Host        = uinta.math.utah.edu
Command     = ./tallqp >>tallqp.lst-intel-ia32-g++-g 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-g++-g CC=g++ -Wall CFLAGS=-DIEEE -DMAXTEST=200000 -g  
Date        = Mon May 27 09:30:50 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)


 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (1-EPS,1+EPS), WHERE EPS =     4.7684e-07


 ALOG(X) WAS LARGER  6966 TIMES,
             AGREED186192 TIMES, AND
        WAS SMALLER  6842 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.0837e-19 =    2 ** -63.00
    OCCURRED FOR X =     1.000000e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.9633e-20 =    2 ** -65.47
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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


 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     7.0711e-01,     9.3750e-01)


 ALOG(X) WAS LARGER     0 TIMES,
             AGREED155538 TIMES, AND
        WAS SMALLER 44462 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.0842e-19 =    2 ** -63.00
    OCCURRED FOR X =     7.788000e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     3.9893e-20 =    2 ** -64.44
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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


 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     3.1623e-01,     9.0000e-01)


 ALOG10(X) WAS LARGER     0 TIMES,
               AGREED 88095 TIMES, AND
          WAS SMALLER111905 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     2.9596e-19 =    2 ** -61.55
    OCCURRED FOR X =     8.999298e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.45


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     7.3666e-20 =    2 ** -63.56
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.44


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


 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     1.6000e+01,     2.4000e+02)


 ALOG(X) WAS LARGER  5446 TIMES,
             AGREED194554 TIMES, AND
        WAS SMALLER     0 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 =     5.464202e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.3558e-20 =    2 ** -66.00
 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)

  1.5767815e+01  0.0000000e+00

  1.6034764e+01  0.0000000e+00

  1.5129860e+01  0.0000000e+00

  1.6097985e+01  0.0000000e+00

  1.6734298e+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

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (    -1.2500e-01,     1.2500e-01)


 ASIN(X) WAS LARGER 49142 TIMES,
             AGREED102804 TIMES, AND
        WAS SMALLER 48054 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.0842e-19 =    2 ** -63.00
    OCCURRED FOR X =    -6.245969e-02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.3591e-20 =    2 ** -64.02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF ACOS(X) VS TAYLOR SERIES

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (    -1.2500e-01,     1.2500e-01)


 ACOS(X) WAS LARGER 45689 TIMES,
             AGREED105444 TIMES, AND
        WAS SMALLER 48867 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     7.5007e-20 =    2 ** -63.53
    OCCURRED FOR X =     1.249995e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.47


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.7619e-20 =    2 ** -64.19
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF ASIN(X) VS TAYLOR SERIES

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     7.5000e-01,     1.0000e+00)


 ASIN(X) WAS LARGER   144 TIMES,
             AGREED 74172 TIMES, AND
        WAS SMALLER125684 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     2.0343e-19 =    2 ** -62.09
    OCCURRED FOR X =     8.752371e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.91


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     6.6946e-20 =    2 ** -63.70
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.30


1TEST OF ACOS(X) VS TAYLOR SERIES

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     7.5000e-01,     1.0000e+00)


 ACOS(X) WAS LARGER 56597 TIMES,
             AGREED 85803 TIMES, AND
        WAS SMALLER 57600 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.1194e-13 =    2 ** -43.02
    OCCURRED FOR X =     1.000000e-00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS  20.98


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     2.5044e-16 =    2 ** -51.83
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS  12.17


1TEST OF ACOS(X) VS TAYLOR SERIES

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (    -1.0000e+00,    -7.5000e-01)


 ACOS(X) WAS LARGER 38388 TIMES,
             AGREED122057 TIMES, AND
        WAS SMALLER 39555 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.4505e-18 =    2 ** -59.26
    OCCURRED FOR X =    -9.999974e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   4.74


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.1778e-20 =    2 ** -64.07
 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)
 -4.4977743e-01  0.0000000e+00

 -9.4982339e-01  0.0000000e+00

 -9.7512699e-01  0.0000000e+00

 -4.9910253e-01  0.0000000e+00

 -3.3852621e-01  0.0000000e+00

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

        X         X - F(X)
  7.6288016e-21  0.0000000e+00

  3.8144008e-21  0.0000000e+00

  1.9072004e-21  0.0000000e+00

  9.5360020e-22  0.0000000e+00

  4.7680010e-22  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

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (    -6.2500e-02,     6.2500e-02)


