Replace original netlib amos routines with those in scipy.

Note: apparently, one could also use amos from openspecfun
https://github.com/JuliaMath/openspecfun

Former-commit-id: 77d61fe6486803684201480410021fd173172cc0

amos/README.md

@@ -0,0 +1,31 @@
+# AMOS
+
+A Portable Package for Bessel Functions of a Complex Argument
+and Nonnegative Order
+
+This algorithm is a package of subroutines for computing Bessel
+functions and Airy functions.  The routines are updated
+versions of those routines found in TOMS algorithm 644.
+
+## Disclaimer
+
+```
+* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+*                 ISSUED BY SANDIA LABORATORIES,
+*                   A PRIME CONTRACTOR TO THE
+*               UNITED STATES DEPARTMENT OF ENERGY
+* * * * * * * * * * * * * *  NOTICE   * * * * * * * * * * * * * * *
+* THIS REPORT WAS PREPARED AS AN ACCOUNT OF WORK SPONSORED BY THE
+* UNITED STATES GOVERNMENT.  NEITHER THE UNITED STATES NOR THE
+* UNITED STATES DEPARTMENT OF ENERGY, NOR ANY OF THEIR
+* EMPLOYEES, NOR ANY OF THEIR CONTRACTORS, SUBCONTRACTORS, OR THEIR
+* EMPLOYEES, MAKES ANY WARRANTY, EXPRESS OR IMPLIED, OR ASSUMES ANY
+* LEGAL LIABILITY OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS
+* OR USEFULNESS OF ANY INFORMATION, APPARATUS, PRODUCT OR PROCESS
+* DISCLOSED, OR REPRESENTS THAT ITS USE WOULD NOT INFRINGE
+* PRIVATELY OWNED RIGHTS.
+* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+* THIS CODE HAS BEEN APPROVED FOR UNLIMITED RELEASE.
+* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+```

amos/zabs.f

@@ -1,12 +1,12 @@
-      DOUBLE PRECISION FUNCTION ZABS(ZR, ZI)
+      DOUBLE PRECISION FUNCTION AZABS(ZR, ZI)
-C***BEGIN PROLOGUE  ZABS
+C***BEGIN PROLOGUE  AZABS
 C***REFER TO  ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY
 C
-C     ZABS COMPUTES THE ABSOLUTE VALUE OR MAGNITUDE OF A DOUBLE
+C     AZABS COMPUTES THE ABSOLUTE VALUE OR MAGNITUDE OF A DOUBLE
 C     PRECISION COMPLEX VARIABLE CMPLX(ZR,ZI)
 C
 C***ROUTINES CALLED  (NONE)
-C***END PROLOGUE  ZABS
+C***END PROLOGUE  AZABS
       DOUBLE PRECISION ZR, ZI, U, V, Q, S
       U = DABS(ZR)
       V = DABS(ZI)
@@ -19,11 +19,11 @@ C-----------------------------------------------------------------------
       IF (S.EQ.0.0D+0) GO TO 20
       IF (U.GT.V) GO TO 10
       Q = U/V
-      ZABS = V*DSQRT(1.D+0+Q*Q)
+      AZABS = V*DSQRT(1.D+0+Q*Q)
       RETURN
    10 Q = V/U
-      ZABS = U*DSQRT(1.D+0+Q*Q)
+      AZABS = U*DSQRT(1.D+0+Q*Q)
       RETURN
-   20 ZABS = 0.0D+0
+   20 AZABS = 0.0D+0
       RETURN
       END

amos/zacai.f

@@ -14,19 +14,19 @@ C     ZACAI IS THE SAME AS ZACON WITH THE PARTS FOR LARGER ORDERS AND
 C     RECURRENCE REMOVED. A RECURSIVE CALL TO ZACON CAN RESULT IF ZACON
 C     IS CALLED FROM ZAIRY.
 C
-C***ROUTINES CALLED  ZASYI,ZBKNU,ZMLRI,ZSERI,ZS1S2,D1MACH,ZABS
+C***ROUTINES CALLED  ZASYI,ZBKNU,ZMLRI,ZSERI,ZS1S2,D1MACH,AZABS
 C***END PROLOGUE  ZACAI
 C     COMPLEX CSGN,CSPN,C1,C2,Y,Z,ZN,CY
       DOUBLE PRECISION ALIM, ARG, ASCLE, AZ, CSGNR, CSGNI, CSPNR,
      * CSPNI, C1R, C1I, C2R, C2I, CYR, CYI, DFNU, ELIM, FMR, FNU, PI,
-     * RL, SGN, TOL, YY, YR, YI, ZR, ZI, ZNR, ZNI, D1MACH, ZABS
+     * RL, SGN, TOL, YY, YR, YI, ZR, ZI, ZNR, ZNI, D1MACH, AZABS
       INTEGER INU, IUF, KODE, MR, N, NN, NW, NZ
       DIMENSION YR(N), YI(N), CYR(2), CYI(2)
       DATA PI / 3.14159265358979324D0 /
       NZ = 0
       ZNR = -ZR
       ZNI = -ZI
-      AZ = ZABS(ZR,ZI)
+      AZ = AZABS(ZR,ZI)
       NN = N
       DFNU = FNU + DBLE(FLOAT(N-1))
       IF (AZ.LE.2.0D0) GO TO 10

amos/zacon.f

@@ -11,7 +11,7 @@ C
 C     TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT
 C     HALF Z PLANE
 C
-C***ROUTINES CALLED  ZBINU,ZBKNU,ZS1S2,D1MACH,ZABS,ZMLT
+C***ROUTINES CALLED  ZBINU,ZBKNU,ZS1S2,D1MACH,AZABS,ZMLT
 C***END PROLOGUE  ZACON
 C     COMPLEX CK,CONE,CSCL,CSCR,CSGN,CSPN,CY,CZERO,C1,C2,RZ,SC1,SC2,ST,
 C    *S1,S2,Y,Z,ZN
@@ -20,7 +20,7 @@ C    *S1,S2,Y,Z,ZN
      * CSR, CSRR, CSSR, CYI, CYR, C1I, C1M, C1R, C2I, C2R, ELIM, FMR,
      * FN, FNU, FNUL, PI, PTI, PTR, RAZN, RL, RZI, RZR, SC1I, SC1R,
      * SC2I, SC2R, SGN, SPN, STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR,
-     * YY, ZEROR, ZI, ZNI, ZNR, ZR, D1MACH, ZABS
+     * YY, ZEROR, ZI, ZNI, ZNR, ZR, D1MACH, AZABS
       INTEGER I, INU, IUF, KFLAG, KODE, MR, N, NN, NW, NZ
       DIMENSION YR(N), YI(N), CYR(2), CYI(2), CSSR(3), CSRR(3), BRY(3)
       DATA PI / 3.14159265358979324D0 /
@@ -102,7 +102,7 @@ C-----------------------------------------------------------------------
       IF (N.EQ.2) RETURN
       CSPNR = -CSPNR
       CSPNI = -CSPNI
-      AZN = ZABS(ZNR,ZNI)
+      AZN = AZABS(ZNR,ZNI)
       RAZN = 1.0D0/AZN
       STR = ZNR*RAZN
       STI = -ZNI*RAZN
@@ -125,7 +125,7 @@ C-----------------------------------------------------------------------
       BRY(1) = ASCLE
       BRY(2) = 1.0D0/ASCLE
       BRY(3) = D1MACH(2)
-      AS2 = ZABS(S2R,S2I)
+      AS2 = AZABS(S2R,S2I)
       KFLAG = 2
       IF (AS2.GT.BRY(1)) GO TO 50
       KFLAG = 1

amos/zairy.f

@@ -19,7 +19,7 @@ C
 C         WHILE THE AIRY FUNCTIONS AI(Z) AND DAI(Z)/DZ ARE ANALYTIC IN
 C         THE WHOLE Z PLANE, THE CORRESPONDING SCALED FUNCTIONS DEFINED
 C         FOR KODE=2 HAVE A CUT ALONG THE NEGATIVE REAL AXIS.
-C         DEFINTIONS AND NOTATION ARE FOUND IN THE NBS HANDBOOK OF
+C         DEFINITIONS AND NOTATION ARE FOUND IN THE NBS HANDBOOK OF
 C         MATHEMATICAL FUNCTIONS (REF. 1).
 C
 C         INPUT      ZR,ZI ARE DOUBLE PRECISION
@@ -124,14 +124,14 @@ C               A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
 C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
 C                 MATH. SOFTWARE, 1986
 C
-C***ROUTINES CALLED  ZACAI,ZBKNU,ZEXP,ZSQRT,I1MACH,D1MACH
+C***ROUTINES CALLED  ZACAI,ZBKNU,AZEXP,AZSQRT,I1MACH,D1MACH
 C***END PROLOGUE  ZAIRY
 C     COMPLEX AI,CONE,CSQ,CY,S1,S2,TRM1,TRM2,Z,ZTA,Z3
       DOUBLE PRECISION AA, AD, AII, AIR, AK, ALIM, ATRM, AZ, AZ3, BK,
      * CC, CK, COEF, CONEI, CONER, CSQI, CSQR, CYI, CYR, C1, C2, DIG,
      * DK, D1, D2, ELIM, FID, FNU, PTR, RL, R1M5, SFAC, STI, STR,
      * S1I, S1R, S2I, S2R, TOL, TRM1I, TRM1R, TRM2I, TRM2R, TTH, ZEROI,
-     * ZEROR, ZI, ZR, ZTAI, ZTAR, Z3I, Z3R, D1MACH, ZABS, ALAZ, BB
+     * ZEROR, ZI, ZR, ZTAI, ZTAR, Z3I, Z3R, D1MACH, AZABS, ALAZ, BB
       INTEGER ID, IERR, IFLAG, K, KODE, K1, K2, MR, NN, NZ, I1MACH
       DIMENSION CYR(1), CYI(1)
       DATA TTH, C1, C2, COEF /6.66666666666666667D-01,
@@ -144,7 +144,7 @@ C***FIRST EXECUTABLE STATEMENT  ZAIRY
       IF (ID.LT.0 .OR. ID.GT.1) IERR=1
       IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1
       IF (IERR.NE.0) RETURN
-      AZ = ZABS(ZR,ZI)
+      AZ = AZABS(ZR,ZI)
       TOL = DMAX1(D1MACH(4),1.0D-18)
       FID = DBLE(FLOAT(ID))
       IF (AZ.GT.1.0D0) GO TO 70
@@ -201,10 +201,10 @@ C-----------------------------------------------------------------------
       AIR = S1R*C1 - C2*(ZR*S2R-ZI*S2I)
       AII = S1I*C1 - C2*(ZR*S2I+ZI*S2R)
       IF (KODE.EQ.1) RETURN
-      CALL ZSQRT(ZR, ZI, STR, STI)
+      CALL AZSQRT(ZR, ZI, STR, STI)
       ZTAR = TTH*(ZR*STR-ZI*STI)
       ZTAI = TTH*(ZR*STI+ZI*STR)
-      CALL ZEXP(ZTAR, ZTAI, STR, STI)
+      CALL AZEXP(ZTAR, ZTAI, STR, STI)
       PTR = AIR*STR - AII*STI
       AII = AIR*STI + AII*STR
       AIR = PTR
@@ -220,10 +220,10 @@ C-----------------------------------------------------------------------
       AII = AII + CC*(STR*ZI+STI*ZR)
    60 CONTINUE
       IF (KODE.EQ.1) RETURN
-      CALL ZSQRT(ZR, ZI, STR, STI)
+      CALL AZSQRT(ZR, ZI, STR, STI)
       ZTAR = TTH*(ZR*STR-ZI*STI)
       ZTAI = TTH*(ZR*STI+ZI*STR)
-      CALL ZEXP(ZTAR, ZTAI, STR, STI)
+      CALL AZEXP(ZTAR, ZTAI, STR, STI)
       PTR = STR*AIR - STI*AII
       AII = STR*AII + STI*AIR
       AIR = PTR
@@ -265,7 +265,7 @@ C-----------------------------------------------------------------------
       IF (AZ.GT.AA) GO TO 260
       AA=DSQRT(AA)
       IF (AZ.GT.AA) IERR=3
-      CALL ZSQRT(ZR, ZI, CSQR, CSQI)
+      CALL AZSQRT(ZR, ZI, CSQR, CSQI)
       ZTAR = TTH*(ZR*CSQR-ZI*CSQI)
       ZTAI = TTH*(ZR*CSQI+ZI*CSQR)
 C-----------------------------------------------------------------------

amos/zasyi.f

@@ -8,21 +8,21 @@ C     MEANS OF THE ASYMPTOTIC EXPANSION FOR LARGE CABS(Z) IN THE
 C     REGION CABS(Z).GT.MAX(RL,FNU*FNU/2). NZ=0 IS A NORMAL RETURN.
 C     NZ.LT.0 INDICATES AN OVERFLOW ON KODE=1.
 C
-C***ROUTINES CALLED  D1MACH,ZABS,ZDIV,ZEXP,ZMLT,ZSQRT
+C***ROUTINES CALLED  D1MACH,AZABS,ZDIV,AZEXP,ZMLT,AZSQRT
 C***END PROLOGUE  ZASYI
 C     COMPLEX AK1,CK,CONE,CS1,CS2,CZ,CZERO,DK,EZ,P1,RZ,S2,Y,Z
       DOUBLE PRECISION AA, AEZ, AK, AK1I, AK1R, ALIM, ARG, ARM, ATOL,
      * AZ, BB, BK, CKI, CKR, CONEI, CONER, CS1I, CS1R, CS2I, CS2R, CZI,
      * CZR, DFNU, DKI, DKR, DNU2, ELIM, EZI, EZR, FDN, FNU, PI, P1I,
      * P1R, RAZ, RL, RTPI, RTR1, RZI, RZR, S, SGN, SQK, STI, STR, S2I,
-     * S2R, TOL, TZI, TZR, YI, YR, ZEROI, ZEROR, ZI, ZR, D1MACH, ZABS
+     * S2R, TOL, TZI, TZR, YI, YR, ZEROI, ZEROR, ZI, ZR, D1MACH, AZABS
       INTEGER I, IB, IL, INU, J, JL, K, KODE, KODED, M, N, NN, NZ
       DIMENSION YR(N), YI(N)
       DATA PI, RTPI  /3.14159265358979324D0 , 0.159154943091895336D0 /
       DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 /
 C
       NZ = 0
-      AZ = ZABS(ZR,ZI)
+      AZ = AZABS(ZR,ZI)
       ARM = 1.0D+3*D1MACH(1)
       RTR1 = DSQRT(ARM)
       IL = MIN0(2,N)
@@ -35,7 +35,7 @@ C-----------------------------------------------------------------------
       STI = -ZI*RAZ
       AK1R = RTPI*STR*RAZ
       AK1I = RTPI*STI*RAZ
-      CALL ZSQRT(AK1R, AK1I, AK1R, AK1I)
+      CALL AZSQRT(AK1R, AK1I, AK1R, AK1I)
       CZR = ZR
       CZI = ZI
       IF (KODE.NE.2) GO TO 10
@@ -47,7 +47,7 @@ C-----------------------------------------------------------------------
       KODED = 1
       IF ((DABS(CZR).GT.ALIM) .AND. (N.GT.2)) GO TO 20
       KODED = 0
-      CALL ZEXP(CZR, CZI, STR, STI)
+      CALL AZEXP(CZR, CZI, STR, STI)
       CALL ZMLT(AK1R, AK1I, STR, STI, AK1R, AK1I)
    20 CONTINUE
       FDN = 0.0D0
@@ -120,7 +120,7 @@ C-----------------------------------------------------------------------
         IF (ZR+ZR.GE.ELIM) GO TO 60
         TZR = ZR + ZR
         TZI = ZI + ZI
-        CALL ZEXP(-TZR, -TZI, STR, STI)
+        CALL AZEXP(-TZR, -TZI, STR, STI)
         CALL ZMLT(STR, STI, P1R, P1I, STR, STI)
         CALL ZMLT(STR, STI, CS2R, CS2I, STR, STI)
         S2R = S2R + STR
@@ -149,7 +149,7 @@ C-----------------------------------------------------------------------
         K = K - 1
    80 CONTINUE
       IF (KODED.EQ.0) RETURN
-      CALL ZEXP(CZR, CZI, CKR, CKI)
+      CALL AZEXP(CZR, CZI, CKR, CKI)
       DO 90 I=1,NN
         STR = YR(I)*CKR - YI(I)*CKI
         YI(I) = YR(I)*CKI + YI(I)*CKR

