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524f1.f
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C ABCDEFGHIJKLMNOPQRSTUVWXYZ$0123456789+-*/=(),. MP000011
C MP000021
C MP (VERSION 780802) MP000031
C ******************** MP000041
C MP000051
C $$ ****** COMMENTS ****** MP000061
C MP000071
C MP IS A MULTIPLE-PRECISION FLOATING-POINT ARITHMETIC PACKAGE. MP000081
C IT IS ALMOST COMPLETELY MACHINE-INDEPENDENT, AND SHOULD MP000091
C RUN ON ANY MACHINE WITH AN ANSI STANDARD FORTRAN COMPILER, MP000101
C SUFFICIENT MEMORY, AND A WORDLENGTH OF AT LEAST 16 BITS. MP000111
C MP000121
C FOR A GENERAL DESCRIPTION OF THE PHILOSOPHY AND DESIGN OF MP, MP000131
C SEE - R. P. BRENT, A FORTRAN MULTIPLE-PRECISION ARITHMETIC MP000141
C PACKAGE, ACM TRANS. MATH. SOFTWARE 4 (MARCH 1978), 57-70. MP000151
C SOME ADDITIONAL DETAILS ARE GIVEN IN THE SAME ISSUE, 71-81. MP000161
C FOR DETAILS OF THE IMPLEMENTATION, CALLING SEQUENCES ETC. SEE MP000171
C THE MP USERS GUIDE. MP000181
C MP000191
C MP IS NORMALLY DISTRIBUTED IN FIVE FILES. ALL HAVE 80 CHARACTER MP000201
C LOGICAL RECORDS AND USE ONLY THE (STANDARD FORTRAN) CHARACTERS MP000211
C APPEARING IN LINE MP000011. MP000221
C MP000231
C FILE 1 - THESE COMMENTS AND EXAMPLE PROGRAM. MP000241
C FILE 2 - MP SUBROUTINES (EXCLUDING EXAMPLE AND TEST PROGRAMS). MP000251
C FILE 3 - TEST PROGRAMS (NOT USING AUGMENT INTERFACE). MP000261
C FILE 4 - MP USERS GUIDE. MP000271
C FILE 5 - AUGMENT DESCRIPTION DECK AND JACOBI PROGRAM USING IT. MP000281
C (MP MAY BE USED WITH THE AUGMENT PREPROCESSOR. FOR MP000291
C DETAILS SEE SECTION 4 OF THE USERS GUIDE.) MP000301
C MP000311
C TO INSTALL MP, READ THESE FIVE FILES. PRINT FILE 4 (THE USERS GUIDE) MP000321
C USING THE FIRST CHARACTER (BLANK, 0 OR 1) AS STANDARD FORTRAN MP000331
C PRINTER CONTROL. THEN FOLLOW THE INSTRUCTIONS GIVEN IN SECTION 5 MP000341
C OF THE USERS GUIDE. MP000351
C MP000361
C MP000371
C MP000381
C $$ ****** EXAMPLE ****** MP005460
C MP005470
C THIS PROGRAM COMPUTES PI AND EXP(PI*SQRT(163/9)) TO 100 MP005480
C DECIMAL PLACES, AND EXP(PI*SQRT(163)) TO 90 DECIMAL PLACES, MP005490
C AND WRITES THEM ON LOGICAL UNIT 6. EXECUTION MP005500
C TIME ON A UNIVAC 1108 (WITH FORTRAN SE1D) IS 1.051 SECONDS. MP005510
C MP005520
C TO RUN EXAMPLE THE FOLLOWING MP ROUTINES ARE REQUIRED - MPABS, MP005530
C MPADD, MPADDI, MPADD2, MPADD3, MPART1, MPCHK, MPCIM, MPCLR, MPCMF, MP005540
C MPCMI, MPCMPR, MPCMR, MPCOMP, MPCQM, MPCRM, MPDIVI, MPERR, MP005550
C MPEXP, MPEXP1, MPGCD, MPLNI, MPL235, MPMAXR, MPMLP, MPMUL, MP005560
C MPMULI, MPMULQ, MPMUL2, MPNZR, MPOUT, MPOUT2, MPOVFL, MPPI, MP005570
C MPPWR, MPQPWR, MPREC, MPROOT, MPSET, MPSTR, MPSUB, MPUNFL. MP005580
C MP005590
C CORRECT OUTPUT (EXCLUDING HEADINGS) IS AS FOLLOWS MP005600
C MP005610
C 3.14159265358979323846264338327950288419716939937510 MP005620
C 58209749445923078164062862089986280348253421170680 MP005630
C 640320.00000000060486373504901603947174181881853947577148 MP005640
C 57603665918194652218258286942536340815822646477590 MP005650
C 262537412640768743.99999999999925007259719818568887935385633733699086 MP005660
C 2707537410378210647910118607312951181346 MP005670
C MP005680
C CERTAIN PARAMETERS AND WORKING SPACE IN COMMON. MP005690
COMMON B, T, M, LUN, MXR, R MP005700
C MP005710
C MPEXP REQUIRES 4T+10 WORDS AND WE HAVE T .LE. 62 IF WORDLENGTH MP005720
C AT LEAST 16 BITS, SO 4T+10 .LE. 258. DIMENSIONS CAN BE REDUCED MP005730
C IF WORDLENGTH IS GREATER THAN 16 BITS. MP005740
INTEGER B, T, R(258) MP005750
C MP005760
C VARIABLES NEED T+2 .LE. 64 WORDS AND ALLOW 110 CHARACTERS FOR MP005770
C DECIMAL OUTPUT MP005780
INTEGER PI(64), X(64), C(110) MP005790
C MP005800
C CALL MPSET TO SET OUTPUT LOGICAL UNIT = 6 AND EQUIVALENT MP005810
C NUMBER OF DECIMAL PLACES TO AT LEAST 110. THE LAST TWO MP005820
C PARAMETERS ARE THE DIMENSIONS OF PI (OR X) AND R. MP005830
CALL MPSET (6, 110, 64, 258) MP005840
C MP005850
C COMPUTE MULTIPLE-PRECISION PI MP005860
CALL MPPI(PI) MP005870
C MP005880
C CONVERT TO PRINTABLE FORMAT (F110.100) AND WRITE MP005890
CALL MPOUT (PI, C, 110, 100) MP005900
WRITE (LUN, 10) B, T, C MP005910
10 FORMAT (32H1EXAMPLE OF MP PACKAGE, BASE =, I9, MP005920
$ 12H, DIGITS =, I4 /// 11H PI TO 100D // MP005930
$ 11X, 60A1 / 21X, 50A1) MP005940
C MP005950
C SET X = SQRT(163/9), THEN MULTIPLY BY PI MP005960
CALL MPQPWR (163, 9, 1, 2, X) MP005970
CALL MPMUL (X, PI, X) MP005980
C MP005990
C SET X = EXP(X) MP006000
CALL MPEXP (X, X) MP006010
C MP006020
C CONVERT TO PRINTABLE FORMAT AND WRITE MP006030
CALL MPOUT (X, C, 110, 100) MP006040
WRITE (LUN, 20) C MP006050
20 FORMAT (/ 28H EXP(PI*SQRT(163/9)) TO 100D // MP006060
$ 11X, 60A1 / 21X, 50A1) MP006070
C MP006080
C SET X = X**3 = EXP(PI*SQRT(163)) MP006090
CALL MPPWR (X, 3, X) MP006100
C MP006110
C WRITE IN FORMAT F110.90 MP006120
CALL MPOUT (X, C, 110, 90) MP006130
WRITE (LUN, 30) C MP006140
30 FORMAT (/ 25H EXP(PI*SQRT(163)) TO 90D // MP006150
$ 1X, 70A1 / 21X, 40A1) MP006160
STOP MP006170
END MP006180
SUBROUTINE MPABS (X, Y) MP006200
C SETS Y = ABS(X) FOR MP NUMBERS X AND Y
INTEGER X(1), Y(1)
CALL MPSTR (X, Y)
Y(1) = IABS(Y(1))
RETURN
END
SUBROUTINE MPADD (X, Y, Z) MP006280
C ADDS X AND Y, FORMING RESULT IN Z, WHERE X, Y AND Z ARE MP
C NUMBERS. FOUR GUARD DIGITS ARE USED, AND THEN R*-ROUNDING.
