OUTPUT OF VALUES FROM SMACHAR FIRST LINE IS IBETA, IT, IRND, NGRD, MACHEP, NEGEP, ,IEXP, MINEXP, MAXEXP SECOND LINE IS EPS, EPSNEG, XMIN, XMAX THIRD LINE IS AS SECOND 16 6 0 1 -5 -6 7 -65 63 0.9536743164063E-06 0.5960464477539E-07 0.5397605346934E-78 0.7237005145973E+76 3C100000 3B100000 100000 7FFFFFFF ******************************************************************************** TEST OF SQRT(X*X) - X 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.2500E+00, 0.1000E+01) SQRT(X) WAS LARGER 0 TIMES, AGREED 7 TIMES, AND WAS SMALLER 1993 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.4757E-06 = 16 ** -5.25 OCCURRED FOR X = 0.250577E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.75 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.1840E-06 = 16 ** -5.59 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.41 AVERAGE EVALUATION TIME: 9.2000 MICRO-SECONDS. ******************************************************************************** TEST OF SQRT(X*X) - X 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.1000E+01, 0.4000E+01) SQRT(X) WAS LARGER 0 TIMES, AGREED 2000 TIMES, AND WAS SMALLER 0 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.0000E+00 = 16 **-999.00 OCCURRED FOR X = 0.000000E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.00 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.0000E+00 = 16 **-999.00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.00 AVERAGE EVALUATION TIME: 10.400 MICRO-SECONDS. TEST OF SPECIAL ARGUMENTS SQRT(XMIN) = SQRT( 0.5397605E-78) = 0.7346840E-39 SQRT(1-EPSNEG) = SQRT(1- 0.5960464E-07) = 0.1000000E+01 SQRT(1.0) = SQRT( 0.1000000E+01) = 0.1000000E+01 SQRT(1+EPS) = SQRT(1+ 0.9536743E-06) = 0.1000001E+01 SQRT(XMAX) = SQRT( 0.7237005E+76) = 0.8507059E+38 TEST OF ERROR RETURNS SQRT WILL BE CALLED WITH THE ARGUMENT 0.0000E+00 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE SQRT RETURNED THE VALUE 0.0000E+00 0 SQRT WILL BE CALLED WITH THE ARGUMENT -0.1000E+01 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 18: SQRT ARG NEGATIVE SQRT RETURNED THE VALUE 0.0000E+00 THIS CONCLUDES THE TESTS ******************************************************************************** TEST OF ALOG(X) VS T.S. EXPANSION OF ALOG(1+Y) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL (1-EPS,1+EPS), WHERE EPS = 0.3906E-02 ALOG(X) WAS LARGER 469 TIMES, AGREED 1203 TIMES, AND WAS SMALLER 328 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.9391E-06 = 16 ** -5.01 OCCURRED FOR X = 0.100025E+01 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.99 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.9502E-07 = 16 ** -5.83 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.17 AVERAGE EVALUATION TIME: 11.600 MICRO-SECONDS. TEST OF ALOG(X) VS ALOG(17X/16)-ALOG(17/16) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.7071E+00, 0.9375E+00) ALOG(X) WAS LARGER 0 TIMES, AGREED 1106 TIMES, AND WAS SMALLER 894 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.9225E-06 = 16 ** -5.01 OCCURRED FOR X = 0.937428E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.99 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.2870E-06 = 16 ** -5.43 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.57 AVERAGE EVALUATION TIME: 12.000 MICRO-SECONDS. TEST OF ALOG10(X) VS ALOG10(11X/10)-ALOG10(11/10) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.3162E+00, 0.9000E+00) ALOG10(X) WAS LARGER 0 TIMES, AGREED 997 TIMES, AND WAS SMALLER 1003 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.1350E-05 = 16 ** -4.87 OCCURRED FOR X = 0.897594E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.13 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.3026E-06 = 16 ** -5.41 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.59 AVERAGE EVALUATION TIME: 14.400 MICRO-SECONDS. TEST OF ALOG(X*X) VS 2 * ALOG(X) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.1600E+02, 0.2400E+03) ALOG(X) WAS LARGER 983 TIMES, AGREED 1017 TIMES, AND WAS SMALLER 0 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.2291E-06 = 16 ** -5.51 OCCURRED FOR X = 0.642111E+02 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.49 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.7456E-07 = 16 ** -5.92 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.08 AVERAGE EVALUATION TIME: 12.400 MICRO-SECONDS. SPECIAL TESTS THE IDENTITY ALOG(X) = -ALOG(1/X) WILL BE TESTED. X F(X) + F(1/X) 0.1578326E+02 0.0000000E+00 0.1690732E+02 0.0000000E+00 0.1541536E+02 -0.9536743E-06 0.1692023E+02 -0.9536743E-06 0.1502862E+02 0.0000000E+00 TEST OF SPECIAL ARGUMENTS ALOG(1.0) = 0.0000000E+00 ALOG(XMIN) = ALOG( 0.5397605E-78) = -0.1802183E+03 ALOG(XMAX) = ALOG( 0.7237005E+76) = 0.1746731E+03 TEST OF ERROR RETURNS ALOG WILL BE CALLED WITH THE ARGUMENT -0.2000E+01 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 21: ALOG ARG NEGATIVE OR ZERO ALOG RETURNED THE VALUE 0.6931E+00 ALOG WILL BE CALLED WITH THE ARGUMENT 0.0000E+00 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 21: ALOG ARG NEGATIVE OR ZERO ALOG RETURNED THE VALUE -0.7237E+76 THIS CONCLUDES THE TESTS ******************************************************************************** TEST OF