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公开(公告)号：US20040139139A1
公开(公告)日：2004-07-15
申请号：US10692493
申请日：2003-10-24
发明人： Yuji Suga
IPC分类号： G06F007/38
CPC分类号： G06F7/556 , G06F1/0307 , G06F7/723 , G06F2207/5561
摘要： An exponent calculation apparatus calculates xe based on input two integers x and e. A pre-calculation module pre-calculates x{circumflex over (null)}nulll_inull for each of candidate exponents nulll_inull (0nullinullLnull1) stored in a candidate exponents storing unit, the number of the candidate exponents being L, and stores the obtained values x{circumflex over (null)}nulll_inull in a pre-calculated values storing unit. A dividing module divides the integer e into a plurality of values nullf_inull (0nullinullFnull1) so that each of the values nullf_inull corresponds to one of the candidate exponents nulll_inull. A sequential processing module sequentially updates a calculation result c, which is stored in a calculation result storing unit, for each of the values nullf_inull by using each of the values x{circumflex over (null)}nulll_inull. The updated calculation result c for each of the values nullf_inull is output as xe. Accordingly, the amount of pre-calculation and table size can be reduced and thus the number of calculations can be reduced.
摘要翻译： 指数计算装置基于输入的两个整数x和e计算x
。 预计算模块为存储在候选指数存储单元中的候选指数{l_i}（0 <= i <= L-1）中的每个候选指数存储单元预先计算x {circumflex over（）} {l_i} 指数为L，并将获得的值x {circumflex over（）} {l_i}存储在预先计算的值存储单元中。 分割模块将整数e分成多个值{f_i}（0 <= i <= F-1），使得每个值{f_i}对应于候选指数{1_i}之一。 顺序处理模块通过使用x {circumflex over（）} {l_i}中的每一个顺序地更新存储在计算结果存储单元中的每个值{f_i}的计算结果c。 将每个值{f_i}的更新的计算结果c输出为x 。 因此，可以减少预计算量和表尺寸，从而可以减少计算次数。 -
公开(公告)号：US5974436A
公开(公告)日：1999-10-26
申请号：US954586
申请日：1997-10-20
CPC分类号： G06F7/556 , G06F7/5525 , G06F2207/5561
摘要： An execution processor that can carry out power calculation at high speed includes a base data register, an exponent data register, a multiplier, a multiplication input selector for selecting an input to the multiplier, first and second registers for storing a calculation result of the multiplier, a square root calculation unit, a square root calculation input selector for selecting an input to the square root calculation unit, a third register for storing a calculation result of the square root calculation unit, and a power calculation controller. The power calculation controller checks the integer region of the exponent data register for each bit while providing input/output control of the multiplication input selector, the first register, and the second register, and checks the decimal fraction region of the exponent data register for each bit to provide input/output control of the square root calculation input selector, the multiplication input selector, the first register, the second register, and the third register.
摘要翻译： 可以高速执行功率计算的执行处理器包括基本数据寄存器，指数数据寄存器，乘法器，用于选择到乘法器的输入的乘法输入选择器，用于存储乘法器的计算结果的第一和第二寄存器 平方根计算单元，用于选择对平方根计算单元的输入的平方根计算输入选择器，存储平方根计算单元的计算结果的第三寄存器和功率计算控制器。 功率计算控制器为每个位检查指数数据寄存器的整数区域，同时提供乘法输入选择器，第一寄存器和第二寄存器的输入/输出控制，并且为每个位检查指数数据寄存器的小数部分区域 位提供平方根计算输入选择器，乘法输入选择器，第一寄存器，第二寄存器和第三寄存器的输入/输出控制。
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公开(公告)号：US09372678B2
公开(公告)日：2016-06-21
申请号：US14129438
申请日：2013-06-14
申请人： Intel Corporation
发明人： Ganesh Bikshandi , Daehyun Kim
IPC分类号： G06F9/45
CPC分类号： G06F8/443 , G06F7/4806 , G06F7/556 , G06F8/4434 , G06F8/452 , G06F17/10 , G06F2207/5561
摘要： Technologies for optimizing complex exponential calculations include a computing device with optimizing compiler. The compiler parses source code, optimizes the parsed representation of the source code, and generates output code. During optimization, the compiler identifies a loop in the source code including a call to the exponential function having an argument that is a loop-invariant complex number multiplied by the loop index variable. The compiler tiles the loop to generate a pair of nested loops. The compiler generates code to pre-compute the exponential function and store the resulting values in a pair of coefficient arrays. The size of each coefficient array may be equal to the square root of the number of loop iterations. The compiler applies rewrite rules to replace the exponential function call with a multiplicative expression of one element from each of the coefficient arrays. Other embodiments are described and claimed.