 ATAN(X) WAS LARGER    30 TIMES,
             AGREED198094 TIMES, AND
        WAS SMALLER  1876 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.0243e-19 =    2 ** -63.08
    OCCURRED FOR X =     3.309057e-02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.92


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     6.1339e-21 =    2 ** -67.14
 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))

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     6.2500e-02,     2.6795e-01)


 ATAN(X) WAS LARGER 21320 TIMES,
             AGREED144349 TIMES, AND
        WAS SMALLER 34331 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.4462e-19 =    2 ** -62.58
    OCCURRED FOR X =     1.896537e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.42


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.0817e-20 =    2 ** -64.41
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     2.6795e-01,     4.1421e-01)


 ATAN(X) WAS LARGER 24795 TIMES,
             AGREED145684 TIMES, AND
        WAS SMALLER 29521 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.0353e-19 =    2 ** -63.07
    OCCURRED FOR X =     2.679498e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.93


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.3803e-20 =    2 ** -64.31
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     4.1421e-01,     1.0000e+00)


 ATAN(X) WAS LARGER 13160 TIMES,
             AGREED172763 TIMES, AND
        WAS SMALLER 14077 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.3611e-19 =    2 ** -62.67
    OCCURRED FOR X =     4.207809e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.33


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     2.8066e-20 =    2 ** -64.95
 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)

  1.9195370e+00  0.0000000e+00

  2.5869098e+00  0.0000000e+00

  3.2464918e-01  0.0000000e+00

  2.7449634e+00  0.0000000e+00

  4.3357439e+00  0.0000000e+00

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


        X         X - F(X)

  1.9719938e-20  0.0000000e+00

  9.8599691e-21  0.0000000e+00

  4.9299846e-21  0.0000000e+00

  2.4649923e-21  0.0000000e+00

  1.2324961e-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))
 -3.9416952e-01  1.3410436e-01  0.0000000e+00  3.1415927e+00

 -1.7379132e+00  4.9984569e-02  0.0000000e+00  3.1415927e+00

  1.0383860e+00  2.0226035e-01  0.0000000e+00 -3.1415927e+00

 -6.2914598e-02  9.1155685e-01  0.0000000e+00  3.1415927e+00

 -1.1970926e+00  8.5390689e-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)


 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (    -2.8407e-01,     3.4657e-01)


 EXP(X-V) WAS LARGER 28280 TIMES,
              AGREED144104 TIMES, AND
         WAS SMALLER 27616 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.3602e-19 =    2 ** -62.67
    OCCURRED FOR X =    -1.643082e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.33


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.1152e-20 =    2 ** -64.40
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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


 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (    -3.4657e+00,    -1.1309e+04)


 EXP(X-V) WAS LARGER 28448 TIMES,
              AGREED142380 TIMES, AND
         WAS SMALLER 29172 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.5904e-19 =    2 ** -62.45
    OCCURRED FOR X =    -1.514493e+02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.55


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.2049e-20 =    2 ** -64.37
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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


 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     6.9315e+00,     1.1356e+04)


 EXP(X-V) WAS LARGER 28215 TIMES,
              AGREED142415 TIMES, AND
         WAS SMALLER 29370 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.5790e-19 =    2 ** -62.46
    OCCURRED FOR X =     6.798745e+03
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.54


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.2131e-20 =    2 ** -64.36
 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

  5.7874697e-01  0.0000000e+00

  1.7716947e+00  0.0000000e+00

  2.9171916e-01  0.0000000e+00

  8.8947620e-01  0.0000000e+00

  1.7431796e+00  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


 200000 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 SMALLER200000 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


 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     5.0000e-01,     1.0000e+00)


 X**1.5 WAS LARGER 28485 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER171515 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF      2.1678e-19 =    2 **  -62.00
    OCCURRED FOR X =     5.000463e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      4.8671e-20 =    2 ** -64.16
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF XSQ**1.5 VS XSQ*X


 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     1.0000e+00,   1.0596e+1644)


 X**1.5 WAS LARGER112429 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER 87571 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF      7.6954e-16 =    2 **  -50.21
    OCCURRED FOR X =   1.010043e+1642
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS  13.79


