Host        = blab02.math.utah.edu
Command     = ./tallsp >>tallsp.lst-dec-alpha-gnu-linux-g++-g 2>&1
uname -a    = Linux blab02.math.utah.edu 2.2.19-6.2.1 #1 Mon Apr 9 22:51:32 EDT 2001 alpha unknown unknown GNU/Linux
Make flags  = -i NAME=dec-alpha-gnu-linux-g++-g CC=g++ CFLAGS=-g -mieee 
Date        = Tue May 28 12:48:59 MDT 2002
----------------------------------------
 
ibeta............       2
it...............      24
irnd.............       5
ngrd.............       0
machep...........     -23
negep............     -24
iexp.............       8
minexp...........    -126
maxexp...........     128
eps..............   1.19209289550781250e-07
epsneg...........   5.96046447753906250e-08
xmin.............   1.17549435082228751e-38
xmax.............   3.40282346638528860e+38
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 =     3.9062e-03


 ALOG(X) WAS LARGER     0 TIMES,
             AGREED  1999 TIMES, AND
        WAS SMALLER     1 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     8.5195e-08 =    2 ** -23.48
    OCCURRED FOR X =     9.972708e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.52


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.9050e-09 =    2 ** -28.97
 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  1467 TIMES, AND
        WAS SMALLER   533 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.1918e-07 =    2 ** -23.00
    OCCURRED FOR X =     7.787600e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.4459e-08 =    2 ** -24.42
 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   912 TIMES, AND
          WAS SMALLER  1088 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     3.1670e-07 =    2 ** -21.59
    OCCURRED FOR X =     8.973227e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.41


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.2840e-08 =    2 ** -23.53
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.47


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    66 TIMES,
             AGREED  1934 TIMES, AND
        WAS SMALLER     0 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.1758e-07 =    2 ** -23.02
    OCCURRED FOR X =     5.771053e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.98


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.6332e-08 =    2 ** -25.87
 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)

  1.5111137e+01  0.0000000e+00

  1.6892143e+01  0.0000000e+00

  1.5517789e+01  0.0000000e+00

  1.5723574e+01  0.0000000e+00

  1.5446670e+01  0.0000000e+00



 TEST OF SPECIAL ARGUMENTS


 ALOG(1.0) =   0.0000000e+00


 ALOG(XMIN) = ALOG(  1.1754944e-38) =  -8.7336548e+01


 ALOG(XMAX) = ALOG(  3.4028235e+38) =   8.8722839e+01


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   492 TIMES,
             AGREED  1016 TIMES, AND
        WAS SMALLER   492 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.1913e-07 =    2 ** -23.00
    OCCURRED FOR X =     7.817471e-03
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.9240e-08 =    2 ** -24.01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF ACOS(X) VS TAYLOR SERIES

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


 ACOS(X) WAS LARGER   462 TIMES,
             AGREED  1049 TIMES, AND
        WAS SMALLER   489 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     8.2453e-08 =    2 ** -23.53
    OCCURRED FOR X =     1.246908e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.47


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.2394e-08 =    2 ** -24.19
 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  1701 TIMES,
             AGREED   267 TIMES, AND
        WAS SMALLER    32 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     2.3833e-07 =    2 ** -22.00
    OCCURRED FOR X =     8.416672e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.1963e-07 =    2 ** -22.99
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.01


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   378 TIMES,
             AGREED  1232 TIMES, AND
        WAS SMALLER   390 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.1903e-07 =    2 ** -23.00
    OCCURRED FOR X =     9.688198e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.5796e-08 =    2 ** -24.10
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF ACOS(X) VS TAYLOR SERIES

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


 ACOS(X) WAS LARGER   477 TIMES,
             AGREED  1007 TIMES, AND
        WAS SMALLER   516 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     9.8565e-08 =    2 ** -23.27
    OCCURRED FOR X =    -7.500283e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.73


