Merge pull request #4310 from martin-frbg/lapack904

Apply rounding up to workspace calculations done with reals (Reference-LAPACK PR 904)
OpenMathLib · Nov 12, 2023 · d58c88c · d58c88c
2 parents feeb104 + 2ce67e2
commit d58c88c
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Showing 216 changed files with 1,334 additions and 1,187 deletions.
diff --git a/lapack-netlib/SRC/VARIANTS/qr/LL/cgeqrf.f b/lapack-netlib/SRC/VARIANTS/qr/LL/cgeqrf.f
@@ -176,7 +176,8 @@ SUBROUTINE CGEQRF ( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *     ..
 *     .. External Functions ..
       INTEGER            ILAENV
-      EXTERNAL           ILAENV
+      REAL               SROUNDUP_LWORK
+      EXTERNAL           ILAENV, SROUNDUP_LWORK
 *     ..
 *     .. Executable Statements ..
 
@@ -225,13 +226,13 @@ SUBROUTINE CGEQRF ( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *         Optimal workspace for dlarfb = MAX(1,N)*NT
 *
           LWKOPT = (LBWORK+LLWORK)*NB
-          WORK( 1 ) = (LWKOPT+NT*NT)
+          WORK( 1 ) = SROUNDUP_LWORK(LWKOPT+NT*NT)
 
       ELSE
 
           LBWORK = CEILING(REAL(K)/REAL(NB))*NB
           LWKOPT = (LBWORK+LLWORK-NB)*NB
-          WORK( 1 ) = LWKOPT
+          WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
 
       END IF
 
@@ -413,7 +414,7 @@ SUBROUTINE CGEQRF ( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 
       END IF
 
-      WORK( 1 ) = IWS
+      WORK( 1 ) = SROUNDUP_LWORK(IWS)
       RETURN
 *
 *     End of CGEQRF

diff --git a/lapack-netlib/SRC/VARIANTS/qr/LL/dgeqrf.f b/lapack-netlib/SRC/VARIANTS/qr/LL/dgeqrf.f
@@ -176,7 +176,8 @@ SUBROUTINE DGEQRF ( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *     ..
 *     .. External Functions ..
       INTEGER            ILAENV
-      EXTERNAL           ILAENV
+      DOUBLE PRECISION   DROUNDUP_LWORK
+      EXTERNAL           ILAENV, DROUNDUP_LWORK
 *     ..
 *     .. Executable Statements ..
 
@@ -225,13 +226,13 @@ SUBROUTINE DGEQRF ( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *         Optimal workspace for dlarfb = MAX(1,N)*NT
 *
           LWKOPT = (LBWORK+LLWORK)*NB
-          WORK( 1 ) = (LWKOPT+NT*NT)
+          WORK( 1 ) = DROUNDUP_LWORK(LWKOPT+NT*NT)
 
       ELSE
 
           LBWORK = CEILING(REAL(K)/REAL(NB))*NB
           LWKOPT = (LBWORK+LLWORK-NB)*NB
-          WORK( 1 ) = LWKOPT
+          WORK( 1 ) = DROUNDUP_LWORK(LWKOPT)
 
       END IF
 
@@ -413,7 +414,7 @@ SUBROUTINE DGEQRF ( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 
       END IF
 
-      WORK( 1 ) = IWS
+      WORK( 1 ) = DROUNDUP_LWORK(IWS)
       RETURN
 *
 *     End of DGEQRF

diff --git a/lapack-netlib/SRC/VARIANTS/qr/LL/sgeqrf.f b/lapack-netlib/SRC/VARIANTS/qr/LL/sgeqrf.f
@@ -176,7 +176,8 @@ SUBROUTINE SGEQRF ( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *     ..
 *     .. External Functions ..
       INTEGER            ILAENV
-      EXTERNAL           ILAENV
+      DOUBLE PRECISION   DROUNDUP_LWORK
+      EXTERNAL           ILAENV, DROUNDUP_LWORK
 *     ..
 *     .. Executable Statements ..
 
