======================================================================= RELEASE_NOTES for LAPACK Version 1.0 : February 29, 1992 Revised, Version 1.0a: June 30, 1992 Revised, Version 1.0b: October 31, 1992 Revised, Version 1.1: March 31, 1993 Version 2.0: September 30, 1994 ======================================================================= ======= UPDATED: August 17, 1995 ======= This file contains a list of known problems, bugs, and compiler errors for LAPACK maintained on netlib, as well as ERRATA for the LAPACK Users' Guide (LUG) and ERRATA for the LAPACK code itself. For a copy of this report, send email to netlib@ornl.gov with a message of the form: send release_notes from lapack. ERRATA for the LUG and the LAPACK code is listed FIRST, followed by the machine-specific implementation information. Please NOTE that no claim is made as to the accuracy of the implementation information for specific computers; in some cases, no attempts were made at verification. *********************************************************************** ============================================= Errata in LAPACK Users' Guide, Second Edition ============================================= VERSION 2.0 : September 30, 1994 DATE: August 30, 1998 page ---- 95: Misspelled word: Choleksy --> Cholesky 128: Description of SSPGV/CHPGV. "Computes all eigenvalues and eigenvectors ..." should instead be "Computes all eigenvalues, and optionally, the eigenvectors ..." 129: Description of SSYGV/CHEGV. "Computes all eigenvalues and eigenvectors ..." should instead be "Computes all eigenvalues, and optionally, the eigenvectors ..." 133: Misspelled word: Peforms --> Performs Description of CLACRT replaced by: "Performs the transformation ( c s ) ( x ), where ( -s c ) ( y ) c, s, x, and y are complex." 137: Description of SLASQ4 is erroneous. It should say: "Estimates the singular value of a bidiagonal matrix." 143: Missing \hline in title of BLAS description table. 230: Specification for SPBRFS/CPBRFS: AB should be declared as REAL/COMPLEX array. 251: Specification for SPTTRS/CPTTRS: B should be declared as REAL/COMPLEX array. 289: Specification for STGEVC/CTGEVC: VR should be declared as REAL/COMPLEX array. *********************************************************************** ================ ERRATA in LAPACK ================ VERSION 2.0 : September 30, 1994 DATE: November 14, 1994 Note: Unless otherwise stated, changes to single precision routines (names beginning with S or C) apply also to the corresponding double precision routines (names beginning with D and Z). ------------- ------- -------------- -------------------------- DIRECTORY ROUTINE LAST MODIFIED DESCRIPTION OF CHANGE ------------- ------- -------------- -------------------------- LAPACK/ BLAS/SRC/ INSTALL/ SRC/ sggglm.f/ Nov. 14, 1994 Incorrect value set in WORK(1). cggglm.f TESTING/ TESTING/LIN/ TESTING/EIG/ serrst.f/ Oct. 20, 1994 Set KD --> 1 in INFOT=9 cerrst.f call to SSBEV/CHBEV. TIMING/ TIMING/LIN/ ctimaa.f Oct. 20, 1994 Dimension E( 2*NMAX ) instead of E( NMAX ) TIMING/EIG/ stimee.f/ Nov. 14, 1994 Moved "INTRINSIC MAX" declar- ctimee.f to preceed PARAMETER statements ctim22.f Nov. 14, 1994 Incorrect size of RWORK speci- fied in Argument section TIMING/EIG/ EIGSRC/ *********************************************************************** -------------- KNOWN FAILURES: -------------- No specific failure occurred everywhere in the LAPACK testing process. However, similar failures did appear on several machines. The failures noted below were reported to us and are still under investigation. Please contact us (lapack@cs.utk.edu) if you feel that an entry is out-of-date or incorrect. *********************************************************************** ------------------------------- KNOWN MACHINE-SPECIFIC FAILURES: ------------------------------- Entries are listed in ALPHABETICAL ORDER by the computer name. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ TEMPLATE FOR THE ENTRIES: + +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ================================================================== + Computer name, version of OS, and version of fortran compiler used + ================================================================== + + Compiler/options: + + BLAS: + + Test status: + + Notes: + + ----- Date reported: + + ================================================================== + +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ====================================================================== Apollo DN2500 Compiler : Fortran 77 compiler 68K Rev 10.8(190). Notes: When the code was compiled with optimization on (-O), xlintstc failed with floating-point overflow at line 173 in CHETRS: BKM1 = B( K-1, J ) / AKM1K When the code was compiled without optimization, xlintstc failed with floating-point overflow at line 117 in CLACON: X( I ) = X( I ) / CMPLX( ABS( X( I ) ) ) Similar failures occurred in xlintstz. No failures occurred when xLABAD was modified to take the square-root of SMALL and LARGE. (Floating-point arithmetic on this machine is approximately IEEE 754.) All this is consistent with a naive implementation of complex division. We believe that the fault has been introduced in a fairly recent version of the compiler, because our own tests of complex division used to pass on this machine (but now fail). ----- Date reported: March 23, 1992 ====================================================================== ====================================================================== CONVEX C-4640 Compiler: LAPACK: VERSION 2.0 Compiler/options: BLAS: Test status: ======================================================================= ======================================================================= CRAY C90, Unicos 8.0 and CFT77 ?.0. LAPACK: VERSION 2.0 Compiler/options: cf77 -Zp BLAS: /lib/libsci.a (version 1.1) except for SNRM2 and SCNRM2 (use Fortran versions) Test status: Notes: The Cray compilers implement a complex divide without scaling. To run the complex linear equation tests on the T3D, I had to modify SLABAD to take the square root of overflow and underflow. I ran the eigenvalue tests with the default version of SLABAD. I also needed the Fortran SNRM2 when running the real linear equation tests on a CRAY C90. ----- Date reported: ======================================================================= ======================================================================= CRAY Y-MP, Unicos 7.06 and CF77 6.0.2. LAPACK: VERSION 2.0 Compiler/options: cf77 -Zp BLAS: /lib/libsci.a except for SNRM2 and SCNRM2 (use Fortran versions) Test status: S, C, and D routines tested: failures in cgqr.out, csep.out, dsep.out -------- cgqr.out -------- N= 3 M= 0, P= 20, type 8, test 4, ratio= 0.864169E+11 N= 3 M= 3, P= 20, type 8, test 4, ratio= 0.875571E+11 N= 3 M= 10, P= 20, type 8, test 4, ratio= 0.805868E+11 GQR: 3 out of 1728 tests failed to pass the threshold -------- csep.out -------- SEP: NB = 3, NBMIN = 2, NX = 9 CCHKST: SSTEBZ(I) returned INFO= 2. N= 10, JTYPE= 10, ISEED=( 3400, 2891, 2948, 1953) Matrix order= 10, type=10, seed=3400,2891,2948,1953, result 19 is 7.037E+13 CST: 1 out of 2723 tests failed to pass the threshold *** Error code from CCHKST = 2 SEP: NB = 20, NBMIN = 2, NX = 1 CCHKST: SSTEBZ(I) returned INFO= 2. N= 10, JTYPE= 10, ISEED=( 1156, 3580, 2418, 1201) Matrix order= 10, type=10, seed=1156,3580,2418,1201, result 19 is 7.037E+13 CST: 1 out of 2723 tests failed to pass the threshold *** Error code from CCHKST = 2 -------- dsep.out -------- SEP: NB = 3, NBMIN = 2, NX = 9 All tests for DST passed the threshold (2730 tests run) DDRVST: DSYEVX(N,I,U) returned INFO= 2. N= 16, JTYPE= 10, ISEED=( 1174, 3001, 2457, 3017) Matrix order= 16, type=10, seed=1174,3001,2457,3017, result 69 is 1.981E+28 DST drivers: 1 out of 11025 tests failed to pass the threshold *** Error code from DDRVST = 2 Notes: ----- Date reported: October 14, 1994 ======================================================================= ======================================================================= DEC 