Host        = eilat.math.utah.edu
Command     = ./tallqp >>tallqp.lst-sgi-irix-CC-O3 2>&1
uname -a    = IRIX64 eilat 6.5 04151556 IP27 mips unknown Irix
Make flags  = -i NAME=sgi-irix-CC-O3 CC=CC CFLAGS=-O3  
Date        = Tue May 28 13:43:16 MDT 2002
----------------------------------------
 
ibeta............       2
it...............     107
irnd.............       5
ngrd.............       0
machep...........    -106
negep............    -107
iexp.............      11
minexp...........    -916
maxexp...........    1129
eps..............     1.2325951644078309459558258832543530e-32
epsneg...........     6.1629758220391547297791294162717670e-33
xmin.............    1.8051943758648295760692620811737470e-276
xmax.............                                          inf
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 =     2.9104e-11


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


 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     0.0000e+00 =    2 **-999.00
    OCCURRED FOR X =     0.000000e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     0.0000e+00 =    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
      (     7.0711e-01,     9.3750e-01)


 ALOG(X) WAS LARGER     0 TIMES,
             AGREED  1241 TIMES, AND
        WAS SMALLER   759 TIMES.


 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     8.4522e-32 =    2 **-103.22
    OCCURRED FOR X =     9.212440e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   3.78


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.0386e-32 =    2 **-106.25
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.75


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


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     3.1623e-01,     9.0000e-01)


 ALOG10(X) WAS LARGER     0 TIMES,
               AGREED   713 TIMES, AND
          WAS SMALLER  1287 TIMES.


 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     3.4172e-32 =    2 **-104.53
    OCCURRED FOR X =     8.782948e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.47


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.0141e-32 =    2 **-106.28
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.72


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


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     1.6000e+01,     2.4000e+02)


 ALOG(X) WAS LARGER   189 TIMES,
             AGREED  1811 TIMES, AND
        WAS SMALLER     0 TIMES.


 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     1.4978e-32 =    2 **-105.72
    OCCURRED FOR X =     2.689064e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.28


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     2.7750e-33 =    2 **-108.15
 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)

  1.6927012e+01  0.0000000e+00

  1.6850494e+01  0.0000000e+00

  1.6383894e+01  0.0000000e+00

  1.6681105e+01  0.0000000e+00

  1.5295194e+01  2.4651903e-32



 TEST OF SPECIAL ARGUMENTS


 ALOG(1.0) =   0.0000000e+00


 ALOG(XMIN) = ALOG( 1.8051944e-276) =  -6.3492282e+02


 ALOG(XMAX) = ALOG(            inf) =             inf


1TEST OF ERROR RETURNS


 ALOG WILL BE CALLED WITH THE ARGUMENT    -2.0000e+00
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 ALOG RETURNED THE VALUE            nan


 ALOG WILL BE CALLED WITH THE ARGUMENT     0.0000e+00
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 ALOG RETURNED THE VALUE           -inf



 THIS CONCLUDES THE TESTS
1TEST OF ASIN(X) VS TAYLOR SERIES

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (    -1.2500e-01,     1.2500e-01)


 ASIN(X) WAS LARGER   478 TIMES,
             AGREED   839 TIMES, AND
        WAS SMALLER   683 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     4.0311e-32 =    2 **-104.29
    OCCURRED FOR X =    -3.821215e-02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.71


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.3891e-33 =    2 **-106.56
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.44


1TEST OF ACOS(X) VS TAYLOR SERIES

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (    -1.2500e-01,     1.2500e-01)


 ACOS(X) WAS LARGER   456 TIMES,
             AGREED  1084 TIMES, AND
        WAS SMALLER   460 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.6772e-32 =    2 **-105.56
    OCCURRED FOR X =     1.008154e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.44


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.6181e-33 =    2 **-107.13
 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
      (     7.5000e-01,     1.0000e+00)


 ASIN(X) WAS LARGER   439 TIMES,
             AGREED  1178 TIMES, AND
        WAS SMALLER   383 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.1604e-32 =    2 **-105.19
    OCCURRED FOR X =     7.551047e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.81


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     6.1061e-33 =    2 **-107.01
 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
      (     7.5000e-01,     1.0000e+00)


