Host        = ee.ece.utah.edu
Command     = ./tallsp >>tallsp.lst-intel-ia32-freebsd-c89-g 2>&1
uname -a    = FreeBSD ee.ece.utah.edu 4.4-RELEASE FreeBSD 4.4-RELEASE #0: Tue Oct i386 unknown unknown FreeBSD
Make flags  = -i NAME=intel-ia32-freebsd-c89-g CC=c89 CFLAGS=-g  
Date        = Tue May 28 14:58:10 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  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 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  1720 TIMES, AND
        WAS SMALLER   280 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.1908e-07 =    2 ** -23.00
    OCCURRED FOR X =     8.823805e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     3.5858e-08 =    2 ** -24.73
 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   938 TIMES, AND
          WAS SMALLER  1062 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     7.7197e-08 =    2 ** -23.63
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.37


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    41 TIMES,
             AGREED  1959 TIMES, AND
        WAS SMALLER     0 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.1608e-07 =    2 ** -23.04
    OCCURRED FOR X =     6.081747e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.96


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.2552e-08 =    2 ** -26.25
 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 -1.2816622e-07

  1.6892143e+01 -8.0789789e-08

  1.5517789e+01 -1.5457983e-08

  1.5723574e+01 -3.2693400e-08

  1.5446670e+01  4.0887351e-09



 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 RETURNED THE VALUE            NaN


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


 ALOG RETURNED THE VALUE           -Inf



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

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


 ASIN(X) WAS LARGER   493 TIMES,
             AGREED  1015 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     5.9259e-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   444 TIMES,
             AGREED  1082 TIMES, AND
        WAS SMALLER   474 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     5.1500e-08 =    2 ** -24.21
 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  1655 TIMES,
             AGREED   316 TIMES, AND
        WAS SMALLER    29 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     1.2056e-07 =    2 ** -22.98
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.02


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  1238 TIMES, AND
        WAS SMALLER   384 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     5.5650e-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   383 TIMES,
             AGREED  1192 TIMES, AND
        WAS SMALLER   425 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     5.7048e-08 =    2 ** -24.06
 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)
 -7.7694035e-01  0.0000000e+00

 -1.1754654e-01 -2.3066260e-09

 -6.9331807e-01  0.0000000e+00

 -6.6475576e-01  0.0000000e+00

 -9.4467744e-02 -2.0065190e-09

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

        X         X - F(X)
  4.8188475e-08 -1.9852335e-23

  2.4094238e-08 -3.3087225e-24

  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 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   207 TIMES,
             AGREED  1573 TIMES, AND
        WAS SMALLER   220 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.1902e-07 =    2 ** -23.00
    OCCURRED FOR X =     2.557714e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.0617e-08 =    2 ** -24.55
 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   137 TIMES,
             AGREED  1677 TIMES, AND
        WAS SMALLER   186 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.1345e-07 =    2 ** -23.07
    OCCURRED FOR X =     2.688942e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.93


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     3.7746e-08 =    2 ** -24.66
 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    86 TIMES,
             AGREED  1847 TIMES, AND
        WAS SMALLER    67 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.1908e-07 =    2 ** -23.00
    OCCURRED FOR X =     5.470342e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.00


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     2.2956e-08 =    2 ** -25.38
 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  1.0087628e-08

  4.7303557e+00  3.9372186e-08

  1.2944715e+00 -1.1819944e-08

  1.8089334e+00 -5.4734826e-08

  1.1166750e+00  1.7888949e-08

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


        X         X - F(X)

  5.4650016e-08  5.2939559e-23

  2.7325008e-08  6.6174449e-24

  1.3662504e-08  1.6543612e-24

  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))
  4.3756694e-01  1.7396699e-01 -2.7768996e-08 -3.1415927e+00

