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Add tests for NRM2 that involve scaling (from Reference-LAPACK PR 925)

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Martin Kroeker GitHub 2 years ago
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4 changed files with 1183 additions and 46 deletions
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  1. +302
    -12
      test/cblat1.f
  2. +291
    -11
      test/dblat1.f
  3. +288
    -11
      test/sblat1.f
  4. +302
    -12
      test/zblat1.f

+ 302
- 12
test/cblat1.f View File

@@ -30,17 +30,14 @@
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date April 2012
*
*> \ingroup complex_blas_testing
*
* =====================================================================
PROGRAM CBLAT1
*
* -- Reference BLAS test routine (version 3.7.0) --
* -- 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..--
* April 2012
*
* =====================================================================
*
@@ -86,6 +83,9 @@
*
99999 FORMAT (' Complex BLAS Test Program Results',/1X)
99998 FORMAT (' ----- PASS -----')
*
* End of CBLAT1
*
END
SUBROUTINE HEADER
* .. Parameters ..
@@ -114,11 +114,15 @@
RETURN
*
99999 FORMAT (/' Test of subprogram number',I3,12X,A6)
*
* End of HEADER
*
END
SUBROUTINE CHECK1(SFAC)
* .. Parameters ..
INTEGER NOUT
PARAMETER (NOUT=6)
REAL THRESH
PARAMETER (NOUT=6, THRESH=10.0E0)
* .. Scalar Arguments ..
REAL SFAC
* .. Scalars in Common ..
@@ -127,18 +131,18 @@
* .. Local Scalars ..
COMPLEX CA
REAL SA
INTEGER I, J, LEN, NP1
INTEGER I, IX, J, LEN, NP1
* .. Local Arrays ..
COMPLEX CTRUE5(8,5,2), CTRUE6(8,5,2), CV(8,5,2), CX(8),
+ MWPCS(5), MWPCT(5)
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)
INTEGER ITRUE3(5), ITRUEC(5)
* .. External Functions ..
REAL SCASUM, SCNRM2
INTEGER ICAMAX
EXTERNAL SCASUM, SCNRM2, ICAMAX
* .. External Subroutines ..
EXTERNAL CSCAL, CSSCAL, CTEST, ITEST1, STEST1
EXTERNAL CB1NRM2, CSCAL, CSSCAL, CTEST, ITEST1, STEST1
* .. Intrinsic Functions ..
INTRINSIC MAX
* .. Common blocks ..
@@ -173,6 +177,9 @@
+ (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),
@@ -238,6 +245,7 @@
+ (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
@@ -249,6 +257,10 @@
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
@@ -268,12 +280,25 @@
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
@@ -315,6 +340,9 @@
CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)
END IF
RETURN
*
* End of CHECK1
*
END
SUBROUTINE CHECK2(SFAC)
* .. Parameters ..
@@ -327,11 +355,13 @@
LOGICAL PASS
* .. Local Scalars ..
COMPLEX CA
INTEGER I, J, KI, KN, KSIZE, LENX, LENY, MX, MY
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), CX(7), CX1(7), CY(7), CY1(7)
+ 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
@@ -546,6 +576,23 @@
* .. 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)
@@ -559,6 +606,9 @@
40 CONTINUE
60 CONTINUE
RETURN
*
* End of CHECK2
*
END
SUBROUTINE STEST(LEN,SCOMP,STRUE,SSIZE,SFAC)
* ********************************* STEST **************************
@@ -615,6 +665,9 @@
+ ' 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 *****************************
@@ -640,6 +693,9 @@
CALL STEST(1,SCOMP,STRUE,SSIZE,SFAC)
*
RETURN
*
* End of STEST1
*
END
REAL FUNCTION SDIFF(SA,SB)
* ********************************* SDIFF **************************
@@ -650,6 +706,9 @@
* .. Executable Statements ..
SDIFF = SA - SB
RETURN
*
* End of SDIFF
*
END
SUBROUTINE CTEST(LEN,CCOMP,CTRUE,CSIZE,SFAC)
* **************************** CTEST *****************************
@@ -681,6 +740,9 @@
*
CALL STEST(2*LEN,SCOMP,STRUE,SSIZE,SFAC)
RETURN
*
* End of CTEST
*
END
SUBROUTINE ITEST1(ICOMP,ITRUE)
* ********************************* ITEST1 *************************
@@ -721,4 +783,232 @@
+ ' 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

+ 291
- 11
test/dblat1.f View File

@@ -30,17 +30,14 @@
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date April 2012
*
*> \ingroup double_blas_testing
*
* =====================================================================
PROGRAM DBLAT1
*
* -- Reference BLAS test routine (version 3.8.0) --
* -- 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..--
* April 2012
*
* =====================================================================
*
@@ -91,6 +88,9 @@
*
99999 FORMAT (' Real BLAS Test Program Results',/1X)
99998 FORMAT (' ----- PASS -----')
*
* End of DBLAT1
*
END
SUBROUTINE HEADER
* .. Parameters ..
