Compilers: principles, techniques, and tools
Compilers: principles, techniques, and tools
The C programming language
Compiler support for floating-point computation
Software—Practice & Experience
Floating-point standards—theory and practice
Reliability in computing: the role of interval methods in scientific computing
A Simple but Realistic Model of Floating-Point Computation
ACM Transactions on Mathematical Software (TOMS)
27 bits are not enough for 8-digit accuracy
Communications of the ACM
The Art of Computer Programming Volumes 1-3 Boxed Set
The Art of Computer Programming Volumes 1-3 Boxed Set
Contributions to a proposed standard for binary floating-point arithmetic (computer arithmetic)
Contributions to a proposed standard for binary floating-point arithmetic (computer arithmetic)
The design of floating-point data types
ACM Letters on Programming Languages and Systems (LOPLAS)
Solving polynomial systems for curve, surface and solid modeling
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Infinity arithmetic, comparisons and J
APL '95 Proceedings of the international conference on Applied programming languages
The philosophy of nothing and everything
APL '95 Proceedings of the international conference on Applied programming languages
Handling floating-point exceptions in numeric programs
ACM Transactions on Programming Languages and Systems (TOPLAS)
Mantissa-Preserving Operations and Robust Algorithm-Based Fault Tolerance for Matrix Computations
IEEE Transactions on Computers
Algorithm-Based Fault Tolerant Synthesis for Linear Operations
IEEE Transactions on Computers
Robust adaptive floating-point geometric predicates
Proceedings of the twelfth annual symposium on Computational geometry
IEEE Transactions on Computers
Semi-Logarithmic Number Systems
IEEE Transactions on Computers
A Mechanically Checked Proof of the AMD5K86TM Floating-Point Division Program
IEEE Transactions on Computers
Toward Correctly Rounded Transcendentals
IEEE Transactions on Computers
Proceedings of the 14th international conference on Supercomputing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A Family of Variable-Precision Interval Arithmetic Processors
IEEE Transactions on Computers
Floating Point Verification in HOL Light: The Exponential Function
Formal Methods in System Design
Monte Carlo arithmetic: how to gamble with floating point and win
Computing in Science and Engineering
A Low Power Approach to Floating Point Adder Design for DSP Applications
Journal of VLSI Signal Processing Systems
Computer assisted proof of optimal approximability results
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Recursive algorithm with C++ program for floating-point arithmetic
ACM SIGCSE Bulletin
The Journal of Supercomputing
You could learn a lot from a quadratic: overloading considered harmful
ACM SIGPLAN Notices
Hardware Designs for Exactly Rounded Elementary Functions
IEEE Transactions on Computers
Which pivot to solve linear systems?
Journal of Computational and Applied Mathematics
Rapid multiplication modulo the sum and difference of highly composite numbers
Mathematics of Computation
ACM Transactions on Mathematical Software (TOMS)
Propagation of Roundoff Errors in Finite Precision Computations: A Semantics Approach
ESOP '02 Proceedings of the 11th European Symposium on Programming Languages and Systems
Asserting the Precision of Floating-Point Computations: A Simple Abstract Interpreter
ESOP '02 Proceedings of the 11th European Symposium on Programming Languages and Systems
A Machine-Checked Theory of Floating Point Arithmetic
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
A Generic Library for Floating-Point Numbers and Its Application to Exact Computing
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Static Analyses of the Precision of Floating-Point Operations
SAS '01 Proceedings of the 8th International Symposium on Static Analysis
Static Analysis of the Numerical Stability of Loops
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Controlling Control Systems: An Application of Evolving Retrenchment
ZB '02 Proceedings of the 2nd International Conference of B and Z Users on Formal Specification and Development in Z and B
Solving Constraints over Floating-Point Numbers
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Small Multiplier-Based Multiplication and Division Operators for Virtex-II Devices
FPL '02 Proceedings of the Reconfigurable Computing Is Going Mainstream, 12th International Conference on Field-Programmable Logic and Applications
Novel techniques for robust voxelization and visualization of implicit surfaces
Graphical Models - Volume modeling
Enhanced word clustering for hierarchical text classification
Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
ICS '03 Proceedings of the 17th annual international conference on Supercomputing
Numerical difficulties in pre-university informatics education and competitions
Informatics in education
A divisive information theoretic feature clustering algorithm for text classification
The Journal of Machine Learning Research
Floating point arithmetic teaching for computational science
Future Generation Computer Systems - Special issue: Selected papers from the workshop on education in computational sciences held at the ICCS 2002
CORDIC Processor for Variable-Precision Interval Arithmetic
Journal of VLSI Signal Processing Systems