  9.8349154e-01  2.3411068e-01 -4.4521340e-08 -3.1415925e+00

 -9.4465744e-01  9.7945464e-01  0.0000000e+00  3.1415927e+00

 -2.7268049e-01  9.7873473e-01  0.0000000e+00  3.1415927e+00

 -6.3263291e-01  7.3022205e-01  0.0000000e+00  3.1415927e+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   242 TIMES,
              AGREED  1478 TIMES, AND
         WAS SMALLER   280 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     4.3297e-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   225 TIMES,
              AGREED  1496 TIMES, AND
         WAS SMALLER   279 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     4.2812e-08 =    2 ** -24.48
 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   193 TIMES,
              AGREED  1515 TIMES, AND
         WAS SMALLER   292 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     4.3322e-08 =    2 ** -24.46
 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 -7.2365467e-08

  1.7746665e+00 -3.0098093e-09

  1.8333218e+00 -1.4013494e-08

  1.1652287e+00 -1.7262451e-08

  1.6535881e+00 -6.7645217e-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 RETURNED THE VALUE     0.0000e+00



 EXP WILL BE CALLED WITH THE ARGUMENT     9.2234e+18
 THIS SHOULD TRIGGER AN ERROR MESSAGE


 EXP RETURNED THE VALUE            Inf



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


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


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


 THERE ARE   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   116 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1884 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      2.9036e-08 =    2 ** -25.04
 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   129 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1871 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      3.0214e-08 =    2 ** -24.98
 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   692 TIMES,
           AGREED     0 TIMES, AND
      WAS SMALLER  1308 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF      5.2264e-07 =    2 **  -20.87
    OCCURRED FOR X =     5.999712e+00 Y =    -1.908201e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   3.13


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS      1.4682e-07 =    2 ** -22.70
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.30


1SPECIAL TESTS


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

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

  8.7694035e+00  2.1754653e+00        0.0000000e+00

  7.9331803e+00  7.6475573e+00        3.3064737e-07

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

  1.5856048e+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   985 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1015 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     9.0983e-08 =    2 ** -23.39
    OCCURRED FOR X =     1.385806e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.61


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     2.9697e-08 =    2 ** -25.01
 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   994 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1006 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     8.4257e-08 =    2 ** -23.50
    OCCURRED FOR X =     1.923276e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.50


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     2.9657e-08 =    2 ** -25.01
 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   981 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1019 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     9.2791e-08 =    2 ** -23.36
    OCCURRED FOR X =     2.330554e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.64


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     3.0456e-08 =    2 ** -24.97
 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 -3.8646325e-10

  1.6725838e+01  1.8871095e-08

  1.7278650e+01 -5.9744396e-09

  1.0982022e+01  2.3782485e-08

  1.5584701e+01  1.0970742e-10

 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)
  1.2384432e+01  1.2779555e-08

  2.3904302e+00  1.5673644e-08

  1.6060429e+01  1.0826659e-08

  9.5006523e+00 -2.1426411e-08

  5.9564587e-02  2.8567170e-08

 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) =-5.942493e-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     8 TIMES,
             AGREED  1982 TIMES, AND
        WAS SMALLER    10 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.1742e-07 =    2 ** -23.02
    OCCURRED FOR X =     4.880311e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.98


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     7.8175e-09 =    2 ** -26.93
 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  1944 TIMES, AND
        WAS SMALLER    24 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.1626e-07 =    2 ** -23.04
    OCCURRED FOR X =     2.246170e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.96


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     1.8449e-08 =    2 ** -25.69
 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     5 TIMES,
             AGREED   993 TIMES, AND
        WAS SMALLER  1002 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     2.2699e-07 =    2 ** -22.07
    OCCURRED FOR X =     3.515723e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.93


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     6.2027e-08 =    2 ** -23.94
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.06


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    10 TIMES,
             AGREED   956 TIMES, AND
        WAS SMALLER  1034 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.7373e-07 =    2 ** -22.46
    OCCURRED FOR X =     4.475301e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.54


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     6.3188e-08 =    2 ** -23.92
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.08


1SPECIAL TESTS

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

        X            F(X) + F(-X)