@@ -122,6 +122,9 @@
RETURN
*
99999 FORMAT (/' Test of subprogram number',I3,12X,A6)
*
* End of HEADER
*
END
SUBROUTINE CHECK0(SFAC)
* .. Parameters ..
@@ -238,28 +241,33 @@
END IF
20 CONTINUE
40 RETURN
*
* End of CHECK0
*
END
SUBROUTINE CHECK1(SFAC)
* .. Parameters ..
DOUBLE PRECISION THRESH
INTEGER NOUT
PARAMETER (NOUT=6)
PARAMETER (NOUT=6, THRESH=10.0D0)
* .. Scalar Arguments ..
DOUBLE PRECISION SFAC
* .. Scalars in Common ..
INTEGER ICASE, INCX, INCY, N
LOGICAL PASS
* .. Local Scalars ..
INTEGER I, LEN, NP1
INTEGER I, IX, LEN, NP1
* .. Local Arrays ..
DOUBLE PRECISION DTRUE1(5), DTRUE3(5), DTRUE5(8,5,2), DV(8,5,2),
+ SA(10), STEMP(1), STRUE(8), SX(8)
INTEGER ITRUE2(5)
+ DVR(8), SA(10), STEMP(1), STRUE(8), SX(8),
+ SXR(15)
INTEGER ITRUE2(5), ITRUEC(5)
* .. External Functions ..
DOUBLE PRECISION DASUM, DNRM2
INTEGER IDAMAX
EXTERNAL DASUM, DNRM2, IDAMAX
* .. External Subroutines ..
EXTERNAL ITEST1, DSCAL, STEST, STEST1
EXTERNAL ITEST1, DB1NRM2, DSCAL, STEST, STEST1
* .. Intrinsic Functions ..
INTRINSIC MAX
* .. Common blocks ..
@@ -280,6 +288,8 @@
+ 0.2D0, 3.0D0, -0.6D0, 5.0D0, 0.3D0, 2.0D0,
+ 2.0D0, 2.0D0, 0.1D0, 4.0D0, -0.3D0, 6.0D0,
+ -0.5D0, 7.0D0, -0.1D0, 3.0D0/
DATA DVR/8.0D0, -7.0D0, 9.0D0, 5.0D0, 9.0D0, 8.0D0,
+ 7.0D0, 7.0D0/
DATA DTRUE1/0.0D0, 0.3D0, 0.5D0, 0.7D0, 0.6D0/
DATA DTRUE3/0.0D0, 0.3D0, 0.7D0, 1.1D0, 1.0D0/
DATA DTRUE5/0.10D0, 2.0D0, 2.0D0, 2.0D0, 2.0D0,
@@ -297,6 +307,7 @@
+ 0.03D0, 4.0D0, -0.09D0, 6.0D0, -0.15D0, 7.0D0,
+ -0.03D0, 3.0D0/
DATA ITRUE2/0, 1, 2, 2, 3/
DATA ITRUEC/0, 1, 1, 1, 1/
* .. Executable Statements ..
DO 80 INCX = 1, 2
DO 60 NP1 = 1, 5
@@ -309,6 +320,10 @@
*
IF (ICASE.EQ.7) THEN
* .. DNRM2 ..
* Test scaling when some entries are tiny or huge
CALL DB1NRM2(N,(INCX-2)*2,THRESH)
CALL DB1NRM2(N,INCX,THRESH)
* Test with hardcoded mid range entries
STEMP(1) = DTRUE1(NP1)
CALL STEST1(DNRM2(N,SX,INCX),STEMP(1),STEMP,SFAC)
ELSE IF (ICASE.EQ.8) THEN
@@ -325,13 +340,29 @@
ELSE IF (ICASE.EQ.10) THEN
* .. IDAMAX ..
CALL ITEST1(IDAMAX(N,SX,INCX),ITRUE2(NP1))
DO 100 I = 1, LEN
SX(I) = 42.0D0
100 CONTINUE
CALL ITEST1(IDAMAX(N,SX,INCX),ITRUEC(NP1))
ELSE
WRITE (NOUT,*) ' Shouldn''t be here in CHECK1'
STOP
END IF
60 CONTINUE
IF (ICASE.EQ.10) THEN
N = 8
IX = 1
DO 120 I = 1, N
SXR(IX) = DVR(I)
IX = IX + INCX
120 CONTINUE
CALL ITEST1(IDAMAX(N,SXR,INCX),3)
END IF
80 CONTINUE
RETURN
*
* End of CHECK1
*
END
SUBROUTINE CHECK2(SFAC)
* .. Parameters ..
@@ -345,7 +376,7 @@
* .. Local Scalars ..
