Host        = blab02.math.utah.edu
Command     = ./talldp >>talldp.lst-lst-dec-alpha-gnu-linux-g++-O5 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=lst-dec-alpha-gnu-linux-g++-O5 CC=g++ CFLAGS=-DIEEE -O5 -Wall -pedantic -ansi 
Date        = Mon May 27 16:35:49 MDT 2002
----------------------------------------
 
ibeta............       2
it...............      53
irnd.............       2
ngrd.............       0
machep...........     -52
negep............     -53
iexp.............      11
minexp...........   -1022
maxexp...........    1024
eps..............   2.22044604925031308e-16
epsneg...........   1.11022302462515654e-16
xmin.............  2.22507385850720138e-308
xmax.............  1.79769313486231571e+308
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 =     7.6294e-06


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


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


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


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     0.0000e+00 =    2 **-999.00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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


   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     7.0711e-01,     9.3750e-01)


 ALOG(X) WAS LARGER     0 TIMES,
             AGREED  1548 TIMES, AND
        WAS SMALLER   452 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.2193e-16 =    2 ** -52.00
    OCCURRED FOR X =     7.786997e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     7.6531e-17 =    2 ** -53.54
 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   946 TIMES, AND
          WAS SMALLER  1054 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     5.8445e-16 =    2 ** -50.60
    OCCURRED FOR X =     8.964164e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.40


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.5312e-16 =    2 ** -52.54
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.46


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    53 TIMES,
             AGREED  1947 TIMES, AND
        WAS SMALLER     0 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.2119e-16 =    2 ** -52.01
    OCCURRED FOR X =     5.544888e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.99


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     2.7516e-17 =    2 ** -55.01
 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)

  1.5983318e+01  4.4408921e-16

  1.5339606e+01  0.0000000e+00

  1.5347572e+01  4.4408921e-16

  1.5813231e+01  0.0000000e+00

  1.5740176e+01  0.0000000e+00



 TEST OF SPECIAL ARGUMENTS


 ALOG(1.0) =   0.0000000e+00


 ALOG(XMIN) = ALOG( 2.2250739e-308) =  -7.0839642e+02


 ALOG(XMAX) = ALOG( 1.7976931e+308) =   7.0978271e+02


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   527 TIMES,
             AGREED   987 TIMES, AND
        WAS SMALLER   486 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.2195e-16 =    2 ** -52.00
    OCCURRED FOR X =     3.125874e-02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.1165e-16 =    2 ** -52.99
 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   522 TIMES,
             AGREED  1003 TIMES, AND
        WAS SMALLER   475 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.5360e-16 =    2 ** -52.53
    OCCURRED FOR X =     1.248467e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.47


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.0027e-16 =    2 ** -53.15
 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   383 TIMES,
             AGREED  1256 TIMES, AND
        WAS SMALLER   361 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.2191e-16 =    2 ** -52.00
    OCCURRED FOR X =     8.418029e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.0505e-16 =    2 ** -53.08
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF ACOS(X) VS TAYLOR SERIES

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


 ACOS(X) WAS LARGER   366 TIMES,
             AGREED  1246 TIMES, AND
        WAS SMALLER   388 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.2178e-16 =    2 ** -52.00
    OCCURRED FOR X =     9.688372e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.0339e-16 =    2 ** -53.10
 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   493 TIMES,
             AGREED   990 TIMES, AND
        WAS SMALLER   517 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     1.8354e-16 =    2 ** -52.27
    OCCURRED FOR X =    -7.504321e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.73


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.1900e-16 =    2 ** -52.90
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.10


1SPECIAL TESTS

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

        X         F(X) + F(-X)
 -5.0384110e-01  0.0000000e+00

 -5.1721352e-01  0.0000000e+00

 -4.6127087e-01  0.0000000e+00

 -3.5739680e-01  0.0000000e+00

 -3.2497569e-01  0.0000000e+00

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

        X         X - F(X)
  8.2729394e-17  0.0000000e+00

  4.1364697e-17  0.0000000e+00

  2.0682348e-17  0.0000000e+00

  1.0341174e-17  0.0000000e+00

  5.1705871e-18  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       ASIN(1.821832e-231) =1.821832e-231

