Updated values of TWOPI and PIOVER2 to 39 significant digits,

Serguei Patchkovskii · Serguei Patchkovskii · commit 9db9ff8556bc · 2020-08-07T16:05:22.000+02:00
to prevent accuracy loss when REAL or DOUBLE PRECISION types
correspond to an extended precision real kind. These constants
should be sufficient to work with 128-bit extended-IEEE data
type.

Rebuilding the modified source using the default gfortran make.inc
(with gfortran 7.5.0) does not add any new test failures. The
only test failure, which is also present in the master baranch, is:

 ZDRGEV3: ZGGEV31 returned INFO=     7.
   N=    12, JTYPE=    16, ISEED=( 2855, 3551, 2406, 2393)

Additionally, included a sample build file for quadruple-precision
compilation using gfortran (version 4.7 or later). With this
config file, both REAL and DOUBLE PRECISION are mapped onto
a 128-bit REAL(16) type, with the corresponding change to the
COMPLEX and COMPLEX*16.

There are numerical failure 6 failures for each type, all in
*GBSVX type 6 matrix, with S/D routines losing 4 significant
digits, and C/Z routines 5 digits relative to the expected
result. I am not really qualified to debug this failure ...
diff --git a/INSTALL/make.inc.gfortran-quad b/INSTALL/make.inc.gfortran-quad
@@ -0,0 +1,90 @@
+####################################################################
+#  LAPACK make include file.                                       #
+#  LAPACK, Version 3.7.0                                           #
+#  November 2017                                                   #
+####################################################################
+
+SHELL = /bin/sh
+
+#  CC is the C compiler, normally invoked with options CFLAGS.
+#
+CC = gcc
+CFLAGS = -O3
+
+#  Modify the FC and FFLAGS definitions to the desired compiler
+#  and desired compiler options for your machine.  NOOPT refers to
+#  the compiler options desired when NO OPTIMIZATION is selected.
+#
+#  Note: During a regular execution, LAPACK might create NaN and Inf
+#  and handle these quantities appropriately. As a consequence, one
+#  should not compile LAPACK with flags such as -ffpe-trap=overflow.
+#
+#  The -freal-4-real-16 -freal-8-real-16 flags instruct gfortran
+#  to treal REAL, DOUBLE PRECISION, and corresponding COMPLEX
+#  declarations as 128-bit floating-point types. These flags
+#  are supported from gfortran 4.7 on. Please note that both
+#  s*/c* and d*/z* entry points will expect 128-bit floating-point
+#  type.
+#
+FC = gfortran
+FFLAGS = -O2 -frecursive -freal-4-real-16 -freal-8-real-16
+FFLAGS_DRV = $(FFLAGS)
+FFLAGS_NOOPT = -O0 -frecursive -freal-4-real-16 -freal-8-real-16
+
+#  Define LDFLAGS to the desired linker options for your machine.
+#
+LDFLAGS =
+
+#  The archiver and the flag(s) to use when building an archive
+#  (library).  If your system has no ranlib, set RANLIB = echo.
+#
+AR = ar
+ARFLAGS = cr
+RANLIB = ranlib
+
+#  Timer for the SECOND and DSECND routines
+#
+#  Default:  SECOND and DSECND will use a call to the
+#  EXTERNAL FUNCTION ETIME
+#TIMER = EXT_ETIME
+#  For RS6K:  SECOND and DSECND will use a call to the
+#  EXTERNAL FUNCTION ETIME_
+#TIMER = EXT_ETIME_
+#  For gfortran compiler:  SECOND and DSECND will use a call to the
+#  INTERNAL FUNCTION ETIME
+#TIMER = INT_ETIME
+#  If your Fortran compiler does not provide etime (like Nag Fortran
+#  Compiler, etc...) SECOND and DSECND will use a call to the
+#  INTERNAL FUNCTION CPU_TIME
+#TIMER = INT_CPU_TIME
+#  If none of these work, you can use the NONE value.
+#  In that case, SECOND and DSECND will always return 0.
+TIMER = NONE
+
+#  Uncomment the following line to include deprecated routines in
+#  the LAPACK library.
+#
+#BUILD_DEPRECATED = Yes
+
+#  LAPACKE has the interface to some routines from tmglib.
