A. V. Aho, R. Sethi, and J. D. Ullman, Compilers: principles, techniques and tools, p.84, 1986.

S. [. Balakrishnan and . Boyd, On computing the worst-case peak gain of linear systems, Systems & Control Letters, vol.19, issue.4, pp.265-269, 1992.
DOI : 10.1016/0167-6911(92)90064-Y

N. Brisebarre and S. Chevillard, Efficient polynomial lapproximations Guillaume Melquiond, and Sylvain Pion. The design of the boost interval arithmetic library, 18th IEEE Symposium on Computer Arithmetic, pp.25-27, 2006.

T. Bollaert, Catapult Synthesis: A Practical Introduction to Interactive C Synthesis, High-Level Synthesis, pp.29-52, 2008.
DOI : 10.1007/978-1-4020-8588-8_3

W. [. Choi and . Burleson, Search-based wordlength optimization for VLSI/DSP synthesis, Proceedings of 1994 IEEE Workshop on VLSI Signal Processing, pp.198-207, 1994.
DOI : 10.1109/VLSISP.1994.574744

G. M. Andrea, H. Cilio, and . Corporaal, Floating point to fixed point conversion of c code, Proceedings of the 8th International Conference on Compiler Construction, Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS'99, pp.229-243, 1999.

P. [. Constantinides, W. Cheung, and . Luk, The multiple wordlength paradigm, Field-Programmable Custom Computing Machines, 2001. FCCM '01. The 9th Annual IEEE Symposium on, pp.51-60, 2001.

[. Chen, X. Deng, and A. Haimovich, Layered turbo space-time coded mimo-ofdm systems for time varying channels, Proc. of the 2003 IEEE Global Telecommunications Conference (GLOBECOM'03), pp.1831-1836, 2003.

A. Chapoutot, L. Didier, and F. Villers, Range estimation of floating-point variables in simulink models, DASIP, pp.1-8, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00816115

J. Cong, K. G. Liu, Z. Zhang, S. Zhou, and Y. Zou, Evaluation of Static Analysis Techniques for Fixed-Point Precision Optimization, 2009 17th IEEE Symposium on Field Programmable Custom Computing Machines, pp.231-234, 2009.
DOI : 10.1109/FCCM.2009.35

C. Cln-+-]-sylvain-chevillard, H. Lauter, N. Diep-nguyen, F. Revol, and . Rouiller, Multiple precision floating-point interval library Available at http://gforge.inria

H. Thomas, C. E. Cormen, R. L. Leiserson, C. Rivest, and . Stein, Introduction to Algorithms (3, p.115, 2009.

J. [. Chen, R. H. Wu, J. Istepanian, and . Chu, Optimizing stability bounds of finite-precision pid controller structures. Automatic Control, IEEE Transactions on, vol.44, issue.11, pp.2149-2153, 1999.

]. F. De-dinechin and B. Pasca, Designing Custom Arithmetic Data Paths with FloPoCo, IEEE Design & Test of Computers, vol.28, issue.4, pp.18-27, 2011.
DOI : 10.1109/MDT.2011.44

URL : https://hal.archives-ouvertes.fr/ensl-00646282

J. Henrique-de-figueiredo and . Stolfi, Affine Arithmetic: Concepts and Applications, Numerical Algorithms, vol.37, issue.1-4, pp.147-158, 2004.
DOI : 10.1023/B:NUMA.0000049462.70970.b6

D. Milo?, L. Ercegovac, D. W. Imbert, J. Matula, G. Muller et al., Improving Goldschmidt division, square root, and square root reciprocal, IEEE Trans. Computers, vol.49, issue.7, pp.759-763, 2000.

D. Milo?, T. Ercegovac, and . Lang, Digital Arithmetic, p.62, 2004.

G. Laurent-fousse, V. Hanrot, P. Lefèvre, P. Pélissier, and . Zimmermann, MPFR, ACM Transactions on Mathematical Software, vol.33, issue.2, pp.13-14, 2007.
DOI : 10.1145/1236463.1236468

C. F. Fang, R. A. Rutenbar, and T. Chen, Fast, accurate static analysis for fixed-point finite-precision effects in DSP designs, ICCAD-2003. International Conference on Computer Aided Design (IEEE Cat. No.03CH37486), pp.275-305, 2003.
DOI : 10.1109/ICCAD.2003.159701

F. Glover, Tabu Search: A Tutorial, Interfaces, vol.20, issue.4, pp.74-94, 1990.
DOI : 10.1287/inte.20.4.74

D. Goldberg, What every computer scientist should know about floating-point arithmetic, ACM Computing Surveys, vol.23, issue.1, pp.5-48, 1991.
DOI : 10.1145/103162.103163

R. Joseph and . Guerci, Space-time adaptive processing for radar, p.126, 2003.

]. E. Han75 and . Hansen, A generalized interval arithmetic, Interval Mathematics, Lecture Notes in Computer Science, vol.29, issue.30, pp.7-18, 1975.

