CN109144570A - 具有带有复数指数非线性函数的指令集的数字处理器 - Google Patents

具有带有复数指数非线性函数的指令集的数字处理器 Download PDF

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CN109144570A
CN109144570A CN201810754065.3A CN201810754065A CN109144570A CN 109144570 A CN109144570 A CN 109144570A CN 201810754065 A CN201810754065 A CN 201810754065A CN 109144570 A CN109144570 A CN 109144570A
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complex exponential
input value
processing unit
exponential function
value
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K.阿扎德特
A.莫利纳
J.H.奥斯莫
P.万卡塔拉加瓦恩
于盟林
J.威廉姆斯
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Intel Corp
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Abstract

提供了一种数字处理器，其包括具有复数指数函数的指令集。该数字处理器针对输入值x通过以下操作求复数指数函数的值：获取复数指数软件指令，以输入值x的作为输入，并且响应于该复数指数软件指令：调用至少一个复数指数函数单元，所述复数指数函数单元实施复数指数软件指令以将复数指数函数应用于输入值x；并且生成对应于输入值x的复数指数的输出。输入值x的复数指数函数可通过以下操作来求解：约束该输入值以保持给定的范围；利用查找表计算粗略近似角度；调整所述粗略近似角度以获取从0到θ的角度；以及利用多项式近似计算精确校正值。

