PROGRAM test WRITE(*,*) NEAREST(0.d0,1.d0) END >> gfortran test.f90 t.f90:3.21: WRITE(*,*) NEAREST(0.d0,1.d0) 1 Error: Result of NEAREST underflows its kind at (1)

*** Bug 34194 has been marked as a duplicate of this bug. ***

I believe there is indeed a bug in gfortran. The standard says that the "the nearest different machine-representable number" is returned. However, gfortran returns a number which is not representable (denormal or smaller?) and rounded to zero (= same number). Result (gfortran 4.3.0): a) The program is wrongly rejected b) With -fno-range-check, the wrong number is used. For the example the dump shows: static real(kind=8) C.859 = 0.0; The expected result is some denormal number like: 5.E-324, 4.9406564584124654E-324, 2.225073858507201E-308, 4.94065645841246544E-324, 4.940656458412465E-324. (The ifort result of 2e-308 looks wrong in this regard as there is a nearer number.) gfortran 4.1.3 returns: 4.940656458412465E-324 gfortran 4.2.2 rejects it and has an ICE with -fno-range-check Besides fixing this bug, we should also consider mentioning -fno-range-check in the error message. (Though, in this case -fno-range-check would have concealed the real bug.) The Fortran 2003 standard states: "NEAREST (X, S) Description. Returns the nearest different machine-representable number in a given direction. X shall be of type real. S shall be of type real and not equal to zero. Result Characteristics. Same as X. Result Value. The result has a value equal to the machine-representable number distinct from X and nearest to it in the direction of the infinity with the same sign as S. NOTE 13.16 Unlike other floating-point manipulation functions, NEAREST operates on machine-representable numbers rather than model numbers. On many systems there are machine-representable numbers that lie between adjacent model numbers."

Seemingly the problem was introduced by the following patch, which fixed another NEAREST problem. http://gcc.gnu.org/ml/gcc-cvs/2006-10/msg00249.html http://gcc.gnu.org/viewcvs?view=rev&revision=117584 2006-10-09 Steven G. Kargl <kargl@gcc.gnu.org> [...] PR fortran/15441 PR fortran/29312 [...] * simplify.c (gfc_simplify_nearest): Remove explicit subnormalization.

Regarding the range check: We need to disable the check for denormal numbers; as overflow etc. cannot occur, this boils down to check only for NaN. Regarding the result, I think we have a problem with MPFR. The following program prints: Result (GMP_RNDN): 0 Result (GMP_RNDU): 4.94066e-324 As mpfr_nexttoward should return a representable number, there should be no rounding needed, or should it? By the way, changing GFC_REAL_8_DIGITS did not change the result. See also: http://www.mpfr.org/mpfr-2.3.0/mpfr.html#index-mpfr_005fnexttoward-224 #include <gmp.h> #include <mpfr.h> #include <stdio.h> #define GFC_REAL_8_DIGITS 53 int main() { mpfr_t x; mpfr_t y; int base2prec; double result; mpfr_set_default_prec (GFC_REAL_8_DIGITS); mpfr_init(x); mpfr_init(y); mpfr_set_d (x, 0.0, GMP_RNDN); /* x = 0.0 */ mpfr_set_inf (y, 1); /* y = INF */ mpfr_nexttoward (x, y); /* x = x + epsilon */ printf("Result (GMP_RNDN): %g\n", mpfr_get_d(x, GMP_RNDN)); printf("Result (GMP_RNDU): %g\n", mpfr_get_d(x, GMP_RNDU)); return 0; }

Hmm, this does not seem to be easily possible in MPFR. http://websympa.loria.fr/wwsympa/arc/mpfr/2007-11/msg00026.html Possible implementation (as of 2005) by Tobias Schlüter: http://gcc.gnu.org/ml/fortran/2005-04/msg00389.html Steve writes to my MPFR email of today: | This is a point I had not fully appreciated when I patched | gfc_simplify_nearest. Try restoring the code that I removed. | I don't remember why I removed the code, although I suspect | that range_check function should properly handle subnormal | numbers.

Created attachment 14609 [details] Patch (reverted Rev 117584) plus test case Initial implementation by reverting Rev. 117584 as suggested by Steve. Problems: - nearest(x,-1) for negative denormal x does not give a smaller number - returned values are not the smallest possible: 4.9406564584124654E-324 vs. 1.11253692925360069E-308 1.4012985E-45 vs. 5.87747175E-39 - NaN, INF, -INF test cases missing. Probably makes sense to check this in first and worry about the rest later.

(In reply to comment #6) > Created an attachment (id=14609) [edit] > Patch (reverted Rev 117584) plus test case > > Initial implementation by reverting Rev. 117584 as suggested by Steve. > > Problems: > - nearest(x,-1) for negative denormal x does not give a smaller number > - returned values are not the smallest possible: > 4.9406564584124654E-324 vs. 1.11253692925360069E-308 > 1.4012985E-45 vs. 5.87747175E-39 To fix this problem, I believe that you need to set emin to emin - prec + 1 Something like + mpfr_set_emin ((mp_exp_t) (gfc_real_kinds[sgn].min_exponent - gfc_real_kinds[sgn].digit + 1)); It might be a -1. IIRC, mpfr always stores a normalized significand, so you need to play with emin to properly account for gradual underflow.

Subject: Bug number PR 34192 A patch for this bug has been added to the patch tracker. The mailing list url for the patch is http://gcc.gnu.org/ml/gcc-patches/2007-11/msg01240.html

Subject: Bug 34192 Author: burnus Date: Fri Nov 23 21:03:48 2007 New Revision: 130383 URL: http://gcc.gnu.org/viewcvs?root=gcc&view=rev&rev=130383 Log: 2007-11-23 Tobias Burnus <burnus@net-b.de> Steven G. Kargl <kargl@gcc.gnu.org> PR fortran/34192 * simplify.c (gfc_simplify_nearest): Fix NEAREST for subnormal numbers. 2007-11-23 Tobias Burnus <burnus@net-b.de> PR fortran/34192 * gfortran.dg/nearest_2.f90: New. Added: trunk/gcc/testsuite/gfortran.dg/nearest_2.f90 Modified: trunk/gcc/fortran/ChangeLog trunk/gcc/fortran/simplify.c trunk/gcc/testsuite/ChangeLog

FIXED on the trunk (4.3.0). I do not indent to backport it to GCC 4.2.x; but I can be convince otherwise.

Subject: Bug 34192 Author: burnus Date: Sat Nov 24 13:18:27 2007 New Revision: 130396 URL: http://gcc.gnu.org/viewcvs?root=gcc&view=rev&rev=130396 Log: 2007-11-24 Tobias Burnus <burnus@net-b.de> PR fortran/34192 * gfortran.dg/nearest_2.f90: Add INF/NAN tests. Modified: trunk/gcc/testsuite/ChangeLog trunk/gcc/testsuite/gfortran.dg/nearest_2.f90