Arithmetic exceptionality of generalized Lattès maps
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We consider the arithmetic exceptionality problem for the generalized Lattès maps on $\mathbf{P}^2$. We prove an existence result for maps arising from the product $E \times E$ of elliptic curves $E$ with CM.In chapter 7, the function of the arithmetic unit has been defined loosely as the performance of arithmetic operations. As such, the capabilities of the arithmetic unit have been compared to those of a desk calculator. Although this analogy is valid in a general sense, the capabilities of arithmetic units exceed those of the desk calculator: in addition to arithmetic operations, certain logic data manipulations can be performed. Moreover, the particular manner in which operations are performed is influenced by the electronic design. In the following paragraphs we shall discuss three types of operations: fixed-point arithmetic operations, logic operations, and floating-point arithmetic operations. Incidental to this discussion, we shall see structures required for the implementation of the individual operations. In conclusion, several sample layouts of arithmetic units are indicated in which the individual requirements are combined.
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A method of high precision arithmetic has been devised for the CDC-3800 computer based on nonstandard type. The precision extends up to 324 bits for normal arithmetic operations, and up to approximately 310 bits for exponentiation.
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We present an implementation of double precision interval arithmetic us- ing the single-instruction-multiple-data SSE-2 instruction and register set extensions. The implementation is part of a package for exact real arithmetic, which defines the interval arithmetic variation that must be used: incorrect operations such as division by zero cause exceptions, loose evaluation of the operations is in effect, and performance is more impor- tant than tightness of the produced bounds. The SSE2 extensions are suitable for the job, because they can be used to operate on a pair of double precision numbers and include separate rounding mode control and detection of the exceptional conditions. The paper de- scribes the ideas we use to fit interval arithmetic to this set of instructions, shows a perfor- mance comparison with other freely available interval arithmetic packages, and discusses possible very simple hardware extensions that can significantly increase the performance of interval arithmetic.
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The basic arithmetic of matching the string's mode and KMP arithmetic are discussed in this paper.The new arithmetic was put forward through the analysis for the two arithmetic.This arithmetic has some advantage of less time complexity and more simple than KMP arithmetic.
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So far we have only been concerned with single byte arithmetic, that is, arithmetic using 8-bit operands and giving 8-bit results. The range of numeric values which can be manipulated by 8-bit arithmetic is small, so we often need to use more than one byte to hold our numbers; we then need to carry out arithmetic using sixteen or more bits. The microprocessor inside the ZX81 has assembly language instructions which allow 16-bit arithmetic to be performed directly. These instructions can also be used to provide 32-bit arithmetic, 48-bit arithmetic and so on. The 16-bit arithmetic instructions also allow additional loop facilities.
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Arithmetic circuit complexity
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It is not unusual in the schools to study numeration systems other than our own decimal system. A good unit of this type can stimulate the students' interest in arithmetic and can be helpful in providing for practice in computation.
Decimal
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