DOUBLE PRECISION SA
INTEGER I, J, KI, KN, KNI, KPAR, KSIZE, LENX, LENY,
$ MX, MY
$ LINCX, LINCY, MX, MY
* .. Local Arrays ..
DOUBLE PRECISION DT10X(7,4,4), DT10Y(7,4,4), DT7(4,4),
$ DT8(7,4,4), DX1(7),
@@ -354,7 +385,8 @@
$ DPAR(5,4), DT19X(7,4,16),DT19XA(7,4,4),
$ DT19XB(7,4,4), DT19XC(7,4,4),DT19XD(7,4,4),
$ DT19Y(7,4,16), DT19YA(7,4,4),DT19YB(7,4,4),
$ DT19YC(7,4,4), DT19YD(7,4,4), DTEMP(5)
$ DT19YC(7,4,4), DT19YD(7,4,4), DTEMP(5),
$ STY0(1), SX0(1), SY0(1)
INTEGER INCXS(4), INCYS(4), LENS(4,2), NS(4)
* .. External Functions ..
DOUBLE PRECISION DDOT, DSDOT
@@ -628,6 +660,23 @@
60 CONTINUE
CALL DCOPY(N,SX,INCX,SY,INCY)
CALL STEST(LENY,SY,STY,SSIZE2(1,1),1.0D0)
IF (KI.EQ.1) THEN
SX0(1) = 42.0D0
SY0(1) = 43.0D0
IF (N.EQ.0) THEN
STY0(1) = SY0(1)
ELSE
STY0(1) = SX0(1)
END IF
LINCX = INCX
INCX = 0
LINCY = INCY
INCY = 0
CALL DCOPY(N,SX0,INCX,SY0,INCY)
CALL STEST(1,SY0,STY0,SSIZE2(1,1),1.0D0)
INCX = LINCX
INCY = LINCY
END IF
ELSE IF (ICASE.EQ.6) THEN
* .. DSWAP ..
CALL DSWAP(N,SX,INCX,SY,INCY)
@@ -677,6 +726,9 @@
100 CONTINUE
120 CONTINUE
RETURN
*
* End of CHECK2
*
END
SUBROUTINE CHECK3(SFAC)
* .. Parameters ..
@@ -883,6 +935,9 @@
CALL STEST(5,COPYY,MWPSTY,MWPSTY,SFAC)
200 CONTINUE
RETURN
*
* End of CHECK3
*
END
SUBROUTINE STEST(LEN,SCOMP,STRUE,SSIZE,SFAC)
* ********************************* STEST **************************
@@ -939,6 +994,9 @@
+ ' COMP(I) TRUE(I) DIFFERENCE',
+ ' SIZE(I)',/1X)
99997 FORMAT (1X,I4,I3,2I5,I3,2D36.8,2D12.4)
*
* End of STEST
*
END
SUBROUTINE TESTDSDOT(SCOMP,STRUE,SSIZE,SFAC)
* ********************************* STEST **************************
@@ -987,6 +1045,9 @@
+ ' COMP(I) TRUE(I) DIFFERENCE',
+ ' SIZE(I)',/1X)
99997 FORMAT (1X,I4,I3,1I5,I3,2E36.8,2E12.4)
*
* End of TESTDSDOT
*
END
SUBROUTINE STEST1(SCOMP1,STRUE1,SSIZE,SFAC)
* ************************* STEST1 *****************************
@@ -1012,6 +1073,9 @@
CALL STEST(1,SCOMP,STRUE,SSIZE,SFAC)
*
RETURN
*
* End of STEST1
*
END
DOUBLE PRECISION FUNCTION SDIFF(SA,SB)
* ********************************* SDIFF **************************
@@ -1022,6 +1086,9 @@
* .. Executable Statements ..
SDIFF = SA - SB
RETURN
*
* End of SDIFF
*
END
SUBROUTINE ITEST1(ICOMP,ITRUE)
* ********************************* ITEST1 *************************
@@ -1063,4 +1130,217 @@
+ ' COMP TRUE DIFFERENCE',
+ /1X)
99997 FORMAT (1X,I4,I3,2I5,2I36,I12)
*
* End of ITEST1
*
END
SUBROUTINE DB1NRM2(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
DOUBLE PRECISION THRESH
*
* =====================================================================
* .. Parameters ..
INTEGER NMAX, NOUT, NV
PARAMETER (NMAX=20, NOUT=6, NV=10)
DOUBLE PRECISION HALF, ONE, TWO, ZERO
PARAMETER (HALF=0.5D+0, ONE=1.0D+0, TWO= 2.0D+0,
& ZERO=0.0D+0)
* .. External Functions ..
DOUBLE PRECISION DNRM2
EXTERNAL DNRM2
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, MAX, MIN, SQRT
* .. Model parameters ..