  1.6670571e-01  2.4365565e-10

  2.8382134e+00 -3.3384526e-07

  7.7668285e-01  7.9852782e-09

  1.0853601e+00  1.1404085e-08

  6.7000502e-01 -4.0307335e-09

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

        X         X - F(X)

  5.4650016e-08 -2.6469780e-23

  2.7325008e-08  3.7332802e-16

  1.3662504e-08  9.3332006e-17

  6.8312520e-09  2.3333002e-17

  3.4156260e-09  0.0000000e+00

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

        X         F(X) - F(-X)

  1.8281752e+00 -2.0484681e-08

  5.2190095e-01 -3.0192755e-08

  2.2376187e+00  1.3973099e-08

  7.0233208e-01 -2.0257639e-08

  7.9150689e-01  2.6330211e-08

 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 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 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   994 TIMES,
            AGREED     1 TIMES, AND
       WAS SMALLER  1005 TIMES.

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


 THE MAXIMUM RELATIVE ERROR OF     1.2031e-07 =    2 ** -22.99
    OCCURRED FOR X =     5.357448e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.01


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.1754e-08 =    2 ** -24.51
 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   980 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1020 TIMES.

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


 THE MAXIMUM RELATIVE ERROR OF     1.4408e-07 =    2 ** -22.73
    OCCURRED FOR X =     3.387144e+00
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.27


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.3505e-08 =    2 ** -24.45
 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  1022 TIMES,
            AGREED     1 TIMES, AND
       WAS SMALLER   977 TIMES.

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


 THE MAXIMUM RELATIVE ERROR OF     1.3474e-07 =    2 ** -22.82
    OCCURRED FOR X =     1.885741e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.18


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.2367e-08 =    2 ** -24.49
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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


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


 COT(X) WAS LARGER   947 TIMES,
            AGREED     0 TIMES, AND
       WAS SMALLER  1053 TIMES.


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


 THE MAXIMUM RELATIVE ERROR OF     1.6617e-07 =    2 ** -22.52
    OCCURRED FOR X =     1.909350e+01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   1.48


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     4.6094e-08 =    2 ** -24.37
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


1SPECIAL TESTS


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

        X         F(X) + F(-X)

  1.0474429e+00  3.3395601e-08

  1.7833021e+01 -3.6969701e-09

  4.8800426e+00  7.4156219e-08

  6.8195181e+00 -2.9736571e-08

  4.2097654e+00  1.7813260e-08

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

        X         X - F(X)

  5.4650016e-08 -5.2939559e-23

  2.7325008e-08 -6.6174449e-24

  1.3662504e-08 -1.6543612e-24

  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   312 TIMES,
             AGREED  1609 TIMES, AND
        WAS SMALLER    79 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.1867e-07 =    2 ** -23.01
    OCCURRED FOR X =     1.262302e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.99


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     3.5566e-08 =    2 ** -24.74
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.00


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   243 TIMES,
             AGREED  1589 TIMES, AND
        WAS SMALLER   168 TIMES.

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

 THE MAXIMUM RELATIVE ERROR OF     1.0120e-07 =    2 ** -23.24
    OCCURRED FOR X =     6.760752e-01
 THE ESTIMATED LOSS OF BASE   2 SIGNIFICANT DIGITS IS   0.76


 THE ROOT MEAN SQUARE RELATIVE ERROR WAS     2.8213e-08 =    2 ** -25.08
 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 -1.1337373e-08

  9.5631576e-01 -5.6985985e-09

  5.3947014e-01 -9.6786144e-09

  4.3376642e-01  1.1403416e-08

  2.2080407e-01 -6.7675563e-09

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


        X         X - F(X)

  3.5793104e-08  1.3234890e-23

  1.7896552e-08  3.3087225e-24

  8.9482759e-09 -8.0071639e-17

  4.4741379e-09 -2.0017910e-17

  2.2370690e-09 -5.0044774e-18

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


        X         1 - F(X)

  9.3574867e+00 -1.4901167e-08

  1.3357487e+01 -4.9987792e-12

  1.7357487e+01 -1.6653345e-15

  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
