Approximating Functions
First Claim
1. A binary logic circuit for approximating a mathematical function over a predefined range as a series of linear segments, each linear segment having one of a predetermined set of fixed gradients and a corresponding base value, wherein each of the fixed gradients in the predetermined set of fixed gradients has a respective minimum extended Hamming weight which is less than or equal to a threshold value, the binary logic circuit comprising:
- an input for receiving an input variable in the predefined range;
a plurality of logic chains each comprising;
a binary multiplier configured to perform multiplication by a respective fixed gradient of the set of fixed gradients using a number of binary adders, wherein said number is one less than the minimum extended Hamming weight for the respective fixed gradient, anda binary adder configured to add a base value to an input or output of the binary multiplier; and
selection logic configured to select one of the logic chains in dependence on the input variable so as to provide, for the received input variable, an approximate value of the mathematical function.
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Abstract
A binary logic circuit for approximating a mathematical function over a predefined range as a series of linear segments, each linear segment having one of a predetermined set of fixed gradients and a corresponding base value, the binary logic circuit comprising: an input for receiving an input variable in the predefined range; a plurality of logic chains each comprising: a binary multiplier adapted to perform multiplication by a respective one of the set of fixed gradients using h-1 binary adders, where h is the extended Hamming weight; and a binary adder adapted to add a base value to the input or output of the binary multiplier; and selection logic configured to select one of the logic chains in dependence on the input variable so as to provide, for the received input variable, an approximate value of the mathematical function.
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Citations
20 Claims
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1. A binary logic circuit for approximating a mathematical function over a predefined range as a series of linear segments, each linear segment having one of a predetermined set of fixed gradients and a corresponding base value, wherein each of the fixed gradients in the predetermined set of fixed gradients has a respective minimum extended Hamming weight which is less than or equal to a threshold value, the binary logic circuit comprising:
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an input for receiving an input variable in the predefined range; a plurality of logic chains each comprising; a binary multiplier configured to perform multiplication by a respective fixed gradient of the set of fixed gradients using a number of binary adders, wherein said number is one less than the minimum extended Hamming weight for the respective fixed gradient, and a binary adder configured to add a base value to an input or output of the binary multiplier; and selection logic configured to select one of the logic chains in dependence on the input variable so as to provide, for the received input variable, an approximate value of the mathematical function. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
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16. A method of deriving a hardware representation of a binary logic circuit configured to approximate a mathematical function over a predefined range as a series of linear segments, the method comprising:
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fitting a plurality of linear segments to the function over the predefined range, each segment extending between a pair of break points and having a fixed gradient selected from a predetermined set of fixed gradients, wherein each of the fixed gradients in the predetermined set of fixed gradients has a minimum extended Hamming weight which is less than or equal to a threshold value, determining a base value for each of the segments; and deriving a hardware representation for a binary logic circuit which comprises; for each of the plurality of linear segments; a binary multiplier configured to perform multiplication by the selected fixed gradient of the segment using a number of binary adders, wherein said number is one less than the minimum extended Hamming weight for the selected fixed gradient, and a binary adder configured to add the determined base value for the segment to an input or output of the binary multiplier; and selection logic configured to select, for a given input variable in the predefined range, one of the plurality of binary multipliers in dependence on the determined break points. - View Dependent Claims (17, 18, 19)
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20. A method of manufacturing a binary logic circuit in accordance with a hardware representation derived using a method configured to approximate a mathematical function over a predefined range as a series of linear segments, comprising the steps of:
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fitting a plurality of linear segments to the function over the predefined range, each segment extending between a pair of break points and having a fixed gradient selected from a predetermined set of fixed gradients, wherein each of the fixed gradients in the predetermined set of fixed gradients has a minimum extended Hamming weight which is less than or equal to a threshold value, determining a base value for each of the segments; and deriving a hardware representation for a binary logic circuit which comprises; for each of the plurality of linear segments; a binary multiplier configured to perform multiplication by the selected fixed gradient of the segment using a number of binary adders, wherein said number is one less than the minimum extended Hamming weight for the selected fixed gradient, and a binary adder configured to add the determined base value for the segment to an input or output of the binary multiplier; and selection logic configured to select, for a given input variable in the predefined range, one of the plurality of binary multipliers in dependence on the determined break points.
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Specification