C PROGRAM TO TEST SIN/COS 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 FIVE 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 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 EPSNEG - THE SMALLEST POSITIVE FLOATING-POINT C NUMBER SUCH THAT 1.0-EPSNEG .NE. 1.0 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, COS, FLOAT, SIN, 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,IOUT,IRND,IT,I1,J,K1,K2,K3,MACHEP, 1 MAXEXP,MINEXP,N,NEGEP,NGRD REAL A,AIT,ALBETA,B,BETA,BETAP,C,DEL,EPS,EPSNEG,EXPON,ONE,REN, 1 R6,R7,THREE,W,X,XL,XMAX,XMIN,XN,X1,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) AIT = FLOAT(IT) ONE = 1.0E0 ZERO = 0.0E0 THREE = 3.0E0 A = ZERO B = 1.570796327E0 C = B N = 2000 XN = FLOAT(N) I1 = 0 C----------------------------------------------------------------- C RANDOM ARGUMENT ACCURACY TESTS C----------------------------------------------------------------- DO 300 J = 1, 3 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 Y = X / THREE Y = (X + Y) - X X = THREE * Y IF (J .EQ. 3) GO TO 100 Z = SIN(X) ZZ = SIN(Y) W = ONE IF (Z .NE. ZERO) W = (Z - ZZ*(THREE-4.0E0*ZZ*ZZ)) / Z GO TO 110 100 Z = COS(X) ZZ = COS(Y) W = ONE IF (Z .NE. ZERO) W = (Z + ZZ*(THREE-4.0E0*ZZ*ZZ)) / Z 110 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) IF (J .EQ. 3) 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 = -999.0E0 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 A = 18.84955592E0 IF (J .EQ. 2) A = B + C B = A + C 300 CONTINUE C----------------------------------------------------------------- C SPECIAL TESTS C----------------------------------------------------------------- WRITE (IOUT,1025) C = ONE / BETA ** (IT/2) Z = (SIN(A+C) - SIN(A-C)) / (C + C) WRITE (IOUT,1026) Z C WRITE (IOUT,1030) C DO 320 I = 1, 5 X = REN(I1) * A Z = SIN(X) + SIN(-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 - SIN(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 = COS(X) - COS(-X) WRITE (IOUT,1060) X, Z 340 CONTINUE C WRITE (IOUT,1035) EXPON = FLOAT(MINEXP) * 0.75E0 X = BETA ** EXPON Y = SIN(X) WRITE (IOUT,1061) X, Y WRITE (IOUT,1040) Z = SQRT(BETAP) X = Z * (ONE - EPSNEG) Y = SIN(X) WRITE (IOUT,1061) X, Y Y = SIN(Z) WRITE (IOUT,1061) Z, Y X = Z * (ONE + EPS) Y = SIN(X) WRITE (IOUT,1061) X, Y C----------------------------------------------------------------- C TEST OF ERROR RETURNS C----------------------------------------------------------------- WRITE (IOUT,1050) X = BETAP WRITE (IOUT,1052) X Y = SIN(X) WRITE (IOUT,1055) Y WRITE (IOUT,1100) STOP 1000 FORMAT(43H1TEST OF SIN(X) VS 3*SIN(X/3)-4*SIN(X/3)**3 //) 1005 FORMAT(43H1TEST OF COS(X) VS 4*COS(X/3)**3-3*COS(X/3) //) 1010 FORMAT(I7,47H RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL / 1 6X,1H(,E15.4,1H,,E15.4,1H)//) 1011 FORMAT(18H SIN(X) WAS LARGER,I6,7H TIMES, / 1 11X,7H AGREED,I6,11H TIMES, AND / 1 7X,11HWAS SMALLER,I6,7H TIMES.//) 1012 FORMAT(18H COS(X) WAS LARGER,I6,7H TIMES, / 1 11X,7H AGREED,I6,11H TIMES, AND / 1 7X,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//) 1026 FORMAT(4H IF ,E13.6,21H IS NOT ALMOST 1.0E0,, 1 4X,25HSIN HAS THE WRONG PERIOD. //) 1030 FORMAT(51H THE IDENTITY SIN(-X) = -SIN(X) WILL BE TESTED.// 1 8X,1HX,9X,12HF(X) + F(-X)/) 1031 FORMAT(51H THE IDENTITY SIN(X) = X , X SMALL, WILL BE TESTED.// 1 8X,1HX,9X,8HX - F(X)/) 1032 FORMAT(50H THE IDENTITY COS(-X) = COS(X) WILL BE TESTED.// 1 8X,1HX,9X,12HF(X) - F(-X)/) 1035 FORMAT(43H TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.) 1040 FORMAT(49H THE FOLLOWING THREE LINES ILLUSTRATE THE LOSS IN, 1 13H SIGNIFICANCE/36H FOR LARGE ARGUMENTS. THE ARGUMENTS, 2 17H ARE CONSECUTIVE.) 1050 FORMAT(22H1TEST OF ERROR RETURNS//) 1052 FORMAT(37H SIN WILL BE CALLED WITH THE ARGUMENT,E15.4/ 1 37H THIS SHOULD TRIGGER AN ERROR MESSAGE//) 1055 FORMAT(23H SIN RETURNED THE VALUE,E15.4///) 1060 FORMAT(2E15.7/) 1061 FORMAT(/6X,5H SIN(,E13.6,3H) =,E13.6) 1100 FORMAT(25H THIS CONCLUDES THE TESTS ) C ---------- LAST CARD OF SIN/COS 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