*> \brief \b CBLAT1 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * PROGRAM CBLAT1 * * *> \par Purpose: * ============= *> *> \verbatim *> *> Test program for the COMPLEX Level 1 BLAS. *> Based upon the original BLAS test routine together with: *> *> F06GAF Example Program Text *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex_blas_testing * * ===================================================================== PROGRAM CBLAT1 * * -- Reference BLAS test routine -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * ===================================================================== * * .. Parameters .. INTEGER NOUT PARAMETER (NOUT=6) * .. Scalars in Common .. INTEGER ICASE, INCX, INCY, MODE, N LOGICAL PASS * .. Local Scalars .. REAL SFAC INTEGER IC * .. External Subroutines .. EXTERNAL CHECK1, CHECK2, HEADER * .. Common blocks .. COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS * .. Data statements .. DATA SFAC/9.765625E-4/ * .. Executable Statements .. WRITE (NOUT,99999) DO 20 IC = 1, 10 ICASE = IC CALL HEADER * * Initialize PASS, INCX, INCY, and MODE for a new case. * The value 9999 for INCX, INCY or MODE will appear in the * detailed output, if any, for cases that do not involve * these parameters. * PASS = .TRUE. INCX = 9999 INCY = 9999 MODE = 9999 IF (ICASE.LE.5) THEN CALL CHECK2(SFAC) ELSE IF (ICASE.GE.6) THEN CALL CHECK1(SFAC) END IF * -- Print IF (PASS) WRITE (NOUT,99998) 20 CONTINUE STOP * 99999 FORMAT (' Complex BLAS Test Program Results',/1X) 99998 FORMAT (' ----- PASS -----') * * End of CBLAT1 * END SUBROUTINE HEADER * .. Parameters .. INTEGER NOUT PARAMETER (NOUT=6) * .. Scalars in Common .. INTEGER ICASE, INCX, INCY, MODE, N LOGICAL PASS * .. Local Arrays .. CHARACTER*6 L(10) * .. Common blocks .. COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS * .. Data statements .. DATA L(1)/'CDOTC '/ DATA L(2)/'CDOTU '/ DATA L(3)/'CAXPY '/ DATA L(4)/'CCOPY '/ DATA L(5)/'CSWAP '/ DATA L(6)/'SCNRM2'/ DATA L(7)/'SCASUM'/ DATA L(8)/'CSCAL '/ DATA L(9)/'CSSCAL'/ DATA L(10)/'ICAMAX'/ * .. Executable Statements .. WRITE (NOUT,99999) ICASE, L(ICASE) RETURN * 99999 FORMAT (/' Test of subprogram number',I3,12X,A6) * * End of HEADER * END SUBROUTINE CHECK1(SFAC) * .. Parameters .. INTEGER NOUT REAL THRESH PARAMETER (NOUT=6, THRESH=10.0E0) * .. Scalar Arguments .. REAL SFAC * .. Scalars in Common .. INTEGER ICASE, INCX, INCY, MODE, N LOGICAL PASS * .. Local Scalars .. COMPLEX CA REAL SA INTEGER I, IX, J, LEN, NP1 * .. Local Arrays .. COMPLEX CTRUE5(8,5,2), CTRUE6(8,5,2), CV(8,5,2), CVR(8), + CX(8), CXR(15), MWPCS(5), MWPCT(5) REAL STRUE2(5), STRUE4(5) INTEGER ITRUE3(5), ITRUEC(5) * .. External Functions .. REAL SCASUM, SCNRM2 INTEGER ICAMAX EXTERNAL SCASUM, SCNRM2, ICAMAX * .. External Subroutines .. EXTERNAL CB1NRM2, CSCAL, CSSCAL, CTEST, ITEST1, STEST1 * .. Intrinsic Functions .. INTRINSIC MAX * .. Common blocks .. COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS * .. Data statements .. DATA SA, CA/0.3E0, (0.4E0,-0.7E0)/ DATA ((CV(I,J,1),I=1,8),J=1,5)/(0.1E0,0.1E0), + (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0), + (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0), + (1.0E0,2.0E0), (0.3E0,-0.4E0), (3.0E0,4.0E0), + (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0), + (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0), + (0.1E0,-0.3E0), (0.5E0,-0.1E0), (5.0E0,6.0E0), + (5.0E0,6.0E0), (5.0E0,6.0E0), (5.0E0,6.0E0), + (5.0E0,6.0E0), (5.0E0,6.0E0), (0.1E0,0.1E0), + (-0.6E0,0.1E0), (0.1E0,-0.3E0), (7.0E0,8.0E0), + (7.0E0,8.0E0), (7.0E0,8.0E0), (7.0E0,8.0E0), + (7.0E0,8.0E0), (0.3E0,0.1E0), (0.5E0,0.0E0), + (0.0E0,0.5E0), (0.0E0,0.2E0), (2.0E0,3.0E0), + (2.0E0,3.0E0), (2.0E0,3.0E0), (2.0E0,3.0E0)/ DATA ((CV(I,J,2),I=1,8),J=1,5)/(0.1E0,0.1E0), + (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0), + (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0), + (4.0E0,5.0E0), (0.3E0,-0.4E0), (6.0E0,7.0E0), + (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0), + (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0), + (0.1E0,-0.3E0), (8.0E0,9.0E0), (0.5E0,-0.1E0), + (2.0E0,5.0E0), (2.0E0,5.0E0), (2.0E0,5.0E0), + (2.0E0,5.0E0), (2.0E0,5.0E0), (0.1E0,0.1E0), + (3.0E0,6.0E0), (-0.6E0,0.1E0), (4.0E0,7.0E0), + (0.1E0,-0.3E0), (7.0E0,2.0E0), (7.0E0,2.0E0), + (7.0E0,2.0E0), (0.3E0,0.1E0), (5.0E0,8.0E0), + (0.5E0,0.0E0), (6.0E0,9.0E0), (0.0E0,0.5E0), + (8.0E0,3.0E0), (0.0E0,0.2E0), (9.0E0,4.0E0)/ DATA CVR/(8.0E0,8.0E0), (-7.0E0,-7.0E0), + (9.0E0,9.0E0), (5.0E0,5.0E0), (9.0E0,9.0E0), + (8.0E0,8.0E0), (7.0E0,7.0E0), (7.0E0,7.0E0)/ DATA STRUE2/0.0E0, 0.5E0, 0.6E0, 0.7E0, 0.8E0/ DATA STRUE4/0.0E0, 0.7E0, 1.0E0, 1.3E0, 1.6E0/ DATA ((CTRUE5(I,J,1),I=1,8),J=1,5)/(0.1E0,0.1E0), + (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0), + (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0), + (1.0E0,2.0E0), (-0.16E0,-0.37E0), (3.0E0,4.0E0), + (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0), + (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0), + (-0.17E0,-0.19E0), (0.13E0,-0.39E0), + (5.0E0,6.0E0), (5.0E0,6.0E0), (5.0E0,6.0E0), + (5.0E0,6.0E0), (5.0E0,6.0E0), (5.0E0,6.0E0), + (0.11E0,-0.03E0), (-0.17E0,0.46E0), + (-0.17E0,-0.19E0), (7.0E0,8.0E0), (7.0E0,8.0E0), + (7.0E0,8.0E0), (7.0E0,8.0E0), (7.0E0,8.0E0), + (0.19E0,-0.17E0), (0.20E0,-0.35E0), + (0.35E0,0.20E0), (0.14E0,0.08E0), + (2.0E0,3.0E0), (2.0E0,3.0E0), (2.0E0,3.0E0), + (2.0E0,3.0E0)/ DATA ((CTRUE5(I,J,2),I=1,8),J=1,5)/(0.1E0,0.1E0), + (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0), + (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0), + (4.0E0,5.0E0), (-0.16E0,-0.37E0), (6.0E0,7.0E0), + (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0), + (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0), + (-0.17E0,-0.19E0), (8.0E0,9.0E0), + (0.13E0,-0.39E0), (2.0E0,5.0E0), (2.0E0,5.0E0), + (2.0E0,5.0E0), (2.0E0,5.0E0), (2.0E0,5.0E0), + (0.11E0,-0.03E0), (3.0E0,6.0E0), + (-0.17E0,0.46E0), (4.0E0,7.0E0), + (-0.17E0,-0.19E0), (7.0E0,2.0E0), (7.0E0,2.0E0), + (7.0E0,2.0E0), (0.19E0,-0.17E0), (5.0E0,8.0E0), + (0.20E0,-0.35E0), (6.0E0,9.0E0), + (0.35E0,0.20E0), (8.0E0,3.0E0), + (0.14E0,0.08E0), (9.0E0,4.0E0)/ DATA ((CTRUE6(I,J,1),I=1,8),J=1,5)/(0.1E0,0.1E0), + (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0), + (1.0E0,2.0E0), (1.0E0,2.0E0), (1.0E0,2.0E0), + (1.0E0,2.0E0), (0.09E0,-0.12E0), (3.0E0,4.0E0), + (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0), + (3.0E0,4.0E0), (3.0E0,4.0E0), (3.0E0,4.0E0), + (0.03E0,-0.09E0), (0.15E0,-0.03E0), + (5.0E0,6.0E0), (5.0E0,6.0E0), (5.0E0,6.0E0), + (5.0E0,6.0E0), (5.0E0,6.0E0), (5.0E0,6.0E0), + (0.03E0,0.03E0), (-0.18E0,0.03E0), + (0.03E0,-0.09E0), (7.0E0,8.0E0), (7.0E0,8.0E0), + (7.0E0,8.0E0), (7.0E0,8.0E0), (7.0E0,8.0E0), + (0.09E0,0.03E0), (0.15E0,0.00E0), + (0.00E0,0.15E0), (0.00E0,0.06E0), (2.0E0,3.0E0), + (2.0E0,3.0E0), (2.0E0,3.0E0), (2.0E0,3.0E0)/ DATA ((CTRUE6(I,J,2),I=1,8),J=1,5)/(0.1E0,0.1E0), + (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0), + (4.0E0,5.0E0), (4.0E0,5.0E0), (4.0E0,5.0E0), + (4.0E0,5.0E0), (0.09E0,-0.12E0), (6.0E0,7.0E0), + (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0), + (6.0E0,7.0E0), (6.0E0,7.0E0), (6.0E0,7.0E0), + (0.03E0,-0.09E0), (8.0E0,9.0E0), + (0.15E0,-0.03E0), (2.0E0,5.0E0), (2.0E0,5.0E0), + (2.0E0,5.0E0), (2.0E0,5.0E0), (2.0E0,5.0E0), + (0.03E0,0.03E0), (3.0E0,6.0E0), + (-0.18E0,0.03E0), (4.0E0,7.0E0), + (0.03E0,-0.09E0), (7.0E0,2.0E0), (7.0E0,2.0E0), + (7.0E0,2.0E0), (0.09E0,0.03E0), (5.0E0,8.0E0), + (0.15E0,0.00E0), (6.0E0,9.0E0), (0.00E0,0.15E0), + (8.0E0,3.0E0), (0.00E0,0.06E0), (9.0E0,4.0E0)/ DATA ITRUE3/0, 1, 2, 2, 2/ DATA ITRUEC/0, 1, 1, 1, 1/ * .. Executable Statements .. DO 60 INCX = 1, 2 DO 40 NP1 = 1, 5 N = NP1 - 1 LEN = 2*MAX(N,1) * .. Set vector arguments .. DO 20 I = 1, LEN CX(I) = CV(I,NP1,INCX) 20 CONTINUE IF (ICASE.EQ.6) THEN * .. SCNRM2 .. * Test scaling when some entries are tiny or huge CALL CB1NRM2(N,(INCX-2)*2,THRESH) CALL CB1NRM2(N,INCX,THRESH) * Test with hardcoded mid range entries CALL STEST1(SCNRM2(N,CX,INCX),STRUE2(NP1),STRUE2(NP1), + SFAC) ELSE IF (ICASE.EQ.7) THEN * .. SCASUM .. CALL STEST1(SCASUM(N,CX,INCX),STRUE4(NP1),STRUE4(NP1), + SFAC) ELSE IF (ICASE.EQ.8) THEN * .. CSCAL .. CALL CSCAL(N,CA,CX,INCX) CALL CTEST(LEN,CX,CTRUE5(1,NP1,INCX),CTRUE5(1,NP1,INCX), + SFAC) ELSE IF (ICASE.EQ.9) THEN * .. CSSCAL .. CALL CSSCAL(N,SA,CX,INCX) CALL CTEST(LEN,CX,CTRUE6(1,NP1,INCX),CTRUE6(1,NP1,INCX), + SFAC) ELSE IF (ICASE.EQ.10) THEN * .. ICAMAX .. CALL ITEST1(ICAMAX(N,CX,INCX),ITRUE3(NP1)) DO 160 I = 1, LEN CX(I) = (42.0E0,43.0E0) 160 CONTINUE CALL ITEST1(ICAMAX(N,CX,INCX),ITRUEC(NP1)) ELSE WRITE (NOUT,*) ' Shouldn''t be here in CHECK1' STOP END IF * 40 CONTINUE IF (ICASE.EQ.10) THEN N = 8 IX = 1 DO 180 I = 1, N CXR(IX) = CVR(I) IX = IX + INCX 180 CONTINUE CALL ITEST1(ICAMAX(N,CXR,INCX),3) END IF 60 CONTINUE * INCX = 1 IF (ICASE.EQ.8) THEN * CSCAL * Add a test for alpha equal to zero. CA = (0.0E0,0.0E0) DO 80 I = 1, 5 MWPCT(I) = (0.0E0,0.0E0) MWPCS(I) = (1.0E0,1.0E0) 80 CONTINUE CALL CSCAL(5,CA,CX,INCX) CALL CTEST(5,CX,MWPCT,MWPCS,SFAC) ELSE IF (ICASE.EQ.9) THEN * CSSCAL * Add a test for alpha equal to zero. SA = 0.0E0 DO 100 I = 1, 5 MWPCT(I) = (0.0E0,0.0E0) MWPCS(I) = (1.0E0,1.0E0) 100 CONTINUE CALL CSSCAL(5,SA,CX,INCX) CALL CTEST(5,CX,MWPCT,MWPCS,SFAC) * Add a test for alpha equal to one. SA = 1.0E0 DO 120 I = 1, 5 MWPCT(I) = CX(I) MWPCS(I) = CX(I) 120 CONTINUE CALL CSSCAL(5,SA,CX,INCX) CALL CTEST(5,CX,MWPCT,MWPCS,SFAC) * Add a test for alpha equal to minus one. SA = -1.0E0 DO 140 I = 1, 5 MWPCT(I) = -CX(I) MWPCS(I) = -CX(I) 140 CONTINUE CALL CSSCAL(5,SA,CX,INCX) CALL CTEST(5,CX,MWPCT,MWPCS,SFAC) END IF RETURN * * End of CHECK1 * END SUBROUTINE CHECK2(SFAC) * .. Parameters .. INTEGER NOUT PARAMETER (NOUT=6) * .. Scalar Arguments .. REAL SFAC * .. Scalars in Common .. INTEGER ICASE, INCX, INCY, MODE, N