amos/zbesh.f

@@ -152,13 +152,13 @@ C               A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
 C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
 C                 MATH. SOFTWARE, 1986
 C
-C***ROUTINES CALLED  ZACON,ZBKNU,ZBUNK,ZUOIK,ZABS,I1MACH,D1MACH
+C***ROUTINES CALLED  ZACON,ZBKNU,ZBUNK,ZUOIK,AZABS,I1MACH,D1MACH
 C***END PROLOGUE  ZBESH
 C
 C     COMPLEX CY,Z,ZN,ZT,CSGN
       DOUBLE PRECISION AA, ALIM, ALN, ARG, AZ, CYI, CYR, DIG, ELIM,
      * FMM, FN, FNU, FNUL, HPI, RHPI, RL, R1M5, SGN, STR, TOL, UFL, ZI,
-     * ZNI, ZNR, ZR, ZTI, D1MACH, ZABS, BB, ASCLE, RTOL, ATOL, STI,
+     * ZNI, ZNR, ZR, ZTI, D1MACH, AZABS, BB, ASCLE, RTOL, ATOL, STI,
      * CSGNR, CSGNI
       INTEGER I, IERR, INU, INUH, IR, K, KODE, K1, K2, M,
      * MM, MR, N, NN, NUF, NW, NZ, I1MACH
@@ -208,7 +208,7 @@ C-----------------------------------------------------------------------
 C-----------------------------------------------------------------------
 C     TEST FOR PROPER RANGE
 C-----------------------------------------------------------------------
-      AZ = ZABS(ZR,ZI)
+      AZ = AZABS(ZR,ZI)
       AA = 0.5D0/TOL
       BB=DBLE(FLOAT(I1MACH(9)))*0.5D0
       AA = DMIN1(AA,BB)

amos/zbesi.f

@@ -0,0 +1,269 @@
+      SUBROUTINE ZBESI(ZR, ZI, FNU, KODE, N, CYR, CYI, NZ, IERR)
+C***BEGIN PROLOGUE  ZBESI
+C***DATE WRITTEN   830501   (YYMMDD)
+C***REVISION DATE  890801   (YYMMDD)
+C***CATEGORY NO.  B5K
+C***KEYWORDS  I-BESSEL FUNCTION,COMPLEX BESSEL FUNCTION,
+C             MODIFIED BESSEL FUNCTION OF THE FIRST KIND
+C***AUTHOR  AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+C***PURPOSE  TO COMPUTE I-BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C***DESCRIPTION
+C
+C                    ***A DOUBLE PRECISION ROUTINE***
+C         ON KODE=1, ZBESI COMPUTES AN N MEMBER SEQUENCE OF COMPLEX
+C         BESSEL FUNCTIONS CY(J)=I(FNU+J-1,Z) FOR REAL, NONNEGATIVE
+C         ORDERS FNU+J-1, J=1,...,N AND COMPLEX Z IN THE CUT PLANE
+C         -PI.LT.ARG(Z).LE.PI. ON KODE=2, ZBESI RETURNS THE SCALED
+C         FUNCTIONS
+C
+C         CY(J)=EXP(-ABS(X))*I(FNU+J-1,Z)   J = 1,...,N , X=REAL(Z)
+C
+C         WITH THE EXPONENTIAL GROWTH REMOVED IN BOTH THE LEFT AND
+C         RIGHT HALF PLANES FOR Z TO INFINITY. DEFINITIONS AND NOTATION
+C         ARE FOUND IN THE NBS HANDBOOK OF MATHEMATICAL FUNCTIONS
+C         (REF. 1).
+C
+C         INPUT      ZR,ZI,FNU ARE DOUBLE PRECISION
+C           ZR,ZI  - Z=CMPLX(ZR,ZI),  -PI.LT.ARG(Z).LE.PI
+C           FNU    - ORDER OF INITIAL I FUNCTION, FNU.GE.0.0D0
+C           KODE   - A PARAMETER TO INDICATE THE SCALING OPTION
+C                    KODE= 1  RETURNS
+C                             CY(J)=I(FNU+J-1,Z), J=1,...,N
+C                        = 2  RETURNS
+C                             CY(J)=I(FNU+J-1,Z)*EXP(-ABS(X)), J=1,...,N
+C           N      - NUMBER OF MEMBERS OF THE SEQUENCE, N.GE.1
+C
+C         OUTPUT     CYR,CYI ARE DOUBLE PRECISION
+C           CYR,CYI- DOUBLE PRECISION VECTORS WHOSE FIRST N COMPONENTS
+C                    CONTAIN REAL AND IMAGINARY PARTS FOR THE SEQUENCE
+C                    CY(J)=I(FNU+J-1,Z)  OR
+C                    CY(J)=I(FNU+J-1,Z)*EXP(-ABS(X))  J=1,...,N
+C                    DEPENDING ON KODE, X=REAL(Z)
+C           NZ     - NUMBER OF COMPONENTS SET TO ZERO DUE TO UNDERFLOW,
+C                    NZ= 0   , NORMAL RETURN
+C                    NZ.GT.0 , LAST NZ COMPONENTS OF CY SET TO ZERO
+C                              TO UNDERFLOW, CY(J)=CMPLX(0.0D0,0.0D0)
+C                              J = N-NZ+1,...,N
+C           IERR   - ERROR FLAG
+C                    IERR=0, NORMAL RETURN - COMPUTATION COMPLETED
+C                    IERR=1, INPUT ERROR   - NO COMPUTATION
+C                    IERR=2, OVERFLOW      - NO COMPUTATION, REAL(Z) TOO
+C                            LARGE ON KODE=1
+C                    IERR=3, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE
+C                            BUT LOSSES OF SIGNIFCANCE BY ARGUMENT
+C                            REDUCTION PRODUCE LESS THAN HALF OF MACHINE
+C                            ACCURACY
+C                    IERR=4, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA-
+C                            TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI-
+C                            CANCE BY ARGUMENT REDUCTION
+C                    IERR=5, ERROR              - NO COMPUTATION,
+C                            ALGORITHM TERMINATION CONDITION NOT MET
+C
+C***LONG DESCRIPTION
+C
+C         THE COMPUTATION IS CARRIED OUT BY THE POWER SERIES FOR
+C         SMALL CABS(Z), THE ASYMPTOTIC EXPANSION FOR LARGE CABS(Z),
+C         THE MILLER ALGORITHM NORMALIZED BY THE WRONSKIAN AND A
+C         NEUMANN SERIES FOR IMTERMEDIATE MAGNITUDES, AND THE
+C         UNIFORM ASYMPTOTIC EXPANSIONS FOR I(FNU,Z) AND J(FNU,Z)
+C         FOR LARGE ORDERS. BACKWARD RECURRENCE IS USED TO GENERATE
+C         SEQUENCES OR REDUCE ORDERS WHEN NECESSARY.
+C
+C         THE CALCULATIONS ABOVE ARE DONE IN THE RIGHT HALF PLANE AND
+C         CONTINUED INTO THE LEFT HALF PLANE BY THE FORMULA
+C
+C         I(FNU,Z*EXP(M*PI)) = EXP(M*PI*FNU)*I(FNU,Z)  REAL(Z).GT.0.0
+C                       M = +I OR -I,  I**2=-1
+C
+C         FOR NEGATIVE ORDERS,THE FORMULA
+C
+C              I(-FNU,Z) = I(FNU,Z) + (2/PI)*SIN(PI*FNU)*K(FNU,Z)
+C
+C         CAN BE USED. HOWEVER,FOR LARGE ORDERS CLOSE TO INTEGERS, THE
+C         THE FUNCTION CHANGES RADICALLY. WHEN FNU IS A LARGE POSITIVE
+C         INTEGER,THE MAGNITUDE OF I(-FNU,Z)=I(FNU,Z) IS A LARGE
+C         NEGATIVE POWER OF TEN. BUT WHEN FNU IS NOT AN INTEGER,
+C         K(FNU,Z) DOMINATES IN MAGNITUDE WITH A LARGE POSITIVE POWER OF
+C         TEN AND THE MOST THAT THE SECOND TERM CAN BE REDUCED IS BY
+C         UNIT ROUNDOFF FROM THE COEFFICIENT. THUS, WIDE CHANGES CAN
+C         OCCUR WITHIN UNIT ROUNDOFF OF A LARGE INTEGER FOR FNU. HERE,
+C         LARGE MEANS FNU.GT.CABS(Z).
+C
+C         IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE-
+C         MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS
+C         LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR.
+C         CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN
+C         LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG
+C         IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS
+C         DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION.
+C         IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS
+C         LOST AND IERR=4. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS
+C         MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE
+C         INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS
+C         RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3
+C         ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION
+C         ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION
+C         ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN
+C         THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT
+C         TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS
+C         IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC.
+C         SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES.
+C
+C         THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX
+C         BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT
+C         ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE-
+C         SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE
+C         ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))),
+C         ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF
+C         CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY
+C         HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN
+C         ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY
+C         SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER
+C         THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K,
+C         0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS
+C         THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER
+C         COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY
+C         BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER
+C         COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE
+C         MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES,
+C         THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P,
+C         OR -PI/2+P.
+C
+C***REFERENCES  HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ
+C                 AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF
+C                 COMMERCE, 1955.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 BY D. E. AMOS, SAND83-0083, MAY, 1983.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983
+C
+C               A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85-
+C                 1018, MAY, 1985
+C
+C               A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
+C                 MATH. SOFTWARE, 1986
+C
+C***ROUTINES CALLED  ZBINU,I1MACH,D1MACH
+C***END PROLOGUE  ZBESI
+C     COMPLEX CONE,CSGN,CW,CY,CZERO,Z,ZN
+      DOUBLE PRECISION AA, ALIM, ARG, CONEI, CONER, CSGNI, CSGNR, CYI,
+     * CYR, DIG, ELIM, FNU, FNUL, PI, RL, R1M5, STR, TOL, ZI, ZNI, ZNR,
+     * ZR, D1MACH, AZ, BB, FN, AZABS, ASCLE, RTOL, ATOL, STI
+      INTEGER I, IERR, INU, K, KODE, K1,K2,N,NZ,NN, I1MACH
+      DIMENSION CYR(N), CYI(N)
+      DATA PI /3.14159265358979324D0/
+      DATA CONER, CONEI /1.0D0,0.0D0/
+C
+C***FIRST EXECUTABLE STATEMENT  ZBESI
+      IERR = 0
+      NZ=0
+      IF (FNU.LT.0.0D0) IERR=1
+      IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1
+      IF (N.LT.1) IERR=1
+      IF (IERR.NE.0) RETURN
+C-----------------------------------------------------------------------
+C     SET PARAMETERS RELATED TO MACHINE CONSTANTS.
+C     TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18.
+C     ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT.
+C     EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL    AND
+C     EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL       ARE INTERVALS NEAR
+C     UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE.
+C     RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z.
+C     DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
+C     FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU.
+C-----------------------------------------------------------------------
+      TOL = DMAX1(D1MACH(4),1.0D-18)
+      K1 = I1MACH(15)
+      K2 = I1MACH(16)
+      R1M5 = D1MACH(5)
+      K = MIN0(IABS(K1),IABS(K2))
+      ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0)
+      K1 = I1MACH(14) - 1
+      AA = R1M5*DBLE(FLOAT(K1))
+      DIG = DMIN1(AA,18.0D0)
+      AA = AA*2.303D0
+      ALIM = ELIM + DMAX1(-AA,-41.45D0)
+      RL = 1.2D0*DIG + 3.0D0
+      FNUL = 10.0D0 + 6.0D0*(DIG-3.0D0)
+C-----------------------------------------------------------------------------
+C     TEST FOR PROPER RANGE
+C-----------------------------------------------------------------------
+      AZ = AZABS(ZR,ZI)
+      FN = FNU+DBLE(FLOAT(N-1))
+      AA = 0.5D0/TOL
+      BB=DBLE(FLOAT(I1MACH(9)))*0.5D0
+      AA = DMIN1(AA,BB)
+      IF (AZ.GT.AA) GO TO 260
+      IF (FN.GT.AA) GO TO 260
+      AA = DSQRT(AA)
+      IF (AZ.GT.AA) IERR=3
+      IF (FN.GT.AA) IERR=3
+      ZNR = ZR
+      ZNI = ZI
+      CSGNR = CONER
+      CSGNI = CONEI
+      IF (ZR.GE.0.0D0) GO TO 40
+      ZNR = -ZR
+      ZNI = -ZI
+C-----------------------------------------------------------------------
+C     CALCULATE CSGN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE
+C     WHEN FNU IS LARGE
+C-----------------------------------------------------------------------
+      INU = INT(SNGL(FNU))
+      ARG = (FNU-DBLE(FLOAT(INU)))*PI
+      IF (ZI.LT.0.0D0) ARG = -ARG
+      CSGNR = DCOS(ARG)
+      CSGNI = DSIN(ARG)
+      IF (MOD(INU,2).EQ.0) GO TO 40
+      CSGNR = -CSGNR
+      CSGNI = -CSGNI
+   40 CONTINUE
+      CALL ZBINU(ZNR, ZNI, FNU, KODE, N, CYR, CYI, NZ, RL, FNUL, TOL,
+     * ELIM, ALIM)
+      IF (NZ.LT.0) GO TO 120
+      IF (ZR.GE.0.0D0) RETURN
+C-----------------------------------------------------------------------
+C     ANALYTIC CONTINUATION TO THE LEFT HALF PLANE
+C-----------------------------------------------------------------------
+      NN = N - NZ
+      IF (NN.EQ.0) RETURN
+      RTOL = 1.0D0/TOL
+      ASCLE = D1MACH(1)*RTOL*1.0D+3
+      DO 50 I=1,NN
+C       STR = CYR(I)*CSGNR - CYI(I)*CSGNI
+C       CYI(I) = CYR(I)*CSGNI + CYI(I)*CSGNR
+C       CYR(I) = STR
+        AA = CYR(I)
+        BB = CYI(I)
+        ATOL = 1.0D0
+        IF (DMAX1(DABS(AA),DABS(BB)).GT.ASCLE) GO TO 55
+          AA = AA*RTOL
+          BB = BB*RTOL
+          ATOL = TOL
+   55   CONTINUE
+        STR = AA*CSGNR - BB*CSGNI
+        STI = AA*CSGNI + BB*CSGNR
+        CYR(I) = STR*ATOL
+        CYI(I) = STI*ATOL
+        CSGNR = -CSGNR
+        CSGNI = -CSGNI
+   50 CONTINUE
+      RETURN
+  120 CONTINUE
+      IF(NZ.EQ.(-2)) GO TO 130
+      NZ = 0
+      IERR=2
+      RETURN
+  130 CONTINUE
+      NZ=0
+      IERR=5
+      RETURN
+  260 CONTINUE
+      NZ=0
+      IERR=4
+      RETURN
+      END

