 This is talog: ELEFUNT in Java: version 1.00 of Wed May 29 19:21:35 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 =         0.0039


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


 THERE ARE  24 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  1434 TIMES, AND
        WAS SMALLER   566 TIMES.


 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      1.1918E-7 =    2 ** -23.00
    OCCURRED FOR X =         0.778759
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      4.5779E-8 =    2 ** -24.38
 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,         0.8999)


 ALOG10(X) WAS LARGER     0 TIMES,
               AGREED   922 TIMES, AND
          WAS SMALLER  1078 TIMES.


 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      2.6090E-7 =    2 ** -21.87
    OCCURRED FOR X =         0.876773
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.13


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      7.7652E-8 =    2 ** -23.62
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.38


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    41 TIMES,
             AGREED  1959 TIMES, AND
        WAS SMALLER     0 TIMES.


 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      1.1607E-7 =    2 ** -23.04
    OCCURRED FOR X =        60.817466
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.96


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      1.2552E-8 =    2 ** -26.25
 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)

     15.1111373  -2.3841857E-7

     16.8921432            0.0

     15.5177888            0.0

     15.7235736            0.0

     15.4466695            0.0



 TEST OF SPECIAL ARGUMENTS


 ALOG(1.0) =             0.0


 ALOG(XMIN) = ALOG(  1.1754943E-38) =     -87.3365478


 ALOG(XMAX) = ALOG(   3.4028234E38) =      88.7228393


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 19:21:35 2002

1TEST OF ASIN(X) VS TAYLOR SERIES

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


 ASIN(X) WAS LARGER   491 TIMES,
             AGREED  1017 TIMES, AND
        WAS SMALLER   492 TIMES.

 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF      1.1913E-7 =    2 ** -23.00
    OCCURRED FOR X =         0.007817
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      5.9224E-8 =    2 ** -24.01
 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   444 TIMES,
             AGREED  1082 TIMES, AND
        WAS SMALLER   474 TIMES.

 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF      8.2453E-8 =    2 ** -23.53
    OCCURRED FOR X =         0.124690
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.47


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      5.1500E-8 =    2 ** -24.21
 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   338 TIMES,
             AGREED  1329 TIMES, AND
        WAS SMALLER   333 TIMES.

 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF      1.1916E-7 =    2 ** -23.00
    OCCURRED FOR X =         0.841667
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      5.2965E-8 =    2 ** -24.17
 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   375 TIMES,
             AGREED  1227 TIMES, AND
        WAS SMALLER   398 TIMES.

 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF      1.1903E-7 =    2 ** -23.00
    OCCURRED FOR X =         0.968819
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      5.6047E-8 =    2 ** -24.09
 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
      (           -1.0,          -0.75)


 ACOS(X) WAS LARGER   390 TIMES,
             AGREED  1187 TIMES, AND
        WAS SMALLER   423 TIMES.

 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF      9.8564E-8 =    2 ** -23.27
    OCCURRED FOR X =        -0.750028
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.73


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      5.7170E-8 =    2 ** -24.06
 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)
     -0.7769403            0.0

     -0.1175465            0.0

     -0.6933180            0.0

     -0.6647557            0.0

     -0.0944677            0.0

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

        X         X - F(X)
   4.8188475E-8            0.0

   2.4094237E-8            0.0

   1.2047118E-8            0.0

   6.0235594E-9            0.0

   3.0117797E-9            0.0

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       ASIN( 3.569976E-29) = 3.569976E-29

1TEST OF ERROR RETURNS


 ASIN WILL BE CALLED WITH THE ARGUMENT         1.2000
 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 19:21:35 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     0 TIMES,
             AGREED  2000 TIMES, AND
        WAS SMALLER     0 TIMES.

 THERE ARE  24 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 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   424 TIMES,
             AGREED  1393 TIMES, AND
        WAS SMALLER   183 TIMES.

 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF      1.1919E-7 =    2 ** -23.00
    OCCURRED FOR X =         0.255374
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      4.5997E-8 =    2 ** -24.37
 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   274 TIMES,
             AGREED  1455 TIMES, AND
        WAS SMALLER   271 TIMES.

 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF      1.1373E-7 =    2 ** -23.07
    OCCURRED FOR X =         0.268200
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.93


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      4.8476E-8 =    2 ** -24.30
 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   128 TIMES,
             AGREED  1751 TIMES, AND
        WAS SMALLER   121 TIMES.