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     6.3571e-08 =    2 ** -23.91
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.09


1SPECIAL TESTS

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

        X         F(X) + F(-X)
 -7.7694035e-01  0.0000000e+00

 -1.1754654e-01  0.0000000e+00

 -6.9331807e-01  0.0000000e+00

 -6.6475576e-01  0.0000000e+00

 -9.4467744e-02  0.0000000e+00

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

        X         X - F(X)
  4.8188475e-08  0.0000000e+00

  2.4094238e-08  0.0000000e+00

  1.2047119e-08  0.0000000e+00

  6.0235594e-09  0.0000000e+00

  3.0117797e-09  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       ASIN( 3.569977e-29) = 3.569977e-29

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  2000 TIMES, AND
        WAS SMALLER     0 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     0.0000e+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 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   421 TIMES,
             AGREED  1394 TIMES, AND
        WAS SMALLER   185 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.1919e-07 =    2 ** -23.00
    OCCURRED FOR X =     2.553749e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.5955e-08 =    2 ** -24.38
 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   269 TIMES,
             AGREED  1435 TIMES, AND
        WAS SMALLER   296 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.1373e-07 =    2 ** -23.07
    OCCURRED FOR X =     2.682003e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.93


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.9571e-08 =    2 ** -24.27
 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   140 TIMES,
             AGREED  1717 TIMES, AND
        WAS SMALLER   143 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.1911e-07 =    2 ** -23.00
    OCCURRED FOR X =     5.468479e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     3.2286e-08 =    2 ** -24.88
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1SPECIAL TESTS

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


        X         F(X) + F(-X)

  2.7784285e-01  0.0000000e+00

  4.7303557e+00  0.0000000e+00

  1.2944715e+00  0.0000000e+00

  1.8089335e+00  0.0000000e+00

  1.1166750e+00  0.0000000e+00

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


        X         X - F(X)

  5.4650016e-08  0.0000000e+00

  2.7325008e-08  0.0000000e+00

  1.3662504e-08  0.0000000e+00

  6.8312520e-09  0.0000000e+00

  3.4156260e-09  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))
  4.3756700e-01  1.7396699e-01  0.0000000e+00 -3.1415920e+00

  9.8349166e-01  2.3411068e-01  0.0000000e+00 -3.1415920e+00

 -9.4465744e-01  9.7945464e-01  0.0000000e+00  3.1415920e+00

 -2.7268052e-01  9.7873473e-01  0.0000000e+00  3.1415918e+00

 -6.3263285e-01  7.3022205e-01  0.0000000e+00  3.1415918e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       ATAN( 3.569977e-29) = 3.569977e-29
1TEST OF ERROR RETURNS


 ATAN WILL BE CALLED WITH THE ARGUMENT  3.4028235e+38
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN( 3.402823e+38) = 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
  1.1754944e-38  3.4028235e+38

 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN2( 1.175494e-38 3.402823e+38) = 0.000000e+00
 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
  3.4028235e+38  1.1754944e-38

 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN2( 3.402823e+38 1.175494e-38) = 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   238 TIMES,
              AGREED  1480 TIMES, AND
         WAS SMALLER   282 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.1890e-07 =    2 ** -23.00
    OCCURRED FOR X =     6.511503e-02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.3378e-08 =    2 ** -24.46
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (    -3.4657e+00,    -6.9315e+01)


 EXP(X-V) WAS LARGER   220 TIMES,
              AGREED  1506 TIMES, AND
         WAS SMALLER   274 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.1909e-07 =    2 ** -23.00
    OCCURRED FOR X =    -3.184387e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.2368e-08 =    2 ** -24.49
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     6.9315e+00,     8.8617e+01)


 EXP(X-V) WAS LARGER   203 TIMES,
              AGREED  1508 TIMES, AND
         WAS SMALLER   289 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.1912e-07 =    2 ** -23.00
    OCCURRED FOR X =     5.479925e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.3492e-08 =    2 ** -24.45
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1SPECIAL TESTS


