APPARATUS, METHOD, AND PROGRAM FOR ARITHMETIC PROCESSING

• US 20100030833A1
• Filed: 07/28/2009
• Published: 02/04/2010
• Est. Priority Date: 07/29/2008
• Status: Active Grant

• Current Assignee: Sony Corporation (Sony Group Corp.)
• Original Assignee: Sony Corporation (Sony Group Corp.)
• Inventors: Mogi, Yukihiko
• Granted Patent: US 8,631,061 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
• CPC Class Codes: G06F 7/552 Powers or roots , e.g. Pythagorean sums

Abstract

A mantissa/exponent splitter splits an input value X=(1+X₁/2²³)×(2̂X₂) into a mantissa X₁ and an exponent X₂. An interpolation processor references the mantissa/exponent splitter using the mantissa X₁ and determines a power value (log₂(1+X₁/2²³)) through an interpolation process. A logarithmic calculator determines a logarithmic value Z=log₂X^Y=Y(X₂+log₂ (1+X₁/2²³)) from the exponent X₂ and the power value from the interpolation processor. The integer/fraction splitter splits the logarithmic value Z into an integer Z_int and a fraction Z_amari. The interpolation processor references a power of fraction table storage unit in response to the fraction Z_amari and determines a power value (2̂Z_amari)through the interpolation process. The power calculator determines X^Y=2̂Z=(2̂Z_amari)×(2̂Z_int), thereby resulting in the input value X to the power of Y.

Claims

1. An arithmetic processing apparatus for determining an arithmetic value P, the arithmetic value P being an input value X raised to the power of a variable Y as an exponent, and the input value X represented by a base-M system with M being a predetermined constant number, the arithmetic processing apparatus comprising:

mantissa/exponent splitting means for splitting the input X in floating-point type data into a mantissa X₁ and an exponent X₂, the mantissa X₁ being a mantissa part representing a mantissa of the input value X of a floating-point number, and the exponent X₂ being an exponent part representing an exponent of the input value X of the floating-point number;

first recording means for recording a logarithmic value of the mantissa of the input value X having the constant number M as a base thereof, determined with respect to the mantissa X₁;

interpolating means for performing an interpolation process on a plurality of logarithmic values retrieved from the first recording means in response to the mantissa X₁ in order to determine the final logarithmic value of the mantissa;

logarithmic calculation means for calculating a logarithmic value Z of the arithmetic value P having the constant number M as a base thereof, based on the variable Y, the exponent X₂, and the logarithmic value of the mantissa determined by the interpolating means; and

power calculation means for calculating the arithmetic value P by raising the constant value M to the power of the logarithmic value Z of the arithmetic value P as an exponent.

2. The arithmetic processing apparatus according to claim 1, further comprising:

integer/fraction splitting means for splitting the logarithmic value Z of the arithmetic value P into an integer Z_int as an integer part of the logarithmic value Z and a fraction Z_amari as a fraction part of the logarithmic value Z; and

second recording means for recording the power value of the constant number M determined by raising the constant value M to the power of the fraction part Z_amari as an exponent,

wherein the power calculation means calculates the arithmetic value P based on the power value of the constant number M retrieved from the second recording means in response to the fraction Z_amari, and the integer Z_int.

3. The arithmetic processing apparatus according to claim 2, wherein the interpolating means determines the final power value of the constant number M by performing the interpolation process on a plurality of power values retrieved from the second recording means in response to the fraction Z_amari, and

wherein the power calculation means calculates the arithmetic value P based on the power value of the constant number M determined by the interpolating means, and the integer Z_int.

4. An arithmetic processing method of an arithmetic processing apparatus for determining an arithmetic value P, the arithmetic value P being an input value X raised to the power of a variable Y as an exponent, and the input value X represented by a base-M system with M being a predetermined constant number, the processing apparatus including mantissa/exponent splitting means for splitting the input X in floating-point type data into a mantissa X₁ and an exponent X₂, the mantissa X₁ being a mantissa part representing a mantissa of the input value X of a floating-point number, and the exponent X₂ being an exponent part representing an exponent of the input value X of the floating-point number;

recording means for recording a logarithmic value of the mantissa of the input value X having the constant number M as a base thereof, determined with respect to the mantissa X₁;

interpolating means for performing an interpolation process on a plurality of logarithmic values retrieved from the recording means in response to the mantissa X₁ in order to determine the final logarithmic value of the mantissa;

