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1. 发明授权

US07366748B1 Methods and apparatus for fast argument reduction in a computing system 有权
标题翻译：计算系统中快速论证的减少方法和装置
公开(公告)号：US07366748B1
公开(公告)日：2008-04-29
申请号：US09609496
申请日：2000-06-30
申请人： Ping Tak Peter Tang , John Harrison , Theodore Kubaska
发明人： Ping Tak Peter Tang , John Harrison , Theodore Kubaska
IPC分类号： G06F7/38
CPC分类号： G06F7/544
摘要： There is disclosed method, software and apparatus for evaluating a function f in a computing device using a reduction, core approximation and final reconstruction stage. According to one embodiment of the invention, an argument reduction stage uses an approximate reciprocal table in the computing device. According to another embodiment, an approximate reciprocal instruction I is operative on the computing device to use the approximate reciprocal table such that the argument reduction stage provides that—C:=I(X) and R:=X×C−1, the core approximation stage provides that p(R) is computed so that it approximates f(1+R), and the final reconstruction stage provides that T=f(1/C) is fetched and calculated if necessary, and f(X) is reconstructed based on f(X)=f([1/C]×[X×C])=g(f(1/C), f(1+R)).
摘要翻译：公开了使用减少，核心近似和最终重构阶段来评估计算装置中的功能f的方法，软件和装置。根据本发明的一个实施例，参数减少阶段在计算设备中使用近似的倒数表。根据另一个实施例，近似的倒数指令I在计算设备上操作以使用近似的倒数表，使得自变量减少级提供了C：= I（X）和R：= X×C-1，核心近似级提供p（R）被计算为使其近似于f（1 + R），并且最终重构阶段提供如果需要，获取和计算T = f（1 / C），并且基于 f（X）= f（[1 / C] x [XxC]）= g（f（1 / C），f（1 + R））。

2. 发明授权

US6141670A Apparatus and method useful for evaluating periodic functions 失效
标题翻译：用于评估周期性功能的装置和方法
公开(公告)号：US6141670A
公开(公告)日：2000-10-31
申请号：US941359
申请日：1997-09-30
申请人： Shane A. Story , Ping Tak Peter Tang
发明人： Shane A. Story , Ping Tak Peter Tang
IPC分类号： G06F7/548 , G06F1/02 , G06F7/38
CPC分类号： G06F7/548
摘要： A computer and a method of using the computer to reduce an original argument to obtain a periodic function of the argument. A special number P.sub.j is employed that is close to a nontrivial even-integral multiple .pi.. The technique subtracts a non-negative integral multiple of P.sub.j from the original argument to obtain a first reduced argument. Then, a second non-negative integer multiple of a floating-point representation of .pi./2 is subtracted from the first reduced argument to obtain a second reduced argument. Next, a periodic function of a third argument equal to a sum of the second reduced argument plus the product of the first non-negative integral multiple and a floating-point representation of an offset .delta..sub.j is evaluated to obtain a result.
摘要翻译：计算机和使用计算机来减少原始参数以获得参数的周期性函数的方法。采用特殊数字Pj，其接近非平凡的均匀多重pi。该技术从原始参数中减去Pj的非负整数倍以获得第一个简化参数。然后，从第一个缩减参数中减去+ E的浮点表示的第二个非负整数倍，得到第二个缩减参数。接下来，评估等于第二缩减参数加上第一非负整数倍的乘积和偏移量Δj的浮点表示的乘积的第三参数的周期函数，以获得结果。

3. 发明授权

US07013320B2 Apparatus and method for remainder calculation using short approximate floating-point quotient 失效
公开(公告)号：US07013320B2
公开(公告)日：2006-03-14
申请号：US10058187
申请日：2002-01-25
申请人： Ping Tak Peter Tang
发明人： Ping Tak Peter Tang
IPC分类号： G06F7/44
CPC分类号： G06F7/4873
摘要： An apparatus and method for creating lookup tables of approximate floating-point quotients which exactly represent the underlying value, within the range of the specified precision. The lookup tables are created without any extraneous data beyond what is needed and also without sacrificing numerical accuracy, and may be creating for any radix.

4. 发明授权

US06598063B1 Fast calculation of (A/B)K by a parallel floating-point processor 失效
标题翻译：通过并行浮点处理器快速计算（A / B）K
公开(公告)号：US06598063B1
公开(公告)日：2003-07-22
申请号：US09638442
申请日：2000-08-14
申请人： Ping Tak Peter Tang , Theodore E. Kubaska
发明人： Ping Tak Peter Tang , Theodore E. Kubaska
IPC分类号： G06F7552
CPC分类号： G06F7/552 , G06F7/548
摘要： A method suitable for calculating an expression having the form (A/B)K by a processor that features separate sets of floating point units which can operate in parallel for greater speed of execution. The processor issues instructions to determine an approximate reciprocal R0 of a first variable B. Further instructions are issued to raise a second variable to the power of a third variable K by a first set of arithmetic units of the processor, where the second variable is a function of the approximate reciprocal R0. Still further instructions are issued to calculate a polynomial q at a fourth variable delta by a second set of arithmetic units of the processor. The fourth variable delta is also a function of the approximate reciprocal R0. Finally, one or more instructions are issued to multiply the calculated polynomial by the second variable, having been raised to the power of the third variable, to yield (A/B)K.
摘要翻译：一种适用于通过处理器计算具有形式（A / B）K的表达式的方法，所述处理器具有独立的浮点单元组，其可以并行操作以获得更高的执行速度。处理器发出指令以确定第一变量B的近似倒数R0。发出另外的指令以通过处理器的第一组算术单元将第二变量升高到第三变量K的功率，其中第二变量为函数近似相等的R0。还发出另外的指令，以通过处理器的第二组运算单元计算第四变量增量的多项式q。第四个可变增量也是近似倒数R0的函数。最后，发出一个或多个指令，将计算出的多项式乘以已经被提高到第三个变量的幂的第二个变量，以产生（A / B）K。