@@ -225,13 +226,13 @@ SUBROUTINE SGEQRF ( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *         Optimal workspace for dlarfb = MAX(1,N)*NT
 *
           LWKOPT = (LBWORK+LLWORK)*NB
-          WORK( 1 ) = (LWKOPT+NT*NT)
+          WORK( 1 ) = DROUNDUP_LWORK(LWKOPT+NT*NT)
 
       ELSE
 
           LBWORK = CEILING(REAL(K)/REAL(NB))*NB
           LWKOPT = (LBWORK+LLWORK-NB)*NB
-          WORK( 1 ) = LWKOPT
+          WORK( 1 ) = DROUNDUP_LWORK(LWKOPT)
 
       END IF
 
@@ -413,7 +414,7 @@ SUBROUTINE SGEQRF ( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 
       END IF
 
-      WORK( 1 ) = IWS
+      WORK( 1 ) = DROUNDUP_LWORK(IWS)
       RETURN
 *
 *     End of SGEQRF

diff --git a/lapack-netlib/SRC/VARIANTS/qr/LL/zgeqrf.f b/lapack-netlib/SRC/VARIANTS/qr/LL/zgeqrf.f
@@ -176,7 +176,8 @@ SUBROUTINE ZGEQRF ( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *     ..
 *     .. External Functions ..
       INTEGER            ILAENV
-      EXTERNAL           ILAENV
+      REAL               SROUNDUP_LWORK
+      EXTERNAL           ILAENV, SROUNDUP_LWORK
 *     ..
 *     .. Executable Statements ..
 
@@ -225,13 +226,13 @@ SUBROUTINE ZGEQRF ( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *         Optimal workspace for dlarfb = MAX(1,N)*NT
 *
           LWKOPT = (LBWORK+LLWORK)*NB
-          WORK( 1 ) = (LWKOPT+NT*NT)
+          WORK( 1 ) = SROUNDUP_LWORK(LWKOPT+NT*NT)
 
       ELSE
 
           LBWORK = CEILING(REAL(K)/REAL(NB))*NB
           LWKOPT = (LBWORK+LLWORK-NB)*NB
-          WORK( 1 ) = LWKOPT
+          WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
 
       END IF
 
@@ -413,7 +414,7 @@ SUBROUTINE ZGEQRF ( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 
       END IF
 
-      WORK( 1 ) = IWS
+      WORK( 1 ) = SROUNDUP_LWORK(IWS)
       RETURN
 *
 *     End of ZGEQRF

diff --git a/lapack-netlib/SRC/cgees.f b/lapack-netlib/SRC/cgees.f
@@ -189,7 +189,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complexGEeigen
+*> \ingroup gees
 *
 *  =====================================================================
       SUBROUTINE CGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS,
@@ -230,13 +230,13 @@ SUBROUTINE CGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS,
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           CCOPY, CGEBAK, CGEBAL, CGEHRD, CHSEQR, CLACPY,
-     $                   CLASCL, CTRSEN, CUNGHR, SLABAD, XERBLA
+     $                   CLASCL, CTRSEN, CUNGHR, XERBLA
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
       INTEGER            ILAENV
-      REAL               CLANGE, SLAMCH
-      EXTERNAL           LSAME, ILAENV, CLANGE, SLAMCH
+      REAL               CLANGE, SLAMCH, SROUNDUP_LWORK
+      EXTERNAL           LSAME, ILAENV, CLANGE, SLAMCH, SROUNDUP_LWORK
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          MAX, SQRT
@@ -292,7 +292,7 @@ SUBROUTINE CGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS,
                MAXWRK = MAX( MAXWRK, HSWORK )
             END IF
          END IF
-         WORK( 1 ) = MAXWRK
+         WORK( 1 ) = SROUNDUP_LWORK(MAXWRK)
 *
          IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
             INFO = -12
@@ -318,7 +318,6 @@ SUBROUTINE CGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS,
       EPS = SLAMCH( 'P' )
       SMLNUM = SLAMCH( 'S' )
       BIGNUM = ONE / SMLNUM
-      CALL SLABAD( SMLNUM, BIGNUM )
       SMLNUM = SQRT( SMLNUM ) / EPS
       BIGNUM = ONE / SMLNUM
 *
@@ -413,7 +412,7 @@ SUBROUTINE CGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS,
          CALL CCOPY( N, A, LDA+1, W, 1 )
       END IF
 *
-      WORK( 1 ) = MAXWRK
+      WORK( 1 ) = SROUNDUP_LWORK(MAXWRK)
       RETURN
 *
 *     End of CGEES