amos/zbesj.f

@@ -147,7 +147,7 @@ C
 C     COMPLEX CI,CSGN,CY,Z,ZN
       DOUBLE PRECISION AA, ALIM, ARG, CII, CSGNI, CSGNR, CYI, CYR, DIG,
      * ELIM, FNU, FNUL, HPI, RL, R1M5, STR, TOL, ZI, ZNI, ZNR, ZR,
-     * D1MACH, BB, FN, AZ, ZABS, ASCLE, RTOL, ATOL, STI
+     * D1MACH, BB, FN, AZ, AZABS, ASCLE, RTOL, ATOL, STI
       INTEGER I, IERR, INU, INUH, IR, K, KODE, K1, K2, N, NL, NZ, I1MACH
       DIMENSION CYR(N), CYI(N)
       DATA HPI /1.57079632679489662D0/
@@ -186,7 +186,7 @@ C-----------------------------------------------------------------------
 C-----------------------------------------------------------------------
 C     TEST FOR PROPER RANGE
 C-----------------------------------------------------------------------
-      AZ = ZABS(ZR,ZI)
+      AZ = AZABS(ZR,ZI)
       FN = FNU+DBLE(FLOAT(N-1))
       AA = 0.5D0/TOL
       BB=DBLE(FLOAT(I1MACH(9)))*0.5D0

amos/zbesk.f

@@ -0,0 +1,281 @@
+      SUBROUTINE ZBESK(ZR, ZI, FNU, KODE, N, CYR, CYI, NZ, IERR)
+C***BEGIN PROLOGUE  ZBESK
+C***DATE WRITTEN   830501   (YYMMDD)
+C***REVISION DATE  890801   (YYMMDD)
+C***CATEGORY NO.  B5K
+C***KEYWORDS  K-BESSEL FUNCTION,COMPLEX BESSEL FUNCTION,
+C             MODIFIED BESSEL FUNCTION OF THE SECOND KIND,
+C             BESSEL FUNCTION OF THE THIRD KIND
+C***AUTHOR  AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+C***PURPOSE  TO COMPUTE K-BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C***DESCRIPTION
+C
+C                      ***A DOUBLE PRECISION ROUTINE***
+C
+C         ON KODE=1, CBESK COMPUTES AN N MEMBER SEQUENCE OF COMPLEX
+C         BESSEL FUNCTIONS CY(J)=K(FNU+J-1,Z) FOR REAL, NONNEGATIVE
+C         ORDERS FNU+J-1, J=1,...,N AND COMPLEX Z.NE.CMPLX(0.0,0.0)
+C         IN THE CUT PLANE -PI.LT.ARG(Z).LE.PI. ON KODE=2, CBESK
+C         RETURNS THE SCALED K FUNCTIONS,
+C
+C         CY(J)=EXP(Z)*K(FNU+J-1,Z) , J=1,...,N,
+C
+C         WHICH REMOVE THE EXPONENTIAL BEHAVIOR IN BOTH THE LEFT AND
+C         RIGHT HALF PLANES FOR Z TO INFINITY. DEFINITIONS AND
+C         NOTATION ARE FOUND IN THE NBS HANDBOOK OF MATHEMATICAL
+C         FUNCTIONS (REF. 1).
+C
+C         INPUT      ZR,ZI,FNU ARE DOUBLE PRECISION
+C           ZR,ZI  - Z=CMPLX(ZR,ZI), Z.NE.CMPLX(0.0D0,0.0D0),
+C                    -PI.LT.ARG(Z).LE.PI
+C           FNU    - ORDER OF INITIAL K FUNCTION, FNU.GE.0.0D0
+C           N      - NUMBER OF MEMBERS OF THE SEQUENCE, N.GE.1
+C           KODE   - A PARAMETER TO INDICATE THE SCALING OPTION
+C                    KODE= 1  RETURNS
+C                             CY(I)=K(FNU+I-1,Z), I=1,...,N
+C                        = 2  RETURNS
+C                             CY(I)=K(FNU+I-1,Z)*EXP(Z), I=1,...,N
+C
+C         OUTPUT     CYR,CYI ARE DOUBLE PRECISION
+C           CYR,CYI- DOUBLE PRECISION VECTORS WHOSE FIRST N COMPONENTS
+C                    CONTAIN REAL AND IMAGINARY PARTS FOR THE SEQUENCE
+C                    CY(I)=K(FNU+I-1,Z), I=1,...,N OR
+C                    CY(I)=K(FNU+I-1,Z)*EXP(Z), I=1,...,N
+C                    DEPENDING ON KODE
+C           NZ     - NUMBER OF COMPONENTS SET TO ZERO DUE TO UNDERFLOW.
+C                    NZ= 0   , NORMAL RETURN
+C                    NZ.GT.0 , FIRST NZ COMPONENTS OF CY SET TO ZERO DUE
+C                              TO UNDERFLOW, CY(I)=CMPLX(0.0D0,0.0D0),
+C                              I=1,...,N WHEN X.GE.0.0. WHEN X.LT.0.0
+C                              NZ STATES ONLY THE NUMBER OF UNDERFLOWS
+C                              IN THE SEQUENCE.
+C
+C           IERR   - ERROR FLAG
+C                    IERR=0, NORMAL RETURN - COMPUTATION COMPLETED
+C                    IERR=1, INPUT ERROR   - NO COMPUTATION
+C                    IERR=2, OVERFLOW      - NO COMPUTATION, FNU IS
+C                            TOO LARGE OR CABS(Z) IS TOO SMALL OR BOTH
+C                    IERR=3, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE
+C                            BUT LOSSES OF SIGNIFCANCE BY ARGUMENT
+C                            REDUCTION PRODUCE LESS THAN HALF OF MACHINE
+C                            ACCURACY
+C                    IERR=4, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA-
+C                            TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI-
+C                            CANCE BY ARGUMENT REDUCTION
+C                    IERR=5, ERROR              - NO COMPUTATION,
+C                            ALGORITHM TERMINATION CONDITION NOT MET
+C
+C***LONG DESCRIPTION
+C
+C         EQUATIONS OF THE REFERENCE ARE IMPLEMENTED FOR SMALL ORDERS
+C         DNU AND DNU+1.0 IN THE RIGHT HALF PLANE X.GE.0.0. FORWARD
+C         RECURRENCE GENERATES HIGHER ORDERS. K IS CONTINUED TO THE LEFT
+C         HALF PLANE BY THE RELATION
+C
+C         K(FNU,Z*EXP(MP)) = EXP(-MP*FNU)*K(FNU,Z)-MP*I(FNU,Z)
+C         MP=MR*PI*I, MR=+1 OR -1, RE(Z).GT.0, I**2=-1
+C
+C         WHERE I(FNU,Z) IS THE I BESSEL FUNCTION.
+C
+C         FOR LARGE ORDERS, FNU.GT.FNUL, THE K FUNCTION IS COMPUTED
+C         BY MEANS OF ITS UNIFORM ASYMPTOTIC EXPANSIONS.
+C
+C         FOR NEGATIVE ORDERS, THE FORMULA
+C
+C                       K(-FNU,Z) = K(FNU,Z)
+C
+C         CAN BE USED.
+C
+C         CBESK ASSUMES THAT A SIGNIFICANT DIGIT SINH(X) FUNCTION IS
+C         AVAILABLE.
+C
+C         IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE-
+C         MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS
+C         LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR.
+C         CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN
+C         LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG
+C         IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS
+C         DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION.
+C         IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS
+C         LOST AND IERR=4. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS
+C         MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE
+C         INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS
+C         RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3
+C         ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION
+C         ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION
+C         ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN
+C         THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT
+C         TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS
+C         IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC.
+C         SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES.
+C
+C         THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX
+C         BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT
+C         ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE-
+C         SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE
+C         ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))),
+C         ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF
+C         CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY
+C         HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN
+C         ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY
+C         SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER
+C         THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K,
+C         0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS
+C         THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER
+C         COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY
+C         BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER
+C         COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE
+C         MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES,
+C         THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P,
+C         OR -PI/2+P.
+C
+C***REFERENCES  HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ
+C                 AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF
+C                 COMMERCE, 1955.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 BY D. E. AMOS, SAND83-0083, MAY, 1983.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983.
+C
+C               A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85-
+C                 1018, MAY, 1985
+C
+C               A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
+C                 MATH. SOFTWARE, 1986
+C
+C***ROUTINES CALLED  ZACON,ZBKNU,ZBUNK,ZUOIK,AZABS,I1MACH,D1MACH
+C***END PROLOGUE  ZBESK
+C
+C     COMPLEX CY,Z
+      DOUBLE PRECISION AA, ALIM, ALN, ARG, AZ, CYI, CYR, DIG, ELIM, FN,
+     * FNU, FNUL, RL, R1M5, TOL, UFL, ZI, ZR, D1MACH, AZABS, BB
+      INTEGER IERR, K, KODE, K1, K2, MR, N, NN, NUF, NW, NZ, I1MACH
+      DIMENSION CYR(N), CYI(N)
+C***FIRST EXECUTABLE STATEMENT  ZBESK
+      IERR = 0
+      NZ=0
+      IF (ZI.EQ.0.0E0 .AND. ZR.EQ.0.0E0) IERR=1
+      IF (FNU.LT.0.0D0) IERR=1
+      IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1
+      IF (N.LT.1) IERR=1
+      IF (IERR.NE.0) RETURN
+      NN = N
+C-----------------------------------------------------------------------
+C     SET PARAMETERS RELATED TO MACHINE CONSTANTS.
+C     TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18.
+C     ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT.
+C     EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL    AND
+C     EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL       ARE INTERVALS NEAR
+C     UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE.
+C     RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z.
+C     DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
+C     FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU
+C-----------------------------------------------------------------------
+      TOL = DMAX1(D1MACH(4),1.0D-18)
+      K1 = I1MACH(15)
+      K2 = I1MACH(16)
+      R1M5 = D1MACH(5)
+      K = MIN0(IABS(K1),IABS(K2))
+      ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0)
+      K1 = I1MACH(14) - 1
+      AA = R1M5*DBLE(FLOAT(K1))
+      DIG = DMIN1(AA,18.0D0)
+      AA = AA*2.303D0
+      ALIM = ELIM + DMAX1(-AA,-41.45D0)
+      FNUL = 10.0D0 + 6.0D0*(DIG-3.0D0)
+      RL = 1.2D0*DIG + 3.0D0
+C-----------------------------------------------------------------------------
+C     TEST FOR PROPER RANGE
+C-----------------------------------------------------------------------
+      AZ = AZABS(ZR,ZI)
+      FN = FNU + DBLE(FLOAT(NN-1))
+      AA = 0.5D0/TOL
+      BB=DBLE(FLOAT(I1MACH(9)))*0.5D0
+      AA = DMIN1(AA,BB)
+      IF (AZ.GT.AA) GO TO 260
+      IF (FN.GT.AA) GO TO 260
+      AA = DSQRT(AA)
+      IF (AZ.GT.AA) IERR=3
+      IF (FN.GT.AA) IERR=3
+C-----------------------------------------------------------------------
+C     OVERFLOW TEST ON THE LAST MEMBER OF THE SEQUENCE
+C-----------------------------------------------------------------------
+C     UFL = DEXP(-ELIM)
+      UFL = D1MACH(1)*1.0D+3
+      IF (AZ.LT.UFL) GO TO 180
+      IF (FNU.GT.FNUL) GO TO 80
+      IF (FN.LE.1.0D0) GO TO 60
+      IF (FN.GT.2.0D0) GO TO 50
+      IF (AZ.GT.TOL) GO TO 60
+      ARG = 0.5D0*AZ
+      ALN = -FN*DLOG(ARG)
+      IF (ALN.GT.ELIM) GO TO 180
+      GO TO 60
+   50 CONTINUE
+      CALL ZUOIK(ZR, ZI, FNU, KODE, 2, NN, CYR, CYI, NUF, TOL, ELIM,
+     * ALIM)
+      IF (NUF.LT.0) GO TO 180
+      NZ = NZ + NUF
+      NN = NN - NUF
+C-----------------------------------------------------------------------
+C     HERE NN=N OR NN=0 SINCE NUF=0,NN, OR -1 ON RETURN FROM CUOIK
+C     IF NUF=NN, THEN CY(I)=CZERO FOR ALL I
+C-----------------------------------------------------------------------
+      IF (NN.EQ.0) GO TO 100
+   60 CONTINUE
+      IF (ZR.LT.0.0D0) GO TO 70
+C-----------------------------------------------------------------------
+C     RIGHT HALF PLANE COMPUTATION, REAL(Z).GE.0.
+C-----------------------------------------------------------------------
+      CALL ZBKNU(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, TOL, ELIM, ALIM)
+      IF (NW.LT.0) GO TO 200
+      NZ=NW
+      RETURN
+C-----------------------------------------------------------------------
+C     LEFT HALF PLANE COMPUTATION
+C     PI/2.LT.ARG(Z).LE.PI AND -PI.LT.ARG(Z).LT.-PI/2.
+C-----------------------------------------------------------------------
+   70 CONTINUE
+      IF (NZ.NE.0) GO TO 180
+      MR = 1
+      IF (ZI.LT.0.0D0) MR = -1
+      CALL ZACON(ZR, ZI, FNU, KODE, MR, NN, CYR, CYI, NW, RL, FNUL,
+     * TOL, ELIM, ALIM)
+      IF (NW.LT.0) GO TO 200
+      NZ=NW
+      RETURN
+C-----------------------------------------------------------------------
+C     UNIFORM ASYMPTOTIC EXPANSIONS FOR FNU.GT.FNUL
+C-----------------------------------------------------------------------
+   80 CONTINUE
+      MR = 0
+      IF (ZR.GE.0.0D0) GO TO 90
+      MR = 1
+      IF (ZI.LT.0.0D0) MR = -1
+   90 CONTINUE
+      CALL ZBUNK(ZR, ZI, FNU, KODE, MR, NN, CYR, CYI, NW, TOL, ELIM,
+     * ALIM)
+      IF (NW.LT.0) GO TO 200
+      NZ = NZ + NW
+      RETURN
+  100 CONTINUE
+      IF (ZR.LT.0.0D0) GO TO 180
+      RETURN
+  180 CONTINUE
+      NZ = 0
+      IERR=2
+      RETURN
+  200 CONTINUE
+      IF(NW.EQ.(-1)) GO TO 180
+      NZ=0
+      IERR=5
+      RETURN
+  260 CONTINUE
+      NZ=0
+      IERR=4
+      RETURN
+      END

amos/zbinu.f

@@ -5,16 +5,16 @@ C***REFER TO  ZBESH,ZBESI,ZBESJ,ZBESK,ZAIRY,ZBIRY
 C
 C     ZBINU COMPUTES THE I FUNCTION IN THE RIGHT HALF Z PLANE
 C
-C***ROUTINES CALLED  ZABS,ZASYI,ZBUNI,ZMLRI,ZSERI,ZUOIK,ZWRSK
+C***ROUTINES CALLED  AZABS,ZASYI,ZBUNI,ZMLRI,ZSERI,ZUOIK,ZWRSK
 C***END PROLOGUE  ZBINU
       DOUBLE PRECISION ALIM, AZ, CWI, CWR, CYI, CYR, DFNU, ELIM, FNU,
-     * FNUL, RL, TOL, ZEROI, ZEROR, ZI, ZR, ZABS
+     * FNUL, RL, TOL, ZEROI, ZEROR, ZI, ZR, AZABS
       INTEGER I, INW, KODE, N, NLAST, NN, NUI, NW, NZ
       DIMENSION CYR(N), CYI(N), CWR(2), CWI(2)
       DATA ZEROR,ZEROI / 0.0D0, 0.0D0 /
 C
       NZ = 0
-      AZ = ZABS(ZR,ZI)
+      AZ = AZABS(ZR,ZI)
       NN = N
       DFNU = FNU + DBLE(FLOAT(N-1))
       IF (AZ.LE.2.0D0) GO TO 10

