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    • 54. 发明申请
    • Transcendental and Non-Linear Components Using Series Expansion
    • 超越和非线性组件使用系列扩展
    • US20130262540A1
    • 2013-10-03
    • US13435900
    • 2012-03-30
    • Vaughn T. ArnoldBrijesh TripathiAlbert Kuo
    • Vaughn T. ArnoldBrijesh TripathiAlbert Kuo
    • G06F17/17G06F7/523G06F7/50G06F1/03
    • G06F7/544G06F1/03G06F1/0307G06F1/0356G06F2101/08G06F2101/12
    • In an embodiment, hardware implementing a transcendental or other non-linear function is based on a series expansion of the function. For example, a Taylor series expansion may be used as the basis. One or more of the initial terms of the Taylor series may be used, and may be implemented in hardware. In some embodiments, modifications to the Taylor series expansion may be used to increase the accuracy of the result. In one embodiment, a variety of bit widths for the function operands may be acceptable for use in a given implementation. A methodology for building a library of series-approximated components for use in integrated circuit design is provided which synthesizes the acceptable implementations and tests the results for accuracy. A smallest (area-wise) implementation which produces a desired level of accuracy may be selected as the library element.
    • 在一个实施例中,实现先验或其他非线性函数的硬件基于功能的一系列扩展。 例如,可以使用泰勒级数展开作为基础。 可以使用泰勒级数的一个或多个初始项,并且可以以硬件实现。 在一些实施例中,可以使用对泰勒级数展开的修改来提高结果的准确性。 在一个实施例中,功能操作数的各种位宽可以被接受以用于给定的实现。 提供了一种用于构建用于集成电路设计的串联近似组件库的方法,其综合了可接受的实现并且测试结果的准确性。 可以选择产生所需精度水平的最小(区域)实现作为库元件。
    • 59. 发明申请
    • Method and system for approximating sine and cosine functions
    • 近似正弦和余弦函数的方法和系统
    • US20050071401A1
    • 2005-03-31
    • US10987487
    • 2004-11-12
    • Daniel Clifton
    • Daniel Clifton
    • G06F1/035G06F7/00
    • G06F1/0356G06F7/483G06F2101/08G06F2101/10G06F2101/12
    • A technique for approximating output values of a function based on LaGrange polynomials is provided. Factorization of a LaGrange polynomial results in a simplified representation of the LaGrange polynomial. With this simplified representation, an output value of a function may be determined based on an input value comprising a fixed point input mantissa and an input exponent. Based on a first portion of the fixed point input mantissa, a point value and at least one slope value are provided. At least one slope value is based on a LaGrange polynomial approximation of the function. Thereafter, the point value and the at least one slope value are combined with a second portion of the fixed point input mantissa to provide an output mantissa. Based on this technique, a single set of relatively simple hardware elements may be used to implement a variety of functions with high precision.
    • 提供了一种用于近似基于LaGrange多项式的函数的输出值的技术。 LaGrange多项式的因式分解导致LaGrange多项式的简化表示。 利用这种简化的表示,可以基于包括固定点输入尾数和输入指数的输入值来确定功能的输出值。 基于固定点输入尾数的第一部分,提供点值和至少一个斜率值。 至少一个斜率值是基于函数的LaGrange多项式近似。 此后,将点值和至少一个斜率值与固定点输入尾数的第二部分组合以提供输出尾数。 基于这种技术,可以使用一组相对简单的硬件元件来实现高精度的各种功能。