logarithmic calculation means for calculating a logarithmic value Z of the arithmetic value P having the constant number M as a base thereof, based on the variable Y, the exponent X₂, and the logarithmic value of the mantissa determined by the interpolating means; and

power calculation means for calculating the arithmetic value P by raising the constant value M to the power of the logarithmic value Z of the arithmetic value P as an exponent,

the arithmetic processing method comprising the steps of;

splitting the input value X into the mantissa X₁ and the exponent X₂;

performing the interpolation process on the plurality of logarithmic values in order to determine the final logarithmic value of the mantissa;

calculating the logarithmic value Z; and

calculating the arithmetic value P by raising the constant value M to the power of the logarithmic value Z as an exponent.

5. A program for causing an arithmetic processing apparatus to determine an arithmetic value P, the arithmetic value P being an input value X raised to the power of a variable Y as an exponent, and the input value X represented by a base-M system with M being a predetermined constant number, the program comprising the steps of:

splitting the input X in floating-point type data into a mantissa X₁ and an exponent X₂, the mantissa X₁ being a mantissa part representing a mantissa of the input value X of a floating-point number, and the exponent X₂ being an exponent part representing an exponent of the input value X of the floating-point number;

performing an interpolation process on a plurality of logarithmic values of the mantissa of the input value X having the constant number M as a base determined with respect to the mantissa X₁ in order to determine the final logarithmic value of the mantissa;

calculating a logarithmic value Z of the arithmetic value P having the constant number M as a base thereof, based on the variable Y, the exponent X₂, and the logarithmic value of the mantissa determined in the interpolation process; and

calculating the arithmetic value P by raising the constant value M to the power of the logarithmic value Z of the arithmetic value P as an exponent.

6. An arithmetic processing apparatus for determining an arithmetic value P, the arithmetic value P being an input value X raised to the power of a variable Y as an exponent, and the input value X represented by a base-M system with M being a predetermined constant number, the arithmetic processing apparatus comprising:

logarithmic calculation means for calculating a logarithmic value Z of the arithmetic value P having the constant number M as a base thereof, based on the input value X and the variable Y;

integer/fraction splitting means for splitting the logarithmic value Z of the arithmetic value P into an integer Z_int as an integer part of the logarithmic value Z and a fraction Z_amari as a fraction part of the logarithmic value Z;

first recording means for recording a power value of the constant number M raised to the power of the fraction Z_amari as an exponent;

interpolating means for performing an interpolation process on a plurality of logarithmic values retrieved from the first recording means in response to the fraction Z_amari in order to determine the final power value of the constant number M; and

power calculation means for calculating the arithmetic value P by raising the constant value M to the power of the logarithmic value Z of the arithmetic value P as an exponent, based on the power value of the constant number M determined by the interpolating means and the integer Z_int.

7. The arithmetic processing apparatus according to claim 6, further comprising:

mantissa/exponent splitting means for splitting the input X in floating-point type data into a mantissa X₁ and an exponent X₂, the mantissa X₁ being a mantissa part representing a mantissa of the input value X of a floating-point number, and the exponent X₂ being an exponent part representing an exponent of the input value X of the floating-point number,

wherein the logarithmic calculation means calculates the logarithmic value Z of the arithmetic value P based on the mantissa X₁, the exponent X₂, and the variable Y.

8. The arithmetic processing apparatus according to claim 7, further comprising:

second recording means for recording the logarithmic value of the mantissa of the input value X having the constant number M as a base, determined with respect to the mantissa X₁,

wherein the logarithmic calculation means calculates the logarithmic value Z of the arithmetic value P, based on the logarithmic value of the mantissa retrieved from the second recording means in response to the mantissa X₁, the variable Y, and the exponent X₂.

9. An arithmetic processing method of an arithmetic processing apparatus for determining an arithmetic value P, the arithmetic value P being an input value X raised to the power of a variable Y as an exponent, and the input value X represented by a base-M system with M being a predetermined constant number, the arithmetic processing apparatus including logarithmic calculation means for calculating a logarithmic value Z of the arithmetic value P having the constant number M as a base thereof, based on the input value X and the variable Y;

integer/fraction splitting means for splitting the logarithmic value Z of the arithmetic value P into an integer Z_int as an integer part of the logarithmic value Z and a fraction Z_amari as a fraction part of the logarithmic value Z;

recording means for recording a power value of the constant number M raised to the power of the fraction Z_amari as an exponent;