INTEGER X(1), Y(1), Z(1)
CALL MPADD2 (X, Y, Z, Y, 0)
RETURN
END
SUBROUTINE MPADDI (X, IY, Z) MP006360
C ADDS MULTIPLE-PRECISION X TO INTEGER IY
C GIVING MULTIPLE-PRECISION Z.
C DIMENSION OF R IN CALLING PROGRAM MUST BE
C AT LEAST 2T+6 (BUT Z(1) MAY BE R(T+5)).
COMMON B, T, M, LUN, MXR, R
C DIMENSION R(6) BECAUSE RALPH COMPILER ON UNIVAC 1100 COMPUTERS
C OBJECTS TO DIMENSION R(1).
INTEGER B, T, R(6), X(1), Z(1)
C CHECK LEGALITY OF B, T, M, LUN AND MXR
CALL MPCHK (2, 6)
CALL MPCIM (IY, R(T+5))
CALL MPADD (X, R(T+5), Z)
RETURN
END
SUBROUTINE MPADDQ (X, I, J, Y) MP006520
C ADDS THE RATIONAL NUMBER I/J TO MP NUMBER X, MP RESULT IN Y
C DIMENSION OF R MUST BE AT LEAST 2T+6
COMMON B, T, M, LUN, MXR, R
INTEGER B, T, R(6), X(1), Y(1)
C CHECK LEGALITY OF B, T, M, LUN AND MXR
CALL MPCHK (2, 6)
CALL MPCQM (I, J, R(T+5))
CALL MPADD (X, R(T+5), Y)
RETURN
END
SUBROUTINE MPADD2 (X, Y, Z, Y1, TRUNC) MP006640
C CALLED BY MPADD, MPSUB ETC.
C X, Y AND Z ARE MP NUMBERS, Y1 AND TRUNC ARE INTEGERS.
C TO FORCE CALL BY REFERENCE RATHER THAN VALUE/RESULT, Y1 IS
C DECLARED AS AN ARRAY, BUT ONLY Y1(1) IS EVER USED.
C SETS Z = X + Y1(1)*ABS(Y), WHERE Y1(1) = +- Y(1).
C IF TRUNC.EQ.0 R*-ROUNDING IS USED, OTHERWISE TRUNCATION.
C R*-ROUNDING IS DEFINED IN KUKI AND CODI, COMM. ACM
C 16(1973), 223. (SEE ALSO BRENT, IEEE TC-22(1973), 601.)
COMMON B, T, M, LUN, MXR, R
INTEGER B, T, R(1), X(2), Y(2), Z(1), Y1(1), TRUNC
INTEGER S, ED, RS, RE
C CHECK FOR X OR Y ZERO
IF (X(1).NE.0) GO TO 20
C X = 0 OR NEGLIGIBLE, SO RESULT = +-Y
10 CALL MPSTR(Y, Z)
Z(1) = Y1(1)
RETURN
20 IF (Y1(1).NE.0) GO TO 40
C Y = 0 OR NEGLIGIBLE, SO RESULT = X
30 CALL MPSTR (X, Z)
RETURN
C COMPARE SIGNS
40 S = X(1)*Y1(1)
IF (IABS(S).LE.1) GO TO 60
CALL MPCHK (1, 4)
WRITE (LUN, 50)
50 FORMAT (44H *** SIGN NOT 0, +1 OR -1 IN CALL TO MPADD2,,
$ 33H POSSIBLE OVERWRITING PROBLEM ***)
CALL MPERR
Z(1) = 0
RETURN
C COMPARE EXPONENTS
60 ED = X(2) - Y(2)
MED = IABS(ED)
IF (ED) 90, 70, 120
C EXPONENTS EQUAL SO COMPARE SIGNS, THEN FRACTIONS IF NEC.
