US 2002/0165890 A1Published application

Method and apparatus for linear interpolation using gradient tables

AssigneeTexas Instruments Incorporated

InventorVivek Kumar Thakur

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Abstract

This invention is a method and apparatus for interpolation which enables simpler and cost efficient implementation in hardware or software. A function table stores values of the function at addresses corresponding to the argument points where the function is known. The input value enables identification of the function values for arguments immediately below and above the input value. Respective bits of the absolute value of the difference between these two function values enables corresponding gradient value tables. A set of gradient values are stored in these gradient value tables. The least significant bits of the input value, those bits less significant than the arguments of the stored function values, address entries in the enabled gradient value tables. The desired interpolation value is the sum of the first function value and the gradient value recalled from the gradient tables.

Claims6

Dependent claims

A method of forming an interpolation value of a function for input values between argument values for which the function value is known, comprising the steps of:

storing in a memory function values corresponding to discrete values of an argument of the function for which the function value is known;
receiving an input value;
determining a first argument value for which the function value is known immediately less than the input value;
forming a least significant bit difference between the input value and the first argument value having a predetermined number of less significant bits, each such bit less significant than a least significant bit of the first argument value;
determining a second argument value for which the function value is known immediately greater than the input value;
recalling from the memory a first function value for the first argument value;
recalling from the memory a second function value for the second argument value;
forming an absolute value of a difference between the second function value minus the first function value;
determining a sign of the difference between the second function value minus the first function value;
storing in a memory a set of gradient values for each bit of the absolute value of the difference and each of the predetermined number of less significant bits;
recalling from the memory gradient values for the least significant bit difference corresponding to bits where the absolute value of the difference is 1;
summing the recalled gradient values;
if the sign of the difference is 1, adding the sum of the recalled gradient values to the first function value;
and
if the sign of the difference is 0, subtracting the sum of the recalled gradient values from the first function value.

12 more elements

An apparatus for interpolation comprising:

an input for receiving an input value;
a function value lookup table memory connected to the input storing function values corresponding to discrete values of an argument of the function for which the function value is known, the function value lookup table memory addressed by a first predetermined number of most significant bits of said input value to recall a first function value corresponding to said first predetermined number of most significant bits of the input value and a second function value corresponding to a next greater argument;
a subtractor connected to said function value lookup table, said subtractor forming an absolute value of a difference of the second function value minus the first function value and an indication of the sign of the difference of the second function value minus the first function value;
a set of gradient value lookup table memories, one for each bit of a second predetermined number of least significant bits of said absolute value of said difference, each gradient value lookup table memory having an enable input connected to a corresponding one of said second predetermined number of least significant bits of said absolute value of said difference and addressed by second predetermined number of least significant bits of said input value and storing a gradient value for each the predetermined number of less significant bits;
a set of first adders connected to said set of gradient value lookup table memories, said set of first adders adding the gradient values of enabled ones of the gradient value lookup table memories;
and
a second adder connected to said function value lookup table memory, said subtractor and said set of first adders, said second adder
if the sign of the difference is positive, adding the sum of the recalled gradient values to the first function value, and
if the sign of the difference is negative, subtracting the sum of the recalled gradient values from the first function value.

6 more elements

Dependencies are inferred from the claim text.