Host        = uinta.math.utah.edu
Command     = ./tallqp >>tallqp.lst-intel-ia32-gnu-linux-g++-O3 2>&1
uname -a    = Linux uinta.math.utah.edu 2.4.9-31smp #1 SMP Tue Feb 26 06:55:00 EST 2002 i686 unknown unknown GNU/Linux
Make flags  = -i NAME=intel-ia32-gnu-linux-g++-O3 CC=g++ CFLAGS=-O3  
Date        = Tue May 28 14:51:56 MDT 2002
----------------------------------------
 
ibeta............       2
it...............      64
irnd.............       5
ngrd.............       0
machep...........     -63
negep............     -64
iexp.............      15
minexp...........  -16382
maxexp...........   16384
eps..............     1.0842021724855044340074528008699417e-19
epsneg...........     5.4210108624275221700372640043497086e-20
xmin.............   3.3621031431120935062626778173217526e-4932
xmax.............   1.1897314953572317650212638530309702e+4932
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 =     4.7684e-07


 ALOG(X) WAS LARGER    69 TIMES,
             AGREED  1870 TIMES, AND
        WAS SMALLER    61 TIMES.


 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     1.0657e-19 =    2 ** -63.02
    OCCURRED FOR X =     1.000000e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.98


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.9112e-20 =    2 ** -65.50
 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  1575 TIMES, AND
        WAS SMALLER   425 TIMES.


 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     1.0829e-19 =    2 ** -63.00
    OCCURRED FOR X =     7.785660e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     3.8643e-20 =    2 ** -64.49
 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
      (     3.1623e-01,     9.0000e-01)


 ALOG10(X) WAS LARGER     0 TIMES,
               AGREED   894 TIMES, AND
          WAS SMALLER  1106 TIMES.


 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.5622e-19 =    2 ** -61.76
    OCCURRED FOR X =     8.853302e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.24


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     7.1911e-20 =    2 ** -63.59
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.41


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    48 TIMES,
             AGREED  1952 TIMES, AND
        WAS SMALLER     0 TIMES.


 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     1.0522e-19 =    2 ** -63.04
    OCCURRED FOR X =     6.165253e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.96


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.2942e-20 =    2 ** -66.07
 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  0.0000000e+00



 TEST OF SPECIAL ARGUMENTS


 ALOG(1.0) =   0.0000000e+00


 ALOG(XMIN) = ALOG(3.3621031e-4932) =  -1.1355137e+04


 ALOG(XMAX) = ALOG(1.1897315e+4932) =   1.1356523e+04


1TEST OF ERROR RETURNS


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


ALOG(): Numerical argument out of domain
 ALOG RETURNED THE VALUE            nan


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


ALOG(): Numerical result out of range
 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   506 TIMES,
             AGREED   995 TIMES, AND
        WAS SMALLER   499 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.0838e-19 =    2 ** -63.00
    OCCURRED FOR X =    -1.247180e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.4645e-20 =    2 ** -63.99
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.01


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   447 TIMES,
             AGREED  1044 TIMES, AND
        WAS SMALLER   509 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     7.4991e-20 =    2 ** -63.53
    OCCURRED FOR X =     1.247035e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.47


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.7897e-20 =    2 ** -64.18
 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     3 TIMES,
             AGREED   701 TIMES, AND
        WAS SMALLER  1296 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.0268e-19 =    2 ** -62.10
    OCCURRED FOR X =     8.771401e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.90


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     6.8293e-20 =    2 ** -63.67
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.33


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   554 TIMES,
             AGREED   853 TIMES, AND
        WAS SMALLER   593 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.5149e-17 =    2 ** -55.87
    OCCURRED FOR X =     9.996518e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   8.13


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.3403e-19 =    2 ** -60.70
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   3.30


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   360 TIMES,
             AGREED  1245 TIMES, AND
        WAS SMALLER   395 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.3979e-19 =    2 ** -62.63
    OCCURRED FOR X =    -9.992286e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.37


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.0371e-20 =    2 ** -64.11
 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)
  3.9748266e-20  0.0000000e+00

  1.9874133e-20  0.0000000e+00

  9.9370665e-21  0.0000000e+00

  4.9685333e-21  0.0000000e+00

  2.4842666e-21  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       ASIN(2.482895e-3699) =2.482895e-3699

