C ALGORITHM 822, COLLECTED ALGORITHMS FROM ACM. C THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE, C VOL. 28,NO. 4, December, 2002, P. 436--447. #! /bin/sh # This is a shell archive, meaning: # 1. Remove everything above the #! /bin/sh line. # 2. Save the resulting text in a file. # 3. Execute the file with /bin/sh (not csh) to create the files: # Doc/ # Doc/Makefile # Fortran77/ # Fortran77/Drivers/ # Fortran77/Drivers/Dp/ # Fortran77/Drivers/Dp/driver.f # Fortran77/Drivers/Dp/port.f # Fortran77/Drivers/Dp/res1 # Fortran77/Drivers/Dp/res2 # Fortran77/Drivers/Dp/res3 # Fortran77/Drivers/Dp/res4 # Fortran77/Src/ # Fortran77/Src/Dp/ # Fortran77/Src/Dp/src.f # Fortran77/Src/Dp/src_819.f # This archive created: Wed Apr 16 10:42:34 2003 export PATH; PATH=/bin:$PATH if test ! -d 'Doc' then mkdir 'Doc' fi cd 'Doc' if test -f 'Makefile' then echo shar: will not over-write existing file "'Makefile'" else cat << "SHAR_EOF" > 'Makefile' FFLAGS= -sloppy -C -d5 -g -temp=/tmp -u FC=epcf90 OBJS = driver.o src.o airy.f port.f res : $(OBJS) $(FC) $(FFLAGS) $(OBJS) a.out SHAR_EOF fi # end of overwriting check cd .. if test ! -d 'Fortran77' then mkdir 'Fortran77' fi cd 'Fortran77' if test ! -d 'Drivers' then mkdir 'Drivers' fi cd 'Drivers' if test ! -d 'Dp' then mkdir 'Dp' fi cd 'Dp' if test -f 'driver.f' then echo shar: will not over-write existing file "'driver.f'" else cat << "SHAR_EOF" > 'driver.f' PROGRAM SCTEST CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC TEST PROGRAM OF HIZ, GIZ. TEST OF THE ADDITION FORMULAS: CCC A) UNSCALED FUNCTIONS: CCC HI(Z+W)=SUM_K W**K/K!HI^(K)(Z) (SAME FOR GI(Z)) CCC B) SCALED FUNCTIONS: CCC HI(Z+W)=EXP((2/3)*Z**(3/2))* CCC EXP(-(2/3)*(Z+W)**(3/2))* CCC SUM_K W**K/K!HI^(K)(Z) (SAME FOR GI(Z)) CCC CCC REMEMBER THAT HI(Z) IS SCALED IN THE SECTOR |ARG(Z)|<=PI/3 CCC WHILE GI(Z) IS SCALED IN THE SECTOR PI/3<=ARG(Z)<=PI. CCC BOTH THE UNSCALED AND SCALED FUNCTIONS ARE TESTED. CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC WARNING: LOSS OF RELATIVE ACCURACY FOR THE TEST OF THE CCC PHASE IS UNAVOIDABLE WHEN THE REAL OR IMAGINARY CCC PART VANISHES. CCC LOSS OF RELATIVE ACCURACY FOR THE TEST OF THE CCC MODULUS IS UNAVOIDABLE NEAR THE ZEROS OF THE CCC FUNCTION. CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC WE TEST THE RELATIONS FOR Z=R*EXP(I*PHI) WHERE CCC 0<=R<=30, 0<=PHI<=PI CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION PI,X,Y,R,PH,W DOUBLE PRECISION ERRO1M,ERRO1P,ERRO2M,ERRO2P,ERRO3M, + ERRO3P,ERRO4M,ERRO4P DOUBLE PRECISION EM1MAX,EM2MAX,EM3MAX,EM4MAX,EP1MAX, + EP2MAX,EP3MAX,EP4MAX INTEGER I,J,IFAC PI=3.1415926535897932385D0 OPEN(UNIT=10,FILE='Res3',STATUS='UNKNOWN') WRITE(10,*)' ' WRITE(10,*)'TEST OF THE UNSCALED HI(Z)' WRITE(10,*)'CHECK THE FOLLOWING RELATION:' WRITE(10,*)' ' WRITE(10,*)' HI(Z+W)=SUM_K W**K/K!HI^(K)(Z) ' WRITE(10,*)' ' WRITE(10,30)'X','Y','MODULUS','PHASE' OPEN(UNIT=11,FILE='Res4',STATUS='UNKNOWN') WRITE(11,*)' ' WRITE(11,*)'TEST OF THE SCALED HI(Z)' WRITE(11,*)'CHECK THE FOLLOWING