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

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

  1.0061973e+00 -5.9604645e-08

  1.7746665e+00  0.0000000e+00

  1.8333218e+00  0.0000000e+00

  1.1652287e+00  0.0000000e+00

  1.6535881e+00 -5.9604645e-08



 TEST OF SPECIAL ARGUMENTS


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

 EXP(-8.700000e+01) = 1.645811e-38

 EXP( 8.800000e+01) = 1.651636e+38

 IF EXP( 4.400000e+01) =  1.285160e+19 IS NOT ABOUT
 EXP( 2.200000e+01)**2 = 1.285160e+19 THERE IS AN ARG RED ERROR
1TEST OF ERROR RETURNS


 EXP WILL BE CALLED WITH THE ARGUMENT    -9.2234e+18
 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     9.2234e+18
 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   24 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   171 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1829 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF      1.1900e-07 =    2 **  -23.00
    OCCURRED FOR X =     6.303301e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      3.4017e-08 =    2 ** -24.81
 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,     6.9815e+12)


 X**1.5 WAS LARGER   189 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1811 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF      1.1901e-07 =    2 **  -23.00
    OCCURRED FOR X =     4.400547e+12
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      3.7105e-08 =    2 ** -24.68
 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 (    -1.9266e+01,     1.9266e+01)


 X**Y  WAS LARGER   696 TIMES,
           AGREED     0 TIMES, AND
      WAS SMALLER  1304 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF      6.4007e-07 =    2 **  -20.58
    OCCURRED FOR X =     2.445568e+00 Y =    -1.893141e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   3.42


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      1.5409e-07 =    2 ** -22.63
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.37


1SPECIAL TESTS


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

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

  8.7694035e+00  2.1754656e+00        0.0000000e+00

  7.9331808e+00  7.6475577e+00       -1.3225876e-07

  1.9446775e+00  9.0846844e+00        4.3512313e-07

  1.5856049e+00  4.2006044e+00        0.0000000e+00

  1.0755668e+00  1.0445845e+01        2.2278758e-07

1TEST OF ERROR RETURNS


 ( 2.0000000e+00) ** (-1.2600000e+02) WILL BE COMPUTED.
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS      1.1755e-38



 ( 2.0000000e+00) ** ( 1.2700000e+02) WILL BE COMPUTED.
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS      1.7014e+38



 ( 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   398 TIMES,
            AGREED  1244 TIMES, AND
       WAS SMALLER   358 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.6271e-07 =    2 ** -22.55
    OCCURRED FOR X =     8.222308e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.45


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.7328e-08 =    2 ** -24.33
 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   390 TIMES,
            AGREED  1202 TIMES, AND
       WAS SMALLER   408 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.6574e-07 =    2 ** -22.52
    OCCURRED FOR X =     1.965229e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.48


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.8285e-08 =    2 ** -24.30
 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   291 TIMES,
            AGREED  1146 TIMES, AND
       WAS SMALLER   563 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.6734e-07 =    2 ** -22.51
    OCCURRED FOR X =     2.276907e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.49


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.0708e-08 =    2 ** -24.23
 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)
  9.4831867e+00  0.0000000e+00

  1.6725838e+01  0.0000000e+00

  1.7278650e+01  0.0000000e+00

  1.0982022e+01  0.0000000e+00

  1.5584701e+01  0.0000000e+00

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

  2.0817287e-08  0.0000000e+00

  1.0408644e-08  0.0000000e+00

  5.2043219e-09  0.0000000e+00

  2.6021609e-09  0.0000000e+00

  1.3010805e-09  0.0000000e+00

 THE IDENTITY   COS(-X) = COS(X)   WILL BE TESTED.
        X         F(X) - F(-X)
  1.2384433e+01  0.0000000e+00

  2.3904302e+00  0.0000000e+00

  1.6060429e+01  0.0000000e+00

  9.5006523e+00  0.0000000e+00

  5.9564587e-02  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.