interpolating means for performing an interpolation process on a plurality of logarithmic values retrieved from the recording means in response to the fraction Z_amari in order to determine the final power value of the constant number M; and

power calculation means for calculating the arithmetic value P by raising the constant value M to the power of the logarithmic value Z of the arithmetic value P as an exponent, based on the power value of the constant number M determined by the interpolating means and the integer Z_int,

the arithmetic processing method comprising the steps of;

calculating the logarithmic value Z, based on the input value X and the variable Y;

splitting the logarithmic value Z into the integer Z_int and the fraction Z_amari;

performing the interpolation process on the plurality of logarithmic values in order to determine the final power value of the constant number M;

calculating the logarithmic value Z; and

calculating the arithmetic value P by raising the constant value M to the power of the logarithmic value Z as an exponent, based on the power value of the constant number M and the integer Z_int.

10. A program for causing an arithmetic processing apparatus to determine an arithmetic value P, the arithmetic value P being an input value X raised to the power of a variable Y as an exponent, and the input value X represented by a base-M system with M being a predetermined constant number, the program comprising the steps of:

calculating a logarithmic value Z of the arithmetic value P having the constant number M as a base thereof, based on the input value X and the variable Y;

splitting the logarithmic value Z of the arithmetic value P into an integer Z_int as an integer part of the logarithmic value Z and a fraction Z_amari as a fraction part of the logarithmic value Z;

performing an interpolation process on a plurality of power values of the constant number M calculated by raising the constant number M to the power of the fraction Z_amari as an exponent in order to determine the final power value of the constant number M; and

calculating the arithmetic value P by raising the constant value M to the power of the logarithmic value Z of the arithmetic value P as an exponent, based on the power value of the constant number M determined in the interpolation process and the integer Z_int.

11. An arithmetic processing apparatus for determining an integer of an arithmetic value P, the arithmetic value P being an input value X raised to the power of a variable Y as an exponent, and the input value X represented by a base-M system with M being a predetermined constant number, the arithmetic processing apparatus comprising:

logarithmic calculation means for calculating a logarithmic value Z of the arithmetic value P having the constant number M as a base thereof, based on the input value X and the variable Y;

integer/fraction splitting means for splitting the logarithmic value Z of the arithmetic value P into an integer Z_int as an integer part of the logarithmic value Z and a fraction Z_amari as a fraction part of the logarithmic value Z; and

power integer converting means for determining the integer of the arithmetic value P by performing a right-shift operation on fixed-point data indicating the power value of the constant number M to the power of the fraction Z_amari as an exponent, by the number of bits, the number of bit being obtained by subtracting the integer Z_int from the number of bits of the fixed-point data from the least significant bit of the fixed-point data to the position of the decimal point of the fixed-point data.

12. The arithmetic processing apparatus according to claim 11, further comprising recording means for recording the power value of the constant number M determined by raising the constant number M to the power of the fraction Z_amari as an exponent,

wherein the power integer converting means determines the integer of the arithmetic value P, based on the power value of the constant number M retrieved from the recording means in response to the fraction Z_amari, and the integer Z_int.

13. The arithmetic processing apparatus according to claim 12, further comprising interpolating means for performing an interpolation process on a plurality of power values retrieved from the recording means in response to the fraction Z_amari in order to determine the final power value of the constant number M,

wherein the power integer converting means determines the integer of the arithmetic value P, based on the power value of the constant number M determined in the interpolation process, and the integer Z_int.

14. An arithmetic processing method of an arithmetic processing apparatus for determining an integer of an arithmetic value P, the arithmetic value P being an input value X raised to the power of a variable Y as an exponent, and the input value X represented by a base-M system with M being a predetermined constant number, including logarithmic calculation means for calculating a logarithmic value Z of the arithmetic value P having the constant number M as a base thereof, based on the input value X and the variable Y;

integer/fraction splitting means for splitting the logarithmic value Z of the arithmetic value P into an integer Z_int as an integer part of the logarithmic value Z and a fraction Z_amari as a fraction part of the logarithmic value Z; and

power integer converting means for determining the integer of the arithmetic value P by performing a right-shift operation on fixed-point data indicating the power value of the constant number M to the power of the fraction Z_amari as an exponent, by the number of bits, the number of bits being obtained by subtracting the integer Z_int from the number of bits of the fixed-point data from the least significant bit of the fixed-point data to the position of the decimal point of the fixed-point data,

the arithmetic processing method comprising the steps of;

calculating the logarithmic value Z based on the input value X and the variable Y;

splitting the logarithmic value Z into the integer Z_int and the fraction Z_amari; and

performing the right-shift operation to determine the integer of the arithmetic value P.