+#  If LAPACKE_WITH_TMG is defined, add those routines to LAPACKE.
+#
+#LAPACKE_WITH_TMG = Yes
+
+#  Location of the extended-precision BLAS (XBLAS) Fortran library
+#  used for building and testing extended-precision routines.  The
+#  relevant routines will be compiled and XBLAS will be linked only
+#  if USEXBLAS is defined.
+#
+#USEXBLAS = Yes
+#XBLASLIB = -lxblas
+
+#  The location of the libraries to which you will link.  (The
+#  machine-specific, optimized BLAS library should be used whenever
+#  possible.)
+#
+BLASLIB      = $(TOPSRCDIR)/librefblas.a
+CBLASLIB     = $(TOPSRCDIR)/libcblas.a
+LAPACKLIB    = $(TOPSRCDIR)/liblapack.a
+TMGLIB       = $(TOPSRCDIR)/libtmglib.a
+LAPACKELIB   = $(TOPSRCDIR)/liblapacke.a
diff --git a/SRC/cbbcsd.f b/SRC/cbbcsd.f
@@ -354,12 +354,13 @@ SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
 *     .. Parameters ..
       INTEGER            MAXITR
       PARAMETER          ( MAXITR = 6 )
-      REAL               HUNDRED, MEIGHTH, ONE, PIOVER2, TEN, ZERO
+      REAL               HUNDRED, MEIGHTH, ONE, TEN, ZERO
       PARAMETER          ( HUNDRED = 100.0E0, MEIGHTH = -0.125E0,
-     $                     ONE = 1.0E0, PIOVER2 = 1.57079632679489662E0,
-     $                     TEN = 10.0E0, ZERO = 0.0E0 )
+     $                     ONE = 1.0E0, TEN = 10.0E0, ZERO = 0.0E0 )
       COMPLEX            NEGONECOMPLEX
       PARAMETER          ( NEGONECOMPLEX = (-1.0E0,0.0E0) )
+      REAL               PIOVER2
+      PARAMETER ( PIOVER2 = 1.57079632679489661923132169163975144210E0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            COLMAJOR, LQUERY, RESTART11, RESTART12,
diff --git a/SRC/clarnv.f b/SRC/clarnv.f
@@ -120,7 +120,7 @@ SUBROUTINE CLARNV( IDIST, ISEED, N, X )
       INTEGER            LV
       PARAMETER          ( LV = 128 )
       REAL               TWOPI
-      PARAMETER          ( TWOPI = 6.2831853071795864769252867663E+0 )
+      PARAMETER  ( TWOPI = 6.28318530717958647692528676655900576839E+0 )
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, IL, IV
diff --git a/SRC/dbbcsd.f b/SRC/dbbcsd.f
@@ -354,12 +354,13 @@ SUBROUTINE DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
 *     .. Parameters ..
       INTEGER            MAXITR
       PARAMETER          ( MAXITR = 6 )
-      DOUBLE PRECISION   HUNDRED, MEIGHTH, ONE, PIOVER2, TEN, ZERO
+      DOUBLE PRECISION   HUNDRED, MEIGHTH, ONE, TEN, ZERO
       PARAMETER          ( HUNDRED = 100.0D0, MEIGHTH = -0.125D0,
-     $                     ONE = 1.0D0, PIOVER2 = 1.57079632679489662D0,
-     $                     TEN = 10.0D0, ZERO = 0.0D0 )
+     $                     ONE = 1.0D0, TEN = 10.0D0, ZERO = 0.0D0 )
       DOUBLE PRECISION   NEGONE
       PARAMETER          ( NEGONE = -1.0D0 )
+      DOUBLE PRECISION   PIOVER2
+      PARAMETER ( PIOVER2 = 1.57079632679489661923132169163975144210D0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            COLMAJOR, LQUERY, RESTART11, RESTART12,
diff --git a/SRC/dlarnv.f b/SRC/dlarnv.f
@@ -118,7 +118,7 @@ SUBROUTINE DLARNV( IDIST, ISEED, N, X )
       INTEGER            LV
       PARAMETER          ( LV = 128 )
       DOUBLE PRECISION   TWOPI
-      PARAMETER          ( TWOPI = 6.2831853071795864769252867663D+0 )
+      PARAMETER  ( TWOPI = 6.28318530717958647692528676655900576839D+0 )
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, IL, IL2, IV
diff --git a/SRC/sbbcsd.f b/SRC/sbbcsd.f
@@ -354,12 +354,13 @@ SUBROUTINE SBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
 *     .. Parameters ..