       SIN( 3.569977e-29) =  3.569977e-29
 THE FOLLOWING THREE LINES ILLUSTRATE THE LOSS IN SIGNIFICANCE
 FOR LARGE ARGUMENTS.  THE ARGUMENTS ARE CONSECUTIVE.

       SIN( 4.096000e+03) =-5.948383e-01

       SIN( 4.096000e+03) =-5.946420e-01

       SIN( 4.096000e+03) =-5.942494e-01
1TEST OF ERROR RETURNS


 SIN WILL BE CALLED WITH THE ARGUMENT     1.6777e+07
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 SIN RETURNED THE VALUE    -7.7956e-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   268 TIMES,
             AGREED  1460 TIMES, AND
        WAS SMALLER   272 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.3984e-07 =    2 ** -22.77
    OCCURRED FOR X =     4.142701e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.23


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.3519e-08 =    2 ** -24.45
 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    47 TIMES,
             AGREED  1917 TIMES, AND
        WAS SMALLER    36 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.1788e-07 =    2 ** -23.02
    OCCURRED FOR X =     1.497976e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.98


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     2.2493e-08 =    2 ** -25.41
 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,     8.8723e+01)


 SINH(X) WAS LARGER    59 TIMES,
             AGREED   939 TIMES, AND
        WAS SMALLER  1002 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     2.3154e-07 =    2 ** -22.04
    OCCURRED FOR X =     1.666479e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.96


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     6.7416e-08 =    2 ** -23.82
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.18


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

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     3.0000e+00,     8.8723e+01)


 COSH(X) WAS LARGER    52 TIMES,
             AGREED   941 TIMES, AND
        WAS SMALLER  1007 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     2.3672e-07 =    2 ** -22.01
    OCCURRED FOR X =     4.859132e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.99


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     6.7534e-08 =    2 ** -23.82
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.18


1SPECIAL TESTS

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

        X            F(X) + F(-X)

  1.6670570e-01  0.0000000e+00

  2.8382134e+00  0.0000000e+00

  7.7668285e-01  0.0000000e+00

  1.0853601e+00  0.0000000e+00

  6.7000496e-01  0.0000000e+00

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

        X         X - F(X)

  5.4650016e-08  0.0000000e+00

  2.7325008e-08  0.0000000e+00

  1.3662504e-08  0.0000000e+00

  6.8312520e-09  0.0000000e+00

  3.4156260e-09  0.0000000e+00

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

        X         F(X) - F(-X)

  1.8281753e+00  0.0000000e+00

  5.2190095e-01  0.0000000e+00

  2.2376187e+00  0.0000000e+00

  7.0233202e-01  0.0000000e+00

  7.9150689e-01  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

      SINH( 3.569977e-29) = 3.569977e-29

1TEST OF ERROR RETURNS


 SINH WILL BE CALLED WITH THE ARGUMENT     8.8848e+01
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 SINH RETURNED THE VALUE     1.9280e+38



SINH WILL BE CALLED WITH THE ARGUMENT     1.6777e+07
 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  24 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  24 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(  1.1754944e-38) =   1.0842022e-19


 SQRT(1-EPSNEG) = SQRT(1-  5.9604645e-08) =   9.9999994e-01


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


 SQRT(1+EPS) = SQRT(1+  1.1920929e-07) =   1.0000000e+00


 SQRT(XMAX) = SQRT(  3.4028235e+38) =   1.8446743e+19


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)


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


 TAN(X) WAS LARGER   490 TIMES,
            AGREED  1062 TIMES, AND
       WAS SMALLER   448 TIMES.

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


 THE MAXIMUM RELATIVE ERROR OF     1.9870e-07 =    2 ** -22.26
    OCCURRED FOR X =     1.488788e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.74


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     6.0965e-08 =    2 ** -23.97
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.03


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   340 TIMES,
            AGREED  1304 TIMES, AND
       WAS SMALLER   356 TIMES.