1TEST OF ERROR RETURNS


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


asin(): Numerical argument out of domain
 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     0 TIMES,
             AGREED  1986 TIMES, AND
        WAS SMALLER    14 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     7.0858e-20 =    2 ** -63.61
    OCCURRED FOR X =     4.785203e-02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.39


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.0069e-21 =    2 ** -67.44
 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   208 TIMES,
             AGREED  1455 TIMES, AND
        WAS SMALLER   337 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.0840e-19 =    2 ** -63.00
    OCCURRED FOR X =     1.256762e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.0510e-20 =    2 ** -64.42
 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
      (     2.6795e-01,     4.1421e-01)


 ATAN(X) WAS LARGER   247 TIMES,
             AGREED  1478 TIMES, AND
        WAS SMALLER   275 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.0350e-19 =    2 ** -63.07
    OCCURRED FOR X =     2.680350e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.93


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.2916e-20 =    2 ** -64.34
 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
      (     4.1421e-01,     1.0000e+00)


 ATAN(X) WAS LARGER   120 TIMES,
             AGREED  1750 TIMES, AND
        WAS SMALLER   130 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.0811e-19 =    2 ** -63.00
    OCCURRED FOR X =     5.481945e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     2.6451e-20 =    2 ** -65.04
 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)

  3.3569654e-20  0.0000000e+00

  1.6784827e-20  0.0000000e+00

  8.3924136e-21  0.0000000e+00

  4.1962068e-21  0.0000000e+00

  2.0981034e-21  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  0.0000000e+00 -3.1415927e+00

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

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       ATAN(2.482895e-3699) =2.482895e-3699
1TEST OF ERROR RETURNS


 ATAN WILL BE CALLED WITH THE ARGUMENT1.1897315e+4932
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN(1.189731e+4932) = 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
3.3621031e-49321.1897315e+4932

 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN2(3.362103e-49321.189731e+4932) = 0.000000e+00
 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
1.1897315e+49323.3621031e-4932

 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN2(1.189731e+49323.362103e-4932) = 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   277 TIMES,
              AGREED  1445 TIMES, AND
         WAS SMALLER   278 TIMES.


 THERE ARE   64 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     1.0838e-19 =    2 ** -63.00
    OCCURRED FOR X =     6.290551e-02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.0648e-20 =    2 ** -64.42
 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
      (    -3.4657e+00,    -1.1309e+04)


 EXP(X-V) WAS LARGER   276 TIMES,
              AGREED  1442 TIMES, AND
         WAS SMALLER   282 TIMES.


 THERE ARE   64 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     1.2971e-19 =    2 ** -62.74
    OCCURRED FOR X =    -2.670835e+03
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.26


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.1729e-20 =    2 ** -64.38
 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
      (     6.9315e+00,     1.1356e+04)


 EXP(X-V) WAS LARGER   306 TIMES,
              AGREED  1410 TIMES, AND
         WAS SMALLER   284 TIMES.


 THERE ARE   64 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     1.0840e-19 =    2 ** -63.00
    OCCURRED FOR X =     5.541059e+03
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.2487e-20 =    2 ** -64.35
 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  0.0000000e+00

  9.1676463e-01  0.0000000e+00

  9.8649347e-01  0.0000000e+00



 TEST OF SPECIAL ARGUMENTS


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

 EXP(-1.135500e+04) =3.856186e-4932

 EXP( 1.135600e+04) =7.049146e+4931

 IF EXP( 5.678000e+03) = 8.395919e+2465 IS NOT ABOUT
 EXP( 2.839000e+03)**2 =8.395919e+2465 THERE IS AN ARG RED ERROR
1TEST OF ERROR RETURNS


 EXP WILL BE CALLED WITH THE ARGUMENT  -5.4537e+2465
 THIS SHOULD TRIGGER AN ERROR MESSAGE


EXP(): Numerical result out of range
 EXP RETURNED THE VALUE     0.0000e+00



 EXP WILL BE CALLED WITH THE ARGUMENT   5.4537e+2465
 THIS SHOULD TRIGGER AN ERROR MESSAGE


EXP(): Numerical result out of range
 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   64 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   305 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1695 TIMES.


 THERE ARE   64 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      1.9989e-19 =    2 **  -62.12
    OCCURRED FOR X =     5.137548e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.88


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      5.1301e-20 =    2 ** -64.08
 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
      (     1.0000e+00,   1.0596e+1644)


 X**1.5 WAS LARGER  1183 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER   817 TIMES.