       INTEGER            MAXITR
       PARAMETER          ( MAXITR = 6 )
-      REAL               HUNDRED, MEIGHTH, ONE, PIOVER2, TEN, ZERO
+      REAL               HUNDRED, MEIGHTH, ONE, TEN, ZERO
       PARAMETER          ( HUNDRED = 100.0E0, MEIGHTH = -0.125E0,
-     $                     ONE = 1.0E0, PIOVER2 = 1.57079632679489662E0,
-     $                     TEN = 10.0E0, ZERO = 0.0E0 )
+     $                     ONE = 1.0E0, TEN = 10.0E0, ZERO = 0.0E0 )
       REAL               NEGONE
       PARAMETER          ( NEGONE = -1.0E0 )
+      REAL               PIOVER2
+      PARAMETER ( PIOVER2 = 1.57079632679489661923132169163975144210E0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            COLMAJOR, LQUERY, RESTART11, RESTART12,
diff --git a/SRC/slarnv.f b/SRC/slarnv.f
@@ -118,7 +118,7 @@ SUBROUTINE SLARNV( IDIST, ISEED, N, X )
       INTEGER            LV
       PARAMETER          ( LV = 128 )
       REAL               TWOPI
-      PARAMETER          ( TWOPI = 6.2831853071795864769252867663E+0 )
+      PARAMETER  ( TWOPI = 6.28318530717958647692528676655900576839E+0 )
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, IL, IL2, IV
diff --git a/SRC/zbbcsd.f b/SRC/zbbcsd.f
@@ -354,12 +354,13 @@ SUBROUTINE ZBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
 *     .. Parameters ..
       INTEGER            MAXITR
       PARAMETER          ( MAXITR = 6 )
-      DOUBLE PRECISION   HUNDRED, MEIGHTH, ONE, PIOVER2, TEN, ZERO
+      DOUBLE PRECISION   HUNDRED, MEIGHTH, ONE, TEN, ZERO
       PARAMETER          ( HUNDRED = 100.0D0, MEIGHTH = -0.125D0,
-     $                     ONE = 1.0D0, PIOVER2 = 1.57079632679489662D0,
-     $                     TEN = 10.0D0, ZERO = 0.0D0 )
+     $                     ONE = 1.0D0, TEN = 10.0D0, ZERO = 0.0D0 )
       COMPLEX*16         NEGONECOMPLEX
       PARAMETER          ( NEGONECOMPLEX = (-1.0D0,0.0D0) )
+      DOUBLE PRECISION   PIOVER2
+      PARAMETER ( PIOVER2 = 1.57079632679489661923132169163975144210D0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            COLMAJOR, LQUERY, RESTART11, RESTART12,
diff --git a/SRC/zlarnv.f b/SRC/zlarnv.f
@@ -120,7 +120,7 @@ SUBROUTINE ZLARNV( IDIST, ISEED, N, X )
       INTEGER            LV
       PARAMETER          ( LV = 128 )
       DOUBLE PRECISION   TWOPI
-      PARAMETER          ( TWOPI = 6.2831853071795864769252867663D+0 )
+      PARAMETER  ( TWOPI = 6.28318530717958647692528676655900576839D+0 )
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, IL, IV
diff --git a/TESTING/EIG/cckcsd.f b/TESTING/EIG/cckcsd.f
@@ -208,13 +208,14 @@ SUBROUTINE CCKCSD( NM, MVAL, PVAL, QVAL, NMATS, ISEED, THRESH,
       PARAMETER          ( NTESTS = 15 )
       INTEGER            NTYPES
       PARAMETER          ( NTYPES = 4 )
-      REAL               GAPDIGIT, ORTH, PIOVER2, REALONE, REALZERO, TEN
+      REAL               GAPDIGIT, ORTH, REALONE, REALZERO, TEN
       PARAMETER          ( GAPDIGIT = 10.0E0, ORTH = 1.0E-4,
-     $                     PIOVER2 = 1.57079632679489662E0,
      $                     REALONE = 1.0E0, REALZERO = 0.0E0,
      $                     TEN = 10.0E0 )
       COMPLEX            ONE, ZERO
       PARAMETER          ( ONE = (1.0E0,0.0E0), ZERO = (0.0E0,0.0E0) )
+      REAL               PIOVER2
+      PARAMETER ( PIOVER2 = 1.57079632679489661923132169163975144210E0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            FIRSTT
diff --git a/TESTING/EIG/ccsdts.f b/TESTING/EIG/ccsdts.f
@@ -248,11 +248,12 @@ SUBROUTINE CCSDTS( M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T,
 *  =====================================================================
 *
 *     .. Parameters ..