EXP(X- 0.0625) VS EXP(X)/ EXP( 0.0625) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( -0.2841E+00, 0.3466E+00) EXP(X-V) WAS LARGER 1196 TIMES, AGREED 692 TIMES, AND WAS SMALLER 112 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.1554E-05 = 16 ** -4.82 OCCURRED FOR X = 0.267487E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.18 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.4177E-06 = 16 ** -5.30 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.70 AVERAGE EVALUATION TIME: 15.200 MICRO-SECONDS. ******************************************************************************** TEST OF EXP(X- 2.8125) VS EXP(X)/ EXP( 2.8125) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( -0.3466E+01, -0.1622E+03) EXP(X-V) WAS LARGER 973 TIMES, AGREED 879 TIMES, AND WAS SMALLER 148 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.1238E-05 = 16 ** -4.91 OCCURRED FOR X = -0.129839E+03 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.09 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.2958E-06 = 16 ** -5.42 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.58 AVERAGE EVALUATION TIME: 14.800 MICRO-SECONDS. ******************************************************************************** TEST OF EXP(X- 2.8125) VS EXP(X)/ EXP( 2.8125) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.6931E+01, 0.1746E+03) EXP(X-V) WAS LARGER 946 TIMES, AGREED 884 TIMES, AND WAS SMALLER 170 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.9533E-06 = 16 ** -5.00 OCCURRED FOR X = 0.665824E+02 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.00 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.2984E-06 = 16 ** -5.42 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.58 AVERAGE EVALUATION TIME: 15.200 MICRO-SECONDS. SPECIAL TESTS THE IDENTITY EXP(X)* EXP(-X) = 1.0 WILL BE TESTED. X F(X)*F(-X) - 1 0.5821940E+01 -0.5960464E-07 0.7742585E+01 -0.4768372E-06 0.7823152E+01 -0.1788139E-06 0.1893950E+01 -0.5960464E-07 0.1274390E+02 0.0000000E+00 TEST OF SPECIAL ARGUMENTS EXP(0.0) - 1.0E0 = 0.0000000E+00 EXP(-0.180000E+03) = 0.671418E-78 EXP( 0.174000E+03) = 0.369181E+76 0IF EXP( 0.870000E+02) = 0.607603E+38 IS NOT ABOUT EXP( 0.435000E+02)**2 = 0.607603E+38 THERE IS AN ARG RED ERROR TEST OF ERROR RETURNS 0 EXP WILL BE CALLED WITH THE ARGUMENT -0.1361E+40 THIS SHOULD TRIGGER AN ERROR MESSAGE EXP RETURNED THE VALUE 0.0000E+00 0 EXP WILL BE CALLED WITH THE ARGUMENT 0.1361E+40 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 19: EXP ARG GREATER THAN 174.6731 EXP RETURNED THE VALUE 0.7237E+76 THIS CONCLUDES THE TESTS ******************************************************************************** TEST OF X**1.0 VS X 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.6250E-01, 0.1000E+01) X**1.0 WAS LARGER 699 TIMES, AGREED 1301 TIMES, AND WAS SMALLER 0 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.9497E-06 = 16 ** -5.00 OCCURRED FOR X = 0.627633E-01 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.00 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.1540E-06 = 16 ** -5.66 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.34 AVERAGE EVALUATION TIME: 25.600 MICRO-SECONDS. TEST OF XSQ**1.5 VS XSQ*X 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.6250E-01, 0.1000E+01) X**1.5 WAS LARGER 161 TIMES, AGREED 1668 TIMES, AND WAS SMALLER 171 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.8745E-06 = 16 ** -5.03 OCCURRED FOR X = 0.162109E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.97 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.9928E-07 = 16 ** -5.82 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.18 AVERAGE EVALUATION TIME: 25.600 MICRO-SECONDS. TEST OF XSQ**1.5 VS XSQ*X 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.1000E+01, 0.1934E+26) X**1.5 WAS LARGER 178 TIMES, AGREED 1683 TIMES, AND WAS SMALLER 139 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.9423E-06 = 16 ** -5.00 OCCURRED FOR X = 0.770690E+25 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.00 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.1012E-06 = 16 ** -5.81 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.19 AVERAGE EVALUATION TIME: 26.400 MICRO-SECONDS. TEST OF X**Y VS XSQ**(Y/2) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE REGION X IN ( 0.1000E-01, 0.1000E+02), Y IN ( -0.3913E+02, 0.3913E+02) X**Y WAS LARGER 339 TIMES, AGREED 1298 TIMES, AND WAS SMALLER 363 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.9534E-06 = 16 ** -5.00 OCCURRED FOR X = 0.368750E+01 Y = 0.849889E+01 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.00 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.1791E-06 = 16 ** -5.60 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.40 AVERAGE EVALUATION TIME: 24.800 MICRO-SECONDS. TEST OF X**N VS X**FLOAT(N) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE REGION X IN ( -0.1000E+03, 0.1000E+03), J IN ( -100, 100) X**N WAS LARGER 333 TIMES, AGREED 1554 TIMES, AND WAS SMALLER 113 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.8756E-06 = 16 ** -5.03 OCCURRED FOR X = 0.130000E+02 Y = 0.533567E+02 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.97 