DOUBLE PRECISION BIGNUM, SAFMAX, SAFMIN, SMLNUM, ULP
PARAMETER (BIGNUM=0.99792015476735990583D+292,
& SAFMAX=0.44942328371557897693D+308,
& SAFMIN=0.22250738585072013831D-307,
& SMLNUM=0.10020841800044863890D-291,
& ULP=0.22204460492503130808D-015)
* .. Local Scalars ..
DOUBLE PRECISION ROGUE, SNRM, TRAT, V0, V1, WORKSSQ, Y1, Y2,
& YMAX, YMIN, YNRM, ZNRM
INTEGER I, IV, IW, IX
LOGICAL FIRST
* .. Local Arrays ..
DOUBLE PRECISION VALUES(NV), WORK(NMAX), X(NMAX), Z(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) = DXVALS(V0,2)
VALUES(10) = DXVALS(V0,3)
ROGUE = -1234.5678D+0
FIRST = .TRUE.
*
* Check that the arrays are large enough
*
IF (N*ABS(INCX).GT.NMAX) THEN
WRITE (NOUT,99) "DNRM2", 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 (N-1) values in (-1,1).
*
DO I = 2, N
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 = 2, N
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
END IF
Z(1) = V0
DO IW = 1, NV
V1 = VALUES(IW)
IF (ABS(V1).GT.ONE) THEN
V1 = (V1*HALF) / SQRT(DBLE(N))
END IF
DO I = 2, N
Z(I) = V1*WORK(I)
END DO
*
* Compute the expected value of the 2-norm
*
Y1 = ABS(V0)
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 (YMAX == ZERO) THEN
YNRM = ZERO
ELSE IF (YMIN == YMAX) THEN
YNRM = SQRT(TWO)*YMAX
ELSE
YNRM = YMAX*SQRT(ONE + (YMIN / YMAX)**2)
END IF
*
* Fill the input array to DNRM2 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 DNRM2 to compute the 2-norm
*
SNRM = DNRM2(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
ZNRM = SQRT(DBLE(N))*ABS(X(1))
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 (SNRM == ZNRM) THEN
TRAT = ZERO
ELSE IF (ZNRM == ZERO) THEN
TRAT = SNRM / ULP
ELSE
TRAT = (ABS(SNRM-ZNRM) / ZNRM) / (DBLE(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) "DNRM2", 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
DOUBLE PRECISION FUNCTION DXVALS(XX,K)
* .. Scalar Arguments ..
DOUBLE PRECISION XX
INTEGER K
* .. Local Scalars ..
DOUBLE PRECISION 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
DXVALS = X
RETURN
END
END

+ 288
- 11
test/sblat1.f View File

@@ -30,17 +30,14 @@
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date April 2012
*
*> \ingroup single_blas_testing
*
* =====================================================================
PROGRAM SBLAT1
*
* -- Reference BLAS test routine (version 3.8.0) --
* -- 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..--
* April 2012
*
* =====================================================================
*
@@ -91,6 +88,9 @@
*
99999 FORMAT (' Real BLAS Test Program Results',/1X)
99998 FORMAT (' ----- PASS -----')
*
* End of SBLAT1
*
END
SUBROUTINE HEADER
* .. Parameters ..
@@ -122,6 +122,9 @@
RETURN
*
99999 FORMAT (/' Test of subprogram number',I3,12X,A6)
*
* End of HEADER
*
END
SUBROUTINE CHECK0(SFAC)
* .. Parameters ..
@@ -238,28 +241,33 @@
END IF
20 CONTINUE
40 RETURN
*
* End of CHECK0
*
END
SUBROUTINE CHECK1(SFAC)
* .. Parameters ..
INTEGER NOUT
PARAMETER (NOUT=6)
REAL THRESH
PARAMETER (NOUT=6, THRESH=10.0E0)
* .. Scalar Arguments ..
REAL SFAC
* .. Scalars in Common ..
INTEGER ICASE, INCX, INCY, N
LOGICAL PASS
* .. Local Scalars ..
INTEGER I, LEN, NP1
INTEGER I, IX, LEN, NP1
* .. Local Arrays ..
REAL DTRUE1(5), DTRUE3(5), DTRUE5(8,5,2), DV(8,5,2),
+ SA(10), STEMP(1), STRUE(8), SX(8)
INTEGER ITRUE2(5)
+ DVR(8), SA(10), STEMP(1), STRUE(8), SX(8),
+ SXR(15)
INTEGER ITRUE2(5), ITRUEC(5)
* .. External Functions ..
REAL SASUM, SNRM2
INTEGER ISAMAX
EXTERNAL SASUM, SNRM2, ISAMAX
* .. External Subroutines ..
EXTERNAL ITEST1, SSCAL, STEST, STEST1
EXTERNAL ITEST1, SB1NRM2, SSCAL, STEST, STEST1
* .. Intrinsic Functions ..
INTRINSIC MAX
* .. Common blocks ..
