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OpenLibm/slatec/cunk2.f
Viral B. Shah c977aa998f Add Makefile.extras to build libopenlibm-extras. 
Replace amos with slatec
2012-12-31 16:37:05 -05:00

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Fortran
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*DECK CUNK2
SUBROUTINE CUNK2 (Z, FNU, KODE, MR, N, Y, NZ, TOL, ELIM, ALIM)
C***BEGIN PROLOGUE CUNK2
C***SUBSIDIARY
C***PURPOSE Subsidiary to CBESK
C***LIBRARY SLATEC
C***TYPE ALL (CUNK2-A, ZUNK2-A)
C***AUTHOR Amos, D. E., (SNL)
C***DESCRIPTION
C
C CUNK2 COMPUTES K(FNU,Z) AND ITS ANALYTIC CONTINUATION FROM THE
C RIGHT HALF PLANE TO THE LEFT HALF PLANE BY MEANS OF THE
C UNIFORM ASYMPTOTIC EXPANSIONS FOR H(KIND,FNU,ZN) AND J(FNU,ZN)
C WHERE ZN IS IN THE RIGHT HALF PLANE, KIND=(3-MR)/2, MR=+1 OR
C -1. HERE ZN=ZR*I OR -ZR*I WHERE ZR=Z IF Z IS IN THE RIGHT
C HALF PLANE OR ZR=-Z IF Z IS IN THE LEFT HALF PLANE. MR INDIC-
C ATES THE DIRECTION OF ROTATION FOR ANALYTIC CONTINUATION.
C NZ=-1 MEANS AN OVERFLOW WILL OCCUR
C
C***SEE ALSO CBESK
C***ROUTINES CALLED CAIRY, CS1S2, CUCHK, CUNHJ, R1MACH
C***REVISION HISTORY (YYMMDD)
C 830501 DATE WRITTEN
C 910415 Prologue converted to Version 4.0 format. (BAB)
C***END PROLOGUE CUNK2
COMPLEX AI, ARG, ASUM, BSUM, CFN, CI, CIP,
* CK, CONE, CRSC, CR1, CR2, CS, CSCL, CSGN, CSPN, CSR, CSS, CY,
* CZERO, C1, C2, DAI, PHI, RZ, S1, S2, Y, Z, ZB, ZETA1,
* ZETA2, ZN, ZR, PHID, ARGD, ZETA1D, ZETA2D, ASUMD, BSUMD
REAL AARG, AIC, ALIM, ANG, APHI, ASC, ASCLE, BRY, CAR, CPN, C2I,
* C2M, C2R, ELIM, FMR, FN, FNF, FNU, HPI, PI, RS1, SAR, SGN, SPN,
* TOL, X, YY, R1MACH
INTEGER I, IB, IFLAG, IFN, IL, IN, INU, IUF, K, KDFLG, KFLAG, KK,
* KODE, MR, N, NAI, NDAI, NW, NZ, IDUM, J, IPARD, IC
DIMENSION BRY(3), Y(N), ASUM(2), BSUM(2), PHI(2), ARG(2),
* ZETA1(2), ZETA2(2), CY(2), CIP(4), CSS(3), CSR(3)
DATA CZERO, CONE, CI, CR1, CR2 /
1 (0.0E0,0.0E0),(1.0E0,0.0E0),(0.0E0,1.0E0),
1(1.0E0,1.73205080756887729E0),(-0.5E0,-8.66025403784438647E-01)/
DATA HPI, PI, AIC /
1 1.57079632679489662E+00, 3.14159265358979324E+00,
1 1.26551212348464539E+00/
DATA CIP(1),CIP(2),CIP(3),CIP(4)/
1 (1.0E0,0.0E0), (0.0E0,-1.0E0), (-1.0E0,0.0E0), (0.0E0,1.0E0)/
C***FIRST EXECUTABLE STATEMENT CUNK2
KDFLG = 1
NZ = 0
C-----------------------------------------------------------------------
C EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION GREATER THAN
C THE UNDERFLOW LIMIT
C-----------------------------------------------------------------------
CSCL = CMPLX(1.0E0/TOL,0.0E0)
CRSC = CMPLX(TOL,0.0E0)
CSS(1) = CSCL
CSS(2) = CONE
CSS(3) = CRSC
CSR(1) = CRSC
CSR(2) = CONE
CSR(3) = CSCL
BRY(1) = 1.0E+3*R1MACH(1)/TOL
BRY(2) = 1.0E0/BRY(1)
BRY(3) = R1MACH(2)
X = REAL(Z)
ZR = Z
IF (X.LT.0.0E0) ZR = -Z
YY = AIMAG(ZR)
ZN = -ZR*CI
ZB = ZR
INU = FNU
FNF = FNU - INU
ANG = -HPI*FNF
CAR = COS(ANG)
SAR = SIN(ANG)
CPN = -HPI*CAR
SPN = -HPI*SAR
C2 = CMPLX(-SPN,CPN)
KK = MOD(INU,4) + 1
CS = CR1*C2*CIP(KK)
IF (YY.GT.0.0E0) GO TO 10
ZN = CONJG(-ZN)
ZB = CONJG(ZB)
10 CONTINUE