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


 THE MAXIMUM RELATIVE ERROR OF     1.6899e-07 =    2 ** -22.50
    OCCURRED FOR X =     3.185654e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.50


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.0449e-08 =    2 ** -24.24
 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   463 TIMES,
            AGREED  1075 TIMES, AND
       WAS SMALLER   462 TIMES.

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


 THE MAXIMUM RELATIVE ERROR OF     2.1277e-07 =    2 ** -22.16
    OCCURRED FOR X =     1.936025e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.84


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     6.0511e-08 =    2 ** -23.98
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.02


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


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


 COT(X) WAS LARGER   410 TIMES,
            AGREED  1046 TIMES, AND
       WAS SMALLER   544 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     2.6345e-07 =    2 ** -21.86
    OCCURRED FOR X =     1.948447e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.14


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     6.6946e-08 =    2 ** -23.83
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.17


1SPECIAL TESTS


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

        X         F(X) + F(-X)

  1.0474428e+00  0.0000000e+00

  1.7833021e+01  0.0000000e+00

  4.8800426e+00  0.0000000e+00

  6.8195186e+00  0.0000000e+00

  4.2097654e+00  0.0000000e+00

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

        X         X - F(X)

  5.4650016e-08  0.0000000e+00

  2.7325008e-08  0.0000000e+00

  1.3662504e-08  0.0000000e+00

  6.8312520e-09  0.0000000e+00

  3.4156260e-09  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       TAN( 3.569977e-29) = 3.569977e-29

 THE RELATIVE ERROR IN TAN(11) IS -2.2158758e-08 =    2 ** -25.43 WHERE

      TAN( 1.100000e+01) =-2.259509e+02

 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF ERROR RETURNS


 TAN WILL BE CALLED WITH THE ARGUMENT     4.0960e+03
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 TAN RETURNED THE VALUE    -7.3961e-01




TAN WILL BE CALLED WITH THE ARGUMENT     1.6777e+07
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 TAN RETURNED THE VALUE    -1.2447e+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   675 TIMES,
             AGREED   940 TIMES, AND
        WAS SMALLER   385 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     2.4567e-07 =    2 ** -21.96
    OCCURRED FOR X =     3.814031e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.04


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     6.8374e-08 =    2 ** -23.80
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.20


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,     9.3575e+00)


 TANH(X) WAS LARGER   208 TIMES,
             AGREED  1085 TIMES, AND
        WAS SMALLER   707 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.9263e-07 =    2 ** -22.31
    OCCURRED FOR X =     7.231383e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.69


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.4276e-08 =    2 ** -24.43
 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)

  3.9965051e-01  0.0000000e+00

  9.5631576e-01  0.0000000e+00

  5.3947014e-01  0.0000000e+00

  4.3376642e-01  0.0000000e+00

  2.2080407e-01  0.0000000e+00

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


        X         X - F(X)

  3.5793104e-08 -3.5527137e-15

  1.7896552e-08  0.0000000e+00

  8.9482759e-09  0.0000000e+00

  4.4741379e-09  0.0000000e+00

  2.2370690e-09  0.0000000e+00

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


        X         1 - F(X)

  9.3574867e+00  0.0000000e+00

  1.3357487e+01  0.0000000e+00

  1.7357487e+01  0.0000000e+00

  2.1357487e+01  0.0000000e+00

  2.5357487e+01  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       TANH( 3.569977e-29) = 3.569977e-29
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT  3.4028235e+38
       TANH( 3.402823e+38) = 1.000000e+00
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT  1.1754944e-38
       TANH( 1.175494e-38) = 1.175494e-38
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT  0.0000000e+00
       TANH( 0.000000e+00) = 0.000000e+00
 THIS CONCLUDES THE TESTS