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.1542E-06 = 16 ** -5.66 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.34 AVERAGE EVALUATION TIME: 20.000 MICRO-SECONDS. SPECIAL TESTS THE IDENTITY X ** Y = (1/X) ** (-Y) WILL BE TESTED. X Y (X**Y-(1/X)**(-Y) / X**Y 0.7703258E+01 0.8907244E+01 -0.3239029E-05 0.9405526E+01 0.1690883E+01 -0.3448605E-06 0.7360414E+01 0.6051806E+01 -0.2481153E-05 0.2475968E+01 0.5496172E+01 -0.7320275E-06 0.3021516E+01 0.3689539E+01 -0.2580546E-06 TEST OF ERROR RETURNS ( 0.1600000E+02 ) ** (-0.6400000E+02 ) WILL BE COMPUTED. THIS SHOULD NOT TRIGGER AN ERROR MESSAGE THE VALUE RETURNED IS 0.8636E-77 ( 0.1600000E+02 ) ** ( 0.6200000E+02 ) WILL BE COMPUTED. THIS SHOULD NOT TRIGGER AN ERROR MESSAGE THE VALUE RETURNED IS 0.4523E+75 ( 0.0000000E+00 ) ** ( 0.2000000E+01 ) WILL BE COMPUTED. THIS SHOULD NOT TRIGGER AN ERROR MESSAGE THE VALUE RETURNED IS 0.0000E+00 (-0.2000000E+01 ) ** ( 0.0000000E+00 ) WILL BE COMPUTED. THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 23: NEGATIVE S.P. VALUE RAISED TO A NON-INTEGER POWER THE VALUE RETURNED IS 0.1000E+01 (-0.2000000E+01 ) ** ( 0.2000000E+01 ) WILL BE COMPUTED. THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 23: NEGATIVE S.P. VALUE RAISED TO A NON-INTEGER POWER THE VALUE RETURNED IS 0.4000E+01 ( 0.0000000E+00 ) ** ( 0.0000000E+00 ) WILL BE COMPUTED. THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 22: S.P. ZERO RAISED TO NON-POSITIVE POWER THE VALUE RETURNED IS 0.7237E+76 ( 0.0000000E+00 ) ** ( -1) WILL BE COMPUTED. THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 22: S.P. ZERO RAISED TO NON-POSITIVE POWER THE VALUE RETURNED IS 0.0000E+00 THIS CONCLUDES THE TESTS ******************************************************************************** TEST OF SIN(X) VS 3* SIN(X/3)-4* SIN(X/3)**3 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.0000E+00, 0.1571E+01) SIN(X) WAS LARGER 1740 TIMES, AGREED 228 TIMES, AND WAS SMALLER 32 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.1231E-05 = 16 ** -4.91 OCCURRED FOR X = 0.194946E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.09 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.3162E-06 = 16 ** -5.40 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.60 AVERAGE EVALUATION TIME: 13.200 MICRO-SECONDS. ******************************************************************************** TEST OF SIN(X) VS 3* SIN(X/3)-4* SIN(X/3)**3 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.1885E+02, 0.2042E+02) SIN(X) WAS LARGER 1763 TIMES, AGREED 188 TIMES, AND WAS SMALLER 49 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.1055E-05 = 16 ** -4.96 OCCURRED FOR X = 0.190776E+02 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.04 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.3226E-06 = 16 ** -5.39 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.61 AVERAGE EVALUATION TIME: 13.200 MICRO-SECONDS. TEST OF COS(X) VS 4* COS(X/3)**3-3* COS(X/3) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.2199E+02, 0.2356E+02) COS(X) WAS LARGER 1866 TIMES, AGREED 111 TIMES, AND WAS SMALLER 23 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.1261E-05 = 16 ** -4.90 OCCURRED FOR X = 0.233717E+02 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.10 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.4041E-06 = 16 ** -5.31 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.69 AVERAGE EVALUATION TIME: 12.800 MICRO-SECONDS. SPECIAL TESTS IF 0.100000E+01 IS NOT ALMOST 1.0E0, SIN HAS THE WRONG PERIOD. THE IDENTITY SIN(-X) = - SIN(X) WILL BE TESTED. X F(X) + F(-X) 0.1170326E+02 0.0000000E+00 0.1149189E+02 0.0000000E+00 0.3920447E+01 0.0000000E+00 0.1881734E+02 0.0000000E+00 0.1482341E+02 0.0000000E+00 THE IDENTITY SIN(X) = X , X SMALL, WILL BE TESTED. X X - F(X) 0.1793191E-07 0.0000000E+00 0.1120745E-08 0.0000000E+00 0.7004654E-10 0.0000000E+00 0.4377909E-11 0.0000000E+00 0.2736193E-12 0.0000000E+00 THE IDENTITY COS(-X) = COS(X) WILL BE TESTED. X F(X) - F(-X) 0.1142192E+02 0.0000000E+00 0.1402339E+02 0.0000000E+00 0.1876524E+02 0.0000000E+00 0.8313172E+01 0.0000000E+00 0.2421477E+01 0.0000000E+00 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT. SIN( 0.199136E-58) = 0.199136E-58 THE FOLLOWING THREE LINES ILLUSTRATE THE LOSS IN SIGNIFICANCE FOR LARGE ARGUMENTS. THE ARGUMENTS ARE CONSECUTIVE. SIN( 0.409600E+04) =-0.594838E+00 SIN( 0.409600E+04) =-0.594642E+00 SIN( 0.409600E+04) =-0.591497E+00 TEST OF ERROR RETURNS SIN WILL BE CALLED WITH THE ARGUMENT 0.1678E+08 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 26: SIN ARG MAGNITUDE GREATER THAN 5.274E7 SIN RETURNED THE VALUE 0.0000E+00 COS WILL BE CALLED WITH THE ARGUMENT 0.1678E+08 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 27: COS ARG MAGNITUDE GREATER THAN 5.274E7 COS RETURNED THE VALUE 0.0000E+00 THIS CONCLUDES THE TESTS ******************************************************************************** TEST OF TAN(X) VS 2* TAN(X/2)/(1- TAN(X/2)**2) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.0000E+00, 0.7854E+00) TAN(X) WAS LARGER 433 TIMES, AGREED 352 TIMES, AND WAS SMALLER 1215 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.1675E-05 = 16 ** -4.80 OCCURRED FOR X = 0.710374E-01 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.20 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.3883E-06 = 16 ** -5.32 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.68 AVERAGE EVALUATION TIME: 12.800 MICRO-SECONDS. ******************************************************************************** TEST OF TAN(X) VS 2* TAN(X/2)/(1- TAN(X/2)**2) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.2749E+01, 0.3534E+01) TAN(X) WAS LARGER 588 TIMES, AGREED 319 TIMES, AND WAS SMALLER 1093 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.2446E-05 = 16 ** -4.66 OCCURRED FOR X = 0.326284E+01 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.34 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.6090E-06 = 16 ** -5.16 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.84 AVERAGE EVALUATION TIME: 12.800 MICRO-SECONDS. ******************************************************************************** TEST OF TAN(X) VS 2* TAN(X/2)/(1- TAN(X/2)**2) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.1885E+02, 0.1963E+02) TAN(X) WAS LARGER 840 TIMES, AGREED 374 TIMES, AND WAS SMALLER 786 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.1721E-05 = 16 ** -4.79 OCCURRED FOR X = 0.189872E+02 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.21 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.3858E-06 = 16 ** -5.33 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.67 AVERAGE EVALUATION TIME: 12.800 MICRO-SECONDS. TEST OF COTAN(X) VS ( COTAN(X/2)**2-1)/(2* COTAN(X/2)) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.1885E+02, 0.1963E+02) COTAN(X) WAS LARGER 537 TIMES, AGREED 968 TIMES, AND WAS SMALLER 495 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.1586E-05 = 16 ** -4.82 OCCURRED FOR X = 0.189678E+02 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.18 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.4794E-06 = 16 ** -5.25 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.75 AVERAGE EVALUATION TIME: 13.600 MICRO-SECONDS. SPECIAL TESTS THE IDENTITY TAN(-X) = - TAN(X) WILL BE TESTED. X F(X) + F(-X) 0.1018615E+02 0.0000000E+00 0.1034947E+02 0.0000000E+00 0.1191457E+02 0.0000000E+00 0.2070400E+00 0.0000000E+00 0.7030465E+01 0.0000000E+00 THE IDENTITY TAN(X) = X , X SMALL, WILL BE TESTED. X X - F(X) 0.3708845E-07 0.0000000E+00 0.2318028E-08 0.0000000E+00 0.1448767E-09 0.0000000E+00 0.9054797E-11 0.0000000E+00 0.5659248E-12 0.0000000E+00 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT. TAN( 0.199136E-58) = 0.199136E-58 THE RELATIVE ERROR IN TAN(11) IS -0.6974733E-06 = 16 ** -5.11 WHERE TAN( 0.110000E+02) =-0.225951E+03 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.89 TEST OF ERROR RETURNS TAN WILL BE CALLED WITH THE ARGUMENT 0.4096E+04 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE TAN RETURNED THE VALUE -0.7396E+00 0 TAN WILL BE CALLED WITH THE ARGUMENT 0.1678E+08 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 28: TAN/COTAN ARG MAGNITUDE GREATER THAN 2.633E7 TAN RETURNED THE VALUE 0.7237E+76 0 COTAN WILL BE CALLED WITH THE ARGUMENT 0.0000E+00 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 41: COTAN ARG SMALL IN MAGNITUDE COTAN RETURNED THE VALUE 0.7237E+76 THIS CONCLUDES THE TESTS ******************************************************************************** TEST OF ASIN(X) VS TAYLOR SERIES 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( -0.1250E+00, 0.1250E+00) ASIN(X) WAS LARGER 0 TIMES, AGREED 1023 TIMES, AND WAS SMALLER 977 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.9513E-06 = 16 ** -5.00 OCCURRED FOR X = -0.626156E-01 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.00 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.3544E-06 = 16 ** -5.36 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.64 AVERAGE EVALUATION TIME: 8.8000 MICRO-SECONDS. TEST OF ACOS(X) VS TAYLOR SERIES 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( -0.1250E+00, 0.1250E+00) ACOS(X) WAS LARGER 0 TIMES, AGREED 395 TIMES, AND WAS SMALLER 1605 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.6597E-06 = 16 ** -5.13 OCCURRED FOR X = 0.124927E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.87 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.5450E-06 = 16 ** -5.20 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.80 AVERAGE EVALUATION TIME: 9.6000 MICRO-SECONDS. ******************************************************************************** TEST OF ASIN(X) VS TAYLOR SERIES 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.7500E+00, 0.1000E+01) ASIN(X) WAS LARGER 0 TIMES, AGREED 227 TIMES, AND WAS SMALLER 1773 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.9535E-06 = 16 ** -5.00 OCCURRED FOR X = 0.841581E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.00 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.6237E-06 = 16 ** -5.15 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.85 AVERAGE EVALUATION TIME: 21.600 MICRO-SECONDS. TEST OF ACOS(X) VS TAYLOR SERIES 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.7500E+00, 0.1000E+01) ACOS(X) WAS LARGER 0 TIMES, AGREED 986 TIMES, AND WAS SMALLER 1014 