70 IF (S.GT.0) GO TO 100
DO 80 J = 1, T
IF (X(J+2) - Y(J+2)) 100, 80, 130
80 CONTINUE
C RESULT IS ZERO
Z(1) = 0
RETURN
C HERE EXPONENT(Y) .GE. EXPONENT(X)
90 IF (MED.GT.T) GO TO 10
100 RS = Y1(1)
RE = Y(2)
CALL MPADD3 (X, Y, S, MED, RE)
C NORMALIZE, ROUND OR TRUNCATE, AND RETURN
110 CALL MPNZR (RS, RE, Z, TRUNC)
RETURN
C ABS(X) .GT. ABS(Y)
120 IF (MED.GT.T) GO TO 30
130 RS = X(1)
RE = X(2)
CALL MPADD3 (Y, X, S, MED, RE)
GO TO 110
END
SUBROUTINE MPADD3 (X, Y, S, MED, RE) MP007240
C CALLED BY MPADD2, DOES INNER LOOPS OF ADDITION
COMMON B, T, M, LUN, MXR, R
INTEGER B, T, R(1), X(1), Y(1), S, RE, C, TED
TED = T + MED
I2 = T + 4
I = I2
C = 0
C CLEAR GUARD DIGITS TO RIGHT OF X DIGITS
10 IF (I.LE.TED) GO TO 20
R(I) = 0
I = I - 1
GO TO 10
20 IF (S.LT.0) GO TO 130
C HERE DO ADDITION, EXPONENT(Y) .GE. EXPONENT(X)
IF (I.LE.T) GO TO 40
30 J = I - MED
R(I) = X(J+2)
I = I - 1
IF (I.GT.T) GO TO 30
40 IF (I.LE.MED) GO TO 60
J = I - MED
C = Y(I+2) + X(J+2) + C
IF (C.LT.B) GO TO 50
C CARRY GENERATED HERE
R(I) = C - B
C = 1
I = I - 1
GO TO 40
C NO CARRY GENERATED HERE
50 R(I) = C
C = 0
I = I - 1
GO TO 40
60 IF (I.LE.0) GO TO 90
C = Y(I+2) + C
IF (C.LT.B) GO TO 70
R(I) = 0
C = 1
I = I - 1
GO TO 60
70 R(I) = C
I = I - 1
C NO CARRY POSSIBLE HERE
80 IF (I.LE.0) RETURN
R(I) = Y(I+2)
I = I - 1
GO TO 80
90 IF (C.EQ.0) RETURN
C MUST SHIFT RIGHT HERE AS CARRY OFF END
I2P = I2 + 1
DO 100 J = 2, I2
I = I2P - J
100 R(I+1) = R(I)
R(1) = 1
RE = RE + 1
RETURN
C HERE DO SUBTRACTION, ABS(Y) .GT. ABS(X)
110 J = I - MED
R(I) = C - X(J+2)
C = 0
IF (R(I).GE.0) GO TO 120
C BORROW GENERATED HERE
C = -1
R(I) = R(I) + B
120 I = I - 1
130 IF (I.GT.T) GO TO 110
140 IF (I.LE.MED) GO TO 160
J = I - MED
C = Y(I+2) + C - X(J+2)
IF (C.GE.0) GO TO 150
C BORROW GENERATED HERE
R(I) = C + B
C = -1
I = I - 1
GO TO 140
C NO BORROW GENERATED HERE
150 R(I) = C
C = 0
I = I - 1
GO TO 140
160 IF (I.LE.0) RETURN
C = Y(I+2) + C
IF (C.GE.0) GO TO 70
R(I) = C + B
C = -1
I = I - 1
GO TO 160
END
SUBROUTINE MPART1 (N, Y) MP008140
C COMPUTES MP Y = ARCTAN(1/N), ASSUMING INTEGER N .GT. 1.
C USES SERIES ARCTAN(X) = X - X**3/3 + X**5/5 - ...
C DIMENSION OF R IN CALLING PROGRAM MUST BE
C AT LEAST 2T+6
COMMON B, T, M, LUN, MXR, R
INTEGER B, T, R(1), Y(2), B2, TS
C CHECK LEGALITY OF B, T, M, MXR AND LUN
CALL MPCHK (2, 6)
IF (N.GT.1) GO TO 20
WRITE (LUN, 10)
10 FORMAT (35H *** N .LE. 1 IN CALL TO MPART1 ***)
CALL MPERR
Y(1) = 0
RETURN
20 I2 = T + 5
TS = T
C SET SUM TO X = 1/N
CALL MPCQM (1, N, Y)
C SET ADDITIVE TERM TO X
CALL MPSTR (Y, R(I2))
I = 1
ID = 0
C ASSUME AT LEAST 16-BIT WORD.
B2 = MAX0 (B, 64)
IF (N.LT.B2) ID = (7*B2*B2)/(N*N)
C MAIN LOOP. FIRST REDUCE T IF POSSIBLE
30 T = TS + 2 + R(I2+1) - Y(2)
IF (T.LT.2) GO TO 60
T = MIN0 (T, TS)
C IF (I+2)*N**2 IS NOT REPRESENTABLE AS AN INTEGER THE DIVISION
C FOLLOWING HAS TO BE PERFORMED IN SEVERAL STEPS.
IF (I.GE.ID) GO TO 40
CALL MPMULQ (R(I2), -I, (I+2)*N*N, R(I2))
GO TO 50
40 CALL MPMULQ (R(I2), -I, I+2, R(I2))
CALL MPDIVI (R(I2), N, R(I2))
CALL MPDIVI (R(I2), N, R(I2))
50 I = I + 2
C RESTORE T
T = TS
C ADD TO SUM, USING MPADD2 (FASTER THAN MPADD)
CALL MPADD2 (R(I2), Y, Y, Y, 0)
IF (R(I2).NE.0) GO TO 30
60 T = TS
RETURN
END
SUBROUTINE MPASIN (X, Y) MP008620
C RETURNS Y = ARCSIN(X), ASSUMING ABS(X) .LE. 1,
C FOR MP NUMBERS X AND Y.
C Y IS IN THE RANGE -PI/2 TO +PI/2.
C METHOD IS TO USE MPATAN, SO TIME IS O(M(T)T).
C DIMENSION OF R MUST BE AT LEAST 5T+12
COMMON B, T, M, LUN, MXR, R
INTEGER B, T, R(1), X(2), Y(1)
C CHECK LEGALITY OF B, T, M, MXR AND LUN
CALL MPCHK (5, 12)
I3 = 4*T + 11
IF (X(1).EQ.0) GO TO 30
IF (X(2).LE.0) GO TO 40
C HERE ABS(X) .GE. 1. SEE IF X = +-1
CALL MPCIM (X(1), R(I3))
IF (MPCOMP(X, R(I3)).NE.0) GO TO 10
C X = +-1 SO RETURN +-PI/2
CALL MPPI (Y)
CALL MPDIVI (Y, 2*R(I3), Y)
RETURN
10 WRITE (LUN, 20)
20 FORMAT (40H *** ABS(X) .GT. 1 IN CALL TO MPASIN ***)
CALL MPERR
30 Y(1) = 0
RETURN
C HERE ABS(X) .LT. 1 SO USE ARCTAN(X/SQRT(1 - X**2))
40 I2 = I3 - (T+2)
CALL MPCIM (1, R(I2))
CALL MPSTR (R(I2), R(I3))
CALL MPSUB (R(I2), X, R(I2))
CALL MPADD (R(I3), X, R(I3))
CALL MPMUL (R(I2), R(I3), R(I3))
CALL MPROOT (R(I3), -2, R(I3))
CALL MPMUL (X, R(I3), Y)
CALL MPATAN (Y, Y)
RETURN
END
SUBROUTINE MPATAN (X, Y) MP008996
C RETURNS Y = ARCTAN(X) FOR MP X AND Y, USING AN O(T.M(T)) METHOD
C WHICH COULD EASILY BE MODIFIED TO AN O(SQRT(T)M(T))
C METHOD (AS IN MPEXP1). Y IS IN THE RANGE -PI/2 TO +PI/2.
C FOR AN ASYMPTOTICALLY FASTER METHOD, SEE - FAST MULTIPLE-
C PRECISION EVALUATION OF ELEMENTARY FUNCTIONS
C (BY R. P. BRENT), J. ACM 23 (1976), 242-251,
C AND THE COMMENTS IN MPPIGL.
