ANS FORTH CELEFUNT TEST RESULTS FOR |Z|
zabs.fs vs. 0.9.3
dnw 19Jan05

These results were obtained with pfe 0.33.58 compiled with gcc
3.3.3 on my MacOS X 10.3.7, PowerMac dual G4 system.  Leaving
aside the pfe C-primitive tests, Gforth 0.6.2 gives the same
results as pfe on the same system, except for the way NaN and
Inf are treated.

Results from Cody's original Fortran code are included for
reference.  It was compiled with GNU Fortran (GCC) 3.4 20031015
(experimental) under MacOS X.

The "fsl" version calls zabs.seq, extracted from Everett
Carter's Forth Scientific Library code for ZABS, vs. 1.4.

The "normal" version calls complex.fs vs. 0.8.2, Julian Noble's
original code for |Z|.

The "kahan" version calls complex-kahan.fs vs. 0.8.7, which uses
the Kahan algorithm without treatment of IEEE 754
underflow/overflow exceptions.

The "pfe prim" version calls the pfe complex module vs. 0.8.7,
which codes the Kahan algorithm in C with treatment of
underflow/overflow exceptions.  This module is part of the pfe
0.33.xx series distribution.

N=  = number out of 2000 random trials that are equal
MRE = maxium relative error
RMS = rms relative err
ULP = estimated units in last place
      (loss of base 2 significant digits)

Floating point numbers have 53 significant bits, with at most 7
significant decimal digits printed out below.

|3*x+4i*x| vs. 5x, 1 <= x <= 20
           N=    MRE       ULP   RMS       ULP
g77       2000  0.00e0    0.00  0.00e0    0.00
fsl       2000  0.00e0    0.00  0.00e0    0.00
normal    2000  0.00e0    0.00  0.00e0    0.00
kahan     2000  0.00e0    0.00  0.00e0    0.00
pfe prim  2000  0.00e0    0.00  0.00e0    0.00

|5*x+12i*x| vs. 13x, 1 <= x <= 20
           N=    MRE       ULP   RMS       ULP
g77       1246  1.37e-16  0.30  7.56e-17  0.00
fsl       2000  0.00e0    0.00  0.00e0    0.00
normal    1012  2.22e-16  1.00  9.81e-17  0.00
kahan     2000  0.00e0    0.00  0.00e0    0.00
pfe prim  2000  0.00e0    0.00  0.00e0    0.00

            |3*xmin
             + 4i*xmin|    5*xmin          difference
g77         1.112537e-307  1.112537e-307   0.000000e+00
fsl         1.112537e-307  1.112537e-307   0.000000e+00
normal      1.112537e-307  1.112537e-307   0.000000e+00 
kahan       1.112537e-307  1.112537e-307   0.000000e+00
pfe prim    1.112537e-307  1.112537e-307   0.000000e+00

            |3*xmax/5
             + 4i*xmax/5|  xmax            difference
g77         na             na              na 
fsl         NAN            1.797693e+308   NAN
normal      1.797693e+308  1.797693e+308   0.000000e+00 
kahan       1.797693e+308  1.797693e+308   0.000000e+00
pfe prim    1.797693e+308  1.797693e+308   0.000000e+00

           |5*xmax/16
            + 12i*xmax/16| 13*xmax/16      difference
g77         1.460626e+308  na              na
fsl         NAN            1.460626e+308   NAN
normal      1.460626e+308  1.460626e+308  -1.995840e+292
kahan       1.460626e+308  1.460626e+308   0.000000e+00
pfe prim    1.460626e+308  1.460626e+308   0.000000e+00

|(xmax/4)*3 + i xmax| =
|1.348270E+308 + i 1.797693e+308| =            
  g77        Inf
  fsl        Inf
  normal     Inf
  kahan      Inf
  pfe prim   Inf