@@ -280,6 +288,8 @@
+ 0.2E0, 3.0E0, -0.6E0, 5.0E0, 0.3E0, 2.0E0,
+ 2.0E0, 2.0E0, 0.1E0, 4.0E0, -0.3E0, 6.0E0,
+ -0.5E0, 7.0E0, -0.1E0, 3.0E0/
DATA DVR/8.0E0, -7.0E0, 9.0E0, 5.0E0, 9.0E0, 8.0E0,
+ 7.0E0, 7.0E0/
DATA DTRUE1/0.0E0, 0.3E0, 0.5E0, 0.7E0, 0.6E0/
DATA DTRUE3/0.0E0, 0.3E0, 0.7E0, 1.1E0, 1.0E0/
DATA DTRUE5/0.10E0, 2.0E0, 2.0E0, 2.0E0, 2.0E0,
@@ -297,6 +307,7 @@
+ 0.03E0, 4.0E0, -0.09E0, 6.0E0, -0.15E0, 7.0E0,
+ -0.03E0, 3.0E0/
DATA ITRUE2/0, 1, 2, 2, 3/
DATA ITRUEC/0, 1, 1, 1, 1/
* .. Executable Statements ..
DO 80 INCX = 1, 2
DO 60 NP1 = 1, 5
@@ -309,6 +320,10 @@
*
IF (ICASE.EQ.7) THEN
* .. SNRM2 ..
* Test scaling when some entries are tiny or huge
CALL SB1NRM2(N,(INCX-2)*2,THRESH)
CALL SB1NRM2(N,INCX,THRESH)
* Test with hardcoded mid range entries
STEMP(1) = DTRUE1(NP1)
CALL STEST1(SNRM2(N,SX,INCX),STEMP(1),STEMP,SFAC)
ELSE IF (ICASE.EQ.8) THEN
@@ -325,13 +340,29 @@
ELSE IF (ICASE.EQ.10) THEN
* .. ISAMAX ..
CALL ITEST1(ISAMAX(N,SX,INCX),ITRUE2(NP1))
DO 100 I = 1, LEN
SX(I) = 42.0E0
100 CONTINUE
CALL ITEST1(ISAMAX(N,SX,INCX),ITRUEC(NP1))
ELSE
WRITE (NOUT,*) ' Shouldn''t be here in CHECK1'
STOP
END IF
60 CONTINUE
IF (ICASE.EQ.10) THEN
N = 8
IX = 1
DO 120 I = 1, N
SXR(IX) = DVR(I)
IX = IX + INCX
120 CONTINUE
CALL ITEST1(ISAMAX(N,SXR,INCX),3)
END IF
80 CONTINUE
RETURN
*
* End of CHECK1
*
END
SUBROUTINE CHECK2(SFAC)
* .. Parameters ..
@@ -345,7 +376,7 @@
* .. Local Scalars ..
REAL SA
INTEGER I, J, KI, KN, KNI, KPAR, KSIZE, LENX, LENY,
$ MX, MY
$ LINCX, LINCY, MX, MY
* .. Local Arrays ..
REAL DT10X(7,4,4), DT10Y(7,4,4), DT7(4,4),
$ DT8(7,4,4), DX1(7),
@@ -355,7 +386,7 @@
$ DT19XB(7,4,4), DT19XC(7,4,4),DT19XD(7,4,4),
$ DT19Y(7,4,16), DT19YA(7,4,4),DT19YB(7,4,4),
$ DT19YC(7,4,4), DT19YD(7,4,4), DTEMP(5),
$ ST7B(4,4)
$ ST7B(4,4), STY0(1), SX0(1), SY0(1)
INTEGER INCXS(4), INCYS(4), LENS(4,2), NS(4)
* .. External Functions ..
REAL SDOT, SDSDOT
@@ -631,6 +662,23 @@
60 CONTINUE
CALL SCOPY(N,SX,INCX,SY,INCY)
CALL STEST(LENY,SY,STY,SSIZE2(1,1),1.0E0)
IF (KI.EQ.1) THEN
SX0(1) = 42.0E0
SY0(1) = 43.0E0
IF (N.EQ.0) THEN
STY0(1) = SY0(1)
ELSE
STY0(1) = SX0(1)
END IF
LINCX = INCX
INCX = 0
LINCY = INCY
INCY = 0
CALL SCOPY(N,SX0,INCX,SY0,INCY)
CALL STEST(1,SY0,STY0,SSIZE2(1,1),1.0E0)
INCX = LINCX
INCY = LINCY
END IF
ELSE IF (ICASE.EQ.6) THEN
* .. SSWAP ..
CALL SSWAP(N,SX,INCX,SY,INCY)
@@ -680,6 +728,9 @@
100 CONTINUE
120 CONTINUE
RETURN
*
* End of CHECK2
*
END
SUBROUTINE CHECK3(SFAC)
* .. Parameters ..