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    49 TIMES,
             AGREED  1951 TIMES, AND
        WAS SMALLER     0 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.1922e-16 =    2 ** -52.02
    OCCURRED FOR X =     3.166343e-02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.98


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     2.3203e-17 =    2 ** -55.26
 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   431 TIMES,
             AGREED  1373 TIMES, AND
        WAS SMALLER   196 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.2199e-16 =    2 ** -52.00
    OCCURRED FOR X =     1.256840e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.6152e-17 =    2 ** -53.37
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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

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


 ATAN(X) WAS LARGER   292 TIMES,
             AGREED  1401 TIMES, AND
        WAS SMALLER   307 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.1197e-16 =    2 ** -52.07
    OCCURRED FOR X =     2.680413e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.93


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.4702e-17 =    2 ** -53.23
 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   149 TIMES,
             AGREED  1699 TIMES, AND
        WAS SMALLER   152 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.2064e-16 =    2 ** -52.01
    OCCURRED FOR X =     5.504280e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.99


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     5.9466e-17 =    2 ** -53.90
 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)

  2.4582943e+00  0.0000000e+00

  8.4901561e-01  0.0000000e+00

  8.6893012e-01  0.0000000e+00

  2.0330784e+00  0.0000000e+00

  1.8504397e+00  0.0000000e+00

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


        X         X - F(X)

  6.9279836e-17  0.0000000e+00

  3.4639918e-17  0.0000000e+00

  1.7319959e-17  0.0000000e+00

  8.6599794e-18  0.0000000e+00

  4.3299897e-18  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))
 -9.1978515e-01  5.8925193e-01  0.0000000e+00  3.1415927e+00

 -1.7546973e+00  2.1346841e-01  0.0000000e+00  3.1415927e+00

 -2.2456381e-01  2.9761609e-01  0.0000000e+00  3.1415927e+00

 -9.9445784e-01  8.9905633e-01  0.0000000e+00  3.1415927e+00

  1.0204660e+00  6.9518594e-01  0.0000000e+00 -3.1415927e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       ATAN(1.821832e-231) =1.821832e-231
1TEST OF ERROR RETURNS


 ATAN WILL BE CALLED WITH THE ARGUMENT 1.7976931e+308
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN(1.797693e+308) = 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
 2.2250739e-308 1.7976931e+308

 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN2(2.225074e-3081.797693e+308) = 0.000000e+00
 ATAN2 WILL BE CALLED WITH THE ARGUMENTS
 1.7976931e+308 2.2250739e-308

 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


       ATAN2(1.797693e+3082.225074e-308) = 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   258 TIMES,
              AGREED  1483 TIMES, AND
         WAS SMALLER   259 TIMES.


 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.2196e-16 =    2 ** -52.00
    OCCURRED FOR X =     6.288667e-02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.0963e-17 =    2 ** -53.46
 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,    -6.7027e+02)


 EXP(X-V) WAS LARGER   290 TIMES,
              AGREED  1482 TIMES, AND
         WAS SMALLER   228 TIMES.


 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.2204e-16 =    2 ** -52.00
    OCCURRED FOR X =    -4.920946e+02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.3386e-17 =    2 ** -53.41
 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,     7.0968e+02)


 EXP(X-V) WAS LARGER   293 TIMES,
              AGREED  1482 TIMES, AND
         WAS SMALLER   225 TIMES.


