### Abstract

This paper presents a method for designing linear, quadratic and cubic interpolators that compute elementary functions using truncated multipliers, squarers and cubers. Initial coefficient values are obtained using a Chebyshev series approximation. A direct search algorithm is then used to optimize the quantized coefficient values to meet a user-specified error constraint. The algorithm minimizes coefficient lengths to reduce lookup table requirements, maximizes the number of truncated columns to reduce the area, delay and power of the arithmetic units, and minimizes the maximum absolute error of the interpolator output. The method can be used to design interpolators to approximate any function to a user-specified accuracy, up to and beyond 53-bits of precision (e.g., IEEE double precision significand). Linear, quadratic and cubic interpolator designs that approximate reciprocal, square root, reciprocal square root and sine are presented and analyzed. Area, delay and power estimates are given for 16, 24 and 32-bit interpolators that compute the reciprocal function, targeting a 65 nm CMOS technology from IBM. Results indicate the proposed method uses smaller arithmetic units and has reduced lookup table sizes compared to previously proposed methods. The method can be used to optimize coefficients in other systems while accounting for coefficient quantization as well as truncation and rounding effects of multiple arithmetic units.

Original language | English (US) |
---|---|

Journal | Electronics |

Volume | 5 |

Issue number | 2 |

DOIs | |

State | Published - Apr 8 2016 |

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### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Signal Processing
- Hardware and Architecture
- Computer Networks and Communications
- Electrical and Electronic Engineering

### Cite this

*Electronics*,

*5*(2). https://doi.org/10.3390/electronics5020017

}

*Electronics*, vol. 5, no. 2. https://doi.org/10.3390/electronics5020017

**Optimized linear, quadratic and cubic interpolators for elementary function hardware implementations.** / Sadeghian, Masoud; Stine, James E.; Walters, III, Eugene George.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Optimized linear, quadratic and cubic interpolators for elementary function hardware implementations

AU - Sadeghian, Masoud

AU - Stine, James E.

AU - Walters, III, Eugene George

PY - 2016/4/8

Y1 - 2016/4/8

N2 - This paper presents a method for designing linear, quadratic and cubic interpolators that compute elementary functions using truncated multipliers, squarers and cubers. Initial coefficient values are obtained using a Chebyshev series approximation. A direct search algorithm is then used to optimize the quantized coefficient values to meet a user-specified error constraint. The algorithm minimizes coefficient lengths to reduce lookup table requirements, maximizes the number of truncated columns to reduce the area, delay and power of the arithmetic units, and minimizes the maximum absolute error of the interpolator output. The method can be used to design interpolators to approximate any function to a user-specified accuracy, up to and beyond 53-bits of precision (e.g., IEEE double precision significand). Linear, quadratic and cubic interpolator designs that approximate reciprocal, square root, reciprocal square root and sine are presented and analyzed. Area, delay and power estimates are given for 16, 24 and 32-bit interpolators that compute the reciprocal function, targeting a 65 nm CMOS technology from IBM. Results indicate the proposed method uses smaller arithmetic units and has reduced lookup table sizes compared to previously proposed methods. The method can be used to optimize coefficients in other systems while accounting for coefficient quantization as well as truncation and rounding effects of multiple arithmetic units.

AB - This paper presents a method for designing linear, quadratic and cubic interpolators that compute elementary functions using truncated multipliers, squarers and cubers. Initial coefficient values are obtained using a Chebyshev series approximation. A direct search algorithm is then used to optimize the quantized coefficient values to meet a user-specified error constraint. The algorithm minimizes coefficient lengths to reduce lookup table requirements, maximizes the number of truncated columns to reduce the area, delay and power of the arithmetic units, and minimizes the maximum absolute error of the interpolator output. The method can be used to design interpolators to approximate any function to a user-specified accuracy, up to and beyond 53-bits of precision (e.g., IEEE double precision significand). Linear, quadratic and cubic interpolator designs that approximate reciprocal, square root, reciprocal square root and sine are presented and analyzed. Area, delay and power estimates are given for 16, 24 and 32-bit interpolators that compute the reciprocal function, targeting a 65 nm CMOS technology from IBM. Results indicate the proposed method uses smaller arithmetic units and has reduced lookup table sizes compared to previously proposed methods. The method can be used to optimize coefficients in other systems while accounting for coefficient quantization as well as truncation and rounding effects of multiple arithmetic units.

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UR - http://www.scopus.com/inward/citedby.url?scp=84962920898&partnerID=8YFLogxK

U2 - 10.3390/electronics5020017

DO - 10.3390/electronics5020017

M3 - Article

VL - 5

JO - Electronics

JF - Electronics

SN - 0039-0895

IS - 2

ER -