摘要翻译： 用于优化复数指数计算的技术包括具有优化编译器的计算设备。 编译器解析源代码，优化源代码的解析表示，并生成输出代码。 在优化期间，编译器识别源代码中的循环，包括对具有循环不变复数乘以循环索引变量的参数的指数函数的调用。 编译器平铺循环以生成一对嵌套循环。 编译器生成代码以预先计算指数函数，并将结果值存储在一对系数数组中。 每个系数数组的大小可以等于循环次数的平方根。 编译器使用重写规则来替换来自每个系数数组的一个元素的乘法表达式的指数函数调用。 描述和要求保护其他实施例。
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公开(公告)号：US3426184A
公开(公告)日：1969-02-04
申请号：US3426184D
申请日：1966-04-04
申请人： ORION RESEARCH
发明人： RISEMAN JOHN H
CPC分类号： G06F7/556 , G06F2207/5561 , H03M1/62
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公开(公告)号：US20170308357A1
公开(公告)日：2017-10-26
申请号：US15138846
申请日：2016-04-26
CPC分类号： G06F7/556 , G06F7/49915 , G06F2207/5523 , G06F2207/5561
摘要： Embodiments of the present invention may provide the capability to evaluate logarithm and power (exponentiation) functions using either hardware specific instructions, or a hardware specific implementation with reduced memory requirements. An input comprising a floating point representation of a real number may be received and a mantissa and an exponent may be extracted. A function of a logarithm of a mantissa of the real number may be approximated by utilizing a polynomial based on the mantissa. The approximated function of the logarithm may be combined with the exponent for calculating a value comprising a logarithm of the real number. Likewise, an input comprising a floating point representation of a real number and a representation of a second number may be received and an approximation of the real number to the power of the second number may be generated.
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公开(公告)号：US20090238360A1
公开(公告)日：2009-09-24
申请号：US12054249
申请日：2008-03-24
CPC分类号： G06F7/723 , G06F7/556 , G06F2207/5561 , H04L9/3013 , H04L9/302
摘要： Method and apparatus for data security using exponentiation. This is suitable for public key cryptography authentication and other data security applications using a one-way function. A type of exponentiation is disclosed here where the bits of an exponent value expressed in binary form correspond to a course (path) in a given graph defining the one-way function. This uses an approach called here F sequences. Each value is in a ladder of a sequence of values, as defined from its predecessor values. This ladder satisfies certain algebraic identities and is readily calculated by a computer program or logic circuitry.
摘要翻译： 使用取幂的数据安全的方法和装置。 这适用于使用单向功能的公钥加密认证和其他数据安全应用。 这里公开了一种取幂类型，其中以二进制形式表示的指数值的位对应于定义单向函数的给定图中的路线（路径）。 这使用一种称为F序列的方法。 每个值都位于一系列值的梯形图中，如其前导值所定义。 该梯子满足某些代数标识，并且可以由计算机程序或逻辑电路容易地计算出来。
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公开(公告)号：US07337203B2
公开(公告)日：2008-02-26
申请号：US10692493
申请日：2003-10-24
申请人： Yuji Suga
发明人： Yuji Suga
IPC分类号： G06F7/38
CPC分类号： G06F7/556 , G06F1/0307 , G06F7/723 , G06F2207/5561
摘要： An exponent calculation apparatus calculates xe based on input two integers x and e. A pre-calculation module pre-calculates x^{l_i} for each of candidate exponents {l_i} (0≦i≦L−1) stored in a candidate exponents storing unit, the number of the candidate exponents being L, and stores the obtained values x^{l_i} in a pre-calculated values storing unit. A dividing module divides the integer e into a plurality of values {f_i} (0≦i≦F−1) so that each of the values {f_i} corresponds to one of the candidate exponents {l_i}. A sequential processing module sequentially updates a calculation result c, which is stored in a calculation result storing unit, for each of the values {f_i} by using each of the values x^{l_i}. The updated calculation result c for each of the values {f_i} is output as xe. Accordingly, the amount of pre-calculation and table size can be reduced and thus the number of calculations can be reduced.
