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"Are you familiar with the IEEE floating point arithmetic standard? Would you like to understand it better? This book gives a broad overview of numerical computing, in a historical context, with special focus on the IEEE standard for binary floating point arithmetic. Key ideas are developed step by step, taking the reader from floating point representation, correctly rounded arithmetic, and the IEEE philosophy on exceptions, to an understanding of the crucial concepts of conditioning and stability, explained in a simple yet rigorous context. It gives technical details that are not readily available elsewhere, and includes challenging exercises that go beyond the topics covered in the text.Numerical Computing with IEEE Floating Point Arithmetic provides an easily accessible yet detailed discussion of IEEE Std 754-1985, arguably the most important standard in the computer industry. The result of an unprecedented cooperation between academic computer scientists and the cutting edge of industry, it is supported by virtually every modern computer. Other topics include the floating point architecture of the Intel microprocessors and a discussion of programming language support for the standard."

"This is the first book to focus on the problem of ensuring the correctness of floating-point hardware designs through mathematical methods. Formal Verification of Floating-Point Hardware Design advances a verification methodology based on a unified theory of register-transfer logic and floating-point arithmetic that has been developed and applied to the formal verification of commercial floating-point units over the course of more than two decades, during which the author was employed by several major microprocessor design companies. The book consists of five parts, the first two of which present a rigorous exposition of the general theory based on the first principles of arithmetic. Part I covers bit vectors and the bit manipulation primitives, integer and fixed-point encodings, and bit-wise logical operations. Part II addresses the properties of floating-point numbers, the formats in which they are encoded as bit vectors, and the various modes of floating-point rounding. In Part III, the theory is extended to the analysis of several algorithms and optimization techniques that are commonly used in commercial implementations of elementary arithmetic operations. As a basis for the formal verification of such implementations, Part IV contains high-level specifications of correctness of the basic arithmetic instructions of several major industry-standard floating-point architectures, including all details pertaining to the handling of exceptional conditions. Part V illustrates the methodology, applying the preceding theory to the comprehensive verification of a state-of-the-art commercial floating-point unit. All of these results have been formalized in the logic of the ACL2 theorem prover and mechanically checked to ensure their correctness. They are presented here, however, in simple conventional mathematical notation. The book presupposes no familiarity with ACL2, logic design, or any mathematics beyond basic high school algebra. It will be of interest to verification engineers as well as arithmetic circuit designers who appreciate the value of a rigorous approach to their art, and is suitable as a graduate text in computer arithmetic."

"Penjumlahan n bilangan floating point biasanya dilakukan dengan menggunakan metode rekursif biasa (metode original). Tugas akhir ini membahas beberapa metode alternatif untuk menjumlah n bilangan floating point, yaitu metode increasing, decreasing, psum, pairwise, insertion, dan plus-minus. Ketelitian dari metode-metode ini dibandingkan dengan analisis batas atas kesalahan dan percobaan numerik. Tidak ada satu metode yang secara seragam lebih akurat daripada metode lainnya. Tetapi untuk kasus khusus, diberikan petunjuk untuk memilih metode penjumlahan tertentu."

"Metode penjumlahan rekursif biasa (Original) umumnya dipakai untuk menjumlahkan n bilangan floating-point. Metode ini memiliki variasi: Increasing dan Decreasing. Pada tugas akhir ini akan dibahas cara memperbaiki ketelitian penjumlahan rekursif floating-point dengan metode compensated. Untuk membandingkan ketelitian metode-metode tersebut digunakan analisa kesalahan pembulatan dan percobaan-percobaan numerik. Metode Compensated sangat efektif untuk memperbaiki ketelitian penjumlahan rekursif floating-point, dengan batas atas kesalahan|En| < (2u + 0(nu2)) Σ|Xi|"

"This paper describes a research toward the accuracy of floating-point values, and effort to reveal the real accuracy. The methods used in this research paper are assignment of values, assignment of value of arithmetic expressions, and output the values using floating-point value format that helps reveal the accuracy. The programming-tool used are Visual C# 9, Visual C++ 9, Java 5, and Visual BASIC 9. These tools run on top of Intel 80 x 86 hardware. The results show that 1*10-x cannot be accurately represented, and the approximate accuracy ranges only from 7 to 16 decimal digits."

"A revised textbook for introductory courses in numerical methods, MATLAB and technical computing, which emphasises the use of mathematical software."

"This book takes readers on a thrilling tour of some of the most important and powerful areas of contemporary numerical mathematics. The tour is organized along the 10 problems of the SIAM 100-Digit Challenge, a contest posed by Nick Trefethen of Oxford University in the January/February 2002 issue of SIAM News. The complete story of the contest as well as a lively interview with Nick Trefethen are also included."