(PR#3979) Re: [Rd] Re: R 1.7.x and inaccurate log1p() on OpenBSD
3.2 and NetBSD 1.6 (PR#3979)
Prof Brian Ripley
ripley at stats.ox.ac.uk
Fri Aug 29 22:03:28 MEST 2003
The fix I proposed is now in the R-devel sources, if you could please try
it. (It should appear in the next snapshot after now.)
On Mon, 25 Aug 2003, Prof Brian Ripley wrote:
> There is already a usable log1p implementation in src/nmath/log1p, for
> platforms without it. All we need to do is to arrange to use it on those
> systems with broken versions. That's not easy without access to such a
> platform to test it, though.
>
> On Mon, 25 Aug 2003 beebe at math.utah.edu wrote:
>
> > >> I have come across your reported log1p error (#2837) on a NetBSD (1.6W)
> > >> system.
> >
> > I've just made further experiments on the deficient log1p() function
> > on OpenBSD 3.2 and NetBSD 1.6 with this test program:
> >
> > % cat bug-log1p.c
> > #include <stdio.h>
> > #include <stdlib.h>
> > #include <math.h>
> >
> > int
> > main(int argc, char* argv[])
> > {
> > int k;
> > double x;
> >
> > for (k = 0; k <= 100; ++k)
> > {
> > x = pow(2.0,(double)(-k));
> > printf("%3d\t%.15e\t%.15e\n", k, log1p(x), log(1.0 + x));
> > }
> >
> > return (EXIT_SUCCESS);
> > }
> >
> > % cc bug-log1p.c -lm && ./a.out
> > 0 6.931471805599453e-01 6.931471805599453e-01
> > 1 4.054651081081644e-01 4.054651081081644e-01
> > 2 2.231435513142098e-01 2.231435513142098e-01
> > ...
> > 51 4.440892098500625e-16 4.440892098500625e-16
> > 52 2.220446049250313e-16 2.220446049250313e-16
> > 53 0.000000000000000e+00 0.000000000000000e+00
> > 54 0.000000000000000e+00 0.000000000000000e+00
> > ...
> > 99 0.000000000000000e+00 0.000000000000000e+00
> > 100 0.000000000000000e+00 0.000000000000000e+00
> >
> > Evidently, on these systems, log1p(x) is carelessly implemented as
> > log(1+x). Correct output from FreeBSD 5.0, Sun Solaris 9, ... looks
> > like this:
> >
> > % cc bug-log1p.c -lm && ./a.out
> > 0 6.931471805599453e-01 6.931471805599453e-01
> > 1 4.054651081081644e-01 4.054651081081644e-01
> > 2 2.231435513142098e-01 2.231435513142098e-01
> > ...
> > 51 4.440892098500625e-16 4.440892098500625e-16
> > 52 2.220446049250313e-16 2.220446049250313e-16
> > 53 1.110223024625157e-16 0.000000000000000e+00
> > 54 5.551115123125783e-17 0.000000000000000e+00
> > ...
> > 99 1.577721810442024e-30 0.000000000000000e+00
> > 100 7.888609052210118e-31 0.000000000000000e+00
> >
> > The whole point of log1p(x) is to return accurate results for
> > |x| << 1, and the OpenBSD/FreeBSD folks failed to understand that.
> >
> > The simple solution for a missing log1p() that I adopted in hoc is
> > this internal function:
> >
> > fp_t
> > Log1p(fp_t x)
> > {
> > #if defined(HAVE_LOG1PF) || defined(HAVE_LOG1P) || defined(HAVE_LOG1PL)
> > return (log1p(x));
> > #else
> > fp_t u;
> > /* Use log(), corrected to first order for truncation loss */
> > u = FP(1.0) + x;
> > if (u == FP(1.0))
> > return (x);
> > else
> > return (log(u) * (x / (u - FP(1.0)) ));
> > #endif
> > }
> >
> > I have yet to put in an accuracy test in hoc's configure.in that will
> > check for a broken log1p(), and use the internal fallback
> > implementation instead.