15. A computer program for causing an arithmetic processing apparatus to determine an integer of an arithmetic value P, the arithmetic value P being an input value X raised to the power of a variable Y as an exponent, and the input value X represented by a base-M system with M being a predetermined constant number, the computer program comprising the steps of:

calculating a logarithmic value Z of the arithmetic value P having the constant number M as a base thereof, based on the input value X and the variable Y;

splitting the logarithmic value Z of the arithmetic value P into an integer Z_int as an integer part of the logarithmic value Z and a fraction Z_amari as a fraction part of the logarithmic value Z; and

determining the integer of the arithmetic value P by performing a right-shift operation on fixed-point data indicating the power value of the constant number M to the power of the fraction Z_amari as an exponent, by the number of bits, the number of bits being obtained by subtracting the integer Z_int from the number of bits of the fixed-point data from the least significant bit of the fixed-point data to the position of the decimal point of the fixed-point data.

16. An arithmetic processing apparatus for determining an arithmetic value P, the arithmetic value P being an input value X raised to the power of a variable Y as an exponent, and the input value X represented by a base-M system with M being a predetermined constant number, the arithmetic processing apparatus comprising:

a mantissa/exponent splitting unit splitting the input X in floating-point type data into a mantissa X₁ and an exponent X₂, the mantissa X₁ being a mantissa part representing a mantissa of the input value X of a floating-point number, and the exponent X₂ being an exponent part representing an exponent of the input value X of the floating-point number;

a first recording unit recording a logarithmic value of the mantissa of the input value X having the constant number M as a base thereof, determined with respect to the mantissa X₁;

an interpolating unit performing an interpolation process on a plurality of logarithmic values retrieved from the first recording unit in response to the mantissa X₁ in order to determine the final logarithmic value of the mantissa;

a logarithmic calculation unit calculating a logarithmic value Z of the arithmetic value P having the constant number M as a base thereof, based on the variable Y, the exponent X₂, and the logarithmic value of the mantissa determined by the interpolating unit; and

a power calculation unit calculating the arithmetic value P by raising the constant value M to the power of the logarithmic value Z of the arithmetic value P as an exponent.

17. An arithmetic processing apparatus for determining an arithmetic value P, the arithmetic value P being an input value X raised to the power of a variable Y as an exponent, and the input value X represented by a base-M system with M being a predetermined constant number, the arithmetic processing apparatus comprising:

a logarithmic calculation unit calculating a logarithmic value Z of the arithmetic value P having the constant number M as a base thereof, based on the input value X and the variable Y;

an integer/fraction splitting unit splitting the logarithmic value Z of the arithmetic value P into an integer Z_int as an integer part of the logarithmic value Z and a fraction Z_amari as a fraction part of the logarithmic value Z;

a first recording unit recording a power value of the constant number M raised to the power of the fraction Z_amari as an exponent;

interpolating unit performing an interpolation process on a plurality of logarithmic values retrieved from the first recording unit in response to the fraction Z_amari in order to determine the final power value of the constant number M; and

a power calculation unit calculating the arithmetic value P by raising the constant value M to the power of the logarithmic value Z of the arithmetic value P as an exponent, based on the power value of the constant number M determined by the interpolating unit and the integer Z_int.

18. An arithmetic processing apparatus for determining an integer of an arithmetic value P, the arithmetic value P being an input value X raised to the power of a variable Y as an exponent, and the input value X represented by a base-M system with M being a predetermined constant number, the arithmetic processing apparatus comprising:

a logarithmic calculation unit calculating a logarithmic value Z of the arithmetic value P having the constant number M as a base thereof, based on the input value X and the variable Y;

an integer/fraction splitting unit splitting the logarithmic value Z of the arithmetic value P into an integer Z_int as an integer part of the logarithmic value Z and a fraction Z_amari as a fraction part of the logarithmic value Z; and

a power integer converting unit determining the integer of the arithmetic value P by performing a right-shift operation on fixed-point data indicating the power value of the constant number M to the power of the fraction Z_amari as an exponent, by the number of bits, the number of bits being obtained by subtracting the integer Z_int from the number of bits of the fixed-point data from the least significant bit of the fixed-point data to the position of the decimal point of the fixed-point data.