 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.2199e-16 =    2 ** -52.00
    OCCURRED FOR X =     2.925483e+02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.1603e-17 =    2 ** -53.44
 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

  7.8325859e-01  0.0000000e+00

  4.1536184e-01  2.2204460e-16

  2.8620958e-02  0.0000000e+00

  1.2024206e+00  0.0000000e+00

  1.8213778e+00  0.0000000e+00



 TEST OF SPECIAL ARGUMENTS


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

 EXP(-7.080000e+02) =3.307553e-308

 EXP( 7.090000e+02) =8.218407e+307

 IF EXP( 3.545000e+02) = 9.065543e+153 IS NOT ABOUT
 EXP( 1.772500e+02)**2 =9.065543e+153 THERE IS AN ARG RED ERROR
1TEST OF ERROR RETURNS


 EXP WILL BE CALLED WITH THE ARGUMENT   -6.7039e+153
 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    6.7039e+153
 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   53 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   108 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1892 TIMES.


 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      2.0943e-16 =    2 **  -52.08
    OCCURRED FOR X =     6.423635e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.92


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      5.1373e-17 =    2 ** -54.11
 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,    5.6438e+102)


 X**1.5 WAS LARGER   111 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1889 TIMES.


 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF      2.1194e-16 =    2 **  -52.07
    OCCURRED FOR X =    2.866055e+102
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.93


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      4.7720e-17 =    2 ** -54.22
 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 (    -1.5413e+02,     1.5413e+02)


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


 THERE ARE   53 BASE    2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


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


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      0.0000e+00 =    2 **-999.00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1SPECIAL TESTS


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

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

  6.0384110e+00  6.1721352e+00       -4.4054454e-16

  5.6127087e+00  4.5739680e+00       -1.7024686e-16

  4.2497569e+00  8.4516013e+00        0.0000000e+00

  2.2708162e+00  7.5027289e+00       -2.4175382e-16

  6.1387364e+00  3.7554795e+00       -2.4953170e-16

1TEST OF ERROR RETURNS


 ( 2.0000000e+00) ** (-1.0220000e+03) WILL BE COMPUTED.
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS     2.2251e-308



 ( 2.0000000e+00) ** ( 1.0230000e+03) WILL BE COMPUTED.
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 THE VALUE RETURNED IS     8.9885e+307



 ( 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   405 TIMES,
            AGREED  1205 TIMES, AND
       WAS SMALLER   390 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.4822e-16 =    2 ** -51.84
    OCCURRED FOR X =     1.120528e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.16


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.0606e-17 =    2 ** -53.29
 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   389 TIMES,
            AGREED  1248 TIMES, AND
       WAS SMALLER   363 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.6053e-16 =    2 ** -51.77
    OCCURRED FOR X =     1.906428e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.23


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.6621e-17 =    2 ** -53.36
 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)

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


 COS(X) WAS LARGER   389 TIMES,
            AGREED  1250 TIMES, AND
       WAS SMALLER   361 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     2.8652e-16 =    2 ** -51.63
    OCCURRED FOR X =     2.346492e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.37


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.7470e-17 =    2 ** -53.34
 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)
  7.3820383e+00  0.0000000e+00

  3.9146931e+00  0.0000000e+00

  2.6974617e-01  0.0000000e+00

  1.1332547e+01  0.0000000e+00

  1.7166081e+01  0.0000000e+00

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

  5.7051156e-17  0.0000000e+00

  2.8525578e-17  0.0000000e+00

  1.4262789e-17  0.0000000e+00

  7.1313945e-18  0.0000000e+00

  3.5656973e-18  0.0000000e+00

 THE IDENTITY   COS(-X) = COS(X)   WILL BE TESTED.
        X         F(X) - F(-X)
  4.4566459e+00  0.0000000e+00

  4.8316547e+00  0.0000000e+00

  2.1326225e+00  0.0000000e+00

  1.5061690e+01  0.0000000e+00

  2.2071794e+00  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.


       SIN(1.821832e-231) = 1.821832e-231
 THE FOLLOWING THREE LINES ILLUSTRATE THE LOSS IN SIGNIFICANCE
 FOR LARGE ARGUMENTS.  THE ARGUMENTS ARE CONSECUTIVE.

