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Floating Point Numbers
"... f is negative the number n is negative. If e is negative, the number is less than one. The essential idea of scientific notation is to separate the significant digits of a number from its magnitude. The number of significant digits is determined by the size of f and the range of magnitude is determ ..."
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is determined by the size of e. We wrote the speed of light as 3 10 8 meters per second. If that is not precise enough, we can write 2.997 10 8 to express the same number with four digits of precision. Floating Point Numbers Floatingpoint number systems apply this same idea  separating
Floating Point Numbers
, 1999
"... this paper. In 1985, the Institute of Electrical and Electronic Engineers published IEEE Standard 754 for floatingpoint arithmetic. Virtually all general purpose processors built today have floatingpoint units which conform to IEEE 754. The examples in this paper describe IEEE 754 floatingpoint n ..."
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number formats. Instead of using base ten and powers of ten like scientific notation, IEEE 754 floatingpoint uses a binary fraction and an exponent that is considered to be a power of two. The format of a singleprecision floatingpoint number is shown in Figure 1. The leftmost bit indicates the sign
Floatingpoint Number LISP
, 1991
"... This paper describes the implementation, provides some measurements of its efficiency, and discusses the feasibility of this type of implementation ..."
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Cited by 1 (0 self)
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This paper describes the implementation, provides some measurements of its efficiency, and discusses the feasibility of this type of implementation
27. Floating Point Numbers
"... 28. floatApproximation #1 29. floatApproximation #2 30. floatApproximation #3 31. floatApproximation Example Program 32. float Literal Constants ..."
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28. floatApproximation #1 29. floatApproximation #2 30. floatApproximation #3 31. floatApproximation Example Program 32. float Literal Constants
Solving Constraints over FloatingPoint Numbers
, 2001
"... This paper introduces a new framework for tackling constraints over the floatingpoint numbers. An important application area where such solvers are required is program analysis (e.g., structural test case generation, correctness proof of numeric operations). Albeit the floatingpoint numbers are a ..."
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Cited by 18 (4 self)
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This paper introduces a new framework for tackling constraints over the floatingpoint numbers. An important application area where such solvers are required is program analysis (e.g., structural test case generation, correctness proof of numeric operations). Albeit the floatingpoint numbers are a
Abstract Printing FloatingPoint Numbers Quickly and Accurately
"... This paper presents a fast and accurate algorithm for printing floatingpoint numbers in both free and fixedformat modes. In freeformat mode, the algorithm generates the shortest, correctly rounded output string that converts to the same number when read back in, regardless of how the reader brea ..."
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This paper presents a fast and accurate algorithm for printing floatingpoint numbers in both free and fixedformat modes. In freeformat mode, the algorithm generates the shortest, correctly rounded output string that converts to the same number when read back in, regardless of how the reader
Polynomial Approximation and FloatingPoint Numbers
, 2007
"... For purposes of numerical implementation of mathematical functions, one is interested in finding low degree polynomials with floatingpoint coefficients approximating a given function to a certain precision. The basic idea of the method presented here is to look for a constrained approximant interpo ..."
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For purposes of numerical implementation of mathematical functions, one is interested in finding low degree polynomials with floatingpoint coefficients approximating a given function to a certain precision. The basic idea of the method presented here is to look for a constrained approximant
Printing FloatingPoint Numbers Quickly and Accurately
 In Proc. of the ACM SIGPLAN ’96 Conference on Programming Language Design and Implementation
"... This paper presents a fast and accurate algorithm for printing floatingpoint numbers in both free and fixedformat modes. In freeformat mode, the algorithm generates the shortest, correctly rounded output string that converts to the same number when read back in, accommodating whatever rounding m ..."
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Cited by 18 (2 self)
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This paper presents a fast and accurate algorithm for printing floatingpoint numbers in both free and fixedformat modes. In freeformat mode, the algorithm generates the shortest, correctly rounded output string that converts to the same number when read back in, accommodating whatever rounding
On the Precision Attainable with Various FloatingPoint Number Systems
"... 1 Introduction A real number x is usually approximated in a digital computer by an element fl(x) of a finite set F of "floatingpoint " numbers. We regard the elements of F as exactly representable real numbers, and take fl(x) as the floatingpoint number closest to x. The definiti ..."
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1 Introduction A real number x is usually approximated in a digital computer by an element fl(x) of a finite set F of "floatingpoint " numbers. We regard the elements of F as exactly representable real numbers, and take fl(x) as the floatingpoint number closest to x
Accurate Matrix Multiplication with Multiple Floatingpoint Numbers
"... Abstract—This paper is concerned with an accurate computation of matrix multiplication, where components of matrices are represented by summation of floatingpoint numbers. Recently, an accurate summation algorithm is developed by the latter three of the authors. In this paper, it is specialized to ..."
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Abstract—This paper is concerned with an accurate computation of matrix multiplication, where components of matrices are represented by summation of floatingpoint numbers. Recently, an accurate summation algorithm is developed by the latter three of the authors. In this paper, it is specialized
Results 1  10
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