C PROGRAM TO TEST DASIN/DACOS C C DATA REQUIRED C C NONE C C SUBPROGRAMS REQUIRED FROM THIS PACKAGE C C MACHAR - AN ENVIRONMENTAL INQUIRY PROGRAM PROVIDING C INFORMATION ON THE FLOATING-POINT ARITHMETIC C SYSTEM. NOTE THAT THE CALL TO MACHAR CAN C BE DELETED PROVIDED THE FOLLOWING FOUR C PARAMETERS ARE ASSIGNED THE VALUES INDICATED C C IBETA - THE RADIX OF THE FLOATING-POINT SYSTEM C IT - THE NUMBER OF BASE-IBETA DIGITS IN THE C SIGNIFICAND OF A FLOATING-POINT NUMBER C IRND - 0 IF FLOATING-POINT ADDITION CHOPS, C 1 IF FLOATING-POINT ADDITION ROUNDS C MINEXP - THE LARGEST IN MAGNITUDE NEGATIVE C INTEGER SUCH THAT DFLOAT(IBETA)**MINEXP C IS A POSITIVE FLOATING-POINT NUMBER C C REN(K) - A FUNCTION SUBPROGRAM RETURNING RANDOM REAL C NUMBERS UNIFORMLY DISTRIBUTED OVER (0,1) C C C STANDARD FORTRAN SUBPROGRAMS REQUIRED C C DABS, DACOS, DLOG, DLOG10, DMAX1, DASIN, DFLOAT, IDINT, DSQRT C C C LATEST REVISION - DECEMBER 6, 1979 C C AUTHOR - W. J. CODY C ARGONNE NATIONAL LABORATORY C C INTEGER I,IBETA,IEXP,IOUT,IRND,IT,I1,J,K,K1,K2,K3,L,M, 1 MACHEP,MAXEXP,MINEXP,N,NEGEP,NGRD REAL*8 A,AIT,ALBETA,B,BETA,BETAP,C1,C2,DEL,EPS,EPSNEG,HALF,REN, 1 R6,R7,S,SUM,W,X,XL,XM,XMAX,XMIN,XN,X1,Y,YSQ,Z,ZERO,ZZ C IOUT = 6 CALL MACHAR(IBETA,IT,IRND,NGRD,MACHEP,NEGEP,IEXP,MINEXP, 1 MAXEXP,EPS,EPSNEG,XMIN,XMAX) BETA = DFLOAT(IBETA) ALBETA = DLOG(BETA) ZERO = 0.0D0 HALF = 0.5D0 AIT = DFLOAT(IT) K = IDINT(DLOG10(BETA**IT)) + 1 IF (IBETA .NE. 10) GO TO 20 C1 = 1.57D0 C2 = 7.9632679489661923132D-4 GO TO 30 20 C1 = 201.0D0/128.0D0 C2 = 4.8382679489661923132D-4 30 A = -0.125D0 B = -A N = 2000 XN = DFLOAT(N) I1 = 0 L = -1 C----------------------------------------------------------------- C RANDOM ARGUMENT ACCURACY TESTS C----------------------------------------------------------------- DO 300 J = 1, 5 K1 = 0 K3 = 0 L = -L X1 = ZERO R6 = ZERO R7 = ZERO DEL = (B - A) / XN XL = A C DO 200 I = 1, N X = DEL*REN(I1) + XL IF (J .LE. 2) GO TO 40 YSQ = HALF - HALF*DABS(X) X = (HALF - (YSQ+YSQ)) + HALF IF (J .EQ. 5) X = -X Y = DSQRT(YSQ) Y = Y + Y GO TO 50 40 Y = X YSQ = Y*Y 50 SUM = ZERO XM = DFLOAT(K+K+1) IF (L .GT. 0) Z = DASIN(X) IF (L .LT. 0) Z = DACOS(X) C DO 60 M = 1, K SUM = YSQ*(SUM + 1.0D0/XM) XM = XM - 2.0D0 SUM = SUM*(XM/(XM+1.0D0)) 60 CONTINUE C SUM = SUM*Y IF ((J .NE. 1) .AND. (J .NE. 4)) GO TO 70 ZZ = Y + SUM SUM = (Y - ZZ) + SUM IF (IRND .NE. 1) ZZ = ZZ + (SUM+SUM) GO TO 110 70 S = C1 + C2 SUM = ((C1 - S) + C2) - SUM ZZ = S + SUM SUM = ((S - ZZ) + SUM) - Y S = ZZ ZZ = S + SUM SUM = (S - ZZ) + SUM IF (IRND .NE. 1) ZZ = ZZ + (SUM+SUM) 110 W = 1.0D0 IF (Z .NE. ZERO) W = (Z-ZZ)/Z IF (W .GT. ZERO) K1 = K1 + 1 IF (W .LT. ZERO) K3 = K3 + 1 W = DABS(W) IF (W .LE. R6) GO TO 120 R6 = W X1 = X 120 R7 = R7 + W*W XL = XL + DEL 200 CONTINUE C K2 = N - K3 - K1 R7 = DSQRT(R7/XN) IF (L .LT. 0) GO TO 210 WRITE (IOUT,1000) WRITE (IOUT,1010) N,A,B WRITE (IOUT,1011) K1,K2,K3 GO TO 220 210 WRITE (IOUT,1005) WRITE (IOUT,1010) N,A,B WRITE (IOUT,1012) K1,K2,K3 220 WRITE (IOUT,1020) IT,IBETA W = -999.0D0 IF (R6 .NE. ZERO) W = DLOG(DABS(R6))/ALBETA WRITE (IOUT,1021) R6,IBETA,W,X1 W = DMAX1(AIT+W,ZERO) WRITE (IOUT,1022) IBETA,W W = -999.0D0 IF (R7 .NE. ZERO) W = DLOG(DABS(R7))/ALBETA WRITE (IOUT,1023) R7,IBETA,W W = DMAX1(AIT+W,ZERO) WRITE (IOUT,1022) IBETA,W IF (J .NE. 2) GO TO 250 A = 0.75D0 B = 1.0D0 250 IF (J .NE. 4) GO TO 300 B = -A A = -1.0D0 C1 = C1 + C1 C2 = C2 + C2 L = -L 300 CONTINUE C----------------------------------------------------------------- C SPECIAL TESTS C----------------------------------------------------------------- WRITE (IOUT,1025) WRITE (IOUT,1030) C DO 320 I = 1, 5 X = REN(I1)*A Z = DASIN(X) + DASIN(-X) WRITE (IOUT,1060) X, Z 320 CONTINUE C WRITE (IOUT,1031) BETAP = BETA ** IT X = REN(I1) / BETAP C DO 330 I = 1, 5 Z = X - DASIN(X) WRITE (IOUT,1060) X, Z X = X / BETA 330 CONTINUE C WRITE (IOUT,1035) X = BETA ** (DFLOAT(MINEXP)*0.75D0) Y = DASIN(X) WRITE (IOUT,1061) X, Y C----------------------------------------------------------------- C TEST OF ERROR RETURNS C----------------------------------------------------------------- WRITE (IOUT,1050) X = 1.2D0 WRITE (IOUT,1052) X Y = DASIN(X) WRITE (IOUT,1055) Y WRITE (IOUT,1100) STOP 1000 FORMAT(34H1TEST OF DASIN(X) VS TAYLOR SERIES //) 1005 FORMAT(34H1TEST OF DACOS(X) VS TAYLOR SERIES //) 1010 FORMAT(I7,47H RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL / 1 6X,1H(,E15.4,1H,,E15.4,1H)//) 1011 FORMAT(20H DASIN(X) WAS LARGER,I6,7H TIMES, / 1 12X,7H AGREED,I6,11H TIMES, AND / 2 8X,11HWAS SMALLER,I6,7H TIMES.//) 1012 FORMAT(20H DACOS(X) WAS LARGER,I6,7H TIMES, / 1 12X,7H AGREED,I6,11H TIMES, AND / 2 8X,11HWAS SMALLER,I6,7H TIMES.//) 1020 FORMAT(10H THERE ARE,I4,5H BASE,I4, 1 46H SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER //) 1021 FORMAT(30H THE MAXIMUM RELATIVE ERROR OF,E15.4,3H = ,I4,3H **, 1 F7.2/4X,16HOCCURRED FOR X =,E17.6) 1022 FORMAT(27H THE ESTIMATED LOSS OF BASE,I4, 1 22H SIGNIFICANT DIGITS IS,F7.2//) 1023 FORMAT(40H THE ROOT MEAN SQUARE RELATIVE ERROR WAS,E15.4, 1 3H = ,I4,3H **,F7.2) 1025 FORMAT(14H1SPECIAL TESTS//) 1030 FORMAT(53H THE IDENTITY DASIN(-X) = -DASIN(X) WILL BE TESTED.// 1 8X,1HX,9X,12HF(X) + F(-X)/) 1031 FORMAT(53H THE IDENTITY DASIN(X) = X , X SMALL, WILL BE TESTED.// 1 8X,1HX,9X,8HX - F(X)/) 1035 FORMAT(43H TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT. /) 1050 FORMAT(22H1TEST OF ERROR RETURNS//) 1052 FORMAT(39H DASIN WILL BE CALLED WITH THE ARGUMENT,E15.4/ 1 37H THIS SHOULD TRIGGER AN ERROR MESSAGE//) 1055 FORMAT(25H DASIN RETURNED THE VALUE,E15.4///) 1060 FORMAT(2E15.7/) 1061 FORMAT(6X,7H DASIN(,E13.6,3H) =,E13.6/) 1100 FORMAT(25H THIS CONCLUDES THE TESTS ) C ---------- LAST CARD OF DASIN/DACOS TEST PROGRAM ---------- END DOUBLE PRECISION FUNCTION REN(K) C C RANDOM NUMBER GENERATOR - BASED ON ALGORITHM 266 BY PIKE AND C HILL (MODIFIED BY HANSSON), COMMUNICATIONS OF THE ACM, C VOL. 8, NO. 10, OCTOBER 1965. C C THIS SUBPROGRAM IS INTENDED FOR USE ON COMPUTERS WITH C FIXED POINT WORDLENGTH OF AT LEAST 29 BITS. IT IS C BEST IF THE FLOATING POINT SIGNIFICAND HAS AT MOST C 29 BITS. C INTEGER IY,J,K DATA IY/100001/ C J = K IY = IY * 125 IY = IY - (IY/2796203) * 2796203 REN = DFLOAT(IY) / 2796203.0D0 * (1.0D0 + 1.0D-6 + 1.0D-12) RETURN C ---------- LAST CARD OF REN ---------- END