libm implementations -------------------- unix v7 libm by Robert Morris (rhm) around 1979 see: "Computer Approximations" by Hart & Cheney, 1968 used in: plan9, go cephes by Stephen L. Moshier, 1984-1992 http://www.netlib.org/cephes/ see: "Methods and Programs for Mathematical Functions" by Moshier 1989 fdlibm by K. C. Ng around 1993, updated in 1995? (1993: copyright notice: "Developed at SunPro ..") (1995: copyright notice: "Developed at SunSoft ..") see: "Argument Reduction for Huge Arguments: Good to the Last Bit" by Ng 1992 http://www.netlib.org/fdlibm used in: netbsd, openbsd, freebsd, bionic, musl libultim by Abraham Ziv around 2001 (gpl) (also known as the ibm accurate portable math lib) see: "Fast evaluation of elementary mathematical functions with correctly rounded last bit" by Ziv 1991 http://web.archive.org/web/20050207110205/http://oss.software.ibm.com/mathlib/ used in: glibc libmcr by K. C. Ng, 2004 (sun's correctly rounded libm) mathcw by Nelson H. F. Beebe, 2010? http://ftp.math.utah.edu/pub/mathcw/ (no sources available?) sleef by Naoki Shibata, 2010 (simd lib for evaluating elementary functions) http://shibatch.sourceforge.net/ crlibm by ens-lyon, 2004-2010 http://lipforge.ens-lyon.fr/www/crlibm/ see: crlibm.pdf at http://lipforge.ens-lyon.fr/frs/?group_id=8&release_id=123 see: "Elementary Functions" by Jean-Michel Muller 2005 see: "Handbook of Floating-Point Arithmetic" by (many authors from Lyon) 2009 (closed: intel libm, hp libm for itanium, ..) libm tests ---------- http://www.netlib.org/fp/ucbtest.tgz http://www.jhauser.us/arithmetic/TestFloat.html http://cant.ua.ac.be/old/ieeecc754.html http://www.loria.fr/~zimmerma/mpcheck/ http://gforge.inria.fr/projects/mpcheck/ http://people.inf.ethz.ch/gonnet/FPAccuracy/Analysis.html http://www.math.utah.edu/~beebe/software/ieee/ http://www.vinc17.org/research/testlibm/index.en.html http://www.vinc17.org/research/fptest.en.html tests in crlibm multiprecision libs (useful for tests) http://mpfr.org/ http://www.multiprecision.org/index.php?prog=mpc http://pari.math.u-bordeaux.fr/ http://www.apfloat.org/apfloat/ http://code.google.com/p/fastfunlib/ scs_lib in crlibm other ----- ieee standard: http://754r.ucbtest.org/ extended precision issues: http://www.vinc17.org/research/extended.en.html correctly rounded mult: http://perso.ens-lyon.fr/jean-michel.muller/MultConstant.html table based sincos: http://perso.ens-lyon.fr/damien.stehle/IMPROVEDGAL.html finding worst cases: http://perso.ens-lyon.fr/damien.stehle/WCLR.html finding worst cases: http://perso.ens-lyon.fr/damien.stehle/DECIMALEXP.html finding worst cases: http://www.loria.fr/equipes/spaces/slz.en.html finding worst cases: http://perso.ens-lyon.fr/jean-michel.muller/Intro-to-TMD.htm fast conversion to fixedpoint: http://stereopsis.com/sree/fpu2006.html double-double, quad-double arithmetics: http://crd-legacy.lbl.gov/~dhbailey/mpdist/ papers by kahan: http://www.cs.berkeley.edu/~wkahan/ fp paper by goldberg: http://download.oracle.com/docs/cd/E19957-01/806-3568/ncg_goldberg.html