 ACOS(X) WAS LARGER   598 TIMES,
             AGREED   778 TIMES, AND
        WAS SMALLER   624 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     4.7704e-32 =    2 **-104.05
    OCCURRED FOR X =     9.916662e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.95


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.9057e-33 =    2 **-106.32
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.68


1TEST OF ACOS(X) VS TAYLOR SERIES

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (    -1.0000e+00,    -7.5000e-01)


 ACOS(X) WAS LARGER   343 TIMES,
             AGREED  1340 TIMES, AND
        WAS SMALLER   317 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.9298e-32 =    2 **-105.35
    OCCURRED FOR X =    -8.327389e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.65


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.3681e-33 =    2 **-107.20
 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)
 -5.6652790e-01  0.0000000e+00

 -4.0167077e-01  0.0000000e+00

 -7.7675762e-01  0.0000000e+00

 -9.2769624e-01  0.0000000e+00

 -2.5054690e-02  0.0000000e+00

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

        X         X - F(X)
  4.5188547e-33  0.0000000e+00

  2.2594273e-33  0.0000000e+00

  1.1297137e-33  0.0000000e+00

  5.6485684e-34  0.0000000e+00

  2.8242842e-34  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       ASIN(1.557374e-207) =1.557374e-207

1TEST OF ERROR RETURNS


 ASIN WILL BE CALLED WITH THE ARGUMENT     1.2000e+00
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 ASIN RETURNED THE VALUE            nan


 THIS CONCLUDES THE TESTS
1TEST OF ATAN(X) VS TRUNCATED TAYLOR SERIES

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (    -6.2500e-02,     6.2500e-02)


 ATAN(X) WAS LARGER   191 TIMES,
             AGREED  1488 TIMES, AND
        WAS SMALLER   321 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.5254e-32 =    2 **-104.97
    OCCURRED FOR X =     2.859899e-03
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.03


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.3251e-33 =    2 **-107.51
 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
      (     6.2500e-02,     2.6795e-01)


 ATAN(X) WAS LARGER   720 TIMES,
             AGREED   986 TIMES, AND
        WAS SMALLER   294 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     3.6346e-32 =    2 **-104.44
    OCCURRED FOR X =     2.599738e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.56


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.2460e-33 =    2 **-106.58
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.42


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

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     2.6795e-01,     4.1421e-01)


 ATAN(X) WAS LARGER   615 TIMES,
             AGREED   932 TIMES, AND
        WAS SMALLER   453 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     4.7032e-32 =    2 **-104.07
    OCCURRED FOR X =     2.682462e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.93


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.0540e-33 =    2 **-106.45
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.55


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

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     4.1421e-01,     1.0000e+00)


 ATAN(X) WAS LARGER   276 TIMES,
             AGREED  1263 TIMES, AND
        WAS SMALLER   461 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.4522e-32 =    2 **-105.01
    OCCURRED FOR X =     5.497516e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.99


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.9176e-33 =    2 **-107.06
 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)

  4.8175293e+00  0.0000000e+00

  4.6262342e+00  0.0000000e+00

  3.4597345e+00  0.0000000e+00

  4.2027635e+00  0.0000000e+00

  7.3798469e-01  0.0000000e+00

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


        X         X - F(X)

  3.8164278e-33  0.0000000e+00

  1.9082139e-33  0.0000000e+00

  9.5410696e-34  0.0000000e+00

  4.7705348e-34  0.0000000e+00

  2.3852674e-34  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))
 -1.3160311e+00  8.0813875e-02  0.0000000e+00  3.1415927e+00

  1.9036551e+00  7.5721863e-01  0.0000000e+00 -3.1415927e+00

 -1.3386203e+00  4.8494512e-01  0.0000000e+00  3.1415927e+00

  9.6675600e-01  4.1605706e-01  1.2325952e-32 -3.1415927e+00

  8.8564171e-01  5.1107663e-01  0.0000000e+00 -3.1415927e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       ATAN(1.557374e-207) =1.557374e-207
1TEST OF ERROR RETURNS


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


       ATAN(          inf) = 1.570796e+00
 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
  1.0000000e+00  0.0000000e+00