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      3.4500e-16 =    2 ** -51.36
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS  12.64


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


 200000 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   381 TIMES,
           AGREED     0 TIMES, AND
      WAS SMALLER199619 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF      6.1569e-16 =    2 **  -50.53
    OCCURRED FOR X =     9.215137e+00 Y =     2.351508e+03
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS  13.47


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      6.8077e-18 =    2 ** -57.03
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   6.97


1SPECIAL TESTS


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

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

  5.4977743e+00  1.0498234e+01        0.0000000e+00

  1.0751270e+01  5.9910253e+00        0.0000000e+00

  4.3852621e+00  2.4072655e+00        0.0000000e+00

  8.5849250e+00  7.6053109e+00        0.0000000e+00

  8.9545798e+00  3.6719198e+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

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     0.0000e+00,     1.5708e+00)


 SIN(X) WAS LARGER 40060 TIMES,
            AGREED124810 TIMES, AND
       WAS SMALLER 35130 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.5705e-19 =    2 ** -62.47
    OCCURRED FOR X =     7.619826e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.53


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.2439e-20 =    2 ** -64.35
 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

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     1.8850e+01,     2.0420e+01)


 SIN(X) WAS LARGER 40072 TIMES,
            AGREED124893 TIMES, AND
       WAS SMALLER 35035 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.5278e-19 =    2 ** -62.51
    OCCURRED FOR X =     1.963855e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.49


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.2335e-20 =    2 ** -64.36
 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)

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     2.1991e+01,     2.3562e+01)


 COS(X) WAS LARGER 40037 TIMES,
            AGREED124895 TIMES, AND
       WAS SMALLER 35068 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.5711e-19 =    2 ** -62.46
    OCCURRED FOR X =     2.280033e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.54


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.2400e-20 =    2 ** -64.35
 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)
  5.4545616e+00  0.0000000e+00

  1.6697829e+01  0.0000000e+00

  2.7493884e+00  0.0000000e+00

  8.3831156e+00  0.0000000e+00

  1.6429081e+01  0.0000000e+00

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

  1.8125315e-20  0.0000000e+00

  9.0626576e-21  0.0000000e+00

  4.5313288e-21  0.0000000e+00

  2.2656644e-21  0.0000000e+00

  1.1328322e-21  0.0000000e+00

 THE IDENTITY   COS(-X) = COS(X)   WILL BE TESTED.
        X         F(X) - F(-X)
  8.8476534e+00  0.0000000e+00

  6.3363278e+00  0.0000000e+00

  1.5863460e+01  0.0000000e+00

  4.0105653e+00  0.0000000e+00

  9.1128155e+00  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)

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     0.0000e+00,     5.0000e-01)


 SINH(X) WAS LARGER 62696 TIMES,
             AGREED117302 TIMES, AND
        WAS SMALLER 20002 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     2.1612e-19 =    2 ** -62.00
    OCCURRED FOR X =     4.827048e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.0503e-20 =    2 ** -64.10
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     0.0000e+00,     5.0000e-01)


 COSH(X) WAS LARGER  5046 TIMES,
             AGREED190833 TIMES, AND
        WAS SMALLER  4121 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.0839e-19 =    2 ** -63.00
    OCCURRED FOR X =     2.227123e-02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     2.1506e-20 =    2 ** -65.33
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     3.0000e+00,     1.1357e+04)


 SINH(X) WAS LARGER 26202 TIMES,
             AGREED125344 TIMES, AND
        WAS SMALLER 48454 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     2.0551e-18 =    2 ** -58.76
    OCCURRED FOR X =     2.297633e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   5.24


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.1844e-20 =    2 ** -64.06
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     3.0000e+00,     1.1357e+04)


 COSH(X) WAS LARGER  1617 TIMES,
             AGREED195345 TIMES, AND
        WAS SMALLER  3038 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF            inf =    2 **    inf
    OCCURRED FOR X =     7.095236e+02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS    inf


 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)

  1.1517222e+00  0.0000000e+00

  1.5521459e+00  0.0000000e+00

  1.9478951e-01  0.0000000e+00

  1.6469781e+00  0.0000000e+00

  2.6014463e+00  0.0000000e+00

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

        X         X - F(X)