3000-500 ALPHA OS: OSF/1 V3.2 COMPILER: F90 LAPACK: VERSION 2.0 Compiler/options: f90 -O BLAS: Fortran BLAS Test status: All tests passed. ----- Date reported: August 16, 1995 ======================================================================= ======================================================================= Hewlett Packard HP 9000 Model 715 OS: HP-UX 9.01 COMPILER: F77 version ? PATCHES to fix complex arithmetic problems: PHSS_3373 - fix to compiler for complex division/absolute value PHSS_3381 - fix to compiler libraries for complex division/abs. LAPACK: VERSION 2.0 Compiler/options: f77 +O3 +U77 BLAS: Fortran BLAS Test status: 2 failures in ded.out (DES and DSX); zsvd.out hangs (under investigation). ------- ded.out ------- DDRVES: DGEES1 returned INFO= 6. N= 5, JTYPE= 17, ISEED=( 100, 2082, 33, 613) N= 5, IWK= 2, seed= 100,2082, 33, 613, type 17, test( 7)= .450E+16 DES: 1 out of 3270 tests failed to pass the threshold *** Error code from DGEES = 6 DGET24: DGEESX1 returned INFO= 6. N= 5, JTYPE= 17, ISEED=( 100, 2082, 33, 613) N= 5, IWK= 2, seed= 100,2082, 33, 613, type 17, test( 7)= .450E+16 DSX: 1 out of 3500 tests failed to pass the threshold Notes: 1. Due to unscaled complex divide, you must set LAPACK/SRC/slabad.f and dlabad.f to take the square root of SMLNUM and BIGNUM as for the Cray. 2. Must have the following compiler patches to fix complex arithmetic problems: PHSS_3373 - fix to compiler for complex division/absolute value PHSS_3381 - fix to compiler libraries for complex division/abs. You must receive the aforementioned PATCHES for the F77 Compiler or practically all complex testing will fail. See recent postings on comp.sys.hp.hpux for details. ----- Date reported: November 24, 1994 ======================================================================= ======================================================================= Hewlett Packard HP Apollo 9000 Model 720 OS: HP-UX 9.01 COMPILER: F77 version ? Compiler/options: For making BLAS: +OP (Fortran Optimizing Preprocesor, all types) For making LAPACK: -O +E1 (to use the "intrinsic" function SECNDS, all types) BLAS: Fortran BLAS Test status: Two errors (one minor) REAL SINGLE Matrix order= 5, type=19, seed=2438,3579,3697,1157, result 7 is 22.12 SGG drivers: 1 out of 1274 tests failed to pass the threshold COMPLEX SINGLE Error in CTRSYL: RMAX = .689E+04 LMAX = 2593 NINFO= 1530 KNT= 5832 Error in CTRSEN: RMAX = .297E+01 .641E+03 .129E+04 LMAX = 25 10 10 NINFO= 0 0 0 KNT= 60 Notes: LAPACK 2.0, September 1994 release. slabad.f and dlabad.f modified to "Hmm... it looks like a CRAY" when making LAPACK COMPLEX and COMPLEX16 libraries.(do I need any patches?) Using -K (all variables static) when making tmglib, testing and timing to avoid segmentation faults. --- Date reported: March, 1995 ======================================================================= ======================================================================= IBM RISC/6000 model 550 OS: AIX VERSION 3.2.5 COMPILER: IBM AIX XL FORTRAN Compiler/6000 Version 3.1 LAPACK: VERSION 2.0 Compiler/options: xlf -O3 -qmaxmem=-1 -u (except -O2 for TIMING/EIG/deispack.f and TIMING/EIG/zeispack.f ) BLAS: -lessl (ESSL version 2.2.1) Test status: 1 minor failure in sgg.out. Notes: (1) use XLF-supplied routine ETIME_ for second.f and dsecnd.f ----- Date reported: September 30, 1994 ==================================================================== ==================================================================== IBM RISC/6000 model 320H OS: AIX VERSION 3.2.5 COMPILER: IBM AIX XL FORTRAN Compiler/6000 Version 2.3. LAPACK: VERSION 2.0 Compiler/options: xlf -O -u -NQ20000 -qmaxmem=-1 The options "-NQ20000 -qmaxmem=-1" are only needed for big routines, but were used everywhere. BLAS: -lblas (optimized IBM BLAS) Test status: Failures in ded.out (DES and DSX) (under investigation) ------- ded.out ------- N= 5, IWK= 1, seed= 100,2082, 33, 613, type 17, test( 7)= .450E+16 DDRVES: DGEES1 returned INFO= 6. N= 5, JTYPE= 17, ISEED=( 100, 2082, 33, 613) N= 