 This is talog: ELEFUNT in Java: version 1.00 of Wed May 29 17:12:35 2002

1TEST 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 =      7.6293E-6


 ALOG(X) WAS LARGER     0 TIMES,
             AGREED  2000 TIMES, AND
        WAS SMALLER     0 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF            0.0 =    2 **-999.00
    OCCURRED FOR X =              0.0
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS            0.0 =    2 **-999.00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF ALOG(X) VS ALOG(17X/16)-ALOG(17/16)


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (         0.7071,         0.9375)


 ALOG(X) WAS LARGER     0 TIMES,
             AGREED  1514 TIMES, AND
        WAS SMALLER   486 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.2192E-16 =    2 ** -52.00
    OCCURRED FOR X =         0.778699
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     7.9907E-17 =    2 ** -53.47
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF ALOG10(X) VS ALOG10(11X/10)-ALOG10(11/10)


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (         0.3162,            0.9)


 ALOG10(X) WAS LARGER     0 TIMES,
               AGREED   843 TIMES, AND
          WAS SMALLER  1157 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     5.6527E-16 =    2 ** -50.65
    OCCURRED FOR X =         0.893098
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.35


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.5780E-16 =    2 ** -52.49
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.51


1TEST OF ALOG(X*X) VS 2 * LOG(X)


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (           16.0,          240.0)


 ALOG(X) WAS LARGER    63 TIMES,
             AGREED  1937 TIMES, AND
        WAS SMALLER     0 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.2042E-16 =    2 ** -52.01
    OCCURRED FOR X =        56.228227
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.99


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     2.9647E-17 =    2 ** -54.90
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1SPECIAL TESTS


 THE IDENTITY  ALOG(X) = -ALOG(1/X)  WILL BE TESTED.

        X         F(X) + F(1/X)

     15.9833177  4.4408920E-16

     15.3396062            0.0

     15.3475720  4.4408920E-16

     15.8132313            0.0

     15.7401758            0.0



 TEST OF SPECIAL ARGUMENTS


 ALOG(1.0) =             0.0


 ALOG(XMIN) = ALOG( 2.2250738E-308) =    -708.3964185


 ALOG(XMAX) = ALOG(  1.7976931E308) =     709.7827128


1TEST OF ERROR RETURNS


 ALOG WILL BE CALLED WITH THE ARGUMENT           -2.0
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 ALOG RETURNED THE VALUE            NaN


 ALOG WILL BE CALLED WITH THE ARGUMENT            0.0
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 ALOG RETURNED THE VALUE      -Infinity



 THIS CONCLUDES THE TESTS
 This is tasin: ELEFUNT in Java: version 1.00 of Wed May 29 17:12:35 2002

1TEST OF ASIN(X) VS TAYLOR SERIES

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (         -0.125,          0.125)


 ASIN(X) WAS LARGER   529 TIMES,
             AGREED  1024 TIMES, AND
        WAS SMALLER   447 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.2194E-16 =    2 ** -52.00
    OCCURRED FOR X =         0.031258
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.0937E-16 =    2 ** -53.02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF ACOS(X) VS TAYLOR SERIES

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (         -0.125,          0.125)


 ACOS(X) WAS LARGER   187 TIMES,
             AGREED  1109 TIMES, AND
        WAS SMALLER   704 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.5360E-16 =    2 ** -52.53
    OCCURRED FOR X =         0.124880
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.47


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.4715E-17 =    2 ** -53.23
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF ASIN(X) VS TAYLOR SERIES

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (           0.75,            1.0)


 ASIN(X) WAS LARGER    97 TIMES,
             AGREED  1274 TIMES, AND
        WAS SMALLER   629 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.6100E-16 =    2 ** -51.77
    OCCURRED FOR X =         0.751768
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.23


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.0025E-16 =    2 ** -53.15
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF ACOS(X) VS TAYLOR SERIES