K. Han, I. Eo, K. Kim, and H. Cho, Numerical wordlength optimization for cdma demodulator, Circuits and Systems The 2001 IEEE International Symposium on, pp.290-293, 2001.

. Hig02, J. Nicholas, and . Higham, Accuracy and Stability of Numerical Algorithms, Society for Industrial and Applied Mathematics, vol.125, p.104, 2002.

D. Nguyen-hai-nam, O. Ménard, and . Sentieys, Novel Algorithms for Word-length Optimization, 19th European Signal Processing Conference (EUSIPCO-2011), p.41, 2011.

L. John, D. A. Hennessy, and . Patterson, Computer Architecture, Fourth Edition: A Quantitative Approach, pp.10-11, 2006.

A. Irturk, B. Benson, S. Mirzaei, and R. Kastner, An FPGA Design Space Exploration Tool for Matrix Inversion Architectures, 2008 Symposium on Application Specific Processors, pp.42-47, 2008.
DOI : 10.1109/SASP.2008.4570784

A. Irturk, B. Benson, S. Mirzaei, and R. Kastner, GUSTO, ACM Transactions on Embedded Computing Systems, vol.9, issue.4, pp.1-32, 2010.
DOI : 10.1145/1721695.1721698

A. Irturk, S. Mirzaei, and R. Kastner, An efficient fpga implementation of scalable matrix inversion core using qr decomposition, Matrix, pp.1-12, 2009.

]. L. Jac70 and . Jackson, Roundoff-noise analysis for fixed-point digital filters realized in cascade or parallel form, Standardization. Programming Languages ? C. ISO/IEC Standard Audio and Electroacoustics IEEE Transactions on, vol.9899, issue.182, pp.107-122, 1970.

J. M. Chesneaux, Cadna: a library for estimating round-off error propagation, Computer Physics Communications, vol.178, issue.12, pp.933-955, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01146486

C. Jeannerod and J. , Simultaneous floatingpoint sine and cosine for VLIW integer processors, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00672327

S. Henry and . Warren-jr, Hacker's Delight, pp.55-63, 2002.

R. David, S. C. Koes, and . Goldstein, Near-optimal instruction selection on DAGs, International Symposium on Code Generation and Optimization (CGO'08), p.84, 2008.

[. Kim, K. Il-kum, and W. Sung, Fixed-point optimization utility for c and c++ based digital signal processing programs, IEEE Trans. Circuits and Systems II, pp.1455-1464, 1996.

M. [. Keding, M. Willems, H. Coors, and . Meyr, FRIDGE: a fixed-point design and simulation environment, Proceedings Design, Automation and Test in Europe, pp.429-435, 1998.
DOI : 10.1109/DATE.1998.655893

[. Lauter, Arrondi correct de fonctions mathématiques -fonctions univariées et bivariées, certification et automatisation, p.87, 2008.

[. Lee, R. C. Cheung, W. Luk, and J. D. Villasenor, Hardware Implementation Trade-Offs of Polynomial Approximations and Interpolations, IEEE Transactions on Computers, vol.57, issue.5, pp.686-701, 2008.
DOI : 10.1109/TC.2007.70847

D. Lee, R. C. Gaffar, O. Cheung, W. Mencer, G. A. Luk et al., Accuracy-Guaranteed Bit-Width Optimization, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol.25, issue.10, pp.1990-2000, 2006.
DOI : 10.1109/TCAD.2006.873887

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.385.6194

[. Lopez, T. Hilaire, and L. Didier, Sum-ofproducts evaluation schemes with fixed-point arithmetic, and their application to IIR filter implementation, Conf. on Design and Architectures for Signal and Image Processing (DASIP), p.26, 2012.

B. Lopez, T. Hilaire, and L. Didier, Formatting bits to better implement signal processing algorithms, PECCS, pp.104-111, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01076049

[. Lee and J. D. Villasenor, Optimized Custom Precision Function Evaluation for Embedded Processors, IEEE Transactions on Computers, vol.58, issue.1, pp.46-59, 2009.
DOI : 10.1109/TC.2008.124

[. Muller, N. Brisebarre, F. De-dinechin, C. Jeannerod, V. Lefèvre et al., Handbook of Floating-Point Arithmetic, Nathalie Revol, p.18, 2010.
DOI : 10.1007/978-0-8176-4705-6

URL : https://hal.archives-ouvertes.fr/ensl-00379167

D. Menard, D. Chillet, F. Charot, and O. Sentieys, Automatic floating-point to fixed-point conversion for DSP code generation, Proceedings of the international conference on Compilers, architecture, and synthesis for embedded systems , CASES '02, pp.270-276, 2002.
DOI : 10.1145/581630.581674

URL : https://hal.archives-ouvertes.fr/inria-00482916

G. Melquiond and É. Lyon, De l'arithmétique d'intervalles à la certification de programmes, p.78, 2006.

R. E. Moore, R. Baker-kearfott, and M. J. Cloud, Introduction to Interval Analysis, Society for Industrial and Applied Mathematics, p.28, 2009.
DOI : 10.1137/1.9780898717716