How to read floating point numbers accurately
ACM SIGPLAN Notices - Best of PLDI 1979-1999
Validation of assembler programs for DSPs: a static analyzer
Proceedings of the 5th ACM SIGPLAN-SIGSOFT workshop on Program analysis for software tools and engineering
Recursive de Casteljau bisection and rounding errors
Computer Aided Geometric Design
ISVLSI '05 Proceedings of the IEEE Computer Society Annual Symposium on VLSI: New Frontiers in VLSI Design
Fuzzy Memoization for Floating-Point Multimedia Applications
IEEE Transactions on Computers
Encyclopedia of Computer Science
Journal of Computing Sciences in Colleges
Termination of Floating-Point Computations
Journal of Automated Reasoning
Perturbing and evaluating numerical programs without recompilation: the wonglediff way
Software—Practice & Experience
Design and implementation of a modular and portable IEEE 754 compliant floating-point unit
Proceedings of the conference on Design, automation and test in Europe: Designers' forum
SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
Provably faithful evaluation of polynomials
Proceedings of the 2006 ACM symposium on Applied computing
Semantics of roundoff error propagation in finite precision calculations
Higher-Order and Symbolic Computation
Using model checking with symbolic execution to verify parallel numerical programs
Proceedings of the 2006 international symposium on Software testing and analysis
Stayin' alert:: moulding failure and exceptions to your needs
Proceedings of the 5th international conference on Generative programming and component engineering
Chaos and Graphics: Robust visualization of strange attractors using affine arithmetic
Computers and Graphics
Efficient histogram generation using scattering on GPUs
Proceedings of the 2007 symposium on Interactive 3D graphics and games
A translator system for the MATLAB language: Research Articles
Software—Practice & Experience
Computing in Science and Engineering
Standardization and testing of implementations of mathematical functions in floating point numbers
Programming and Computing Software
A note on Platt's probabilistic outputs for support vector machines
Machine Learning
A Tool for Unbiased Comparison between Logarithmic and Floating-point Arithmetic
Journal of VLSI Signal Processing Systems
One-way hash function construction based on 2D coupled map lattices
Information Sciences: an International Journal
Classroom examples of robustness problems in geometric computations
Computational Geometry: Theory and Applications
A two-steps algorithm for approximating real roots of a polynomial in Bernstein basis
Mathematics and Computers in Simulation
TAPIA '07 Proceedings of the 2007 conference on Diversity in computing
Combining symbolic execution with model checking to verify parallel numerical programs
ACM Transactions on Software Engineering and Methodology (TOSEM)
The pitfalls of verifying floating-point computations
ACM Transactions on Programming Languages and Systems (TOPLAS)
Faster projection based methods for circuit level verification
Proceedings of the 2008 Asia and South Pacific Design Automation Conference
An efficient algorithm for a sharp approximation of universally quantified inequalities
Proceedings of the 2008 ACM symposium on Applied computing
Computing Properties of Numerical Imperative Programs by Symbolic Computation
Fundamenta Informaticae - Half a Century of Inspirational Research: Honoring the Scientific Influence of Antoni Mazurkiewicz
High-performance computing of 1/√xi and exp(±xi) for a vector of inputs xi on Alpha and IA-64 CPUs
Journal of Systems Architecture: the EUROMICRO Journal
Reliable Implementation of Real Number Algorithms: Theory and Practice
Test Construction for Mathematical Functions
TestCom '08 / FATES '08 Proceedings of the 20th IFIP TC 6/WG 6.1 international conference on Testing of Software and Communicating Systems: 8th International Workshop
The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Program transformation for numerical precision
Proceedings of the 2009 ACM SIGPLAN workshop on Partial evaluation and program manipulation
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Integration strategies for Computational Science & Engineering software
SECSE '09 Proceedings of the 2009 ICSE Workshop on Software Engineering for Computational Science and Engineering
Search-based failure discovery using testability transformations to generate pseudo-oracles
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Fool me twice: Exploring and exploiting error tolerance in physics-based animation
ACM Transactions on Graphics (TOG)
What every agent-based modeller should know about floating point arithmetic
Environmental Modelling & Software
Enhancing the implementation of mathematical formulas for fixed-point and floating-point arithmetics
Formal Methods in System Design
Behavior detection using confidence intervals of hidden Markov models
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Evaluating the performance of space plasma simulations using FPGA's
VECPAR'02 Proceedings of the 5th international conference on High performance computing for computational science
An approach to teaching computer arithmetic
VECPAR'02 Proceedings of the 5th international conference on High performance computing for computational science
Trusting floating point benchmarks - are your benchmarks really data independent?
