Apparatus and method for computing a logarithm of a floating-point number

• US 20040010532A1
• Filed: 07/09/2002
• Published: 01/15/2004
• Est. Priority Date: 07/09/2002
• Status: Active Grant

• Current Assignee: Silicon Integrated Systems Corporation (Silicon Integrated Systems Corporation Taiwan)
• Original Assignee: Silicon Integrated Systems Corporation (Silicon Integrated Systems Corporation Taiwan)
• Inventors: Lu, Chung-Yen
• Granted Patent: US 6,981,009 B2
• Time in Patent Office: Days
• US Class Current: 708/512
• CPC Class Codes: G06F 7/483 Computations with numbers represented by a non-linear combination of denominational numbers, e.g. rational numbers, logarithmic number system or floating-point numbers G06F7/4806, G06F7/4824, G06F7/49, G06F7/491, G06F7/544 take precedence

Abstract

An apparatus for computing a logarithm to a base p of a floating-point number X. The floating-point number X is represented in the format of (−1)^Sx·2^Ex·M_x, where M_x=(1+f_x)=(1+A_x·2^−K)+(B_x·2^−N), where S_x is a sign, E_x is an exponent, M_x is a mantissa, 1≦M_x<2, f_x is a N-bit fraction, A_x is a value of the most significant K bits of f_x, B_x is a value of the least significant (N−K) bits of f_x, 0≦K<N, and p, K, N are natural numbers. The apparatus includes: a first multiplier, a logarithmic table, a first adder, a divider, a Taylor-Series approximation circuit, a second multiplier, and a second adder.

Claims

1. An apparatus for computing a logarithm to a base p of a floating-point number X wherein the floating-point number X is represented in the format of (−

1)^Sx·

2^Ex·

M_x, where M_x =(1+f_x)=(1+A_x·

2<sup>−

K</sup>)+(B_x·

2<sup>−

N</sup>), where S_x is a sign, E_x is an exponent, M_x is a mantissa, 1≦

M_x<

2, f_x is a N-bit fraction, A_x is a value of the most significant K bits of f_x, B_x is a value of the least significant (N−

K) bits of f_x, 0≦

K<

N, and p, K, N are natural numbers, the apparatus comprising;

a first multiplier for multiplying a number whose value is log_p 2 and the exponent E_x and outputting a multiplying result;

a logarithmic table for receiving the value A_x and checking the logarithmic table to output a result;

a first adder connected to the first multiplier and the logarithmic table for adding the multiplying result and the result to output an adding result;

a divider for receiving the value B_x and an adding number whose value is (2^K+A_x) and dividing the value B_x by the adding number to output a dividing result R_d;

a Taylor-Series approximation circuit connected to the divider for receiving the dividing result R_d, finding a value of ln(1+R_d) and outputting the value of ln(1+R_d);

a second multiplier for multiplying a number whose value is 1/ln(p) and the value of ln(1+R_d) to output a second multiplying result; and

a second adder connected to the first adder and the second multiplier for adding the adding result and the second multiplying result to output the logarithm Y.

2. The apparatus as claimed in claim 1, wherein, when computing a logarithm to a base 2 of a floating-point number X, the first multiplier is not required.

3. The apparatus as claimed in claim 1, wherein, when computing a natural logarithm of a floating-point number X, the second multiplier is not required.

4. The apparatus as claimed in claim 1 further comprising a fixed-point circuit for receiving the logarithm Y and representing the logarithm Y in the format of (−

1)^Sy·

2^Ey·

M_y, where S_y is a sign, E_y is an exponent, M_y is a mantissa, 1≦

M_y<

2.

5. The apparatus as claimed in claim 1, wherein the logarithmic table is a predetermined logarithmic table for computing the logarithm of the value A_x to the base p.

6. The apparatus as claimed in claim 1, wherein the Taylor-Series approximation circuit is a predetermined circuit to find the value of ln(1+R_d) with three-term approximation.

12. The method as claimed in claim 4, wherein the Taylor-Series approximation circuit is a predetermined circuit to find the value of ln(1+R_d) with three-term approximation.

7. A method for computing a logarithm to a base p of a floating-point number X wherein the floating-point number X is represented in the format of (−

1)^Sx·

2^Ex·

M_x, where M_x=(1+f_x)=(1+A_x·

2<sup>−

K</sup>)+(B_x·

2<sup>−

N</sup>), where S_x is a sign, E_x is an exponent, M_x is a mantissa, 1≦

M_x<

2, f_x is a N-bit fraction, A_x is a value of the most significant K bits of f_x, B_x is a value of the least significant (N−

K) bits of f_x, 0≦

K<

N, and p, K, N are natural numbers, the method comprising the steps of;

multiplying a number whose value is log_{p 2} and the exponent E_x to get a multiplying result to output by a first multiplier;

receiving the value A_x by a logarithmic table and checking the logarithmic table to get a result to output;

adding the multiplying result and the result to get an adding result to output by a first adder;

dividing the value B_x by an adding number whose value is (2^K+A_x) to get a dividing result R_d to output by a divider;

receiving the dividing result R_d and finding a value of ln(1+R_d) to output by a Taylor-Series approximation circuit;

multiplying a number whose value is 1/ln(p) and the value of ln(1+R_d) to get a second multiplying result to output by a second multiplier; and

adding the adding result and the second multiplying result to get the logarithm Y to output by a second adder.

8. The method as claimed in claim 7, wherein, when computing a logarithm to a base 2 of a floating-point number X, the first multiplier is not required.

9. The method as claimed in claim 7, wherein, when computing a natural logarithm of a floating-point number X, the second multiplier is not required.

10. The method as claimed in claim 7 further comprising a fixed-point circuit for receiving the logarithm Y and representing the logarithm Y in the format of (−

1)^Sy·

2<sup>Ey ·

M</sup>_y, where S_x is a sign, E_x is an exponent, M_x is a mantissa, 1≦

M_x<

2.

11. The method as claimed in claim 7, wherein the logarithmic table is a predetermined logarithmic table for computing the logarithm of the value A_x to the base p.