C DIMENSION OF R IN CALLING PROGRAM MUST BE AT LEAST 5T+12
COMMON B, T, M, LUN, MXR, R
INTEGER B, T, R(1), X(2), Y(1), Q, TS
C CHECK LEGALITY OF B, T, M, MXR AND LUN
CALL MPCHK (5, 12)
I2 = 3*T + 9
I3 = I2 + T + 2
IF (X(1).NE.0) GO TO 10
Y(1) = 0
RETURN
10 CALL MPSTR (X, R(I3))
IE = IABS(X(2))
IF (IE.LE.2) CALL MPCMR (X, RX)
Q = 1
C REDUCE ARGUMENT IF NECESSARY BEFORE USING SERIES
20 IF (R(I3+1).LT.0) GO TO 30
IF ((R(I3+1).EQ.0).AND.((2*(R(I3+2)+1)).LE.B)) GO TO 30
Q = 2*Q
CALL MPMUL (R(I3), R(I3), Y)
CALL MPADDI (Y, 1, Y)
CALL MPSQRT (Y, Y)
CALL MPADDI (Y, 1, Y)
CALL MPDIV (R(I3), Y, R(I3))
GO TO 20
C USE POWER SERIES NOW ARGUMENT IN (-0.5, 0.5)
30 CALL MPSTR (R(I3), Y)
CALL MPMUL (R(I3), R(I3), R(I2))
I = 1
TS = T
C SERIES LOOP. REDUCE T IF POSSIBLE.
40 T = TS + 2 + R(I3+1)
IF (T.LE.2) GO TO 50
T = MIN0 (T, TS)
CALL MPMUL (R(I3), R(I2), R(I3))
CALL MPMULQ (R(I3), -I, I+2, R(I3))
I = I + 2
T = TS
CALL MPADD (Y, R(I3), Y)
IF (R(I3).NE.0) GO TO 40
C RESTORE T, CORRECT FOR ARGUMENT REDUCTION, AND EXIT
50 T = TS
CALL MPMULI (Y, Q, Y)
C CHECK THAT RELATIVE ERROR LESS THAN 0.01 UNLESS EXPONENT
C OF X IS LARGE (WHEN ATAN MIGHT NOT WORK)
IF (IE.GT.2) RETURN
CALL MPCMR (Y, RY)
IF (ABS(RY - ATAN(RX)) .LT. (0.01*ABS(RY))) RETURN
WRITE (LUN, 60)
C THE FOLLOWING MESSAGE MAY INDICATE THAT B**(T-1) IS TOO SMALL.
60 FORMAT (51H *** ERROR OCCURRED IN MPATAN, RESULT INCORRECT ***)
CALL MPERR
RETURN
END
FUNCTION MPBASA (X) MP009553
C RETURNS THE MP BASE (FIRST WORD IN COMMON).
C X IS A DUMMY MP ARGUMENT.
COMMON B, T, M, LUN, MXR, R
INTEGER B, T, R(1), X(1)
MPBASA = B
RETURN
END
SUBROUTINE MPBASB (I, X) MP009573
C SETS THE MP BASE (FIRST WORD OF COMMON) TO I.
C I SHOULD BE AN INTEGER SUCH THAT I .GE. 2
C AND (8*I*I-1) IS REPRESENTABLE AS A SINGLE-PRECISION INTEGER.
C X IS A DUMMY MP ARGUMENT (AUGMENT EXPECTS ONE).
COMMON B, T, M, LUN, MXR, R
INTEGER B, T, R(1), X(1)
C SET BASE TO I, THEN CHECK VALIDITY
B = I
CALL MPCHK (1, 4)
RETURN
END
SUBROUTINE MPBERN (N, P, X) MP009620
C COMPUTES THE BERNOULLI NUMBERS B2 = 1/6, B4 = -1/30,
C B6 = 1/42, B8 = -1/30, B10 = 5/66, B12 = -691/2730, ETC.,
C DEFINED BY THE GENERATING FUNCTION Y/(EXP(Y)-1).
C N AND P ARE SINGLE-PRECISION INTEGERS, WITH 2*P .GE. T+2.
C X SHOULD BE A ONE-DIMENSIONAL INTEGER ARRAY OF DIMENSION AT
C LEAST P*N. THE BERNOULLI NUMBERS B2, B4, ... , B(2N) ARE
C RETURNED IN PACKED FORMAT IN X, WITH B(2J) IN LOCATIONS
C X((J-1)*P+1), ... , X(P*J). THUS, TO GET B(2J) IN USUAL
C MP FORMAT IN Y, ONE SHOULD CALL MPUNPK (X(IX), Y) AFTER
C CALLING MPBERN, WHERE IX = (J-1)*P+1.
C
C ALTERNATIVELY (SIMPLER BUT NONSTANDARD) -
C X MAY BE A TWO-DIMENSIONAL INTEGER ARRAY DECLARED WITH
C DIMENSION (P, N1), WHERE N1 .GE. N AND 2*P .GE. T+2.
C THEN B2, B4, ... , B(2N) ARE RETURNED IN PACKED FORMAT IN
C X, WITH B(2J) IN X(1,J), ... , X(P,J). THUS, TO GET
C B(2J) IN USUAL MP FORMAT IN Y ONE SHOULD
C CALL MPUNPK (X(1, J), Y) AFTER CALLING MPBERN.
C
C THE WELL-KNOWN RECURRENCE IS UNSTABLE (LOSING ABOUT 2J BITS
C OF RELATIVE ACCURACY IN THE COMPUTED B(2J)), SO WE USE A
C DIFFERENT RECURRENCE DERIVED BY EQUATING COEFFICIENTS IN
C (EXP(Y)+1)*(2Y/(EXP(2Y)-1)) = 2*(Y/(EXP(Y)-1)). THE RELATION
C B(2J) = -2*((-1)**J)*FACTORIAL(2J)*ZETA(2J)/((2PI)**(2J))
C IS USED IF ZETA(2J) IS EQUAL TO 1 TO WORKING ACCURACY.
C A DIFFERENT METHOD IS GIVEN BY KNUTH AND BUCKHOLTZ IN
C MATH. COMP. 21 (1967), 663-688.
C THE RELATIVE ERROR IN B(2J) IS O((J**2)*(B**(1-T))).
C TIME IS O(T*(MIN(N, T)**2) + N*M(T)), SPACE = 8T+18.
COMMON B, T, M, LUN, MXR, R
INTEGER B, B2, T, R(1), P, X(1)
IF (N.LE.0) RETURN
C CHECK LEGALITY OF B, T, M, LUN AND MXR
CALL MPCHK (8, 18)
IF ((2*P).GE.(T+2)) GO TO 20
WRITE (LUN, 10)
10 FORMAT (38H *** P TOO SMALL IN CALL TO MPBERN ***)
CALL MPERR
RETURN
20 I2 = 4*T + 11
I3 = I2 + T + 2
I4 = I3 + T + 2
I5 = I4 + T + 2
B2 = MAX0 (B/2, 32)
C COMPUTE UPPER LIMIT FOR RECURRENCE RELATION METHOD.