RELATION:' WRITE(11,*)' ' WRITE(11,*)' HI(Z+W)=EXP((2/3)*Z**(3/2))* ' WRITE(11,*)' EXP(-(2/3)*(Z+W)**(3/2))*' WRITE(11,*)' SUM_K W**K/K!HI^(K)(Z) ' WRITE(11,30)'X','Y','MODULUS','PHASE' OPEN(UNIT=12,FILE='Res1',STATUS='UNKNOWN') WRITE(12,*)' ' WRITE(12,*)' ' WRITE(12,*)'TEST OF THE UNSCALED GI(Z)' WRITE(12,*)'CHECK THE FOLLOWING RELATION:' WRITE(12,*)' ' WRITE(12,*)' GI(Z+W)=SUM_K W**K/K!GI^(K)(Z) ' WRITE(12,*)' ' WRITE(12,30)'X','Y','MODULUS','PHASE' OPEN(UNIT=14,FILE='Res2',STATUS='UNKNOWN') WRITE(14,*)' ' WRITE(14,*)'TEST OF THE SCALED GI(Z)' WRITE(14,*)'CHECK THE FOLLOWING RELATION:' WRITE(14,*)' ' WRITE(14,*)' GI(Z+W)=EXP((2/3)*Z**(3/2))* ' WRITE(14,*)' EXP(-(2/3)*(Z+W)**(3/2))*' WRITE(14,*)' SUM_K W**K/K!GI^(K)(Z) ' WRITE(14,30)'X','Y','MODULUS','PHASE' EM1MAX=0.D0 EM2MAX=0.D0 EM3MAX=0.D0 EM4MAX=0.D0 EP1MAX=0.D0 EP2MAX=0.D0 EP3MAX=0.D0 EP4MAX=0.D0 W=0.1D0 DO 1 I=1,300,6 R=I*0.1D0 DO 2 J=10,1800,6 PH=J*PI/1800.D0 X=R*COS(PH) Y=R*SIN(PH) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC CHECK THE UNSCALED HI(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC IFAC=1 CALL HITEST(IFAC,X,Y,W,ERRO1M,ERRO1P) IF (ERRO1M.GT.EM1MAX) THEN EM1MAX=ERRO1M ENDIF IF (ERRO1P.GT.EP1MAX) THEN EP1MAX=ERRO1P ENDIF WRITE(10,33)X,Y,ERRO1M,ERRO1P IF (PH.LE.PI/3.D0) THEN CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC CHECK THE SCALED HI(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC IFAC=2 CALL HITEST(IFAC,X,Y,W,ERRO2M,ERRO2P) IF (ERRO2M.GT.EM2MAX) THEN EM2MAX=ERRO2M ENDIF IF (ERRO2P.GT.EP2MAX) THEN EP2MAX=ERRO2P ENDIF WRITE(11,33)X,Y,ERRO2M,ERRO2P ENDIF CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC CHECK THE UNSCALED GI(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC IFAC=1 CALL GITEST(IFAC,X,Y,W,ERRO3M,ERRO3P) IF (ERRO3M.GT.EM3MAX) THEN EM3MAX=ERRO3M ENDIF IF (ERRO3P.GT.EP3MAX) THEN EP3MAX=ERRO3P ENDIF WRITE(12,33)X,Y,ERRO3M,ERRO3P IF (R.GT.0.D0) THEN IF ((PH.GT.PI/3.D0).AND.(PH.LT.PI)) THEN CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC CHECK THE SCALED GI(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC IFAC=2 CALL GITEST(IFAC,X,Y,-W,ERRO4M,ERRO4P) IF (ERRO4M.GT.EM4MAX) THEN EM4MAX=ERRO4M ENDIF IF (ERRO4P.GT.EP4MAX) THEN EP4MAX=ERRO4P ENDIF WRITE(14,33)X,Y,ERRO4M,ERRO4P ENDIF ENDIF 2 CONTINUE 1 CONTINUE WRITE(10,*)' ' WRITE(10,*)'MAXIMUM VALUE OF THE MODULUS OF THE CHECK =',EM1MAX WRITE(10,*)' ' WRITE(10,*)'MAXIMUM VALUE OF THE PHASE OF THE CHECK =',EP1MAX WRITE(11,*)' ' WRITE(11,*)'MAXIMUM VALUE OF THE MODULUS OF THE CHECK =',EM2MAX WRITE(11,*)' ' WRITE(11,*)'MAXIMUM VALUE OF THE PHASE OF THE CHECK =',EP2MAX WRITE(12,*)' ' WRITE(12,*)'MAXIMUM VALUE OF THE MODULUS OF THE CHECK =',EM3MAX WRITE(12,*)' ' WRITE(12,*)'MAXIMUM VALUE OF THE PHASE OF THE CHECK =',EP3MAX WRITE(14,*)' ' WRITE(14,*)'MAXIMUM VALUE OF THE MODULUS OF THE CHECK =',EM4MAX WRITE(14,*)' ' WRITE(14,*)'MAXIMUM VALUE OF THE PHASE OF THE CHECK =',EP4MAX 30 FORMAT(6X,A1,18X,A1,12X,A5,11X,A5) C31 FORMAT(6X,A1,18X,A1,12X,A6) 33 FORMAT(D16.9,1X,D16.9,1X,D16.9,1X,D16.9) END SUBROUTINE