C-----------------------------------------------------------------------
C K(FNU,Z) IS COMPUTED FROM H(2,FNU,-I*Z) WHERE Z IS IN THE FIRST
C QUADRANT. FOURTH QUADRANT VALUES (YY.LE.0.0E0) ARE COMPUTED BY
C CONJUGATION SINCE THE K FUNCTION IS REAL ON THE POSITIVE REAL AXIS
C-----------------------------------------------------------------------
J = 2
DO 70 I=1,N
C-----------------------------------------------------------------------
C J FLIP FLOPS BETWEEN 1 AND 2 IN J = 3 - J
C-----------------------------------------------------------------------
J = 3 - J
FN = FNU + (I-1)
CALL CUNHJ(ZN, FN, 0, TOL, PHI(J), ARG(J), ZETA1(J), ZETA2(J),
* ASUM(J), BSUM(J))
IF (KODE.EQ.1) GO TO 20
CFN = CMPLX(FN,0.0E0)
S1 = ZETA1(J) - CFN*(CFN/(ZB+ZETA2(J)))
GO TO 30
20 CONTINUE
S1 = ZETA1(J) - ZETA2(J)
30 CONTINUE
C-----------------------------------------------------------------------
C TEST FOR UNDERFLOW AND OVERFLOW
C-----------------------------------------------------------------------
RS1 = REAL(S1)
IF (ABS(RS1).GT.ELIM) GO TO 60
IF (KDFLG.EQ.1) KFLAG = 2
IF (ABS(RS1).LT.ALIM) GO TO 40
C-----------------------------------------------------------------------
C REFINE TEST AND SCALE
C-----------------------------------------------------------------------
APHI = ABS(PHI(J))
AARG = ABS(ARG(J))
RS1 = RS1 + ALOG(APHI) - 0.25E0*ALOG(AARG) - AIC
IF (ABS(RS1).GT.ELIM) GO TO 60
IF (KDFLG.EQ.1) KFLAG = 1
IF (RS1.LT.0.0E0) GO TO 40
IF (KDFLG.EQ.1) KFLAG = 3
40 CONTINUE
C-----------------------------------------------------------------------
C SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
C EXPONENT EXTREMES
C-----------------------------------------------------------------------
C2 = ARG(J)*CR2
CALL CAIRY(C2, 0, 2, AI, NAI, IDUM)
CALL CAIRY(C2, 1, 2, DAI, NDAI, IDUM)
S2 = CS*PHI(J)*(AI*ASUM(J)+CR2*DAI*BSUM(J))
C2R = REAL(S1)
C2I = AIMAG(S1)
C2M = EXP(C2R)*REAL(CSS(KFLAG))
S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I))
S2 = S2*S1
IF (KFLAG.NE.1) GO TO 50
CALL CUCHK(S2, NW, BRY(1), TOL)
IF (NW.NE.0) GO TO 60
50 CONTINUE
IF (YY.LE.0.0E0) S2 = CONJG(S2)
CY(KDFLG) = S2
Y(I) = S2*CSR(KFLAG)
CS = -CI*CS
IF (KDFLG.EQ.2) GO TO 75
KDFLG = 2
GO TO 70
60 CONTINUE
IF (RS1.GT.0.0E0) GO TO 300
C-----------------------------------------------------------------------
C FOR X.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
C-----------------------------------------------------------------------
IF (X.LT.0.0E0) GO TO 300
KDFLG = 1
Y(I) = CZERO
CS = -CI*CS
NZ=NZ+1
IF (I.EQ.1) GO TO 70
IF (Y(I-1).EQ.CZERO) GO TO 70
Y(I-1) = CZERO
NZ=NZ+1
70 CONTINUE
I=N
75 CONTINUE
RZ = CMPLX(2.0E0,0.0E0)/ZR
CK = CMPLX(FN,0.0E0)*RZ
IB = I + 1
IF (N.LT.IB) GO TO 170
C-----------------------------------------------------------------------
C TEST LAST MEMBER FOR UNDERFLOW AND OVERFLOW, SET SEQUENCE TO ZERO
C ON UNDERFLOW
C-----------------------------------------------------------------------
FN = FNU+(N-1)
IPARD = 1
IF (MR.NE.0) IPARD = 0
CALL CUNHJ(ZN,FN,IPARD,TOL,PHID,ARGD,ZETA1D,ZETA2D,ASUMD,BSUMD)