N2 = MIN0 (N, INT(0.5E0+ALOG(FLOAT(B))*FLOAT(T)/ALOG(4E0)))
C SET ALL RESULTS TO ZERO
DO 30 I = 1, N2
IX = (I-1)*P + 2
30 X(IX) = 0
CALL MPCQM (1, 8, R(I2))
CALL MPSTR (R(I2), R(I3))
CALL MPCIM (-1, R(I5))
C MAIN LOOP TO GENERATE SCALED BERNOULLI NUMBERS
DO 70 J = 1, N2
CALL MPDIVI (R(I3), 2, R(I3))
CALL MPDIVI (R(I5), 4, R(I5))
CALL MPADDI (R(I5), 1, R(I4))
CALL MPDIV (R(I3), R(I4), R(I3))
IX = (J-1)*P + 1
CALL MPPACK (R(I3), X(IX))
IF (J.GE.N2) GO TO 80
CALL MPDIVI (R(I2), 4*J-2, R(I2))
CALL MPDIVI (R(I2), 4*J+4, R(I2))
CALL MPSTR (R(I2), R(I3))
DO 60 I = 1, J
IX = (I-1)*P + 1
CALL MPUNPK (X(IX), R(I4))
IF ((J-I).GE.B2) GO TO 40
CALL MPDIVI (R(I4), 8*(2*(J-I)+1)*(J+1-I), R(I4))
GO TO 50
C HERE SPLIT UP IN CASE WOULD GET OVERFLOW IN ONE CALL TO MPDIVI
40 CALL MPDIVI (R(I4), 4*(J+1-I), R(I4))
CALL MPDIVI (R(I4), 4*(J-I)+2, R(I4))
50 CALL MPPACK (R(I4), X(IX))
60 CALL MPSUB (R(I3), R(I4), R(I3))
70 CONTINUE
C NOW UNSCALE RESULTS
80 CALL MPCIM (1, R(I2))
IF (N2.LE.1) GO TO 100
I = N2
90 CALL MPMULI (R(I2), (4*(N2-I)+4), R(I2))
CALL MPMULI (R(I2), (4*(N2-I)+2), R(I2))
I = I - 1
IX = (I-1)*P + 1
CALL MPUNPK (X(IX), R(I4))
CALL MPMUL (R(I2), R(I4), R(I4))
CALL MPPACK (R(I4), X(IX))
IF (I.GT.1) GO TO 90
C NOW HAVE B(2J)/FACTORIAL(2J) IN X
CALL MPCIM (1, R(I2))
100 DO 110 I = 1, N2
CALL MPMULI (R(I2), 2*I-1, R(I2))
CALL MPMULI (R(I2), 2*I, R(I2))
IX = (I-1)*P + 1
CALL MPUNPK (X(IX), R(I4))
CALL MPMUL (R(I2), R(I4), R(I4))
110 CALL MPPACK (R(I4), X(IX))
C RETURN IF FINISHED
IF (N.LE.N2) RETURN
C ELSE COMPUTE REMAINING NUMBERS
CALL MPPI (R(I3))
CALL MPPWR (R(I3), -2, R(I3))
CALL MPDIVI (R(I3), -4, R(I3))
N2 = N2 + 1
DO 120 I = N2, N
CALL MPMUL (R(I4), R(I3), R(I4))
CALL MPMULI (R(I4), 2*I-1, R(I4))
CALL MPMULI (R(I4), 2*I, R(I4))
IX = (I-1)*P + 1
120 CALL MPPACK (R(I4), X(IX))
RETURN
END
SUBROUTINE MPBESJ (X, NU, Y) MP010770
C RETURNS Y = J(NU,X), THE FIRST-KIND BESSEL FUNCTION OF ORDER NU,
C FOR SMALL INTEGER NU, MP X AND Y. ABS(NU) MUST BE
C .LE. MAX(B, 64). METHOD IS HANKELS ASYMPTOTIC EXPANSION IF
C ABS(X) LARGE, THE POWER SERIES IF ABS(X) SMALL, AND THE
C BACKWARD RECURRENCE METHOD OTHERWISE.
C RESULTS FOR NEGATIVE ARGUMENTS ARE DEFINED BY
C J(-NU,X) = J(NU,-X) = ((-1)**NU)*J(NU,X).
C ERROR COULD BE INDUCED BY O(B**(1-T)) PERTURBATIONS
C IN X AND Y. TIME IS O(T.M(T)) FOR FIXED X AND NU, INCREASES
C AS X AND NU INCREASE, UNLESS X LARGE ENOUGH FOR ASYMPTOTIC
C SERIES TO BE USED. SPACE = 14T+156
COMMON B, T, M, LUN, MXR, R
INTEGER B, B2, T, R(1), X(2), Y(1), TS, TS2, TM, ERROR
C CHECK LEGALITY OF B, T, M, LUN AND MXR
CALL MPCHK (14, 156)
TS = T
B2 = MAX0 (B, 64)
NUA = IABS(NU)
C CHECK THAT ABS(NU) IS .LE. MAX(B, 64). THIS RESTRICTION
C ENSURES THAT 4*(NU**2) IS REPRESENTABLE AS AN INTEGER.
IF (NUA.LE.B2) GO TO 20
WRITE (LUN, 10)
10 FORMAT (44H *** ABS(NU) TOO LARGE IN CALL TO MPBESJ ***)
GO TO 120
C CHECK FOR X ZERO
20 IF (X(1).NE.0) GO TO 30
C J(NU,0) = 0 IF NU .EQ. 0, 1 IF NU .NE. 0
Y(1) = 0
IF (NU.EQ.0) CALL MPCIM (1, Y)
RETURN
C SEE IF ABS(X) SO LARGE THAT NO ACCURACY POSSIBLE
30 IF (X(2).GE.T) GO TO 100
C X NONZERO SO TRY HANKEL ASYMPTOTIC SERIES WITH ONE GUARD DIGIT
I2 = 11*T + 36
CALL MPCLR (R(I2), T+1)
CALL MPSTR (X, R(I2))
T = T + 1
CALL MPHANK (R(I2), NUA, R(I2), ERROR)
T = TS
CALL MPSTR (R(I2), Y)
C RETURN IF ASYMPTOTIC SERIES WAS ACCURATE ENOUGH
IF (ERROR.EQ.0) GO TO 90
C ASYMPTOTIC SERIES INADEQUATE HERE, SO USE POWER SERIES
C MAY NEED TO INCREASE T LATER SO PREPARE FOR THIS
C MAX ALLOWABLE T IS APPROXIMATELY DOUBLE
TM = 2*T + 20
I2 = 4*TM + 11
I3 = I2 + TM + 2
I4 = I3 + TM + 2
C ZERO TRAILING DIGITS OF R(I2) AND R(I4)
CALL MPCLR (R(I2), TM)
CALL MPCLR (R(I4), TM)
TS2 = T
C NO APPRECIABLE CANCELLATION IN POWER SERIES IF ABS(X) .LT. 1
IF (X(2).LE.0) GO TO 40
C SHOULD BE OK TO CONVERT TO REAL HERE AS X NOT TOO LARGE OR SMALL.