HITEST(IFAC,X,Y,W,ERROR1,ERROR2) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCC TEST FOR HI(Z): CCCC IFAC=1: CCCC THE TEST IS BASED ON THE ADDITION CCCC FORMULA: CCCC HI(Z+W)=SUM(K=0,INFTY)W**K/K!HI(K)(Z) CCCC IFAC=2: CCCC TEST FOR NORMALIZED FUNCTIONS. CCCC THE ADDITION FORMULA READS NOW: CCCC HI(Z+W)=EXP((2/3*Z**3/2)* CCCC (1-(1+W/Z)**(3/2)))* CCCC SUM(K=0,INFTY)W**K/K!HI(K)(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X,Y,W DOUBLE PRECISION EPS,D1MACH,PI,F23,RH0,RH1,RH2,RH3,IH0,IH1, +IH2,IH3,RES,IMS,D,T,P,Q,IMSU DOUBLE PRECISION PH,PHASE,R,R2,R32,TH15,TH2,S1,C1,F23R,DF1, +DF2,S11,C11,DEX,DRE,DIMA,RZ32,RZ2 DOUBLE PRECISION W2,W3,RZW32,RDENO,RNUME,DMDENO,DRE2,DIMA2, +DRE3,DIMA3,RESU DOUBLE PRECISION DMODU1,DMODU2,DPHAS1,DPHAS2,ERROR1,ERROR2 DOUBLE PRECISION IZ2,IZ32,IZW32,IDENO,INUME INTEGER IFAC,K,N,IERROH EPS=D1MACH(3) PI=ACOS(-1.D0) F23=.6666666666666667D0 IF (IFAC.EQ.2) THEN PH=PHASE(X,Y) IF (PH.GT.PI/3.D0) THEN WRITE(*,*)'WARNING: THE TEST IS MEANINGLESS FOR H' WRITE(*,*)'Z IS OUTSIDE THE NORMALIZATION SECTOR' ENDIF ENDIF CALL HIZ(IFAC,X,Y,RH0,IH0,RH1,IH1,IERROH) IF (IFAC.EQ.1) THEN RH2=X*RH0-Y*IH0+1.D0/PI IH2=Y*RH0+X*IH0 ELSE PH=PHASE(X,Y) R=SQRT(X*X+Y*Y) R2=R*R R32=R*SQRT(R) TH15=1.5D0*PH TH2=2.D0*PH S1=SIN(TH15) C1=COS(TH15) F23R=F23*R32 DF1=F23R*C1 DF2=F23R*S1 S11=SIN(DF2) C11=COS(DF2) DEX=EXP(-DF1) DRE=DEX*C11 DIMA=-DEX*S11 RH2=X*RH0-Y*IH0+DRE/PI IH2=Y*RH0+X*IH0+DIMA/PI RZ32=R32*C1 IZ32=R32*S1 RZ2=R2*COS(TH2) IZ2=R2*SIN(TH2) ENDIF T=W RES=RH0+T*RH1 IMS=IH0+T*IH1 T=T*W/2.D0 RES=RES+T*RH2 IMS=IMS+T*IH2 K=0 N=3 D=1.D0 50 RH3=X*RH1-Y*IH1+(K+1)*RH0 IH3=Y*RH1+X*IH1+(K+1)*IH0 T=T*W/N N=N+1 K=K+1 P=T*RH3 Q=T*IH3 D=ABS(P)+ABS(Q) RES=RES+P IMS=IMS+Q RH0=RH1 IH0=IH1 RH1=RH2 IH1=IH2 RH2=RH3 IH2=IH3 IF (RES.NE.0) THEN IF (ABS(P/RES).GT.EPS) GOTO 50 ENDIF IF (IMS.NE.0) THEN IF (ABS(Q/IMS).GT.EPS) GOTO 50 ENDIF CALL HIZ(IFAC,X+W,Y,RH0,IH0,RH1,IH1,IERROH) IF (IFAC.EQ.2) THEN W2=W*W W3=W2*W PH=PHASE(X+W,Y) R=SQRT((X+W)*(X+W)+Y*Y) R32=R*SQRT(R) TH15=1.5D0*PH S1=SIN(TH15) C1=COS(TH15) RZW32=R32*C1 IZW32=R32*S1 RDENO=RZ32+RZW32 IDENO=IZ32+IZW32 RNUME=-(2.D0*RZ2*W+2.D0*X*W2+2.D0/3.D0*W3) INUME=-(2.D0*IZ2*W+2.D0*Y*W2) DMDENO=RDENO*RDENO+IDENO*IDENO DRE2=(RNUME*RDENO+INUME*IDENO)/DMDENO DIMA2=(INUME*RDENO-RNUME*IDENO)/DMDENO DRE3=EXP(DRE2)*COS(DIMA2) DIMA3=EXP(DRE2)*SIN(DIMA2) RESU=RES*DRE3-IMS*DIMA3 IMSU=RES*DIMA3+IMS*DRE3 RES=RESU IMS=IMSU ENDIF DMODU1=ABS(RH0)+ABS(IH0) DMODU2=ABS(RES)+ABS(IMS) DPHAS1=IH0/RH0 DPHAS2=IMS/RES IF (DMODU2.NE.0.D0) THEN ERROR1=ABS(1.D0-DMODU1/DMODU2) ENDIF IF (DPHAS2.NE.0.D0) THEN ERROR2=ABS(1.D0-DPHAS1/DPHAS2) ENDIF END SUBROUTINE GITEST(IFAC,X,Y,W,ERROR1,ERROR2) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCC TEST FOR GI(Z): CCCC IFAC=1: CCCC THE TEST IS BASED ON THE ADDITION CCCC FORMULA: CCCC GI(Z+W)=SUM(K=0,INFTY)W**K/K!GI(K)(Z) CCCC IFAC=2: CCCC TEST FOR NORMALIZED FUNCTIONS. CCCC THE ADDITION FORMULA READS NOW: CCCC GI(Z+W)=EXP(-(2/3*Z**3/2)* CCCC (1-(1+W/Z)**(3/2)))* CCCC SUM(K=0,INFTY)W**K/K!GI(K)(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X,Y,W DOUBLE