Abstract: Herein are techniques for dynamic aggregation of results of a database request, including concurrent grouping of result items in memory based on quasi-dense keys. Each of many computational threads concurrently performs as follows. A hash code is calculated that represents a particular natural grouping key (NGK) for an aggregate result of a database request. Based on the hash code, the thread detects that a set of distinct NGKs that are already stored in the aggregate result does not contain the particular NGK. A distinct dense grouping key for the particular NGK is statefully generated. The dense grouping key is bound to the particular NGK. Based on said binding, the particular NGK is added to the set of distinct NGKs in the aggregate result.

Abstract: Herein are techniques for dynamic aggregation of results of a database request, including concurrent grouping of result items in memory based on quasi-dense keys. Each of many computational threads concurrently performs as follows. A hash code is calculated that represents a particular natural grouping key (NGK) for an aggregate result of a database request. Based on the hash code, the thread detects that a set of distinct NGKs that are already stored in the aggregate result does not contain the particular NGK. A distinct dense grouping key for the particular NGK is statefully generated. The dense grouping key is bound to the particular NGK. Based on said binding, the particular NGK is added to the set of distinct NGKs in the aggregate result.

Abstract: Herein are techniques for dynamic aggregation of results of a database request, including concurrent grouping of result items in memory based on quasi-dense keys. Each of many computational threads concurrently performs as follows. A hash code is calculated that represents a particular natural grouping key (NGK) for an aggregate result of a database request. Based on the hash code, the thread detects that a set of distinct NGKs that are already stored in the aggregate result does not contain the particular NGK. A distinct dense grouping key for the particular NGK is statefully generated. The dense grouping key is bound to the particular NGK. Based on said binding, the particular NGK is added to the set of distinct NGKs in the aggregate result.

Abstract: Techniques described herein perform spherical PIP analysis by detecting whether a test ray (defined by a test point (TP) and a point (EP) that is external to a spherical polygon) crosses edge arcs (“edges”) of the polygon based on relative orientations of vertices of the test ray and edges. A classifier vector (CV) for a test ray is calculated based on the cross-product of the TP and the EP. Using the CV, the orientation of each vertex of the polygon with respect to the test ray is determined. Candidate edges having vertices with opposite orientations with respect to the test ray are identified. Crossing edges are determine by calculating CVs for each candidate edge, and determining orientations of the TP and EP with respect to each candidate edge. A set of crossing edges is determined, where the TP and the EP have opposite orientations with respect to each crossing edge.

Abstract: Herein are techniques for dynamic aggregation of results of a database request, including concurrent grouping of result items in memory based on quasi-dense keys. Each of many computational threads concurrently performs as follows. A hash code is calculated that represents a particular natural grouping key (NGK) for an aggregate result of a database request. Based on the hash code, the thread detects that a set of distinct NGKs that are already stored in the aggregate result does not contain the particular NGK. A distinct dense grouping key for the particular NGK is statefully generated. The dense grouping key is bound to the particular NGK. Based on said binding, the particular NGK is added to the set of distinct NGKs in the aggregate result.

Abstract: Herein are techniques for dynamic aggregation of results of a database request, including concurrent grouping of result items in memory based on quasi-dense keys. Each of many computational threads concurrently performs as follows. A hash code is calculated that represents a particular natural grouping key (NGK) for an aggregate result of a database request. Based on the hash code, the thread detects that a set of distinct NGKs that are already stored in the aggregate result does not contain the particular NGK. A distinct dense grouping key for the particular NGK is statefully generated. The dense grouping key is bound to the particular NGK. Based on said binding, the particular NGK is added to the set of distinct NGKs in the aggregate result.

Abstract: Techniques described herein perform spherical PIP analysis by detecting whether a test ray (defined by a test point (TP) and a point (EP) that is external to a spherical polygon) crosses edge arcs (“edges”) of the polygon based on relative orientations of vertices of the test ray and edges. A classifier vector (CV) for a test ray is calculated based on the cross-product of the TP and the EP. Using the CV, the orientation of each vertex of the polygon with respect to the test ray is determined. Candidate edges having vertices with opposite orientations with respect to the test ray are identified. Crossing edges are determine by calculating CVs for each candidate edge, and determining orientations of the TP and EP with respect to each candidate edge. A set of crossing edges is determined, where the TP and the EP have opposite orientations with respect to each crossing edge.

Abstract: Herein are techniques for dynamic aggregation of results of a database request, including concurrent grouping of result items in memory based on quasi-dense keys. Each of many computational threads concurrently performs as follows. A hash code is calculated that represents a particular natural grouping key (NGK) for an aggregate result of a database request. Based on the hash code, the thread detects that a set of distinct NGKs that are already stored in the aggregate result does not contain the particular NGK. A distinct dense grouping key for the particular NGK is statefully generated. The dense grouping key is bound to the particular NGK. Based on said binding, the particular NGK is added to the set of distinct NGKs in the aggregate result.