CALL MPCMR (X, RX)
C ESTIMATE NUMBER OF DIGITS REQUIRED TO COMPENSATE FOR CANCELLATION
TS2 = MAX0 (TS, T + 1 + INT((ABS(RX)+(FLOAT(NUA)+0.5E0)*
$ ALOG(0.5E0*ABS(RX)))/ALOG(FLOAT(B))))
C IF NEED MORE DIGITS THAN SPACE ALLOWS FOR POWER SERIES THEN
C USE RECURRENCE METHOD INSTEAD
IF (TS2.GT.TM) GO TO 130
C PREPARE FOR POWER SERIES LOOP
40 CALL MPDIVI (X, 2, R(I4))
CALL MPPWR (R(I4), NUA, R(I4))
CALL MPGAMQ (NUA+1, 1, R(I3))
CALL MPDIV (R(I4), R(I3), R(I4))
CALL MPMUL (X, X, R(I2))
CALL MPDIVI (R(I2), -4, R(I2))
T = TS2
CALL MPSTR (R(I4), R(I3))
IE = R(I3+1)
K = 0
C POWER SERIES LOOP, REDUCE T IF POSSIBLE
50 T = MIN0 (TS2, TS2 + 2 + R(I4+1) - IE)
IF (T.LT.2) GO TO 80
CALL MPMUL (R(I2), R(I4), R(I4))
K = K + 1
C MAY NEED TO SPLIT UP CALL TO MPDIVI
IF (K.GT.B2) GO TO 60
CALL MPDIVI (R(I4), K*(K+NUA), R(I4))
GO TO 70
C HERE IT IS SPLIT UP TO AVOID OVERFLOW
60 CALL MPDIVI (R(I4), K, R(I4))
CALL MPDIVI (R(I4), K+NUA, R(I4))
C RESTORE T FOR ADDITION
70 T = TS2
CALL MPADD (R(I3), R(I4), R(I3))
IF ((R(I4).NE.0).AND.(R(I4+1).GE.(R(I3+1)-TS))) GO TO 50
C RESTORE T AND MOVE FINAL RESULT
80 T = TS
CALL MPSTR (R(I3), Y)
C CORRECT SIGN IF NU ODD AND NEGATIVE
90 IF ((NU.LT.0).AND.(MOD(NUA,2).NE.0)) Y(1) = -Y(1)
RETURN
C HERE ABS(X) SO LARGE THAT NO SIGNIFICANT DIGITS COULD BE
C GUARANTEED
100 WRITE (LUN, 110)
110 FORMAT (43H *** ABS(X) TOO LARGE IN CALL TO MPBESJ ***)
120 CALL MPERR
T = TS
Y(1) = 0
RETURN
C HERE USE BACKWARD RECURRENCE METHOD WITH TWO GUARD DIGITS
130 CALL MPABS (X, R(I4))
T = T + 2
CALL MPBES2 (R(I4), NUA, R(I3))
C CORRECT SIGN IF NUA ODD
IF (MOD (NUA,2) .NE. 0) R(I3) = X(1)*R(I3)
GO TO 80
END
SUBROUTINE MPBES2 (X, NU, Y) MP011906
C USES THE BACKWARD RECURRENCE METHOD TO EVALUATE Y = J(NU,X),
C WHERE X AND Y ARE MP NUMBERS, NU (THE INDEX) IS AN INTEGER,
C AND J IS THE BESSEL FUNCTION OF THE FIRST KIND. ASSUMES THAT
C 0 .LE. NU .LE. MAX(B,64) AND X .GT. 0. ALSO ASSUMED THAT X
C CAN BE CONVERTED TO REAL WITHOUT FLOATING-POINT OVERFLOW OR
C UNDERFLOW. FOR NORMALIZATION THE IDENTITY
C J(0,X) + 2*J(2,X) + 2*J(4,X) + ... = 1 IS USED.
C CALLED BY MPBESJ AND NOT RECOMMENDED FOR INDEPENDENT USE.
C SPACE = 8T+18
COMMON B, T, M, LUN, MXR, R
INTEGER B, T, R(1), X(1), Y(1)
C CHECK LEGALITY OF B, T, M, LUN AND MXR
CALL MPCHK (8, 18)
C CHECK LEGALITY OF NU AND X
IF ((NU.GE.0).AND.(NU.LE.MAX0(B,64)).AND.(X(1).EQ.1)) GO TO 20
WRITE (LUN, 10)
10 FORMAT (50H *** NU .LT. 0 OR NU TOO LARGE OR X .LE. 0 IN CALL,
$ 14H TO MPBES2 ***)
CALL MPERR
Y(1) = 0
RETURN
C ASSUME CONVERSION TO REAL IS POSSIBLE WITHOUT OVERFLOW (TRUE
C WHEN CALLED BY MPBESJ ELSE MPHANK OR POWER SERIES WOULD BE USED).
20 CALL MPCMR (X, RX)
C COMPUTE STARTING POINT NU1 FOR BACKWARD RECURRENCE
FLNU = FLOAT (MAX0 (1, NU))
RY = AMAX1 (1E0, ALOG(2E0*FLNU/RX) - 1E0)
C 1.35914 IS E/2 ROUNDED DOWN, 1.35915 IS E/2 ROUNDED UP
RY = (FLNU*RY + 0.5E0*FLOAT(T)*ALOG(FLOAT(B)))/(1.35914E0*RX)
RY = AMAX1 (2E0, RY)
RT = RY
C ITERATE AN EVEN NUMBER OF TIMES TO OVERESTIMATE NU1
DO 30 I = 1, 4
30 RT = AMAX1 (2E0, RY/ALOG(RT))
NU1 = 2 + INT(1.35915E0*RX*RT)
I2 = 3*T + 9
I3 = I2 + T + 2
I4 = I3 + T + 2
I5 = I4 + T + 2
I6 = I5 + T + 2
CALL MPCIM (MOD(NU1+1,2), R(I6))
CALL MPREC (X, R(I2))
CALL MPMULI (R(I2), 2, R(I2))
R(I3) = 0
CALL MPCIM (1, R(I4))
C BACKWARD RECURRENCE LOOP
40 CALL MPMUL (R(I4), R(I2), R(I5))
CALL MPMULI (R(I5), NU1, R(I5))
CALL MPSUB (R(I5), R(I3), R(I5))
NU1 = NU1 - 1
C FASTER TO INTERCHANGE POINTERS THAN MP NUMBERS
I3S = I3
I3 = I4
I4 = I5
I5 = I3S
IF (MOD(NU1,2) .NE. 0) GO TO 50
C NU1 EVEN SO UPDATE NORMALIZING SUM
IF (NU1.EQ.0) CALL MPMULI (R(I6), 2, R(I6))
CALL MPADD (R(I6), R(I4), R(I6))
C SAVE UNNORMALIZED RESULT IF NU1 .EQ. NU
50 IF (NU1.EQ.NU) CALL MPSTR (R(I4), Y)
IF (NU1.GT.0) GO TO 40
C NORMALIZE RESULT AND RETURN
CALL MPDIV (Y, R(I6), Y)
RETURN
END
SUBROUTINE MPCAM (A, X) MP012493
C CONVERTS THE HOLLERITH STRING A TO AN MP NUMBER X.