 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF      1.1907E-7 =    2 ** -23.00
    OCCURRED FOR X =         0.547034
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      2.9967E-8 =    2 ** -24.99
 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)

      0.2778428            0.0

      4.7303557            0.0

      1.2944715            0.0

      1.8089334            0.0

      1.1166750            0.0

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


        X         X - F(X)

   5.4650016E-8            0.0

   2.7325008E-8            0.0

   1.3662504E-8            0.0

   6.8312520E-9            0.0

   3.4156260E-9            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))
      0.4375669      0.1739669            0.0     -3.1415927

      0.9834916      0.2341106            0.0     -3.1415927

     -0.9446574      0.9794546            0.0      3.1415927

     -0.2726805      0.9787347            0.0      3.1415925

     -0.6326328      0.7302220            0.0      3.1415925

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       ATAN( 3.569976E-29) = 3.569976E-29
1TEST OF ERROR RETURNS


 ATAN WILL BE CALLED WITH THE ARGUMENT   3.4028234E38
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN(  3.402823E38) =     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
  1.1754943E-38   3.4028234E38

 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN2( 1.175494E-38  3.402823E38) =          0.0
 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
   3.4028234E38  1.1754943E-38

 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN2(  3.402823E38 1.175494E-38) =     1.570796
 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
            0.0            0.0

 THIS SHOULD TRIGGER AN ERROR MESSAGE


       ATAN2(          0.0          0.0) =          NaN
 THIS CONCLUDES THE TESTS
 This is texp: ELEFUNT in Java: version 1.00 of Wed May 29 19:21:35 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   238 TIMES,
              AGREED  1479 TIMES, AND
         WAS SMALLER   283 TIMES.


 THERE ARE   24 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      1.1889E-7 =    2 ** -23.00
    OCCURRED FOR X =         0.065115
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      4.3432E-8 =    2 ** -24.46
 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,       -69.3147)


 EXP(X-V) WAS LARGER   220 TIMES,
              AGREED  1507 TIMES, AND
         WAS SMALLER   273 TIMES.


 THERE ARE   24 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      1.1909E-7 =    2 ** -23.00
    OCCURRED FOR X =       -31.843872
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      4.2339E-8 =    2 ** -24.49
 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,        88.6174)


 EXP(X-V) WAS LARGER   202 TIMES,
              AGREED  1510 TIMES, AND
         WAS SMALLER   288 TIMES.


 THERE ARE   24 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      1.1912E-7 =    2 ** -23.00
    OCCURRED FOR X =        54.799247
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      4.3442E-8 =    2 ** -24.46
 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

      1.0061973  -5.9604644E-8

      1.7746665            0.0

      1.8333218            0.0

      1.1652287            0.0

      1.6535880  -5.9604644E-8



 TEST OF SPECIAL ARGUMENTS


 EXP(0.0) - 1.0E0F =             0.0

 EXP(        -87.0) = 1.645811E-38

 EXP(         88.0) =  1.651636E38

 IF EXP(         44.0) =   1.285159E19 IS NOT ABOUT
 EXP(         22.0)**2 =  1.285160E19 THERE IS AN ARG RED ERROR
1TEST OF ERROR RETURNS


 EXP WILL BE CALLED WITH THE ARGUMENT     -9.2233E18
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 EXP RETURNED THE VALUE            0.0



 EXP WILL BE CALLED WITH THE ARGUMENT      9.2233E18
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 EXP RETURNED THE VALUE       Infinity



 THIS CONCLUDES THE TESTS
ibeta............ 2
it............... 24
irnd............. 5
ngrd............. 0
machep........... -23
negep............ -24
iexp............. 8
minexp........... -126
maxexp........... 128
eps.............. 1.1920929E-7
epsneg........... 5.9604645E-8
xmin............. 1.17549435E-38
xmax............. 3.4028235E38
 This is tpower: ELEFUNT in Java: version 1.00 of Wed May 29 19:21:35 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   24 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   116 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1884 TIMES.


 THERE ARE   24 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF       1.1899E-7 =    2 **  -23.00
    OCCURRED FOR X =         0.630330
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS       2.8980E-8 =    2 ** -25.04
 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,      6.9814E12)


 X**1.5 WAS LARGER   127 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1873 TIMES.


 THERE ARE   24 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF       1.1900E-7 =    2 **  -23.00
    OCCURRED FOR X =      4.400547E12
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS       3.0220E-8 =    2 ** -24.98
 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 (         0.0099,           10.0), Y IN (       -19.2659,        19.2659)


 X**Y  WAS LARGER   688 TIMES,
           AGREED     0 TIMES, AND
      WAS SMALLER  1312 TIMES.


