Apparatus, method, and program for arithmetic processing

• US 8,631,061 B2
• Filed: 07/28/2009
• Issued: 01/14/2014
• Est. Priority Date: 07/29/2008
• Status: Expired due to Fees

• Current Assignee: Sony Corporation (Sony Group Corp.)
• Original Assignee: Sony Corporation (Sony Group Corp.)
• Inventors: Mogi, Yukihiko
• Primary Examiner(s): SUN, SCOTT C
• Application Number:
  US12/510,674
• Publication Number:
  US 20100030833A1
• Time in Patent Office: 1,631 Days
• Field of Search: None
• 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)×(2^X₂) 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=log₂ X^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 (2^Z_amari) through the interpolation process. The power calculator determines X^Y=2^Z=(2^Z_amari)×(2^Z_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 a 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:

at least one processor; and

at least one storage medium having encoded thereon computer-executable instructions that, when executed by the at least one processor, cause the at least one processor to;

split the input value 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;

record, in a first storage 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;

perform an interpolation process on a plurality of logarithmic values retrieved from the first storage in response to the mantissa X₁ in order to determine the logarithmic value of the mantissa;

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

calculate 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, wherein the computer-executable instructions, when executed by the at least one processor, further cause the at least one processor to:

split 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

record, in a second storage, a 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 arithmetic value P is calculated based on the power value of the constant number M retrieved from the second storage in response to the fraction Z_amari, and the integer Z_int.

3. The arithmetic processing apparatus according to claim 2, wherein the interpolation process to determine the power value of the constant number M comprises performing the interpolation process on a plurality of power values retrieved from the second storage in response to the fraction Z_amari, and

wherein the arithmetic value P is calculated based on the power value of the constant number M, 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 a 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:

at least one processor; and

at least one storage medium having encoded thereon computer-executable instructions;

mantissa/exponent splitting means for splitting the input value 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 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 the 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;

executing the computer-executable instructions by the at least one processor to cause the arithmetic processing apparatus to;

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

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

calculate the logarithmic value Z; and

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

5. A non-transitory computer-readable storage medium comprising computer-executable instructions that, when executed by a computer, cause an arithmetic processing apparatus to perform a method of 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 method comprising:

splitting the input value 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 a final logarithmic value of the mantissa;

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

calculating the arithmetic value P by raising the constant value M to a 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 a 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:

at least one processor; and

at least one storage medium having encoded thereon computer-executable instructions that, when executed by the at least one processor, cause the at least one processor to;

split the input value 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;

record, in a first recording unit, 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;

perform 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 logarithmic value of the mantissa;

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

calculate 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.