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.9445E-06 = 16 ** -5.00 OCCURRED FOR X = 0.998010E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.00 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.1312E-06 = 16 ** -5.72 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.28 AVERAGE EVALUATION TIME: 20.800 MICRO-SECONDS. TEST OF ACOS(X) VS TAYLOR SERIES 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( -0.1000E+01, -0.7500E+00) ACOS(X) WAS LARGER 0 TIMES, AGREED 0 TIMES, AND WAS SMALLER 2000 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.7879E-06 = 16 ** -5.07 OCCURRED FOR X = -0.751239E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.93 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.4371E-06 = 16 ** -5.28 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.72 AVERAGE EVALUATION TIME: 21.200 MICRO-SECONDS. SPECIAL TESTS THE IDENTITY ASIN(-X) = - ASIN(X) WILL BE TESTED.// X F(X) + F(-X) -0.8953098E+00 0.0000000E+00 -0.9137273E+00 0.0000000E+00 -0.2159117E+00 0.0000000E+00 -0.9889650E+00 0.0000000E+00 -0.6206294E+00 0.0000000E+00 THE IDENTITY ASIN(X) = X , X SMALL, WILL BE TESTED. X X - F(X) 0.3449227E-07 0.0000000E+00 0.2155767E-08 0.0000000E+00 0.1347354E-09 0.0000000E+00 0.8420965E-11 0.0000000E+00 0.5263103E-12 0.0000000E+00 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT. ASIN( 0.199136E-58) = 0.199136E-58 TEST OF ERROR RETURNS ASIN WILL BE CALLED WITH THE ARGUMENT 0.1200E+01 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 29: ASIN ARG MAGNITUDE GREATER THAN 1.0 ASIN RETURNED THE VALUE 0.7237E+76 ACOS WILL BE CALLED WITH THE ARGUMENT 0.1200E+01 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 30: ACOS ARG MAGNITUDE GREATER THAN 1.0 ACOS RETURNED THE VALUE 0.7237E+76 THIS CONCLUDES THE TESTS ******************************************************************************** TEST OF ATAN(X) VS TRUNCATED TAYLOR SERIES 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( -0.6250E-01, 0.6250E-01) ATAN(X) WAS LARGER 60 TIMES, AGREED 1106 TIMES, AND WAS SMALLER 834 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.9512E-06 = 16 ** -5.00 OCCURRED FOR X = -0.391646E-02 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.00 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.1622E-06 = 16 ** -5.64 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.36 AVERAGE EVALUATION TIME: 9.6000 MICRO-SECONDS. TEST OF ATAN(X) VS ATAN(1/16) + ATAN((X-1/16)/(1+X/16)) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.6250E-01, 0.2679E+00) ATAN(X) WAS LARGER 1462 TIMES, AGREED 538 TIMES, AND WAS SMALLER 0 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.9471E-06 = 16 ** -5.00 OCCURRED FOR X = 0.126541E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.00 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.4141E-06 = 16 ** -5.30 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.70 AVERAGE EVALUATION TIME: 9.2000 MICRO-SECONDS. TEST OF 2* ATAN(X) VS ATAN(2X/(1-X*X)) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.2679E+00, 0.4142E+00) ATAN(X) WAS LARGER 1144 TIMES, AGREED 509 TIMES, AND WAS SMALLER 347 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.4460E-06 = 16 ** -5.27 OCCURRED FOR X = 0.273868E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.73 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.1451E-06 = 16 ** -5.68 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.32 AVERAGE EVALUATION TIME: 11.600 MICRO-SECONDS. TEST OF 2* ATAN(X) VS ATAN(2X/(1-X*X)) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.4142E+00, 0.1000E+01) ATAN(X) WAS LARGER 825 TIMES, AGREED 1175 TIMES, AND WAS SMALLER 0 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.9626E-06 = 16 ** -5.00 OCCURRED FOR X = 0.425729E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.00 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.3860E-06 = 16 ** -5.33 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.67 AVERAGE EVALUATION TIME: 11.600 MICRO-SECONDS. SPECIAL TESTS THE IDENTITY ATAN(-X) = - ATAN(X) WILL BE TESTED. X F(X) + F(-X) 0.5223724E+00 0.0000000E+00 0.2965825E+00 0.0000000E+00 0.2072818E+01 0.0000000E+00 0.4102254E+01 0.0000000E+00 0.2781752E+01 0.0000000E+00 THE IDENTITY ATAN(X) = X , X SMALL, WILL BE TESTED. X X - F(X) 0.3241392E-07 0.0000000E+00 0.2025870E-08 0.0000000E+00 0.1266169E-09 0.0000000E+00 0.7913553E-11 0.0000000E+00 0.4945971E-12 0.0000000E+00 THE IDENTITY ATAN(X/Y) = ATAN2(X,Y) WILL BE TESTED THE FIRST COLUMN OF RESULTS SHOULD BE 0, THE SECOND +-PI X Y F1(X/Y)-F2(X,Y) F1(X/(-Y))-F2(X,(-Y)) 0.1907655E+01 0.1142116E+00 0.0000000E+00 -0.3141593E+01 -0.8941679E+00 0.5572639E+00 0.0000000E+00 0.3141593E+01 0.6319513E+00 0.2484991E+00 0.0000000E+00 -0.3141593E+01 -0.1750437E+01 0.7988347E+00 0.0000000E+00 0.3141593E+01 0.1417353E+01 0.7922733E+00 0.0000000E+00 -0.3141593E+01 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT. ATAN( 0.199136E-58) = 0.199136E-58 TEST OF ERROR RETURNS ATAN WILL BE CALLED WITH THE ARGUMENT 0.7237005E+76 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE ATAN( 0.723701E+76) = 0.157080E+01 ATAN2 WILL BE CALLED WITH THE ARGUMENTS 0.1000000E+01 0.0000000E+00 