 THERE ARE   24 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF       5.0548E-7 =    2 **  -20.92
    OCCURRED FOR X =         8.657083 Y =        18.144813
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   3.08


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS       1.4616E-7 =    2 ** -22.71
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.29


1SPECIAL TESTS


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

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

      8.7694034      2.1754655          112.5638351

      7.9331808      7.6475577            7560936.0

      1.9446774      9.0846843          420.8129882

      1.5856049      4.2006044            6.9332990

      1.0755667     10.4458446            2.1403219

1TEST OF ERROR RETURNS


 (           2.0) ** (        -126.0) WILL BE COMPUTED.
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS      1.1754E-38



 (           2.0) ** (         127.0) WILL BE COMPUTED.
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS       1.7014E38



 (           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 19:21:35 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   374 TIMES,
            AGREED  1251 TIMES, AND
       WAS SMALLER   375 TIMES.

 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF      1.4864E-7 =    2 ** -22.68
    OCCURRED FOR X =         0.100412
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.32


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      4.6750E-8 =    2 ** -24.35
 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   370 TIMES,
            AGREED  1215 TIMES, AND
       WAS SMALLER   415 TIMES.

 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF      1.4206E-7 =    2 ** -22.75
    OCCURRED FOR X =        19.282505
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.25


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      4.7369E-8 =    2 ** -24.33
 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   375 TIMES,
            AGREED  1243 TIMES, AND
       WAS SMALLER   382 TIMES.

 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF      1.3229E-7 =    2 ** -22.85
    OCCURRED FOR X =        23.449069
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.15


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      4.6554E-8 =    2 ** -24.36
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1SPECIAL TESTS

 IF           1.0 IS NOT ALMOST 1.0E0F,    SIN HAS THE WRONG PERIOD.

 THE IDENTITY   SIN(-X) = -SIN(X)   WILL BE TESTED.
     X        F(X) + F(-X)
      9.4831867            0.0

     16.7258377            0.0

     17.2786502            0.0

     10.9820222            0.0

     15.5847005            0.0

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

   2.0817287E-8            0.0

   1.0408643E-8            0.0

   5.2043218E-9            0.0

   2.6021609E-9            0.0

   1.3010804E-9            0.0

 THE IDENTITY   COS(-X) = COS(X)   WILL BE TESTED.
        X         F(X) - F(-X)
     12.3844327            0.0

      2.3904302            0.0

     16.0604286            0.0

      9.5006523            0.0

      0.0595645            0.0

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.


       SIN( 3.569976E-29) =  3.569976E-29
 THE FOLLOWING THREE LINES ILLUSTRATE THE LOSS IN SIGNIFICANCE
 FOR LARGE ARGUMENTS.  THE ARGUMENTS ARE CONSECUTIVE.

       SIN(  4095.999755) =    -0.594838

       SIN(       4096.0) =    -0.594641

       SIN(  4096.000488) =    -0.594249
1TEST OF ERROR RETURNS


 SIN WILL BE CALLED WITH THE ARGUMENT       1.6777E7
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 SIN RETURNED THE VALUE        -0.7795



 THIS CONCLUDES THE TESTS
 This is tsinh: ELEFUNT in Java: version 1.00 of Wed May 29 19:21:35 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     8 TIMES,
             AGREED  1979 TIMES, AND
        WAS SMALLER    13 TIMES.


 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      1.1741E-7 =    2 ** -23.02
    OCCURRED FOR X =         0.488031
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.98


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      8.2943E-9 =    2 ** -26.85
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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    16 TIMES,
             AGREED  1967 TIMES, AND
        WAS SMALLER    17 TIMES.


 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      1.1626E-7 =    2 ** -23.04
    OCCURRED FOR X =         0.224616
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.96


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      1.4285E-8 =    2 ** -26.06
 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,        88.7228)


 SINH(X) WAS LARGER    46 TIMES,
             AGREED   962 TIMES, AND
        WAS SMALLER   992 TIMES.


 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      1.8102E-7 =    2 ** -22.40
    OCCURRED FOR X =        24.535526
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.60


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      6.5565E-8 =    2 ** -23.86
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.14


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

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (            3.0,        88.7228)


 COSH(X) WAS LARGER    41 TIMES,
             AGREED   952 TIMES, AND
        WAS SMALLER  1007 TIMES.