amos/zbiry.f

@@ -0,0 +1,364 @@
+      SUBROUTINE ZBIRY(ZR, ZI, ID, KODE, BIR, BII, IERR)
+C***BEGIN PROLOGUE  ZBIRY
+C***DATE WRITTEN   830501   (YYMMDD)
+C***REVISION DATE  890801   (YYMMDD)
+C***CATEGORY NO.  B5K
+C***KEYWORDS  AIRY FUNCTION,BESSEL FUNCTIONS OF ORDER ONE THIRD
+C***AUTHOR  AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+C***PURPOSE  TO COMPUTE AIRY FUNCTIONS BI(Z) AND DBI(Z) FOR COMPLEX Z
+C***DESCRIPTION
+C
+C                      ***A DOUBLE PRECISION ROUTINE***
+C         ON KODE=1, CBIRY COMPUTES THE COMPLEX AIRY FUNCTION BI(Z) OR
+C         ITS DERIVATIVE DBI(Z)/DZ ON ID=0 OR ID=1 RESPECTIVELY. ON
+C         KODE=2, A SCALING OPTION CEXP(-AXZTA)*BI(Z) OR CEXP(-AXZTA)*
+C         DBI(Z)/DZ IS PROVIDED TO REMOVE THE EXPONENTIAL BEHAVIOR IN
+C         BOTH THE LEFT AND RIGHT HALF PLANES WHERE
+C         ZTA=(2/3)*Z*CSQRT(Z)=CMPLX(XZTA,YZTA) AND AXZTA=ABS(XZTA).
+C         DEFINITIONS AND NOTATION ARE FOUND IN THE NBS HANDBOOK OF
+C         MATHEMATICAL FUNCTIONS (REF. 1).
+C
+C         INPUT      ZR,ZI ARE DOUBLE PRECISION
+C           ZR,ZI  - Z=CMPLX(ZR,ZI)
+C           ID     - ORDER OF DERIVATIVE, ID=0 OR ID=1
+C           KODE   - A PARAMETER TO INDICATE THE SCALING OPTION
+C                    KODE= 1  RETURNS
+C                             BI=BI(Z)                 ON ID=0 OR
+C                             BI=DBI(Z)/DZ             ON ID=1
+C                        = 2  RETURNS
+C                             BI=CEXP(-AXZTA)*BI(Z)     ON ID=0 OR
+C                             BI=CEXP(-AXZTA)*DBI(Z)/DZ ON ID=1 WHERE
+C                             ZTA=(2/3)*Z*CSQRT(Z)=CMPLX(XZTA,YZTA)
+C                             AND AXZTA=ABS(XZTA)
+C
+C         OUTPUT     BIR,BII ARE DOUBLE PRECISION
+C           BIR,BII- COMPLEX ANSWER DEPENDING ON THE CHOICES FOR ID AND
+C                    KODE
+C           IERR   - ERROR FLAG
+C                    IERR=0, NORMAL RETURN - COMPUTATION COMPLETED
+C                    IERR=1, INPUT ERROR   - NO COMPUTATION
+C                    IERR=2, OVERFLOW      - NO COMPUTATION, REAL(Z)
+C                            TOO LARGE ON KODE=1
+C                    IERR=3, CABS(Z) LARGE      - COMPUTATION COMPLETED
+C                            LOSSES OF SIGNIFCANCE BY ARGUMENT REDUCTION
+C                            PRODUCE LESS THAN HALF OF MACHINE ACCURACY
+C                    IERR=4, CABS(Z) TOO LARGE  - NO COMPUTATION
+C                            COMPLETE LOSS OF ACCURACY BY ARGUMENT
+C                            REDUCTION
+C                    IERR=5, ERROR              - NO COMPUTATION,
+C                            ALGORITHM TERMINATION CONDITION NOT MET
+C
+C***LONG DESCRIPTION
+C
+C         BI AND DBI ARE COMPUTED FOR CABS(Z).GT.1.0 FROM THE I BESSEL
+C         FUNCTIONS BY
+C
+C                BI(Z)=C*SQRT(Z)*( I(-1/3,ZTA) + I(1/3,ZTA) )
+C               DBI(Z)=C *  Z  * ( I(-2/3,ZTA) + I(2/3,ZTA) )
+C                               C=1.0/SQRT(3.0)
+C                             ZTA=(2/3)*Z**(3/2)
+C
+C         WITH THE POWER SERIES FOR CABS(Z).LE.1.0.
+C
+C         IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE-
+C         MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z IS LARGE, LOSSES
+C         OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. CONSEQUENTLY, IF
+C         THE MAGNITUDE OF ZETA=(2/3)*Z**1.5 EXCEEDS U1=SQRT(0.5/UR),
+C         THEN LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR
+C         FLAG IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS
+C         DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION.
+C         ALSO, IF THE MAGNITUDE OF ZETA IS LARGER THAN U2=0.5/UR, THEN
+C         ALL SIGNIFICANCE IS LOST AND IERR=4. IN ORDER TO USE THE INT
+C         FUNCTION, ZETA MUST BE FURTHER RESTRICTED NOT TO EXCEED THE
+C         LARGEST INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF ZETA
+C         MUST BE RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2,
+C         AND U3 ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE
+C         PRECISION ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE
+C         PRECISION ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMIT-
+C         ING IN THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT THE MAG-
+C         NITUDE OF Z CANNOT EXCEED 3.1E+4 IN SINGLE AND 2.1E+6 IN
+C         DOUBLE PRECISION ARITHMETIC. THIS ALSO MEANS THAT ONE CAN
+C         EXPECT TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES,
+C         NO DIGITS IN SINGLE PRECISION AND ONLY 7 DIGITS IN DOUBLE
+C         PRECISION ARITHMETIC. SIMILAR CONSIDERATIONS HOLD FOR OTHER
+C         MACHINES.
+C
+C         THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX
+C         BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT
+C         ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE-
+C         SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE
+C         ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))),
+C         ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF
+C         CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY
+C         HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN
+C         ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY
+C         SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER
+C         THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K,
+C         0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS
+C         THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER
+C         COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY
+C         BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER
+C         COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE
+C         MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES,
+C         THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P,
+C         OR -PI/2+P.
+C
+C***REFERENCES  HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ
+C                 AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF
+C                 COMMERCE, 1955.
+C
+C               COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+C                 AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983
+C
+C               A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85-
+C                 1018, MAY, 1985
+C
+C               A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+C                 ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
+C                 MATH. SOFTWARE, 1986
+C
+C***ROUTINES CALLED  ZBINU,AZABS,ZDIV,AZSQRT,D1MACH,I1MACH
+C***END PROLOGUE  ZBIRY
+C     COMPLEX BI,CONE,CSQ,CY,S1,S2,TRM1,TRM2,Z,ZTA,Z3
+      DOUBLE PRECISION AA, AD, AK, ALIM, ATRM, AZ, AZ3, BB, BII, BIR,
+     * BK, CC, CK, COEF, CONEI, CONER, CSQI, CSQR, CYI, CYR, C1, C2,
+     * DIG, DK, D1, D2, EAA, ELIM, FID, FMR, FNU, FNUL, PI, RL, R1M5,
+     * SFAC, STI, STR, S1I, S1R, S2I, S2R, TOL, TRM1I, TRM1R, TRM2I,
+     * TRM2R, TTH, ZI, ZR, ZTAI, ZTAR, Z3I, Z3R, D1MACH, AZABS
+      INTEGER ID, IERR, K, KODE, K1, K2, NZ, I1MACH
+      DIMENSION CYR(2), CYI(2)
+      DATA TTH, C1, C2, COEF, PI /6.66666666666666667D-01,
+     * 6.14926627446000736D-01,4.48288357353826359D-01,
+     * 5.77350269189625765D-01,3.14159265358979324D+00/
+      DATA CONER, CONEI /1.0D0,0.0D0/
+C***FIRST EXECUTABLE STATEMENT  ZBIRY
+      IERR = 0
+      NZ=0
+      IF (ID.LT.0 .OR. ID.GT.1) IERR=1
+      IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1
+      IF (IERR.NE.0) RETURN
+      AZ = AZABS(ZR,ZI)
+      TOL = DMAX1(D1MACH(4),1.0D-18)
+      FID = DBLE(FLOAT(ID))
+      IF (AZ.GT.1.0E0) GO TO 70
+C-----------------------------------------------------------------------
+C     POWER SERIES FOR CABS(Z).LE.1.
+C-----------------------------------------------------------------------
+      S1R = CONER
+      S1I = CONEI
+      S2R = CONER
+      S2I = CONEI
+      IF (AZ.LT.TOL) GO TO 130
+      AA = AZ*AZ
+      IF (AA.LT.TOL/AZ) GO TO 40
+      TRM1R = CONER
+      TRM1I = CONEI
+      TRM2R = CONER
+      TRM2I = CONEI
+      ATRM = 1.0D0
+      STR = ZR*ZR - ZI*ZI
+      STI = ZR*ZI + ZI*ZR
+      Z3R = STR*ZR - STI*ZI
+      Z3I = STR*ZI + STI*ZR
+      AZ3 = AZ*AA
+      AK = 2.0D0 + FID
+      BK = 3.0D0 - FID - FID
+      CK = 4.0D0 - FID
+      DK = 3.0D0 + FID + FID
+      D1 = AK*DK
+      D2 = BK*CK
+      AD = DMIN1(D1,D2)
+      AK = 24.0D0 + 9.0D0*FID
+      BK = 30.0D0 - 9.0D0*FID
+      DO 30 K=1,25
+        STR = (TRM1R*Z3R-TRM1I*Z3I)/D1
+        TRM1I = (TRM1R*Z3I+TRM1I*Z3R)/D1
+        TRM1R = STR
+        S1R = S1R + TRM1R
+        S1I = S1I + TRM1I
+        STR = (TRM2R*Z3R-TRM2I*Z3I)/D2
+        TRM2I = (TRM2R*Z3I+TRM2I*Z3R)/D2
+        TRM2R = STR
+        S2R = S2R + TRM2R
+        S2I = S2I + TRM2I
+        ATRM = ATRM*AZ3/AD
+        D1 = D1 + AK
+        D2 = D2 + BK
+        AD = DMIN1(D1,D2)
+        IF (ATRM.LT.TOL*AD) GO TO 40
+        AK = AK + 18.0D0
+        BK = BK + 18.0D0
+   30 CONTINUE
+   40 CONTINUE
+      IF (ID.EQ.1) GO TO 50
+      BIR = C1*S1R + C2*(ZR*S2R-ZI*S2I)
+      BII = C1*S1I + C2*(ZR*S2I+ZI*S2R)
+      IF (KODE.EQ.1) RETURN
+      CALL AZSQRT(ZR, ZI, STR, STI)
+      ZTAR = TTH*(ZR*STR-ZI*STI)
+      ZTAI = TTH*(ZR*STI+ZI*STR)
+      AA = ZTAR
+      AA = -DABS(AA)
+      EAA = DEXP(AA)
+      BIR = BIR*EAA
+      BII = BII*EAA
+      RETURN
+   50 CONTINUE
+      BIR = S2R*C2
+      BII = S2I*C2
+      IF (AZ.LE.TOL) GO TO 60
+      CC = C1/(1.0D0+FID)
+      STR = S1R*ZR - S1I*ZI
+      STI = S1R*ZI + S1I*ZR
+      BIR = BIR + CC*(STR*ZR-STI*ZI)
+      BII = BII + CC*(STR*ZI+STI*ZR)
+   60 CONTINUE
+      IF (KODE.EQ.1) RETURN
+      CALL AZSQRT(ZR, ZI, STR, STI)
+      ZTAR = TTH*(ZR*STR-ZI*STI)
+      ZTAI = TTH*(ZR*STI+ZI*STR)
+      AA = ZTAR
+      AA = -DABS(AA)
+      EAA = DEXP(AA)
+      BIR = BIR*EAA
+      BII = BII*EAA
+      RETURN
+C-----------------------------------------------------------------------
+C     CASE FOR CABS(Z).GT.1.0
+C-----------------------------------------------------------------------
+   70 CONTINUE
+      FNU = (1.0D0+FID)/3.0D0
+C-----------------------------------------------------------------------
+C     SET PARAMETERS RELATED TO MACHINE CONSTANTS.
+C     TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18.
+C     ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT.
+C     EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL    AND
+C     EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL       ARE INTERVALS NEAR
+C     UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE.
+C     RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z.
+C     DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
+C     FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU.
+C-----------------------------------------------------------------------
+      K1 = I1MACH(15)
+      K2 = I1MACH(16)
+      R1M5 = D1MACH(5)
+      K = MIN0(IABS(K1),IABS(K2))
+      ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0)
+      K1 = I1MACH(14) - 1
+      AA = R1M5*DBLE(FLOAT(K1))
+      DIG = DMIN1(AA,18.0D0)
+      AA = AA*2.303D0
+      ALIM = ELIM + DMAX1(-AA,-41.45D0)
+      RL = 1.2D0*DIG + 3.0D0
+      FNUL = 10.0D0 + 6.0D0*(DIG-3.0D0)
+C-----------------------------------------------------------------------
+C     TEST FOR RANGE
+C-----------------------------------------------------------------------
+      AA=0.5D0/TOL
+      BB=DBLE(FLOAT(I1MACH(9)))*0.5D0
+      AA=DMIN1(AA,BB)
+      AA=AA**TTH
+      IF (AZ.GT.AA) GO TO 260
+      AA=DSQRT(AA)
+      IF (AZ.GT.AA) IERR=3
+      CALL AZSQRT(ZR, ZI, CSQR, CSQI)
+      ZTAR = TTH*(ZR*CSQR-ZI*CSQI)
+      ZTAI = TTH*(ZR*CSQI+ZI*CSQR)
+C-----------------------------------------------------------------------
+C     RE(ZTA).LE.0 WHEN RE(Z).LT.0, ESPECIALLY WHEN IM(Z) IS SMALL
+C-----------------------------------------------------------------------
+      SFAC = 1.0D0
+      AK = ZTAI
+      IF (ZR.GE.0.0D0) GO TO 80
+      BK = ZTAR
+      CK = -DABS(BK)
+      ZTAR = CK
+      ZTAI = AK
+   80 CONTINUE
+      IF (ZI.NE.0.0D0 .OR. ZR.GT.0.0D0) GO TO 90
+      ZTAR = 0.0D0
+      ZTAI = AK
+   90 CONTINUE
+      AA = ZTAR
+      IF (KODE.EQ.2) GO TO 100
+C-----------------------------------------------------------------------
+C     OVERFLOW TEST
+C-----------------------------------------------------------------------
+      BB = DABS(AA)
+      IF (BB.LT.ALIM) GO TO 100
+      BB = BB + 0.25D0*DLOG(AZ)
+      SFAC = TOL
+      IF (BB.GT.ELIM) GO TO 190
+  100 CONTINUE
+      FMR = 0.0D0
+      IF (AA.GE.0.0D0 .AND. ZR.GT.0.0D0) GO TO 110
+      FMR = PI
+      IF (ZI.LT.0.0D0) FMR = -PI
+      ZTAR = -ZTAR
+      ZTAI = -ZTAI
+  110 CONTINUE
+C-----------------------------------------------------------------------
+C     AA=FACTOR FOR ANALYTIC CONTINUATION OF I(FNU,ZTA)
+C     KODE=2 RETURNS EXP(-ABS(XZTA))*I(FNU,ZTA) FROM CBESI
+C-----------------------------------------------------------------------
+      CALL ZBINU(ZTAR, ZTAI, FNU, KODE, 1, CYR, CYI, NZ, RL, FNUL, TOL,
+     * ELIM, ALIM)
+      IF (NZ.LT.0) GO TO 200
+      AA = FMR*FNU
+      Z3R = SFAC
+      STR = DCOS(AA)
+      STI = DSIN(AA)
+      S1R = (STR*CYR(1)-STI*CYI(1))*Z3R
+      S1I = (STR*CYI(1)+STI*CYR(1))*Z3R
+      FNU = (2.0D0-FID)/3.0D0
+      CALL ZBINU(ZTAR, ZTAI, FNU, KODE, 2, CYR, CYI, NZ, RL, FNUL, TOL,
+     * ELIM, ALIM)
+      CYR(1) = CYR(1)*Z3R
+      CYI(1) = CYI(1)*Z3R
+      CYR(2) = CYR(2)*Z3R
+      CYI(2) = CYI(2)*Z3R
+C-----------------------------------------------------------------------
+C     BACKWARD RECUR ONE STEP FOR ORDERS -1/3 OR -2/3
+C-----------------------------------------------------------------------
+      CALL ZDIV(CYR(1), CYI(1), ZTAR, ZTAI, STR, STI)
+      S2R = (FNU+FNU)*STR + CYR(2)
+      S2I = (FNU+FNU)*STI + CYI(2)
+      AA = FMR*(FNU-1.0D0)
+      STR = DCOS(AA)
+      STI = DSIN(AA)
+      S1R = COEF*(S1R+S2R*STR-S2I*STI)
+      S1I = COEF*(S1I+S2R*STI+S2I*STR)
+      IF (ID.EQ.1) GO TO 120
+      STR = CSQR*S1R - CSQI*S1I
+      S1I = CSQR*S1I + CSQI*S1R
+      S1R = STR
+      BIR = S1R/SFAC
+      BII = S1I/SFAC
+      RETURN
+  120 CONTINUE
+      STR = ZR*S1R - ZI*S1I
+      S1I = ZR*S1I + ZI*S1R
+      S1R = STR
+      BIR = S1R/SFAC
+      BII = S1I/SFAC
+      RETURN
+  130 CONTINUE
+      AA = C1*(1.0D0-FID) + FID*C2
+      BIR = AA
+      BII = 0.0D0
+      RETURN
+  190 CONTINUE
+      IERR=2
+      NZ=0
+      RETURN
+  200 CONTINUE
+      IF(NZ.EQ.(-1)) GO TO 190
+      NZ=0
+      IERR=5
+      RETURN
+  260 CONTINUE
+      IERR=4
+      NZ=0
+      RETURN
+      END