C A CAN BE A STRING OF DIGITS ACCEPTABLE TO ROUTINE MPIN
C AND TERMINATED BY A DOLLAR ($), E.G. 7H-5.367$,
C OR ONE OF THE FOLLOWING SPECIAL STRINGS -
C EPS (MP MACHINE-PRECISION, SEE MPEPS),
C EUL (EULERS CONSTANT 0.5772..., SEE MPEUL),
C MAXR (LARGEST VALID MP NUMBER, SEE MPMAXR),
C MINR (SMALLEST POSTIVE MP NUMBER, SEE MPMINR),
C PI (PI = 3.14..., SEE MPPI).
C ONLY THE FIRST TWO CHARACTERS OF THESE STRINGS ARE CHECKED.
C SPACE REQUIRED IS NO MORE THAN 5*T+L+14, WHERE L IS THE
C NUMBER OF CHARACTERS IN THE STRING A (EXCLUDING $).
C IF SPACE IS LESS 3*T+L+11 THE STRING A WILL EFFECTIVELY BE TRUNCATED
COMMON B, T, M, LUN, MXR, R
INTEGER B, T, R(1), A(1), X(1), ERROR, C(6), D(2)
DATA C(1) /1HA/, C(2) /1HE/, C(3) /1HI/
DATA C(4) /1HM/, C(5) /1HP/, C(6) /1HU/
C UNPACK FIRST 2 CHARACTERS OF A
CALL MPUPK (A, D, 2, N)
IF (N.NE.2) GO TO 10
C SET X TO ZERO AFTER SAVING A(1) IN CASE A AND X COINCIDE
I = A(1)
X(1) = 0
C CHECK FOR SPECIAL STRINGS
IF ((D(1).EQ.C(2)).AND.(D(2).EQ.C(5))) CALL MPEPS (X)
IF ((D(1).EQ.C(2)).AND.(D(2).EQ.C(6))) CALL MPEUL (X)
IF ((D(1).EQ.C(4)).AND.(D(2).EQ.C(1))) CALL MPMAXR (X)
IF ((D(1).EQ.C(4)).AND.(D(2).EQ.C(3))) CALL MPMINR (X)
IF ((D(1).EQ.C(5)).AND.(D(2).EQ.C(3))) CALL MPPI (X)
C RETURN IF X NONZERO (SO ONE OF ABOVE TESTS SUCCEEDED)
IF (X(1).NE.0) RETURN
C RESTORE A(1) AND UNPACK, THEN CALL MPIN TO DECODE.
A(1) = I
10 I2 = 3*T + 12
CALL MPUPK (A, R(I2), MXR+1-I2, N)
CALL MPIN (R(I2), X, N, ERROR)
IF (ERROR.EQ.0) RETURN
WRITE (LUN, 20)
20 FORMAT (53H *** ERROR IN HOLLERITH CONSTANT IN CALL TO MPCAM ***)
CALL MPERR
RETURN
END
SUBROUTINE MPCDM (DX, Z) MP012590
C CONVERTS DOUBLE-PRECISION NUMBER DX TO MULTIPLE-PRECISION Z.
C SOME NUMBERS WILL NOT CONVERT EXACTLY ON MACHINES
C WITH BASE OTHER THAN TWO, FOUR OR SIXTEEN.
C THIS ROUTINE IS NOT CALLED BY ANY OTHER ROUTINE IN MP,
C SO MAY BE OMITTED IF DOUBLE-PRECISION IS NOT AVAILABLE.
DOUBLE PRECISION DB, DJ, DX, DBLE
COMMON B, T, M, LUN, MXR, R
INTEGER B, T, R(1), Z(1), RS, RE, TP
C CHECK LEGALITY OF B, T, M, MXR AND LUN
CALL MPCHK (1, 4)
I2 = T + 4
C CHECK SIGN
IF (DX) 20, 10, 30
C IF DX = 0D0 RETURN 0
10 Z(1) = 0
RETURN
C DX .LT. 0D0
20 RS = -1
DJ = -DX
GO TO 40
C DX .GT. 0D0
30 RS = 1
DJ = DX
40 IE = 0
50 IF (DJ.LT.1D0) GO TO 60
C INCREASE IE AND DIVIDE DJ BY 16.
IE = IE + 1
DJ = 0.0625D0*DJ
GO TO 50
60 IF (DJ.GE.0.0625D0) GO TO 70
IE = IE - 1
DJ = 16D0*DJ
GO TO 60
C NOW DJ IS DY DIVIDED BY SUITABLE POWER OF 16
C SET EXPONENT TO 0
70 RE = 0
C DB = DFLOAT(B) IS NOT ANSI STANDARD SO USE FLOAT AND DBLE
DB = DBLE(FLOAT(B))
C CONVERSION LOOP (ASSUME DOUBLE-PRECISION OPS. EXACT)
DO 80 I = 1, I2
DJ = DB*DJ
R(I) = IDINT(DJ)
80 DJ = DJ - DBLE(FLOAT(R(I)))
C NORMALIZE RESULT
CALL MPNZR (RS, RE, Z, 0)
IB = MAX0(7*B*B, 32767)/16
TP = 1
C NOW MULTIPLY BY 16**IE
IF (IE) 90, 130, 110
90 K = -IE
DO 100 I = 1, K
TP = 16*TP
IF ((TP.LE.IB).AND.(TP.NE.B).AND.(I.LT.K)) GO TO 100
CALL MPDIVI (Z, TP, Z)
TP = 1
100 CONTINUE
RETURN
110 DO 120 I = 1, IE
TP = 16*TP
IF ((TP.LE.IB).AND.(TP.NE.B).AND.(I.LT.IE)) GO TO 120
CALL MPMULI (Z, TP, Z)
TP = 1
120 CONTINUE
130 RETURN
END
SUBROUTINE MPCHK (I, J) MP013260
C CHECKS LEGALITY OF B, T, M, MXR AND LUN WHICH SHOULD BE SET
C IN COMMON.