 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN2( 1.000000e+00 0.000000e+00) = 1.570796e+00
 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
 1.8051944e-276            inf

 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN2(1.805194e-276          inf) = 0.000000e+00
 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
            inf 1.8051944e-276

 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN2(          inf1.805194e-276) = 1.570796e+00
 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
  0.0000000e+00  0.0000000e+00

 THIS SHOULD TRIGGER AN ERROR MESSAGE


       ATAN2( 0.000000e+00 0.000000e+00) = 0.000000e+00
 THIS CONCLUDES THE TESTS
1TEST OF EXP(X- 0.0625) VS EXP(X)/EXP( 0.0625)


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (    -2.8407e-01,     3.4657e-01)


 EXP(X-V) WAS LARGER   146 TIMES,
              AGREED   925 TIMES, AND
         WAS SMALLER   929 TIMES.


 THERE ARE  107 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     3.2864e-32 =    2 **-104.59
    OCCURRED FOR X =     1.804363e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.41


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     7.8531e-33 =    2 **-106.65
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.35


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


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (    -3.4657e+00,    -5.5937e+02)


 EXP(X-V) WAS LARGER   577 TIMES,
              AGREED  1051 TIMES, AND
         WAS SMALLER   372 TIMES.


 THERE ARE  107 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.4553e-32 =    2 **-105.01
    OCCURRED FOR X =    -1.462101e+02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.99


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     7.2002e-33 =    2 **-106.78
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.22


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


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     6.9315e+00,            inf)


 EXP(X-V) WAS LARGER     0 TIMES,
              AGREED  2000 TIMES, AND
         WAS SMALLER     0 TIMES.


 THERE ARE  107 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     0.0000e+00 =    2 **-999.00
    OCCURRED FOR X =     0.000000e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS            nan =    2 **nan0x10000000
 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

  5.5969256e-01  0.0000000e+00

  6.6046707e-02  0.0000000e+00

  3.0403658e-01 -1.2325952e-32

  9.1676463e-01 -6.1629758e-33

  9.8649347e-01  1.2325952e-32



 TEST OF SPECIAL ARGUMENTS


 EXP(0.0) - 1.0E0 =   0.0000000e+00

 EXP(-6.340000e+02) =4.542537e-276

 EXP( 2.147484e+09) =          inf

 IF EXP( 1.073742e+09) =           inf IS NOT ABOUT
 EXP( 5.368709e+08)**2 =          inf THERE IS AN ARG RED ERROR
1TEST OF ERROR RETURNS


 EXP WILL BE CALLED WITH THE ARGUMENT   -7.4428e+137
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 EXP RETURNED THE VALUE     0.0000e+00



 EXP WILL BE CALLED WITH THE ARGUMENT    7.4428e+137
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 EXP RETURNED THE VALUE            inf



 THIS CONCLUDES THE TESTS
1TEST OF X**1.0 VS X


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     5.0000e-01,     1.0000e+00)


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


 THERE ARE  107 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      0.0000e+00 =    2 ** -999.00
    OCCURRED FOR X =     0.000000e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      0.0000e+00 =    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
      (     5.0000e-01,     1.0000e+00)


 X**1.5 WAS LARGER   515 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1485 TIMES.


 THERE ARE  107 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      2.4803e-32 =    2 ** -104.99
    OCCURRED FOR X =     7.196547e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.01


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      6.9715e-33 =    2 **-106.82
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.18


1TEST OF XSQ**1.5 VS XSQ*X


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     1.0000e+00,            inf)


 X**1.5 WAS LARGER     0 TIMES,
            AGREED  2000 TIMES, AND
       WAS SMALLER     0 TIMES.