Description

具有带有复数指数非线性函数的指令集的数字处理器
对相关申请交叉引用
本申请要求序列号为61/552,242、2011年10月27日提交的、名称为“SoftwareDigital Front End(SoftDFE)Signal Processing and Digital Radio”的美国专利临时申请的优先权，该申请通过引用并入本文。
本申请关联于序列号为12/324,926、名称为“Digital Signal Processor havingInstruction Set with One or More Non-Linear Complex Functions”的美国专利申请和序列号为12/362,879、名称为“Digital Signal Processor having Instruction Setwith An Exponential Function Using Reduced Look-UP Table”的美国专利申请，上述申请均在2008年11月28日提交，并通过引用并入本文。
技术领域
本发明涉及数字处理技术，并且更特别地，涉及用于复数指数函数的数字处理的技术。
背景技术
数字信号处理器(DSP)为用于数字处理的专用处理器。信号通常从模拟形式转换至数字形式，以数字形式操作，并且然后转换回模拟形式，以进行进一步处理。数字信号处理算法通常需要针对一组数据快速并且高效地执行大量的数学操作。
因此DSP经常结合专用硬件以执行数学密集型(math-intensive)处理应用所需要的软件操作，如加法，乘法，乘法累加(MAC)，和移位累加。乘法累加体系结构，例如，认识到很多公共数据处理操作涉及两数相乘，将结果值加到另一值然后累加结果。这些基本操作可使用专用高速乘法器和累加器有效地执行。
向量处理器实施包括对向量(即，一维数据阵列)操作的指令的指令集。另一方面，标量DSP，具有对单个数据项操作的指令。向量处理器针对特定工作量提供了增强的性能。
然而，DSP和向量处理器，通常不提供专用指令来支持复数指数函数。然而，逐渐地，在处理器中需要复数指数操作。例如，当第一复数乘以第二复数时需要复数指数操作。复数指数函数是重要的，因为其为周期性信号提供基础并且能够表征线性、非时变信号。
因此，需要具有支持复数指数函数的指令集的数字处理器，例如DSP和向量处理器。
发明内容
一般地，提供了一种数字处理器，其包括具有复数指数函数的指令集。根据本发明的一方面，所公开的数字处理器通过获取一个或多个复数指数软件指令，以输入值x作为输入，针对输入值x求复数指数函数的值；并响应于至少一个复数指数软件指令，执行如下步骤：调用至少一个复数指数函数单元，所述复数指数函数单元实施一个或多个复数指数软件指令，以将该复数指数函数应用至输入值x；并生成对应于输入值x的复数指数的输出。
根据本发明另一方面，所公开的数字处理器通过约束输入值以保持给定范围，针对输入值x求复数指数函数的值；利用输入值的多个最高有效位(MSB)使用查找表计算粗略近似角；调整(scale)粗略近似角以获取从0至θ的角度；并利用多项式近似计算精确校正值。该多项式近似包括，例如，泰勒级数(Taylor Series)，诸如三次近似。
该数字处理器执行来自程序代码的软件指令，并可以是，例如向量处理器或标量处理器。在一个变型中，对称属性用于减小查找表的大小。此外，角度可选地能够在复数指数函数内累加，并且变量的复数指数和/或当前累加值被返回。在另一变型中，输入信号乘以复数指数函数的变量的指数。
对本发明更全面的理解，以及本发明的进一步特征和优点，将参考如下详细描述和附图而获取。
附图说明
图1为结合本发明的特征的示例性数字处理器的示意性框图；
图2为描述结合本发明特征的复数指数函数计算处理的示例性实现方式的流程图；
图3说明了利用查找表对复数指数的粗略估计的计算；以及
图4为根据本发明实施例同时处理一个或多个实数的示例性的基于向量的数字处理器的示意性框图。
具体实施方式
本发明的一些方面提供了数字处理器，其利用两阶段粗略和精确估计方案支持复数指数函数。一般地，一个或多个查找氛存储复数指数函数(如exp(j＊2＊π＊x))的至少一部分计算的粗略估计值。本发明的另一些方面认识到当输入值的动态范围被限制时泰勒级数近似可应用于计算复数指数函数的精确校正，如下进一步讨论。
如本文所使用，术语“数字处理器”可以是执行程序代码中的指令的的处理器，如DSP或向量处理器。需要进一步注意，所公开的复数指数函数可以应用于为标量或向量输入的值x。
本发明可应以用于手机、基站和其他网络元件。
图1为结合本发明特征的示例性数字处理器100的示意性框图。示例性数字处理器100可以被实现为DSP或向量处理器。如图1所示，示例性数字处理器100包括用于复数指数函数的一个或多个函数单元110。此外，数字处理器100包括一个或多个查找表120，其存储用于计算复数指数函数的粗略估计的值，如下文结合图3进一步讨论。
一般地，如果数字处理器100正在处理包括对应于复数指数函数的预定义指令关键字和用于该函数的任何合适的操作数的软件代码，指令解码器必须触发处理指令所需的合适的复数指数函数单元110。注意，复数指数函数单元110可以由多于一个的指令共享。
一般地，本发明的一些方面扩展了传统数字处理器，以提供利用一个或多个查找表支持复数指数函数的增强指令集。根据本发明的一些方面的数字处理器100接收至少一个实数作为输入，将复数指数函数应用于该输入并生成输出值。
公开的数字处理器100可以具有标量体系结构，如图1所示，其每次处理单个数字，或如下文结合图4讨论的同时处理一个或多个数字的向量体系结构。在基于向量的数字处理器实现方式的情况下，输入数字为包括多个被并行处理的标量数字的向量。
所公开的复数指数函数可以用于例如基带信号的数字上变频或调制和需要两数相乘的其他信号处理，如快速傅里叶变换(FFT)算法。
图2为描述结合本发明的特征以计算exp(j＊2＊π＊x)的复数指数函数计算处理200的示例性实现方式的流程图。一般地，示例性复数指数函数计算处理200实现两个步骤的方案，其中粗略估计最初被获取然后利用精确估计来校正。
如图2所示，示例性复数指数函数计算处理200首先在步骤210期间约束(wrap)2＊π＊x输入值以将其带入范围[0，2＊π]中，例如利用取模(modulo)操作，或可选地将x约束在范围[0， 1]中。其后，复数指数函数计算处理200在步骤220期间利用4位查找表120使用x的4个最高有效位(MSB)计算粗略近似角，如下文结合图3进一步讨论。
在步骤230期间，复数指数函数计算处理200调整步骤220的角度结果以获取从0到θ的角，其中θ为小值。最终，在步骤240期间，复数指数函数计算处理200利用泰勒级数计算精确校正exp(j＊2π*ε)值，如下文进一步讨论。已经发现，相比于2K表，四次泰勒级数扩展给出了足够的精确度。
数学上，由复数指数函数计算处理200执行的操作可以表示如下：
2π·x←2π·x mod[2π] (1)
x＝x0+ε (2)
公式(2)第一项提供了范围0到15/16的值并且公式(2)的第二项提供1/16以下的值。公式(2)可表示如下：
exp(j2π·x)＝exp(j2π·x0)·exp(j2π·ε) (3)
公式(3)的第一项为获取自查找表120的粗略相位估计，如下文结合图3进一步讨论。公式(3)的第二项提供利用泰勒级数扩展计算的剩余相位或精确校正值。
图3说明了利用查找表的复数指数的粗璐相位估计的计算。如图3所示，4个MSB利用圆形图示300转换为角度，其中四个位的值标识查找表120中的一个条目310。
复数指数函数的多项式近似
本发明的一些方面认识到复数指数函数的精确校正可利用泰勒级数来近似。因此，复数指数函数，exp(j＊2＊pi＊x)，可以表示为：
此外，本发明认识到三次近似(即，包括直到泰勒级数中的x3)或四次近似(即，包括直到泰勒级数中的x4)通常提供足够的精确度。下表说明了对比于2K查找表，三次和四次近似的示例性误差：
图4为根据本发明实施例的示例性的同时处理一个或多个数字的基于向量的数字处理器400的示意性框图。一般地，通过同时执行不同的处理，相对于图1的标量实现方式，图4的基于向量的实现方式增加了MIPS(每秒指令)的数量。因此，基于向量的数字处理器400包括用于复数指数函数310-1至310-N的多个函数单元。例如，双数字处理器400包括两个函数单元310-1和310-2，其能够同时执行两个独立的复数指数函数操作。
一般地，基于向量的数字处理器400处理输入x的向量并生成输出向量，exp(j·2π·x)。示例性的基于向量的数字处理器400示出用于16通道向量处理器expj指令，其实现为：
vec_expj(x1，x2，...，xl6)，x[k]的范围从0到1
在一个变型中，查找表的大小可通过使用对称性而被降低。例如，正弦波上下振荡，因此顶部和底部对称性可被平衡，以将查找表减少一半(0到π/2)或甚至利用四分之一对称(0到π/4)。在又一变型中，复数指数函数可以在函数内将角度进行累加(即，通过函数调用传递的固定量或角度量，函数还执行应用于输入数据的角度递增)。带有角度累加的复数指数函数可以返回两个结果，指数的变量和当前累加。
在另一变型中，所公开的复数指数(，-Θ)函数还可用于调制以将输入信号x乘以变量，-Θ的指数。该操作可选地可以由复数指数指令(或复数乘法累加(CMAC)单元)执行，以使变量的指数被计算并且该结果乘以输入信号x。
结论
尽管本发明的示例性实施例已相对于数字处理器中的数字逻辑块和存储器表来被描述，本领域技术人员显而易见的是，多种功能可以在数字域中实现，作为软件程序的处理步骤，通过电路元件或者状态机在硬件中实现，或者硬件和软件两者的结合。这样的软件可以应用于，例如数字信号处理器，专用集成电路或微控制器。该硬件和软件可以体现在集成电路中实现的电路中。
因此，本发明的功能可以以为用于实践该方法的方法和装置的形式来体现。本发明中的一个或多个方面可以以程序代码的形式来体现，而不论例如储存在存储介质中，载入机器和/或由其执行，其中，当程序代码载入机器中(如处理器)并由其执行时，该机器成为用于实践本发明的装置。当实现于通用处理器时，程序代码段联合该处理器来提供类似于专用逻辑电路来操作的设备。本发明还可以在集成电路、数字处理器、微处理器和微控制器中的一个或多个中实现。
应当理解，本文示出和描述的实施例和变型仅仅是说明本发明的原理，并且多种修改可以由本领域技术人员实现，而不偏离本发明的范围和精神。