  1.9719938e-20  0.0000000e+00

  9.8599691e-21  0.0000000e+00

  4.9299846e-21  0.0000000e+00

  2.4649923e-21  0.0000000e+00

  1.2324961e-21  0.0000000e+00

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

        X         F(X) - F(-X)

  1.2043729e+00  0.0000000e+00

  4.0231307e-01  0.0000000e+00

  1.9656513e-01  0.0000000e+00

  1.4995371e-01  0.0000000e+00

  2.2787895e+00  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


 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
       (     7.0711e-01,     1.0000e+00)


 SQRT(X) WAS LARGER     0 TIMES,
             AGREED200000 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


 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
       (     1.0000e+00,     1.4142e+00)


 SQRT(X) WAS LARGER     0 TIMES,
             AGREED200000 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(): Numerical argument out of domain
 SQRT RETURNED THE VALUE             nan



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


 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
    (     0.0000e+00,     7.8540e-01)


 TAN(X) WAS LARGER 46925 TIMES,
            AGREED109882 TIMES, AND
       WAS SMALLER 43193 TIMES.

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


 THE MAXIMUM RELATIVE ERROR OF     2.3848e-19 =    2 ** -61.86
    OCCURRED FOR X =     4.259514e-02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.14


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.5135e-20 =    2 ** -63.98
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.02


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


 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
    (     2.7489e+00,     3.5343e+00)


 TAN(X) WAS LARGER 37170 TIMES,
            AGREED125692 TIMES, AND
       WAS SMALLER 37138 TIMES.

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


 THE MAXIMUM RELATIVE ERROR OF     2.0914e-19 =    2 ** -62.05
    OCCURRED FOR X =     2.887968e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.95


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.7853e-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)


 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
    (     1.8850e+01,     1.9635e+01)


 TAN(X) WAS LARGER 46819 TIMES,
            AGREED110025 TIMES, AND
       WAS SMALLER 43156 TIMES.

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


 THE MAXIMUM RELATIVE ERROR OF     2.4437e-19 =    2 ** -61.83
    OCCURRED FOR X =     1.893255e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.17


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.5052e-20 =    2 ** -63.98
 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))


 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
    (     1.8850e+01,     1.9635e+01)


 COT(X) WAS LARGER 47748 TIMES,
            AGREED101421 TIMES, AND
       WAS SMALLER 50831 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     2.4514e-19 =    2 ** -61.82
    OCCURRED FOR X =     1.912500e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.18


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     6.1957e-20 =    2 ** -63.81
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.19


1SPECIAL TESTS


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

        X         F(X) + F(-X)

  7.2364839e+00  0.0000000e+00

  9.7524203e+00  0.0000000e+00

  1.2238986e+00  0.0000000e+00

  1.0348268e+01  0.0000000e+00

  1.6345369e+01  0.0000000e+00

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

        X         X - F(X)

  1.9719938e-20  0.0000000e+00

  9.8599691e-21  0.0000000e+00

  4.9299846e-21  0.0000000e+00

  2.4649923e-21  0.0000000e+00

  1.2324961e-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))

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     1.2500e-01,     5.4931e-01)


 TANH(X) WAS LARGER 76659 TIMES,
             AGREED 77169 TIMES, AND
        WAS SMALLER 46172 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     3.2175e-19 =    2 ** -61.43
    OCCURRED FOR X =     3.506714e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.57


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     7.5169e-20 =    2 ** -63.53
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.47


1TEST OF TANH(X) VS (TANH(X-1/8)+TANH(1/8))/(1+TANH(X-1/8)TANH(1/8))

 200000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     6.7431e-01,     2.3220e+01)


 TANH(X) WAS LARGER 59273 TIMES,
             AGREED 81517 TIMES, AND
        WAS SMALLER 59210 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     2.9369e-19 =    2 ** -61.56
    OCCURRED FOR X =     9.467941e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.44


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.1774e-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)

  8.6420156e-01  0.0000000e+00

  4.4916195e-01  0.0000000e+00

  8.9108802e-01  0.0000000e+00

  5.8787470e-01  0.0000000e+00

  7.0028428e-01  0.0000000e+00

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


        X         X - F(X)

  2.1478944e-20  0.0000000e+00

  1.0739472e-20  0.0000000e+00

  5.3697360e-21  0.0000000e+00

  2.6848680e-21  0.0000000e+00

  1.3424340e-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