amos/zbknu.f

@@ -5,8 +5,8 @@ C***REFER TO  ZBESI,ZBESK,ZAIRY,ZBESH
 C
 C     ZBKNU COMPUTES THE K BESSEL FUNCTION IN THE RIGHT HALF Z PLANE.
 C
-C***ROUTINES CALLED  DGAMLN,I1MACH,D1MACH,ZKSCL,ZSHCH,ZUCHK,ZABS,ZDIV,
+C***ROUTINES CALLED  DGAMLN,I1MACH,D1MACH,ZKSCL,ZSHCH,ZUCHK,AZABS,ZDIV,
-C                    ZEXP,ZLOG,ZMLT,ZSQRT
+C                    AZEXP,AZLOG,ZMLT,AZSQRT
 C***END PROLOGUE  ZBKNU
 C
       DOUBLE PRECISION AA, AK, ALIM, ASCLE, A1, A2, BB, BK, BRY, CAZ,
@@ -16,7 +16,7 @@ C
      * FI, FK, FKS, FMUI, FMUR, FNU, FPI, FR, G1, G2, HPI, PI, PR, PTI,
      * PTR, P1I, P1R, P2I, P2M, P2R, QI, QR, RAK, RCAZ, RTHPI, RZI,
      * RZR, R1, S, SMUI, SMUR, SPI, STI, STR, S1I, S1R, S2I, S2R, TM,
-     * TOL, TTH, T1, T2, YI, YR, ZI, ZR, DGAMLN, D1MACH, ZABS, ELM,
+     * TOL, TTH, T1, T2, YI, YR, ZI, ZR, DGAMLN, D1MACH, AZABS, ELM,
      * CELMR, ZDR, ZDI, AS, ALAS, HELIM, CYR, CYI
       INTEGER I, IFLAG, INU, K, KFLAG, KK, KMAX, KODE, KODED, N, NZ,
      * IDUM, I1MACH, J, IC, INUB, NW
@@ -38,7 +38,7 @@ C
      3    -2.15241674114950973D-04,    -2.01348547807882387D-05,
      4     1.13302723198169588D-06,     6.11609510448141582D-09/
 C
-      CAZ = ZABS(ZR,ZI)
+      CAZ = AZABS(ZR,ZI)
       CSCLR = 1.0D0/TOL
       CRSCR = TOL
       CSSR(1) = CSCLR
@@ -68,7 +68,7 @@ C-----------------------------------------------------------------------
 C     SERIES FOR CABS(Z).LE.R1
 C-----------------------------------------------------------------------
       FC = 1.0D0
-      CALL ZLOG(RZR, RZI, SMUR, SMUI, IDUM)
+      CALL AZLOG(RZR, RZI, SMUR, SMUI, IDUM)
       FMUR = SMUR*DNU
       FMUI = SMUI*DNU
       CALL ZSHCH(FMUR, FMUI, CSHR, CSHI, CCHR, CCHI)
@@ -104,7 +104,7 @@ C-----------------------------------------------------------------------
       G2 = (T1+T2)*0.5D0
       FR = FC*(CCHR*G1+SMUR*G2)
       FI = FC*(CCHI*G1+SMUI*G2)
-      CALL ZEXP(FMUR, FMUI, STR, STI)
+      CALL AZEXP(FMUR, FMUI, STR, STI)
       PR = 0.5D0*STR/T2
       PI = 0.5D0*STI/T2
       CALL ZDIV(0.5D0, 0.0D0, STR, STI, PTR, PTI)
@@ -151,7 +151,7 @@ C-----------------------------------------------------------------------
       YR(1) = S1R
       YI(1) = S1I
       IF (KODED.EQ.1) RETURN
-      CALL ZEXP(ZR, ZI, STR, STI)
+      CALL AZEXP(ZR, ZI, STR, STI)
       CALL ZMLT(S1R, S1I, STR, STI, YR(1), YI(1))
       RETURN
 C-----------------------------------------------------------------------
@@ -198,7 +198,7 @@ C-----------------------------------------------------------------------
       S1R = S1R*STR
       S1I = S1I*STR
       IF (KODED.EQ.1) GO TO 210
-      CALL ZEXP(ZR, ZI, FR, FI)
+      CALL AZEXP(ZR, ZI, FR, FI)
       CALL ZMLT(S1R, S1I, FR, FI, S1R, S1I)
       CALL ZMLT(S2R, S2I, FR, FI, S2R, S2I)
       GO TO 210
@@ -209,7 +209,7 @@ C     KODED=2 AND A TEST FOR ON SCALE VALUES IS MADE DURING FORWARD
 C     RECURSION
 C-----------------------------------------------------------------------
   110 CONTINUE
-      CALL ZSQRT(ZR, ZI, STR, STI)
+      CALL AZSQRT(ZR, ZI, STR, STI)
       CALL ZDIV(RTHPI, CZEROI, STR, STI, COEFR, COEFI)
       KFLAG = 2
       IF (KODED.EQ.2) GO TO 120
@@ -320,7 +320,7 @@ C-----------------------------------------------------------------------
 C     COMPUTE (P2/CS)=(P2/CABS(CS))*(CONJG(CS)/CABS(CS)) FOR BETTER
 C     SCALING
 C-----------------------------------------------------------------------
-      TM = ZABS(CSR,CSI)
+      TM = AZABS(CSR,CSI)
       PTR = 1.0D0/TM
       S1R = P2R*PTR
       S1I = P2I*PTR
@@ -337,7 +337,7 @@ C-----------------------------------------------------------------------
 C-----------------------------------------------------------------------
 C     COMPUTE P1/P2=(P1/CABS(P2)*CONJG(P2)/CABS(P2) FOR SCALING
 C-----------------------------------------------------------------------
-      TM = ZABS(P2R,P2I)
+      TM = AZABS(P2R,P2I)
       PTR = 1.0D0/TM
       P1R = P1R*PTR
       P1I = P1I*PTR
@@ -472,11 +472,11 @@ C-----------------------------------------------------------------------
         S1I = STI
         CKR = CKR+RZR
         CKI = CKI+RZI
-        AS = ZABS(S2R,S2I)
+        AS = AZABS(S2R,S2I)
         ALAS = DLOG(AS)
         P2R = -ZDR+ALAS
         IF(P2R.LT.(-ELIM)) GO TO 263
-        CALL ZLOG(S2R,S2I,STR,STI,IDUM)
+        CALL AZLOG(S2R,S2I,STR,STI,IDUM)
         P2R = -ZDR+STR
         P2I = -ZDI+STI
         P2M = DEXP(P2R)/TOL

amos/zbuni.f

@@ -9,12 +9,12 @@ C     FNU+N-1 GREATER THAN FNUL BY ADDING NUI AND COMPUTING
 C     ACCORDING TO THE UNIFORM ASYMPTOTIC EXPANSION FOR I(FNU,Z)
 C     ON IFORM=1 AND THE EXPANSION FOR J(FNU,Z) ON IFORM=2
 C
-C***ROUTINES CALLED  ZUNI1,ZUNI2,ZABS,D1MACH
+C***ROUTINES CALLED  ZUNI1,ZUNI2,AZABS,D1MACH
 C***END PROLOGUE  ZBUNI
 C     COMPLEX CSCL,CSCR,CY,RZ,ST,S1,S2,Y,Z
       DOUBLE PRECISION ALIM, AX, AY, CSCLR, CSCRR, CYI, CYR, DFNU,
      * ELIM, FNU, FNUI, FNUL, GNU, RAZ, RZI, RZR, STI, STR, S1I, S1R,
-     * S2I, S2R, TOL, YI, YR, ZI, ZR, ZABS, ASCLE, BRY, C1R, C1I, C1M,
+     * S2I, S2R, TOL, YI, YR, ZI, ZR, AZABS, ASCLE, BRY, C1R, C1I, C1M,
      * D1MACH
       INTEGER I, IFLAG, IFORM, K, KODE, N, NL, NLAST, NUI, NW, NZ
       DIMENSION YR(N), YI(N), CYR(2), CYI(2), BRY(3)
@@ -46,7 +46,7 @@ C-----------------------------------------------------------------------
    20 CONTINUE
       IF (NW.LT.0) GO TO 50
       IF (NW.NE.0) GO TO 90
-      STR = ZABS(CYR(1),CYI(1))
+      STR = AZABS(CYR(1),CYI(1))
 C----------------------------------------------------------------------
 C     SCALE BACKWARD RECURRENCE, BRY(3) IS DEFINED BUT NEVER USED
 C----------------------------------------------------------------------
@@ -72,7 +72,7 @@ C----------------------------------------------------------------------
       S1I = CYI(2)*CSCLR
       S2R = CYR(1)*CSCLR
       S2I = CYI(1)*CSCLR
-      RAZ = 1.0D0/ZABS(ZR,ZI)
+      RAZ = 1.0D0/AZABS(ZR,ZI)
       STR = ZR*RAZ
       STI = -ZI*RAZ
       RZR = (STR+STR)*RAZ

amos/zdiv.f

@@ -4,11 +4,11 @@ C***REFER TO  ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY
 C
 C     DOUBLE PRECISION COMPLEX DIVIDE C=A/B.
 C
-C***ROUTINES CALLED  ZABS
+C***ROUTINES CALLED  AZABS
 C***END PROLOGUE  ZDIV
       DOUBLE PRECISION AR, AI, BR, BI, CR, CI, BM, CA, CB, CC, CD
-      DOUBLE PRECISION ZABS
+      DOUBLE PRECISION AZABS
-      BM = 1.0D0/ZABS(BR,BI)
+      BM = 1.0D0/AZABS(BR,BI)
       CC = BR*BM
       CD = BI*BM
       CA = (AR*CC+AI*CD)*BM

amos/zexp.f

@@ -1,11 +1,11 @@
-      SUBROUTINE ZEXP(AR, AI, BR, BI)
+      SUBROUTINE AZEXP(AR, AI, BR, BI)
-C***BEGIN PROLOGUE  ZEXP
+C***BEGIN PROLOGUE  AZEXP
 C***REFER TO  ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY
 C
 C     DOUBLE PRECISION COMPLEX EXPONENTIAL FUNCTION B=EXP(A)
 C
 C***ROUTINES CALLED  (NONE)
-C***END PROLOGUE  ZEXP
+C***END PROLOGUE  AZEXP
       DOUBLE PRECISION AR, AI, BR, BI, ZM, CA, CB
       ZM = DEXP(AR)
       CA = ZM*DCOS(AI)

amos/zkscl.f

@@ -6,12 +6,12 @@ C     SET K FUNCTIONS TO ZERO ON UNDERFLOW, CONTINUE RECURRENCE
 C     ON SCALED FUNCTIONS UNTIL TWO MEMBERS COME ON SCALE, THEN
 C     RETURN WITH MIN(NZ+2,N) VALUES SCALED BY 1/TOL.
 C
-C***ROUTINES CALLED  ZUCHK,ZABS,ZLOG
+C***ROUTINES CALLED  ZUCHK,AZABS,AZLOG
 C***END PROLOGUE  ZKSCL
 C     COMPLEX CK,CS,CY,CZERO,RZ,S1,S2,Y,ZR,ZD,CELM
       DOUBLE PRECISION ACS, AS, ASCLE, CKI, CKR, CSI, CSR, CYI,
      * CYR, ELIM, FN, FNU, RZI, RZR, STR, S1I, S1R, S2I,
-     * S2R, TOL, YI, YR, ZEROI, ZEROR, ZRI, ZRR, ZABS,
+     * S2R, TOL, YI, YR, ZEROI, ZEROR, ZRI, ZRR, AZABS,
      * ZDR, ZDI, CELMR, ELM, HELIM, ALAS
       INTEGER I, IC, IDUM, KK, N, NN, NW, NZ
       DIMENSION YR(N), YI(N), CYR(2), CYI(2)
@@ -25,13 +25,13 @@ C
         S1I = YI(I)
         CYR(I) = S1R
         CYI(I) = S1I
-        AS = ZABS(S1R,S1I)
+        AS = AZABS(S1R,S1I)
         ACS = -ZRR + DLOG(AS)
         NZ = NZ + 1
         YR(I) = ZEROR
         YI(I) = ZEROI
         IF (ACS.LT.(-ELIM)) GO TO 10
-        CALL ZLOG(S1R, S1I, CSR, CSI, IDUM)
+        CALL AZLOG(S1R, S1I, CSR, CSI, IDUM)
         CSR = CSR - ZRR
         CSI = CSI - ZRI
         STR = DEXP(CSR)/TOL
@@ -78,14 +78,14 @@ C
         S1I = CSI
         CKR = CKR + RZR
         CKI = CKI + RZI
-        AS = ZABS(S2R,S2I)
+        AS = AZABS(S2R,S2I)
         ALAS = DLOG(AS)
         ACS = -ZDR + ALAS
         NZ = NZ + 1
         YR(I) = ZEROR
         YI(I) = ZEROI
         IF (ACS.LT.(-ELIM)) GO TO 25
-        CALL ZLOG(S2R, S2I, CSR, CSI, IDUM)
+        CALL AZLOG(S2R, S2I, CSR, CSI, IDUM)
         CSR = CSR - ZDR
         CSI = CSI - ZDI
         STR = DEXP(CSR)/TOL