C THE CONDITION ON MXR (THE DIMENSION OF R IN COMMON) IS THAT
C MXR .GE. (I*T + J)
COMMON B, T, M, LUN, MXR, R
INTEGER B, T, R(1)
C FIRST CHECK THAT LUN IN RANGE 1 TO 99, IF NOT PRINT ERROR
C MESSAGE ON LOGICAL UNIT 6.
IF ((0.LT.LUN).AND.(LUN.LT.100)) GO TO 20
WRITE (6, 10) LUN
10 FORMAT (10H *** LUN =, I10, 26H ILLEGAL IN CALL TO MPCHK,,
$ 49H PERHAPS NOT SET BEFORE CALL TO AN MP ROUTINE ***)
LUN = 6
CALL MPERR
C NOW CHECK LEGALITY OF B, T AND M
20 IF (B.GT.1) GO TO 40
WRITE (LUN, 30) B
30 FORMAT (8H *** B =, I10, 26H ILLEGAL IN CALL TO MPCHK,/
$ 49H PERHAPS NOT SET BEFORE CALL TO AN MP ROUTINE ***)
CALL MPERR
40 IF (T.GT.1) GO TO 60
WRITE (LUN, 50) T
50 FORMAT (8H *** T =, I10, 26H ILLEGAL IN CALL TO MPCHK,/
$ 49H PERHAPS NOT SET BEFORE CALL TO AN MP ROUTINE ***)
CALL MPERR
60 IF (M.GT.T) GO TO 80
WRITE (LUN, 70)
70 FORMAT (31H *** M .LE. T IN CALL TO MPCHK,/
$ 49H PERHAPS NOT SET BEFORE CALL TO AN MP ROUTINE ***)
CALL MPERR
C 8*B*B-1 SHOULD BE REPRESENTABLE, IF NOT WILL OVERFLOW
C AND MAY BECOME NEGATIVE, SO CHECK FOR THIS
80 IB = 4*B*B - 1
IF ((IB.GT.0).AND.((2*IB+1).GT.0)) GO TO 100
WRITE (LUN, 90)
90 FORMAT (37H *** B TOO LARGE IN CALL TO MPCHK ***)
CALL MPERR
C CHECK THAT SPACE IN COMMON IS SUFFICIENT
100 MX = I*T + J
IF (MXR.GE.MX) RETURN
C HERE COMMON IS TOO SMALL, SO GIVE ERROR MESSAGE.
WRITE (LUN, 110) I, J, MX, MXR, T
110 FORMAT (51H *** MXR TOO SMALL OR NOT SET TO DIM(R) BEFORE CALL,
$ 21H TO AN MP ROUTINE *** /
$ 27H *** MXR SHOULD BE AT LEAST, I3, 4H*T +, I4, 2H =, I6, 5H ***
$ / 19H *** ACTUALLY MXR =, I10, 9H, AND T =, I10, 5H ***)
CALL MPERR
RETURN
END
SUBROUTINE MPCIM (IX, Z) MP013770
C CONVERTS INTEGER IX TO MULTIPLE-PRECISION Z.
COMMON B, T, M, LUN, MXR, R
INTEGER B, T, R(1), Z(2)
C CHECK LEGALITY OF B, T, M, MXR AND LUN
CALL MPCHK (1, 4)
N = IX
IF (N) 20, 10, 30
10 Z(1) = 0
RETURN
20 N = -N
Z(1) = -1
GO TO 40
30 Z(1) = 1
C SET EXPONENT TO T
40 Z(2) = T
C CLEAR FRACTION
DO 50 I = 2, T
50 Z(I+1) = 0
C INSERT N
Z(T+2) = N
C NORMALIZE BY CALLING MPMUL2
CALL MPMUL2 (Z, 1, Z, 1)
RETURN
END
SUBROUTINE MPCLR (X, N) MP014040
C SETS X(T+3), ... , X(N+2) TO ZERO, USEFUL
C IF PRECISION IS GOING TO BE INCREASED.
COMMON B, T, M, LUN, MXR, R
INTEGER B, T, R(1), X(1)
IF (N.LE.T) RETURN
I2 = T + 3
I3 = N + 2
DO 10 I = I2, I3
10 X(I) = 0
RETURN
END
SUBROUTINE MPCMD (X, DZ) MP014170
C CONVERTS MULTIPLE-PRECISION X TO DOUBLE-PRECISION DZ.
C ASSUMES X IS IN ALLOWABLE RANGE FOR DOUBLE-PRECISION
C NUMBERS. THERE IS SOME LOSS OF ACCURACY IF THE
C EXPONENT IS LARGE.
DOUBLE PRECISION DB, DZ, DZ2, DBLE, DLOG, DABS
COMMON B, T, M, LUN, MXR, R
INTEGER B, T, R(1), X(2), TM
C CHECK LEGALITY OF B, T, M, MXR AND LUN
CALL MPCHK (1, 4)
DZ = 0D0
IF (X(1).EQ.0) RETURN
C DB = DFLOAT(B) IS NOT ANSI STANDARD, SO USE FLOAT AND DBLE
DB = DBLE(FLOAT(B))
DO 10 I = 1, T
DZ = DB*DZ + DBLE(FLOAT(X(I+2)))
TM = I
C CHECK IF FULL DOUBLE-PRECISION ACCURACY ATTAINED
DZ2 = DZ + 1D0
C TEST BELOW NOT ALWAYS EQUIVALENT TO - IF (DZ2.LE.DZ) GO TO 20,
C FOR EXAMPLE ON CYBER 76.
IF ((DZ2-DZ).LE.0D0) GO TO 20
10 CONTINUE
C NOW ALLOW FOR EXPONENT
20 DZ = DZ*(DB**(X(2)-TM))
C CHECK REASONABLENESS OF RESULT.
IF (DZ.LE.0D0) GO TO 30
C LHS SHOULD BE .LE. 0.5 BUT ALLOW FOR SOME ERROR IN DLOG
IF (DABS(DBLE(FLOAT(X(2)))-(DLOG(DZ)/
$ DLOG(DBLE(FLOAT(B)))+0.5D0)).GT.0.6D0) GO TO 30
IF (X(1).LT.0) DZ = -DZ
RETURN
C FOLLOWING MESSAGE INDICATES THAT X IS TOO LARGE OR SMALL -
C TRY USING MPCMDE INSTEAD.
30 WRITE (LUN, 40)
40 FORMAT (48H *** FLOATING-POINT OVER/UNDER-FLOW IN MPCMD ***)
CALL MPERR
RETURN
END
SUBROUTINE MPCMDE (X, N, DX) MP014570
C RETURNS INTEGER N AND DOUBLE-PRECISION DX SUCH THAT MP
C X = DX*10**N (APPROXIMATELY), WHERE 1 .LE. ABS(DX) .LT. 10
C UNLESS DX = 0. SPACE = 6T+14
COMMON B, T, M, LUN, MXR, R
INTEGER B, T, R(1), X(1)
DOUBLE PRECISION DX, DBLE, DABS