5, IWK= 2, seed= 100,2082, 33, 613, type 17, test( 7)= .450E+16 DES: 2 out of 3264 tests failed to pass the threshold *** Error code from DGEES = 6 and N= 5, IWK= 1, seed= 100,2082, 33, 613, type 17, test( 7)= .450E+16 DGET24: DGEESX1 returned INFO= 6. N= 5, JTYPE= 17, ISEED=( 100, 2082, 33, 613) N= 5, IWK= 2, seed= 100,2082, 33, 613, type 17, test( 7)= .450E+16 DSX: 2 out of 3494 tests failed to pass the threshold ----- Date reported: October 11, 1994 ====================================================================== ======================================================================= IBM POWER2 model 590 OS: AIX VERSION 3.2.5 COMPILER: XLF Version 3.1 LAPACK: VERSION 2.0 Compiler/options: xlf -O3 -qmaxmem=8192 -qarch=pwrx -u (except -O2 for TIMING/EIG/deispack.f and TIMING/EIG/zeispack.f ) BLAS: -lblas Test status: Failures in ded.out (DES and DSX) and minor failure in sgg.out (ratio = 21.61) ------- ded.out ------- DGEES passed the tests of the error exits ( 6 tests done) DDRVES: DGEES1 returned INFO= 6. N= 5, JTYPE= 17, ISEED=( 100, 2082, 33, 613) N= 5, IWK= 1, seed= 100,2082, 33, 613, type 17, test( 7)= .450E+16 DDRVES: DGEES1 returned INFO= 6. N= 5, JTYPE= 17, ISEED=( 100, 2082, 33, 613) N= 5, IWK= 2, seed= 100,2082, 33, 613, type 17, test( 7)= .450E+16 DES: 2 out of 3264 tests failed to pass the threshold *** Error code from DGEES = 6 DGEESX passed the tests of the error exits ( 7 tests done) DGET24: DGEESX1 returned INFO= 6. N= 5, JTYPE= 17, ISEED=( 100, 2082, 33, 613) N= 5, IWK= 1, seed= 100,2082, 33, 613, type 17, test( 7)= .450E+16 DGET24: DGEESX1 returned INFO= 6. N= 5, JTYPE= 17, ISEED=( 100, 2082, 33, 613) N= 5, IWK= 2, seed= 100,2082, 33, 613, type 17, test( 7)= .450E+16 DSX: 2 out of 3494 tests failed to pass the threshold ------- sgg.out ------- SGG: NB = 1, NBMIN = 100, NS = 2, MAXB = 100, NBCOL = 100 Matrix order= 10, type=25, seed= 649,3851,1781,2241, result 6 is 21.61 SGG drivers: 1 out of 1274 tests failed to pass the threshold Notes: (1) use XLF-supplied routine ETIME_ for second.f and dsecnd.f ----- Date reported: October 14, 1994 ==================================================================== ======================================================================= IBM POWER2 model 590 OS: AIX VERSION 4.1 COMPILER: XLF Version 3.1.1 LAPACK: VERSION 2.0 Compiler/options: xlf -O3 -qmaxmem=8192 -qarch=pwrx -u (except -O2 for TIMING/EIG/deispack.f and TIMING/EIG/zeispack.f ) BLAS: -lesslp2 (ESSL version 2.2.1) Test status: Minor failure in sgg.out (ratio = 21.61) (same as mentioned above) Notes: (1) use XLF-supplied routine ETIME_ for second.f and dsecnd.f ----- Date reported: September 30, 1994 ==================================================================== ==================================================================== IBM MVS/VM platforms The intrinsic function DBLE does not accept arguments of type complex*16 on VS FORTRAN 2.5. This means that all Zxxxxx routines that use this function will not compile using VSF 2.5. Replace DBLE with DREAL when the argument is COMPLEX*16. See also Appendix D: "Caveats" of LAPACK Working Note 41 (Installation Guide for LAPACK). ----- Date reported: May 14, 1992 ==================================================================== Intel Paragon XP/S 10 (1 Node) Operating System OSF/1 R 1.3.1, Compiler R 5.0.1 Compiler/options: if77 -O4 BLAS: CLASSPACK Basic Math Library Release 1.3 by Kuck & Assoc. LAPACK, VERSION 2.0 Test status: Failures in zec.out zec.out ======= Tests of the Nonsymmetric eigenproblem condition estimation routines ZTRSYL, CTREXC, CTRSNA, CTRSEN Relative machine precision (EPS) = 0.222045D-15 Safe minimum (SFMIN) = 0.222507-307 Routines pass computational tests if test ratio is less than 20.00 ZEC routines passed the tests of the error exits ( 33 tests done) Error in ZTRSNA: RMAX = 0.168D+08 0.168D+08 0.168D+08 LMAX = 40 40 40 NINFO= 0 0 0 KNT= 66 Error in ZTRSEN: RMAX = 0.168D+08 0.138D+01 0.270D+05 LMAX = 31 49 46 NINFO= 0 0 0 KNT= 60 Notes: 1. Must set LAPACK/SRC/slabad.f