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    • 35. 发明授权
    • Computing floating-point polynomials in an integrated circuit device
    • 计算集成电路器件中的浮点多项式
    • US08949298B1
    • 2015-02-03
    • US13234419
    • 2011-09-16
    • Martin Langhammer
    • Martin Langhammer
    • G06F7/00
    • G06F7/552G06F7/483G06F7/548G06F2207/5523
    • Polynomial circuitry for calculating a polynomial having terms including powers of an input variable, where the input variable has a mantissa and an exponent, and the circuitry has a number of bits of precision, includes multiplier circuitry that calculates a common power of the input variable factored out of terms of the polynomial having powers of the variable greater than 1. The polynomial circuitry further includes, for each respective remaining term of the polynomial that contributes to the number of bits of precision: (1) a coefficient memory loaded with a plurality of instances of a coefficient for the respective term, each instance being shifted by a different number of bits, (2) address circuitry for selecting one of the instances of the coefficient based on the exponent, and (3) circuitry for combining the selected instance of the coefficient with a corresponding power of the input variable to compute the respective term.
    • 用于计算具有包括输入变量的功率的项的多项式的多项式电路,其中所述输入变量具有尾数和指数,并且所述电路具有多个精度位,所述多项式电路包括计算所述输入变量的公共功率的乘法器电路 对于具有大于1的变量的幂的多项式的项,多项式电路还包括对有助于精度位数的多项式的每个相应剩余项:(1)加载多个 用于各个术语的系数的实例,每个实例被移位不同位数,(2)用于基于指数选择系数的一个实例的地址电路,以及(3)用于组合所选择的实例的电路 该系数具有输入变量的相应功率以计算相应的项。
    • 36. 发明授权
    • Reduced matrix Reed-Solomon encoding
    • 减少矩阵里德 - 所罗门编码
    • US08898551B1
    • 2014-11-25
    • US13530683
    • 2012-06-22
    • Martin LanghammerDaniel Elphick
    • Martin LanghammerDaniel Elphick
    • H03M13/15
    • H03M13/1515H03M13/15H03M13/611H03M13/616H03M13/6502
    • In an arrangement of the disclosed systems, devices, and methods, a matrix representation of a block code comprising m bit-planes is obtained, a generator matrix corresponding to each of the m bit-planes from the matrix representation is extracted, a transformed generator matrix and a transformed data symbol vector for the first bit-plane of the block code are determined, a reverse-mapped transformed generator matrix for each of the second bit-plane through the mth bit-plane of the block code are determined, and instructions for the encoder architecture based on the transformed generator matrix for the first bit-plane and the reverse-mapped transformed generator matrix for each of the second bit-plane through the mth bit-plane of the block code are generated.
    • 在公开的系统,装置和方法的布置中,获得包括m个位平面的块码的矩阵表示,提取与矩阵表示中的每个m位平面对应的生成矩阵,变换后的生成器 矩阵和用于块码的第一比特平面的经变换的数据符号向量,确定通过块码的第m位平面的第二位平面中的每一个的反向映射变换的生成器矩阵,以及指令 生成基于用于第一位平面的经变换的生成矩阵和通过块代码的第m位平面的第二位平面中的每一个的反向映射变换的生成器矩阵的编码器架构。
    • 38. 发明授权
    • Cholesky decomposition in an integrated circuit device
    • 集成电路器件中的Cholesky分解
    • US08805911B1
    • 2014-08-12
    • US13149661
    • 2011-05-31
    • Lei XuMartin Langhammer
    • Lei XuMartin Langhammer
    • G06F7/38
    • G06F17/16
    • Efficient and scalable circuitry for performing Cholesky decomposition is based on two types of processing elements. A first type of processing element provides inverse square root and multiplication operations. A second type of processing element includes a first computation path for outputting an inner product difference element and a second computation path for outputting an inner product element. Processing elements of the first and second type may be cascaded to achieve a decomposition of a matrix of an arbitrary size. The circuitry is flexible to allow different throughput requirements, and can be optimized to reduce latency and resource consumption.
    • 用于执行Cholesky分解的高效和可扩展的电路基于两种类型的处理元件。 第一类处理元件提供反平方根和乘法运算。 第二类型的处理元件包括用于输出内积差元件的第一计算路径和用于输出内积元件的第二计算路径。 可以级联第一和第二类型的处理元件以实现任意大小的矩阵的分解。 该电路是灵活的,以允许不同的吞吐量要求,并且可以被优化以减少延迟和资源消耗。
    • 39. 发明授权
    • Double-clocked specialized processing block in an integrated circuit device
    • 集成电路设备中的双时钟专用处理模块
    • US08645451B2
    • 2014-02-04
    • US13044680
    • 2011-03-10
    • Martin Langhammer
    • Martin Langhammer
    • G06F7/523
    • G06F7/5324
    • Circuitry for increasing the precision of multipliers by a desired factor while limiting the increase in arithmetic complexity of the multiplier to that factor can be provided in a fixed logic device, or can be configured into a programmable integrated circuit device such as a programmable logic device (PLD). The smaller increase in arithmetic complexity, so that the increase is proportional to the increase in precision, rather than to the square of the increase in precision, is achieved by using specialized processing block components differently on alternating clock cycles. For example, to implement double precision, the same multiplier components are used in each of two clock cycles, but some specialized processing block internal structures (e.g., shifters and adders) are used differently in the two cycles, so that over the two cycles, a larger multiplication may be calculated from smaller partial products.
    • 可以在固定逻辑器件中提供用于将乘法器的精度提高所需因数的电路,同时将乘法器的算术复杂度的增加限制为固定逻辑器件,或者可以配置成可编程集成电路器件,例如可编程逻辑器件( PLD)。 算术复杂度的增加较小,因此,通过在交替的时钟周期中不同地使用专门的处理块组件来实现增加与精度的增加成比例,而不是精度增加的平方。 例如,要实现双精度,在两个时钟周期的每一个中使用相同的乘法器组件,但是在两个周期中使用了一些专门的处理块内部结构(例如,移位器和加法器),因此在两个周期中, 可以从较小的部分乘积计算较大的乘积。
    • 40. 发明授权
    • Multi-operand floating point operations in a programmable integrated circuit device
    • 可编程集成电路器件中的多操作数浮点运算
    • US08412756B1
    • 2013-04-02
    • US12557952
    • 2009-09-11
    • Martin Langhammer
    • Martin Langhammer
    • G06F7/00G06F15/00
    • G06F7/5095G06F7/485
    • A programmable logic device is programmed to add a plurality N of unnormalized numbers at once. Because the inputs are not normalized, they could all have different exponents. The largest exponent of the N exponents is found, and for each of the inputs, its mantissa is right-shifted at by the difference between the largest exponent and the exponent of that particular input. The N shifted mantissas are combined, optionally with sign data, in an (N+1):2 compressor to provide carry and save vectors which may be combined in a carry-propagate adder. Numbers may converted back to normalized form at the end of the operation. If necessary to avoid data loss, a number may be normalized after an intermediate step.
    • 可编程逻辑器件被编程为一次添加多个N个非标准化数字。 由于输入不正则化,它们都可能具有不同的指数。 找到N个指数的最大指数,并且对于每个输入,其尾数通过最大指数和该特定输入的指数之间的差进行右移。 N个移位尾数与(N + 1):2压缩器中的符号数据可选地组合,以提供携带和保存向量,其可以组合在进位传播加法器中。 数字可能会在操作结束时转换回规范化形式。 如果需要避免数据丢失,可以在中间步骤之后对数字进行归一化。