Power series truncation using constant tables for function interpolation in transcendental functions

A computer system, comprising:

• one or more processors coupled to one or more memories;
• the processor operative to interpolate a primary interval for convergence of at least one power series in a transcendental function while selecting a number of one or more interpolation points for a truncated expansion of the at least one power series by a selected order of truncation;
• the processor operative to evaluate a function and at least one derivative of the function of the truncated expansion of the selected order of truncation at the one or more interpolation points;
• the processor operative to save each separate value evaluated for the function and each of the at least one derivative in a table;
• wherein the table is looked up for efficiently computing a result of the truncated expansion of the at least one power series;
• the processor operative, responsive to saving the table, to compute an index into the table for a particular interpolation point of the one or more interpolation points in a truncated expansion by rotating, shifting, and masking operations to a scaled convergent boundary value;
• the processor operative to look up at least two values at the index into the table;
• the processor operative to compute a result of the sum of the looked up at least two values;
• and
• the processor operative to return the result for the particular interpolation point as the result of the transcendental function.

A computer program product comprising one or more computer-readable storage devices and program instructions, stored on at least one of the one or more storage devices, the stored program instructions comprising:

• program instructions to interpolate a primary interval for convergence of at least one power series in a transcendental function while selecting a number of one or more interpolation points for a truncated expansion of the at least one power series by a selected order of truncation;
• program instructions to evaluate a function and at least one derivative of the function of the truncated expansion of the selected order of truncation at the one or more interpolation points;
• program instructions to save each separate value evaluated for the function and each of the at least one derivative in a table, wherein the table is looked up for efficiently computing a result of the truncated expansion of the at least one power series;
• program instructions to, responsive to saving the table, compute an index into the table for a particular interpolation point of the one or more interpolation points in a truncated expansion by rotating, shifting, and masking operations to a scaled convergent boundary value;
• program instructions to look up at least two values at the index into the table;
• program instructions to compute a result of the sum of the looked up at least two values;
• and
• program instructions to return the result for the particular interpolation point as the result of the transcendental function.