IF (KODE.EQ.1) GO TO 80
CFN=CMPLX(FN,0.0E0)
S1=ZETA1D-CFN*(CFN/(ZB+ZETA2D))
GO TO 90
80 CONTINUE
S1=ZETA1D-ZETA2D
90 CONTINUE
RS1=REAL(S1)
IF (ABS(RS1).GT.ELIM) GO TO 95
IF (ABS(RS1).LT.ALIM) GO TO 100
C-----------------------------------------------------------------------
C REFINE ESTIMATE AND TEST
C-----------------------------------------------------------------------
APHI=ABS(PHID)
AARG = ABS(ARGD)
RS1=RS1+ALOG(APHI)-0.25E0*ALOG(AARG)-AIC
IF (ABS(RS1).LT.ELIM) GO TO 100
95 CONTINUE
IF (RS1.GT.0.0E0) GO TO 300
C-----------------------------------------------------------------------
C FOR X.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
C-----------------------------------------------------------------------
IF (X.LT.0.0E0) GO TO 300
NZ=N
DO 96 I=1,N
Y(I) = CZERO
96 CONTINUE
RETURN
100 CONTINUE
C-----------------------------------------------------------------------
C SCALED FORWARD RECURRENCE FOR REMAINDER OF THE SEQUENCE
C-----------------------------------------------------------------------
S1 = CY(1)
S2 = CY(2)
C1 = CSR(KFLAG)
ASCLE = BRY(KFLAG)
DO 120 I=IB,N
C2 = S2
S2 = CK*S2 + S1
S1 = C2
CK = CK + RZ
C2 = S2*C1
Y(I) = C2
IF (KFLAG.GE.3) GO TO 120
C2R = REAL(C2)
C2I = AIMAG(C2)
C2R = ABS(C2R)
C2I = ABS(C2I)
C2M = MAX(C2R,C2I)
IF (C2M.LE.ASCLE) GO TO 120
KFLAG = KFLAG + 1
ASCLE = BRY(KFLAG)
S1 = S1*C1
S2 = C2
S1 = S1*CSS(KFLAG)
S2 = S2*CSS(KFLAG)
C1 = CSR(KFLAG)
120 CONTINUE
170 CONTINUE
IF (MR.EQ.0) RETURN
C-----------------------------------------------------------------------
C ANALYTIC CONTINUATION FOR RE(Z).LT.0.0E0
C-----------------------------------------------------------------------
NZ = 0
FMR = MR
SGN = -SIGN(PI,FMR)
C-----------------------------------------------------------------------
C CSPN AND CSGN ARE COEFF OF K AND I FUNCTIONS RESP.
C-----------------------------------------------------------------------
CSGN = CMPLX(0.0E0,SGN)
IF (YY.LE.0.0E0) CSGN = CONJG(CSGN)
IFN = INU + N - 1
ANG = FNF*SGN
CPN = COS(ANG)
SPN = SIN(ANG)
CSPN = CMPLX(CPN,SPN)
IF (MOD(IFN,2).EQ.1) CSPN = -CSPN
C-----------------------------------------------------------------------
C CS=COEFF OF THE J FUNCTION TO GET THE I FUNCTION. I(FNU,Z) IS
C COMPUTED FROM EXP(I*FNU*HPI)*J(FNU,-I*Z) WHERE Z IS IN THE FIRST
C QUADRANT. FOURTH QUADRANT VALUES (YY.LE.0.0E0) ARE COMPUTED BY
C CONJUGATION SINCE THE I FUNCTION IS REAL ON THE POSITIVE REAL AXIS
C-----------------------------------------------------------------------
CS = CMPLX(CAR,-SAR)*CSGN
IN = MOD(IFN,4) + 1
C2 = CIP(IN)
CS = CS*CONJG(C2)
ASC = BRY(1)
KK = N
KDFLG = 1
IB = IB-1
IC = IB-1
IUF = 0
DO 270 K=1,N
C-----------------------------------------------------------------------
C LOGIC TO SORT OUT CASES WHOSE PARAMETERS WERE SET FOR THE K
C FUNCTION ABOVE
C-----------------------------------------------------------------------
FN = FNU+(KK-1)
IF (N.GT.2) GO TO 180
175 CONTINUE
PHID = PHI(J)
ARGD = ARG(J)
ZETA1D = ZETA1(J)
ZETA2D = ZETA2(J)
ASUMD = ASUM(J)
BSUMD = BSUM(J)
J = 3 - J