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (           0.75,            1.0)


 ACOS(X) WAS LARGER   280 TIMES,
             AGREED  1178 TIMES, AND
        WAS SMALLER   542 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     4.1797E-16 =    2 ** -51.09
    OCCURRED FOR X =         0.862178
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.91


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.1322E-16 =    2 ** -52.97
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.03


1TEST OF ACOS(X) VS TAYLOR SERIES

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (           -1.0,          -0.75)


 ACOS(X) WAS LARGER    65 TIMES,
             AGREED  1367 TIMES, AND
        WAS SMALLER   568 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.8355E-16 =    2 ** -52.27
    OCCURRED FOR X =        -0.750344
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.73


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.4607E-17 =    2 ** -53.23
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1SPECIAL TESTS

 THE IDENTITY  ASIN(-X) = -ASIN(X)  WILL BE TESTED.

        X         F(X) + F(-X)
     -0.5038411            0.0

     -0.5172135            0.0

     -0.4612708            0.0

     -0.3573967            0.0

     -0.3249756            0.0

 THE IDENTITY ASIN(X) = X , X SMALL, WILL BE TESTED.

        X         X - F(X)
  8.2729393E-17            0.0

  4.1364696E-17            0.0

  2.0682348E-17            0.0

  1.0341174E-17            0.0

  5.1705871E-18            0.0

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       ASIN(1.821831E-231) =1.821831E-231

1TEST OF ERROR RETURNS


 ASIN WILL BE CALLED WITH THE ARGUMENT            1.2
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 ASIN RETURNED THE VALUE            NaN


 THIS CONCLUDES THE TESTS
 This is tatan: ELEFUNT in Java: version 1.00 of Wed May 29 17:12:35 2002

1TEST OF ATAN(X) VS TRUNCATED TAYLOR SERIES

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (        -0.0625,         0.0625)


 ATAN(X) WAS LARGER     9 TIMES,
             AGREED  1991 TIMES, AND
        WAS SMALLER     0 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.7961E-16 =    2 ** -52.31
    OCCURRED FOR X =         0.038650
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.69


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.2089E-18 =    2 ** -56.59
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF ATAN(X) VS ATAN(1/16) + ATAN((X-1/16)/(1+X/16))

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (         0.0625,         0.2679)


 ATAN(X) WAS LARGER   451 TIMES,
             AGREED  1354 TIMES, AND
        WAS SMALLER   195 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.2199E-16 =    2 ** -52.00
    OCCURRED FOR X =         0.125684
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.7027E-17 =    2 ** -53.35
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF 2*ATAN(X) VS ATAN(2X/(1-X*X))

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (         0.2679,         0.4142)


 ATAN(X) WAS LARGER   625 TIMES,
             AGREED  1259 TIMES, AND
        WAS SMALLER   116 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     4.1104E-16 =    2 ** -51.11
    OCCURRED FOR X =         0.276862
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.89


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.0643E-16 =    2 ** -53.06
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF 2*ATAN(X) VS ATAN(2X/(1-X*X))

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (         0.4142,            1.0)


 ATAN(X) WAS LARGER   149 TIMES,
             AGREED  1395 TIMES, AND
        WAS SMALLER   456 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     4.4128E-16 =    2 ** -51.01
    OCCURRED FOR X =         0.550427
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.99


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.0042E-17 =    2 ** -53.30
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1SPECIAL TESTS

 THE IDENTITY   ATAN(-X) = -ATAN(X)   WILL BE TESTED.


        X         F(X) + F(-X)

      2.4582943            0.0

      0.8490156            0.0

      0.8689301            0.0

      2.0330784            0.0

      1.8504396            0.0

 THE IDENTITY ATAN(X) = X , X SMALL, WILL BE TESTED.