 THERE ARE   64 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      7.6744e-16 =    2 **  -50.21
    OCCURRED FOR X =   1.253488e+1643
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS  13.79


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      3.3992e-16 =    2 ** -51.39
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS  12.61


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 (    -2.4660e+03,     2.4660e+03)


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


 THERE ARE   64 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      6.1568e-16 =    2 **  -50.53
    OCCURRED FOR X =     4.477888e+00 Y =    -2.303072e+03
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS  13.47


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      5.6283e-17 =    2 ** -53.98
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS  10.02


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        0.0000000e+00

  8.7675762e+00  1.0276962e+01        0.0000000e+00

  1.2505469e+00  8.3322609e+00        2.0194314e-19

  6.3057557e+00  3.2057483e+00        0.0000000e+00

  8.3580924e+00  4.5756310e+00        0.0000000e+00

1TEST OF ERROR RETURNS


 ( 2.0000000e+00) ** (-1.6382000e+04) WILL BE COMPUTED.
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS    3.3621e-4932



 ( 2.0000000e+00) ** ( 1.6383000e+04) WILL BE COMPUTED.
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS    5.9487e+4931



 ( 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   386 TIMES,
            AGREED  1256 TIMES, AND
       WAS SMALLER   358 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.3183e-19 =    2 ** -62.72
    OCCURRED FOR X =     1.029881e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.28


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.2681e-20 =    2 ** -64.34
 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
      (     1.8850e+01,     2.0420e+01)


 SIN(X) WAS LARGER   350 TIMES,
            AGREED  1239 TIMES, AND
       WAS SMALLER   411 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.3075e-19 =    2 ** -62.73
    OCCURRED FOR X =     1.982731e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.27


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.2800e-20 =    2 ** -64.34
 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
      (     2.1991e+01,     2.3562e+01)


 COS(X) WAS LARGER   394 TIMES,
            AGREED  1259 TIMES, AND
       WAS SMALLER   347 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.2054e-19 =    2 ** -62.85
    OCCURRED FOR X =     2.244349e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.15


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.2108e-20 =    2 ** -64.36
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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)

  8.0912214e-21  0.0000000e+00

  4.0456107e-21  0.0000000e+00

  2.0228053e-21  0.0000000e+00

  1.0114027e-21  0.0000000e+00

  5.0570133e-22  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(2.482895e-3699) = 2.482895e-3699
 THE FOLLOWING THREE LINES ILLUSTRATE THE LOSS IN SIGNIFICANCE
 FOR LARGE ARGUMENTS.  THE ARGUMENTS ARE CONSECUTIVE.

       SIN( 4.294967e+09) =-4.619866e-01

       SIN( 4.294967e+09) =-4.619866e-01

       SIN( 4.294967e+09) =-4.619866e-01
1TEST OF ERROR RETURNS


 SIN WILL BE CALLED WITH THE ARGUMENT     1.8447e+19
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 SIN RETURNED THE VALUE     3.1282e-01



 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   609 TIMES,
             AGREED  1205 TIMES, AND
        WAS SMALLER   186 TIMES.


 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     1.5178e-19 =    2 ** -62.51
    OCCURRED FOR X =     8.917520e-02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.49


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.9510e-20 =    2 ** -64.13
 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    42 TIMES,
             AGREED  1923 TIMES, AND
        WAS SMALLER    35 TIMES.


 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     1.0743e-19 =    2 ** -63.01
    OCCURRED FOR X =     1.355818e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.99


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.9681e-20 =    2 ** -65.46
 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,     1.1357e+04)


 SINH(X) WAS LARGER   283 TIMES,
             AGREED  1215 TIMES, AND
        WAS SMALLER   502 TIMES.


 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     4.4154e-19 =    2 ** -60.97
    OCCURRED FOR X =     1.545442e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   3.03


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.0102e-20 =    2 ** -64.11
 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,     1.1357e+04)


 COSH(X) WAS LARGER    23 TIMES,
             AGREED  1955 TIMES, AND
        WAS SMALLER    22 TIMES.


 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     1.4300e-19 =    2 ** -62.60
    OCCURRED FOR X =     1.244896e+02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.40


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

  3.3569654e-20  0.0000000e+00

  1.6784827e-20  0.0000000e+00

  8.3924136e-21  0.0000000e+00

  4.1962068e-21  0.0000000e+00

  2.0981034e-21  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(2.482895e-3699) =2.482895e-3699

1TEST OF ERROR RETURNS


 SINH WILL BE CALLED WITH THE ARGUMENT     1.1357e+04
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 SINH RETURNED THE VALUE   6.7407e+4931



SINH WILL BE CALLED WITH THE ARGUMENT     1.8447e+19
 THIS SHOULD TRIGGER AN ERROR MESSAGE


SINH(): Numerical result out of range
 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     0 TIMES,
             AGREED  2000 TIMES, AND
        WAS SMALLER     0 TIMES.