PRECISION EPS,D1MACH,PI,F23,RH0,RH1,RH2,RH3,IH0,IH1, +IH2,IH3,RES,IMS,D,T,P,Q,IMSU DOUBLE PRECISION PH,PHASE,R,R2,R32,TH15,TH2,S1,C1,F23R,DF1, +DF2,S11,C11,DEX,DRE,DIMA,RZ32,RZ2 DOUBLE PRECISION W2,W3,RZW32,RDENO,RNUME,DMDENO,DRE2,DIMA2, +DRE3,DIMA3,RESU DOUBLE PRECISION DMODU1,DMODU2,DPHAS1,DPHAS2,ERROR1,ERROR2 DOUBLE PRECISION IZ2,IZ32,IZW32,IDENO,INUME INTEGER IFAC,K,N,IERROH EPS=D1MACH(3) PI=ACOS(-1.D0) F23=.6666666666666667D0 IF (IFAC.EQ.2) THEN PH=PHASE(X,Y) IF (PH.LT.PI/3.D0) THEN WRITE(*,*)'WARNING: THE TEST IS MEANINGLESS FOR G' WRITE(*,*)'Z IS OUTSIDE THE NORMALIZATION SECTOR' ENDIF ENDIF CALL GIZ(IFAC,X,Y,RH0,IH0,RH1,IH1,IERROH) IF (IFAC.EQ.1) THEN RH2=X*RH0-Y*IH0-1.D0/PI IH2=Y*RH0+X*IH0 ELSE PH=PHASE(X,Y) R=SQRT(X*X+Y*Y) R2=R*R R32=R*SQRT(R) TH15=1.5D0*PH TH2=2.D0*PH S1=SIN(TH15) C1=COS(TH15) F23R=F23*R32 DF1=F23R*C1 DF2=F23R*S1 S11=SIN(DF2) C11=COS(DF2) DEX=EXP(DF1) DRE=DEX*C11 DIMA=DEX*S11 RH2=X*RH0-Y*IH0-DRE/PI IH2=Y*RH0+X*IH0-DIMA/PI RZ32=R32*C1 IZ32=R32*S1 RZ2=R2*COS(TH2) IZ2=R2*SIN(TH2) ENDIF T=W RES=RH0+T*RH1 IMS=IH0+T*IH1 T=T*W/2.D0 RES=RES+T*RH2 IMS=IMS+T*IH2 K=0 N=3 D=1.D0 51 RH3=X*RH1-Y*IH1+(K+1)*RH0 IH3=Y*RH1+X*IH1+(K+1)*IH0 T=T*W/N N=N+1 K=K+1 P=T*RH3 Q=T*IH3 D=ABS(P)+ABS(Q) RES=RES+P IMS=IMS+Q RH0=RH1 IH0=IH1 RH1=RH2 IH1=IH2 RH2=RH3 IH2=IH3 IF (RES.NE.0) THEN IF (ABS(P/RES).GT.EPS) GOTO 51 ENDIF IF (IMS.NE.0) THEN IF (ABS(Q/IMS).GT.EPS) GOTO 51 ENDIF CALL GIZ(IFAC,X+W,Y,RH0,IH0,RH1,IH1,IERROH) IF (IFAC.EQ.2) THEN W2=W*W W3=W2*W PH=PHASE(X+W,Y) R=SQRT((X+W)*(X+W)+Y*Y) R32=R*SQRT(R) TH15=1.5D0*PH S1=SIN(TH15) C1=COS(TH15) RZW32=R32*C1 IZW32=R32*S1 RDENO=RZ32+RZW32 IDENO=IZ32+IZW32 RNUME=(2.D0*RZ2*W+2.D0*X*W2+2.D0/3.D0*W3) INUME=(2.D0*IZ2*W+2.D0*Y*W2) DMDENO=RDENO*RDENO+IDENO*IDENO DRE2=(RNUME*RDENO+INUME*IDENO)/DMDENO DIMA2=(INUME*RDENO-RNUME*IDENO)/DMDENO DRE3=EXP(DRE2)*COS(DIMA2) DIMA3=EXP(DRE2)*SIN(DIMA2) RESU=RES*DRE3-IMS*DIMA3 IMSU=RES*DIMA3+IMS*DRE3 RES=RESU IMS=IMSU ENDIF DMODU1=ABS(RH0)+ABS(IH0) DMODU2=ABS(RES)+ABS(IMS) DPHAS1=IH0/RH0 DPHAS2=IMS/RES IF (DMODU2.NE.0.D0) THEN ERROR1=ABS(1.D0-DMODU1/DMODU2) ENDIF IF (DPHAS2.NE.0.D0) THEN ERROR2=ABS(1.D0-DPHAS1/DPHAS2) ENDIF END SHAR_EOF fi # end of overwriting check if test -f 'port.f' then echo shar: will not over-write existing file "'port.f'" else cat << "SHAR_EOF" > 'port.f' DOUBLE PRECISION FUNCTION D1MACH(I) INTEGER I C C DOUBLE-PRECISION MACHINE CONSTANTS C D1MACH( 1) = B**(EMIN-1), THE SMALLEST POSITIVE MAGNITUDE. C D1MACH( 2) = B**EMAX*(1 - B**(-T)), THE LARGEST MAGNITUDE. C D1MACH( 3) = B**(-T), THE SMALLEST RELATIVE SPACING. C D1MACH( 4) = B**(1-T), THE LARGEST RELATIVE SPACING. C D1MACH( 5) = LOG10(B) C INTEGER SMALL(2) INTEGER LARGE(2) INTEGER RIGHT(2) INTEGER DIVER(2) INTEGER LOG10(2) INTEGER SC, CRAY1(38), J COMMON /D9MACH/ CRAY1 SAVE SMALL, LARGE, RIGHT, DIVER, LOG10, SC DOUBLE PRECISION DMACH(5) EQUIVALENCE (DMACH(1),SMALL(1)) EQUIVALENCE (DMACH(2),LARGE(1)) EQUIVALENCE (DMACH(3),RIGHT(1)) EQUIVALENCE (DMACH(4),DIVER(1)) EQUIVALENCE (DMACH(5),LOG10(1)) C THIS VERSION ADAPTS AUTOMATICALLY TO