Claims (10)

1.一种由数字处理器执行的方法，用于针对输入值x求复数指数函数的值，所述方法包括：
获取一个或多个复数指数软件指令，以所述输入值x作为输入；
响应于所述复数指数软件指令中的至少一个，执行如下步骤：
调用至少一个复数指数函数单元，其实施所述一个或多个复数指数软件指令，以将所述复数指数函数应用于所述输入值x；并且
生成对应于所述输入值x的所述复数指数的输出。
2.根据权利要求1所述的方法，进一步包括以下步骤：在所述复数指数函数中累加角度，以及返回变量的复数指数和当前累加值中的一个或多个。
3.一种由数字处理器执行的方法，用于针对输入值x求复数指数函数的值，所述方法包括：
约束所述输入值以保持给定的范围；
利用查找表使用所述输入值的多个最高有效位(MSB)计算粗略近似角度；
调整所述粗略近似角度以获取从0到θ的角度；以及
利用多项式近似计算精确校正值。
4.根据权利要求3所述的方法，进一步包括使用对称属性来降低所述查找表的大小的步骤。
5.一种数字处理器，其针对输入值x求复数指数函数的值，所述数字处理器包括：
存储器；以及
至少一个硬件设备，耦合于该存储器，可操作用于：
获取一个或多个复数指数软件指令，以所述输入值x作为输入，并响应于所述复数指数软件指令中的至少一个，执行如下操作：
调用至少一个复数指数函数单元，其实施所述一个或多个复数指数软件指令，以将所述复数指数函数应用于所述输入值x；以及
生成对应于所述输入值x的所述复数指数的输出。
6.根据权利要求5所述的数字处理器，其中所述至少一个硬件设备被进一步配置为在所述复数指数函数内累加角度，以及返回变量的复数指数和当前累加值中的一个或多个。
7.根据权利要求5所述的数字处理器，其中所述至少一个硬件设备被进一步配置为将输入信号乘以所述复数指数函数的变量的指数。
8.一种数字处理器，其针对输入值x求复数指数函数的值，所述数字处理器包括：
存储器；以及
至少一个硬件设备，耦合于该存储器，可操作用于：
约束所述输入值以保持给定的范围；
利用查找表使用所述输入值的多个最高有效位(MSB)计算粗略近似角度；
调整所述粗略近似角度以获取从0到θ的角度；以及
利用多项式近似计算精确校正值。
9.根据权利要求8所述的数字处理器，其中所述多项式近似包括泰勒级数以及三次近似中的一个或多个。
10.根据权利要求8所述的数字处理器，其中所述至少一个硬件设备被进一步配置为使用对称属性来降低所述查找表的大小。
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