LOGICAL PASS * .. Local Scalars .. COMPLEX CA INTEGER I, J, KI, KN, KSIZE, LENX, LENY, LINCX, LINCY, + MX, MY * .. Local Arrays .. COMPLEX CDOT(1), CSIZE1(4), CSIZE2(7,2), CSIZE3(14), + CT10X(7,4,4), CT10Y(7,4,4), CT6(4,4), CT7(4,4), + CT8(7,4,4), CTY0(1), CX(7), CX0(1), CX1(7), + CY(7), CY0(1), CY1(7) INTEGER INCXS(4), INCYS(4), LENS(4,2), NS(4) * .. External Functions .. COMPLEX CDOTC, CDOTU EXTERNAL CDOTC, CDOTU * .. External Subroutines .. EXTERNAL CAXPY, CCOPY, CSWAP, CTEST * .. Intrinsic Functions .. INTRINSIC ABS, MIN * .. Common blocks .. COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS * .. Data statements .. DATA CA/(0.4E0,-0.7E0)/ DATA INCXS/1, 2, -2, -1/ DATA INCYS/1, -2, 1, -2/ DATA LENS/1, 1, 2, 4, 1, 1, 3, 7/ DATA NS/0, 1, 2, 4/ DATA CX1/(0.7E0,-0.8E0), (-0.4E0,-0.7E0), + (-0.1E0,-0.9E0), (0.2E0,-0.8E0), + (-0.9E0,-0.4E0), (0.1E0,0.4E0), (-0.6E0,0.6E0)/ DATA CY1/(0.6E0,-0.6E0), (-0.9E0,0.5E0), + (0.7E0,-0.6E0), (0.1E0,-0.5E0), (-0.1E0,-0.2E0), + (-0.5E0,-0.3E0), (0.8E0,-0.7E0)/ DATA ((CT8(I,J,1),I=1,7),J=1,4)/(0.6E0,-0.6E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.32E0,-1.41E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.32E0,-1.41E0), + (-1.55E0,0.5E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.32E0,-1.41E0), (-1.55E0,0.5E0), + (0.03E0,-0.89E0), (-0.38E0,-0.96E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0)/ DATA ((CT8(I,J,2),I=1,7),J=1,4)/(0.6E0,-0.6E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.32E0,-1.41E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (-0.07E0,-0.89E0), + (-0.9E0,0.5E0), (0.42E0,-1.41E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.78E0,0.06E0), (-0.9E0,0.5E0), + (0.06E0,-0.13E0), (0.1E0,-0.5E0), + (-0.77E0,-0.49E0), (-0.5E0,-0.3E0), + (0.52E0,-1.51E0)/ DATA ((CT8(I,J,3),I=1,7),J=1,4)/(0.6E0,-0.6E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.32E0,-1.41E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (-0.07E0,-0.89E0), + (-1.18E0,-0.31E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.78E0,0.06E0), (-1.54E0,0.97E0), + (0.03E0,-0.89E0), (-0.18E0,-1.31E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0)/ DATA ((CT8(I,J,4),I=1,7),J=1,4)/(0.6E0,-0.6E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.32E0,-1.41E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.32E0,-1.41E0), (-0.9E0,0.5E0), + (0.05E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.32E0,-1.41E0), + (-0.9E0,0.5E0), (0.05E0,-0.6E0), (0.1E0,-0.5E0), + (-0.77E0,-0.49E0), (-0.5E0,-0.3E0), + (0.32E0,-1.16E0)/ DATA CT7/(0.0E0,0.0E0), (-0.06E0,-0.90E0), + (0.65E0,-0.47E0), (-0.34E0,-1.22E0), + (0.0E0,0.0E0), (-0.06E0,-0.90E0), + (-0.59E0,-1.46E0), (-1.04E0,-0.04E0), + (0.0E0,0.0E0), (-0.06E0,-0.90E0), + (-0.83E0,0.59E0), (0.07E0,-0.37E0), + (0.0E0,0.0E0), (-0.06E0,-0.90E0), + (-0.76E0,-1.15E0), (-1.33E0,-1.82E0)/ DATA CT6/(0.0E0,0.0E0), (0.90E0,0.06E0), + (0.91E0,-0.77E0), (1.80E0,-0.10E0), + (0.0E0,0.0E0), (0.90E0,0.06E0), (1.45E0,0.74E0), + (0.20E0,0.90E0), (0.0E0,0.0E0), (0.90E0,0.06E0), + (-0.55E0,0.23E0), (0.83E0,-0.39E0), + (0.0E0,0.0E0), (0.90E0,0.06E0), (1.04E0,0.79E0), + (1.95E0,1.22E0)/ DATA ((CT10X(I,J,1),I=1,7),J=1,4)/(0.7E0,-0.8E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.6E0,-0.6E0), (-0.9E0,0.5E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.6E0,-0.6E0), + (-0.9E0,0.5E0), (0.7E0,-0.6E0), (0.1E0,-0.5E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0)/ DATA ((CT10X(I,J,2),I=1,7),J=1,4)/(0.7E0,-0.8E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.7E0,-0.6E0), (-0.4E0,-0.7E0), + (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.8E0,-0.7E0), + (-0.4E0,-0.7E0), (-0.1E0,-0.2E0), + (0.2E0,-0.8E0), (0.7E0,-0.6E0), (0.1E0,0.4E0), + (0.6E0,-0.6E0)/ DATA ((CT10X(I,J,3),I=1,7),J=1,4)/(0.7E0,-0.8E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (-0.9E0,0.5E0), (-0.4E0,-0.7E0), + (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.1E0,-0.5E0), + (-0.4E0,-0.7E0), (0.7E0,-0.6E0), (0.2E0,-0.8E0), + (-0.9E0,0.5E0), (0.1E0,0.4E0), (0.6E0,-0.6E0)/ DATA ((CT10X(I,J,4),I=1,7),J=1,4)/(0.7E0,-0.8E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.6E0,-0.6E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.6E0,-0.6E0), (0.7E0,-0.6E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.6E0,-0.6E0), + (0.7E0,-0.6E0), (-0.1E0,-0.2E0), (0.8E0,-0.7E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0)/ DATA ((CT10Y(I,J,1),I=1,7),J=1,4)/(0.6E0,-0.6E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.7E0,-0.8E0), (-0.4E0,-0.7E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.7E0,-0.8E0), + (-0.4E0,-0.7E0), (-0.1E0,-0.9E0), + (0.2E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0)/ DATA ((CT10Y(I,J,2),I=1,7),J=1,4)/(0.6E0,-0.6E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (-0.1E0,-0.9E0), (-0.9E0,0.5E0), + (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (-0.6E0,0.6E0), + (-0.9E0,0.5E0), (-0.9E0,-0.4E0), (0.1E0,-0.5E0), + (-0.1E0,-0.9E0), (-0.5E0,-0.3E0), + (0.7E0,-0.8E0)/ DATA ((CT10Y(I,J,3),I=1,7),J=1,4)/(0.6E0,-0.6E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (-0.1E0,-0.9E0), (0.7E0,-0.8E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (-0.6E0,0.6E0), + (-0.9E0,-0.4E0), (-0.1E0,-0.9E0), + (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0)/ DATA ((CT10Y(I,J,4),I=1,7),J=1,4)/(0.6E0,-0.6E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.7E0,-0.8E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.7E0,-0.8E0), (-0.9E0,0.5E0), + (-0.4E0,-0.7E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.7E0,-0.8E0), + (-0.9E0,0.5E0), (-0.4E0,-0.7E0), (0.1E0,-0.5E0), + (-0.1E0,-0.9E0), (-0.5E0,-0.3E0), + (0.2E0,-0.8E0)/ DATA CSIZE1/(0.0E0,0.0E0), (0.9E0,0.9E0), + (1.63E0,1.73E0), (2.90E0,2.78E0)/ DATA CSIZE3/(0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (1.17E0,1.17E0), + (1.17E0,1.17E0), (1.17E0,1.17E0), + (1.17E0,1.17E0), (1.17E0,1.17E0), + (1.17E0,1.17E0), (1.17E0,1.17E0)/ DATA CSIZE2/(0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (0.0E0,0.0E0), + (0.0E0,0.0E0), (0.0E0,0.0E0), (1.54E0,1.54E0), + (1.54E0,1.54E0), (1.54E0,1.54E0), + (1.54E0,1.54E0), (1.54E0,1.54E0), + (1.54E0,1.54E0), (1.54E0,1.54E0)/ * .. Executable Statements .. DO 60 KI = 1, 4 INCX = INCXS(KI) INCY = INCYS(KI) MX = ABS(INCX) MY = ABS(INCY) * DO 40 KN = 1, 4 N = NS(KN) KSIZE = MIN(2,KN) LENX = LENS(KN,MX) LENY = LENS(KN,MY) * .. initialize all argument arrays .. DO 20 I = 1, 7 CX(I) = CX1(I) CY(I) = CY1(I) 20 CONTINUE IF (ICASE.EQ.1) THEN * .. CDOTC .. CDOT(1) = CDOTC(N,CX,INCX,CY,INCY) CALL CTEST(1,CDOT,CT6(KN,KI),CSIZE1(KN),SFAC) ELSE