 THERE ARE  64 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 SQRT(X*X) - X


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
       (     1.0000e+00,     1.4142e+00)


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


 THERE ARE  64 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 SPECIAL ARGUMENTS


 SQRT(XMIN) = SQRT(3.3621031e-4932) = 1.8336039e-2466


 SQRT(1-EPSNEG) = SQRT(1-  5.4210109e-20) =   1.0000000e-00


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


 SQRT(1+EPS) = SQRT(1+  1.0842022e-19) =   1.0000000e+00


 SQRT(XMAX) = SQRT(1.1897315e+4932) = 1.0907481e+2466


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   468 TIMES,
            AGREED  1106 TIMES, AND
       WAS SMALLER   426 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.1061e-19 =    2 ** -62.04
    OCCURRED FOR X =     3.216285e-02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.96


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.4609e-20 =    2 ** -63.99
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.01


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   371 TIMES,
            AGREED  1263 TIMES, AND
       WAS SMALLER   366 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     1.5379e-19 =    2 ** -62.50
    OCCURRED FOR X =     3.097561e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.50


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.7759e-20 =    2 ** -64.18
 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
    (     1.8850e+01,     1.9635e+01)


 TAN(X) WAS LARGER   438 TIMES,
            AGREED  1126 TIMES, AND
       WAS SMALLER   436 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     1.8020e-19 =    2 ** -62.27
    OCCURRED FOR X =     1.885896e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.73


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.4255e-20 =    2 ** -64.00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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   465 TIMES,
            AGREED   994 TIMES, AND
       WAS SMALLER   541 TIMES.


 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.2747e-19 =    2 ** -61.93
    OCCURRED FOR X =     1.945984e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.07


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     6.3837e-20 =    2 ** -63.76
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.24


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)

  3.3569654e-20  0.0000000e+00

  1.6784827e-20  0.0000000e+00

  8.3924136e-21  0.0000000e+00

  4.1962068e-21  0.0000000e+00

  2.0981034e-21  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       TAN(2.482895e-3699) =2.482895e-3699

 THE RELATIVE ERROR IN TAN(11) IS  3.2139672e-18 =    2 ** -58.11 WHERE

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

 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   5.89


1TEST OF ERROR RETURNS


 TAN WILL BE CALLED WITH THE ARGUMENT     4.2950e+09
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 TAN RETURNED THE VALUE     5.2091e-01




TAN WILL BE CALLED WITH THE ARGUMENT     1.8447e+19
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 TAN RETURNED THE VALUE    -3.2935e-01



 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   802 TIMES,
             AGREED   749 TIMES, AND
        WAS SMALLER   449 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.3425e-19 =    2 ** -61.89
    OCCURRED FOR X =     3.621702e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.11


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     7.5659e-20 =    2 ** -63.52
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.48


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,     2.3220e+01)


 TANH(X) WAS LARGER   620 TIMES,
             AGREED   791 TIMES, AND
        WAS SMALLER   589 TIMES.

 THERE ARE  64 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.4427e-19 =    2 ** -62.59
    OCCURRED FOR X =     9.763999e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.41


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.1669e-20 =    2 ** -64.07
 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)

  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)

  2.4061647e-20  0.0000000e+00

  1.2030824e-20  0.0000000e+00

  6.0154118e-21  0.0000000e+00

  3.0077059e-21  0.0000000e+00

  1.5038530e-21  0.0000000e+00

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


        X         1 - F(X)

  2.3220431e+01  0.0000000e+00

  2.7220431e+01  0.0000000e+00

  3.1220431e+01  0.0000000e+00

  3.5220431e+01  0.0000000e+00

  3.9220431e+01  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       TANH(2.482895e-3699) =2.482895e-3699
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT1.1897315e+4932
       TANH(1.189731e+4932) = 1.000000e+00
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT3.3621031e-4932
       TANH(3.362103e-4932) =3.362103e-4932
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT  0.0000000e+00
       TANH( 0.000000e+00) = 0.000000e+00
 THIS CONCLUDES THE TESTS
