C PROGRAM TO TEST SINH/COSH 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 SIX 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 FLOAT(IBETA)**MINEXP C IS A POSITIVE FLOATING-POINT NUMBER C EPS - THE SMALLEST POSITIVE FLOATING-POINT C NUMBER SUCH THAT 1.0+EPS .NE. 1.0 C XMAX - THE LARGEST FINITE FLOATING-POINT NO. 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 ABS, ALOG, AMAX1, COSH, FLOAT, INT, SINH, SQRT C C C LATEST REVISION - DECEMBER 6, 1979 C C AUTHOR - W. J. CODY C ARGONNE NATIONAL LABORATORY C C INTEGER I,IBETA,IEXP,II,IOUT,IRND,IT,I1,I2,J,K1,K2,K3, 1 MACHEP,MAXEXP,MINEXP,N,NEGEP,NGRD,NIT REAL A,AIND,AIT,ALBETA,ALXMAX,B,BETA,BETAP,C,C0,DEL,DEN,EPS, 1 EPSNEG,FIVE,ONE,RAN,R6,R7,THREE,W,X,XL,XMAX,XMIN,XN,X1, 2 XSQ,Y,Z,ZERO,ZZ C IOUT = 6 CALL MACHAR(IBETA,IT,IRND,NGRD,MACHEP,NEGEP,IEXP,MINEXP, 1 MAXEXP,EPS,EPSNEG,XMIN,XMAX) BETA = FLOAT(IBETA) ALBETA = ALOG(BETA) ALXMAX = ALOG(XMAX) - 0.5E0 AIT = FLOAT(IT) ZERO = 0.0E0 ONE = 1.0E0 THREE = 3.0E0 FIVE = 5.0E0 C0 = FIVE/16.0E0 + 1.152713683194269979E-2 A = ZERO B = 0.5E0 C = (AIT + ONE) * 0.35E0 IF (IBETA .EQ. 10) C = C * THREE N = 2000 XN = FLOAT(N) I1 = 0 I2 = 2 NIT = 2 - (INT(ALOG(EPS)*THREE))/20 AIND = FLOAT(NIT+NIT+1) C----------------------------------------------------------------- C RANDOM ARGUMENT ACCURACY TESTS C----------------------------------------------------------------- DO 300 J = 1, 4 IF (J .NE. 2) GO TO 30 AIND = AIND - ONE I2 = 1 30 K1 = 0 K3 = 0 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 .GT. 2) GO TO 80 XSQ = X * X ZZ = ONE DEN = AIND C DO 40 II = I2, NIT W = ZZ * XSQ/(DEN*(DEN-ONE)) ZZ = W + ONE DEN = DEN - 2.0E0 40 CONTINUE C IF (J .EQ. 2) GO TO 50 W = X*XSQ*ZZ/6.0E0 ZZ = X + W Z = SINH(X) IF (IRND .NE. 0) GO TO 110 W = (X - ZZ) + W ZZ = ZZ + (W + W) GO TO 110 50 Z = COSH(X) IF (IRND .NE. 0) GO TO 110 W = (ONE - ZZ) + W ZZ = ZZ + (W + W) GO TO 110 80 Y = X X = Y - ONE W = X - ONE IF (J .EQ. 4) GO TO 100 Z = SINH(X) ZZ = (SINH(Y) + SINH(W)) * C0 GO TO 110 100 Z = COSH(X) ZZ = (COSH(Y) + COSH(W)) * C0 110 W = ONE IF (Z .NE. ZERO) W = (Z - ZZ)/Z IF (W .GT. ZERO) K1 = K1 + 1 IF (W .LT. ZERO) K3 = K3 + 1 W = ABS(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 = SQRT(R7/XN) I = (J/2) * 2 IF (J .EQ. 1) WRITE (IOUT,1000) IF (J .EQ. 2) WRITE (IOUT,1005) IF (J .EQ. 3) WRITE (IOUT,1001) IF (J .EQ. 4) WRITE (IOUT,1006) WRITE (IOUT,1010) N,A,B IF (I .NE. J) WRITE (IOUT,1011) K1,K2,K3 IF (I .EQ. J) WRITE (IOUT,1012) K1,K2,K3 WRITE (IOUT,1020) IT,IBETA W = -999.0E0 IF (R6 .NE. ZERO) W = ALOG(ABS(R6))/ALBETA WRITE (IOUT,1021) R6,IBETA,W,X1 W = AMAX1(AIT+W,ZERO) WRITE (IOUT,1022) IBETA,W W = -999.0E0 IF (R7 .NE. ZERO) W = ALOG(ABS(R7))/ALBETA WRITE (IOUT,1023) R7,IBETA,W W = AMAX1(AIT+W,ZERO) WRITE (IOUT,1022) IBETA,W IF (J .NE. 2) GO TO 300 B = ALXMAX A = THREE 300 CONTINUE C----------------------------------------------------------------- C SPECIAL TESTS C----------------------------------------------------------------- WRITE (IOUT,1025) WRITE (IOUT,1030) C DO 320 I = 1, 5 X = REN(I1) * A Z = SINH(X) + SINH(-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 - SINH(X) WRITE (IOUT,1060) X, Z X = X / BETA 330 CONTINUE C WRITE (IOUT,1032) C DO 340 I = 1, 5 X = REN(I1) * A Z = COSH(X) - COSH(-X) WRITE (IOUT,1060) X, Z 340 CONTINUE C WRITE (IOUT,1035) X = BETA ** (FLOAT(MINEXP)*0.75E0) Y = SINH(X) WRITE (IOUT,1061) X, Y C----------------------------------------------------------------- C TEST OF ERROR RETURNS C----------------------------------------------------------------- WRITE (IOUT,1050) X = ALXMAX + 0.125E0 WRITE (IOUT,1051) X Y = SINH(X) WRITE (IOUT,1055) Y X = BETAP WRITE (IOUT,1052) X Y = SINH(X) WRITE (IOUT,1055) Y WRITE (IOUT,1100) STOP 1000 FORMAT(45H1TEST OF SINH(X) VS T.S. EXPANSION OF SINH(X) //) 1001 FORMAT(43H1TEST OF SINH(X) VS C*(SINH(X+1)+SINH(X-1)) //) 1005 FORMAT(45H1TEST OF COSH(X) VS T.S. EXPANSION OF COSH(X) //) 1006 FORMAT(43H1TEST OF COSH(X) VS C*(COSH(X+1)+COSH(X-1)) //) 1010 FORMAT(I7,47H RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL / 1 6X,1H(,E15.4,1H,,E15.4,1H)//) 1011 FORMAT(19H SINH(X) WAS LARGER,I6,7H TIMES, / 1 12X,7H AGREED,I6,11H TIMES, AND / 1 8X,11HWAS SMALLER,I6,7H TIMES.//) 1012 FORMAT(19H COSH(X) WAS LARGER,I6,7H TIMES, / 1 12X,7H AGREED,I6,11H TIMES, AND / 1 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(51H THE IDENTITY SINH(-X) = -SINH(X) WILL BE TESTED.// 1 8X,1HX,9X,12HF(X) + F(-X)/) 1031 FORMAT(52H THE IDENTITY SINH(X) = X , X SMALL, WILL BE TESTED.// 1 8X,1HX,9X,8HX - F(X)/) 1032 FORMAT(50H THE IDENTITY COSH(-X) = COSH(X) WILL BE TESTED.// 1 8X,1HX,9X,12HF(X) - F(-X)/) 1035 FORMAT(43H TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT. /) 1050 FORMAT(22H1TEST OF ERROR RETURNS//) 1051 FORMAT(38H SINH WILL BE CALLED WITH THE ARGUMENT,E15.4/ 1 41H THIS SHOULD NOT TRIGGER AN ERROR MESSAGE//) 1052 FORMAT(38H0SINH WILL BE CALLED WITH THE ARGUMENT,E15.4/ 1 37H THIS SHOULD TRIGGER AN ERROR MESSAGE//) 1055 FORMAT(24H SINH RETURNED THE VALUE,E15.4///) 1060 FORMAT(2E15.7/) 1061 FORMAT(6X,6H SINH(,E13.6,3H) =,E13.6/) 1100 FORMAT(25H THIS CONCLUDES THE TESTS ) C ---------- LAST CARD OF SINH/COSH TEST PROGRAM ---------- END REAL 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 = FLOAT(IY) / 2796203.0E0 RETURN C ---------- LAST CARD OF RAN ---------- END