amos/zlog.f

@@ -1,13 +1,13 @@
-      SUBROUTINE ZLOG(AR, AI, BR, BI, IERR)
+      SUBROUTINE AZLOG(AR, AI, BR, BI, IERR)
-C***BEGIN PROLOGUE  ZLOG
+C***BEGIN PROLOGUE  AZLOG
 C***REFER TO  ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY
 C
 C     DOUBLE PRECISION COMPLEX LOGARITHM B=CLOG(A)
 C     IERR=0,NORMAL RETURN      IERR=1, Z=CMPLX(0.0,0.0)
-C***ROUTINES CALLED  ZABS
+C***ROUTINES CALLED  AZABS
-C***END PROLOGUE  ZLOG
+C***END PROLOGUE  AZLOG
       DOUBLE PRECISION AR, AI, BR, BI, ZM, DTHETA, DPI, DHPI
-      DOUBLE PRECISION ZABS
+      DOUBLE PRECISION AZABS
       DATA DPI , DHPI  / 3.141592653589793238462643383D+0,
      1                   1.570796326794896619231321696D+0/
 C
@@ -31,7 +31,7 @@ C
       BI = 0.0D+0
       RETURN
    40 IF (AR.LT.0.0D+0) DTHETA = DTHETA + DPI
-   50 ZM = ZABS(AR,AI)
+   50 ZM = AZABS(AR,AI)
       BR = DLOG(ZM)
       BI = DTHETA
       RETURN

amos/zmlri.f

@@ -5,20 +5,20 @@ C
 C     ZMLRI COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY THE
 C     MILLER ALGORITHM NORMALIZED BY A NEUMANN SERIES.
 C
-C***ROUTINES CALLED  DGAMLN,D1MACH,ZABS,ZEXP,ZLOG,ZMLT
+C***ROUTINES CALLED  DGAMLN,D1MACH,AZABS,AZEXP,AZLOG,ZMLT
 C***END PROLOGUE  ZMLRI
 C     COMPLEX CK,CNORM,CONE,CTWO,CZERO,PT,P1,P2,RZ,SUM,Y,Z
       DOUBLE PRECISION ACK, AK, AP, AT, AZ, BK, CKI, CKR, CNORMI,
      * CNORMR, CONEI, CONER, FKAP, FKK, FLAM, FNF, FNU, PTI, PTR, P1I,
      * P1R, P2I, P2R, RAZ, RHO, RHO2, RZI, RZR, SCLE, STI, STR, SUMI,
      * SUMR, TFNF, TOL, TST, YI, YR, ZEROI, ZEROR, ZI, ZR, DGAMLN,
-     * D1MACH, ZABS
+     * D1MACH, AZABS
       INTEGER I, IAZ, IDUM, IFNU, INU, ITIME, K, KK, KM, KODE, M, N, NZ
       DIMENSION YR(N), YI(N)
       DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 /
       SCLE = D1MACH(1)/TOL
       NZ=0
-      AZ = ZABS(ZR,ZI)
+      AZ = AZABS(ZR,ZI)
       IAZ = INT(SNGL(AZ))
       IFNU = INT(SNGL(FNU))
       INU = IFNU + N - 1
@@ -52,7 +52,7 @@ C-----------------------------------------------------------------------
         P1I = PTI
         CKR = CKR + RZR
         CKI = CKI + RZI
-        AP = ZABS(P2R,P2I)
+        AP = AZABS(P2R,P2I)
         IF (AP.GT.TST*AK*AK) GO TO 20
         AK = AK + 1.0D0
    10 CONTINUE
@@ -85,12 +85,12 @@ C-----------------------------------------------------------------------
         P1I = PTI
         CKR = CKR + RZR
         CKI = CKI + RZI
-        AP = ZABS(P2R,P2I)
+        AP = AZABS(P2R,P2I)
         IF (AP.LT.TST) GO TO 30
         IF (ITIME.EQ.2) GO TO 40
-        ACK = ZABS(CKR,CKI)
+        ACK = AZABS(CKR,CKI)
         FLAM = ACK + DSQRT(ACK*ACK-1.0D0)
-        FKAP = AP/ZABS(P1R,P1I)
+        FKAP = AP/AZABS(P1R,P1I)
         RHO = DMIN1(FLAM,FKAP)
         TST = TST*DSQRT(RHO/(RHO*RHO-1.0D0))
         ITIME = 2
@@ -172,7 +172,7 @@ C-----------------------------------------------------------------------
       PTR = ZR
       PTI = ZI
       IF (KODE.EQ.2) PTR = ZEROR
-      CALL ZLOG(RZR, RZI, STR, STI, IDUM)
+      CALL AZLOG(RZR, RZI, STR, STI, IDUM)
       P1R = -FNF*STR + PTR
       P1I = -FNF*STI + PTI
       AP = DGAMLN(1.0D0+FNF,IDUM)
@@ -184,9 +184,9 @@ C     IN THE DENOMINATOR BY SQUARING LARGE QUANTITIES
 C-----------------------------------------------------------------------
       P2R = P2R + SUMR
       P2I = P2I + SUMI
-      AP = ZABS(P2R,P2I)
+      AP = AZABS(P2R,P2I)
       P1R = 1.0D0/AP
-      CALL ZEXP(PTR, PTI, STR, STI)
+      CALL AZEXP(PTR, PTI, STR, STI)
       CKR = STR*P1R
       CKI = STI*P1R
       PTR = P2R*P1R

amos/zrati.f

@@ -9,18 +9,18 @@ C     MATHEMATICAL SCIENCES, VOL 77B, P111-114, SEPTEMBER, 1973,
 C     BESSEL FUNCTIONS I AND J OF COMPLEX ARGUMENT AND INTEGER ORDER,
 C     BY D. J. SOOKNE.
 C
-C***ROUTINES CALLED  ZABS,ZDIV
+C***ROUTINES CALLED  AZABS,ZDIV
 C***END PROLOGUE  ZRATI
 C     COMPLEX Z,CY(1),CONE,CZERO,P1,P2,T1,RZ,PT,CDFNU
       DOUBLE PRECISION AK, AMAGZ, AP1, AP2, ARG, AZ, CDFNUI, CDFNUR,
      * CONEI, CONER, CYI, CYR, CZEROI, CZEROR, DFNU, FDNU, FLAM, FNU,
      * FNUP, PTI, PTR, P1I, P1R, P2I, P2R, RAK, RAP1, RHO, RT2, RZI,
-     * RZR, TEST, TEST1, TOL, TTI, TTR, T1I, T1R, ZI, ZR, ZABS
+     * RZR, TEST, TEST1, TOL, TTI, TTR, T1I, T1R, ZI, ZR, AZABS
       INTEGER I, ID, IDNU, INU, ITIME, K, KK, MAGZ, N
       DIMENSION CYR(N), CYI(N)
       DATA CZEROR,CZEROI,CONER,CONEI,RT2/
      1 0.0D0, 0.0D0, 1.0D0, 0.0D0, 1.41421356237309505D0 /
-      AZ = ZABS(ZR,ZI)
+      AZ = AZABS(ZR,ZI)
       INU = INT(SNGL(FNU))
       IDNU = INU + N - 1
       MAGZ = INT(SNGL(AZ))
@@ -42,8 +42,8 @@ C     COMPLEX Z,CY(1),CONE,CZERO,P1,P2,T1,RZ,PT,CDFNU
       T1R = T1R + RZR
       T1I = T1I + RZI
       IF (ID.GT.0) ID = 0
-      AP2 = ZABS(P2R,P2I)
+      AP2 = AZABS(P2R,P2I)
-      AP1 = ZABS(P1R,P1I)
+      AP1 = AZABS(P1R,P1I)
 C-----------------------------------------------------------------------
 C     THE OVERFLOW TEST ON K(FNU+I-1,Z) BEFORE THE CALL TO CBKNU
 C     GUARANTEES THAT P2 IS ON SCALE. SCALE TEST1 AND ALL SUBSEQUENT
@@ -70,10 +70,10 @@ C-----------------------------------------------------------------------
       P1I = PTI
       T1R = T1R + RZR
       T1I = T1I + RZI
-      AP2 = ZABS(P2R,P2I)
+      AP2 = AZABS(P2R,P2I)
       IF (AP1.LE.TEST) GO TO 10
       IF (ITIME.EQ.2) GO TO 20
-      AK = ZABS(T1R,T1I)*0.5D0
+      AK = AZABS(T1R,T1I)*0.5D0
       FLAM = AK + DSQRT(AK*AK-1.0D0)
       RHO = DMIN1(AP2/AP1,FLAM)
       TEST = TEST1*DSQRT(RHO/(RHO*RHO-1.0D0))
@@ -116,7 +116,7 @@ C-----------------------------------------------------------------------
       DO 60 I=2,N
         PTR = CDFNUR + (T1R*RZR-T1I*RZI) + CYR(K+1)
         PTI = CDFNUI + (T1R*RZI+T1I*RZR) + CYI(K+1)
-        AK = ZABS(PTR,PTI)
+        AK = AZABS(PTR,PTI)
         IF (AK.NE.CZEROR) GO TO 50
         PTR = TOL
         PTI = TOL

amos/zs1s2.f

@@ -11,16 +11,16 @@ C     MAGNITUDE, BUT FOR KODE=2 THEY CAN BE OF THE SAME ORDER
 C     OF MAGNITUDE AND THE MAXIMUM MUST BE AT LEAST ONE
 C     PRECISION ABOVE THE UNDERFLOW LIMIT.
 C
-C***ROUTINES CALLED  ZABS,ZEXP,ZLOG
+C***ROUTINES CALLED  AZABS,AZEXP,AZLOG
 C***END PROLOGUE  ZS1S2
 C     COMPLEX CZERO,C1,S1,S1D,S2,ZR
       DOUBLE PRECISION AA, ALIM, ALN, ASCLE, AS1, AS2, C1I, C1R, S1DI,
-     * S1DR, S1I, S1R, S2I, S2R, ZEROI, ZEROR, ZRI, ZRR, ZABS
+     * S1DR, S1I, S1R, S2I, S2R, ZEROI, ZEROR, ZRI, ZRR, AZABS
       INTEGER IUF, IDUM, NZ
       DATA ZEROR,ZEROI  / 0.0D0 , 0.0D0 /
       NZ = 0
-      AS1 = ZABS(S1R,S1I)
+      AS1 = AZABS(S1R,S1I)
-      AS2 = ZABS(S2R,S2I)
+      AS2 = AZABS(S2R,S2I)
       IF (S1R.EQ.0.0D0 .AND. S1I.EQ.0.0D0) GO TO 10
       IF (AS1.EQ.0.0D0) GO TO 10
       ALN = -ZRR - ZRR + DLOG(AS1)
@@ -30,11 +30,11 @@ C     COMPLEX CZERO,C1,S1,S1D,S2,ZR
       S1I = ZEROI
       AS1 = ZEROR
       IF (ALN.LT.(-ALIM)) GO TO 10
-      CALL ZLOG(S1DR, S1DI, C1R, C1I, IDUM)
+      CALL AZLOG(S1DR, S1DI, C1R, C1I, IDUM)
       C1R = C1R - ZRR - ZRR
       C1I = C1I - ZRI - ZRI
-      CALL ZEXP(C1R, C1I, S1R, S1I)
+      CALL AZEXP(C1R, C1I, S1R, S1I)
-      AS1 = ZABS(S1R,S1I)
+      AS1 = AZABS(S1R,S1I)
       IUF = IUF + 1
    10 CONTINUE
       AA = DMAX1(AS1,AS2)

amos/zseri.f

@@ -11,20 +11,20 @@ C     DUE TO UNDERFLOW. NZ.LT.0 MEANS UNDERFLOW OCCURRED, BUT THE
 C     CONDITION CABS(Z).LE.2*SQRT(FNU+1) WAS VIOLATED AND THE
 C     COMPUTATION MUST BE COMPLETED IN ANOTHER ROUTINE WITH N=N-ABS(NZ).
 C
-C***ROUTINES CALLED  DGAMLN,D1MACH,ZUCHK,ZABS,ZDIV,ZLOG,ZMLT
+C***ROUTINES CALLED  DGAMLN,D1MACH,ZUCHK,AZABS,ZDIV,AZLOG,ZMLT
 C***END PROLOGUE  ZSERI
 C     COMPLEX AK1,CK,COEF,CONE,CRSC,CSCL,CZ,CZERO,HZ,RZ,S1,S2,Y,Z
       DOUBLE PRECISION AA, ACZ, AK, AK1I, AK1R, ALIM, ARM, ASCLE, ATOL,
      * AZ, CKI, CKR, COEFI, COEFR, CONEI, CONER, CRSCR, CZI, CZR, DFNU,
      * ELIM, FNU, FNUP, HZI, HZR, RAZ, RS, RTR1, RZI, RZR, S, SS, STI,
      * STR, S1I, S1R, S2I, S2R, TOL, YI, YR, WI, WR, ZEROI, ZEROR, ZI,
-     * ZR, DGAMLN, D1MACH, ZABS
+     * ZR, DGAMLN, D1MACH, AZABS
       INTEGER I, IB, IDUM, IFLAG, IL, K, KODE, L, M, N, NN, NZ, NW
       DIMENSION YR(N), YI(N), WR(2), WI(2)
       DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 /
 C
       NZ = 0
-      AZ = ZABS(ZR,ZI)
+      AZ = AZABS(ZR,ZI)
       IF (AZ.EQ.0.0D0) GO TO 160
       ARM = 1.0D+3*D1MACH(1)
       RTR1 = DSQRT(ARM)
@@ -38,9 +38,9 @@ C
       IF (AZ.LE.RTR1) GO TO 10
       CALL ZMLT(HZR, HZI, HZR, HZI, CZR, CZI)
    10 CONTINUE
-      ACZ = ZABS(CZR,CZI)
+      ACZ = AZABS(CZR,CZI)
       NN = N
-      CALL ZLOG(HZR, HZI, CKR, CKI, IDUM)
+      CALL AZLOG(HZR, HZI, CKR, CKI, IDUM)
    20 CONTINUE
       DFNU = FNU + DBLE(FLOAT(NN-1))
       FNUP = DFNU + 1.0D0
@@ -157,7 +157,7 @@ C-----------------------------------------------------------------------
         YI(K) = CKI
         AK = AK - 1.0D0
         K = K - 1
-        IF (ZABS(CKR,CKI).GT.ASCLE) GO TO 140
+        IF (AZABS(CKR,CKI).GT.ASCLE) GO TO 140
   130 CONTINUE
       RETURN
   140 CONTINUE

amos/zsqrt.f

@@ -1,16 +1,16 @@
-      SUBROUTINE ZSQRT(AR, AI, BR, BI)
+      SUBROUTINE AZSQRT(AR, AI, BR, BI)
-C***BEGIN PROLOGUE  ZSQRT
+C***BEGIN PROLOGUE  AZSQRT
 C***REFER TO  ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY
 C
 C     DOUBLE PRECISION COMPLEX SQUARE ROOT, B=CSQRT(A)
 C
-C***ROUTINES CALLED  ZABS
+C***ROUTINES CALLED  AZABS
-C***END PROLOGUE  ZSQRT
+C***END PROLOGUE  AZSQRT
       DOUBLE PRECISION AR, AI, BR, BI, ZM, DTHETA, DPI, DRT
-      DOUBLE PRECISION ZABS
+      DOUBLE PRECISION AZABS
       DATA DRT , DPI / 7.071067811865475244008443621D-1,
      1                 3.141592653589793238462643383D+0/
-      ZM = ZABS(AR,AI)
+      ZM = AZABS(AR,AI)
       ZM = DSQRT(ZM)
       IF (AR.EQ.0.0D+0) GO TO 10
       IF (AI.EQ.0.0D+0) GO TO 20