       SIN( 9.490627e+07) = 9.419571e-01

       SIN( 9.490627e+07) = 9.419571e-01

       SIN( 9.490627e+07) = 9.419570e-01
1TEST OF ERROR RETURNS


 SIN WILL BE CALLED WITH THE ARGUMENT     9.0072e+15
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 SIN RETURNED THE VALUE    -8.4893e-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   272 TIMES,
             AGREED  1442 TIMES, AND
        WAS SMALLER   286 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.2125e-16 =    2 ** -52.01
    OCCURRED FOR X =     6.268396e-02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.99


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     8.2163e-17 =    2 ** -53.43
 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    32 TIMES,
             AGREED  1927 TIMES, AND
        WAS SMALLER    41 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.2036e-16 =    2 ** -52.01
    OCCURRED FOR X =     1.236239e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.99


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     3.9119e-17 =    2 ** -54.50
 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,     7.0978e+02)


 SINH(X) WAS LARGER  1000 TIMES,
             AGREED   952 TIMES, AND
        WAS SMALLER    48 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     3.4233e-16 =    2 ** -51.38
    OCCURRED FOR X =     5.083371e+02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.62


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.2419e-16 =    2 ** -52.84
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.16


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

   2000 RANDOM ARGUMENTS WERE TESTED FROM THE INTERVAL
      (     3.0000e+00,     7.0978e+02)


 COSH(X) WAS LARGER   984 TIMES,
             AGREED   969 TIMES, AND
        WAS SMALLER    47 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     3.3723e-16 =    2 ** -51.40
    OCCURRED FOR X =     6.948087e+02
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.60


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.2215e-16 =    2 ** -52.86
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.14


1SPECIAL TESTS

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

        X            F(X) + F(-X)

  1.4749766e+00  0.0000000e+00

  5.0940937e-01  0.0000000e+00

  5.2135807e-01  0.0000000e+00

  1.2198471e+00  0.0000000e+00

  1.1102638e+00  0.0000000e+00

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

        X         X - F(X)

  6.9279836e-17  0.0000000e+00

  3.4639918e-17  0.0000000e+00

  1.7319959e-17  0.0000000e+00

  8.6599794e-18  0.0000000e+00

  4.3299897e-18  0.0000000e+00

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

        X         F(X) - F(-X)

  8.1016114e-01  0.0000000e+00

  1.7677558e+00  0.0000000e+00

  1.8397699e-01  0.0000000e+00

  6.4040522e-01  0.0000000e+00

  1.3315771e+00  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

      SINH(1.821832e-231) =1.821832e-231

1TEST OF ERROR RETURNS


 SINH WILL BE CALLED WITH THE ARGUMENT     7.0991e+02
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 SINH RETURNED THE VALUE    1.0185e+308



SINH WILL BE CALLED WITH THE ARGUMENT     9.0072e+15
 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  53 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  53 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( 2.2250739e-308) =  1.4916681e-154


 SQRT(1-EPSNEG) = SQRT(1-  1.1102230e-16) =   1.0000000e-00


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


 SQRT(1+EPS) = SQRT(1+  2.2204460e-16) =   1.0000000e+00


 SQRT(XMAX) = SQRT( 1.7976931e+308) =  1.3407808e+154


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   464 TIMES,
            AGREED  1093 TIMES, AND
       WAS SMALLER   443 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     3.9035e-16 =    2 ** -51.19
    OCCURRED FOR X =     2.771006e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.81


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.1023e-16 =    2 ** -53.01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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


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


 TAN(X) WAS LARGER   364 TIMES,
            AGREED  1288 TIMES, AND
       WAS SMALLER   348 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     2.7870e-16 =    2 ** -51.67
    OCCURRED FOR X =     3.520688e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.33


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.6775e-17 =    2 ** -53.20
 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   427 TIMES,
            AGREED  1083 TIMES, AND
       WAS SMALLER   490 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     4.3423e-16 =    2 ** -51.03
    OCCURRED FOR X =     1.903901e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.97


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.1339e-16 =    2 ** -52.97
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.03


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   484 TIMES,
            AGREED  1018 TIMES, AND
       WAS SMALLER   498 TIMES.