摘要翻译： 指数计算装置基于输入的两个整数x和e来计算x∈E。 预计算模块对存储在候选指数存储单元中的每个候选指数{l_i}（0 <= i <= L-1）预先计算x ^ {l_i}，候选指数的数目为L，以及 将获得的值x ^ {l_i}存储在预先计算的值存储单元中。 分割模块将整数e分成多个值{f_i}（0 <= i <= F-1），使得每个值{f_i}对应于候选指数{1_i}之一。 顺序处理模块通过使用每个值x ^ {l_i}顺序更新存储在计算结果存储单元中的每个值{f_i}的计算结果c。 将每个值{f_i}的更新的计算结果c输出为x
。 因此，可以减少预计算量和表尺寸，从而可以减少计算次数。 -
公开(公告)号：US4410956A
公开(公告)日：1983-10-18
申请号：US249187
申请日：1981-03-30
申请人： Junichi Yoshida
发明人： Junichi Yoshida
CPC分类号： G06F7/556 , G06F2207/5561
摘要： An exponential operation device comprises an exponential operation circuit for carrying out the exponential operation of a term x.sup.y formed of data x and data y; and an operation circuit for judging whether the data x supplied by key depression denotes a positive or negative value, and also whether or not the data y supplied similarly by key depression is an integer. Where the operation circuit judges that the data x denotes a negative value and the data y is an integer, then the exponential operation circuit carries out the exponential operation of the term x.sup.y, thereby providing an answer even when the data x denotes a negative value.
摘要翻译： 指数运算装置包括指数运算电路，用于执行由数据x和数据y形成的项xy的指数运算; 以及用于判断由按键按压提供的数据x是正值还是负值的运算电路，以及类似地按键按压提供的数据y是否为整数。 在运算电路判定数据x表示负值且数据y为整数的情况下，指数运算电路进行项xy的指数运算，即使数据x表示负值也能提供答案。
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公开(公告)号：US20160110171A1
公开(公告)日：2016-04-21
申请号：US14129438
申请日：2013-06-14
申请人： INTEL CORPORATION
发明人： Ganesh BIKSHANDI , Daehyun KIM
IPC分类号： G06F9/45
CPC分类号： G06F8/443 , G06F7/4806 , G06F7/556 , G06F8/4434 , G06F8/452 , G06F17/10 , G06F2207/5561
摘要： Technologies for optimizing complex exponential calculations include a computing device with optimizing compiler. The compiler parses source code, optimizes the parsed representation of the source code, and generates output code. During optimization, the compiler identifies a loop in the source code including a call to the exponential function having an argument that is a loop-invariant complex number multiplied by the loop index variable. The compiler tiles the loop to generate a pair of nested loops. The compiler generates code to pre-compute the exponential function and store the resulting values in a pair of coefficient arrays. The size of each coefficient array may be equal to the square root of the number of loop iterations. The compiler applies rewrite rules to replace the exponential function call with a multiplicative expression of one element from each of the coefficient arrays. Other embodiments are described and claimed.
摘要翻译： 用于优化复数指数计算的技术包括具有优化编译器的计算设备。 编译器解析源代码，优化源代码的解析表示，并生成输出代码。 在优化期间，编译器识别源代码中的循环，包括对具有循环不变复数乘以循环索引变量的参数的指数函数的调用。 编译器平铺循环以生成一对嵌套循环。 编译器生成代码以预先计算指数函数，并将结果值存储在一对系数数组中。 每个系数数组的大小可以等于循环次数的平方根。 编译器使用重写规则来替换来自每个系数数组的一个元素的乘法表达式的指数函数调用。 描述和要求保护其他实施例。
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公开(公告)号：US08014520B2
公开(公告)日：2011-09-06
申请号：US12054249
申请日：2008-03-24
CPC分类号： G06F7/723 , G06F7/556 , G06F2207/5561 , H04L9/3013 , H04L9/302
摘要： Method and apparatus for data security using exponentiation. This is suitable for public key cryptography authentication and other data security applications using a one-way function. A type of exponentiation is disclosed here where the bits of an exponent value expressed in binary form correspond to a course (path) in a given graph defining the one-way function. This uses an approach called here F sequences. Each value is in a ladder of a sequence of values, as defined from its predecessor values. This ladder satisfies certain algebraic identities and is readily calculated by a computer program or logic circuitry.
摘要翻译： 使用取幂的数据安全的方法和装置。 这适用于使用单向功能的公钥加密认证和其他数据安全应用。 这里公开了一种取幂类型，其中以二进制形式表示的指数值的位对应于定义单向函数的给定图中的路线（路径）。 这使用一种称为F序列的方法。 每个值都位于一系列值的梯形图中，如其前导值所定义。 该梯子满足某些代数标识，并且可以由计算机程序或逻辑电路容易地计算出来。
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