amos/zunhj.f

@@ -29,7 +29,7 @@ C         MCONJ=SIGN OF AIMAG(Z), BUT IS AMBIGUOUS WHEN Z IS REAL AND
 C         MUST BE SPECIFIED. IPMTR=0 RETURNS ALL PARAMETERS. IPMTR=
 C         1 COMPUTES ALL EXCEPT ASUM AND BSUM.
 C
-C***ROUTINES CALLED  ZABS,ZDIV,ZLOG,ZSQRT,D1MACH
+C***ROUTINES CALLED  AZABS,ZDIV,AZLOG,AZSQRT,D1MACH
 C***END PROLOGUE  ZUNHJ
 C     COMPLEX ARG,ASUM,BSUM,CFNU,CONE,CR,CZERO,DR,P,PHI,PRZTH,PTFN,
 C    *RFN13,RTZTA,RZTH,SUMA,SUMB,TFN,T2,UP,W,W2,Z,ZA,ZB,ZC,ZETA,ZETA1,
@@ -42,7 +42,7 @@ C    *ZETA2,ZTH
      * SUMAI, SUMAR, SUMBI, SUMBR, TEST, TFNI, TFNR, THPI, TOL, TZAI,
      * TZAR, T2I, T2R, UPI, UPR, WI, WR, W2I, W2R, ZAI, ZAR, ZBI, ZBR,
      * ZCI, ZCR, ZEROI, ZEROR, ZETAI, ZETAR, ZETA1I, ZETA1R, ZETA2I,
-     * ZETA2R, ZI, ZR, ZTHI, ZTHR, ZABS, AC, D1MACH
+     * ZETA2R, ZI, ZR, ZTHI, ZTHR, AZABS, AC, D1MACH
       INTEGER IAS, IBS, IPMTR, IS, J, JR, JU, K, KMAX, KP1, KS, L, LR,
      * LRP1, L1, L2, M, IDUM
       DIMENSION AR(14), BR(14), C(105), ALFA(180), BETA(210), GAMA(30),
@@ -457,7 +457,7 @@ C-----------------------------------------------------------------------
       RFN13 = 1.0D0/FN13
       W2R = CONER - ZBR*ZBR + ZBI*ZBI
       W2I = CONEI - ZBR*ZBI - ZBR*ZBI
-      AW2 = ZABS(W2R,W2I)
+      AW2 = AZABS(W2R,W2I)
       IF (AW2.GT.0.25D0) GO TO 130
 C-----------------------------------------------------------------------
 C     POWER SERIES FOR CABS(W2).LE.0.25D0
@@ -484,8 +484,8 @@ C-----------------------------------------------------------------------
       ZETAI = W2R*SUMAI + W2I*SUMAR
       ARGR = ZETAR*FN23
       ARGI = ZETAI*FN23
-      CALL ZSQRT(SUMAR, SUMAI, ZAR, ZAI)
+      CALL AZSQRT(SUMAR, SUMAI, ZAR, ZAI)
-      CALL ZSQRT(W2R, W2I, STR, STI)
+      CALL AZSQRT(W2R, W2I, STR, STI)
       ZETA2R = STR*FNU
       ZETA2I = STI*FNU
       STR = CONER + EX2*(ZETAR*ZAR-ZETAI*ZAI)
@@ -494,7 +494,7 @@ C-----------------------------------------------------------------------
       ZETA1I = STR*ZETA2I + STI*ZETA2R
       ZAR = ZAR + ZAR
       ZAI = ZAI + ZAI
-      CALL ZSQRT(ZAR, ZAI, STR, STI)
+      CALL AZSQRT(ZAR, ZAI, STR, STI)
       PHIR = STR*RFN13
       PHII = STI*RFN13
       IF (IPMTR.EQ.1) GO TO 120
@@ -565,13 +565,13 @@ C-----------------------------------------------------------------------
 C     CABS(W2).GT.0.25D0
 C-----------------------------------------------------------------------
   130 CONTINUE
-      CALL ZSQRT(W2R, W2I, WR, WI)
+      CALL AZSQRT(W2R, W2I, WR, WI)
       IF (WR.LT.0.0D0) WR = 0.0D0
       IF (WI.LT.0.0D0) WI = 0.0D0
       STR = CONER + WR
       STI = WI
       CALL ZDIV(STR, STI, ZBR, ZBI, ZAR, ZAI)
-      CALL ZLOG(ZAR, ZAI, ZCR, ZCI, IDUM)
+      CALL AZLOG(ZAR, ZAI, ZCR, ZCI, IDUM)
       IF (ZCI.LT.0.0D0) ZCI = 0.0D0
       IF (ZCI.GT.HPI) ZCI = HPI
       IF (ZCR.LT.0.0D0) ZCR = 0.0D0
@@ -581,7 +581,7 @@ C-----------------------------------------------------------------------
       ZETA1I = ZCI*FNU
       ZETA2R = WR*FNU
       ZETA2I = WI*FNU
-      AZTH = ZABS(ZTHR,ZTHI)
+      AZTH = AZABS(ZTHR,ZTHI)
       ANG = THPI
       IF (ZTHR.GE.0.0D0 .AND. ZTHI.LT.0.0D0) GO TO 140
       ANG = HPI
@@ -600,7 +600,7 @@ C-----------------------------------------------------------------------
       CALL ZDIV(RTZTR, RTZTI, WR, WI, ZAR, ZAI)
       TZAR = ZAR + ZAR
       TZAI = ZAI + ZAI
-      CALL ZSQRT(TZAR, TZAI, STR, STI)
+      CALL AZSQRT(TZAR, TZAI, STR, STI)
       PHIR = STR*RFN13
       PHII = STI*RFN13
       IF (IPMTR.EQ.1) GO TO 120

amos/zuni1.f

@@ -12,7 +12,7 @@ C     NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER
 C     FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL.
 C     Y(I)=CZERO FOR I=NLAST+1,N
 C
-C***ROUTINES CALLED  ZUCHK,ZUNIK,ZUOIK,D1MACH,ZABS
+C***ROUTINES CALLED  ZUCHK,ZUNIK,ZUOIK,D1MACH,AZABS
 C***END PROLOGUE  ZUNI1
 C     COMPLEX CFN,CONE,CRSC,CSCL,CSR,CSS,CWRK,CZERO,C1,C2,PHI,RZ,SUM,S1,
 C    *S2,Y,Z,ZETA1,ZETA2
@@ -20,7 +20,7 @@ C    *S2,Y,Z,ZETA1,ZETA2
      * CSCL, CSRR, CSSR, CWRKI, CWRKR, C1R, C2I, C2M, C2R, ELIM, FN,
      * FNU, FNUL, PHII, PHIR, RAST, RS1, RZI, RZR, STI, STR, SUMI,
      * SUMR, S1I, S1R, S2I, S2R, TOL, YI, YR, ZEROI, ZEROR, ZETA1I,
-     * ZETA1R, ZETA2I, ZETA2R, ZI, ZR, CYR, CYI, D1MACH, ZABS
+     * ZETA1R, ZETA2I, ZETA2R, ZI, ZR, CYR, CYI, D1MACH, AZABS
       INTEGER I, IFLAG, INIT, K, KODE, M, N, ND, NLAST, NN, NUF, NW, NZ
       DIMENSION BRY(3), YR(N), YI(N), CWRKR(16), CWRKI(16), CSSR(3),
      * CSRR(3), CYR(2), CYI(2)
@@ -53,7 +53,7 @@ C-----------------------------------------------------------------------
       IF (KODE.EQ.1) GO TO 10
       STR = ZR + ZETA2R
       STI = ZI + ZETA2I
-      RAST = FN/ZABS(STR,STI)
+      RAST = FN/AZABS(STR,STI)
       STR = STR*RAST*RAST
       STI = -STI*RAST*RAST
       S1R = -ZETA1R + STR
@@ -75,7 +75,7 @@ C-----------------------------------------------------------------------
         IF (KODE.EQ.1) GO TO 40
         STR = ZR + ZETA2R
         STI = ZI + ZETA2I
-        RAST = FN/ZABS(STR,STI)
+        RAST = FN/AZABS(STR,STI)
         STR = STR*RAST*RAST
         STI = -STI*RAST*RAST
         S1R = -ZETA1R + STR
@@ -95,7 +95,7 @@ C-----------------------------------------------------------------------
 C-----------------------------------------------------------------------
 C     REFINE  TEST AND SCALE
 C-----------------------------------------------------------------------
-        APHI = ZABS(PHIR,PHII)
+        APHI = AZABS(PHIR,PHII)
         RS1 = RS1 + DLOG(APHI)
         IF (DABS(RS1).GT.ELIM) GO TO 110
         IF (I.EQ.1) IFLAG = 1
@@ -124,7 +124,7 @@ C-----------------------------------------------------------------------
         YI(M) = S2I*CSRR(IFLAG)
    80 CONTINUE
       IF (ND.LE.2) GO TO 100
-      RAST = 1.0D0/ZABS(ZR,ZI)
+      RAST = 1.0D0/AZABS(ZR,ZI)
       STR = ZR*RAST
       STI = -ZI*RAST
       RZR = (STR+STR)*RAST

amos/zuni2.f

@@ -13,7 +13,7 @@ C     NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER
 C     FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL.
 C     Y(I)=CZERO FOR I=NLAST+1,N
 C
-C***ROUTINES CALLED  ZAIRY,ZUCHK,ZUNHJ,ZUOIK,D1MACH,ZABS
+C***ROUTINES CALLED  ZAIRY,ZUCHK,ZUNHJ,ZUOIK,D1MACH,AZABS
 C***END PROLOGUE  ZUNI2
 C     COMPLEX AI,ARG,ASUM,BSUM,CFN,CI,CID,CIP,CONE,CRSC,CSCL,CSR,CSS,
 C    *CZERO,C1,C2,DAI,PHI,RZ,S1,S2,Y,Z,ZB,ZETA1,ZETA2,ZN
@@ -23,7 +23,7 @@ C    *CZERO,C1,C2,DAI,PHI,RZ,S1,S2,Y,Z,ZB,ZETA1,ZETA2,ZN
      * DAIR, ELIM, FN, FNU, FNUL, HPI, PHII, PHIR, RAST, RAZ, RS1, RZI,
      * RZR, STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR, ZBI, ZBR, ZEROI,
      * ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZI, ZNI, ZNR, ZR, CYR,
-     * CYI, D1MACH, ZABS, CAR, SAR
+     * CYI, D1MACH, AZABS, CAR, SAR
       INTEGER I, IFLAG, IN, INU, J, K, KODE, N, NAI, ND, NDAI, NLAST,
      * NN, NUF, NW, NZ, IDUM
       DIMENSION BRY(3), YR(N), YI(N), CIPR(4), CIPI(4), CSSR(3),
@@ -85,7 +85,7 @@ C-----------------------------------------------------------------------
       IF (KODE.EQ.1) GO TO 20
       STR = ZBR + ZETA2R
       STI = ZBI + ZETA2I
-      RAST = FN/ZABS(STR,STI)
+      RAST = FN/AZABS(STR,STI)
       STR = STR*RAST*RAST
       STI = -STI*RAST*RAST
       S1R = -ZETA1R + STR
@@ -106,7 +106,7 @@ C-----------------------------------------------------------------------
         IF (KODE.EQ.1) GO TO 50
         STR = ZBR + ZETA2R
         STI = ZBI + ZETA2I
-        RAST = FN/ZABS(STR,STI)
+        RAST = FN/AZABS(STR,STI)
         STR = STR*RAST*RAST
         STI = -STI*RAST*RAST
         S1R = -ZETA1R + STR
@@ -127,8 +127,8 @@ C-----------------------------------------------------------------------
 C     REFINE  TEST AND SCALE
 C-----------------------------------------------------------------------
 C-----------------------------------------------------------------------
-        APHI = ZABS(PHIR,PHII)
+        APHI = AZABS(PHIR,PHII)
-        AARG = ZABS(ARGR,ARGI)
+        AARG = AZABS(ARGR,ARGI)
         RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC
         IF (DABS(RS1).GT.ELIM) GO TO 120
         IF (I.EQ.1) IFLAG = 1
@@ -171,7 +171,7 @@ C-----------------------------------------------------------------------
         C2R = STR
    90 CONTINUE
       IF (ND.LE.2) GO TO 110
-      RAZ = 1.0D0/ZABS(ZR,ZI)
+      RAZ = 1.0D0/AZABS(ZR,ZI)
       STR = ZR*RAZ
       STI = -ZI*RAZ
       RZR = (STR+STR)*RAZ

amos/zunik.f

@@ -18,7 +18,7 @@ C        1 OR 2 WITH NO CHANGE IN INIT. CWRK IS A COMPLEX WORK
 C        ARRAY. IPMTR=0 COMPUTES ALL PARAMETERS. IPMTR=1 COMPUTES PHI,
 C        ZETA1,ZETA2.
 C
-C***ROUTINES CALLED  ZDIV,ZLOG,ZSQRT,D1MACH
+C***ROUTINES CALLED  ZDIV,AZLOG,AZSQRT,D1MACH
 C***END PROLOGUE  ZUNIK
 C     COMPLEX CFN,CON,CONE,CRFN,CWRK,CZERO,PHI,S,SR,SUM,T,T2,ZETA1,
 C    *ZETA2,ZN,ZR
@@ -131,11 +131,11 @@ C-----------------------------------------------------------------------
       TI = ZRI*RFN
       SR = CONER + (TR*TR-TI*TI)
       SI = CONEI + (TR*TI+TI*TR)
-      CALL ZSQRT(SR, SI, SRR, SRI)
+      CALL AZSQRT(SR, SI, SRR, SRI)
       STR = CONER + SRR
       STI = CONEI + SRI
       CALL ZDIV(STR, STI, TR, TI, ZNR, ZNI)
-      CALL ZLOG(ZNR, ZNI, STR, STI, IDUM)
+      CALL AZLOG(ZNR, ZNI, STR, STI, IDUM)
       ZETA1R = FNU*STR
       ZETA1I = FNU*STI
       ZETA2R = FNU*SRR
@@ -143,7 +143,7 @@ C-----------------------------------------------------------------------
       CALL ZDIV(CONER, CONEI, SRR, SRI, TR, TI)
       SRR = TR*RFN
       SRI = TI*RFN
-      CALL ZSQRT(SRR, SRI, CWRKR(16), CWRKI(16))
+      CALL AZSQRT(SRR, SRI, CWRKR(16), CWRKI(16))
       PHIR = CWRKR(16)*CON(IKFLG)
       PHII = CWRKI(16)*CON(IKFLG)
       IF (IPMTR.NE.0) RETURN