 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER


 THE MAXIMUM RELATIVE ERROR OF     4.0667e-16 =    2 ** -51.13
    OCCURRED FOR X =     1.939765e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.87


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.2390e-16 =    2 ** -52.84
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.16


1SPECIAL TESTS


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

        X         F(X) + F(-X)

  9.2675513e+00  0.0000000e+00

  3.2007135e+00  0.0000000e+00

  3.2757894e+00  0.0000000e+00

  7.6645251e+00  0.0000000e+00

  6.9759933e+00  0.0000000e+00

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

        X         X - F(X)

  6.9279836e-17  0.0000000e+00

  3.4639918e-17  0.0000000e+00

  1.7319959e-17  0.0000000e+00

  8.6599794e-18  0.0000000e+00

  4.3299897e-18  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       TAN(1.821832e-231) =1.821832e-231

 THE RELATIVE ERROR IN TAN(11) IS  5.4049159e-17 =    2 ** -54.04 WHERE

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

 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1TEST OF ERROR RETURNS


 TAN WILL BE CALLED WITH THE ARGUMENT     6.7109e+07
 THIS SHOULD NOT TRIGGER AN ERROR MESSAGE


 TAN RETURNED THE VALUE    -4.6381e-01




TAN WILL BE CALLED WITH THE ARGUMENT     9.0072e+15
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 TAN RETURNED THE VALUE     1.6063e+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   621 TIMES,
             AGREED   860 TIMES, AND
        WAS SMALLER   519 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     4.4440e-16 =    2 ** -51.00
    OCCURRED FOR X =     5.488338e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   2.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.4030e-16 =    2 ** -52.66
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.34


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,     1.9408e+01)


 TANH(X) WAS LARGER   575 TIMES,
             AGREED   933 TIMES, AND
        WAS SMALLER   492 TIMES.

 THERE ARE  53 BASE   2 SIGNIFICANT DIGITS IN A FLOATING-POINT NUMBER

 THE MAXIMUM RELATIVE ERROR OF     3.2488e-16 =    2 ** -51.45
    OCCURRED FOR X =     8.355940e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.55


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     9.2954e-17 =    2 ** -53.26
 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)

  5.5568571e-02  0.0000000e+00

  2.5889429e-01  0.0000000e+00

  2.2333500e-01  0.0000000e+00

  6.0939174e-01  0.0000000e+00

  7.4587289e-01  0.0000000e+00

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


        X         X - F(X)

  2.9291640e-17  0.0000000e+00

  1.4645820e-17  0.0000000e+00

  7.3229100e-18  0.0000000e+00

  3.6614550e-18  0.0000000e+00

  1.8307275e-18  0.0000000e+00

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


        X         1 - F(X)

  1.9408121e+01  0.0000000e+00

  2.3408121e+01  0.0000000e+00

  2.7408121e+01  0.0000000e+00

  3.1408121e+01  0.0000000e+00

  3.5408121e+01  0.0000000e+00

 TEST OF UNDERFLOW FOR VERY SMALL ARGUMENT.

       TANH(1.821832e-231) =1.821832e-231
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT 1.7976931e+308
       TANH(1.797693e+308) = 1.000000e+00
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT 2.2250739e-308
       TANH(2.225074e-308) =2.225074e-308
 THE FUNCTION TANH WILL BE CALLED WITH THE ARGUMENT  0.0000000e+00
       TANH( 0.000000e+00) = 0.000000e+00
 THIS CONCLUDES THE TESTS