MOST CURRENT MACHINES. C R1MACH CAN HANDLE AUTO-DOUBLE COMPILING, BUT THIS VERSION OF C D1MACH DOES NOT, BECAUSE WE DO NOT HAVE QUAD CONSTANTS FOR C MANY MACHINES YET. C TO COMPILE ON OLDER MACHINES, ADD A C IN COLUMN 1 C ON THE NEXT LINE DATA SC/0/ C AND REMOVE THE C FROM COLUMN 1 IN ONE OF THE SECTIONS BELOW. C CONSTANTS FOR EVEN OLDER MACHINES CAN BE OBTAINED BY C mail netlib@research.bell-labs.com C send old1mach from blas C PLEASE SEND CORRECTIONS TO dmg OR ehg@bell-labs.com. C C MACHINE CONSTANTS FOR THE HONEYWELL DPS 8/70 SERIES. C DATA SMALL(1),SMALL(2) / O402400000000, O000000000000 / C DATA LARGE(1),LARGE(2) / O376777777777, O777777777777 / C DATA RIGHT(1),RIGHT(2) / O604400000000, O000000000000 / C DATA DIVER(1),DIVER(2) / O606400000000, O000000000000 / C DATA LOG10(1),LOG10(2) / O776464202324, O117571775714 /, SC/987/ C C MACHINE CONSTANTS FOR PDP-11 FORTRANS SUPPORTING C 32-BIT INTEGERS. C DATA SMALL(1),SMALL(2) / 8388608, 0 / C DATA LARGE(1),LARGE(2) / 2147483647, -1 / C DATA RIGHT(1),RIGHT(2) / 612368384, 0 / C DATA DIVER(1),DIVER(2) / 620756992, 0 / C DATA LOG10(1),LOG10(2) / 1067065498, -2063872008 /, SC/987/ C C MACHINE CONSTANTS FOR THE UNIVAC 1100 SERIES. C DATA SMALL(1),SMALL(2) / O000040000000, O000000000000 / C DATA LARGE(1),LARGE(2) / O377777777777, O777777777777 / C DATA RIGHT(1),RIGHT(2) / O170540000000, O000000000000 / C DATA DIVER(1),DIVER(2) / O170640000000, O000000000000 / C DATA LOG10(1),LOG10(2) / O177746420232, O411757177572 /, SC/987/ C C ON FIRST CALL, IF NO DATA UNCOMMENTED, TEST MACHINE TYPES. IF (SC .NE. 987) THEN DMACH(1) = 1.D13 IF ( SMALL(1) .EQ. 1117925532 * .AND. SMALL(2) .EQ. -448790528) THEN * *** IEEE BIG ENDIAN *** SMALL(1) = 1048576 SMALL(2) = 0 LARGE(1) = 2146435071 LARGE(2) = -1 RIGHT(1) = 1017118720 RIGHT(2) = 0 DIVER(1) = 1018167296 DIVER(2) = 0 LOG10(1) = 1070810131 LOG10(2) = 1352628735 ELSE IF ( SMALL(2) .EQ. 1117925532 * .AND. SMALL(1) .EQ. -448790528) THEN * *** IEEE LITTLE ENDIAN *** SMALL(2) = 1048576 SMALL(1) = 0 LARGE(2) = 2146435071 LARGE(1) = -1 RIGHT(2) = 1017118720 RIGHT(1) = 0 DIVER(2) = 1018167296 DIVER(1) = 0 LOG10(2) = 1070810131 LOG10(1) = 1352628735 ELSE IF ( SMALL(1) .EQ. -2065213935 * .AND. SMALL(2) .EQ. 10752) THEN * *** VAX WITH D_FLOATING *** SMALL(1) = 128 SMALL(2) = 0 LARGE(1) = -32769 LARGE(2) = -1 RIGHT(1) = 9344 RIGHT(2) = 0 DIVER(1) = 9472 DIVER(2) = 0 LOG10(1) = 546979738 LOG10(2) = -805796613 ELSE IF ( SMALL(1) .EQ. 1267827943 * .AND. SMALL(2) .EQ. 704643072) THEN * *** IBM MAINFRAME *** SMALL(1) = 1048576 SMALL(2) = 0 LARGE(1) = 2147483647 LARGE(2) = -1 RIGHT(1) = 856686592 RIGHT(2) = 0 DIVER(1) = 873463808 DIVER(2) = 0 LOG10(1) = 1091781651 LOG10(2) = 1352628735 ELSE IF ( SMALL(1) .EQ. 1120022684 * .AND. SMALL(2) .EQ. -448790528) THEN * *** CONVEX C-1 *** SMALL(1) = 1048576 SMALL(2) = 0 LARGE(1) = 2147483647 LARGE(2) = -1 RIGHT(1) = 1019215872 RIGHT(2) = 0 DIVER(1) = 1020264448 DIVER(2) = 0 LOG10(1) = 1072907283 LOG10(2) = 1352628735 ELSE IF ( SMALL(1) .EQ. 815547074 * .AND. SMALL(2) .EQ. 58688) THEN * *** VAX G-FLOATING *** SMALL(1) = 16 SMALL(2) = 0 LARGE(1) = -32769 LARGE(2) = -1 RIGHT(1) = 15552 RIGHT(2) = 0 DIVER(1) = 15568 DIVER(2) = 0 LOG10(1) = 1142112243 LOG10(2) = 2046775455 ELSE DMACH(2) = 1.D27 + 1 DMACH(3) = 1.D27 LARGE(2) = LARGE(2) - RIGHT(2) IF (LARGE(2) .EQ. 64 .AND. SMALL(2) .EQ. 0) THEN CRAY1(1) = 67291416 DO 10 J = 1, 20 CRAY1(J+1) = CRAY1(J) + CRAY1(J) 10 CONTINUE CRAY1(22) = CRAY1(21) + 321322 DO 20 J = 22, 37 CRAY1(J+1) = CRAY1(J) + CRAY1(J) 20 CONTINUE IF (CRAY1(38) .EQ. SMALL(1)) THEN * *** CRAY *** CALL I1MCRY(SMALL(1), J, 8285, 8388608, 0) SMALL(2) = 0 CALL I1MCRY(LARGE(1), J, 24574, 16777215, 16777215) CALL I1MCRY(LARGE(2), J, 0, 16777215, 16777214) CALL I1MCRY(RIGHT(1), J, 16291, 8388608, 0) RIGHT(2) = 0 CALL I1MCRY(DIVER(1), J, 16292, 8388608, 0) DIVER(2) = 0 CALL I1MCRY(LOG10(1), J, 16383, 10100890, 8715215) CALL I1MCRY(LOG10(2), J, 0, 16226447, 9001388) ELSE WRITE(*,9000) STOP 779 END IF ELSE WRITE(*,9000) STOP 779 END IF END IF SC = 987 END IF * SANITY CHECK IF (DMACH(4) .GE. 1.0D0) STOP 778 IF (I .LT. 1 .OR. I .GT. 5) THEN WRITE(*,*) 'D1MACH(I): I =',I,' is out of bounds.' STOP END IF D1MACH = DMACH(I) RETURN 9000 FORMAT(/' Adjust D1MACH by uncommenting data statements'/ *' appropriate for your machine.') * /* Standard C source for D1MACH -- remove the * in column 1 */ *#include *#include *#include *double d1mach_(long *i) *{ * switch(*i){ * case 1: return DBL_MIN; * case 2: return DBL_MAX; * case 3: return DBL_EPSILON/FLT_RADIX; * case 4: return DBL_EPSILON; * case 5: return log10((double)FLT_RADIX); * } * fprintf(stderr, "invalid argument: d1mach(%ld)\n", *i); * exit(1); return 0; /* some compilers demand return values */ *} END SUBROUTINE I1MCRY(A, A1, B, C, D) **** SPECIAL COMPUTATION FOR OLD CRAY MACHINES **** INTEGER A, A1, B, C, D A1 = 16777216*B + C A = 16777216*A1 + D END SHAR_EOF fi # end of overwriting check if test -f 'res1' then echo shar: will not over-write existing file "'res1'" else cat << "SHAR_EOF" > 'res1' TEST OF THE UNSCALED GI(Z) CHECK THE FOLLOWING RELATION: GI(Z+W)=SUM_K W**K/K!GI^(K)(Z) X Y MODUL PHASE 0.999847695D-01 0.174524064D-02 0.111022302D-15 0.333066907D-15 0.999610115D-01 0.279216387D-02 0.111022302D-15 0.666133815D-15 0.999262916D-01 0.383878091D-02 0.111022302D-15 0.222044605D-15 0.998806137D-01 0.488497698D-02 0.000000000D+00 0.777156117D-15 0.998239828D-01 0.593063736D-02 0.777156117D-15 0.666133815D-15 0.997564050D-01 0.697564737D-02 0.222044605D-15 0.222044605D-15 0.996778878D-01 0.801989243D-02 0.333066907D-15 0.444089210D-15 0.995884399D-01 0.906325802D-02 0.222044605D-15 0.444089210D-15 0.994880709D-01 0.101056297D-01 0.222044605D-15 0.222044605D-15 0.993767919D-01 0.111468932D-01 0.444089210D-15 0.444089210D-15 0.992546152D-01 0.121869343D-01 0.000000000D+00 0.444089210D-15 0.991215540D-01 0.132256390D-01 0.555111512D-15 0.888178420D-15 0.989776231D-01 0.142628934D-01 0.000000000D+00 0.222044605D-15 0.988228381D-01 0.152985836D-01 0.444089210D-15 0.111022302D-15 0.986572162D-01 0.163325962D-01 