and dlabad.f to take the square root of SMLNUM and BIGNUM as for the Cray. UNSCALED COMPLEX DIVIDE? ----- Date reported: August, 1995 ==================================================================== ==================================================================== Computer: SIEMENS S600/20 (Fujitsu VP 2600/20) Operating system: VSP/S Compiler: FORTRAN77/VP V10L30 Compiler options: VP, VPXTBL, VPSOPT(2000), LCH, AE, ALIGNC, BYNAME, LANGLVL(77), INCLUDE, INSOURCE, ISN(D), XOPT(IL,AMOVE,MSG) and of course OBJECT; VP is a special option: ---------------------- It includes: VP(400), ADV(EVL), VOCL and VPE Except for DGTSV and SGTSV which were compiled with XOPT(IL,NOAMOVE) because of optimization errors. BLAS: SIEMENS BLAS Release 3, developed at University of Karlsruhe, Computing Center Test status: Complete S, C, D, and Z testing. All tests pass. ----- Date reported: April 13, 1992 ==================================================================== ==================================================================== SGI POWER INDIGO 2 (with R8000 chip) OS: IRIX 6.0.1 COMPILER: SGI Fortran compiler 6.0.1 LAPACK: VERSION 2.0 Compiler/options: f77 -O -u -OPT:const_copy_limit=12000 set ranlib = echo Compiler defaults include: mips4 (64bit) BLAS: -lblas (SGI blas) Test status: All tests passed. ----- Date reported: February, 1995 ======================================================================= Silicon Graphics Indy, IRIX Release 5.3, Fortran 77, version 4.0.1 ? Compiler/options: -O -u -mips2 -static (EXCEPT compile without optimization SRC/stgevc.f and SRC/dtgevc.f) BLAS: -lblas (bug in IZAMAX, so must link with Fortran 77 IZAMAX) Test status: 2 failures in dsep.out --------------------- excerpt from dsep.out --------------------- SEP: NB = 20, NBMIN = 2, NX = 1 All tests for DST passed the threshold (2730 tests run) DST -- Real Symmetric eigenvalue problem Matrix types (see xDRVST for details): Special Matrices: 1=Zero matrix. 5=Diagonal: clustered entries. 2=Identity matrix. 6=Diagonal: large, evenly spaced. 3=Diagonal: evenly spaced entries. 7=Diagonal: small, evenly spaced. 4=Diagonal: geometr. spaced entries. Dense Symmetric Matrices: 8=Evenly spaced eigenvals. 12=Small, evenly spaced eigenvals. 9=Geometrically spaced eigenvals. 13=Matrix with random O(1) entries. 10=Clustered eigenvalues. 14=Matrix with large random entries. 11=Large, evenly spaced eigenvals. 15=Matrix with small random entries. Tests performed: (S is Tridiag, D is diagonal, U and Z are orthogonal, '=transpose, W is a diagonal matrix of eigenvalues) 1= | A - U S U' | / ( |A| n ulp ) 2= | I - U U' | / ( n ulp ) 3= | S - Z D Z' | / ( |S| n ulp ) 4= | I - Z Z' | / ( n ulp ) 5= | A - UZ D (UZ)' | / ( |A| n ulp ) 6= | I - UZ (UZ)' | / ( n ulp) 7= |D(with Z) - D(w/o Z)| / (|D| ulp) 8= | D(PWK) - D(QR) | / (|D| ulp) 9= Sturm sequence test on W 10= | Z(inv it.) - Z(QR) | / (|Z| ulp) Matrix order= 16, type=10, seed= 931, 71,2417,2713, result 77 is 269.44 Matrix order= 16, type=10, seed= 931, 71,2417,2713, result 83 is 322.42 DST drivers: 2 out of 11025 tests failed to pass the threshold Notes: (1) Set ranlib=echo in make.inc. (2) Used cruv options for ar. (3) Changed run statements in Makefiles from: x* < *.in > $@ 2>&1 to x* < *.in >& $@ ----- Date reported: May, 1995 ======================================================================= =================================================================== SUN SparcStation 10, Model ??, SunOS 4.1.3, f77 ?? (RUDOLPH) Compiler options: f77 -O -u BLAS: Fortran 77 BLAS Test status: All tests pass. ---- Date reported: September 30, 1994 ==================================================================== =================================================================== SUN SparcStation 10, Model ??, Solaris 2.0, f77 ?? (SOL) Compiler options: f77 -O -u BLAS: Fortran 77 BLAS Test status: ---- Date reported: September 30, 1994 ==================================================================== ==================================================================== SUN-4/490 