> >
> > Here is a test comparing accuracy of the two log1p() implementations
> > on Sun Solaris 9, which has a good log1p() implementation:
> >
> > % cat cmp-log1p.c
> > #include <stdio.h>
> > #include <stdlib.h>
> > #include <math.h>
> >
> > double
> > LOG1P(double x)
> > {
> > double u;
> >
> > u = 1.0 + x;
> > if (u == 1.0)
> > return (x);
> > else
> > return (log(u) * (x / (u - 1.0)));
> > }
> >
> >
> > int
> > main(int argc, char* argv[])
> > {
> > int k;
> > double d;
> > double x;
> >
> > for (k = 0; k <= 100; ++k)
> > {
> > x = pow(2.0,(double)(-k));
> >
> > printf("%3d\t%.15e\t%.15e\t%.2e\n",
> > k, log1p(x), LOG1P(x), (LOG1P(x) - log1p(x))/LOG1P(x));
> > }
> >
> > return (EXIT_SUCCESS);
> > }
> >
> > % cc cmp-log1p.c -lm && ./a.out
> > 0 6.931471805599453e-01 6.931471805599453e-01 0.00e+00
> > 1 4.054651081081644e-01 4.054651081081644e-01 0.00e+00
> > 2 2.231435513142098e-01 2.231435513142098e-01 0.00e+00
> > ...
> > 51 4.440892098500625e-16 4.440892098500625e-16 0.00e+00
> > 52 2.220446049250313e-16 2.220446049250313e-16 0.00e+00
> > 53 1.110223024625157e-16 1.110223024625157e-16 0.00e+00
> > 54 5.551115123125783e-17 5.551115123125783e-17 0.00e+00
> > ...
> > 98 3.155443620884047e-30 3.155443620884047e-30 0.00e+00
> > 99 1.577721810442024e-30 1.577721810442024e-30 0.00e+00
> > 100 7.888609052210118e-31 7.888609052210118e-31 0.00e+00
> >
> > At least for test arguments of the form 2^(-k), my LOG1P() is
> > identical to log1p().
> >
> > A simple change to that test program, inserting
> >
> > x *= (double)rand() / (double)(RAND_MAX);
> >
> > after the assignment to x to pick a random value near a power of k,
> > produces output like this:
> >
> > % cc cmp-log1p-2.c -lm && ./a.out
> > 0 4.146697237286190e-01 4.146697237286190e-01 0.00e+00
> > 1 8.421502722841255e-02 8.421502722841256e-02 1.65e-16
> > 2 7.432648260535767e-02 7.432648260535767e-02 0.00e+00
> > ...
> > 48 2.771522173451896e-15 2.771522173451896e-15 1.42e-16
> > 49 1.346294923235749e-15 1.346294923235749e-15 0.00e+00
> > 50 8.498507032336806e-16 8.498507032336806e-16 0.00e+00
> > 51 1.246870549827746e-17 1.246870549827746e-17 0.00e+00
> > 52 7.077345664348359e-17 7.077345664348359e-17 0.00e+00
> > ...
> > 98 2.127061943360297e-30 2.127061943360297e-30 0.00e+00
> > 99 1.276978671673724e-30 1.276978671673724e-30 0.00e+00
> > 100 1.252374165764246e-31 1.252374165764246e-31 0.00e+00
> >
> > For all random test arguments x < 2^(-49), the relative error of
> > LOG1P() vs log1p() is zero.
> >
> > -------------------------------------------------------------------------------
> > - Nelson H. F. Beebe Tel: +1 801 581 5254 -
> > - Center for Scientific Computing FAX: +1 801 581 4148 -
> > - University of Utah Internet e-mail: beebe at math.utah.edu -
> > - Department of Mathematics, 110 LCB beebe at acm.org beebe at computer.org -
> > - 155 S 1400 E RM 233 beebe at ieee.org -
> > - Salt Lake City, UT 84112-0090, USA URL: http://www.math.utah.edu/~beebe -
> >
> > ______________________________________________
> > R-devel at stat.math.ethz.ch mailing list
> > https://www.stat.math.ethz.ch/mailman/listinfo/r-devel
> >
> >
>
>
--
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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