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE ATAN2( 0.100000E+01 0.000000E+00) = 0.157080E+01 ATAN2 WILL BE CALLED WITH THE ARGUMENTS 0.5397605E-78 0.7237005E+76 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE ATAN2( 0.539761E-78 0.723701E+76) = 0.000000E+00 ATAN2 WILL BE CALLED WITH THE ARGUMENTS 0.7237005E+76 0.5397605E-78 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE ATAN2( 0.723701E+76 0.539761E-78) = 0.157080E+01 ATAN2 WILL BE CALLED WITH THE ARGUMENTS 0.0000000E+00 0.0000000E+00 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 31: ATAN2 ARGS ZERO ATAN2( 0.000000E+00 0.000000E+00) = 0.000000E+00 THIS CONCLUDES THE TESTS ******************************************************************************** TEST OF SINH(X) VS T.S. EXPANSION OF SINH(X) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.0000E+00, 0.5000E+00) SINH(X) WAS LARGER 0 TIMES, AGREED 888 TIMES, AND WAS SMALLER 1112 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.9461E-06 = 16 ** -5.00 OCCURRED FOR X = 0.629582E-01 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.00 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.2364E-06 = 16 ** -5.50 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.50 AVERAGE EVALUATION TIME: 6.8000 MICRO-SECONDS. TEST OF COSH(X) VS T.S. EXPANSION OF COSH(X) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.0000E+00, 0.5000E+00) COSH(X) WAS LARGER 0 TIMES, AGREED 930 TIMES, AND WAS SMALLER 1070 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.9537E-06 = 16 ** -5.00 OCCURRED FOR X = 0.104186E-02 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.00 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.6725E-06 = 16 ** -5.13 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.87 AVERAGE EVALUATION TIME: 20.400 MICRO-SECONDS. TEST OF SINH(X) VS C*( SINH(X+1)+ SINH(X-1)) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.3000E+01, 0.1747E+03) SINH(X) WAS LARGER 1140 TIMES, AGREED 627 TIMES, AND WAS SMALLER 233 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.2669E-05 = 16 ** -4.63 OCCURRED FOR X = 0.329957E+02 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.37 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.6400E-06 = 16 ** -5.14 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.86 AVERAGE EVALUATION TIME: 19.600 MICRO-SECONDS. TEST OF COSH(X) VS C*( COSH(X+1)+ COSH(X-1)) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.3000E+01, 0.1747E+03) COSH(X) WAS LARGER 1125 TIMES, AGREED 637 TIMES, AND WAS SMALLER 238 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.2557E-05 = 16 ** -4.64 OCCURRED FOR X = 0.143881E+03 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.36 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.6531E-06 = 16 ** -5.14 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.86 AVERAGE EVALUATION TIME: 19.600 MICRO-SECONDS. SPECIAL TESTS THE IDENTITY SINH(-X) = - SINH(X) WILL BE TESTED. X F(X) + F(-X) 0.2177354E+01 0.0000000E+00 0.2169349E+01 0.0000000E+00 0.1168616E+01 0.0000000E+00 0.2077108E+01 0.0000000E+00 0.1638606E+01 0.0000000E+00 THE IDENTITY SINH(X) = X , X SMALL, WILL BE TESTED. X X - F(X) 0.1640705E-07 0.0000000E+00 0.1025441E-08 0.0000000E+00 0.6409005E-10 0.0000000E+00 0.4005628E-11 0.0000000E+00 0.2503518E-12 0.0000000E+00 THE IDENTITY COSH(-X) = COSH(X) WILL BE TESTED. X F(X) - F(-X) 0.1224265E+01 0.0000000E+00 0.3314887E-01 0.0000000E+00 0.1143610E+01 0.0000000E+00 0.1951262E+01 0.0000000E+00 0.9078546E+00 0.0000000E+00 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT. SINH( 0.199136E-58) = 0.199136E-58 TEST OF ERROR RETURNS SINH WILL BE CALLED WITH THE ARGUMENT 0.1748E+03 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE SINH RETURNED THE VALUE 0.4100E+76 0 SINH WILL BE CALLED WITH THE ARGUMENT 0.1678E+08 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 32: SINH ARG MAGNITUDE GREATER THAN 175.3662 SINH RETURNED THE VALUE 0.7237E+76 COSH WILL BE CALLED WITH THE ARGUMENT 0.1678E+08 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 33: COSH ARG MAGNITUDE GREATER THAN 175.3662 COSH RETURNED THE VALUE 0.7237E+76 THIS CONCLUDES THE TESTS ******************************************************************************** TEST OF TANH(X) VS ( TANH(X-1/8)+ TANH(1/8))/(1+ TANH(X-1/8) TANH(1/8)) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.1250E+00, 0.5493E+00) TANH(X) WAS LARGER 139 TIMES, AGREED 430 TIMES, AND WAS SMALLER 1431 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.9752E-06 = 16 ** -4.99 OCCURRED FOR X = 0.315685E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.01 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.4329E-06 = 16 ** -5.28 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.72 AVERAGE EVALUATION TIME: 7.6000 MICRO-SECONDS. ******************************************************************************** TEST OF TANH(X) VS ( TANH(X-1/8)+ TANH(1/8))/(1+ TANH(X-1/8) TANH(1/8)) 2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL ( 0.6743E+00, 0.1040E+02) TANH(X) WAS LARGER 716 TIMES, AGREED 224 TIMES, AND WAS SMALLER 1060 TIMES. THERE ARE 6 BASE 16 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER THE MAXIMUM