@@ -886,6 +937,9 @@
CALL STEST(5,COPYY,MWPSTY,MWPSTY,SFAC)
200 CONTINUE
RETURN
*
* End of CHECK3
*
END
SUBROUTINE STEST(LEN,SCOMP,STRUE,SSIZE,SFAC)
* ********************************* STEST **************************
@@ -942,6 +996,9 @@
+ ' COMP(I) TRUE(I) DIFFERENCE',
+ ' SIZE(I)',/1X)
99997 FORMAT (1X,I4,I3,2I5,I3,2E36.8,2E12.4)
*
* End of STEST
*
END
SUBROUTINE STEST1(SCOMP1,STRUE1,SSIZE,SFAC)
* ************************* STEST1 *****************************
@@ -967,6 +1024,9 @@
CALL STEST(1,SCOMP,STRUE,SSIZE,SFAC)
*
RETURN
*
* End of STEST1
*
END
REAL FUNCTION SDIFF(SA,SB)
* ********************************* SDIFF **************************
@@ -977,6 +1037,9 @@
* .. Executable Statements ..
SDIFF = SA - SB
RETURN
*
* End of SDIFF
*
END
SUBROUTINE ITEST1(ICOMP,ITRUE)
* ********************************* ITEST1 *************************
@@ -1018,4 +1081,218 @@
+ ' COMP TRUE DIFFERENCE',
+ /1X)
99997 FORMAT (1X,I4,I3,2I5,2I36,I12)
*
* End of ITEST1
*
END
SUBROUTINE SB1NRM2(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
*
IMPLICIT NONE
* .. Scalar Arguments ..
INTEGER INCX, N
REAL THRESH
*
* =====================================================================
* .. Parameters ..
INTEGER NMAX, NOUT, NV
PARAMETER (NMAX=20, NOUT=6, NV=10)
REAL HALF, ONE, TWO, ZERO
PARAMETER (HALF=0.5E+0, ONE=1.0E+0, TWO= 2.0E+0,
& ZERO=0.0E+0)
* .. External Functions ..
REAL SNRM2
EXTERNAL SNRM2
* .. Intrinsic Functions ..
INTRINSIC ABS, 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 ..
REAL ROGUE, SNRM, TRAT, V0, V1, WORKSSQ, Y1, Y2,
& YMAX, YMIN, YNRM, ZNRM
INTEGER I, IV, IW, IX
LOGICAL FIRST
* .. Local Arrays ..
REAL VALUES(NV), WORK(NMAX), X(NMAX), Z(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 = -1234.5678E+0
FIRST = .TRUE.
*
* Check that the arrays are large enough
*
IF (N*ABS(INCX).GT.NMAX) THEN
WRITE (NOUT,99) "SNRM2", 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 (N-1) values in (-1,1).
*
DO I = 2, N
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 = 2, N
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
END IF
Z(1) = V0
DO IW = 1, NV
V1 = VALUES(IW)
IF (ABS(V1).GT.ONE) THEN
V1 = (V1*HALF) / SQRT(REAL(N))
END IF
DO I = 2, N
Z(I) = V1*WORK(I)
END DO
*
* Compute the expected value of the 2-norm
*
Y1 = ABS(V0)
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 SNRM2 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 SNRM2 to compute the 2-norm
*
SNRM = SNRM2(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
ZNRM = SQRT(REAL(N))*ABS(X(1))
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 (SNRM == ZNRM) THEN
TRAT = ZERO
ELSE IF (ZNRM == ZERO) THEN
TRAT = SNRM / ULP
ELSE
TRAT = (ABS(SNRM-ZNRM) / ZNRM) / (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) "SNRM2", 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

+ 302
- 12
test/zblat1.f View File

@@ -30,17 +30,14 @@
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date April 2012
*
*> \ingroup complex16_blas_testing
*
* =====================================================================
PROGRAM ZBLAT1
*
* -- Reference BLAS test routine (version 3.7.0) --
* -- 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..--
* April 2012
*
* =====================================================================
*
@@ -86,6 +83,9 @@
*
99999 FORMAT (' Complex BLAS Test Program Results',/1X)
99998 FORMAT (' ----- PASS -----')
*
* End of ZBLAT1
*
END
SUBROUTINE HEADER
* .. Parameters ..
@@ -114,11 +114,15 @@
RETURN
*
99999 FORMAT (/' Test of subprogram number',I3,12X,A6)
*
* End of HEADER
*
END
SUBROUTINE CHECK1(SFAC)
* .. Parameters ..
INTEGER NOUT
PARAMETER (NOUT=6)
DOUBLE PRECISION THRESH
PARAMETER (NOUT=6, THRESH=10.0D0)
* .. Scalar Arguments ..
DOUBLE PRECISION SFAC
* .. Scalars in Common ..
@@ -127,18 +131,18 @@
* .. Local Scalars ..