-      REAL               PIOVER2, REALONE, REALZERO
-      PARAMETER          ( PIOVER2 = 1.57079632679489662E0,
-     $                     REALONE = 1.0E0, REALZERO = 0.0E0 )
+      REAL               REALONE, REALZERO
+      PARAMETER          ( REALONE = 1.0E0, REALZERO = 0.0E0 )
       COMPLEX            ZERO, ONE
       PARAMETER          ( ZERO = (0.0E0,0.0E0), ONE = (1.0E0,0.0E0) )
+      REAL               PIOVER2
+      PARAMETER ( PIOVER2 = 1.57079632679489661923132169163975144210E0 )
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, INFO, R
diff --git a/TESTING/EIG/dckcsd.f b/TESTING/EIG/dckcsd.f
@@ -208,11 +208,12 @@ SUBROUTINE DCKCSD( NM, MVAL, PVAL, QVAL, NMATS, ISEED, THRESH,
       PARAMETER          ( NTESTS = 15 )
       INTEGER            NTYPES
       PARAMETER          ( NTYPES = 4 )
-      DOUBLE PRECISION   GAPDIGIT, ONE, ORTH, PIOVER2, TEN, ZERO
+      DOUBLE PRECISION   GAPDIGIT, ONE, ORTH, TEN, ZERO
       PARAMETER          ( GAPDIGIT = 18.0D0, ONE = 1.0D0,
      $                     ORTH = 1.0D-12,
-     $                     PIOVER2 = 1.57079632679489662D0,
      $                     TEN = 10.0D0, ZERO = 0.0D0 )
+      DOUBLE PRECISION   PIOVER2
+      PARAMETER ( PIOVER2 = 1.57079632679489661923132169163975144210D0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            FIRSTT
diff --git a/TESTING/EIG/dcsdts.f b/TESTING/EIG/dcsdts.f
@@ -248,11 +248,12 @@ SUBROUTINE DCSDTS( M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T,
 *  =====================================================================
 *
 *     .. Parameters ..
-      DOUBLE PRECISION   PIOVER2, REALONE, REALZERO
-      PARAMETER          ( PIOVER2 = 1.57079632679489662D0,
-     $                     REALONE = 1.0D0, REALZERO = 0.0D0 )
+      DOUBLE PRECISION   REALONE, REALZERO
+      PARAMETER          ( REALONE = 1.0D0, REALZERO = 0.0D0 )
       DOUBLE PRECISION   ZERO, ONE
       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
+      DOUBLE PRECISION   PIOVER2
+      PARAMETER ( PIOVER2 = 1.57079632679489661923132169163975144210D0 )
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, INFO, R
diff --git a/TESTING/EIG/sckcsd.f b/TESTING/EIG/sckcsd.f
@@ -208,11 +208,11 @@ SUBROUTINE SCKCSD( NM, MVAL, PVAL, QVAL, NMATS, ISEED, THRESH,
       PARAMETER          ( NTESTS = 15 )
       INTEGER            NTYPES
       PARAMETER          ( NTYPES = 4 )
-      REAL               GAPDIGIT, ONE, ORTH, PIOVER2, TEN, ZERO
+      REAL               GAPDIGIT, ONE, ORTH, TEN, ZERO
       PARAMETER          ( GAPDIGIT = 10.0E0, ONE = 1.0E0,
-     $                     ORTH = 1.0E-4,
-     $                     PIOVER2 = 1.57079632679489662E0,
-     $                     TEN = 10.0E0, ZERO = 0.0E0 )
+     $                     ORTH = 1.0E-4, TEN = 10.0E0, ZERO = 0.0E0 )
+      REAL               PIOVER2
+      PARAMETER ( PIOVER2 = 1.57079632679489661923132169163975144210E0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            FIRSTT
diff --git a/TESTING/EIG/scsdts.f b/TESTING/EIG/scsdts.f
@@ -248,11 +248,12 @@ SUBROUTINE SCSDTS( M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T,
 *  =====================================================================
 *
 *     .. Parameters ..
