论文信息 - SIPE: Small Integer Plus Exponent

SIPE: Small Integer Plus Exponent

SIPE (Small Integer Plus Exponent) is a mini-library in the form of a C header file, to perform floating-point computations in very low precisions with correct rounding to nearest in radix 2. The goal of such a tool is to do proofs of algorithms/properties or computations of tight error bounds in these precisions by exhaustive tests, in order to try to generalize them to higher precisions. The currently supported operations are addition, subtraction, multiplication (possibly with the error term), FMA, and miscellaneous comparisons and conversions. Timing comparisons have been done with hardware IEEE-754 floating point and with GNU MPFR.

Vincent Lefèvre | V. Lefèvre

[1] Ole Møller. Quasi double-precision in floating point addition , 1965 .

[2] James Demmel,et al. IEEE Standard for Floating-Point Arithmetic , 2008 .

[3] Donald Ervin Knuth,et al. The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information , 1978 .

[4] IEEE standard for binary floating-point arithmetic - IEEE standard 754-1985 , 1985 .

[5] Vincent Lefèvre,et al. On the Computation of Correctly-Rounded Sums , 2009, 2009 19th IEEE Symposium on Computer Arithmetic.

[6] Vincent Lefèvre,et al. MPFR: A multiple-precision binary floating-point library with correct rounding , 2007, TOMS.

[7] Jean-Michel Muller,et al. Computing correctly rounded integer powers in floating-point arithmetic , 2010, TOMS.

[8] Jean-Michel Muller,et al. Handbook of Floating-Point Arithmetic (2nd Ed.) , 2018 .

[9] David Thomas,et al. The Art in Computer Programming , 2001 .