running SunOS 4.1.3, F77 version 1.4 (SC1.0?) Compiler/options: f77 -O -u BLAS: Fortran 77 BLAS Test status: Notes: 1. PLEASE NOTE that there have been numerous patches to the way tmp space is handled in virtual memory in the Sun OS. If all of these patches have not been installed, you may receive a message like the following: f77 -O -u -c cgemv.f cgemv.f: cgemv: cgemv.f, line 180: warning: unexpected parent of complex expression subtree cgemv.f, line 215: warning: unexpected parent of complex expression subtree cgemv.f, line 225: warning: unexpected parent of complex expression subtree pcc_binval: missing IR_CONV in complex op *** Error code 1 make: Fatal error: Command failed for target `cgemv.o' You should contact your local systems administrator and ask about the installation of patches for tmp space bugs in virtual memory for your version of the OS. ----- Date reported: March 3, 1994 ==================================================================== ==================================================================== DECstation 5000/200: (PMAX) Compiler/options: f77 (no modification to make files) -fpe4 flag to use?? Test status: Failures in ded.out, still under investigation. Notes: 1) By default the compiler allocates all local variables on the stack. Several of the test programs failed with stack overflows. This can be remedied by compiling the main program files with the -static switch, or inserting an empty SAVE statement near the beginning of the program. Both have the effect of allocating local variables statically. No modifications are required to any subroutines. 2) The tests zed, zec, zbak, and zbal refuse to run due to input data formatting problems. Once I replace all double precision floating point numbers in the input files with single precision floating point numbers (xx.xDx to xx.xEx), all three tests run correctly to completion. 3) Several modules (primarily in the testing and timing suites) were sufficiently large as to preclude optimization unless the -Olimit switch was used (default is (-Olimit 1500). I did not pursue optimization for these modules. ----- Date reported: February 10, 1992 ==================================================================== ==================================================================== DECstation 5000/240 running Ultrix 4.2A and DEC Fortran for RISC V3.2 Compiler/options: f77 (no modification to make files) -fpe3 -O (reported that -fpe3 (enable gradual underflow) fixed SLAQTR/DLAQTR failures in sec/dec.out.) -static for main testing and timing drivers: LAPACK/TESTING/LIN/*chkaa.f LAPACK/TESTING/EIG/*chkee.f LAPACK/TIMING/LIN/*timaa.f LAPACK/TIMING/EIG/*timee.f (otherwise stack overflows) -static is default for new version of compiler? (Dec. 24, 1992 reported) Test status: Failures from SLAQTR/DLAQTR in sec.out and dec.out. Notes: 1) The tests zed, zec, zbak, and zbal refuse to run due to input data formatting problems. Once I replace all double precision floating point numbers in the input files with single precision floating point numbers (xx.xDx to xx.xEx), all three tests run correctly to completion. Now reported, that xx.xDx format is accepted. (Dec. 24, 1992) 2) The failures in SLAQTR, DLAQTR occur with test problems that are very badly scaled. The tests fail on a VAX because of the narrow exponent range and the lack of gradual underflow. The failures in SLAQTR/DLAQTR occur when the norm of the solution is very close to the underflow threshold (or even underflows to zero). 3) No problem with -Olimit (Dec. 24, 1992) 4) -fpe4 flag (which should be similar) caused horrible problems due to a bug. Somehow 1/RMAX = 1/3.402e+38 = 5.421e-20. I then ran the paranoia program from Netlib, and this revealed a number of serious floating point errors with this option. The -fpe4 option has serious problems with denormalized numbers, so that 1/RMAX = 1/3.402e+38 = 5.421e-20. 