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Computing Correctly Rounded Integer Powers in Floating-Point Arithmetic
- Source :
- ACM Transactions on Mathematical Software, ACM Transactions on Mathematical Software, 2010, 37 (1), pp.4:1-4:23. ⟨10.1145/1644001.1644005⟩, Kornerup, P, Christof, L, Lefevre, V, Louvet, N & Muller, J-M 2010, ' Computing Correctly Rounded Integer Powers in Floating-Point Arithmetic ', ACM Transactions on Mathematical Software, vol. 37, no. 1, pp. 4:1-4:23 ., ACM Transactions on Mathematical Software, Association for Computing Machinery, 2010, 37 (1), pp.4:1-4:23. ⟨10.1145/1644001.1644005⟩
- Publication Year :
- 2008
- Publisher :
- HAL CCSD, 2008.
-
Abstract
- We introduce several algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. For bounded, yet very large values of the exponent, we aim at obtaining correctly rounded results in round-to-nearest mode, that is, our algorithms return the floating-point number that is nearest the exact value.
- Subjects :
- Floating point
ACM: G.: Mathematics of Computing/G.1: NUMERICAL ANALYSIS/G.1.0: General/G.1.0.0: Computer arithmetic
[INFO.INFO-OH]Computer Science [cs]/Other [cs.OH]
Binary scaling
Integer overflow
010103 numerical & computational mathematics
02 engineering and technology
Minifloat
01 natural sciences
Machine epsilon
0202 electrical engineering, electronic engineering, information engineering
Integer square root
Nearest integer function
0101 mathematics
Arithmetic
Hardware_ARITHMETICANDLOGICSTRUCTURES
Fixed-point arithmetic
Fused multiply-add
Mathematics
Discrete mathematics
Applied Mathematics
[INFO.INFO-AO]Computer Science [cs]/Computer Arithmetic
ACM B.2.4
G.1.0
Floating-point arithmetic
Correct rounding
020202 computer hardware & architecture
integer power function
Integer powers
ACM: G.: Mathematics of Computing/G.4: MATHEMATICAL SOFTWARE/G.4.0: Algorithm design and analysis
Software
Subjects
Details
- Language :
- English
- ISSN :
- 00983500
- Database :
- OpenAIRE
- Journal :
- ACM Transactions on Mathematical Software, ACM Transactions on Mathematical Software, 2010, 37 (1), pp.4:1-4:23. ⟨10.1145/1644001.1644005⟩, Kornerup, P, Christof, L, Lefevre, V, Louvet, N & Muller, J-M 2010, ' Computing Correctly Rounded Integer Powers in Floating-Point Arithmetic ', ACM Transactions on Mathematical Software, vol. 37, no. 1, pp. 4:1-4:23 ., ACM Transactions on Mathematical Software, Association for Computing Machinery, 2010, 37 (1), pp.4:1-4:23. ⟨10.1145/1644001.1644005⟩
- Accession number :
- edsair.doi.dedup.....813a6196892d50064f649a4d94eb4360