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 a gradient and a 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 configured to perform multiplication by a 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,wherein each of the gradients has a minimum extended Hamming weight which is less than or equal to a threshold value.
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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 a gradient and a base 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 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, wherein each of the gradients has a minimum extended Hamming weight which is less than or equal to a threshold value. - 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 linear segment having a gradient and a base value; 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 gradient of the segment, and a binary adder configured to add the 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; wherein each of the gradients has a minimum extended Hamming weight which is less than or equal to a threshold value. - 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 an approximation of 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 linear segment having a gradient and a base value; 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 gradient of the segment, and a binary adder configured to add the 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; wherein each of the gradients has a minimum extended Hamming weight which is less than or equal to a threshold value.
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Specification