 THERE ARE  107 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      0.0000e+00 =    2 ** -999.00
    OCCURRED FOR X =     0.000000e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS             nan =    2 **nan0x10000000
 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 (     1.0000e-02,     1.0000e+01), Y IN (           -inf,            nan)


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


 THERE ARE  107 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      0.0000e+00 =    2 ** -999.00
    OCCURRED FOR X =     0.000000e+00 Y =     0.000000e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS             nan =    2 **nan0x10000000
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1SPECIAL TESTS


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

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

  6.6652790e+00  5.0167077e+00        1.4872524e-32

  8.7675762e+00  1.0276962e+01        4.3241687e-32

  1.2505469e+00  8.3322609e+00       -4.5916554e-32

  6.3057557e+00  3.2057483e+00        8.6159752e-33

  8.3580924e+00  4.5756310e+00       -3.6571228e-32

1TEST OF ERROR RETURNS


 ( 2.0000000e+00) ** (-9.1600000e+02) WILL BE COMPUTED.
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS     1.8052e-276



 ( 2.0000000e+00) ** ( 1.1280000e+03) WILL BE COMPUTED.
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS             inf



 ( 0.0000000e+00) ** ( 2.0000000e+00) WILL BE COMPUTED.
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS      0.0000e+00



 (-2.0000000e+00) ** ( 0.0000000e+00) WILL BE COMPUTED.
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS      1.0000e+00



 (-2.0000000e+00) ** ( 2.0000000e+00) WILL BE COMPUTED.
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS      4.0000e+00



 ( 0.0000000e+00) ** ( 0.0000000e+00) WILL BE COMPUTED.
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS      1.0000e+00



 THIS CONCLUDES THE TESTS
1TEST OF SIN(X) VS 3*SIN(X/3)-4*SIN(X/3)**3

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     0.0000e+00,     1.5708e+00)


 SIN(X) WAS LARGER   612 TIMES,
            AGREED   806 TIMES, AND
       WAS SMALLER   582 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     3.2787e-32 =    2 **-104.59
    OCCURRED FOR X =     8.509163e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.41


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.6303e-33 =    2 **-106.51
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.49


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

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     1.8850e+01,     2.0420e+01)


 SIN(X) WAS LARGER   564 TIMES,
            AGREED   784 TIMES, AND
       WAS SMALLER   652 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     3.3060e-32 =    2 **-104.58
    OCCURRED FOR X =     1.913296e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.42


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.9421e-33 =    2 **-106.46
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.54


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

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     2.1991e+01,     2.3562e+01)


 COS(X) WAS LARGER   577 TIMES,
            AGREED   720 TIMES, AND
       WAS SMALLER   703 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     3.4534e-32 =    2 **-104.51
    OCCURRED FOR X =     2.329095e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.49


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.3779e-33 =    2 **-106.39
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.61


1SPECIAL TESTS

 IF  1.000000e+00 IS NOT ALMOST 1.0E0,    SIN HAS THE WRONG PERIOD.

 THE IDENTITY   SIN(-X) = -SIN(X)   WILL BE TESTED.
     X        F(X) + F(-X)
  5.2749781e+00  0.0000000e+00

  6.2247555e-01  0.0000000e+00

  2.8654773e+00  0.0000000e+00

  8.6403031e+00  0.0000000e+00

  9.2974819e+00  0.0000000e+00

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

  9.1986537e-34  0.0000000e+00

  4.5993268e-34  0.0000000e+00

  2.2996634e-34  0.0000000e+00

  1.1498317e-34  0.0000000e+00

  5.7491586e-35  0.0000000e+00

 THE IDENTITY   COS(-X) = COS(X)   WILL BE TESTED.
        X         F(X) - F(-X)
  3.8150525e+00  0.0000000e+00

  1.1330713e+01  0.0000000e+00

  1.4910932e+01  0.0000000e+00

  1.2089636e+01  0.0000000e+00

  1.1860458e+01  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.


       SIN(1.557374e-207) = 1.557374e-207
 THE FOLLOWING THREE LINES ILLUSTRATE THE LOSS IN SIGNIFICANCE
 FOR LARGE ARGUMENTS.  THE ARGUMENTS ARE CONSECUTIVE.

       SIN( 1.273810e+16) = 0.000000e+00

       SIN( 1.273810e+16) = 0.000000e+00

       SIN( 1.273810e+16) = 0.000000e+00
1TEST OF ERROR RETURNS


 SIN WILL BE CALLED WITH THE ARGUMENT     1.6226e+32
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 SIN RETURNED THE VALUE     0.0000e+00



 THIS CONCLUDES THE TESTS
1TEST OF SINH(X) VS T.S. EXPANSION OF SINH(X)

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     0.0000e+00,     5.0000e-01)


 SINH(X) WAS LARGER   279 TIMES,
             AGREED  1463 TIMES, AND
        WAS SMALLER   258 TIMES.