diff --git a/lapack-netlib/SRC/cgeesx.f b/lapack-netlib/SRC/cgeesx.f
@@ -230,7 +230,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complexGEeigen
+*> \ingroup geesx
 *
 *  =====================================================================
       SUBROUTINE CGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W,
@@ -274,13 +274,13 @@ SUBROUTINE CGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W,
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           CCOPY, CGEBAK, CGEBAL, CGEHRD, CHSEQR, CLACPY,
-     $                   CLASCL, CTRSEN, CUNGHR, SLABAD, SLASCL, XERBLA
+     $                   CLASCL, CTRSEN, CUNGHR, SLASCL, XERBLA
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
       INTEGER            ILAENV
-      REAL               CLANGE, SLAMCH
-      EXTERNAL           LSAME, ILAENV, CLANGE, SLAMCH
+      REAL               CLANGE, SLAMCH, SROUNDUP_LWORK
+      EXTERNAL           LSAME, ILAENV, CLANGE, SLAMCH, SROUNDUP_LWORK
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          MAX, SQRT
@@ -350,7 +350,7 @@ SUBROUTINE CGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W,
             IF( .NOT.WANTSN )
      $         LWRK = MAX( LWRK, ( N*N )/2 )
          END IF
-         WORK( 1 ) = LWRK
+         WORK( 1 ) = SROUNDUP_LWORK(LWRK)
 *
          IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
             INFO = -15
@@ -376,7 +376,6 @@ SUBROUTINE CGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W,
       EPS = SLAMCH( 'P' )
       SMLNUM = SLAMCH( 'S' )
       BIGNUM = ONE / SMLNUM
-      CALL SLABAD( SMLNUM, BIGNUM )
       SMLNUM = SQRT( SMLNUM ) / EPS
       BIGNUM = ONE / SMLNUM
 *
@@ -488,7 +487,7 @@ SUBROUTINE CGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W,
          END IF
       END IF
 *
-      WORK( 1 ) = MAXWRK
+      WORK( 1 ) = SROUNDUP_LWORK(MAXWRK)
       RETURN
 *
 *     End of CGEESX

diff --git a/lapack-netlib/SRC/cgeev.f b/lapack-netlib/SRC/cgeev.f
@@ -172,7 +172,7 @@
 *
 *  @generated from zgeev.f, fortran z -> c, Tue Apr 19 01:47:44 2016
 *
-*> \ingroup complexGEeigen
+*> \ingroup geev
 *
 *  =====================================================================
       SUBROUTINE CGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR,
@@ -212,14 +212,15 @@ SUBROUTINE CGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR,
       REAL   DUM( 1 )
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           SLABAD, XERBLA, CSSCAL, CGEBAK, CGEBAL, CGEHRD,
+      EXTERNAL           XERBLA, CSSCAL, CGEBAK, CGEBAL, CGEHRD,
      $                   CHSEQR, CLACPY, CLASCL, CSCAL, CTREVC3, CUNGHR
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
       INTEGER            ISAMAX, ILAENV
-      REAL   SLAMCH, SCNRM2, CLANGE
-      EXTERNAL           LSAME, ISAMAX, ILAENV, SLAMCH, SCNRM2, CLANGE
+      REAL               SLAMCH, SCNRM2, CLANGE, SROUNDUP_LWORK
+      EXTERNAL           LSAME, ISAMAX, ILAENV, SLAMCH, SCNRM2, CLANGE,
+     $                   SROUNDUP_LWORK
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          REAL, CMPLX, CONJG, AIMAG, MAX, SQRT
@@ -291,7 +292,7 @@ SUBROUTINE CGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR,
             HSWORK = INT( WORK(1) )
             MAXWRK = MAX( MAXWRK, HSWORK, MINWRK )
          END IF
-         WORK( 1 ) = MAXWRK
+         WORK( 1 ) = SROUNDUP_LWORK(MAXWRK)
 *
          IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
             INFO = -12
@@ -315,7 +316,6 @@ SUBROUTINE CGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR,
       EPS = SLAMCH( 'P' )
       SMLNUM = SLAMCH( 'S' )
       BIGNUM = ONE / SMLNUM
-      CALL SLABAD( SMLNUM, BIGNUM )
       SMLNUM = SQRT( SMLNUM ) / EPS
       BIGNUM = ONE / SMLNUM
 *
@@ -493,7 +493,7 @@ SUBROUTINE CGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR,
          END IF
       END IF
 *
-      WORK( 1 ) = MAXWRK
+      WORK( 1 ) = SROUNDUP_LWORK(MAXWRK)
       RETURN
 *
 *     End of CGEEV