        X         X - F(X)

  6.9279835E-17            0.0

  3.4639917E-17            0.0

  1.7319958E-17            0.0

  8.6599794E-18            0.0

  4.3299897E-18            0.0

 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))
     -0.9197851      0.5892519            0.0      3.1415926

     -1.7546973      0.2134684            0.0      3.1415926

     -0.2245638      0.2976160            0.0      3.1415926

     -0.9944578      0.8990563  2.2204460E-16      3.1415926

      1.0204659      0.6951859            0.0     -3.1415926

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       ATAN(1.821831E-231) =1.821831E-231
1TEST OF ERROR RETURNS


 ATAN WILL BE CALLED WITH THE ARGUMENT  1.7976931E308
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN( 1.797693E308) =     1.570796
 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
            1.0            0.0

 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN2(          1.0          0.0) =     1.570796
 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
 2.2250738E-308  1.7976931E308

 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN2(2.225073E-308 1.797693E308) =          0.0
 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
  1.7976931E308 2.2250738E-308

 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN2( 1.797693E3082.225073E-308) =     1.570796
 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
            0.0            0.0

 THIS SHOULD TRIGGER AN ERROR MESSAGE


       ATAN2(          0.0          0.0) =          0.0
 THIS CONCLUDES THE TESTS
 This is texp: ELEFUNT in Java: version 1.00 of Wed May 29 17:12:35 2002

1TEST OF EXP(X- 0.0625) VS EXP(X)/EXP( 0.0625)


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (        -0.2840,         0.3465)


 EXP(X-V) WAS LARGER   251 TIMES,
              AGREED  1494 TIMES, AND
         WAS SMALLER   255 TIMES.


 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.2195E-16 =    2 ** -52.00
    OCCURRED FOR X =         0.062886
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.0040E-17 =    2 ** -53.47
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF EXP(X- 2.8125) VS EXP(X)/EXP( 2.8125)


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (        -3.4657,      -670.2733)


 EXP(X-V) WAS LARGER   291 TIMES,
              AGREED  1478 TIMES, AND
         WAS SMALLER   231 TIMES.


 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.2203E-16 =    2 ** -52.00
    OCCURRED FOR X =      -492.094556
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.3695E-17 =    2 ** -53.41
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF EXP(X- 2.8125) VS EXP(X)/EXP( 2.8125)


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (         6.9314,       709.6773)


 EXP(X-V) WAS LARGER   295 TIMES,
              AGREED  1479 TIMES, AND
         WAS SMALLER   226 TIMES.


 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.2198E-16 =    2 ** -52.00
    OCCURRED FOR X =       292.548270
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.1745E-17 =    2 ** -53.44
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1SPECIAL TESTS


 THE IDENTITY EXP(X)*EXP(-X) = 1.0  WILL BE TESTED.

       X        F(X)*F(-X) - 1

      0.7832585            0.0

      0.4153618  2.2204460E-16

      0.0286209            0.0

      1.2024205            0.0

      1.8213777            0.0



 TEST OF SPECIAL ARGUMENTS


 EXP(0.0) - 1.0E0 =             0.0

 EXP(       -708.0) =3.307553E-308

 EXP(        709.0) = 8.218407E307

 IF EXP(        354.5) =  9.065543E153 IS NOT ABOUT
 EXP(       177.25)**2 = 9.065543E153 THERE IS AN ARG RED ERROR
1TEST OF ERROR RETURNS


 EXP WILL BE CALLED WITH THE ARGUMENT    -6.7039E153
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 EXP RETURNED THE VALUE            0.0



 EXP WILL BE CALLED WITH THE ARGUMENT     6.7039E153
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 EXP RETURNED THE VALUE       Infinity



 THIS CONCLUDES THE TESTS
ibeta............ 2
it............... 53
irnd............. 5
ngrd............. 0
machep........... -52
negep............ -53
iexp............. 11
minexp........... -1022
maxexp........... 1024
eps.............. 2.220446049250313E-16
epsneg........... 1.1102230246251565E-16
xmin............. 2.2250738585072014E-308
xmax............. 1.7976931348623157E308
 This is tpower: ELEFUNT in Java: version 1.00 of Wed May 29 17:12:35 2002

1TEST OF X**1.0 VS X


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (            0.5,            1.0)


 X**1.0 WAS LARGER     0 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  2000 TIMES.