amos/zunk1.f

@@ -9,7 +9,7 @@ C     UNIFORM ASYMPTOTIC EXPANSION.
 C     MR INDICATES THE DIRECTION OF ROTATION FOR ANALYTIC CONTINUATION.
 C     NZ=-1 MEANS AN OVERFLOW WILL OCCUR
 C
-C***ROUTINES CALLED  ZKSCL,ZS1S2,ZUCHK,ZUNIK,D1MACH,ZABS
+C***ROUTINES CALLED  ZKSCL,ZS1S2,ZUCHK,ZUNIK,D1MACH,AZABS
 C***END PROLOGUE  ZUNK1
 C     COMPLEX CFN,CK,CONE,CRSC,CS,CSCL,CSGN,CSPN,CSR,CSS,CWRK,CY,CZERO,
 C    *C1,C2,PHI,PHID,RZ,SUM,SUMD,S1,S2,Y,Z,ZETA1,ZETA1D,ZETA2,ZETA2D,ZR
@@ -19,7 +19,7 @@ C    *C1,C2,PHI,PHID,RZ,SUM,SUMD,S1,S2,Y,Z,ZETA1,ZETA1D,ZETA2,ZETA2D,ZR
      * FNF, FNU, PHIDI, PHIDR, PHII, PHIR, PI, RAST, RAZR, RS1, RZI,
      * RZR, SGN, STI, STR, SUMDI, SUMDR, SUMI, SUMR, S1I, S1R, S2I,
      * S2R, TOL, YI, YR, ZEROI, ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R,
-     * ZET1DI, ZET1DR, ZET2DI, ZET2DR, ZI, ZR, ZRI, ZRR, D1MACH, ZABS
+     * ZET1DI, ZET1DR, ZET2DI, ZET2DR, ZI, ZR, ZRI, ZRR, D1MACH, AZABS
       INTEGER I, IB, IFLAG, IFN, IL, INIT, INU, IUF, K, KDFLG, KFLAG,
      * KK, KODE, MR, N, NW, NZ, INITD, IC, IPARD, J
       DIMENSION BRY(3), INIT(2), YR(N), YI(N), SUMR(2), SUMI(2),
@@ -65,7 +65,7 @@ C-----------------------------------------------------------------------
         IF (KODE.EQ.1) GO TO 20
         STR = ZRR + ZETA2R(J)
         STI = ZRI + ZETA2I(J)
-        RAST = FN/ZABS(STR,STI)
+        RAST = FN/AZABS(STR,STI)
         STR = STR*RAST*RAST
         STI = -STI*RAST*RAST
         S1R = ZETA1R(J) - STR
@@ -85,7 +85,7 @@ C-----------------------------------------------------------------------
 C-----------------------------------------------------------------------
 C     REFINE  TEST AND SCALE
 C-----------------------------------------------------------------------
-        APHI = ZABS(PHIR(J),PHII(J))
+        APHI = AZABS(PHIR(J),PHII(J))
         RS1 = RS1 + DLOG(APHI)
         IF (DABS(RS1).GT.ELIM) GO TO 60
         IF (KDFLG.EQ.1) KFLAG = 1
@@ -133,7 +133,7 @@ C-----------------------------------------------------------------------
    70 CONTINUE
       I = N
    75 CONTINUE
-      RAZR = 1.0D0/ZABS(ZRR,ZRI)
+      RAZR = 1.0D0/AZABS(ZRR,ZRI)
       STR = ZRR*RAZR
       STI = -ZRI*RAZR
       RZR = (STR+STR)*RAZR
@@ -156,7 +156,7 @@ C-----------------------------------------------------------------------
       IF (KODE.EQ.1) GO TO 80
       STR = ZRR + ZET2DR
       STI = ZRI + ZET2DI
-      RAST = FN/ZABS(STR,STI)
+      RAST = FN/AZABS(STR,STI)
       STR = STR*RAST*RAST
       STI = -STI*RAST*RAST
       S1R = ZET1DR - STR
@@ -172,7 +172,7 @@ C-----------------------------------------------------------------------
 C----------------------------------------------------------------------------
 C     REFINE ESTIMATE AND TEST
 C-------------------------------------------------------------------------
-      APHI = ZABS(PHIDR,PHIDI)
+      APHI = AZABS(PHIDR,PHIDI)
       RS1 = RS1+DLOG(APHI)
       IF (DABS(RS1).LT.ELIM) GO TO 100
    95 CONTINUE
@@ -287,7 +287,7 @@ C-----------------------------------------------------------------------
         IF (KODE.EQ.1) GO TO 200
         STR = ZRR + ZET2DR
         STI = ZRI + ZET2DI
-        RAST = FN/ZABS(STR,STI)
+        RAST = FN/AZABS(STR,STI)
         STR = STR*RAST*RAST
         STI = -STI*RAST*RAST
         S1R = -ZET1DR + STR
@@ -307,7 +307,7 @@ C-----------------------------------------------------------------------
 C-----------------------------------------------------------------------
 C     REFINE  TEST AND SCALE
 C-----------------------------------------------------------------------
-        APHI = ZABS(PHIDR,PHIDI)
+        APHI = AZABS(PHIDR,PHIDI)
         RS1 = RS1 + DLOG(APHI)
         IF (DABS(RS1).GT.ELIM) GO TO 260
         IF (KDFLG.EQ.1) IFLAG = 1

amos/zunk2.f

@@ -12,7 +12,7 @@ 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***ROUTINES CALLED  ZAIRY,ZKSCL,ZS1S2,ZUCHK,ZUNHJ,D1MACH,ZABS
+C***ROUTINES CALLED  ZAIRY,ZKSCL,ZS1S2,ZUCHK,ZUNHJ,D1MACH,AZABS
 C***END PROLOGUE  ZUNK2
 C     COMPLEX AI,ARG,ARGD,ASUM,ASUMD,BSUM,BSUMD,CFN,CI,CIP,CK,CONE,CRSC,
 C    *CR1,CR2,CS,CSCL,CSGN,CSPN,CSR,CSS,CY,CZERO,C1,C2,DAI,PHI,PHID,RZ,
@@ -26,7 +26,7 @@ C    *S1,S2,Y,Z,ZB,ZETA1,ZETA1D,ZETA2,ZETA2D,ZN,ZR
      * PHII, PHIR, PI, PTI, PTR, RAST, RAZR, RS1, RZI, RZR, SAR, SGN,
      * STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR, YY, ZBI, ZBR, ZEROI,
      * ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZET1DI, ZET1DR, ZET2DI,
-     * ZET2DR, ZI, ZNI, ZNR, ZR, ZRI, ZRR, D1MACH, ZABS
+     * ZET2DR, ZI, ZNI, ZNR, ZR, ZRI, ZRR, D1MACH, AZABS
       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), YR(N), YI(N), ASUMR(2), ASUMI(2), BSUMR(2),
@@ -105,7 +105,7 @@ C-----------------------------------------------------------------------
         IF (KODE.EQ.1) GO TO 30
         STR = ZBR + ZETA2R(J)
         STI = ZBI + ZETA2I(J)
-        RAST = FN/ZABS(STR,STI)
+        RAST = FN/AZABS(STR,STI)
         STR = STR*RAST*RAST
         STI = -STI*RAST*RAST
         S1R = ZETA1R(J) - STR
@@ -125,8 +125,8 @@ C-----------------------------------------------------------------------
 C-----------------------------------------------------------------------
 C     REFINE  TEST AND SCALE
 C-----------------------------------------------------------------------
-        APHI = ZABS(PHIR(J),PHII(J))
+        APHI = AZABS(PHIR(J),PHII(J))
-        AARG = ZABS(ARGR(J),ARGI(J))
+        AARG = AZABS(ARGR(J),ARGI(J))
         RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC
         IF (DABS(RS1).GT.ELIM) GO TO 70
         IF (KDFLG.EQ.1) KFLAG = 1
@@ -193,7 +193,7 @@ C-----------------------------------------------------------------------
    80 CONTINUE
       I = N
    85 CONTINUE
-      RAZR = 1.0D0/ZABS(ZRR,ZRI)
+      RAZR = 1.0D0/AZABS(ZRR,ZRI)
       STR = ZRR*RAZR
       STI = -ZRI*RAZR
       RZR = (STR+STR)*RAZR
@@ -214,7 +214,7 @@ C-----------------------------------------------------------------------
       IF (KODE.EQ.1) GO TO 90
       STR = ZBR + ZET2DR
       STI = ZBI + ZET2DI
-      RAST = FN/ZABS(STR,STI)
+      RAST = FN/AZABS(STR,STI)
       STR = STR*RAST*RAST
       STI = -STI*RAST*RAST
       S1R = ZET1DR - STR
@@ -230,7 +230,7 @@ C-----------------------------------------------------------------------
 C----------------------------------------------------------------------------
 C     REFINE ESTIMATE AND TEST
 C-------------------------------------------------------------------------
-      APHI = ZABS(PHIDR,PHIDI)
+      APHI = AZABS(PHIDR,PHIDI)
       RS1 = RS1+DLOG(APHI)
       IF (DABS(RS1).LT.ELIM) GO TO 120
   105 CONTINUE
@@ -291,7 +291,7 @@ C-----------------------------------------------------------------------
       FMR = DBLE(FLOAT(MR))
       SGN = -DSIGN(PI,FMR)
 C-----------------------------------------------------------------------
-C     CSPN AND CSGN ARE COEFF OF K AND I FUNCIONS RESP.
+C     CSPN AND CSGN ARE COEFF OF K AND I FUNCTIONS RESP.
 C-----------------------------------------------------------------------
       CSGNI = SGN
       IF (YY.LE.0.0D0) CSGNI = -CSGNI
@@ -355,7 +355,7 @@ C-----------------------------------------------------------------------
         IF (KODE.EQ.1) GO TO 220
         STR = ZBR + ZET2DR
         STI = ZBI + ZET2DI
-        RAST = FN/ZABS(STR,STI)
+        RAST = FN/AZABS(STR,STI)
         STR = STR*RAST*RAST
         STI = -STI*RAST*RAST
         S1R = -ZET1DR + STR
@@ -375,8 +375,8 @@ C-----------------------------------------------------------------------
 C-----------------------------------------------------------------------
 C     REFINE  TEST AND SCALE
 C-----------------------------------------------------------------------
-        APHI = ZABS(PHIDR,PHIDI)
+        APHI = AZABS(PHIDR,PHIDI)
-        AARG = ZABS(ARGDR,ARGDI)
+        AARG = AZABS(ARGDR,ARGDI)
         RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC
         IF (DABS(RS1).GT.ELIM) GO TO 280
         IF (KDFLG.EQ.1) IFLAG = 1

amos/zuoik.f

@@ -23,7 +23,7 @@ C     IKFLG=2 AND NUF.EQ.N MEANS ALL Y VALUES WERE SET TO ZERO
 C     IKFLG=2 AND 0.LT.NUF.LT.N NOT CONSIDERED. Y MUST BE SET BY
 C             ANOTHER ROUTINE
 C
-C***ROUTINES CALLED  ZUCHK,ZUNHJ,ZUNIK,D1MACH,ZABS,ZLOG
+C***ROUTINES CALLED  ZUCHK,ZUNHJ,ZUNIK,D1MACH,AZABS,AZLOG
 C***END PROLOGUE  ZUOIK
 C     COMPLEX ARG,ASUM,BSUM,CWRK,CZ,CZERO,PHI,SUM,Y,Z,ZB,ZETA1,ZETA2,ZN,
 C    *ZR
@@ -31,7 +31,7 @@ C    *ZR
      * ASCLE, AX, AY, BSUMI, BSUMR, CWRKI, CWRKR, CZI, CZR, ELIM, FNN,
      * FNU, GNN, GNU, PHII, PHIR, RCZ, STR, STI, SUMI, SUMR, TOL, YI,
      * YR, ZBI, ZBR, ZEROI, ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZI,
-     * ZNI, ZNR, ZR, ZRI, ZRR, D1MACH, ZABS
+     * ZNI, ZNR, ZR, ZRI, ZRR, D1MACH, AZABS
       INTEGER I, IDUM, IFORM, IKFLG, INIT, KODE, N, NN, NUF, NW
       DIMENSION YR(N), YI(N), CWRKR(16), CWRKI(16)
       DATA ZEROR,ZEROI / 0.0D0, 0.0D0 /
@@ -78,7 +78,7 @@ C-----------------------------------------------------------------------
      * ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
       CZR = -ZETA1R + ZETA2R
       CZI = -ZETA1I + ZETA2I
-      AARG = ZABS(ARGR,ARGI)
+      AARG = AZABS(ARGR,ARGI)
    50 CONTINUE
       IF (KODE.EQ.1) GO TO 60
       CZR = CZR - ZBR
@@ -88,7 +88,7 @@ C-----------------------------------------------------------------------
       CZR = -CZR
       CZI = -CZI
    70 CONTINUE
-      APHI = ZABS(PHIR,PHII)
+      APHI = AZABS(PHIR,PHII)
       RCZ = CZR
 C-----------------------------------------------------------------------
 C     OVERFLOW TEST
@@ -117,11 +117,11 @@ C-----------------------------------------------------------------------
       RETURN
   110 CONTINUE
       ASCLE = 1.0D+3*D1MACH(1)/TOL
-      CALL ZLOG(PHIR, PHII, STR, STI, IDUM)
+      CALL AZLOG(PHIR, PHII, STR, STI, IDUM)
       CZR = CZR + STR
       CZI = CZI + STI
       IF (IFORM.EQ.1) GO TO 120
-      CALL ZLOG(ARGR, ARGI, STR, STI, IDUM)
+      CALL AZLOG(ARGR, ARGI, STR, STI, IDUM)
       CZR = CZR - 0.25D0*STR - AIC
       CZI = CZI - 0.25D0*STI
   120 CONTINUE
@@ -151,13 +151,13 @@ C-----------------------------------------------------------------------
      * ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
       CZR = -ZETA1R + ZETA2R
       CZI = -ZETA1I + ZETA2I
-      AARG = ZABS(ARGR,ARGI)
+      AARG = AZABS(ARGR,ARGI)
   160 CONTINUE
       IF (KODE.EQ.1) GO TO 170
       CZR = CZR - ZBR
       CZI = CZI - ZBI
   170 CONTINUE
-      APHI = ZABS(PHIR,PHII)
+      APHI = AZABS(PHIR,PHII)
       RCZ = CZR
       IF (RCZ.LT.(-ELIM)) GO TO 180
       IF (RCZ.GT.(-ALIM)) RETURN
@@ -173,11 +173,11 @@ C-----------------------------------------------------------------------
       GO TO 140
   190 CONTINUE
       ASCLE = 1.0D+3*D1MACH(1)/TOL
-      CALL ZLOG(PHIR, PHII, STR, STI, IDUM)
+      CALL AZLOG(PHIR, PHII, STR, STI, IDUM)
       CZR = CZR + STR
       CZI = CZI + STI
       IF (IFORM.EQ.1) GO TO 200
-      CALL ZLOG(ARGR, ARGI, STR, STI, IDUM)
+      CALL AZLOG(ARGR, ARGI, STR, STI, IDUM)
       CZR = CZR - 0.25D0*STR - AIC
       CZI = CZI - 0.25D0*STI
   200 CONTINUE

amos/zwrsk.f

@@ -6,12 +6,12 @@ C
 C     ZWRSK COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY
 C     NORMALIZING THE I FUNCTION RATIOS FROM ZRATI BY THE WRONSKIAN
 C
-C***ROUTINES CALLED  D1MACH,ZBKNU,ZRATI,ZABS
+C***ROUTINES CALLED  D1MACH,ZBKNU,ZRATI,AZABS
 C***END PROLOGUE  ZWRSK
 C     COMPLEX CINU,CSCL,CT,CW,C1,C2,RCT,ST,Y,ZR
       DOUBLE PRECISION ACT, ACW, ALIM, ASCLE, CINUI, CINUR, CSCLR, CTI,
      * CTR, CWI, CWR, C1I, C1R, C2I, C2R, ELIM, FNU, PTI, PTR, RACT,
-     * STI, STR, TOL, YI, YR, ZRI, ZRR, ZABS, D1MACH
+     * STI, STR, TOL, YI, YR, ZRI, ZRR, AZABS, D1MACH
       INTEGER I, KODE, N, NW, NZ
       DIMENSION YR(N), YI(N), CWR(2), CWI(2)
 C-----------------------------------------------------------------------
@@ -39,7 +39,7 @@ C     THE UNDER AND OVERFLOW LIMITS AND THE NORMALIZATION MUST BE
 C     SCALED TO PREVENT OVER OR UNDERFLOW. CUOIK HAS DETERMINED THAT
 C     THE RESULT IS ON SCALE.
 C-----------------------------------------------------------------------
-      ACW = ZABS(CWR(2),CWI(2))
+      ACW = AZABS(CWR(2),CWI(2))
       ASCLE = 1.0D+3*D1MACH(1)/TOL
       CSCLR = 1.0D0
       IF (ACW.GT.ASCLE) GO TO 20
@@ -66,7 +66,7 @@ C-----------------------------------------------------------------------
       PTI = PTI + C2I
       CTR = ZRR*PTR - ZRI*PTI
       CTI = ZRR*PTI + ZRI*PTR
-      ACT = ZABS(CTR,CTI)
+      ACT = AZABS(CTR,CTI)
       RACT = 1.0D0/ACT
       CTR = CTR*RACT
       CTI = -CTI*RACT