diff --git a/lapack-netlib/SRC/cgeevx.f b/lapack-netlib/SRC/cgeevx.f
@@ -279,7 +279,7 @@
 *
 *  @generated from zgeevx.f, fortran z -> c, Tue Apr 19 01:47:44 2016
 *
-*> \ingroup complexGEeigen
+*> \ingroup geevx
 *
 *  =====================================================================
       SUBROUTINE CGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL,
@@ -323,15 +323,16 @@ SUBROUTINE CGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL,
       REAL   DUM( 1 )
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           SLABAD, SLASCL, XERBLA, CSSCAL, CGEBAK, CGEBAL,
+      EXTERNAL           SLASCL, XERBLA, CSSCAL, CGEBAK, CGEBAL,
      $                   CGEHRD, CHSEQR, CLACPY, CLASCL, CSCAL, CTREVC3,
      $                   CTRSNA, CUNGHR
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
       INTEGER            ISAMAX, ILAENV
-      REAL   SLAMCH, SCNRM2, CLANGE
-      EXTERNAL           LSAME, ISAMAX, ILAENV, SLAMCH, SCNRM2, CLANGE
+      REAL               SLAMCH, SCNRM2, CLANGE, SROUNDUP_LWORK
+      EXTERNAL           LSAME, ISAMAX, ILAENV, SLAMCH, SCNRM2, CLANGE,
+     $                   SROUNDUP_LWORK
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          REAL, CMPLX, CONJG, AIMAG, MAX, SQRT
@@ -434,7 +435,7 @@ SUBROUTINE CGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL,
             END IF
             MAXWRK = MAX( MAXWRK, MINWRK )
          END IF
-         WORK( 1 ) = MAXWRK
+         WORK( 1 ) = SROUNDUP_LWORK(MAXWRK)
 *
          IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
             INFO = -20
@@ -458,7 +459,6 @@ SUBROUTINE CGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL,
       EPS = SLAMCH( 'P' )
       SMLNUM = SLAMCH( 'S' )
       BIGNUM = ONE / SMLNUM
-      CALL SLABAD( SMLNUM, BIGNUM )
       SMLNUM = SQRT( SMLNUM ) / EPS
       BIGNUM = ONE / SMLNUM
 *
@@ -657,7 +657,7 @@ SUBROUTINE CGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL,
          END IF
       END IF
 *
-      WORK( 1 ) = MAXWRK
+      WORK( 1 ) = SROUNDUP_LWORK(MAXWRK)
       RETURN
 *
 *     End of CGEEVX

diff --git a/lapack-netlib/SRC/cgehrd.f b/lapack-netlib/SRC/cgehrd.f
@@ -120,7 +120,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complexGEcomputational
+*> \ingroup gehrd
 *
 *> \par Further Details:
 *  =====================
@@ -201,7 +201,8 @@ SUBROUTINE CGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
 *     ..
 *     .. External Functions ..
       INTEGER            ILAENV
-      EXTERNAL           ILAENV
+      REAL               SROUNDUP_LWORK
+      EXTERNAL           ILAENV, SROUNDUP_LWORK
 *     ..
 *     .. Executable Statements ..
 *
@@ -227,7 +228,7 @@ SUBROUTINE CGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
 *
          NB = MIN( NBMAX, ILAENV( 1, 'CGEHRD', ' ', N, ILO, IHI, -1 ) )
          LWKOPT = N*NB + TSIZE
-         WORK( 1 ) = LWKOPT
+         WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
       END IF
 *
       IF( INFO.NE.0 ) THEN
@@ -344,7 +345,7 @@ SUBROUTINE CGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
 *     Use unblocked code to reduce the rest of the matrix
 *
       CALL CGEHD2( N, I, IHI, A, LDA, TAU, WORK, IINFO )
-      WORK( 1 ) = LWKOPT
+      WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
 *
       RETURN
 *