 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF             0.0 =    2 ** -999.00
    OCCURRED FOR X =              0.0
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS             0.0 =    2 **-999.00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF XSQ**1.5 VS XSQ*X


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (            0.5,            1.0)


 X**1.5 WAS LARGER   126 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1874 TIMES.


 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      2.2130E-16 =    2 **  -52.00
    OCCURRED FOR X =         0.500555
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      5.8292E-17 =    2 ** -53.93
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF XSQ**1.5 VS XSQ*X


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (            1.0,     5.6438E102)


 X**1.5 WAS LARGER   143 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1857 TIMES.


 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      2.2011E-16 =    2 **  -52.01
    OCCURRED FOR X =     8.914342E101
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.99


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      6.1514E-17 =    2 ** -53.85
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF X**Y VS XSQ**(Y/2)


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE REGION
      X IN (           0.01,           10.0), Y IN (      -154.1273,       154.1273)


 X**Y  WAS LARGER   946 TIMES,
           AGREED     0 TIMES, AND
      WAS SMALLER  1054 TIMES.


 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      8.2124E-15 =    2 **  -46.79
    OCCURRED FOR X =         5.686868 Y =       150.440806
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   6.21


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      2.0863E-15 =    2 ** -48.77
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   4.23


1SPECIAL TESTS


 THE IDENTITY  X ** Y = (1/X) ** (-Y)  WILL BE TESTED.

        X              Y         (X**Y-(1/X)**(-Y)) / X**Y

      6.0384110      6.1721352        66063.3105384

      5.6127087      4.5739679         2671.1056674

      4.2497569      8.4516013       204495.0380360

      2.2708161      7.5027288          470.2587069

      6.1387363      3.7554794          911.2015599

1TEST OF ERROR RETURNS


 (           2.0) ** (       -1022.0) WILL BE COMPUTED.
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS     2.2250E-308



 (           2.0) ** (        1023.0) WILL BE COMPUTED.
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS      8.9884E307



 (           0.0) ** (           2.0) WILL BE COMPUTED.
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS             0.0



 (          -2.0) ** (           0.0) WILL BE COMPUTED.
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS             1.0



 (          -2.0) ** (           2.0) WILL BE COMPUTED.
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS             4.0



 (           0.0) ** (           0.0) WILL BE COMPUTED.
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS             1.0



 THIS CONCLUDES THE TESTS
 This is tsin: ELEFUNT in Java: version 1.00 of Wed May 29 17:12:35 2002

1TEST OF SIN(X) VS 3*SIN(X/3)-4*SIN(X/3)**3

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (            0.0,         1.5707)


 SIN(X) WAS LARGER   432 TIMES,
            AGREED  1164 TIMES, AND
       WAS SMALLER   404 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     3.0586E-16 =    2 ** -51.54
    OCCURRED FOR X =         0.812430
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.46


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.4266E-17 =    2 ** -53.24
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF SIN(X) VS 3*SIN(X/3)-4*SIN(X/3)**3

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (        18.8495,        20.4203)


 SIN(X) WAS LARGER   510 TIMES,
            AGREED  1028 TIMES, AND
       WAS SMALLER   462 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     4.1016E-16 =    2 ** -51.11
    OCCURRED FOR X =        19.053982
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.89


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.0704E-16 =    2 ** -53.05
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF COS(X) VS 4*COS(X/3)**3-3*COS(X/3)

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (        21.9911,        23.5619)


 COS(X) WAS LARGER   429 TIMES,
            AGREED  1077 TIMES, AND
       WAS SMALLER   494 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     3.9255E-16 =    2 ** -51.18
    OCCURRED FOR X =        23.275210
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.82


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.0270E-16 =    2 ** -53.11
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1SPECIAL TESTS

 IF           1.0 IS NOT ALMOST 1.0E0,    SIN HAS THE WRONG PERIOD.