IF (ICASE.EQ.2) THEN * .. CDOTU .. CDOT(1) = CDOTU(N,CX,INCX,CY,INCY) CALL CTEST(1,CDOT,CT7(KN,KI),CSIZE1(KN),SFAC) ELSE IF (ICASE.EQ.3) THEN * .. CAXPY .. CALL CAXPY(N,CA,CX,INCX,CY,INCY) CALL CTEST(LENY,CY,CT8(1,KN,KI),CSIZE2(1,KSIZE),SFAC) ELSE IF (ICASE.EQ.4) THEN * .. CCOPY .. CALL CCOPY(N,CX,INCX,CY,INCY) CALL CTEST(LENY,CY,CT10Y(1,KN,KI),CSIZE3,1.0E0) IF (KI.EQ.1) THEN CX0(1) = (42.0E0,43.0E0) CY0(1) = (44.0E0,45.0E0) IF (N.EQ.0) THEN CTY0(1) = CY0(1) ELSE CTY0(1) = CX0(1) END IF LINCX = INCX INCX = 0 LINCY = INCY INCY = 0 CALL CCOPY(N,CX0,INCX,CY0,INCY) CALL CTEST(1,CY0,CTY0,CSIZE3,1.0E0) INCX = LINCX INCY = LINCY END IF ELSE IF (ICASE.EQ.5) THEN * .. CSWAP .. CALL CSWAP(N,CX,INCX,CY,INCY) CALL CTEST(LENX,CX,CT10X(1,KN,KI),CSIZE3,1.0E0) CALL CTEST(LENY,CY,CT10Y(1,KN,KI),CSIZE3,1.0E0) ELSE WRITE (NOUT,*) ' Shouldn''t be here in CHECK2' STOP END IF * 40 CONTINUE 60 CONTINUE RETURN * * End of CHECK2 * END SUBROUTINE STEST(LEN,SCOMP,STRUE,SSIZE,SFAC) * ********************************* STEST ************************** * * THIS SUBR COMPARES ARRAYS SCOMP() AND STRUE() OF LENGTH LEN TO * SEE IF THE TERM BY TERM DIFFERENCES, MULTIPLIED BY SFAC, ARE * NEGLIGIBLE. * * C. L. LAWSON, JPL, 1974 DEC 10 * * .. Parameters .. INTEGER NOUT REAL ZERO PARAMETER (NOUT=6, ZERO=0.0E0) * .. Scalar Arguments .. REAL SFAC INTEGER LEN * .. Array Arguments .. REAL SCOMP(LEN), SSIZE(LEN), STRUE(LEN) * .. Scalars in Common .. INTEGER ICASE, INCX, INCY, MODE, N LOGICAL PASS * .. Local Scalars .. REAL SD INTEGER I * .. External Functions .. REAL SDIFF EXTERNAL SDIFF * .. Intrinsic Functions .. INTRINSIC ABS * .. Common blocks .. COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS * .. Executable Statements .. * DO 40 I = 1, LEN SD = SCOMP(I) - STRUE(I) IF (ABS(SFAC*SD) .LE. ABS(SSIZE(I))*EPSILON(ZERO)) + GO TO 40 * * HERE SCOMP(I) IS NOT CLOSE TO STRUE(I). * IF ( .NOT. PASS) GO TO 20 * PRINT FAIL MESSAGE AND HEADER. PASS = .FALSE. WRITE (NOUT,99999) WRITE (NOUT,99998) 20 WRITE (NOUT,99997) ICASE, N, INCX, INCY, MODE, I, SCOMP(I), + STRUE(I), SD, SSIZE(I) 40 CONTINUE RETURN * 99999 FORMAT (' FAIL') 99998 FORMAT (/' CASE N INCX INCY MODE I ', + ' COMP(I) TRUE(I) DIFFERENCE', + ' SIZE(I)',/1X) 99997 FORMAT (1X,I4,I3,3I5,I3,2E36.8,2E12.4) * * End of STEST * END SUBROUTINE STEST1(SCOMP1,STRUE1,SSIZE,SFAC) * ************************* STEST1 ***************************** * * THIS IS AN INTERFACE SUBROUTINE TO ACCOMMODATE THE FORTRAN * REQUIREMENT THAT WHEN A DUMMY ARGUMENT IS AN ARRAY, THE * ACTUAL ARGUMENT MUST ALSO BE AN ARRAY OR AN ARRAY ELEMENT. * * C.L. LAWSON, JPL, 1978 DEC 6 * * .. Scalar Arguments .. REAL SCOMP1, SFAC, STRUE1 * .. Array Arguments .. REAL SSIZE(*) * .. Local Arrays .. REAL SCOMP(1), STRUE(1) * .. External Subroutines .. EXTERNAL STEST * .. Executable Statements .. * SCOMP(1) = SCOMP1 STRUE(1) = STRUE1 CALL STEST(1,SCOMP,STRUE,SSIZE,SFAC) * RETURN * * End of STEST1 * END REAL FUNCTION SDIFF(SA,SB) * ********************************* SDIFF ************************** * COMPUTES DIFFERENCE OF TWO NUMBERS. C. L. LAWSON, JPL 1974 FEB 15 * * .. Scalar Arguments .. REAL SA, SB * .. Executable Statements .. SDIFF = SA - SB RETURN * * End of SDIFF * END SUBROUTINE CTEST(LEN,CCOMP,CTRUE,CSIZE,SFAC) * **************************** CTEST ***************************** * * C.L. LAWSON, JPL, 1978 DEC 6 * * .. Scalar Arguments .. REAL SFAC INTEGER LEN * .. Array Arguments .. COMPLEX CCOMP(LEN), CSIZE(LEN), CTRUE(LEN) * .. Local Scalars .. INTEGER I * .. Local Arrays .. REAL SCOMP(20), SSIZE(20), STRUE(20) * .. External Subroutines .. EXTERNAL STEST * .. Intrinsic Functions .. INTRINSIC AIMAG, REAL * .. Executable Statements .. DO 20 I = 1, LEN SCOMP(2*I-1) = REAL(CCOMP(I)) SCOMP(2*I) = AIMAG(CCOMP(I)) STRUE(2*I-1) = REAL(CTRUE(I)) STRUE(2*I) = AIMAG(CTRUE(I)) SSIZE(2*I-1) = REAL(CSIZE(I)) SSIZE(2*I) = AIMAG(CSIZE(I)) 20 CONTINUE * CALL STEST(2*LEN,SCOMP,STRUE,SSIZE,SFAC) RETURN * * End of CTEST * END SUBROUTINE ITEST1(ICOMP,ITRUE) * ********************************* ITEST1 ************************* * * THIS SUBROUTINE COMPARES THE VARIABLES ICOMP AND ITRUE FOR * EQUALITY. * C. L. LAWSON, JPL, 1974 DEC 10 * * .. Parameters .. INTEGER NOUT PARAMETER (NOUT=6) * .. Scalar Arguments .. INTEGER ICOMP, ITRUE * .. Scalars in Common .. INTEGER ICASE, INCX, INCY, MODE, N LOGICAL PASS * .. Local Scalars .. INTEGER ID * .. Common blocks .. COMMON /COMBLA/ICASE, N, INCX, INCY, MODE, PASS * .. Executable Statements .. IF (ICOMP.EQ.ITRUE) GO TO 40 * * HERE ICOMP IS NOT EQUAL TO ITRUE. * IF ( .NOT. PASS) GO TO 20 * PRINT FAIL MESSAGE AND HEADER. PASS = .FALSE. WRITE (NOUT,99999) WRITE (NOUT,99998) 20 ID = ICOMP - ITRUE WRITE (NOUT,99997) ICASE, N, INCX, INCY, MODE, ICOMP, ITRUE, ID 40 CONTINUE RETURN * 99999 FORMAT (' FAIL') 99998 FORMAT (/' CASE N INCX INCY MODE ', + ' COMP TRUE DIFFERENCE', + /1X) 99997 FORMAT (1X,I4,I3,3I5,2I36,I12) * * End of ITEST1 * END SUBROUTINE CB1NRM2(N,INCX,THRESH) * Compare NRM2 with a reference computation using combinations * of the following values: * * 0, very small, small, ulp, 1, 1/ulp, big, very big, infinity, NaN * * one of these values is used to initialize x(1) and x(2:N) is * filled with random values from [-1,1] scaled by another of * these values. * * This routine is adapted from the test suite provided by * Anderson E. (2017) * Algorithm 978: Safe Scaling in the Level 1 BLAS * ACM Trans Math Softw 44:1--28 * https://doi.org/10.1145/3061665 * * .. Scalar Arguments .. INTEGER INCX, N REAL THRESH * * ===================================================================== * .. Parameters .. INTEGER NMAX, NOUT, NV PARAMETER (NMAX=20, NOUT=6, NV=10) REAL HALF, ONE, THREE, TWO, ZERO PARAMETER (HALF=0.5E+0, ONE=1.0E+0, TWO= 2.0E+0, & THREE=3.0E+0, ZERO=0.0E+0) * .. External Functions .. REAL SCNRM2 EXTERNAL SCNRM2 * .. Intrinsic Functions .. INTRINSIC AIMAG, ABS, CMPLX, MAX, MIN, REAL, SQRT * .. Model parameters .. REAL BIGNUM, SAFMAX, SAFMIN, SMLNUM, ULP PARAMETER (BIGNUM=0.1014120480E+32, & SAFMAX=0.8507059173E+38, & SAFMIN=0.1175494351E-37, & SMLNUM=0.9860761315E-31, & ULP=0.1192092896E-06) * .. Local Scalars .. COMPLEX ROGUE REAL SNRM, TRAT, V0, V1, WORKSSQ, Y1, Y2, & YMAX, YMIN, YNRM, ZNRM INTEGER I, IV, IW, IX, KS LOGICAL FIRST * .. Local Arrays .. COMPLEX X(NMAX), Z(NMAX) REAL VALUES(NV), WORK(NMAX) * .. Executable Statements .. VALUES(1) = ZERO VALUES(2) = TWO*SAFMIN VALUES(3) = SMLNUM VALUES(4) = ULP VALUES(5) = ONE VALUES(6) = ONE / ULP VALUES(7) = BIGNUM VALUES(8) = SAFMAX VALUES(9) = SXVALS(V0,2) VALUES(10) = SXVALS(V0,3) ROGUE = CMPLX(1234.5678E+0,-1234.5678E+0) FIRST = .TRUE. * * Check that the arrays are large enough * IF (N*ABS(INCX).GT.NMAX) THEN WRITE (NOUT,99) "SCNRM2", NMAX, INCX, N, N*ABS(INCX) RETURN END IF * * Zero-sized inputs are tested in STEST1. IF (N.LE.0) THEN RETURN END IF * * Generate 2*(N-1) values in (-1,1). * KS = 2*(N-1) DO I = 1, KS CALL RANDOM_NUMBER(WORK(I)) WORK(I) = ONE - TWO*WORK(I) END DO * * Compute the sum of squares of the random values * by an unscaled algorithm. * WORKSSQ = ZERO DO I = 1, KS WORKSSQ = WORKSSQ + WORK(I)*WORK(I) END DO * * Construct the test vector with one known value * and the rest from the random work array multiplied * by a scaling factor. * DO IV = 1, NV V0 = VALUES(IV) IF (ABS(V0).GT.ONE) THEN V0 = V0*HALF*HALF END IF Z(1) = CMPLX(V0,-THREE*V0) DO IW = 1, NV V1 = VALUES(IW) IF (ABS(V1).GT.ONE) THEN V1 = (V1*HALF) / SQRT(REAL(KS+1)) END IF DO I = 1, N-1 Z(I+1) = CMPLX(V1*WORK(2*I-1),V1*WORK(2*I)) END DO * * Compute the expected value of the 2-norm * Y1 = ABS(V0) * SQRT(10.0E0) IF (N.GT.1) THEN Y2 = ABS(V1)*SQRT(WORKSSQ) ELSE Y2 = ZERO END IF YMIN = MIN(Y1, Y2) YMAX = MAX(Y1, Y2) * * Expected value is NaN if either is NaN. The test * for YMIN == YMAX avoids further computation if both * are infinity. * IF ((Y1.NE.Y1).OR.(Y2.NE.Y2)) THEN * add to propagate NaN YNRM = Y1 + Y2 ELSE IF (YMIN == YMAX) THEN YNRM = SQRT(TWO)*YMAX ELSE IF (YMAX == ZERO) THEN YNRM = ZERO ELSE YNRM = YMAX*SQRT(ONE + (YMIN / YMAX)**2) END IF * * Fill the input array to SCNRM2 with steps of incx * DO I = 1, N X(I) = ROGUE END DO IX = 1 IF (INCX.LT.0) IX = 1 - (N-1)*INCX DO I = 1, N X(IX) = Z(I) IX = IX + INCX END DO * * Call SCNRM2 to compute the 2-norm * SNRM = SCNRM2(N,X,INCX) * * Compare SNRM and ZNRM. Roundoff error grows like O(n) * in this implementation so we scale the test ratio accordingly. * IF (INCX.EQ.0) THEN Y1 = ABS(REAL(X(1))) Y2 = ABS(AIMAG(X(1))) YMIN = MIN(Y1, Y2) YMAX = MAX(Y1, Y2) IF ((Y1.NE.Y1).OR.(Y2.NE.Y2)) THEN * add to propagate NaN ZNRM = Y1 + Y2 ELSE IF (YMIN == YMAX) THEN ZNRM = SQRT(TWO)*YMAX ELSE IF (YMAX == ZERO) THEN ZNRM = ZERO ELSE ZNRM = YMAX * SQRT(ONE + (YMIN / YMAX)**2) END IF ZNRM = SQRT(REAL(n)) * ZNRM ELSE ZNRM = YNRM END IF * * The tests for NaN rely on the compiler not being overly * aggressive and removing the statements altogether. IF ((SNRM.NE.SNRM).OR.(ZNRM.NE.ZNRM)) THEN IF ((SNRM.NE.SNRM).NEQV.(ZNRM.NE.ZNRM)) THEN TRAT = ONE / ULP ELSE TRAT = ZERO END IF ELSE IF (ZNRM == ZERO) THEN TRAT = SNRM / ULP ELSE TRAT = (ABS(SNRM-ZNRM) / ZNRM) / (TWO*REAL(N)*ULP) END IF IF ((TRAT.NE.TRAT).OR.(TRAT.GE.THRESH)) THEN IF (FIRST) THEN FIRST = .FALSE. WRITE(NOUT,99999) END IF WRITE (NOUT,98) "SCNRM2", N, INCX, IV, IW, TRAT END IF END DO END DO 99999 FORMAT (' FAIL') 99 FORMAT ( ' Not enough space to test ', A6, ': NMAX = ',I6, + ', INCX = ',I6,/,' N = ',I6,', must be at least ',I6 ) 98 FORMAT( 1X, A6, ': N=', I6,', INCX=', I4, ', IV=', I2, ', IW=', + I2, ', test=', E15.8 ) RETURN CONTAINS REAL FUNCTION SXVALS(XX,K) * .. Scalar Arguments .. REAL XX INTEGER K * .. Local Scalars .. REAL X, Y, YY, Z * .. Intrinsic Functions .. INTRINSIC HUGE * .. Executable Statements .. Y = HUGE(XX) Z = YY IF (K.EQ.1) THEN X = -Z ELSE IF (K.EQ.2) THEN X = Z ELSE IF (K.EQ.3) THEN X = Z / Z END IF SXVALS = X RETURN END END