 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.3485e-32 =    2 **-105.07
    OCCURRED FOR X =     2.595035e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.93


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.0705e-33 =    2 **-107.28
 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
      (     0.0000e+00,     5.0000e-01)


 COSH(X) WAS LARGER   109 TIMES,
             AGREED  1606 TIMES, AND
        WAS SMALLER   285 TIMES.


 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.4595e-32 =    2 **-105.00
    OCCURRED FOR X =     6.803707e-02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.2903e-33 =    2 **-107.22
 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
      (     3.0000e+00,            inf)


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


 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     0.0000e+00 =    2 **-999.00
    OCCURRED FOR X =     0.000000e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS            nan =    2 **nan0x10000000
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     3.0000e+00,            inf)


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


 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     0.0000e+00 =    2 **-999.00
    OCCURRED FOR X =     0.000000e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS            nan =    2 **nan0x10000000
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1SPECIAL TESTS

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

        X            F(X) + F(-X)

  2.8905176e+00  0.0000000e+00

  2.7757405e+00  0.0000000e+00

  2.0758407e+00  0.0000000e+00

  2.5216581e+00  0.0000000e+00

  4.4279082e-01  0.0000000e+00

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

        X         X - F(X)

  3.8164278e-33  0.0000000e+00

  1.9082139e-33  0.0000000e+00

  9.5410696e-34  0.0000000e+00

  4.7705348e-34  0.0000000e+00

  2.3852674e-34  0.0000000e+00

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

        X         F(X) - F(-X)

  5.1297671e-01  0.0000000e+00

  2.4244163e-01  0.0000000e+00

  2.9277413e+00  0.0000000e+00

  2.2716559e+00  0.0000000e+00

  4.9603481e-01  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

      SINH(1.557374e-207) =1.557374e-207

1TEST OF ERROR RETURNS


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


 SINH RETURNED THE VALUE            inf



SINH WILL BE CALLED WITH THE ARGUMENT     1.6226e+32
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 SINH RETURNED THE VALUE            inf



 THIS CONCLUDES THE TESTS

1TEST OF SQRT(X*X) - X


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
       (     7.0711e-01,     1.0000e+00)


 SQRT(X) WAS LARGER   155 TIMES,
             AGREED  1737 TIMES, AND
        WAS SMALLER   108 TIMES.


 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     1.6890e-32 =    2 **-105.55
    OCCURRED FOR X =     7.297665e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.45


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     2.9983e-33 =    2 **-108.04
 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
       (     1.0000e+00,     1.4142e+00)


 SQRT(X) WAS LARGER   195 TIMES,
             AGREED  1731 TIMES, AND
        WAS SMALLER    74 TIMES.


 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.4310e-32 =    2 **-105.02
    OCCURRED FOR X =     1.014059e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.98


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.2188e-33 =    2 **-107.55
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF SPECIAL ARGUMENTS


 SQRT(XMIN) = SQRT( 1.8051944e-276) =  1.3435752e-138


 SQRT(1-EPSNEG) = SQRT(1-  6.1629758e-33) =   1.0000000e+00


 SQRT(1.0) = SQRT(  1.0000000e+00) =   1.0000000e+00


 SQRT(1+EPS) = SQRT(1+  1.2325952e-32) =   1.0000000e+00


 SQRT(XMAX) = SQRT(            inf) =             inf


1TEST 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



SQRT WILL BE CALLED WITH THE ARGUMENT     -1.0000e+00
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 SQRT RETURNED THE VALUE             nan



 THIS CONCLUDES THE TESTS
1TEST OF TAN(X) VS 2*TAN(X/2)/(1-TAN(X/2)**2)


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
    (     0.0000e+00,     7.8540e-01)


 TAN(X) WAS LARGER   654 TIMES,
            AGREED   685 TIMES, AND
       WAS SMALLER   661 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     6.3465e-32 =    2 **-103.64
    OCCURRED FOR X =     5.275654e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   3.36


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.1131e-32 =    2 **-106.15
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.85