5. 发明申请

US20140250161A1 FUNCTION APPROXIMATION BASED ON STATISTICAL PROPERTIES 审中-公开
标题翻译：基于统计特性的函数近似
公开(公告)号：US20140250161A1
公开(公告)日：2014-09-04
申请号：US13997644
申请日：2012-03-28
申请人： Ping Tak Peter Tang
发明人： Ping Tak Peter Tang
IPC分类号： G06F1/02
CPC分类号： G06F1/02 , G06F17/17
摘要： Embodiments of techniques and systems for approximating a function are described. In embodiments, a computing device may receive one or more statistical properties associated with application of an approximation function of a function over a target domain. The computing device may formulate one or more constraints on one or more parameters of a functional form of the approximation function, based at least in part on the one or more statistical properties. The computing device may then determine the one or more parameters subject to the constraints and out put results of the determination. In embodiments, the one or more parameters may be determined through application of an optimization procedure. Other embodiments, may be described and claimed.
摘要翻译：描述用于近似功能的技术和系统的实施例。在实施例中，计算设备可以接收与目标域上的函数的逼近函数的应用相关联的一个或多个统计特性。至少部分地基于一个或多个统计特性，计算设备可以对近似函数的函数形式的一个或多个参数制定一个或多个约束。然后，计算设备可以根据约束条件确定一个或多个参数，并输出确定结果。在实施例中，可以通过应用优化过程来确定一个或多个参数。其他实施例可以被描述和要求保护。

6. 发明授权

US08838663B2 Method and apparatus for performing multiplicative functions 有权
标题翻译：用于执行乘法函数的方法和装置
公开(公告)号：US08838663B2
公开(公告)日：2014-09-16
申请号：US11731580
申请日：2007-03-30
申请人： Ping Tak Peter Tang , Robert Cavin
发明人： Ping Tak Peter Tang , Robert Cavin
IPC分类号： G06F7/48 , G06F7/535 , G06F7/544 , G06F7/483
CPC分类号： G06F7/535 , G06F7/483 , G06F7/5443 , G06F2207/5354 , G06F2207/5356
摘要： A new function for calculating the reciprocal residual of a floating-point number X is defined as recip_residual(X)=1−X*recip(X), where recip(X) represents the reciprocal of X. The function may be implemented using a fused multiply-add unit in a processor. The reciprocal value of X, recip(X), may be obtained from a lookup table. The recip_residual function may help reduce the latency of many multiplicative functions that are based on products of multiple numbers and can be expressed in simple terms of functions on each individual number (e.g., log(U*V)=log(U)+log(V)).
摘要翻译：用于计算浮点数X的倒数残差的新函数被定义为recip_residual（X）= 1-X * recip（X），其中，recip（X）表示X的倒数。该函数可以使用融合乘法加法处理器。可以从查找表中获得X，recip（X）的倒数值。 recip_residual函数可以帮助减少基于多个数字的乘积的许多乘法函数的延迟，并且可以在每个单独的数字上以简单的函数表达（例如，log（U * V）= log（U）+ log V））。

7. 发明授权

US06792443B2 Economical on-the-fly rounding for digit-recurrence algorithms 失效
标题翻译：数字递归算法的经济四舍五入
公开(公告)号：US06792443B2
公开(公告)日：2004-09-14
申请号：US09895770
申请日：2001-06-29
申请人： Ping Tak Peter Tang
发明人： Ping Tak Peter Tang
IPC分类号： G06F738
CPC分类号： G06F7/4873 , G06F7/49947
摘要： Apparatus and methods are provided for an improved on-the-fly rounding technique for digit-recurrence algorithms, such as division and square root calculations. According to one embodiment, only two forms of an intermediate result of an operation to be performed by a digit-recurrence algorithm are maintained. A first form is maintained in a first register and a second form is maintained in a second register. Responsive to receiving digits 1 to L−2 of the intermediate result from a digit recurrence unit, where L represents a number of digits that satisfies a predetermined precision for the operation, both forms of the intermediate result are updated by register swapping or concatenation under the control of load and shift control logic and on-the-fly conversion logic. Then, a rounded result is generated by determining digits dL−1 and dL and appending a rounded last digit to the appropriate form of the intermediate result.
摘要翻译：提供装置和方法用于数字复现算法的改进的即时舍入技术，例如除法和平方根计算。根据一个实施例，维持仅由数字复现算法执行的操作的中间结果的两种形式。第一形式保存在第一寄存器中，第二形式被保存在第二寄存器中。响应于从数字重复单元接收中间结果的数字1到L-2，其中L表示满足操作的预定精度的数字数，中间结果的两种形式都通过下面的寄存器交换或级联来更新控制负载和换档控制逻辑以及即时转换逻辑。然后，通过确定数字dL-1和dL并将舍入的最后一个数字附加到中间结果的适当形式来生成舍入结果。