 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      1.8133E-7 =    2 ** -22.39
    OCCURRED FOR X =        11.364037
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.61


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      6.6558E-8 =    2 ** -23.84
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.16


1SPECIAL TESTS

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

        X            F(X) + F(-X)

      0.1667056            0.0

      2.8382134            0.0

      0.7766828            0.0

      1.0853600            0.0

      0.6700049            0.0

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

        X         X - F(X)

   5.4650016E-8            0.0

   2.7325008E-8            0.0

   1.3662504E-8            0.0

   6.8312520E-9            0.0

   3.4156260E-9            0.0

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

        X         F(X) - F(-X)

      1.8281753            0.0

      0.5219009            0.0

      2.2376186            0.0

      0.7023320            0.0

      0.7915068            0.0

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

      SINH( 3.569976E-29) =          0.0

1TEST OF ERROR RETURNS


 SINH WILL BE CALLED WITH THE ARGUMENT        88.8478
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 SINH RETURNED THE VALUE      1.9279E38



SINH WILL BE CALLED WITH THE ARGUMENT       1.6777E7
 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 19:21:35 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  24 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  24 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(  1.1754943E-38) =   1.0842021E-19


 SQRT(1-EPSNEG) = SQRT(1-   5.9604644E-8) =       0.9999999


 SQRT(1.0) = SQRT(            1.0) =             1.0


 SQRT(1+EPS) = SQRT(1+   1.1920928E-7) =             1.0


 SQRT(XMAX) = SQRT(   3.4028234E38) =    1.8446742E19


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 19:21:35 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   470 TIMES,
            AGREED  1080 TIMES, AND
       WAS SMALLER   450 TIMES.

 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      1.9869E-7 =    2 ** -22.26
    OCCURRED FOR X =         0.148878
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.74


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      5.9858E-8 =    2 ** -23.99
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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   337 TIMES,
            AGREED  1299 TIMES, AND
       WAS SMALLER   364 TIMES.

 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      1.6898E-7 =    2 ** -22.50
    OCCURRED FOR X =         3.185653
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.50


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      5.0653E-8 =    2 ** -24.23
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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   454 TIMES,
            AGREED  1075 TIMES, AND
       WAS SMALLER   471 TIMES.

 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      2.0266E-7 =    2 ** -22.23
    OCCURRED FOR X =        18.922948
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.77


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      6.0448E-8 =    2 ** -23.98
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.02


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   368 TIMES,
            AGREED  1223 TIMES, AND
       WAS SMALLER   409 TIMES.


 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      1.6691E-7 =    2 ** -22.51
    OCCURRED FOR X =        19.460357
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.49


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      5.6195E-8 =    2 ** -24.08
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1SPECIAL TESTS


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

        X         F(X) + F(-X)

      1.0474427            0.0

     17.8330211            0.0

      4.8800425            0.0

      6.8195185            0.0

      4.2097654            0.0

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

        X         X - F(X)

   5.4650016E-8            0.0

   2.7325008E-8            0.0

   1.3662504E-8            0.0

   6.8312520E-9            0.0

   3.4156260E-9            0.0

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       TAN( 3.569976E-29) = 3.569976E-29

 THE RELATIVE ERROR IN TAN(11) IS  -2.2158758E-8 =    2 ** -25.43 WHERE

      TAN(         11.0) =  -225.950851

 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF ERROR RETURNS


 TAN WILL BE CALLED WITH THE ARGUMENT         4096.0
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 TAN RETURNED THE VALUE        -0.7396




TAN WILL BE CALLED WITH THE ARGUMENT       1.6777E7
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 TAN RETURNED THE VALUE        -1.2446



 THIS CONCLUDES THE TESTS
 This is ttanh: ELEFUNT in Java: version 1.00 of Wed May 29 19:21:35 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   635 TIMES,
             AGREED  1079 TIMES, AND
        WAS SMALLER   286 TIMES.

 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF      1.6830E-7 =    2 ** -22.50
    OCCURRED FOR X =         0.178958
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.50


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      5.6814E-8 =    2 ** -24.07
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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,         9.3574)


 TANH(X) WAS LARGER   251 TIMES,
             AGREED   925 TIMES, AND
        WAS SMALLER   824 TIMES.

 THERE ARE  24 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF      1.3034E-7 =    2 ** -22.87
    OCCURRED FOR X =         1.554591
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.13


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      5.2977E-8 =    2 ** -24.17
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1SPECIAL TESTS

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


        X         F(X) + F(-X)

      0.3996505            0.0

      0.9563157            0.0

      0.5394701            0.0

      0.4337664            0.0

      0.2208040            0.0

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


        X         X - F(X)

   3.5793103E-8            0.0

   1.7896551E-8            0.0

   8.9482758E-9            0.0

   4.4741379E-9            0.0

   2.2370689E-9            0.0

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


        X         1 - F(X)

      9.3574867            0.0

     13.3574867            0.0

     17.3574867            0.0

     21.3574867            0.0

     25.3574867            0.0

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       TANH( 3.569976E-29) =          0.0
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT   3.4028234E38
       TANH(  3.402823E38) =          NaN
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT  1.1754943E-38
       TANH( 1.175494E-38) =          0.0
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT            0.0
       TANH(          0.0) =          0.0
 THIS CONCLUDES THE TESTS