COMPLEX*16 CA
DOUBLE PRECISION SA
INTEGER I, J, LEN, NP1
INTEGER I, IX, J, LEN, NP1
* .. Local Arrays ..
COMPLEX*16 CTRUE5(8,5,2), CTRUE6(8,5,2), CV(8,5,2), CX(8),
+ MWPCS(5), MWPCT(5)
COMPLEX*16 CTRUE5(8,5,2), CTRUE6(8,5,2), CV(8,5,2), CVR(8),
+ CX(8), CXR(15), MWPCS(5), MWPCT(5)
DOUBLE PRECISION STRUE2(5), STRUE4(5)
INTEGER ITRUE3(5)
INTEGER ITRUE3(5), ITRUEC(5)
* .. External Functions ..
DOUBLE PRECISION DZASUM, DZNRM2
INTEGER IZAMAX
EXTERNAL DZASUM, DZNRM2, IZAMAX
* .. External Subroutines ..
EXTERNAL ZSCAL, ZDSCAL, CTEST, ITEST1, STEST1
EXTERNAL ZB1NRM2, ZSCAL, ZDSCAL, CTEST, ITEST1, STEST1
* .. Intrinsic Functions ..
INTRINSIC MAX
* .. Common blocks ..
@@ -173,6 +177,9 @@
+ (7.0D0,2.0D0), (0.3D0,0.1D0), (5.0D0,8.0D0),
+ (0.5D0,0.0D0), (6.0D0,9.0D0), (0.0D0,0.5D0),
+ (8.0D0,3.0D0), (0.0D0,0.2D0), (9.0D0,4.0D0)/
DATA CVR/(8.0D0,8.0D0), (-7.0D0,-7.0D0),
+ (9.0D0,9.0D0), (5.0D0,5.0D0), (9.0D0,9.0D0),
+ (8.0D0,8.0D0), (7.0D0,7.0D0), (7.0D0,7.0D0)/
DATA STRUE2/0.0D0, 0.5D0, 0.6D0, 0.7D0, 0.8D0/
DATA STRUE4/0.0D0, 0.7D0, 1.0D0, 1.3D0, 1.6D0/
DATA ((CTRUE5(I,J,1),I=1,8),J=1,5)/(0.1D0,0.1D0),
@@ -238,6 +245,7 @@
+ (0.15D0,0.00D0), (6.0D0,9.0D0), (0.00D0,0.15D0),
+ (8.0D0,3.0D0), (0.00D0,0.06D0), (9.0D0,4.0D0)/
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
@@ -249,6 +257,10 @@
20 CONTINUE
IF (ICASE.EQ.6) THEN
* .. DZNRM2 ..
* Test scaling when some entries are tiny or huge
CALL ZB1NRM2(N,(INCX-2)*2,THRESH)
CALL ZB1NRM2(N,INCX,THRESH)
* Test with hardcoded mid range entries
CALL STEST1(DZNRM2(N,CX,INCX),STRUE2(NP1),STRUE2(NP1),
+ SFAC)
ELSE IF (ICASE.EQ.7) THEN
@@ -268,12 +280,25 @@
ELSE IF (ICASE.EQ.10) THEN
* .. IZAMAX ..
CALL ITEST1(IZAMAX(N,CX,INCX),ITRUE3(NP1))
DO 160 I = 1, LEN
CX(I) = (42.0D0,43.0D0)
160 CONTINUE
CALL ITEST1(IZAMAX(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(IZAMAX(N,CXR,INCX),3)
END IF
60 CONTINUE
*
INCX = 1
@@ -315,6 +340,9 @@
CALL CTEST(5,CX,MWPCT,MWPCS,SFAC)
END IF
RETURN
*
* End of CHECK1
*
END
SUBROUTINE CHECK2(SFAC)
* .. Parameters ..
@@ -327,11 +355,13 @@
LOGICAL PASS
* .. Local Scalars ..
COMPLEX*16 CA
INTEGER I, J, KI, KN, KSIZE, LENX, LENY, MX, MY
INTEGER I, J, KI, KN, KSIZE, LENX, LENY, LINCX, LINCY,
+ MX, MY
* .. Local Arrays ..
COMPLEX*16 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), CX(7), CX1(7), CY(7), CY1(7)
+ 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*16 ZDOTC, ZDOTU
@@ -546,6 +576,23 @@
* .. ZCOPY ..
CALL ZCOPY(N,CX,INCX,CY,INCY)
CALL CTEST(LENY,CY,CT10Y(1,KN,KI),CSIZE3,1.0D0)
IF (KI.EQ.1) THEN
CX0(1) = (42.0D0,43.0D0)
CY0(1) = (44.0D0,45.0D0)
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 ZCOPY(N,CX0,INCX,CY0,INCY)
CALL CTEST(1,CY0,CTY0,CSIZE3,1.0D0)
INCX = LINCX
INCY = LINCY
END IF
ELSE IF (ICASE.EQ.5) THEN
* .. ZSWAP ..
