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 by:
• computing a set of scaled values for one or more convergence boundaries of the truncated expansion for a total number of values to be stored in the table;
• for each index value up to a value of the number of the one or more interpolation points, evaluating the function and the at least one derivative of the function of the truncated expansion converging in the set of scaled values to compute separate constant values for each of the primary function and each at least one derivative;
• and
• for each index value, adding each separate constant value to the table with a separate index value;
• and
• 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.

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 by:
• computing a set of scaled values for one or more convergence boundaries of the truncated expansion for a total number of values to be stored in the table;
• for each index value up to a value of the number of the one or more interpolation points, evaluating the function and the at least one derivative of the function of the truncated expansion converging in the set of scaled values to compute separate constant values for each of the primary function and each at least one derivative;
• and
• for each index value, adding each separate constant value to the table with a separate index value;
• and
• 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.