0.000000000D+00 0.444089210D-15 0.984807753D-01 0.173648178D-01 0.333066907D-15 0.666133815D-15 0.982935349D-01 0.183951351D-01 0.444089210D-15 0.000000000D+00 0.980955155D-01 0.194234351D-01 0.222044605D-15 0.333066907D-15 0.978867389D-01 0.204496052D-01 0.000000000D+00 0.222044605D-15 0.976672278D-01 0.214735327D-01 0.000000000D+00 0.222044605D-15 0.974370065D-01 0.224951054D-01 0.222044605D-15 0.555111512D-15 0.971961001D-01 0.235142113D-01 0.000000000D+00 0.888178420D-15 0.969445350D-01 0.245307386D-01 0.111022302D-15 0.222044605D-15 0.966823389D-01 0.255445758D-01 0.222044605D-15 0.555111512D-15 0.964095404D-01 0.265556117D-01 0.000000000D+00 0.333066907D-15 0.961261696D-01 0.275637356D-01 0.222044605D-15 0.111022302D-14 0.958322574D-01 0.285688367D-01 0.111022302D-15 0.000000000D+00 0.955278362D-01 0.295708050D-01 0.111022302D-15 0.777156117D-15 0.952129393D-01 0.305695305D-01 0.444089210D-15 0.666133815D-15 0.948876012D-01 0.315649037D-01 0.333066907D-15 0.444089210D-15 0.945518576D-01 0.325568154D-01 0.222044605D-15 0.222044605D-15 0.942057453D-01 0.335451570D-01 0.666133815D-15 0.111022302D-14 0.938493023D-01 0.345298199D-01 0.222044605D-15 0.333066907D-15 0.934825676D-01 0.355106962D-01 0.444089210D-15 0.777156117D-15 0.931055816D-01 0.364876784D-01 0.222044605D-15 0.222044605D-15 0.927183855D-01 0.374606593D-01 0.222044605D-15 0.333066907D-15 0.923210217D-01 0.384295323D-01 0.222044605D-15 0.000000000D+00 0.919135339D-01 0.393941910D-01 0.000000000D+00 0.444089210D-15 0.914959668D-01 0.403545296D-01 0.222044605D-15 0.666133815D-15 0.910683661D-01 0.413104430D-01 0.444089210D-15 0.777156117D-15 0.906307787D-01 0.422618262D-01 0.222044605D-15 0.444089210D-15 0.901832526D-01 0.432085749D-01 0.222044605D-15 0.444089210D-15 0.897258370D-01 0.441505853D-01 0.222044605D-15 0.777156117D-15 0.892585818D-01 0.450877541D-01 0.222044605D-15 0.000000000D+00 0.887815385D-01 0.460199785D-01 0.222044605D-15 0.000000000D+00 0.882947593D-01 0.469471563D-01 0.000000000D+00 0.222044605D-15 0.877982975D-01 0.478691858D-01 0.333066907D-15 0.444089210D-15 0.872922077D-01 0.487859659D-01 0.000000000D+00 0.444089210D-15 0.867765453D-01 0.496973961D-01 0.333066907D-15 0.666133815D-15 0.862513669D-01 0.506033764D-01 0.000000000D+00 0.222044605D-15 0.857167301D-01 0.515038075D-01 0.000000000D+00 0.111022302D-15 0.851726934D-01 0.523985906D-01 0.444089210D-15 0.444089210D-15 0.846193166D-01 0.532876276D-01 0.000000000D+00 0.333066907D-15 0.840566603D-01 0.541708210D-01 0.222044605D-15 0.000000000D+00 0.834847863D-01 0.550480740D-01 0.444089210D-15 0.888178420D-15 0.829037573D-01 0.559192903D-01 0.000000000D+00 0.111022302D-15 0.823136369D-01 0.567843745D-01 0.000000000D+00 0.000000000D+00 0.817144898D-01 0.576432316D-01 0.444089210D-15 0.888178420D-15 0.811063819D-01 0.584957675D-01 0.222044605D-15 0.444089210D-15 0.804893797D-01 0.593418887D-01 0.222044605D-15 0.222044605D-15 0.798635510D-01 0.601815023D-01 0.222044605D-15 0.444089210D-15 0.792289643D-01 0.610145164D-01 0.333066907D-15 0.888178420D-15 