GO TO 190
180 CONTINUE
IF ((KK.EQ.N).AND.(IB.LT.N)) GO TO 190
IF ((KK.EQ.IB).OR.(KK.EQ.IC)) GO TO 175
CALL CUNHJ(ZN, FN, 0, TOL, PHID, ARGD, ZETA1D, ZETA2D,
* ASUMD, BSUMD)
190 CONTINUE
IF (KODE.EQ.1) GO TO 200
CFN = CMPLX(FN,0.0E0)
S1 = -ZETA1D + CFN*(CFN/(ZB+ZETA2D))
GO TO 210
200 CONTINUE
S1 = -ZETA1D + ZETA2D
210 CONTINUE
C-----------------------------------------------------------------------
C TEST FOR UNDERFLOW AND OVERFLOW
C-----------------------------------------------------------------------
RS1 = REAL(S1)
IF (ABS(RS1).GT.ELIM) GO TO 260
IF (KDFLG.EQ.1) IFLAG = 2
IF (ABS(RS1).LT.ALIM) GO TO 220
C-----------------------------------------------------------------------
C REFINE TEST AND SCALE
C-----------------------------------------------------------------------
APHI = ABS(PHID)
AARG = ABS(ARGD)
RS1 = RS1 + ALOG(APHI) - 0.25E0*ALOG(AARG) - AIC
IF (ABS(RS1).GT.ELIM) GO TO 260
IF (KDFLG.EQ.1) IFLAG = 1
IF (RS1.LT.0.0E0) GO TO 220
IF (KDFLG.EQ.1) IFLAG = 3
220 CONTINUE
CALL CAIRY(ARGD, 0, 2, AI, NAI, IDUM)
CALL CAIRY(ARGD, 1, 2, DAI, NDAI, IDUM)
S2 = CS*PHID*(AI*ASUMD+DAI*BSUMD)
C2R = REAL(S1)
C2I = AIMAG(S1)
C2M = EXP(C2R)*REAL(CSS(IFLAG))
S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I))
S2 = S2*S1
IF (IFLAG.NE.1) GO TO 230
CALL CUCHK(S2, NW, BRY(1), TOL)
IF (NW.NE.0) S2 = CMPLX(0.0E0,0.0E0)
230 CONTINUE
IF (YY.LE.0.0E0) S2 = CONJG(S2)
CY(KDFLG) = S2
C2 = S2
S2 = S2*CSR(IFLAG)
C-----------------------------------------------------------------------
C ADD I AND K FUNCTIONS, K SEQUENCE IN Y(I), I=1,N
C-----------------------------------------------------------------------
S1 = Y(KK)
IF (KODE.EQ.1) GO TO 250
CALL CS1S2(ZR, S1, S2, NW, ASC, ALIM, IUF)
NZ = NZ + NW
250 CONTINUE
Y(KK) = S1*CSPN + S2
KK = KK - 1
CSPN = -CSPN
CS = -CS*CI
IF (C2.NE.CZERO) GO TO 255
KDFLG = 1
GO TO 270
255 CONTINUE
IF (KDFLG.EQ.2) GO TO 275
KDFLG = 2
GO TO 270
260 CONTINUE
IF (RS1.GT.0.0E0) GO TO 300
S2 = CZERO
GO TO 230
270 CONTINUE
K = N
275 CONTINUE
IL = N-K
IF (IL.EQ.0) RETURN
C-----------------------------------------------------------------------
C RECUR BACKWARD FOR REMAINDER OF I SEQUENCE AND ADD IN THE
C K FUNCTIONS, SCALING THE I SEQUENCE DURING RECURRENCE TO KEEP
C INTERMEDIATE ARITHMETIC ON SCALE NEAR EXPONENT EXTREMES.
C-----------------------------------------------------------------------
S1 = CY(1)
S2 = CY(2)
CS = CSR(IFLAG)
ASCLE = BRY(IFLAG)
FN = INU+IL
DO 290 I=1,IL
C2 = S2
S2 = S1 + CMPLX(FN+FNF,0.0E0)*RZ*S2
S1 = C2
FN = FN - 1.0E0
C2 = S2*CS
CK = C2
C1 = Y(KK)
IF (KODE.EQ.1) GO TO 280
CALL CS1S2(ZR, C1, C2, NW, ASC, ALIM, IUF)
NZ = NZ + NW
280 CONTINUE
Y(KK) = C1*CSPN + C2
KK = KK - 1
CSPN = -CSPN
IF (IFLAG.GE.3) GO TO 290
C2R = REAL(CK)
C2I = AIMAG(CK)
C2R = ABS(C2R)
C2I = ABS(C2I)
C2M = MAX(C2R,C2I)
IF (C2M.LE.ASCLE) GO TO 290
IFLAG = IFLAG + 1
ASCLE = BRY(IFLAG)
S1 = S1*CS
S2 = CK
S1 = S1*CSS(IFLAG)
S2 = S2*CSS(IFLAG)
CS = CSR(IFLAG)
290 CONTINUE
RETURN
300 CONTINUE
NZ = -1
RETURN
END
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