Complex logarithmic ALU

A logarithmic and complex number technology, applied in the field of pipelined logarithmic operations, can solve the problems of not providing a lookup table solution for complex number operations, and not providing ALU with real and complex number processing capabilities

Inactive Publication Date: 2007-05-16
TELEFON AB LM ERICSSON (PUBL)
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

In this way, the Coleman process still includes the complexity associated with the multiplication
[0017] While the prior art describes various methods and apparatus for implementing logarithmic operations on real numbers, t

Method used

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  • Complex logarithmic ALU
  • Complex logarithmic ALU
  • Complex logarithmic ALU

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Embodiment Construction

[0035] The present invention provides an ALU for performing logarithmic operations on complex and / or real numbers in logarithmic format. In one embodiment, the ALU utilizes one or more look-up tables to perform logarithmic operations on complex numbers represented in log-polar format. In another embodiment, the ALU performs logarithmic operations on complex and real numbers represented in logarithmic format using at least one complex look-up table and at least one real look-up table, respectively. In order to better understand the details and beneficial effects of the present invention, below, details about numerical representation, conventional interpolation, iterative logarithmic operations, high-precision iterative logarithmic addition, high-precision iterative logarithmic subtraction, and exponential approximation are first provided.

[0036] numerical representation

[0037] Logarithmic operations implemented in the ALU often require specific numeric formats. As noted ...

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Abstract

The present invention relates to an ALU implements logarithmic arithmetic and describes a method and apparatus for performing logarithmic arithmetic with real and/or complex numbers represented in a logarithmic format. In one exemplary embodiment, an ALU implements logarithmic arithmetic on complex numbers represented in a logpolar format. According to this embodiment, memory in the ALU stores a look-up table used to determine logarithms of complex numbers, while a processor in the ALU generates an output logarithm based on complex input operands represented in logpolar format using the stored look-up table. In another exemplary embodiment, the ALU performs logarithmic arithmetic on real and complex numbers represented in logarithmic format. In this embodiment, the memory stores two look-up tables, one for determining logarithms of real numbers and one for determining logarithms of complex numbers, while the processor generates an output logarithm based on real or complex input operands represented in logarithmic format using the real or complex look-up tables, respectively.

Description

technical field [0001] The present invention relates generally to computing and digital signal processing, and more particularly to pipelined logarithmic operations in an arithmetic logic unit (ALU). Background technique [0002] The ALU is traditionally used to implement various arithmetic functions such as addition, subtraction, multiplication, division, etc. on real numbers and / or complex numbers. Conventional systems use fixed-point or floating-point ALUs. ALUs using real logarithms with limited precision are also known. See, for example, "Digital filtering using logarithmicarithmetic" (N.G. Kingsbury and P.J.W. Rayner, Electron. Lett. (Jan. 28, 1971), Vol. 7, No. 2, pp. 56-58). "Arithmetic on the European Logarithmic Microprocessor" (J.N. Coleman, E.I. Chester, C.I. Softley and J. Kadlec, (July 2000) IEEE Trans. Comput., Vol. 49, No. 7, pp. 702-715) provides a high Another example of a precision (32-bit) logarithmic unit. [0003] Fixed-point programming places a bu...

Claims

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Application Information

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IPC IPC(8): G06F7/48
Inventor 保罗·威尔金森·登特
Owner TELEFON AB LM ERICSSON (PUBL)
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