CALL ZSWAP(N,CX,INCX,CY,INCY)
@@ -559,6 +606,9 @@
40 CONTINUE
60 CONTINUE
RETURN
*
* End of CHECK2
*
END
SUBROUTINE STEST(LEN,SCOMP,STRUE,SSIZE,SFAC)
* ********************************* STEST **************************
@@ -615,6 +665,9 @@
+ ' COMP(I) TRUE(I) DIFFERENCE',
+ ' SIZE(I)',/1X)
99997 FORMAT (1X,I4,I3,3I5,I3,2D36.8,2D12.4)
*
* End of STEST
*
END
SUBROUTINE STEST1(SCOMP1,STRUE1,SSIZE,SFAC)
* ************************* STEST1 *****************************
@@ -640,6 +693,9 @@
CALL STEST(1,SCOMP,STRUE,SSIZE,SFAC)
*
RETURN
*
* End of STEST1
*
END
DOUBLE PRECISION FUNCTION SDIFF(SA,SB)
* ********************************* SDIFF **************************
@@ -650,6 +706,9 @@
* .. Executable Statements ..
SDIFF = SA - SB
RETURN
*
* End of SDIFF
*
END
SUBROUTINE CTEST(LEN,CCOMP,CTRUE,CSIZE,SFAC)
* **************************** CTEST *****************************
@@ -681,6 +740,9 @@
*
CALL STEST(2*LEN,SCOMP,STRUE,SSIZE,SFAC)
RETURN
*
* End of CTEST
*
END
SUBROUTINE ITEST1(ICOMP,ITRUE)
* ********************************* ITEST1 *************************
@@ -721,4 +783,232 @@
+ ' COMP TRUE DIFFERENCE',
+ /1X)
99997 FORMAT (1X,I4,I3,3I5,2I36,I12)
*
* End of ITEST1
*
END
SUBROUTINE ZB1NRM2(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
DOUBLE PRECISION THRESH
*
* =====================================================================
* .. Parameters ..
INTEGER NMAX, NOUT, NV
PARAMETER (NMAX=20, NOUT=6, NV=10)
DOUBLE PRECISION HALF, ONE, THREE, TWO, ZERO
PARAMETER (HALF=0.5D+0, ONE=1.0D+0, TWO= 2.0D+0,
& THREE=3.0D+0, ZERO=0.0D+0)
* .. External Functions ..
DOUBLE PRECISION DZNRM2
EXTERNAL DZNRM2
* .. Intrinsic Functions ..
INTRINSIC AIMAG, ABS, DCMPLX, DBLE, MAX, MIN, SQRT
* .. Model parameters ..
DOUBLE PRECISION BIGNUM, SAFMAX, SAFMIN, SMLNUM, ULP
PARAMETER (BIGNUM=0.99792015476735990583D+292,
& SAFMAX=0.44942328371557897693D+308,
& SAFMIN=0.22250738585072013831D-307,
& SMLNUM=0.10020841800044863890D-291,
& ULP=0.22204460492503130808D-015)
* .. Local Scalars ..
COMPLEX*16 ROGUE
DOUBLE PRECISION SNRM, TRAT, V0, V1, WORKSSQ, Y1, Y2,
& YMAX, YMIN, YNRM, ZNRM
INTEGER I, IV, IW, IX, KS
LOGICAL FIRST
* .. Local Arrays ..
COMPLEX*16 X(NMAX), Z(NMAX)
DOUBLE PRECISION 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) = DXVALS(V0,2)
VALUES(10) = DXVALS(V0,3)
ROGUE = DCMPLX(1234.5678D+0,-1234.5678D+0)
FIRST = .TRUE.
*
* Check that the arrays are large enough
*
IF (N*ABS(INCX).GT.NMAX) THEN
WRITE (NOUT,99) "DZNRM2", 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) = DCMPLX(V0,-THREE*V0)
DO IW = 1, NV
V1 = VALUES(IW)
IF (ABS(V1).GT.ONE) THEN
V1 = (V1*HALF) / SQRT(DBLE(KS+1))
END IF
DO I = 1, N-1
Z(I+1) = DCMPLX(V1*WORK(2*I-1),V1*WORK(2*I))
END DO
*
* Compute the expected value of the 2-norm
*
Y1 = ABS(V0) * SQRT(10.0D0)
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 DZNRM2 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 DZNRM2 to compute the 2-norm
*
SNRM = DZNRM2(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(DBLE(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(DBLE(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*DBLE(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) "DZNRM2", 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
DOUBLE PRECISION FUNCTION DXVALS(XX,K)
* .. Scalar Arguments ..
DOUBLE PRECISION XX
INTEGER K
* .. Local Scalars ..
DOUBLE PRECISION 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
DXVALS = X
RETURN
END
END

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