8. 发明授权

US6078939A Apparatus useful in floating point arithmetic 失效
标题翻译：用于浮点算术的装置
公开(公告)号：US6078939A
公开(公告)日：2000-06-20
申请号：US940280
申请日：1997-09-30
申请人： Shane A. Story , Ping Tak Peter Tang
发明人： Shane A. Story , Ping Tak Peter Tang
IPC分类号： G06F7/544 , G06F17/00
CPC分类号： G06F7/5443 , G06F7/483
摘要： A computer and a method of using the computer to separate a floating-point number into high and low parts and for evaluating a dominant arithmetic object and a remainder object. The dominant object is associated with the first arithmetic object by using the high parts of the floating-point number. The evaluation of a remainder arithmetic object associates the first arithmetic object with the high and low parts of the floating-point numbers. A sum of the dominant and remainder arithmetic objects returns a value corresponding to the first arithmetic object.
摘要翻译：一种计算机和使用该计算机将浮点数分离为高和低部分并用于评估主要算术对象和余数对象的方法。主要对象通过使用浮点数的高部分与第一个算术对象相关联。剩余算术对象的评估将第一算术对象与浮点数的高低部分相关联。主要和余数运算对象的总和返回与第一运算对象对应的值。

9. 发明申请

US20140101219A1 FOURIER TRANSFORM COMPUTATION FOR DISTRIBUTED PROCESSING ENVIRONMENTS 有权
标题翻译：用于分布式处理环境的FOURIER变换计算
公开(公告)号：US20140101219A1
公开(公告)日：2014-04-10
申请号：US13648804
申请日：2012-10-10
申请人： Ping Tak Peter Tang , Jong Soo Park , Vladimir Petrov
发明人： Ping Tak Peter Tang , Jong Soo Park , Vladimir Petrov
IPC分类号： G06F17/14
CPC分类号： G06F17/142
摘要： Fourier transform computation for distributed processing environments is disclosed. Example methods disclosed herein to compute a Fourier transform of an input data sequence include performing first processing on the input data sequence using a plurality of processors, the first processing resulting in an output data sequence having more data elements than the input data sequence Such example methods also include performing second processing on the output data sequence using the plurality of processors, the output data sequence being permutated among the plurality of processors, each of the processors performing the second processing on a respective permutated portion of the output data sequence to determine a respective, ordered segment of the Fourier transform of the input data sequence.
摘要翻译：公开了用于分布式处理环境的傅里叶变换计算。用于计算输入数据序列的傅里叶变换的示例方法包括使用多个处理器对输入数据序列执行第一处理，第一处理产生具有比输入数据序列更多的数据元素的输出数据序列。还包括使用多个处理器对输出数据序列执行第二处理，输出数据序列在多个处理器之间被排列，每个处理器对输出数据序列的相应置换部分执行第二处理，以确定相应的，输入数据序列的傅里叶变换的有序段。

10. 发明申请

US20080243985A1 Method and apparatus for performing multiplicative functions 有权
标题翻译：用于执行乘法函数的方法和装置
公开(公告)号：US20080243985A1
公开(公告)日：2008-10-02
申请号：US11731580
申请日：2007-03-30
申请人： Ping Tak Peter Tang , Robert Cavin
发明人： Ping Tak Peter Tang , Robert Cavin
IPC分类号： G06F7/38
CPC分类号： G06F7/535 , G06F7/483 , G06F7/5443 , G06F2207/5354 , G06F2207/5356
摘要： A new function for calculating the reciprocal residual of a floating-point number X is defined as recip_residual(X)=1−X*recip(X), where recip(X) represents the reciprocal of X. The function may be implemented using a fused multiply-add unit in a processor. The reciprocal value of X, recip(X), may be obtained from a lookup table. The recip_residual function may help reduce the latency of many multiplicative functions that are based on products of multiple numbers and can be expressed in simple terms of functions on each individual number (e.g., log(U*V)=log(U)+log(V)).
摘要翻译：用于计算浮点数X的倒数残差的新函数被定义为recip_residual（X）= 1-X * recip（X），其中，recip（X）表示X的倒数。该函数可以使用融合乘法加法处理器。可以从查找表中获得X，recip（X）的倒数值。 recip_residual函数可以帮助减少基于多个数字的乘积的许多乘法函数的延迟，并且可以在每个单独的数字上以简单的函数表达（例如，log（U * V）= log（U）+ log V））。

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