RELATIVE ERROR OF 0.1082E-05 = 16 ** -4.95 OCCURRED FOR X = 0.138069E+01 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.05 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.3196E-06 = 16 ** -5.39 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.61 AVERAGE EVALUATION TIME: 20.800 MICRO-SECONDS. SPECIAL TESTS THE IDENTITY TANH(-X) = - TANH(X) WILL BE TESTED. X F(X) + F(-X) 0.6674010E-01 0.0000000E+00 0.3425184E+00 0.0000000E+00 0.8148010E+00 0.0000000E+00 0.8501250E+00 0.0000000E+00 0.2656216E+00 0.0000000E+00 THE IDENTITY TANH(X) = X , X SMALL, WILL BE TESTED. X X - F(X) 0.1208209E-07 0.0000000E+00 0.7551304E-09 0.0000000E+00 0.4719565E-10 0.0000000E+00 0.2949728E-11 0.0000000E+00 0.1843580E-12 0.0000000E+00 THE IDENTITY TANH(X) = 1 , X LARGE, WILL BE TESTED. X 1 - F(X) 0.1039720E+02 0.0000000E+00 0.1439720E+02 0.0000000E+00 0.1839720E+02 0.0000000E+00 0.2239720E+02 0.0000000E+00 0.2639720E+02 0.0000000E+00 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT. TANH( 0.199136E-58) = 0.199136E-58 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT 0.7237005E+76 TANH( 0.723701E+76) = 0.100000E+01 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT 0.5397605E-78 TANH( 0.539761E-78) = 0.539761E-78 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT 0.0000000E+00 TANH( 0.000000E+00) = 0.000000E+00 THIS CONCLUDES THE TESTS ******************************************************************************** TEST OF GAMMA USING RESULTS FROM FILE. TEST OF--GAMMA-- AGAINST SAMPLE DATA AND RESULTS 0 100 ARGUMENTS IN SAMPLE, BETWEEN 0.00E+00 AND 2.00E+00 SAMPLE DISTRIBUTION UNI ERROR MEASURE REL, REPRESENTATION ERROR = 9.54E-07 PRINT IN FULL FIRST POINT, ALSO PRINT IN FULL IF(ERROR.GE. 50*REP.ERR.) 0 X Y YEXP ERR/REP.ERR 3.72314010747E-03 2.68016845703E+02 2.680168457031E+02 0.00 0MEAN ERROR = 6.82E-07 ( 0.71)*REP.ERR. RMS ERROR = 8.17E-07 ( 0.86)*REP.ERR. MAX ERROR = 1.97E-06 ( 2.06)*REP.ERR. THE MAXIMUM ERROR OF 0.1965E-05 = 16 ** -4.74 OCCURRED FOR X = 0.614899E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.26 THE ROOT MEAN SQUARE ERROR WAS 0.8173E-06 = 16 ** -5.06 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.94 AVERAGE EVALUATION TIME: 13.200 MICRO-SECONDS. TEST OF--GAMMA-- AGAINST SAMPLE DATA AND RESULTS 0 100 ARGUMENTS IN SAMPLE, BETWEEN 2.00E+00 AND 5.70E+01 SAMPLE DISTRIBUTION UNI ERROR MEASURE REL/X, REPRESENTATION ERROR = 9.54E-07 PRINT IN FULL FIRST POINT, ALSO PRINT IN FULL IF(ERROR.GE. 50*REP.ERR.) 0 X Y YEXP ERR/REP.ERR 2.42796039581E+00 1.26530647278E+00 1.265307426453E+00 0.33 0MEAN ERROR = 1.60E-07 ( 0.17)*REP.ERR. RMS ERROR = 4.57E-07 ( 0.48)*REP.ERR. MAX ERROR = 1.35E-06 ( 1.42)*REP.ERR. THE MAXIMUM ERROR OF 0.1354E-05 = 16 ** -4.87 OCCURRED FOR X = 0.166735E+02 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.13 THE ROOT MEAN SQUARE ERROR WAS 0.4569E-06 = 16 ** -5.27 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.73 AVERAGE EVALUATION TIME: 53.600 MICRO-SECONDS. TEST OF ERROR RETURNS GAMMA WILL BE CALLED WITH THE ARGUMENT 0.5690E+02 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE GAMMA RETURNED THE VALUE 0.4750E+75 0 GAMMA WILL BE CALLED WITH THE ARGUMENT 0.5710E+02 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 42: GAMMA ARG MAGNITUDE GREATER THAN 57.0 GAMMA RETURNED THE VALUE 0.7100E+75 GAMMA WILL BE CALLED WITH THE ARGUMENT -0.5690E+02 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE GAMMA RETURNED THE VALUE -0.3761E-75 0 GAMMA WILL BE CALLED WITH THE ARGUMENT -0.5710E+02 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 42: GAMMA ARG MAGNITUDE GREATER THAN 57.0 GAMMA RETURNED THE VALUE 0.0000E+00 GAMMA WILL BE CALLED WITH THE ARGUMENT -0.1000E-73 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE GAMMA RETURNED THE VALUE -0.1000E+75 0 GAMMA WILL BE CALLED WITH THE ARGUMENT 0.1000E-75 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 43: GAMMA ARG NEAR ZERO OR NEGATIVE INTEGER GAMMA RETURNED THE VALUE 0.7143E+76 GAMMA WILL BE CALLED WITH THE ARGUMENT -0.1000E+01 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE GAMMA RETURNED THE VALUE -0.9869E+06 0 GAMMA WILL BE CALLED WITH THE ARGUMENT -0.1000E+01 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 43: GAMMA ARG NEAR ZERO OR NEGATIVE INTEGER GAMMA RETURNED THE VALUE 0.7100E+75 THIS CONCLUDES THE TESTS ******************************************************************************** TEST OF ALGAMA USING RESULTS FROM FILE. TEST OF --ALGAMA-- AGAINST SAMPLE DATA AND RESULTS 0 100 ARGUMENTS IN SAMPLE, BETWEEN 1.00E-24 AND 1.00E+25 SAMPLE DISTRIBUTION LOG ERROR MEASURE REL, REPRESENTATION ERROR = 9.54E-07 PRINT IN FULL FIRST POINT, ALSO PRINT IN FULL IF(ERROR.GE. 20*REP.ERR.) 0 X Y YEXP ERR/REP.ERR 1.68615995028E+23 8.84928936086E+24 8.849289360863E+24 0.00 0MEAN ERROR = 1.84E-07 ( 0.19)*REP.ERR. RMS ERROR = 3.36E-07 ( 0.35)*REP.ERR. MAX ERROR = 9.02E-07 ( 0.95)*REP.ERR. THE MAXIMUM RELATIVE ERROR OF 0.9022E-06 = 16 ** -5.02 OCCURRED FOR X = 0.135201E+07 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.98 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.3361E-06 = 16 ** -5.38 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.62 