Abstract: A method and apparatus for efficiently adding and subtracting multiple digit decimal numbers represented as a series of 8-bit bytes, each 8-bit byte representing one digit of a decimal number. In accordance with the present invention, numeric values are stored internally within a computer in a new format, referred to as "X7B". Numeric input into the computer can be in any form, such as binary, ASCII, EBCDIC, X7B, etc. X7B values are computed by adding the 8-bit binary representation of each decimal digit to a binary value of"0111 1011" (i.e., "7B" hexadecimal).

Abstract: A method and apparatus for increasing the speed of a search through leaf nodes of an inventive key index tree structure, known as a "Q-tree". The present invention identifies "decision-bits" within leaf node entries and uses these decision-bits to accelerate searches for a particular record or for a record adjacent to which a new record is to be inserted. A decision-bit is a particular type of distinction-bit having the smallest value and associated with a search key a greater value then the keys associated with other distinction-bits of the same value within a specified search range. Each decision-bit divides a search range into "left" and "right" parts. One of the two parts will constitute a "new" search range. A "quit-bit" having an ordinal number equal to the value of the decision-bit for the search range, is tested. If the quit-bit is "on", then the right, or greater value, part becomes the new search range. Otherwise, the left, or lesser value, part becomes the new search range.

Abstract: A method and apparatus for performing decimal division using a computer that does not have the capability to perform single instruction decimal multiplication or division. A divisor is normalized such that the value of the first digit of the divisor is not less than 5. Trial quotient digits within a trial quotient table are predetermined. A multiples table comprises multiples of the normalized divisor. The most significant digits of the normalized divisor and the most significant digits of each partial dividend are used to locate trial quotient digits within the trial quotient digit table. The trial quotient digits are used to locate multiples within the multiples table. A single subtraction (or addition) operation from a partial dividend can be used to determine whether the trial quotient digit is the actual quotient digit.

Abstract: A method and apparatus for increasing the speed of a search through leaf nodes of an inventive key index tree structure, known as a "Q-tree". The present invention identifies "decision-bits" within leaf node entries and uses these decision-bits to accelerate searches for a particular record or for a record adjacent to which a new record is to be inserted. A decision-bit is a particular type of distinction-bit having the smallest value and associated with a search key a greater value then the keys associated with other distinction-bits of the same value within a specified search range. Each decision-bit divides a search range into "left" and "right" parts. One of the two parts will constitute a "new" search range. A "quit-bit" having an ordinal number equal to the value of the decision-bit for the search range, is tested. If the quit-bit is "on", then the right, or greater value, part becomes the new search range. Otherwise, the left, or lesser value, part becomes the new search range.

Abstract: A method for sorting data in a computer data storage system that has particular advantages in implementing a key index tree structure. The sorting method uses buffer-size substrings to sort strings of key records into a linked list structure that can be directly transformed into an index tree. The sorting method also may be used for sorting large sets of data records in place on a computer storage system. The method further integrates prefix compression and suffix compression of key records with the sorting method to reduce the number of input/output operations required to create a more compact key index tree structure.

Abstract: A method for sorting data in a computer data storage system that has particular advantages in implementing a key index tree structure. The sorting method uses buffer-size substrings to sort strings of key records into a linked list structure that can be directly transformed into an index tree. The sorting method also may be used for sorting large sets of data records in place on a computer storage system.

Abstract: An improved method for indexing and accessing data stored in a computer storage system, comprising a multi-way tree structure having interconnected branch nodes and leaf nodes. The leaf nodes contain a large number of distinction bits, rather than a smaller number of search keys as known in the prior art. A distinction bit is determined by comparing two selected search keys and determining the ordinal number of the first bit that is different between the two keys. The density of distinction bit entries in the leaf nodes permits shorter access times to obtain data records in a computer storage system.