Granted Patent B2

US 7,657,589 · App. 11/207,024 · Granted Feb 2, 2010

Abstract

Claims (85)

1. A method of generating a fixed point approximation, comprising:

determining a value, denoted N, of the most significant bit in x to serve as an index into a table that contains fixed-point representations of x (N-fractional — bits)y , wherein the retrieved value is denoted as v 1 , and storing the value in a computer readable medium;

forming another index, denoted M, from the k o bits immediately following the most significant bit, wherein M is used as an index to address a second table that contains two output values per table entry:

v 2 =(1 +a 1 2 −1 +a 2 2 −2 + . . . +a k o 2 −k o ) y ;

and

v 3 =y/( 1 +a 1 2 −1 + . . . +a k o 2 −k o );

and storing the two values;

creating a fixed-point number from remaining bits of x if any exist that directly follow the index M;

inserting these remaining bits into the created number starting at the k o +1 fractional-bit to get a result, wherein both the integer-bits and the first k o fractional-bits of the result are all zero, and wherein the remaining bits of the result are the remaining bits of x to generate a second result v 4 , and storing the second result;

computing the final result: x y ≈v 1 ×v 2 ×[1+(v 3 ×v 4 )] using fixed-point arithmetic to generate said fixed point approximation used by an electronic device.

2. A method according to claim 1 , wherein the value of M is calculated based on bits immediately following the most significant bit.

3. A system configured to generate a fixed point approximation comprising:

a processor configured to execute code to determine the most significant bit of a number and to generate an index value based on the value of most significant bit;

a first lookup table configured to store data values of fixed-point representations of x (N-fractional — bits)y , wherein the processor is further configured to retrieve a value based on the index value to retrieve a first term, denoted as v 1 ;

a second lookup table configured to store coefficient values, wherein the processor is configured to generate a second term based on bits following the most significant bit and the (1+a 1 2 −1 +a 2 2 −2 + . . . +a k o 2 −k o ) y values are stored in the second lookup table, wherein the table has an additional output, y/(1+a 1 2 −1 + . . . +a k o 2 −k o ), used for the third term;

wherein the processor is further configured to retrieve the third term, multiplying the third term with the remaining bits of the input and adding 1 to the result to generate an intermediate term; and wherein the processor is further configured to multiply the first, second and intermediate terms together to generate a fixed point approximation used by an electronic device.

4. An electronic method of generating a fixed point approximation of a number x using a data processor device, comprising:

locating the most significant bit of x;

generating a first index value associated with the most significant bit of x;

retrieving a value from a table that contains fixed-point-representation v 1 ;

storing the value v 1 ;

generating a second index from a number of bits, k o bits, immediately following the most significant bit;

addressing a second table to retrieve two output values corresponding to the second index value;

storing the two output values as v 2 and v 3 ;

creating a fixed-point number from remaining bits of x if any exist that directly follow the k o bits;

inserting these remaining bits into the created number starting at the k o +1 fractional-bit to get a result, wherein the remaining bits of the result are the remaining bits of x to generate a second result v 4 ;

storing the second result v 4 ;

computing the final result: x y =v 1 ×v 2 ×[1+(v 3 ×v 4 )] using fixed-point arithmetic to generate a fixed point approximation used by an electronic device.

5. A method according to claim 4 , wherein the values of v 2 and v 3 are

v 2 =(1 +a 1 2 −1 +a 2 2 −2 + . . . +a k o 2 −k o ) y ;

and

v 3 =y /(1 +a 1 2 −1 + . . . +a k o 2 −k o );

respectively.

6. An electronic method of generating a fixed point approximation of a number x with an electronic data processor, comprising:

locating the most significant bit of x;

retrieving a first value from electronic data storage, where the first value is based on a first index value generated from the most significant bit and contains fixed-point representation v 1 located in a first table in storage;

retrieving two output values, v 2 and v 3 , corresponding to a second index value generated from a number of bits, k o bits, immediately following the most significant bit, where the two output values are retrieved from a second table in electronic data storage;

generating a fourth value v 4 corresponding to fractional bits following the k o bits;

computing the final result: x y ≈v 1 ×v 2 ×[1+(v 3 ×v 4 )] using fixed-point arithmetic logic to generate a fixed point approximation used by an electronic device.

7. A method according to claim 6 , further comprising:

creating a fixed-point number from remaining bits of x if any exist that directly follow the k o bits; and

inserting the fixed point number into the created number starting at the k o +1 fractional-bit to get a result, wherein the remaining bits of the result are the remaining bits of x to generate a second result v 4 .