-      REAL               PIOVER2, REALONE, REALZERO
-      PARAMETER          ( PIOVER2 = 1.57079632679489662E0,
-     $                     REALONE = 1.0E0, REALZERO = 0.0E0 )
+      REAL               REALONE, REALZERO
+      PARAMETER          ( REALONE = 1.0E0, REALZERO = 0.0E0 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
+      REAL               PIOVER2
+      PARAMETER ( PIOVER2 = 1.57079632679489661923132169163975144210E0 )
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, INFO, R
diff --git a/TESTING/EIG/zckcsd.f b/TESTING/EIG/zckcsd.f
@@ -208,13 +208,14 @@ SUBROUTINE ZCKCSD( NM, MVAL, PVAL, QVAL, NMATS, ISEED, THRESH,
       PARAMETER          ( NTESTS = 15 )
       INTEGER            NTYPES
       PARAMETER          ( NTYPES = 4 )
-      DOUBLE PRECISION   GAPDIGIT, ORTH, PIOVER2, REALONE, REALZERO, TEN
+      DOUBLE PRECISION   GAPDIGIT, ORTH, REALONE, REALZERO, TEN
       PARAMETER          ( GAPDIGIT = 18.0D0, ORTH = 1.0D-12,
-     $                     PIOVER2 = 1.57079632679489662D0,
      $                     REALONE = 1.0D0, REALZERO = 0.0D0,
      $                     TEN = 10.0D0 )
       COMPLEX*16         ONE, ZERO
       PARAMETER          ( ONE = (1.0D0,0.0D0), ZERO = (0.0D0,0.0D0) )
+      DOUBLE PRECISION   PIOVER2
+      PARAMETER ( PIOVER2 = 1.57079632679489661923132169163975144210D0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            FIRSTT
diff --git a/TESTING/EIG/zcsdts.f b/TESTING/EIG/zcsdts.f
@@ -248,11 +248,12 @@ SUBROUTINE ZCSDTS( M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T,
 *  =====================================================================
 *
 *     .. Parameters ..
-      DOUBLE PRECISION   PIOVER2, REALONE, REALZERO
-      PARAMETER          ( PIOVER2 = 1.57079632679489662D0,
-     $                     REALONE = 1.0D0, REALZERO = 0.0D0 )
+      DOUBLE PRECISION   REALONE, REALZERO
+      PARAMETER          ( REALONE = 1.0D0, REALZERO = 0.0D0 )
       COMPLEX*16         ZERO, ONE
       PARAMETER          ( ZERO = (0.0D0,0.0D0), ONE = (1.0D0,0.0D0) )
+      DOUBLE PRECISION   PIOVER2
+      PARAMETER ( PIOVER2 = 1.57079632679489661923132169163975144210D0 )
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, INFO, R
diff --git a/TESTING/MATGEN/clarnd.f b/TESTING/MATGEN/clarnd.f
@@ -93,7 +93,7 @@ COMPLEX FUNCTION CLARND( IDIST, ISEED )
       REAL               ZERO, ONE, TWO
       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0, TWO = 2.0E+0 )
       REAL               TWOPI
-      PARAMETER          ( TWOPI = 6.2831853071795864769252867663E+0 )
+      PARAMETER  ( TWOPI = 6.28318530717958647692528676655900576839E+0 )
 *     ..
 *     .. Local Scalars ..