5) Errors in large timing sets: _SVDTIM and ZNEPTIM (see below) ----- Date reported: December 3 and 24, 1992 ==================================================================== ==================================================================== VAX/VMS and MicroVax II Notes: The failures in SLAQTR, DLAQTR and DTRSYL occur with test problems that are very badly scaled. The tests fail on a VAX because of the narrow exponent range and the lack of gradual underflow. The output from these test programs when failures occur, is not very helpful: in fact DTRSYL fails on only 6 cases out of 27,648; the failures in SLAQTR/DLAQTR occur when the norm of the solution is very close to the underflow threshold (or even underflows to zero). We believe that these failures could probably be avoided by an even greater degree of care in scaling, but we did not want to delay the release of LAPACK any further. These tests pass successfully on most other machines. Example failures look like the following (taken from MicroVax II output): ======= sec.out ======= Tests of the Nonsymmetric eigenproblem condition estimation routines SLALN2, SLASY2, SLANV2, SLAEXC, STRSYL, STREXC, STRSNA, STRSEN, SLAQTR Relative machine precision (EPS) = 0.119209E-06 Safe minimum (SFMIN) = 0.587747E-38 Routines pass computational tests if test ratio is less than 20.00 SEC routines passed the tests of the error exits ( 35 tests done) Error in SLAQTR: RMAX = 0.561E+13 LMAX = 3089 NINFO= 31600 KNT= 45000 ======= dec.out ======= Tests of the Nonsymmetric eigenproblem condition estimation routines DLALN2, DLASY2, DLANV2, DLAEXC, DTRSYL, DTREXC, DTRSNA, DTRSEN, DLAQTR Relative machine precision (EPS) = 0.277556D-16 Safe minimum (SFMIN) = 0.587747D-38 Routines pass computational tests if test ratio is less than 20.00 DEC routines passed the tests of the error exits ( 35 tests done) Error in DTRSYL: RMAX = 0.155D+07 LMAX = 5323 NINFO= 1600 KNT= 27648 Error in DLAQTR: RMAX = 0.344D+04 LMAX = 15792 NINFO= 26720 KNT= 45000 ----- Date reported: April 21, 1992 ==================================================================== ==================================================================== VAX/VMS 6520 BLAS: In scalar mode, fortran BLAS In vector mode, DEC provided Level 1 BLAS Test status: Only D and Z testing since 32-bit machine. One failure in dec.out (DLAQTR). Tests of the Nonsymmetric eigenproblem condition estimation routines DLALN2, DLASY2, DLANV2, DLAEXC, DTRSYL, DTREXC, DTRSNA, DTRSEN, DLAQTR Relative machine precision (EPS) = 0.222045D-15 Safe minimum (SFMIN) = 0.111254-307 Routines pass computational tests if test ratio is less than 20.00 DEC routines passed the tests of the error exits ( 35 tests done) Error in DLAQTR: RMAX = 0.759+139 LMAX = 3089 NINFO= 31600 KNT= 45000 End of tests Total time used = 163.91 seconds Notes: 1. The failure witnessed was as reported above in the MicroVax II report. Could be in lack of gradual underflow because the G_FLOATING double precision has an exponent range of +-308. 2. One problem with the VAX vector mode. If you want to use the DEC-provided BLAS level 1 routines, you have to remove all EXTERNAL BLAS1 statements in the code. When VMS Fortran sees the BLAS routines in EXTERNAL statements, it assumes they're external and can't use its own. ----- Date reported: June 4, 1992 ==================================================================== ==================================================================== VAX/VMS 6400, VMS version 5.4, 4 processors, no vector mode BLAS: In scalar mode, fortran BLAS In vector mode, DEC provided Level 1 BLAS Test status: Only D and Z testing since 32-bit machine. Failures in dsep.out. Matrix order= 5, type=10, seed= 696,3384,2994, 773, result 43 is 3.603D+16 Matrix order= 5, type=10, seed= 696,3384,2994, 773, result 44 is 3.603D+16 Matrix order= 5, type=10, seed= 696,3384,2994, 773, result 75 is 3.603D+16 Matrix order= 5, type=10, seed= 696,3384,2994, 773, result 76 is 3.603D+16 DST drivers: 4 out of 8812 tests failed to pass the threshold *** Error code from DDRVST = 2 ----- Date reported: December 2, 1992 ====================================================================