8. An electronic method of generating a fixed point approximation of a number x with an electronic data processor, comprising:

determining a value, denoted N, of the most significant bit in x to serve as an index into a table that contains fixed-point representations of x (N-fractional — bits)y , wherein the retrieved value is denoted as v 1 , and storing the value;

forming another index, denoted M, from the k o bits immediately following the most significant bit, wherein M is used as an index to address a second table that contains two output values per table entry:

v 2 =(1 +a 1 2 −1 +a 2 2 −2 + . . . +a k o 2 −k o ) y ;

and

v 3 ′=y ×(1 +a 1 2 −1 +a 2 2 −2 + . . . +a k o 2 −k o ) y /(1 +a 1 2 −1 + . . . +a k o 2 −k o );

and storing the two values;

creating a fixed-point number from remaining bits of x if any exist that directly follow the index M;

inserting these remaining bits into the created number starting at the k o +1 fractional-bit to get a result, wherein both the integer-bits and the first k o fractional-bits of the result are all zero, and wherein the remaining bits of the result are the remaining bits of x to generate a second result v 4 , and storing the second result;

computing the final result: x y ≈v 1 ×[v 2 +(v′ 3 ×v 4 )] using fixed-point arithmetic to generate a fixed point approximation used by an electronic device.

9. A method according to claim 8 , wherein the value of M is calculated based on bits immediately following the most significant bit.

10. A system configured to generate a fixed point approximation comprising:

a processor configured to execute code to determine the most significant bit of a number and to generate an index value based on the value of most significant bit;

a first lookup table configured to store data values of fixed-point representations of x (N-fractional — bits)y , wherein the processor is further configured to retrieve a value based on the index value to retrieve a first term;

a second lookup table configured to store coefficient values, wherein the processor is configured to generate a second term based on bits following the most significant bit and the (1+a 1 2 −1 +a 2 2 −2 + . . . +a k o 2 −k o ) y values are stored in the second lookup table, wherein the table has an additional output, y×(1+a 1 2 −1 +a 2 2 −2 + . . . +a k o 2 −k o ) y /(1+a 1 2 −1 + . . . +a k o 2 −k o ), used for the third term;

wherein the processor is further configured to retrieve the third term, multiplying the third term with the remaining bits of the input and adding 1 to the result to generate an intermediate term; and

wherein the processor is further configured to multiply the first, second and intermediate terms together to generate a fixed point approximation used by an electronic device.

11. An electronic method of generating a fixed point approximation, comprising:

locating the most significant bit of x;

generating a first index value associated with the most significant bit of x;

retrieving a value from a table that contains fixed-point representation v 1 ;

storing the value v 1 ;

generating a second index from a number of bits, k o bits, immediately following the most significant bit;

addressing a second table to retrieve two output values corresponding to the second index value;

storing the two output values as v 2 and v′ 3 ;

creating a fixed-point number from remaining bits of x if any exist that directly follow the k o bits;

inserting these remaining bits into the created number starting at the k o +1 fractional-bit to get a result, wherein the remaining bits of the result are the remaining bits of x to generate a second result v 4 ;

storing the second result v 4 ;

computing the final result: x y ≈v 1 ×[v 2 +(v′ 3 ×v 4 )] using fixed-point arithmetic to generate a fixed point approximation used by an electronic device.

12. A method according to claim 11 , wherein the values of v 2 and v′ 3 are

v 2 =(1 +a 1 2 −1 +a 2 2 −2 + . . . +a k o 2 −k o ) y ;

and

v′ 3 =y ×(1 +a 1 2 −1 +a 2 2 −2 + . . . +a k o 2 −k o ) y /(1 +a 1 2 −1 + . . . +a k o 2 −k o );

respectively.

13. A electronic method of generating a fixed point approximation of a number x with a data processor, comprising:

locating the most significant bit of x;

retrieving a first value from electronic data storage, where the first value is based on a first index value generated from the most significant bit and contains fixed-point representation v 1 located in a table in storage;

retrieving two output values, v 2 and v′ 3 , corresponding to a second index value generated from a number of bits, k o bits, immediately following the most significant bit, where the two output values are retrieved from a table in electronic data storage;

generating a fourth value v 4 corresponding to fractional bits following the k o bits; and

computing the final result: x y ≈v 1 ×[v 2 +(v 3 ×v 4 )] using fixed-point arithmetic to generate a fixed point approximation used by an electronic device.

14. A method according to claim 13 , further comprising:

creating a fixed-point number from remaining bits of x if any exist that directly follow the k o bits; and

inserting the fixed point number into the created number starting at the k o +1 fractional-bit to get a result, wherein the remaining bits of the result are the remaining bits of x to generate a second result v 4 .

Assignments (14)