       REAL               T1, T2
diff --git a/TESTING/MATGEN/clatms.f b/TESTING/MATGEN/clatms.f
@@ -358,7 +358,7 @@ SUBROUTINE CLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
       COMPLEX            CZERO
       PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ) )
       REAL               TWOPI
-      PARAMETER          ( TWOPI = 6.2831853071795864769252867663E+0 )
+      PARAMETER  ( TWOPI = 6.28318530717958647692528676655900576839E+0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            CSYM, GIVENS, ILEXTR, ILTEMP, TOPDWN
diff --git a/TESTING/MATGEN/clatmt.f b/TESTING/MATGEN/clatmt.f
@@ -366,7 +366,7 @@ SUBROUTINE CLATMT( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
       COMPLEX            CZERO
       PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ) )
       REAL               TWOPI
-      PARAMETER          ( TWOPI = 6.2831853071795864769252867663E+0 )
+      PARAMETER  ( TWOPI = 6.28318530717958647692528676655900576839E+0 )
 *     ..
 *     .. Local Scalars ..
       COMPLEX            C, CT, CTEMP, DUMMY, EXTRA, S, ST
diff --git a/TESTING/MATGEN/dlarnd.f b/TESTING/MATGEN/dlarnd.f
@@ -91,7 +91,7 @@ DOUBLE PRECISION FUNCTION DLARND( IDIST, ISEED )
       DOUBLE PRECISION   ONE, TWO
       PARAMETER          ( ONE = 1.0D+0, TWO = 2.0D+0 )
       DOUBLE PRECISION   TWOPI
-      PARAMETER          ( TWOPI = 6.2831853071795864769252867663D+0 )
+      PARAMETER  ( TWOPI = 6.28318530717958647692528676655900576839D+0 )
 *     ..
 *     .. Local Scalars ..
       DOUBLE PRECISION   T1, T2
diff --git a/TESTING/MATGEN/dlatms.f b/TESTING/MATGEN/dlatms.f
@@ -344,7 +344,7 @@ SUBROUTINE DLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
       DOUBLE PRECISION   ONE
       PARAMETER          ( ONE = 1.0D0 )
       DOUBLE PRECISION   TWOPI
-      PARAMETER          ( TWOPI = 6.2831853071795864769252867663D+0 )
+      PARAMETER  ( TWOPI = 6.28318530717958647692528676655900576839D+0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            GIVENS, ILEXTR, ILTEMP, TOPDWN
diff --git a/TESTING/MATGEN/dlatmt.f b/TESTING/MATGEN/dlatmt.f
@@ -354,7 +354,7 @@ SUBROUTINE DLATMT( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
       DOUBLE PRECISION   ONE
       PARAMETER          ( ONE = 1.0D0 )
       DOUBLE PRECISION   TWOPI
-      PARAMETER          ( TWOPI = 6.2831853071795864769252867663D+0 )
+      PARAMETER  ( TWOPI = 6.28318530717958647692528676655900576839D+0 )
 *     ..
 *     .. Local Scalars ..
       DOUBLE PRECISION   ALPHA, ANGLE, C, DUMMY, EXTRA, S, TEMP
diff --git a/TESTING/MATGEN/slarnd.f b/TESTING/MATGEN/slarnd.f
@@ -91,7 +91,7 @@ REAL             FUNCTION SLARND( IDIST, ISEED )
       REAL               ONE, TWO
       PARAMETER          ( ONE = 1.0E+0, TWO = 2.0E+0 )
       REAL               TWOPI
-      PARAMETER          ( TWOPI = 6.2831853071795864769252867663E+0 )
+      PARAMETER  ( TWOPI = 6.28318530717958647692528676655900576839E+0 )
 *     ..
 *     .. Local Scalars ..
       REAL               T1, T2
diff --git a/TESTING/MATGEN/slatms.f b/TESTING/MATGEN/slatms.f
@@ -344,7 +344,7 @@ SUBROUTINE SLATMS( M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX,
       REAL               ONE
       PARAMETER          ( ONE = 1.0E0 )
       REAL               TWOPI
-      PARAMETER          ( TWOPI = 6.2831853071795864769252867663E+0 )
+      PARAMETER  ( TWOPI = 6.28318530717958647692528676655900576839E+0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            GIVENS, ILEXTR, ILTEMP, TOPDWN
diff --git a/TESTING/MATGEN/slatmt.f b/TESTING/MATGEN/slatmt.f
diff --git a/TESTING/MATGEN/zlarnd.f b/TESTING/MATGEN/zlarnd.f
diff --git a/TESTING/MATGEN/zlatms.f b/TESTING/MATGEN/zlatms.f
diff --git a/TESTING/MATGEN/zlatmt.f b/TESTING/MATGEN/zlatmt.f