 THE IDENTITY   SIN(-X) = -SIN(X)   WILL BE TESTED.
     X        F(X) + F(-X)
      7.3820382            0.0

      3.9146930            0.0

      0.2697461            0.0

     11.3325468            0.0

     17.1660811            0.0

 THE IDENTITY SIN(X) = X , X SMALL, WILL BE TESTED.
    X         X - F(X)

  5.7051156E-17            0.0

  2.8525578E-17            0.0

  1.4262789E-17            0.0

  7.1313945E-18            0.0

  3.5656972E-18            0.0

 THE IDENTITY   COS(-X) = COS(X)   WILL BE TESTED.
        X         F(X) - F(-X)
      4.4566458            0.0

      4.8316546            0.0

      2.1326225            0.0

     15.0616904            0.0

      2.2071794            0.0

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.


       SIN(1.821831E-231) = 1.821831E-231
 THE FOLLOWING THREE LINES ILLUSTRATE THE LOSS IN SIGNIFICANCE
 FOR LARGE ARGUMENTS.  THE ARGUMENTS ARE CONSECUTIVE.

       SIN(   9.490626E7) =     0.941957

       SIN(   9.490626E7) =     0.941957

       SIN(   9.490626E7) =     0.941957
1TEST OF ERROR RETURNS


 SIN WILL BE CALLED WITH THE ARGUMENT      9.0071E15
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 SIN RETURNED THE VALUE            0.0



 THIS CONCLUDES THE TESTS
 This is tsinh: ELEFUNT in Java: version 1.00 of Wed May 29 17:12:35 2002

1TEST OF SINH(X) VS T.S. EXPANSION OF SINH(X)

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (            0.0,            0.5)


 SINH(X) WAS LARGER   790 TIMES,
             AGREED   455 TIMES, AND
        WAS SMALLER   755 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     8.1024E-14 =    2 ** -43.49
    OCCURRED FOR X =      9.567560E-4
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   9.51


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.1973E-15 =    2 ** -47.76
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   5.24


1TEST OF COSH(X) VS T.S. EXPANSION OF COSH(X)

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (            0.0,            0.5)


 COSH(X) WAS LARGER   109 TIMES,
             AGREED  1767 TIMES, AND
        WAS SMALLER   124 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.2204E-16 =    2 ** -52.00
    OCCURRED FOR X =         0.001098
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     7.3006E-17 =    2 ** -53.60
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF SINH(X) VS C*(SINH(X+1)+SINH(X-1))

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (            3.0,       709.7827)


 SINH(X) WAS LARGER  1000 TIMES,
             AGREED   954 TIMES, AND
        WAS SMALLER    46 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     3.4232E-16 =    2 ** -51.38
    OCCURRED FOR X =       508.337143
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.62


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.2420E-16 =    2 ** -52.84
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.16


1TEST OF COSH(X) VS C*(COSH(X+1)+COSH(X-1))

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (            3.0,       709.7827)


 COSH(X) WAS LARGER   986 TIMES,
             AGREED   969 TIMES, AND
        WAS SMALLER    45 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     3.3723E-16 =    2 ** -51.40
    OCCURRED FOR X =       694.808725
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.60


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.2246E-16 =    2 ** -52.86
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.14


1SPECIAL TESTS

 THE IDENTITY  SINH(-X) = -SINH(X)  WILL BE TESTED.

        X            F(X) + F(-X)

      1.4749766            0.0

      0.5094093 -2.2204460E-16

      0.5213580            0.0

      1.2198470            0.0

      1.1102638            0.0

 THE IDENTITY SINH(X) = X , X SMALL, WILL BE TESTED.

