Transcendental function approximation apparatus and method
First Claim
1. A function approximation method wherein the function is evaluated over a domain comprising a plurality of the domain wherein each element of the domain is addressable by a unique N bit function argument wherein the function approximation method comprises the steps of:
- (a) dividing each N bit function into a L most significant bit argument and a P least significant bit offset argument for each element of the domain;
(b) storing an N bit regional approximation of the transcendental function, a Q bit profile index, and an R bit offset shift count, in a regional approximation lookup table for each L most significant bit argument wherein the regional approximation lookup table is addressed by the L most significant bit argument for each of the plurality of elements of the domain;
(c) concentrating the P least significant bit offset argument with the Q bit profile index to arrive at a P+Q bit address for each of the plurality of elements of the domain;
(d) storing a P bit offset value and a sign magnitude value in an offset lookup table for each P least significant bit offset argument wherein the offset lookup table is addressed by the P+Q bit address for each set of 2P elements for each one of the plurality of elements of the domain; and
evaluating the value of the function at any one of the plurality of elements of the domain.
1 Assignment
0 Petitions
Accused Products
Abstract
Transcendental function approximation using a regional approximation look-up table, offset lookup table, scaling shifter and interpolation adder/subtractor. Rapid fixed-point arithmetic calculations can be accomplished which approximate values of transcendental functions to a predetermined accuracy. An N bit argument is used to produce an N bit result allowing the placement of the radix point in the two numbers to be different. Different parts of the input argument are fed in parallel to the regional approximation look-up table and the offset lookup table. A scaling shifter converts the output of the offset lookup table and regional lookup table to a result usable by the interpolation adder/subtractor processor. The regional approximation lookup table also provides information to the interpolation processor which provides the N bit approximation.
25 Citations
20 Claims
-
1. A function approximation method wherein the function is evaluated over a domain comprising a plurality of the domain wherein each element of the domain is addressable by a unique N bit function argument wherein the function approximation method comprises the steps of:
-
(a) dividing each N bit function into a L most significant bit argument and a P least significant bit offset argument for each element of the domain; (b) storing an N bit regional approximation of the transcendental function, a Q bit profile index, and an R bit offset shift count, in a regional approximation lookup table for each L most significant bit argument wherein the regional approximation lookup table is addressed by the L most significant bit argument for each of the plurality of elements of the domain; (c) concentrating the P least significant bit offset argument with the Q bit profile index to arrive at a P+Q bit address for each of the plurality of elements of the domain; (d) storing a P bit offset value and a sign magnitude value in an offset lookup table for each P least significant bit offset argument wherein the offset lookup table is addressed by the P+Q bit address for each set of 2P elements for each one of the plurality of elements of the domain; and evaluating the value of the function at any one of the plurality of elements of the domain. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
-
-
11. A function approximation apparatus wherein the function is evaluated over a domain comprising a plurality of elements of the domain wherein each element of the domain is addressable by a unique N bit function argument wherein the function approximation apparatus comprises:
-
(a) a means for dividing each N bit function argument into a L most significant bit argument and a P least significant bit offset argument for each element of the domain; (b) a means for storing an N bit regional approximation of the transcendental function, a Q bit profile index, and an R bit offset shift count, in a regional approximation lookup table for each L most significant bit argument wherein the regional approximation lookup table is addressed by the L most significant bit argument for each of the plurality of elements of the domain; (c) a means for concatenating the P least significant bit offset argument with the Q bit profile index to arrive at a P+Q bit address for each of the plurality of elements of the domain; (d) a means for storing a P bit offset value and a sign magnitude value in an offset lookup table for each P least significant bit offset argument wherein the offset lookup table is addressed by the P+Q bit address for each set of 2P elements for each one of the plurality of elements of the domain; and (e) means for evaluating the value of the function at any one of the plurality of elements of the domain. - View Dependent Claims (12, 13, 14, 15, 16, 17, 18, 19, 20)
-
Specification