R. E. Moore, R. Baker-kearfott, and M. J. Cloud, Introduction to Interval Analysis, SIAM, p.114, 2009.
DOI : 10.1137/1.9780898717716

[. Mouilleron, A. Najahi, and G. Revy, Approach based on instruction selection for fast and certified code generation, Proceedings of the 15th GAMM-IMACS International Symposium on Scientific Computing , Computer Arithmetic and Validated Numerics, 2012.
URL : https://hal.archives-ouvertes.fr/lirmm-00813055

[. Martel, A. Najahi, and G. Revy, Code Size and Accuracy-Aware Synthesis of Fixed-Point Programs for Matrix Multiplication, Proc. of the 4th International Conference on Pervasive and Embedded Computing and Communication Systems, pp.204-214, 2014.
URL : https://hal.archives-ouvertes.fr/lirmm-00860383

[. Martel, A. Najahi, and G. Revy, Toward the synthesis of fixed-point code for matrix inversion based on Cholesky decomposition, Proceedings of the 2014 Conference on Design and Architectures for Signal and Image Processing, pp.73-80, 2014.
DOI : 10.1109/DASIP.2014.7115609

URL : https://hal.archives-ouvertes.fr/lirmm-01212806

C. Mouilleron, A. Najahi, and G. Revy, Automated Synthesis of Target-Dependent Programs for Polynomial Evaluation in Fixed-Point Arithmetic, 2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2014.
DOI : 10.1109/SYNASC.2014.27

URL : https://hal.archives-ouvertes.fr/lirmm-00814338

R. E. Moore, Interval analysis, pp.18-28, 1966.

C. Mouilleron, Efficient computation with structured matrices and arithmetic expressions, pp.82-86, 2011.
URL : https://hal.archives-ouvertes.fr/tel-00688388

C. Mouilleron and G. Revy, Automatic Generation of Fast and Certified Code for Polynomial Evaluation, 2011 IEEE 20th Symposium on Computer Arithmetic, pp.233-242, 2011.
DOI : 10.1109/ARITH.2011.39

URL : https://hal.archives-ouvertes.fr/ensl-00531721

R. Ménard, O. Rocher, N. Sentieys, L. Simon, T. Didier et al., Design of Fixed- Point Embedded Systems (defis) French ANR Project, Proceedings of the Conference on Design and Architectures for Signal and Image Processing, pp.23-25, 2012.

H. Nguyen, Optimisation de la précision de calcul pour la réduction d'énergie des systèmes embarqués. These, Université Rennes 1, pp.39-41, 2011.

[. Nikolic, H. T. Nguyen, and G. Frantz, Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPs, EURASIP Journal on Advances in Signal Processing, vol.2007, issue.1
DOI : 10.1109/29.45619

. Adv, Signal Process, pp.13-13, 2007.

C. [. Nambiar, P. Tang, and . Mars, Genetic and learning automata algorithms for adaptive digital filters ICASSP-92, Acoustics, Speech, and Signal Processing IEEE International Conference on, pp.41-44, 1992.

L. Michael and . Overton, Numerical Computing with IEEE Floating Point Arithmetic, Society for Industrial and Applied Mathematics, 2001.

M. [. Prandoni and . Vetterli, Signal Processing for Communications. Communication and information sciences, p.34, 2008.

[. Raina, FLIP: a Floating-point Library for Integer Processors, p.76, 2006.

G. Revy, Implementation of binary floating-point arithmetic on embedded integer processors -Polynomial evaluation-based algorithms and certified code generation, pp.13-29, 2009.
URL : https://hal.archives-ouvertes.fr/tel-00469661

N. Revol and F. Rouillier, Motivations for an Arbitrary Precision Interval Arithmetic and the MPFI Library, Reliable Computing, vol.2, issue.3, pp.275-290, 2005.
DOI : 10.1007/s11155-005-6891-y

URL : https://hal.archives-ouvertes.fr/inria-00544998

M. Ian, S. , and D. Hoey, Closest-point problems, FOCS, pp.151-162, 1975.

[. Sung and K. Kum, Simulation-based word-length optimization method for fixed-point digital signal processing systems, IEEE Transactions on Signal Processing, vol.43, issue.12, pp.3087-3090, 1995.
DOI : 10.1109/78.476465

. John-von-neumann, First draft of a report on the EDVAC, IEEE Annals of the History of Computing, vol.15, issue.4, pp.27-75, 1993.
DOI : 10.1109/85.238389

M. Püschel, Automatic generation of implementations for DSP transforms on fused multiply-add architectures, International Conference on Acoustics, Speech, and Signal Processing, p.21, 2004.

L. Zhou, L. Qiu, and J. Zhu, A novel adaptive equalization algorithm for MIMO communication system, Proc. of the IEEE 62nd Vehicular Technology Conference (VTC-2005-Fall), pp.2408-2412, 2005.