub.1 s.sub.2 . . . s.sub.n and a second string T=t.sub.1 t.sub.2 . . . t.sub.m, where s.sub.1, s.sub.2, . . . , s.sub.n and t.sub.1, t.sub.2, . . . , t.sub.m are Unicode characters. The method computes a first string weight for the first string S according to a weight function . When S consists of ASCII characters, (S)=S. When S consists of ASCII characters and some accented ASCII characters that are replaceable by ASCII characters, (S)=g(s.sub.1) g(s.sub.2) . . . g(s.sub.n), where g(s.sub.i)=s.sub.i when s.sub.i is an ASCII character and g(s.sub.i)=s.sub.i when s.sub.i is an accented ASCII character that is replaceable by the corresponding ASCII character s.sub.i. When S includes one or more non-replaceable non-ASCII characters, the first string weight concatenates an ASCII weight prefix .sub.A (S) and a Unicode weight suffix .sub.U(S). The method also computes a second string weight for the second text string T. Equality of the strings is tested using the string weights.