        X         X - F(X)

  6.9279835E-17  6.9279835E-17

  3.4639917E-17  3.4639917E-17

  1.7319958E-17  1.7319958E-17

  8.6599794E-18  8.6599794E-18

  4.3299897E-18  4.3299897E-18

 THE IDENTITY  COSH(-X) = COSH(X)  WILL BE TESTED.

        X         F(X) - F(-X)

      0.8101611 -2.2204460E-16

      1.7677557            0.0

      0.1839769            0.0

      0.6404052 -2.2204460E-16

      1.3315771  4.4408920E-16

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

      SINH(1.821831E-231) =          0.0

1TEST OF ERROR RETURNS


 SINH WILL BE CALLED WITH THE ARGUMENT       709.9077
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 SINH RETURNED THE VALUE       Infinity



SINH WILL BE CALLED WITH THE ARGUMENT      9.0071E15
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 SINH RETURNED THE VALUE       Infinity



 THIS CONCLUDES THE TESTS

 This is tsqrt: ELEFUNT in Java: version 1.00 of Wed May 29 17:12:35 2002

1TEST OF SQRT(X*X) - X


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
       (         0.7071,            1.0)


 SQRT(X) WAS LARGER     0 TIMES,
             AGREED  2000 TIMES, AND
        WAS SMALLER     0 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF            0.0 =    2 **-999.00
    OCCURRED FOR X =              0.0
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS            0.0 =    2 **-999.00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF SQRT(X*X) - X


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
       (            1.0,         1.4142)


 SQRT(X) WAS LARGER     0 TIMES,
             AGREED  2000 TIMES, AND
        WAS SMALLER     0 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF            0.0 =    2 **-999.00
    OCCURRED FOR X =              0.0
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS            0.0 =    2 **-999.00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF SPECIAL ARGUMENTS


 SQRT(XMIN) = SQRT( 2.2250738E-308) =  1.4916681E-154


 SQRT(1-EPSNEG) = SQRT(1-  1.1102230E-16) =       0.9999999


 SQRT(1.0) = SQRT(            1.0) =             1.0


 SQRT(1+EPS) = SQRT(1+  2.2204460E-16) =             1.0


 SQRT(XMAX) = SQRT(  1.7976931E308) =   1.3407807E154


1TEST OF ERROR RETURNS


 SQRT WILL BE CALLED WITH THE ARGUMENT             0.0
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 SQRT RETURNED THE VALUE             0.0



SQRT WILL BE CALLED WITH THE ARGUMENT            -1.0
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 SQRT RETURNED THE VALUE             NaN



 THIS CONCLUDES THE TESTS
 This is ttan: ELEFUNT in Java: version 1.00 of Wed May 29 17:12:35 2002

1TEST OF TAN(X) VS 2*TAN(X/2)/(1-TAN(X/2)**2)


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
    (            0.0,         0.7853)


 TAN(X) WAS LARGER   571 TIMES,
            AGREED   871 TIMES, AND
       WAS SMALLER   558 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     4.5892E-16 =    2 ** -50.95
    OCCURRED FOR X =         0.768970
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.05


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.4276E-16 =    2 ** -52.64
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.36


1TEST OF TAN(X) VS 2*TAN(X/2)/(1-TAN(X/2)**2)


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
    (         2.7488,         3.5342)


 TAN(X) WAS LARGER   572 TIMES,
            AGREED   998 TIMES, AND
       WAS SMALLER   430 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     5.4662E-16 =    2 ** -50.70
    OCCURRED FOR X =         2.845870
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.30


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.2861E-16 =    2 ** -52.79
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.21


1TEST OF TAN(X) VS 2*TAN(X/2)/(1-TAN(X/2)**2)


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
    (        18.8495,        19.6349)