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Printing floating-point numbers quickly and accurately with integers
PLDI '10 Proceedings of the 2010 ACM SIGPLAN conference on Programming language design and implementation
Log' version vector: Logging version vectors concisely in dynamic replication
Information Processing Letters
Spatially variant convolution with scaled B-splines
IEEE Transactions on Image Processing
Perturbing numerical calculations for statistical analysis of floating-point program (in)stability
Proceedings of the 19th international symposium on Software testing and analysis
VFloat: A Variable Precision Fixed- and Floating-Point Library for Reconfigurable Hardware
ACM Transactions on Reconfigurable Technology and Systems (TRETS)
A new chaos-based fast image encryption algorithm
Applied Soft Computing
Improved bound for stochastic formal correctness of numerical algorithms
Innovations in Systems and Software Engineering
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
A generic lazy evaluation scheme for exact geometric computations
Science of Computer Programming
Static analysis of finite precision computations
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
VECPAR'10 Proceedings of the 9th international conference on High performance computing for computational science
Dynamic elimination of overflow tests in a trace compiler
CC'11/ETAPS'11 Proceedings of the 20th international conference on Compiler construction: part of the joint European conferences on theory and practice of software
FPGA optimizations for a pipelined floating-point exponential unit
ARC'11 Proceedings of the 7th international conference on Reconfigurable computing: architectures, tools and applications
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
A novel design of a two operand normalization circuit
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Proofs of numerical programs when the compiler optimizes
Innovations in Systems and Software Engineering
Rounding coefficients and artificially underflowing terms in non-numeric expressions
ACM Communications in Computer Algebra
An exact rational mixed-integer programming solver
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Arithmetic operations beyond floating point number precision
International Journal of Computational Science and Engineering
Formal analysis of MPI-based parallel programs
Communications of the ACM
Trustworthy numerical computation in Scala
Proceedings of the 2011 ACM international conference on Object oriented programming systems languages and applications
Algorithms for vector graphic optimization and compression
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
Robust and efficient delaunay triangulations of points on or close to a sphere
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
An overview of semantics for the validation of numerical programs
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Arbitrary 3d resolution discrete ray tracing of implicit surfaces
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Correctness issues of symbolic bisimulation computation for markov chains
MMB&DFT'10 Proceedings of the 15th international GI/ITG conference on Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance
Standardization and testing of mathematical functions
PSI'09 Proceedings of the 7th international Andrei Ershov Memorial conference on Perspectives of Systems Informatics
Multi-Prover verification of floating-point programs
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Weaknesses of COSvd (2,128) stream cipher
ICISC'05 Proceedings of the 8th international conference on Information Security and Cryptology
Bayesian automatic adaptive quadrature: an overview
MMCP'11 Proceedings of the 2011 international conference on Mathematical Modeling and Computational Science
Original article: Computational complexity of iterated maps on the interval
Mathematics and Computers in Simulation
FPGA paranoia: testing numerical properties of FPGA floating point IP-Cores
ARC'12 Proceedings of the 8th international conference on Reconfigurable Computing: architectures, tools and applications
A dynamic program analysis to find floating-point accuracy problems
Proceedings of the 33rd ACM SIGPLAN conference on Programming Language Design and Implementation
A problem in hydrological model calibration in the case of averaged flux input and flux output
Environmental Modelling & Software
Research paper: The saga of minimum spanning trees
Computer Science Review
Operations Research Letters
Searching and mining trillions of time series subsequences under dynamic time warping
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Taking proof-based verified computation a few steps closer to practicality
Security'12 Proceedings of the 21st USENIX conference on Security symposium
Computing Properties of Numerical Imperative Programs by Symbolic Computation
Fundamenta Informaticae - Half a Century of Inspirational Research: Honoring the Scientific Influence of Antoni Mazurkiewicz
On significance of the least significant bits for differential privacy
Proceedings of the 2012 ACM conference on Computer and communications security
Dealing with rounding error problems in evolutionary physical simulation
Artificial Life and Robotics
Engineering Applications of Artificial Intelligence
Refining abstract interpretation based value analysis with constraint programming techniques
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
CUDA accelerated fault tree analysis with C-XSC
SUM'12 Proceedings of the 6th international conference on Scalable Uncertainty Management
Estimation and modeling of actual numerical errors in volume rendering
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
Automatic detection of floating-point exceptions
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
On reproducibility and traceability of simulations
Proceedings of the Winter Simulation Conference
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Automatically adapting programs for mixed-precision floating-point computation
Proceedings of the 27th international ACM conference on International conference on supercomputing
How do you compute the midpoint of an interval?
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Knowledge Discovery from Data (TKDD) - Special Issue on ACM SIGKDD 2012
Precimonious: tuning assistant for floating-point precision
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Data mining a trillion time series subsequences under dynamic time warping
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Efficient energy evaluations for active B-Spline/NURBS surfaces
Computer-Aided Design
Computation of the monodromy matrix in floating point arithmetic with the Wilkinson Model
Computers & Mathematics with Applications
Tool support for software lookup table optimization
Scientific Programming
First order rejection tests for multiple-objective optimization
Journal of Global Optimization
Hand shape classification using depth data for unconstrained 3D interaction
Journal of Ambient Intelligence and Smart Environments - Ambient and Smart Component Technologies for Human Centric Computing
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Floating-point arithmetic is considered as esoteric subject by many people. This is rather surprising, because floating-point is ubiquitous in computer systems: Almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must respond to floating-point exceptions such as overflow. This paper presents a tutorial on the aspects of floating-point that have a direct impact on designers of computer systems. It begins with background on floating-point representation and rounding error, continues with a discussion of the IEEE floating point standard, and concludes with examples of how computer system builders can better support floating point.