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


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
    (     2.7489e+00,     3.5343e+00)


 TAN(X) WAS LARGER   815 TIMES,
            AGREED   752 TIMES, AND
       WAS SMALLER   433 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     5.4897e-32 =    2 **-103.84
    OCCURRED FOR X =     2.816730e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   3.16


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.1110e-32 =    2 **-106.15
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.85


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


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
    (     1.8850e+01,     1.9635e+01)


 TAN(X) WAS LARGER   655 TIMES,
            AGREED   730 TIMES, AND
       WAS SMALLER   615 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     4.9102e-32 =    2 **-104.01
    OCCURRED FOR X =     1.888876e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.99


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.0590e-32 =    2 **-106.22
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.78


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


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
    (     1.8850e+01,     1.9635e+01)


 COT(X) WAS LARGER   778 TIMES,
            AGREED   616 TIMES, AND
       WAS SMALLER   606 TIMES.


 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     6.2164e-32 =    2 **-103.67
    OCCURRED FOR X =     1.931667e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   3.33


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.4618e-32 =    2 **-105.75
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.25


1SPECIAL TESTS


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

        X         F(X) + F(-X)

  1.8161658e+01  0.0000000e+00

  1.7440492e+01  0.0000000e+00

  1.3042892e+01  0.0000000e+00

  1.5844045e+01  0.0000000e+00

  2.7821367e+00  0.0000000e+00

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

        X         X - F(X)

  3.8164278e-33  0.0000000e+00

  1.9082139e-33  0.0000000e+00

  9.5410696e-34  0.0000000e+00

  4.7705348e-34  0.0000000e+00

  2.3852674e-34  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       TAN(1.557374e-207) =1.557374e-207

 THE RELATIVE ERROR IN TAN(11) IS -1.1455809e-33 =    2 **-109.43 WHERE

      TAN( 1.100000e+01) =-2.259508e+02

 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF ERROR RETURNS


 TAN WILL BE CALLED WITH THE ARGUMENT     9.0072e+15
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 TAN RETURNED THE VALUE     0.0000e+00




TAN WILL BE CALLED WITH THE ARGUMENT     1.6226e+32
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 TAN RETURNED THE VALUE     0.0000e+00



 THIS CONCLUDES THE TESTS
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
      (     1.2500e-01,     5.4931e-01)


 TANH(X) WAS LARGER   877 TIMES,
             AGREED   741 TIMES, AND
        WAS SMALLER   382 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     5.6470e-32 =    2 **-103.80
    OCCURRED FOR X =     2.218445e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   3.20


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.2067e-32 =    2 **-106.03
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.97


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
      (     6.7431e-01,     3.8123e+01)


 TANH(X) WAS LARGER   909 TIMES,
             AGREED   715 TIMES, AND
        WAS SMALLER   376 TIMES.

 THERE ARE 107 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     7.4094e-32 =    2 **-103.41
    OCCURRED FOR X =     3.486761e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   3.59


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.7044e-33 =    2 **-106.50
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.50


1SPECIAL TESTS

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


        X         F(X) + F(-X)

  4.9165887e-01  0.0000000e+00

  1.7378602e-01  0.0000000e+00

  3.7008794e-01  0.0000000e+00

  2.7005371e-01  0.0000000e+00

  6.1325663e-02  0.0000000e+00

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


        X         X - F(X)

  2.7354926e-33  0.0000000e+00

  1.3677463e-33  0.0000000e+00

  6.8387315e-34  0.0000000e+00

  3.4193657e-34  0.0000000e+00

  1.7096829e-34  0.0000000e+00

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


        X         1 - F(X)

  3.8123095e+01  0.0000000e+00

  4.2123095e+01  0.0000000e+00

  4.6123095e+01  0.0000000e+00

  5.0123095e+01  0.0000000e+00

  5.4123095e+01  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       TANH(1.557374e-207) =1.557374e-207
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT            inf
       TANH(          inf) = 1.000000e+00
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT 1.8051944e-276
       TANH(1.805194e-276) =1.805194e-276
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT  0.0000000e+00
       TANH( 0.000000e+00) = 0.000000e+00
 THIS CONCLUDES THE TESTS