0.785856893D-01 0.618408395D-01 0.222044605D-15 0.888178420D-15 0.779337965D-01 0.626603811D-01 0.000000000D+00 0.222044605D-15 0.772733573D-01 0.634730513D-01 0.222044605D-15 0.333066907D-15 0.766044443D-01 0.642787610D-01 0.000000000D+00 0.666133815D-15 0.759271307D-01 0.650774217D-01 0.222044605D-15 0.666133815D-15 0.752414909D-01 0.658689460D-01 0.000000000D+00 0.444089210D-15 0.745476000D-01 0.666532470D-01 0.000000000D+00 0.666133815D-15 0.738455341D-01 0.674302388D-01 0.333066907D-15 0.222044605D-15 0.731353702D-01 0.681998360D-01 0.222044605D-15 0.777156117D-15 0.724171861D-01 0.689619544D-01 0.111022302D-15 0.222044605D-15 0.716910608D-01 0.697165103D-01 0.000000000D+00 0.111022302D-15 0.709570737D-01 0.704634210D-01 0.222044605D-15 0.333066907D-15 0.702153053D-01 0.712026046D-01 0.222044605D-15 0.666133815D-15 0.694658370D-01 0.719339800D-01 0.000000000D+00 0.666133815D-15 0.687087511D-01 0.726574671D-01 0.222044605D-15 0.222044605D-15 0.679441304D-01 0.733729865D-01 0.222044605D-15 0.000000000D+00 0.671720589D-01 0.740804596D-01 0.666133815D-15 0.444089210D-15 0.663926213D-01 0.747798090D-01 0.222044605D-15 0.222044605D-15 0.656059029D-01 0.754709580D-01 0.444089210D-15 0.000000000D+00 0.648119901D-01 0.761538308D-01 0.222044605D-15 0.222044605D-15 0.640109699D-01 0.768283524D-01 0.444089210D-15 0.666133815D-15 0.632029303D-01 0.774944489D-01 0.222044605D-15 0.666133815D-15 0.623879597D-01 0.781520472D-01 0.222044605D-15 0.000000000D+00 0.615661475D-01 0.788010754D-01 0.111022302D-15 0.222044605D-15 0.607375840D-01 0.794414621D-01 0.222044605D-15 0.000000000D+00 0.599023599D-01 0.800731371D-01 0.222044605D-15 0.000000000D+00 0.590605668D-01 0.806960312D-01 0.333066907D-15 0.222044605D-15 0.582122970D-01 0.813100761D-01 0.222044605D-15 0.333066907D-15 0.573576436D-01 0.819152044D-01 0.333066907D-15 0.444089210D-15 0.564967003D-01 0.825113498D-01 0.111022302D-15 0.000000000D+00 0.556295616D-01 0.830984469D-01 0.222044605D-15 0.000000000D+00 0.547563223D-01 0.836764313D-01 0.333066907D-15 0.555111512D-15 0.538770785D-01 0.842452397D-01 0.222044605D-15 0.000000000D+00 0.529919264D-01 0.848048096D-01 0.222044605D-15 0.222044605D-15 0.521009632D-01 0.853550797D-01 0.000000000D+00 0.222044605D-15 0.512042865D-01 0.858959897D-01 0.444089210D-15 0.222044605D-15 0.503019947D-01 0.864274802D-01 0.222044605D-15 0.999200722D-15 0.493941867D-01 0.869494930D-01 0.222044605D-15 0.333066907D-15 0.484809620D-01 0.874619707D-01 0.111022302D-15 0.666133815D-15 0.475624209D-01 0.879648573D-01 0.444089210D-15 0.000000000D+00 0.466386640D-01 0.884580975D-01 0.222044605D-15 0.444089210D-15 0.457097927D-01 0.889416373D-01 0.111022302D-15 0.666133815D-15 0.447759088D-01 0.894154237D-01 0.222044605D-15 0.000000000D+00 0.438371147D-01 0.898794046D-01 0.222044605D-15 0.222044605D-15 0.428935133D-01 0.903335293D-01 0.111022302D-15 0.111022302D-15 0.419452082D-01 0.907777479D-01 0.111022302D-15 0.222044605D-15 0.409923034D-01 0.912120116D-01 0.000000000D+00 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