AVERAGE EVALUATION TIME: 20.000 MICRO-SECONDS. TEST OF --ALGAMA-- AGAINST SAMPLE DATA AND RESULTS 0 100 ARGUMENTS IN SAMPLE, BETWEEN 5.00E-01 AND 2.50E+00 SAMPLE DISTRIBUTION UNI ERROR MEASURE ABS, REPRESENTATION ERROR = 9.54E-07 PRINT IN FULL FIRST POINT, ALSO PRINT IN FULL IF(ERROR.GE. 10*REP.ERR.) 0 X Y YEXP ERR/REP.ERR 1.70921039581E+00 -9.38532352448E-02 -9.385341405869E-02 -0.19 0MEAN ERROR = 2.97E-07 ( 0.31)*REP.ERR. RMS ERROR = 5.51E-07 ( 0.58)*REP.ERR. MAX ERROR = 1.68E-06 ( 1.76)*REP.ERR. THE MAXIMUM RELATIVE ERROR OF 0.1676E-05 = 16 ** -4.80 OCCURRED FOR X = 0.967530E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.20 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.5508E-06 = 16 ** -5.20 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.80 AVERAGE EVALUATION TIME: 33.200 MICRO-SECONDS. TEST OF ERROR RETURNS ALGAMA WILL BE CALLED WITH THE ARGUMENT 0.1000E+71 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE ALGAMA RETURNED THE VALUE 0.1602E+73 0ALGAMA WILL BE CALLED WITH THE ARGUMENT 0.1000E+76 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 45: ALGAMA ARG IS GREATER THAN 4.29E73 ALGAMA RETURNED THE VALUE 0.7231E+76 0ALGAMA WILL BE CALLED WITH THE ARGUMENT -0.5690E+02 THIS SHOULD TRIGGER AN ERROR MESSAGE ** ERROR 44: ALGAMA ARG IS NEGATIVE ALGAMA RETURNED THE VALUE 0.0000E+00 THIS CONCLUDES THE TESTS ******************************************************************************** TEST OF ERF USING RESULTS FROM FILE. TEST OF --ERF-- AGAINST SAMPLE DATA AND RESULTS 0 100 ARGUMENTS IN SAMPLE, BETWEEN -6.30E+00 AND 6.30E+00 SAMPLE DISTRIBUTION UNI ERROR MEASURE REL, REPRESENTATION ERROR = 9.54E-07 PRINT IN FULL FIRST POINT, ALSO PRINT IN FULL IF(ERROR.GE. 20*REP.ERR.) 0 X Y YEXP ERR/REP.ERR -6.27652645111E+00 -1.00000000000E+00 -1.000000000000E+00 0.00 0MEAN ERROR = 3.04E-07 ( 0.32)*REP.ERR. RMS ERROR = 7.40E-07 ( 0.78)*REP.ERR. MAX ERROR = 3.13E-06 ( 3.28)*REP.ERR. THE MAXIMUM RELATIVE ERROR OF 0.3129E-05 = 16 ** -4.57 OCCURRED FOR X = -0.183690E+01 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 1.43 THE ROOT MEAN SQUARE RELATIVE ERROR WAS 0.7399E-06 = 16 ** -5.09 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.91 AVERAGE EVALUATION TIME: 14.000 MICRO-SECONDS. TEST OF EXTREME VALUES ERF WILL BE CALLED WITH THE ARGUMENT -0.1000E+02 ERF RETURNED THE VALUE -0.1000E+01 ERF WILL BE CALLED WITH THE ARGUMENT 0.1000E+02 ERF RETURNED THE VALUE 0.1000E+01 THIS CONCLUDES THE TESTS ******************************************************************************** TEST OF ERFC USING RESULTS FROM FILE. TEST OF --ERFC-- AGAINST SAMPLE DATA AND RESULTS 0 35 ARGUMENTS IN SAMPLE, BETWEEN -6.30E+00 AND 5.00E-01 SAMPLE DISTRIBUTION UNI ERROR MEASURE REL, REPRESENTATION ERROR = 9.54E-07 PRINT IN FULL FIRST POINT, ALSO PRINT IN FULL IF(ERROR.GE. 20*REP.ERR.) 0 X Y YEXP ERR/REP.ERR -6.26348590851E+00 2.00000000000E+00 2.000000000000E+00 0.00 0MEAN ERROR = 1.19E-07 ( 0.12)*REP.ERR. RMS ERROR = 2.50E-07 ( 0.26)*REP.ERR. MAX ERROR = 7.33E-07 ( 0.77)*REP.ERR. THE MAXIMUM ERROR OF 0.7327E-06 = 16 ** -5.10 OCCURRED FOR X = -0.273966E+00 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.90 THE ROOT MEAN SQUARE ERROR WAS 0.2502E-06 = 16 ** -5.48 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.52 AVERAGE EVALUATION TIME: 13.610 MICRO-SECONDS. 0 60 ARGUMENTS IN SAMPLE, BETWEEN 5.00E-01 AND 1.23E+01 SAMPLE DISTRIBUTION UNI ERROR MEASURE REL/2*X**2, REPRESENTATION ERROR = 9.54E-07 PRINT IN FULL FIRST POINT, ALSO PRINT IN FULL IF(ERROR.GE. 20*REP.ERR.) 0 X Y YEXP ERR/REP.ERR 6.42596900463E-01 3.63471865654E-01 3.634719252586E-01 0.21 9.56557178497E+00 0.00000000000E+00 1.072405982974E-41 0.00 9.57635974884E+00 0.00000000000E+00 8.713413433636E-42 0.00 9.91481208801E+00 0.00000000000E+00 1.148917845598E-44 0.00 1.01279010773E+01 0.00000000000E+00 1.571543052347E-46 0.00 1.02232990265E+01 0.00000000000E+00 2.234224575992E-47 0.00 1.05529747009E+01 0.00000000000E+00 2.295041853279E-50 0.00 1.06486158371E+01 0.00000000000E+00 2.994130857247E-51 0.00 1.08541650772E+01 0.00000000000E+00 3.535977021827E-53 0.00 1.10156345367E+01 0.00000000000E+00 1.019797250961E-54 0.00 1.12440032959E+01 0.00000000000E+00 6.194182784029E-57 0.00 1.13931407928E+01 0.00000000000E+00 2.089792145941E-58 0.00 1.15744342804E+01 0.00000000000E+00 3.198617010065E-60 0.00 1.18607892990E+01 0.00000000000E+00 3.801532928286E-63 0.00 1.21055393219E+01 0.00000000000E+00 1.056059710654E-65 0.00 1.22215089798E+01 0.00000000000E+00 6.227856513082E-67 0.00 0MEAN ERROR = -6.84E-08 ( -0.07)*REP.ERR. RMS ERROR = 1.70E-07 ( 0.18)*REP.ERR. MAX ERROR = -5.77E-07 ( -0.61)*REP.ERR. THE MAXIMUM SCALED-REL-ERROR OF 0.1703E-06 = 16 ** -5.18 OCCURRED FOR X = 0.102304E+01 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.82 THE ROOT MEAN SQUARE SACLED-REL-ERROR WAS 0.1703E-06 = 16 ** -5.62 THE ESTIMATED LOSS OF BASE 16 SIGNIFICANT DIGITS IS 0.38 AVERAGE EVALUATION TIME: 9.6096 MICRO-SECONDS. TEST OF EXTREME VALUES ERFC WILL BE CALLED WITH THE ARGUMENT -0.1000E+02 ERFC RETURNED THE VALUE 0.2000E+01 ERFC WILL BE CALLED WITH THE ARGUMENT 0.2000E+02 ERFC RETURNED THE VALUE 0.0000E+00 THIS CONCLUDES THE TESTS