 TAN(X) WAS LARGER   576 TIMES,
            AGREED   809 TIMES, AND
       WAS SMALLER   615 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     5.1121E-16 =    2 ** -50.80
    OCCURRED FOR X =        19.564806
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.20


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.4866E-16 =    2 ** -52.58
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.42


1TEST OF COT(X) VS (COT(X/2)**2-1)/(2*COT(X/2))


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
    (        18.8495,        19.6349)


 COT(X) WAS LARGER   589 TIMES,
            AGREED   833 TIMES, AND
       WAS SMALLER   578 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     5.3859E-16 =    2 ** -50.72
    OCCURRED FOR X =        19.394670
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.28


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.5667E-16 =    2 ** -52.50
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.50


1SPECIAL TESTS


 THE IDENTITY  TAN(-X) = -TAN(X)  WILL BE TESTED.

        X         F(X) + F(-X)

      9.2675513            0.0

      3.2007134            0.0

      3.2757893            0.0

      7.6645251            0.0

      6.9759932            0.0

 THE IDENTITY TAN(X) = X , X SMALL, WILL BE TESTED.

        X         X - F(X)

  6.9279835E-17            0.0

  3.4639917E-17            0.0

  1.7319958E-17            0.0

  8.6599794E-18            0.0

  4.3299897E-18            0.0

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       TAN(1.821831E-231) =1.821831E-231

 THE RELATIVE ERROR IN TAN(11) IS -7.1737974E-17 =    2 ** -53.63 WHERE

      TAN(         11.0) =  -225.950846

 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF ERROR RETURNS


 TAN WILL BE CALLED WITH THE ARGUMENT       6.7108E7
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 TAN RETURNED THE VALUE        -0.4638




TAN WILL BE CALLED WITH THE ARGUMENT      9.0071E15
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 TAN RETURNED THE VALUE            0.0



 THIS CONCLUDES THE TESTS
 This is ttanh: ELEFUNT in Java: version 1.00 of Wed May 29 17:12:35 2002

1TEST 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
      (          0.125,         0.5493)


 TANH(X) WAS LARGER   802 TIMES,
             AGREED   427 TIMES, AND
        WAS SMALLER   771 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.6914E-15 =    2 ** -49.07
    OCCURRED FOR X =         0.132035
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   3.93


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     3.1704E-16 =    2 ** -51.49
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.51


1TEST 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
      (         0.6743,        19.4081)


 TANH(X) WAS LARGER   716 TIMES,
             AGREED   628 TIMES, AND
        WAS SMALLER   656 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     5.5511E-16 =    2 ** -50.68
    OCCURRED FOR X =         7.978437
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.32


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.4610E-16 =    2 ** -52.60
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.40


1SPECIAL TESTS

 THE IDENTITY   TANH(-X) = -TANH(X)   WILL BE TESTED.


        X         F(X) + F(-X)

      0.0555685            0.0

      0.2588942 -1.1102230E-16

      0.2233350            0.0

      0.6093917            0.0

      0.7458728            0.0

 THE IDENTITY TANH(X) = X , X SMALL, WILL BE TESTED.


        X         X - F(X)

  2.9291640E-17  2.9291640E-17

  1.4645820E-17  1.4645820E-17

  7.3229100E-18  7.3229100E-18

  3.6614550E-18  3.6614550E-18

  1.8307275E-18  1.8307275E-18

 THE IDENTITY TANH(X) = 1 , X LARGE, WILL BE TESTED.


        X         1 - F(X)

     19.4081210            0.0

     23.4081210            0.0

     27.4081210            0.0

     31.4081210            0.0

     35.4081210            0.0

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       TANH(1.821831E-231) =          0.0
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT  1.7976931E308
       TANH( 1.797693E308) =          NaN
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT 2.2250738E-308
       TANH(2.225073E-308) =          0.0
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT            0.0
       TANH(          0.0) =          0.0
 THIS CONCLUDES THE TESTS
